From a7c30908bd10c3a3b3e82b8c8d1ce3e470fdf64e Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Fri, 10 Apr 2026 09:32:39 +0900 Subject: [PATCH 001/135] RERUN - NEW FEATURE - Make gpec.h5 a self-contained rerun snapshot (#171) Store the full merged TOML, raw equilibrium arrays, and (when enabled) forcing-mode data inside gpec.h5 so a run can be replayed from any directory without the original g-file / CHEASE / auxiliary TOML / forcing inputs. `main("run.h5")` dispatches to `main_from_h5`, which rebuilds the `DirectRunInput` / `InverseRunInput` / `SolovevConfig` / `LargeAspectRatioConfig` directly from the snapshot and hands it to `setup_equilibrium` via the existing `additional_input` channel. The rerun output is written as `_rerun.h5` to guarantee the source is never overwritten; `--output-dir`, `--output-name`, `--override-file`, and repeatable `--override key=value` CLI flags let users retarget or tweak TOML fields without editing the snapshot. Co-Authored-By: Claude Opus 4.6 --- src/Equilibrium/AnalyticEquilibrium.jl | 6 +- src/Equilibrium/Equilibrium.jl | 25 +- src/Equilibrium/EquilibriumTypes.jl | 22 ++ src/Equilibrium/ReadEquilibrium.jl | 108 +++++- src/ForcingTerms/ForcingTerms.jl | 52 ++- src/GeneralizedPerturbedEquilibrium.jl | 130 +++++-- .../PerturbedEquilibrium.jl | 8 +- src/Rerun.jl | 331 ++++++++++++++++++ test/runtests.jl | 1 + test/runtests_rerun_from_h5.jl | 98 ++++++ 10 files changed, 745 insertions(+), 36 deletions(-) create mode 100644 src/Rerun.jl create mode 100644 test/runtests_rerun_from_h5.jl diff --git a/src/Equilibrium/AnalyticEquilibrium.jl b/src/Equilibrium/AnalyticEquilibrium.jl index d4064b43c..779042ad5 100644 --- a/src/Equilibrium/AnalyticEquilibrium.jl +++ b/src/Equilibrium/AnalyticEquilibrium.jl @@ -222,7 +222,8 @@ function lar_run(equil_input::EquilibriumConfig, lar_input::LargeAspectRatioConf rz_in_Z = cubic_interp((rz_in_xs, rz_in_ys), rzphi_fs_nodes[:, :, 2]; itp_2d_opts...) # LAR equilibrium has midplane symmetry, so magnetic axis is at Z = 0 - return InverseRunInput(equil_input, sq_in, rz_in_xs, rz_in_ys, rz_in_R, rz_in_Z, lar_r0, 0.0, psio) + raw_data = Dict{String,Any}("kind" => "analytic", "eq_type" => "lar") + return InverseRunInput(equil_input, sq_in, rz_in_xs, rz_in_ys, rz_in_R, rz_in_Z, lar_r0, 0.0, psio, raw_data) end """ @@ -301,5 +302,6 @@ function sol_run(equil_inputs::EquilibriumConfig, sol_inputs::SolovevConfig) # Print out equilibrium info @info "Generating Solovev equilibrium: mr=$mr, mz=$mz, ma=$ma, e=$(@sprintf("%.3f", e)), a=$(@sprintf("%.3f", a)), r0=$(@sprintf("%.3f", r0)), q0=$(@sprintf("%.3f", q0))" - return DirectRunInput(equil_inputs, sq_in, psi_in, psi_in_xs, psi_in_ys, rmin, rmax, zmin, zmax, psio) + raw_data = Dict{String,Any}("kind" => "analytic", "eq_type" => "sol") + return DirectRunInput(equil_inputs, sq_in, psi_in, psi_in_xs, psi_in_ys, rmin, rmax, zmin, zmax, psio, raw_data) end diff --git a/src/Equilibrium/Equilibrium.jl b/src/Equilibrium/Equilibrium.jl index 1551c23f2..463d7bdc8 100644 --- a/src/Equilibrium/Equilibrium.jl +++ b/src/Equilibrium/Equilibrium.jl @@ -37,7 +37,25 @@ function setup_equilibrium(eq_config::EquilibriumConfig, additional_input=nothin eq_type = eq_config.eq_type - if eq_type in ["efit", "efit_arclength", "efit_by_inversion"] + # Rerun path: caller (e.g. main_from_h5) already rebuilt the solver input from + # the stored raw arrays. Bind it onto the current config and skip the reader. + if additional_input isa DirectRunInput + eq_input = additional_input + eq_input.config = eq_config + # Re-run the separatrix clamp for efit-family replays so an overridden + # psihigh from the rerun TOML is re-validated against the closed flux region. + if eq_type in ["efit", "efit_arclength", "efit_by_inversion"] + psihigh_safe, adjusted = clamp_psihigh_to_separatrix(eq_input) + if adjusted + @warn "psihigh=$(eq_input.config.psihigh) has no closed flux surface in EFIT grid; " * + "clamped to $(round(psihigh_safe; sigdigits=7))" + eq_input.config.psihigh = psihigh_safe + end + end + elseif additional_input isa InverseRunInput + eq_input = additional_input + eq_input.config = eq_config + elseif eq_type in ["efit", "efit_arclength", "efit_by_inversion"] eq_input = read_efit(eq_config) psihigh_safe, adjusted = clamp_psihigh_to_separatrix(eq_input) if adjusted @@ -60,7 +78,7 @@ function setup_equilibrium(eq_config::EquilibriumConfig, additional_input=nothin end eq_input = sol_run(eq_config, additional_input) else - error("Equilibrium type $(equil_in.eq_type) is not implemented") + error("Equilibrium type $(eq_type) is not implemented") end if eq_type == "efit_by_inversion" @@ -71,6 +89,9 @@ function setup_equilibrium(eq_config::EquilibriumConfig, additional_input=nothin plasma_equilibrium = equilibrium_solver(eq_input) end + # Forward raw ingest arrays so the gpec.h5 writer can snapshot them. + plasma_equilibrium.raw_inputs = eq_input.raw_data + equilibrium_global_parameters!(plasma_equilibrium) equilibrium_qfind!(plasma_equilibrium) equilibrium_gse!(plasma_equilibrium) diff --git a/src/Equilibrium/EquilibriumTypes.jl b/src/Equilibrium/EquilibriumTypes.jl index 63a3f990c..0a6304dfd 100644 --- a/src/Equilibrium/EquilibriumTypes.jl +++ b/src/Equilibrium/EquilibriumTypes.jl @@ -298,8 +298,13 @@ mutable struct DirectRunInput{S<:FastInterpolations.CubicSeriesInterpolant,I2D<: zmin::Float64 # Minimum Z-coordinate of the computational grid [m]. zmax::Float64 # Maximum Z-coordinate of the computational grid [m]. psio::Float64 # The total flux difference |ψ_axis - ψ_boundary| [Weber / radian]. + raw_data::Dict{String,Any} # Raw arrays used to build the splines (for gpec.h5 snapshot/replay) end +# Outer constructor: pre-rerun call sites pass 10 positional args; raw_data defaults to empty. +DirectRunInput(config, sq_in, psi_in, psi_in_xs, psi_in_ys, rmin, rmax, zmin, zmax, psio) = + DirectRunInput(config, sq_in, psi_in, psi_in_xs, psi_in_ys, rmin, rmax, zmin, zmax, psio, Dict{String,Any}()) + """ InverseRunInput(...) @@ -327,8 +332,13 @@ mutable struct InverseRunInput{S<:FastInterpolations.CubicSeriesInterpolant,I2D< ro::Float64 # R axis location zo::Float64 # Z axis location psio::Float64 # Total flux difference |psi_axis - psi_boundary| + raw_data::Dict{String,Any} # Raw arrays used to build the splines (for gpec.h5 snapshot/replay) end +# Outer constructor: pre-rerun call sites pass 9 positional args; raw_data defaults to empty. +InverseRunInput(config, sq_in, rz_in_xs, rz_in_ys, rz_in_R, rz_in_Z, ro, zo, psio) = + InverseRunInput(config, sq_in, rz_in_xs, rz_in_ys, rz_in_R, rz_in_Z, ro, zo, psio, Dict{String,Any}()) + """ EquilibriumParameters @@ -583,4 +593,16 @@ mutable struct PlasmaEquilibrium{P<:ProfileSplines,I2D<:FastInterpolations.Cubic ro::Float64 zo::Float64 psio::Float64 + + # Raw ingest data forwarded from DirectRunInput/InverseRunInput for gpec.h5 snapshot/replay. + # Keys depend on equilibrium kind: "direct", "inverse", or "analytic". + raw_inputs::Dict{String,Any} end + +# Outer constructor: pre-rerun call sites pass 16 positional args; raw_inputs defaults to empty. +PlasmaEquilibrium(config, params, profiles, rzphi_xs, rzphi_ys, + rzphi_rsquared, rzphi_offset, rzphi_nu, rzphi_jac, + eqfun_B, eqfun_metric1, eqfun_metric2, ro, zo, psio) = + PlasmaEquilibrium(config, params, profiles, rzphi_xs, rzphi_ys, + rzphi_rsquared, rzphi_offset, rzphi_nu, rzphi_jac, + eqfun_B, eqfun_metric1, eqfun_metric2, ro, zo, psio, Dict{String,Any}()) diff --git a/src/Equilibrium/ReadEquilibrium.jl b/src/Equilibrium/ReadEquilibrium.jl index 256866ce6..a8e2944ec 100644 --- a/src/Equilibrium/ReadEquilibrium.jl +++ b/src/Equilibrium/ReadEquilibrium.jl @@ -117,8 +117,23 @@ function read_efit(config::EquilibriumConfig) psi_in_ys = collect(z_grid) psi_in = cubic_interp((psi_in_xs, psi_in_ys), psi_proc; extrap=ExtendExtrap()) - # --- Bundle everything for the solver --- - return DirectRunInput(config, sq_in, psi_in, psi_in_xs, psi_in_ys, rmin, rmax, zmin, zmax, psio) + # Capture the raw arrays that reconstruct sq_in and psi_in, so the rerun path + # (gpec.h5 → setup_equilibrium) can skip the g-file parse entirely. + raw_data = Dict{String,Any}( + "kind" => "direct", + "sq_xs" => sq_xs, + "sq_fs" => sq_fs_nodes, + "psi_xs" => psi_in_xs, + "psi_ys" => psi_in_ys, + "psi_rz" => psi_proc, + "rmin" => rmin, + "rmax" => rmax, + "zmin" => zmin, + "zmax" => zmax, + "psio" => psio, + ) + + return DirectRunInput(config, sq_in, psi_in, psi_in_xs, psi_in_ys, rmin, rmax, zmin, zmax, psio, raw_data) end @@ -212,8 +227,22 @@ function read_chease_binary(config::EquilibriumConfig) rz_in_R = cubic_interp((rz_in_xs, rz_in_ys), fs_2d[:, :, 1]; bc=(CubicFit(), PeriodicBC()), extrap=(ExtendExtrap(), WrapExtrap())) rz_in_Z = cubic_interp((rz_in_xs, rz_in_ys), fs_2d[:, :, 2]; bc=(CubicFit(), PeriodicBC()), extrap=(ExtendExtrap(), WrapExtrap())) + # Capture the raw arrays that reconstruct sq_in, rz_in_R, rz_in_Z. + raw_data = Dict{String,Any}( + "kind" => "inverse", + "sq_xs" => collect(xs), + "sq_fs" => fs_copy, + "rz_xs" => collect(rz_in_xs), + "rz_ys" => collect(rz_in_ys), + "R_nodes" => fs_2d[:, :, 1], + "Z_nodes" => fs_2d[:, :, 2], + "ro" => ro, + "zo" => zo, + "psio" => psio, + ) + @info "Finished reading CHEASE equilibrium (Binary)" - return InverseRunInput(config, sq_in, rz_in_xs, rz_in_ys, rz_in_R, rz_in_Z, ro, zo, psio) + return InverseRunInput(config, sq_in, rz_in_xs, rz_in_ys, rz_in_R, rz_in_Z, ro, zo, psio, raw_data) end end @@ -375,6 +404,77 @@ function read_chease_ascii(config::EquilibriumConfig) opts2d = (bc=(CubicFit(), PeriodicBC()), extrap=(ExtendExtrap(), WrapExtrap())) rz_in_R = cubic_interp((rz_in_xs, rz_in_ys), R_data; opts2d...) rz_in_Z = cubic_interp((rz_in_xs, rz_in_ys), Z_data; opts2d...) + # Capture the raw arrays that reconstruct sq_in, rz_in_R, rz_in_Z. + raw_data = Dict{String,Any}( + "kind" => "inverse", + "sq_xs" => collect(xs), + "sq_fs" => fs_copy, + "rz_xs" => collect(rz_in_xs), + "rz_ys" => collect(rz_in_ys), + "R_nodes" => Matrix(R_data), + "Z_nodes" => Matrix(Z_data), + "ro" => ro, + "zo" => zo, + "psio" => psio, + ) + @info "Finished reading CHEASE equilibrium. Magnetic axis at (ro=$(@sprintf("%.3f", ro)), zo=$(@sprintf("%.3f", zo))), psio=$(@sprintf("%.3e", psio))" - return InverseRunInput(config, sq_in, rz_in_xs, rz_in_ys, rz_in_R, rz_in_Z, ro, zo, psio) + return InverseRunInput(config, sq_in, rz_in_xs, rz_in_ys, rz_in_R, rz_in_Z, ro, zo, psio, raw_data) +end + + +""" + build_direct_from_raw(config::EquilibriumConfig, raw::Dict) -> DirectRunInput + +Rebuild a `DirectRunInput` from a raw-data dict previously captured by `read_efit` +(or populated from `input/raw_inputs/equilibrium/` inside `gpec.h5`). This is the +inverse of the raw-data capture in `read_efit`; it lets the rerun path skip the +g-file parse entirely while reusing the existing solver dispatch. +""" +function build_direct_from_raw(config::EquilibriumConfig, raw::Dict) + sq_xs = Vector{Float64}(raw["sq_xs"]) + sq_fs = Matrix{Float64}(raw["sq_fs"]) + psi_in_xs = Vector{Float64}(raw["psi_xs"]) + psi_in_ys = Vector{Float64}(raw["psi_ys"]) + psi_rz = Matrix{Float64}(raw["psi_rz"]) + + sq_in = cubic_interp(sq_xs, Series(sq_fs); extrap=ExtendExtrap()) + psi_in = cubic_interp((psi_in_xs, psi_in_ys), psi_rz; extrap=ExtendExtrap()) + + rmin = Float64(raw["rmin"]) + rmax = Float64(raw["rmax"]) + zmin = Float64(raw["zmin"]) + zmax = Float64(raw["zmax"]) + psio = Float64(raw["psio"]) + + return DirectRunInput(config, sq_in, psi_in, psi_in_xs, psi_in_ys, + rmin, rmax, zmin, zmax, psio, Dict{String,Any}(raw)) +end + +""" + build_inverse_from_raw(config::EquilibriumConfig, raw::Dict) -> InverseRunInput + +Rebuild an `InverseRunInput` from a raw-data dict previously captured by +`read_chease_ascii` / `read_chease_binary`. Inverse of that capture; used by the +rerun path to skip the CHEASE parse. +""" +function build_inverse_from_raw(config::EquilibriumConfig, raw::Dict) + sq_xs = Vector{Float64}(raw["sq_xs"]) + sq_fs = Matrix{Float64}(raw["sq_fs"]) + rz_in_xs = Vector{Float64}(raw["rz_xs"]) + rz_in_ys = Vector{Float64}(raw["rz_ys"]) + R_nodes = Matrix{Float64}(raw["R_nodes"]) + Z_nodes = Matrix{Float64}(raw["Z_nodes"]) + + sq_in = cubic_interp(sq_xs, Series(sq_fs); extrap=ExtendExtrap()) + opts2d = (bc=(CubicFit(), PeriodicBC()), extrap=(ExtendExtrap(), WrapExtrap())) + rz_in_R = cubic_interp((rz_in_xs, rz_in_ys), R_nodes; opts2d...) + rz_in_Z = cubic_interp((rz_in_xs, rz_in_ys), Z_nodes; opts2d...) + + ro = Float64(raw["ro"]) + zo = Float64(raw["zo"]) + psio = Float64(raw["psio"]) + + return InverseRunInput(config, sq_in, rz_in_xs, rz_in_ys, rz_in_R, rz_in_Z, + ro, zo, psio, Dict{String,Any}(raw)) end diff --git a/src/ForcingTerms/ForcingTerms.jl b/src/ForcingTerms/ForcingTerms.jl index 6bacc9b3c..27d14508a 100644 --- a/src/ForcingTerms/ForcingTerms.jl +++ b/src/ForcingTerms/ForcingTerms.jl @@ -172,6 +172,56 @@ function load_forcing_hdf5!( end end -export ForcingTermsControl, ForcingMode, load_forcing_data! +""" + save_forcing_to_h5(forcing_modes::Vector{ForcingMode}, group) + +Write forcing modes to an open HDF5 group using the same layout that +`load_forcing_hdf5!` consumes: datasets `n`, `m`, `amplitude_real`, +`amplitude_imag`. Used by the gpec.h5 snapshot writer so the replay path can +re-read forcing data from the output file with no reference to the original +ASCII/HDF5 ingest file. +""" +function save_forcing_to_h5(forcing_modes::Vector{ForcingMode}, group) + n_arr = Int[mode.n for mode in forcing_modes] + m_arr = Int[mode.m for mode in forcing_modes] + re_arr = Float64[real(mode.amplitude) for mode in forcing_modes] + im_arr = Float64[imag(mode.amplitude) for mode in forcing_modes] + group["n"] = n_arr + group["m"] = m_arr + group["amplitude_real"] = re_arr + group["amplitude_imag"] = im_arr + return nothing +end + +""" + load_forcing_from_h5_group!(forcing_modes::Vector{ForcingMode}, group) + +Populate `forcing_modes` from an already-open HDF5 group with datasets `n`, +`m`, `amplitude_real`, `amplitude_imag`. Mirror of `save_forcing_to_h5` for the +rerun path — deliberately accepts an open group rather than a file path so +the snapshot data can live inside `gpec.h5/input/raw_inputs/forcing_terms/`. +""" +function load_forcing_from_h5_group!(forcing_modes::Vector{ForcingMode}, group) + n_array = read(group, "n") + m_array = read(group, "m") + amp_real = read(group, "amplitude_real") + amp_imag = haskey(group, "amplitude_imag") ? read(group, "amplitude_imag") : zeros(length(n_array)) + + if length(n_array) != length(m_array) || length(n_array) != length(amp_real) + error("Inconsistent array lengths in HDF5 forcing group") + end + + empty!(forcing_modes) + for i in eachindex(n_array) + push!(forcing_modes, ForcingMode(; + n=Int(n_array[i]), + m=Int(m_array[i]), + amplitude=complex(amp_real[i], amp_imag[i]) + )) + end + return forcing_modes +end + +export ForcingTermsControl, ForcingMode, load_forcing_data!, save_forcing_to_h5, load_forcing_from_h5_group! end # module ForcingTerms diff --git a/src/GeneralizedPerturbedEquilibrium.jl b/src/GeneralizedPerturbedEquilibrium.jl index 68777f288..4e38c7ed0 100755 --- a/src/GeneralizedPerturbedEquilibrium.jl +++ b/src/GeneralizedPerturbedEquilibrium.jl @@ -48,10 +48,22 @@ using .ForceFreeStates: eulerlagrange_integration, free_run! const _BANNER = "="^60 const _SECTION = "-"^40 +# Rerun snapshot/replay helpers. Depends on the module-level imports above +# (HDF5, TOML, Equilibrium, ForcingTerms) and the `_BANNER` constant, so this +# include has to come after them but before `main`, which dispatches into +# `main_from_h5` on .h5 inputs. +include("Rerun.jl") + function main(args::Vector{String}=String[]) # Parse command line arguments path = length(args) >= 1 ? args[1] : "./" + # Rerun dispatch: when the first positional argument is an HDF5 file, treat it as + # a stored snapshot and hand off to the replay entry point. + if !isempty(args) && endswith(lowercase(args[1]), ".h5") + return main_from_h5(args) + end + # Capture git version for reproducibility git_version = try String(readchomp(`git -C $(@__DIR__) describe --tags --always`)) @@ -60,6 +72,53 @@ function main(args::Vector{String}=String[]) end @info "\n$_BANNER\n GPEC - Generalized Perturbed Equilibrium Code [$git_version]\n$_BANNER" + + # Read input TOML from the working directory and set up the equilibrium. The + # rest of the pipeline is shared with `main_with_inputs` (used by the rerun + # path), which accepts a prebuilt `inputs` dict and equilibrium config. + inputs = TOML.parsefile(joinpath(path, "gpec.toml")) + + if "Equilibrium" in keys(inputs) + eq_config = Equilibrium.EquilibriumConfig(inputs["Equilibrium"], path) + elseif isfile(joinpath(path, "equil.toml")) + @warn "Reading from equil.toml is deprecated. Please move [EQUIL_CONTROL] and [EQUIL_OUTPUT] sections to [Equilibrium] in gpec.toml" + eq_config = Equilibrium.EquilibriumConfig(joinpath(path, "equil.toml")) + else + error("No equilibrium configuration found. Add [Equilibrium] section to gpec.toml") + end + + # LAR/Solovev carry their parameters in a separate auxiliary TOML referenced + # by eq_filename. Merge those parameters into the in-memory `inputs` dict so + # the snapshot writer emits a self-contained TOML blob. + merge_auxiliary_eq_toml!(inputs, eq_config) + + return main_with_inputs(inputs, eq_config, nothing, path, git_version) +end + +""" + main_with_inputs(inputs, eq_config, additional_input, path, git_version; + preloaded_forcing_modes=nothing) + +Shared pipeline body used by both the TOML entry point (`main`) and the rerun +entry point (`main_from_h5`). The caller is responsible for producing a fully +merged `inputs::Dict` and an `EquilibriumConfig`; `additional_input` is forwarded +to `setup_equilibrium` (it may be a prebuilt `DirectRunInput`/`InverseRunInput` +or a `LargeAspectRatioConfig`/`SolovevConfig`, or nothing for the normal path). + +`preloaded_forcing_modes` lets the rerun path inject a `Vector{ForcingMode}` +already read from the source HDF5 snapshot, so `compute_perturbed_equilibrium` +does not have to touch the original `forcing.dat` path. When `nothing`, the +ForcingTerms data is loaded from disk at snapshot time (if PerturbedEquilibrium +is enabled) so it still ends up in `input/raw_inputs/forcing_terms/`. +""" +function main_with_inputs( + inputs::Dict{String,Any}, + eq_config::Equilibrium.EquilibriumConfig, + additional_input, + path::String, + git_version::String; + preloaded_forcing_modes::Union{Nothing,Vector{ForcingTerms.ForcingMode}}=nothing, +) total_start = time() # ---------------------------------------------------------------- @@ -68,22 +127,10 @@ function main(args::Vector{String}=String[]) @info "\n Equilibrium\n$_SECTION" equil_start = time() - # Read input data and set up data structures intr = ForceFreeStatesInternal(; dir_path=path) - inputs = TOML.parsefile(joinpath(intr.dir_path, "gpec.toml")) - ctrl = ForceFreeStatesControl(; (Symbol(k) => v for (k, v) in inputs["ForceFreeStates"])...) - # Set up equilibrium from gpec.toml or fallback to equil.toml if it exists - if "Equilibrium" in keys(inputs) - eq_config = Equilibrium.EquilibriumConfig(inputs["Equilibrium"], intr.dir_path) - equil = Equilibrium.setup_equilibrium(eq_config) - elseif isfile(joinpath(intr.dir_path, "equil.toml")) - @warn "Reading from equil.toml is deprecated. Please move [EQUIL_CONTROL] and [EQUIL_OUTPUT] sections to [Equilibrium] in gpec.toml" - equil = Equilibrium.setup_equilibrium(joinpath(intr.dir_path, "equil.toml")) - else - error("No equilibrium configuration found. Add [Equilibrium] section to gpec.toml") - end + equil = Equilibrium.setup_equilibrium(eq_config, additional_input) @info "Equilibrium construction completed in $(@sprintf("%.3f", time() - equil_start)) s" @@ -105,6 +152,29 @@ function main(args::Vector{String}=String[]) intr.debug_settings = DebugSettings() end + # Forcing-data snapshot: when PerturbedEquilibrium is enabled, load forcing + # modes early so they can be written into `input/raw_inputs/forcing_terms/` + # alongside the TOML blob. On the rerun path the caller passes the modes in + # directly via `preloaded_forcing_modes`, bypassing the original file. + forcing_modes_snapshot = preloaded_forcing_modes + if forcing_modes_snapshot === nothing && "PerturbedEquilibrium" in keys(inputs) + ft_ctrl_snapshot = if "ForcingTerms" in keys(inputs) + ForcingTerms.ForcingTermsControl(; + (Symbol(k) => v for (k, v) in inputs["ForcingTerms"])... + ) + else + ForcingTerms.ForcingTermsControl() + end + forcing_modes_snapshot = ForcingTerms.ForcingMode[] + ForcingTerms.load_forcing_data!( + forcing_modes_snapshot, + path, + ft_ctrl_snapshot.forcing_data_file, + ft_ctrl_snapshot.forcing_data_format, + ctrl.verbose, + ) + end + # ---------------------------------------------------------------- # Force-Free States # ---------------------------------------------------------------- @@ -270,7 +340,7 @@ function main(args::Vector{String}=String[]) end if ctrl.write_outputs_to_HDF5 - write_outputs_to_HDF5(ctrl, equil, intr, odet, ctrl.vac_flag ? vac_data : nothing, ffit, git_version) + write_outputs_to_HDF5(ctrl, equil, intr, odet, ctrl.vac_flag ? vac_data : nothing, ffit, git_version, inputs, forcing_modes_snapshot) @info "Results written to $(ctrl.HDF5_filename)" end @@ -304,6 +374,14 @@ function main(args::Vector{String}=String[]) ) pe_intr = PerturbedEquilibrium.PerturbedEquilibriumInternal(; dir_path=intr.dir_path) + # Reuse the forcing modes loaded at snapshot time (or injected by + # `main_from_h5`) so the PE compute step never re-reads the original + # forcing file. `compute_perturbed_equilibrium` short-circuits + # `load_forcing_data!` when `pe_intr.forcing_modes` is non-empty. + if forcing_modes_snapshot !== nothing + pe_intr.forcing_modes = copy(forcing_modes_snapshot) + end + # Run perturbed equilibrium calculations # Pass vac_data and intr for response matrix calculations pe_state = PerturbedEquilibrium.compute_perturbed_equilibrium( @@ -353,7 +431,9 @@ function write_outputs_to_HDF5( odet::OdeState, vac_data::Union{VacuumData,Nothing}, ffit::Union{FourFitVars,Nothing}=nothing, - git_version::String="unknown" + git_version::String="unknown", + inputs::Union{Nothing,Dict{String,Any}}=nothing, + forcing_modes::Union{Nothing,Vector{ForcingTerms.ForcingMode}}=nothing, ) h5open(joinpath(intr.dir_path, ctrl.HDF5_filename), "w") do out_h5 @@ -361,18 +441,18 @@ function write_outputs_to_HDF5( # Store git version for reproducibility out_h5["info/git_version"] = git_version - # Store input parameters - for (key, val) in zip(fieldnames(ForceFreeStatesControl), getfield.(Ref(ctrl), fieldnames(ForceFreeStatesControl))) - out_h5["input/ForceFreeStates/$key"] = val + # Self-contained run snapshot: the full merged TOML (so a rerun can + # reconstruct every ForceFreeStates/Equilibrium/Wall/PE control struct), + # plus raw equilibrium arrays so the rerun never needs the original + # g-file / CHEASE / auxiliary TOML files. + if inputs !== nothing + out_h5["input/gpec_toml_raw"] = sprint(TOML.print, inputs) end - for (key, val) in zip(fieldnames(Equilibrium.EquilibriumConfig), getfield.(Ref(equil.config), fieldnames(Equilibrium.EquilibriumConfig))) - out_h5["input/EQUIL_CONTROL/$key"] = val + write_equilibrium_raw_inputs!(out_h5, equil) + if forcing_modes !== nothing + forcing_group = create_group(out_h5, "input/raw_inputs/forcing_terms") + ForcingTerms.save_forcing_to_h5(forcing_modes, forcing_group) end - # TODO: assuming EQUIL_OUTPUT is going to be deprecated - # TODO: should we store the equilibrium? difficult since it could be a gfile, sol.in, etc. - # TODO: if we do one input file, can just pass that in instead and loop easily since its parsed - # as a dict already (for (k, v) in inputs["ForceFreeStates"]...). We have to do this since custom structs - # don't inherently have an iterator by default # Write derived run parameters out_h5["info/mpert"] = intr.mpert diff --git a/src/PerturbedEquilibrium/PerturbedEquilibrium.jl b/src/PerturbedEquilibrium/PerturbedEquilibrium.jl index e23a9a6c5..471a5645a 100644 --- a/src/PerturbedEquilibrium/PerturbedEquilibrium.jl +++ b/src/PerturbedEquilibrium/PerturbedEquilibrium.jl @@ -89,8 +89,12 @@ function compute_perturbed_equilibrium( # Step 0: Initialize mode arrays for convenient indexing initialize_mode_arrays!(intr, ffs_intr) - # Step 1: Load forcing data - load_forcing_data!(intr.forcing_modes, intr.dir_path, ft_ctrl.forcing_data_file, ft_ctrl.forcing_data_format, ctrl.verbose) + # Step 1: Load forcing data. Skip the file read when the caller has already + # populated `intr.forcing_modes` (used by the gpec.h5 replay path, which + # hands us modes pulled from `input/raw_inputs/forcing_terms/`). + if isempty(intr.forcing_modes) + load_forcing_data!(intr.forcing_modes, intr.dir_path, ft_ctrl.forcing_data_file, ft_ctrl.forcing_data_format, ctrl.verbose) + end # Step 2: Compute plasma response if ctrl.compute_response diff --git a/src/Rerun.jl b/src/Rerun.jl new file mode 100644 index 000000000..87ca514eb --- /dev/null +++ b/src/Rerun.jl @@ -0,0 +1,331 @@ +""" + Rerun support: helpers for saving run inputs into gpec.h5 and replaying them. + +This file provides the machinery that backs issue #171: turning a gpec.h5 output +into a self-contained run snapshot that can be rerun from any directory, with +optional overrides, without needing the original g-file / CHEASE / wall / TOML +auxiliary inputs. + +Functions here are included directly into the GeneralizedPerturbedEquilibrium +module (via `include("Rerun.jl")`), so they share its imports (TOML, HDF5, +Equilibrium, ForcingTerms, etc.). +""" + +""" + merge_auxiliary_eq_toml!(inputs::Dict{String,Any}, eq_config) + +For analytic equilibria (`lar`, `sol`), the equilibrium parameters live in a +separate auxiliary TOML referenced by `eq_config.eq_filename` (e.g. `sol.toml` +with a `[SOL_INPUT]` section). To make the `gpec.h5` snapshot self-contained, +we merge the relevant auxiliary section into the in-memory `inputs` dict under +the same key (`LAR_INPUT` / `SOL_INPUT`). On replay, `main_from_h5` reads these +sections back into a `LargeAspectRatioConfig` / `SolovevConfig` and passes +them to `setup_equilibrium` as `additional_input`, bypassing the auxiliary +file read entirely. + +No-op for EFIT/CHEASE equilibria — those are snapshotted via `raw_inputs`. +""" +function merge_auxiliary_eq_toml!(inputs::Dict{String,Any}, eq_config::Equilibrium.EquilibriumConfig) + eq_type = eq_config.eq_type + if eq_type != "lar" && eq_type != "sol" + return inputs + end + + filepath = eq_config.eq_filename + if !isfile(filepath) + @warn "Auxiliary equilibrium TOML not found at $filepath; snapshot will not contain analytic parameters" + return inputs + end + + aux = TOML.parsefile(filepath) + section = eq_type == "lar" ? "LAR_INPUT" : "SOL_INPUT" + if haskey(aux, section) + inputs[section] = aux[section] + else + @warn "Auxiliary TOML $filepath has no [$section] section; snapshot will not contain analytic parameters" + end + return inputs +end + +""" + write_equilibrium_raw_inputs!(out_h5, equil) + +Write the raw-data dict captured on `PlasmaEquilibrium.raw_inputs` into +`input/raw_inputs/equilibrium/` inside an open HDF5 file. The layout follows +the `kind` field: `direct`, `inverse`, or `analytic`. On replay, the reader +looks at `kind` to decide whether to rebuild a `DirectRunInput` / +`InverseRunInput` or to reconstruct an analytic config from the TOML snapshot. +""" +function write_equilibrium_raw_inputs!(out_h5, equil::Equilibrium.PlasmaEquilibrium) + raw = equil.raw_inputs + if isempty(raw) + @warn "Equilibrium has no raw_inputs captured; gpec.h5 will not be rerunnable" + return nothing + end + + group_path = "input/raw_inputs/equilibrium" + for (key, val) in raw + out_h5["$group_path/$key"] = val + end + return nothing +end + +""" + read_equilibrium_raw_inputs(in_h5) -> Dict{String,Any} + +Inverse of `write_equilibrium_raw_inputs!`: read every dataset under +`input/raw_inputs/equilibrium/` into a plain dict. Used by `main_from_h5` +to hydrate a `DirectRunInput` / `InverseRunInput` without any filesystem +access. +""" +function read_equilibrium_raw_inputs(in_h5) + group_path = "input/raw_inputs/equilibrium" + if !haskey(in_h5, group_path) + error("gpec.h5 has no $group_path group — the file was produced before rerun snapshot support was added") + end + group = in_h5[group_path] + raw = Dict{String,Any}() + for name in keys(group) + raw[name] = read(group, name) + end + return raw +end + +""" + apply_toml_overrides!(inputs, overrides) + +In-place deep-merge of a nested override dict onto `inputs`. Later values +replace earlier ones at the leaf level; intermediate tables are merged +recursively. Used by the rerun path so users can tweak individual +ForceFreeStates / Equilibrium / PerturbedEquilibrium fields without +re-editing the whole TOML blob. +""" +function apply_toml_overrides!(inputs::Dict{String,Any}, overrides::Dict{String,Any}) + for (k, v) in overrides + if v isa Dict && haskey(inputs, k) && inputs[k] isa Dict + apply_toml_overrides!(inputs[k], v) + else + inputs[k] = v + end + end + return inputs +end + +""" + parse_override_flag(expr::AbstractString) -> Dict{String,Any} + +Parse a `--override section.key=value` expression into a nested override dict. +Values are parsed as Julia literals via `TOML.parse("_k=_v")` so users can pass +numbers, booleans, and quoted strings without worrying about shell quoting. +""" +function parse_override_flag(expr::AbstractString) + eqidx = findfirst(==('='), expr) + eqidx === nothing && error("--override expects key=value, got: $expr") + lhs = String(strip(expr[1:eqidx-1])) + rhs = String(strip(expr[eqidx+1:end])) + isempty(lhs) && error("--override key cannot be empty: $expr") + + parts = split(lhs, '.') + length(parts) < 2 && error("--override key must be dotted (section.key[.subkey]): $expr") + + # Parse RHS as a TOML value by wrapping it in a throwaway key=value line. + parsed_val = try + parsed = TOML.parse("_rerun_override_ = $rhs") + parsed["_rerun_override_"] + catch + # Fall back to string if TOML parse fails (e.g., unquoted bare words). + rhs + end + + # Build nested dict from dotted path. + root = Dict{String,Any}() + cursor = root + for p in parts[1:end-1] + cursor[String(p)] = Dict{String,Any}() + cursor = cursor[String(p)] + end + cursor[String(parts[end])] = parsed_val + return root +end + +""" + parse_rerun_cli(args) -> NamedTuple + +Parse the rerun CLI. Returns `(source_h5, output_dir, output_name, +override_file, overrides)`. Unknown flags error out early. + +Supported flags: + + - `--output-dir ` — directory to write the replay output into (default: pwd()) + - `--output-name ` — output HDF5 filename (default: `_rerun.h5`) + - `--override-file ` — TOML file merged onto the stored TOML + - `--override key=value` — single-field override (repeatable) +""" +function parse_rerun_cli(args::Vector{String}) + isempty(args) && error("main_from_h5 requires a positional source .h5 path") + source_h5 = args[1] + + output_dir = pwd() + output_name = nothing + override_file = nothing + overrides = Dict{String,Any}() + + i = 2 + while i <= length(args) + flag = args[i] + if flag == "--output-dir" + i + 1 > length(args) && error("--output-dir requires a value") + output_dir = args[i+1] + i += 2 + elseif flag == "--output-name" + i + 1 > length(args) && error("--output-name requires a value") + output_name = args[i+1] + i += 2 + elseif flag == "--override-file" + i + 1 > length(args) && error("--override-file requires a value") + override_file = args[i+1] + i += 2 + elseif flag == "--override" + i + 1 > length(args) && error("--override requires a key=value expression") + merged = parse_override_flag(args[i+1]) + apply_toml_overrides!(overrides, merged) + i += 2 + else + error("Unknown rerun flag: $flag") + end + end + + return (source_h5=source_h5, output_dir=output_dir, output_name=output_name, + override_file=override_file, overrides=overrides) +end + +""" + resolve_rerun_output_path(source_h5, output_dir, output_name) -> (dir, name) + +Decide where the rerun output should go. Default naming rule: take the source +basename, drop `.h5`, and append `_rerun.h5`. Refuse to overwrite the source +file if the resolved destination collides. +""" +function resolve_rerun_output_path(source_h5::String, output_dir::String, output_name::Union{Nothing,String}) + source_abs = abspath(source_h5) + if output_name === nothing + base = basename(source_abs) + stem = endswith(lowercase(base), ".h5") ? base[1:end-3] : base + output_name = string(stem, "_rerun.h5") + end + out_abs = abspath(joinpath(output_dir, output_name)) + if out_abs == source_abs + error("Refusing to overwrite source HDF5 at $source_abs. " * + "Pass `--output-dir ` or `--output-name `.") + end + return (output_dir, output_name) +end + +""" + rebuild_equilibrium_input(eq_config, raw) -> Union{DirectRunInput,InverseRunInput,Nothing} + +Dispatch on `raw["kind"]` to rebuild the solver input. Returns `nothing` for +the `analytic` case — the caller should fall back to constructing a +`LargeAspectRatioConfig` / `SolovevConfig` from the restored TOML sections. +""" +function rebuild_equilibrium_input(eq_config::Equilibrium.EquilibriumConfig, raw::Dict{String,Any}) + kind = get(raw, "kind", "") + if kind == "direct" + return Equilibrium.build_direct_from_raw(eq_config, raw) + elseif kind == "inverse" + return Equilibrium.build_inverse_from_raw(eq_config, raw) + elseif kind == "analytic" + return nothing + else + error("Unknown raw equilibrium kind in gpec.h5: $kind") + end +end + +""" + main_from_h5(args::Vector{String}) + +Rerun entry point. Parses the rerun-specific CLI flags, reads the snapshot +out of the source HDF5, applies any overrides, and dispatches back into +`main` with the reconstructed inputs. Never touches the source file's +original ingest paths. +""" +function main_from_h5(args::Vector{String}) + cli = parse_rerun_cli(args) + source_h5 = cli.source_h5 + isfile(source_h5) || error("Source HDF5 not found: $source_h5") + + # Pull the stored TOML, raw equilibrium arrays, and (if present) forcing + # data out of the source file. Forcing modes are only written when the + # original run had a [PerturbedEquilibrium] section, so the group may be + # missing — we signal that with `nothing` and let main_with_inputs fall + # back to loading from `ft_ctrl.forcing_data_file`. + toml_raw, raw_eq, source_git, preloaded_forcing = h5open(source_h5, "r") do in_h5 + haskey(in_h5, "input/gpec_toml_raw") || + error("Source HDF5 $source_h5 has no input/gpec_toml_raw — produced by a pre-rerun version of GPEC") + forcing_modes = if haskey(in_h5, "input/raw_inputs/forcing_terms") + modes = ForcingTerms.ForcingMode[] + ForcingTerms.load_forcing_from_h5_group!(modes, in_h5["input/raw_inputs/forcing_terms"]) + modes + else + nothing + end + ( + read(in_h5, "input/gpec_toml_raw"), + read_equilibrium_raw_inputs(in_h5), + haskey(in_h5, "info/git_version") ? read(in_h5, "info/git_version") : "unknown", + forcing_modes, + ) + end + + # Parse TOML blob and fold in overrides: file overrides first, then CLI flags. + inputs = TOML.parse(toml_raw) + if cli.override_file !== nothing + isfile(cli.override_file) || error("Override file not found: $(cli.override_file)") + file_overrides = TOML.parsefile(cli.override_file) + apply_toml_overrides!(inputs, file_overrides) + end + if !isempty(cli.overrides) + apply_toml_overrides!(inputs, cli.overrides) + end + + output_dir, output_name = resolve_rerun_output_path(source_h5, cli.output_dir, cli.output_name) + isdir(output_dir) || mkpath(output_dir) + + # Force the rerun output file name so the source is never overwritten. + if haskey(inputs, "ForceFreeStates") + inputs["ForceFreeStates"]["HDF5_filename"] = output_name + end + + current_git = try + String(readchomp(`git -C $(@__DIR__) describe --tags --always`)) + catch + "unknown" + end + + @info "\n$_BANNER\n GPEC RERUN [source git: $source_git → current: $current_git]\n" * + " source: $(abspath(source_h5))\n" * + " output: $(abspath(joinpath(output_dir, output_name)))\n$_BANNER" + + # Rebuild the equilibrium solver input from the HDF5-stored arrays (or from + # the merged LAR/SOL sections for analytic kinds), and run the standard + # pipeline. Everything downstream is unchanged. + eq_config = Equilibrium.EquilibriumConfig(inputs["Equilibrium"], output_dir) + # eq_filename won't be used on replay — clear it so any leftover absolute + # path from the source machine can't trip up later code paths. + eq_config.eq_filename = "" + + additional_input = if raw_eq["kind"] == "analytic" + if eq_config.eq_type == "lar" + lar_data = get(inputs, "LAR_INPUT", Dict{String,Any}()) + Equilibrium.LargeAspectRatioConfig(; (Symbol(k) => v for (k, v) in lar_data)...) + else + sol_data = get(inputs, "SOL_INPUT", Dict{String,Any}()) + Equilibrium.SolovevConfig(; (Symbol(k) => v for (k, v) in sol_data)...) + end + else + rebuild_equilibrium_input(eq_config, raw_eq) + end + + return main_with_inputs(inputs, eq_config, additional_input, output_dir, current_git; + preloaded_forcing_modes=preloaded_forcing) +end diff --git a/test/runtests.jl b/test/runtests.jl index 2efa40980..1ce6817c5 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -26,4 +26,5 @@ else include("./runtests_eulerlagrange.jl") include("./runtests_sing.jl") include("./runtests_fullruns.jl") + include("./runtests_rerun_from_h5.jl") end diff --git a/test/runtests_rerun_from_h5.jl b/test/runtests_rerun_from_h5.jl new file mode 100644 index 000000000..9b806d9f5 --- /dev/null +++ b/test/runtests_rerun_from_h5.jl @@ -0,0 +1,98 @@ +using HDF5 + +# Exercise the gpec.h5 snapshot + replay pipeline (issue #171). The source run is +# a regular `main(dir)` invocation; the replay runs `main_from_h5` from a temp +# directory that contains nothing but the captured gpec.h5, proving that the +# snapshot is self-contained (no auxiliary TOML, no g-file, no forcing data). +@testset "Rerun from gpec.h5" begin + template_dir = joinpath(@__DIR__, "test_data", "regression_solovev_ideal_example") + + function read_scalars(path) + return h5open(path, "r") do h5 + ( + et=read(h5, "vacuum/et"), + ep=read(h5, "vacuum/ep"), + ev=read(h5, "vacuum/ev"), + mpert=read(h5, "info/mpert"), + msing=read(h5, "singular/msing"), + sing_psi=read(h5, "singular/psi"), + sing_q=read(h5, "singular/q"), + ) + end + end + + # Copy the regression example into a temp directory and enable HDF5 output + # so the rest of the test can work against a self-contained source snapshot. + # We avoid editing the in-tree fixture (and its shared gpec.toml) directly. + mktempdir() do snapshot_dir + for name in readdir(template_dir) + cp(joinpath(template_dir, name), joinpath(snapshot_dir, name)) + end + toml_path = joinpath(snapshot_dir, "gpec.toml") + toml_text = read(toml_path, String) + toml_text = replace(toml_text, "write_outputs_to_HDF5 = false" => "write_outputs_to_HDF5 = true") + write(toml_path, toml_text) + + @info "Generating source gpec.h5 for rerun tests" + GeneralizedPerturbedEquilibrium.main([snapshot_dir]) + source_h5 = joinpath(snapshot_dir, "gpec.h5") + @test isfile(source_h5) + source_scalars = read_scalars(source_h5) + + @testset "self-contained replay matches source bit-for-bit" begin + mktempdir() do replay_dir + # No gpec.toml, no sol.toml, no g-file in replay_dir — this is + # the hard constraint from issue #171. + GeneralizedPerturbedEquilibrium.main([source_h5, "--output-dir", replay_dir]) + + replay_h5 = joinpath(replay_dir, "gpec_rerun.h5") + @test isfile(replay_h5) + replay_scalars = read_scalars(replay_h5) + + @test replay_scalars.et == source_scalars.et + @test replay_scalars.ep == source_scalars.ep + @test replay_scalars.ev == source_scalars.ev + @test replay_scalars.mpert == source_scalars.mpert + @test replay_scalars.msing == source_scalars.msing + @test replay_scalars.sing_psi == source_scalars.sing_psi + @test replay_scalars.sing_q == source_scalars.sing_q + end + end + + @testset "override changes tolerance without breaking singular structure" begin + mktempdir() do replay_dir + GeneralizedPerturbedEquilibrium.main([ + source_h5, + "--output-dir", replay_dir, + "--override", "ForceFreeStates.eulerlagrange_tolerance=1e-6", + ]) + + replay_h5 = joinpath(replay_dir, "gpec_rerun.h5") + @test isfile(replay_h5) + replay_scalars = read_scalars(replay_h5) + + # Loosening the tolerance should leave the rational-surface + # structure intact and the real eigenvalue unchanged to high + # precision, while the imaginary part (set by integrator + # residuals) is allowed to drift. + @test replay_scalars.mpert == source_scalars.mpert + @test replay_scalars.msing == source_scalars.msing + @test replay_scalars.sing_psi == source_scalars.sing_psi + @test replay_scalars.sing_q == source_scalars.sing_q + @test real(replay_scalars.et[1]) ≈ real(source_scalars.et[1]) rtol = 1e-4 + end + end + + @testset "rerun refuses to overwrite its own source" begin + # Default output name is `_rerun.h5`, so clobbering only + # happens when the user tries to route the rerun back on top of the + # source file. Exercise the guard by aiming the output at the + # snapshot dir with the source filename. + @test_throws ErrorException GeneralizedPerturbedEquilibrium.main([ + source_h5, + "--output-dir", snapshot_dir, + "--output-name", "gpec.h5", + ]) + end + end +end From 0b01abc1969773a865ad90c39baf1a78a454932e Mon Sep 17 00:00:00 2001 From: jmlmir369 Date: Wed, 29 Apr 2026 14:18:58 +0900 Subject: [PATCH 002/135] Modernizing --- .../Bal_salpha_delta_di_summary.ipynb | 252 ++++ src/ForceFreeStates/Bal.jl | 1068 ++++++++++------- 2 files changed, 893 insertions(+), 427 deletions(-) create mode 100644 examples/DIIID-like_ideal_example/Bal_salpha_delta_di_summary.ipynb diff --git a/examples/DIIID-like_ideal_example/Bal_salpha_delta_di_summary.ipynb b/examples/DIIID-like_ideal_example/Bal_salpha_delta_di_summary.ipynb new file mode 100644 index 000000000..d7dbf361d --- /dev/null +++ b/examples/DIIID-like_ideal_example/Bal_salpha_delta_di_summary.ipynb @@ -0,0 +1,252 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "id": "s-alpha-profile-extrema", + "metadata": {}, + "outputs": [], + "source": [ + "using Pkg\n", + "Pkg.activate(\"../..\")\n", + "\n", + "using JPEC\n", + "using Plots\n", + "using Printf\n", + "using Statistics\n", + "\n", + "equil = JPEC.Equilibrium.setup_equilibrium(\"equil.toml\")\n", + "psi_norm = Vector(equil.sq.xs)\n", + "\n", + "function finite_local_extrema(values::AbstractVector{<:Real})\n", + " extrema = Int[]\n", + " for i in 2:length(values)-1\n", + " if !isfinite(values[i - 1]) || !isfinite(values[i]) || !isfinite(values[i + 1])\n", + " continue\n", + " end\n", + " if (values[i] >= values[i - 1] && values[i] >= values[i + 1]) ||\n", + " (values[i] <= values[i - 1] && values[i] <= values[i + 1])\n", + " push!(extrema, i)\n", + " end\n", + " end\n", + " return extrema\n", + "end\n", + "\n", + "function print_extrema_report(name::String, psi::AbstractVector, values::AbstractVector, extrema::AbstractVector{Int})\n", + " println(\"\\n\", name, \" extrema\")\n", + " if isempty(extrema)\n", + " println(\" none\")\n", + " return\n", + " end\n", + " println(\" index\\tpsi_norm\\tvalue\")\n", + " for i in extrema\n", + " @printf(\" %d\\t%.8f\\t%.12e\\n\", i, psi[i], values[i])\n", + " end\n", + "end\n", + "\n", + "s_profile = fill(NaN, length(psi_norm))\n", + "alpha_profile = fill(NaN, length(psi_norm))\n", + "\n", + "for i in eachindex(psi_norm)\n", + " try\n", + " ref = JPEC.DCON.salpha_reference(i, equil)\n", + " s_profile[i] = ref.s_ref\n", + " alpha_profile[i] = ref.alpha_ref\n", + " catch err\n", + " @warn \"s-alpha reference failed\" i psi=psi_norm[i] exception=(err, catch_backtrace())\n", + " end\n", + "end\n", + "\n", + "s_extrema = finite_local_extrema(s_profile)\n", + "alpha_extrema = finite_local_extrema(alpha_profile)\n", + "print_extrema_report(\"s\", psi_norm, s_profile, s_extrema)\n", + "print_extrema_report(\"alpha\", psi_norm, alpha_profile, alpha_extrema)\n", + "\n", + "s_mask = isfinite.(s_profile)\n", + "alpha_mask = isfinite.(alpha_profile)\n", + "\n", + "p_s = plot(\n", + " psi_norm[s_mask], s_profile[s_mask];\n", + " xlabel=\"psi_norm\",\n", + " ylabel=\"s\",\n", + " label=\"s\",\n", + " lw=2,\n", + " title=\"s profile\",\n", + " framestyle=:box,\n", + ")\n", + "scatter!(p_s, psi_norm[s_extrema], s_profile[s_extrema]; label=\"extrema\", marker=:circle, color=:red, ms=5)\n", + "\n", + "p_alpha = plot(\n", + " psi_norm[alpha_mask], alpha_profile[alpha_mask];\n", + " xlabel=\"psi_norm\",\n", + " ylabel=\"alpha\",\n", + " label=\"alpha\",\n", + " lw=2,\n", + " title=\"alpha profile\",\n", + " framestyle=:box,\n", + ")\n", + "scatter!(p_alpha, psi_norm[alpha_extrema], alpha_profile[alpha_extrema]; label=\"extrema\", marker=:circle, color=:red, ms=5)\n", + "\n", + "display(plot(p_s, p_alpha; layout=(1, 2), size=(1100, 420)))\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "delta-di-profile-extrema", + "metadata": {}, + "outputs": [], + "source": [ + "locstab_fs = zeros(length(psi_norm), 4)\n", + "ctrl = JPEC.DCON.DconControl(verbose=false)\n", + "\n", + "println(\"Computing Delta' and Di profiles...\")\n", + "JPEC.DCON.compute_ballooning_stability!(ctrl, locstab_fs, equil; compute_delta_prime=true)\n", + "\n", + "delta_prime = Vector(locstab_fs[:, 4])\n", + "di_profile = fill(NaN, length(psi_norm))\n", + "psi_mask = abs.(psi_norm) .> eps(Float64)\n", + "di_profile[psi_mask] .= locstab_fs[psi_mask, 1] ./ psi_norm[psi_mask]\n", + "\n", + "delta_extrema = finite_local_extrema(delta_prime)\n", + "di_extrema = finite_local_extrema(di_profile)\n", + "print_extrema_report(\"Delta'\", psi_norm, delta_prime, delta_extrema)\n", + "print_extrema_report(\"Di\", psi_norm, di_profile, di_extrema)\n", + "\n", + "delta_mask = isfinite.(delta_prime)\n", + "di_mask = isfinite.(di_profile)\n", + "\n", + "p_delta = plot(\n", + " psi_norm[delta_mask], delta_prime[delta_mask];\n", + " xlabel=\"psi_norm\",\n", + " ylabel=\"Delta'\",\n", + " label=\"Delta'\",\n", + " lw=2,\n", + " title=\"Delta' profile\",\n", + " framestyle=:box,\n", + ")\n", + "scatter!(p_delta, psi_norm[delta_extrema], delta_prime[delta_extrema]; label=\"extrema\", marker=:diamond, color=:red, ms=5)\n", + "\n", + "p_di = plot(\n", + " psi_norm[di_mask], di_profile[di_mask];\n", + " xlabel=\"psi_norm\",\n", + " ylabel=\"Di\",\n", + " label=\"Di\",\n", + " lw=2,\n", + " title=\"Di profile\",\n", + " framestyle=:box,\n", + ")\n", + "scatter!(p_di, psi_norm[di_extrema], di_profile[di_extrema]; label=\"extrema\", marker=:diamond, color=:red, ms=5)\n", + "\n", + "display(plot(p_delta, p_di; layout=(1, 2), size=(1100, 420)))\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "s-alpha-delta-di-maps", + "metadata": {}, + "outputs": [], + "source": [ + "psi_target = 0.75\n", + "psi_idx_scan = argmin(abs.(psi_norm .- psi_target))\n", + "\n", + "println(\"Running s-alpha scan at index $(psi_idx_scan), psi_norm=$(round(psi_norm[psi_idx_scan], digits=6))\")\n", + "\n", + "s_scales = collect(range(0.5, 5.0; length=31))\n", + "alpha_scales = collect(range(0.5, 5.0; length=31))\n", + "\n", + "scan_result = JPEC.DCON.scan_delta_prime_map(\n", + " psi_idx_scan,\n", + " equil;\n", + " theta_k=0.0,\n", + " s_scales=s_scales,\n", + " alpha_scales=alpha_scales,\n", + ")\n", + "\n", + "scan_s = scan_result.s_values\n", + "scan_alpha = scan_result.alpha_values\n", + "scan_delta = permutedims(scan_result.delta_prime, (2, 1))\n", + "scan_di = permutedims(scan_result.di_values, (2, 1))\n", + "\n", + "function symmetric_clims(z)\n", + " finite_vals = vec(z)[isfinite.(vec(z))]\n", + " maxabs = isempty(finite_vals) ? 1.0 : maximum(abs.(finite_vals))\n", + " maxabs = max(maxabs, eps(Float64))\n", + " return (-maxabs, maxabs)\n", + "end\n", + "\n", + "p_scan_delta = contourf(\n", + " scan_s, scan_alpha, scan_delta;\n", + " c=cgrad([:blue, :white, :red]),\n", + " clims=symmetric_clims(scan_delta),\n", + " xlabel=\"s\",\n", + " ylabel=\"alpha\",\n", + " title=\"s-alpha Delta'\",\n", + " colorbar_title=\"Delta'\",\n", + " levels=41,\n", + " framestyle=:box,\n", + ")\n", + "contour!(p_scan_delta, scan_s, scan_alpha, scan_delta; levels=[0.0], color=:black, linewidth=2, label=\"Delta' = 0\")\n", + "scatter!(p_scan_delta, [scan_result.reference.s_ref], [scan_result.reference.alpha_ref]; color=:green, marker=:star5, ms=7, label=\"equilibrium\")\n", + "\n", + "p_scan_di = contourf(\n", + " scan_s, scan_alpha, scan_di;\n", + " c=cgrad([:blue, :white, :red]),\n", + " clims=symmetric_clims(scan_di),\n", + " xlabel=\"s\",\n", + " ylabel=\"alpha\",\n", + " title=\"s-alpha Di\",\n", + " colorbar_title=\"Di\",\n", + " levels=41,\n", + " framestyle=:box,\n", + ")\n", + "contour!(p_scan_di, scan_s, scan_alpha, scan_di; levels=[0.0], color=:black, linewidth=2, label=\"Di = 0\")\n", + "scatter!(p_scan_di, [scan_result.reference.s_ref], [scan_result.reference.alpha_ref]; color=:green, marker=:star5, ms=7, label=\"equilibrium\")\n", + "\n", + "display(plot(p_scan_delta, p_scan_di; layout=(1, 2), size=(1150, 460)))\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "s-alpha-zero-contours", + "metadata": {}, + "outputs": [], + "source": [ + "p_zero = plot(\n", + " xlabel=\"s\",\n", + " ylabel=\"alpha\",\n", + " title=\"s-alpha zero contours\",\n", + " framestyle=:box,\n", + ")\n", + "contour!(p_zero, scan_s, scan_alpha, scan_delta;\n", + " levels=[0.0], color=:blue, linewidth=3,\n", + " label=\"Delta' = 0\", colorbar=false)\n", + "\n", + "contour!(p_zero, scan_s, scan_alpha, scan_di;\n", + " levels=[0.0], color=:red, linewidth=3, linestyle=:dash,\n", + " label=\"Di = 0\", colorbar=false)\n", + "\n", + "\n", + "scatter!(p_zero, [scan_result.reference.s_ref], [scan_result.reference.alpha_ref]; color=:green, marker=:star5, ms=8, label=\"equilibrium\")\n", + "display(p_zero)\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.12.4", + "language": "julia", + "name": "julia-1.12" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.12.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/src/ForceFreeStates/Bal.jl b/src/ForceFreeStates/Bal.jl index c8b34ab2c..634fc3d4c 100644 --- a/src/ForceFreeStates/Bal.jl +++ b/src/ForceFreeStates/Bal.jl @@ -1,499 +1,713 @@ +# ====================================================================== +# Main Driver for Ballooning Stability Analysis +# Computes ballooning stability criterion over all flux surfaces +# ====================================================================== +using LinearAlgebra """ - compute_asymptotic_solutions(poloidal_angle, growth_parameter, asymptotic_interp, asymp_buffer, eigenfunctions, reference_angle) -> Matrix{Float64} + compute_ballooning_stability!(ctrl, locstab_fs, plasma_eq) -Computes the asymptotic pseudo-solutions (alpha series) for the ballooning equation -at a given extended poloidal angle. These solutions are used as boundary conditions for -the numerical ODE integration. +Main driver routine for local high-n stability analysis. Iterates over all +magnetic flux surfaces, prepares ballooning coefficients, stores `det(d0bar)` +as the local `Di` diagnostic, and optionally integrates the ballooning equation +to compute Delta Prime. ## Arguments - - `poloidal_angle::Float64`: Extended poloidal angle θ. - - `growth_parameter::Float64`: Growth parameter α (from Mercier criterion). - - `asymptotic_interp::CubicSeriesInterpolant`: SeriesInterpolant for 5 asymptotic coefficients. - - `asymp_buffer::Vector{Float64}`: Pre-allocated buffer for in-place interpolation. - - `eigenfunctions::Matrix{Float64}`: Zeroth-order eigenfunctions (2×2 matrix). - - `reference_angle::Float64`: Reference poloidal angle (usually 0). + - `ctrl::DconControl`: Control parameters for the analysis. + - `locstab_fs::Matrix{Float64}`: Local stability matrix to store results (modified in place). + - `plasma_eq::Equilibrium.PlasmaEquilibrium`: Plasma equilibrium data. -## Returns +This function modifies `locstab_fs` in place with: - - `asymptotic_matrix::Matrix{Float64}`: 2×2 matrix where each column is an asymptotic solution. + - Column 1: `det(d0bar) * ψ` + - Column 4: Delta Prime (Δ') """ -function compute_asymptotic_solutions(poloidal_angle::Float64, growth_parameter::Float64, - asymptotic_interp::CubicSeriesInterpolant, asymp_buffer::Vector{Float64}, - eigenfunctions::Matrix{Float64}, reference_angle::Float64) - asymptotic_matrix = zeros(Float64, 2, 2) - first_order_correction = zeros(Float64, 2, 2) - - # Evaluate all asymptotic coefficients in-place (zero allocation) - asymptotic_interp(asymp_buffer, poloidal_angle) - a1, a2, a3, a4, a5 = asymp_buffer[1], asymp_buffer[2], asymp_buffer[3], asymp_buffer[4], asymp_buffer[5] - angle_offset = poloidal_angle - reference_angle - - # First-order terms from the asymptotic expansion - first_order_correction[1, 1] = eigenfunctions[1, 1] + a1 / angle_offset - first_order_correction[2, 1] = eigenfunctions[2, 1] + a2 / angle_offset - first_order_correction[1, 2] = eigenfunctions[1, 2] + a3 / angle_offset - first_order_correction[2, 2] = eigenfunctions[2, 2] + a4 / angle_offset - - # Transformed solutions - asymptotic_matrix[1, 1] = first_order_correction[1, 1] - asymptotic_matrix[1, 2] = first_order_correction[1, 2] - asymptotic_matrix[2, 1] = a5 * first_order_correction[1, 1] + first_order_correction[2, 1] - asymptotic_matrix[2, 2] = a5 * first_order_correction[1, 2] + first_order_correction[2, 2] - - # CORRECTED: Match Fortran's thfac = ABS(dtheta)^(alpha+0.5) / dtheta - # This equals: sign(dtheta) * |dtheta|^(alpha - 0.5) - alpha_scaling = sign(angle_offset) * abs(angle_offset)^(growth_parameter - 0.5) - - asymptotic_matrix[1, 1] *= alpha_scaling - asymptotic_matrix[2, 1] *= alpha_scaling * angle_offset - asymptotic_matrix[1, 2] /= (alpha_scaling * angle_offset) - asymptotic_matrix[2, 2] /= alpha_scaling - - return asymptotic_matrix -end +function compute_ballooning_stability!( + ctrl::DconControl, + locstab_fs::Matrix{Float64}, + plasma_eq::Equilibrium.PlasmaEquilibrium; + theta_k::Float64=0.0, + compute_delta_prime::Bool=true +) -# ====================================================================== -# ODE System Definition -# Differential equations for marginal ballooning stability -# ====================================================================== -""" - compute_ballooning_ode!(derivatives, solution, parameters, poloidal_angle) + if ctrl.verbose + println("Evaluating local high-n ballooning stability...") + end -Defines the RHS of the first-order ODE system for ideal marginal ballooning modes. -Used by the DifferentialEquations.jl ODE solver. + num_psi = length(plasma_eq.sq.xs) -The second-order equation `d/dθ(f·dy/dθ) + g·y = 0` is rewritten as a 2x1 system: + # Loop over flux surfaces + for flux_surface_index in 1:num_psi - - `dy₁/dθ = y₂ / f` - - `dy₂/dθ = -g · y₁` + coeff_data = prepare_ballooning_coefficients(flux_surface_index, plasma_eq; theta_k=theta_k) + locstab_fs[flux_surface_index, 1] = coeff_data.di * plasma_eq.sq.xs[flux_surface_index] -where y₁ is the solution and y₂ = f·dy/dθ. + if compute_delta_prime && plasma_eq.sq.xs[flux_surface_index] <= 1.0 + result = integrate_ballooning_ode( + coeff_data.ode_coefficient_spline; + theta_k=theta_k + ) + locstab_fs[flux_surface_index, 4] = result.value + end + end -## Arguments + if ctrl.verbose + println("Ballooning analysis complete.") + end + +end - - `derivatives::Vector{Float64}`: Output vector [dy₁/dθ, dy₂/dθ]. - - `solution::Vector{Float64}`: Current state vector [y₁, y₂]. - - `parameters::Tuple`: (ode_coeff_interp, reference_angle, coeff_buffer, hint). - - `poloidal_angle::Float64`: Current poloidal angle θ (independent variable). -""" -function compute_ballooning_ode!(derivatives, solution, parameters, poloidal_angle) - ode_coeff_interp, reference_angle, coeff_buffer, hint = parameters - # Evaluate all ODE coefficients in-place (zero allocation) - ode_coeff_interp(coeff_buffer, poloidal_angle; hint=hint) - c1, c2, c3, c4, c5 = coeff_buffer[1], coeff_buffer[2], coeff_buffer[3], coeff_buffer[4], coeff_buffer[5] - angle_offset = poloidal_angle - reference_angle - # ODE coefficient f: magnetic shear-related curvature term - f_coefficient = c1 * (angle_offset + c2)^2 + c3 - # ODE coefficient g: pressure-driven instability growth term - g_coefficient = c4 + angle_offset * c5 - # RHS system - derivatives[1] = solution[2] / f_coefficient - derivatives[2] = -solution[1] * g_coefficient +function _collect_surface_response_background( + flux_surface_index::Int, + plasma_eq::Equilibrium.PlasmaEquilibrium, + theta_grid::AbstractVector{<:Real} +)::NamedTuple + sq = plasma_eq.sq + + theta_vals = Float64.(theta_grid) + ntheta = length(theta_vals) + + q0 = Float64(sq.fs[flux_surface_index, 4]) + q0prime = Float64(sq.fs1[flux_surface_index, 4]) + p0prime = Float64(sq.fs1[flux_surface_index, 2]) + two_pi_f0 = Float64(sq.fs[flux_surface_index, 1]) + chi_prime0 = Float64(2pi * plasma_eq.psio) + psi0 = plasma_eq.rzphi.xs[flux_surface_index] + + f0 = zeros(ntheta, 4) + fx0 = zeros(ntheta, 4) + fy0 = zeros(ntheta, 4) + fxy0 = zeros(ntheta, 4) + rho0 = zeros(ntheta) + eta0 = zeros(ntheta) + r0 = zeros(ntheta) + gradpsi_sq0 = zeros(ntheta) + h_theta0 = zeros(ntheta) + C_theta = zeros(ntheta) + Iper0 = zeros(ntheta) + kappas0 = zeros(ntheta) + bsq0 = zeros(ntheta) + jac0 = zeros(ntheta) + bdot_theta_phi0 = zeros(ntheta) + v0 = zeros(ntheta, 3, 3) + v_zeta_psi0 = zeros(ntheta, 3) + v_psi_theta0 = zeros(ntheta, 3) + + for i in eachindex(theta_vals) + theta = theta_vals[i] + f, fx, fy, _, fxy, _ = Spl.bicube_deriv2!(plasma_eq.rzphi, psi0, theta) + + rho = sqrt(f[1]) + eta = 2pi * (theta + f[2]) + ceta = cos(eta) + seta = sin(eta) + r = plasma_eq.ro + rho * ceta + jac = f[4] + + rho_psi = fx[1] / (2 * rho) + rho_theta = fy[1] / (2 * rho) + rho_psitheta = fxy[1] / (2 * rho) - fx[1] * fy[1] / (4 * f[1] * rho) + + eta_psi = 2pi * fx[2] + eta_theta = 2pi * (1 + fy[2]) + eta_psitheta = 2pi * fxy[2] + + Rpsi = rho_psi * ceta - rho * seta * eta_psi + Rtheta = rho_theta * ceta - rho * seta * eta_theta + Zpsi = rho_psi * seta + rho * ceta * eta_psi + Ztheta = rho_theta * seta + rho * ceta * eta_theta + + Rpsitheta = + rho_psitheta * ceta - + rho_psi * seta * eta_theta - + rho_theta * seta * eta_psi - + rho * ceta * eta_psi * eta_theta - + rho * seta * eta_psitheta + + Zpsitheta = + rho_psitheta * seta + + rho_psi * ceta * eta_theta + + rho_theta * ceta * eta_psi - + rho * seta * eta_psi * eta_theta + + rho * ceta * eta_psitheta + + v = zeros(3, 3) + v[1, 1] = fx[1] / (2 * rho * jac) + v[1, 2] = fx[2] * 2pi * rho / jac + v[1, 3] = fx[3] * r / jac + v[2, 1] = fy[1] / (2 * rho * jac) + v[2, 2] = (1 + fy[2]) * 2pi * rho / jac + v[2, 3] = fy[3] * r / jac + v[3, 3] = 2pi * r / jac + + w = zeros(3, 3) + w[1, 1] = (1 + fy[2]) * (2pi)^2 * rho * r / jac + w[1, 2] = -fy[1] * pi * r / (rho * jac) + w[2, 1] = -fx[2] * (2pi)^2 * r * rho / jac + w[2, 2] = fx[1] * pi * r / (rho * jac) + w[3, 1] = (fx[2] * fy[3] - fx[3] * (1 + fy[2])) * 2pi * r * rho / jac + w[3, 2] = (fx[3] * fy[1] - fx[1] * fy[3]) * r / (2 * rho * jac) + w[3, 3] = 1 / (2pi * r) + + grad_psi = Vector(@view w[1, :]) + grad_theta = Vector(@view w[2, :]) + grad_zeta = Vector(@view w[3, :]) + + v_theta_zeta = Vector(@view v[1, :]) + v_zeta_psi = Vector(@view v[2, :]) + v_psi_theta = Vector(@view v[3, :]) + + B_vec = (v_zeta_psi + q0 .* v_psi_theta) * chi_prime0 + bsq = dot(B_vec, B_vec) + gradpsi_sq = dot(grad_psi, grad_psi) + + f0[i, :] .= f + fx0[i, :] .= fx + fy0[i, :] .= fy + fxy0[i, :] .= fxy + rho0[i] = rho + eta0[i] = eta + r0[i] = r + gradpsi_sq0[i] = gradpsi_sq + h_theta0[i] = fy[3] / (2pi) + C_theta[i] = (Rpsitheta * Ztheta - Rtheta * Zpsitheta) / (Rpsi * Ztheta - Rtheta * Zpsi) + Iper0[i] = dot(q0 .* grad_theta .- grad_zeta, grad_psi) / gradpsi_sq + bsq0[i] = bsq + jac0[i] = jac + bdot_theta_phi0[i] = dot(B_vec, v_theta_zeta) + v0[i, :, :] .= v + v_zeta_psi0[i, :] .= v_zeta_psi + v_psi_theta0[i, :] .= v_psi_theta + end + + dbsq_dtheta = _periodic_fft_lowpass_derivative(bsq0, theta_vals; nkeep=16) + dinvbsq_dtheta = .-dbsq_dtheta ./ (bsq0 .^ 2) + + kappas0 .= -dinvbsq_dtheta .* two_pi_f0 ./ (2 .* jac0) + + int_spl = Spl.CubicSpline( + theta_vals, + hcat(1 ./ gradpsi_sq0, r0 .* r0 ./ gradpsi_sq0); + bctype="periodic" + ) + Spl.spline_integrate!(int_spl) + + I0 = Float64(int_spl.fsi[end, 1]) + IR = Float64(int_spl.fsi[end, 2]) + Delta_tilde = Float64(I0 * two_pi_f0^2 + chi_prime0^2) + + return ( + theta_grid=theta_vals, + q0=q0, + q0prime=q0prime, + p0prime=p0prime, + two_pi_f0=two_pi_f0, + chi_prime0=chi_prime0, + r0=r0, + rho0=rho0, + eta0=eta0, + f0=f0, + fx0=fx0, + fy0=fy0, + fxy0=fxy0, + gradpsi_sq0=gradpsi_sq0, + h_theta0=h_theta0, + C_theta=C_theta, + Iper0=Iper0, + bsq0=bsq0, + jac0=jac0, + bdot_theta_phi0=bdot_theta_phi0, + v0=v0, + v_zeta_psi0=v_zeta_psi0, + v_psi_theta0=v_psi_theta0, + kappas0=kappas0, + I0=I0, + IR=IR, + Delta_tilde=Delta_tilde + ) end -# ====================================================================== -# ODE Integration -# Integrates the ideal marginal ballooning equations -# ====================================================================== -""" - integrate_ballooning_ode(ipsi, growth_parameter, ode_coeff_interp, - asymptotic_interp, eigenfunctions, reference_angle, control) -> (Float64, Float64) +function _periodic_fft_lowpass_derivative( + vals::AbstractVector{<:Real}, + xs::AbstractVector{<:Real}; + nkeep::Int=32 +) + nfull = length(vals) + n = nfull - 1 + if n < 2 + throw(ArgumentError("Need at least 3 periodic samples for FFT derivative")) + end -Integrates the ballooning ODE from `-θ_max` to `+θ_max` using adaptive RK integration. + period = Float64(xs[end] - xs[1]) + if !(period > 0.0) + throw(ArgumentError("Periodic grid must span a positive interval")) + end -## Returns + coeffs = FFTW.fft(ComplexF64.(vals[1:n])) + deriv_coeffs = zeros(ComplexF64, n) + maxmode = min(nkeep, fld(n, 2)) - - `(coefficient_1, coefficient_2)`: Asymptotic coefficients determining stability. -""" -function integrate_ballooning_ode(ipsi::Int, growth_parameter::Float64, - ode_coeff_interp::CubicSeriesInterpolant, - asymptotic_interp::CubicSeriesInterpolant, - eigenfunctions::Matrix{Float64}, reference_angle::Float64, - control::ForceFreeStatesControl) + @inbounds for j in 1:n + mode = j <= div(n, 2) + 1 ? j - 1 : j - 1 - n + if abs(mode) <= maxmode + deriv_coeffs[j] = (im * 2pi * mode / period) * coeffs[j] + end + end - TOLERANCE = 1e-5 - MINIMUM_STEP = 1e-10 + deriv = real.(FFTW.ifft(deriv_coeffs)) + return vcat(deriv, deriv[1]) +end - # Determine integration limits (access grid values from SeriesInterpolant) - curvature_ratio = ode_coeff_interp.y[:, 3] ./ ode_coeff_interp.y[:, 1] - theta_max_absolute = sqrt(maximum(abs.(curvature_ratio))) * 10.0 * control.thmax0 - theta_max = min(theta_max_absolute, 100.0) - - # Pre-allocate buffers for in-place interpolation (zero allocation) - coeff_buffer = Vector{Float64}(undef, 5) - asymp_buffer = Vector{Float64}(undef, 5) - hint = Ref(1) - - # Initial conditions from asymptotic solution - theta_start = -theta_max - asymptotic_start = compute_asymptotic_solutions(theta_start, growth_parameter, asymptotic_interp, - asymp_buffer, eigenfunctions, reference_angle) - initial_condition = Vector{Float64}(asymptotic_start[:, 2]) * sinh(1.0) - - # Set up and solve ODE problem - ode_problem = ODEProblem(compute_ballooning_ode!, initial_condition, - (theta_start, theta_max), - (ode_coeff_interp, reference_angle, coeff_buffer, hint)) - - try - ode_solution = solve(ode_problem, DP5(); reltol=TOLERANCE, abstol=TOLERANCE^2, - dtmin=MINIMUM_STEP, adaptive=true, save_everystep=false, save_end=true) - - if ode_solution.retcode == ReturnCode.Success - solution_final = ode_solution.u[end] - theta_final = ode_solution.t[end] - if theta_final < theta_max - return NaN, NaN - end +function _calculate_i_per_perturbed( + bg::NamedTuple, + theta_grid::AbstractVector, + corr_qprime::Float64, + corr_pprime::Float64; + theta_k::Float64=0.0 +) + H = bg.q0 .+ bg.h_theta0 + A = 4pi^2 .* bg.r0 .* bg.r0 ./ (bg.chi_prime0^2 .* bg.gradpsi_sq0) + B = bg.two_pi_f0^2 ./ (bg.chi_prime0^2 .* bg.gradpsi_sq0) - # Asymptotic matching - asymptotic_final = compute_asymptotic_solutions(theta_final, growth_parameter, asymptotic_interp, - asymp_buffer, eigenfunctions, reference_angle) + weight_spl = Spl.CubicSpline(theta_grid, hcat(H .* A, H .* B); bctype="periodic") + Spl.spline_integrate!(weight_spl) + Abar_w = weight_spl.fsi[end, 1] / bg.q0 + Bbar_w = weight_spl.fsi[end, 2] / bg.q0 - det_asymptotic = asymptotic_final[1, 1] * asymptotic_final[2, 2] - - asymptotic_final[1, 2] * asymptotic_final[2, 1] + denom = 1.0 + Bbar_w - coefficient_1 = (solution_final[1] * asymptotic_final[2, 2] - - solution_final[2] * asymptotic_final[1, 2]) / det_asymptotic - coefficient_2 = (solution_final[2] * asymptotic_final[1, 1] - - solution_final[1] * asymptotic_final[2, 1]) / det_asymptotic + AperP = H .* ((A .- Abar_w) .- (Abar_w / denom) .* (B .- Bbar_w)) + Aperq = bg.h_theta0 ./ bg.q0 .+ (H ./ bg.q0) .* ((B .- Bbar_w) ./ denom) - return coefficient_1, coefficient_2 - else - @warn "ODE integration failed for surface ipsi = $ipsi (retcode: $(ode_solution.retcode))" - return NaN, NaN - end - catch e - @warn "ODE integration failed for surface ipsi = $ipsi: $(e)" - return NaN, NaN - end + dI_dtheta = AperP .* corr_pprime .+ Aperq .* corr_qprime + + dI_spl = Spl.CubicSpline(theta_grid, reshape(dI_dtheta, :, 1); bctype="periodic") + Spl.spline_integrate!(dI_spl) + i_per_primitive = copy(dI_spl.fsi[:, 1]) + i_per_spl = Spl.CubicSpline(theta_grid, reshape(i_per_primitive, :, 1); bctype="extrap") + + theta_min = theta_grid[1] + theta_period = theta_grid[end] - theta_min + theta_k_wrapped = mod(theta_k - theta_min, theta_period) + theta_min + i_per_theta_k = Spl.spline_eval!(i_per_spl, theta_k_wrapped)[1] + i_per_perturbed = copy(i_per_spl.fs[:, 1] .- i_per_theta_k) + + + return i_per_perturbed end +function prepare_ballooning_coefficients( + flux_surface_index::Int, + plasma_eq::Equilibrium.PlasmaEquilibrium; + corr_qprime::Float64=0.0, + corr_pprime::Float64=0.0, + theta_k::Float64=0.0 +) + sq = plasma_eq.sq + rzphi = plasma_eq.rzphi + mtheta = length(rzphi.ys) - 1 + theta_grid = Vector(rzphi.ys) + + bg = _collect_surface_response_background(flux_surface_index, plasma_eq, theta_grid) + + theta_min = theta_grid[1] + theta_period = theta_grid[end] - theta_min + theta_k_wrapped = mod(theta_k - theta_min, theta_period) + theta_min + theta_k_reference = Float64(theta_k) + + i_per0_spl = Spl.CubicSpline(theta_grid, reshape(bg.Iper0, :, 1); bctype="periodic") + i_per0_theta_k = Spl.spline_eval!(i_per0_spl, theta_k_wrapped)[1] + i_per0_theta_ref = Spl.spline_eval!(i_per0_spl, theta_min)[1] + i_per0_thetak_shift = i_per0_theta_k - i_per0_theta_ref + i_per0_shifted = bg.Iper0 .- i_per0_theta_k + + two_pi_f = bg.two_pi_f0 + pressure_gradient = bg.p0prime + q = bg.q0 + q_derivative = bg.q0prime + chi_prime = bg.chi_prime0 + + bsq = bg.bsq0 + jac_arr_loop1 = bg.jac0 + jac_psi_loop1 = zeros(mtheta + 1) + bsq_psi_loop1 = zeros(mtheta + 1) + bdot_theta_phi_loop1 = bg.bdot_theta_phi0 + + for itheta in 0:mtheta + idx = itheta + 1 + jac_psi_loop1[idx] = bg.fx0[idx, 4] + drfac_dp = bg.fx0[idx, 1] / (2 * bg.rho0[idx]) + eta_dp = 2pi * bg.fx0[idx, 2] + dr_dp = drfac_dp * cos(bg.eta0[idx]) - bg.rho0[idx] * sin(bg.eta0[idx]) * eta_dp + + dv21_dp = (bg.fxy0[idx, 1] / (2 * bg.rho0[idx]) - bg.fx0[idx, 1] * bg.fy0[idx, 1] / (4 * bg.f0[idx, 1] * bg.rho0[idx])) / bg.jac0[idx] - bg.v0[idx, 2, 1] * jac_psi_loop1[idx] / bg.jac0[idx] + dv22_dp = (bg.fxy0[idx, 2] * 2pi * bg.rho0[idx] + (1 + bg.fy0[idx, 2]) * 2pi * drfac_dp) / bg.jac0[idx] - bg.v0[idx, 2, 2] * jac_psi_loop1[idx] / bg.jac0[idx] + dv23_dp = (bg.fxy0[idx, 3] * bg.r0[idx] + bg.fy0[idx, 3] * dr_dp) / bg.jac0[idx] - bg.v0[idx, 2, 3] * jac_psi_loop1[idx] / bg.jac0[idx] + dv33_dp = (2pi * dr_dp) / bg.jac0[idx] - bg.v0[idx, 3, 3] * jac_psi_loop1[idx] / bg.jac0[idx] + + grad_theta_dp = [dv21_dp, dv22_dp, dv23_dp] + grad_zeta_dp = [0.0, 0.0, dv33_dp] + dbase_dp = grad_theta_dp + q * grad_zeta_dp + q_derivative * (@view bg.v0[idx, 3, :]) + dB_dp = dbase_dp * chi_prime + bsq_psi_loop1[idx] = 2 * dot((@view bg.v_zeta_psi0[idx, :]) .+ q .* (@view bg.v_psi_theta0[idx, :]), dB_dp) * chi_prime + end -# ---------------------------------------------------------------------- -# subprogram 2. bal_prep. -# computes coefficients for the ideal marginal ballooning equations. -# ---------------------------------------------------------------------- -""" - prepare_ballooning_coefficients(ipsi, plasma_eq, hint) -> (di, alpha, ode_coeff_interp, asymptotic_interp, v0, theta0) + bmag = sqrt.(bsq) + kappaw_periodic = zeros(mtheta + 1) -Prepares all coefficients and splines required for the ballooning stability analysis -on a single magnetic flux surface. + spl1 = Spl.CubicSpline(theta_grid, jac_arr_loop1 .* bdot_theta_phi_loop1 ./ bmag; bctype="periodic") -## Arguments + cell1 = -(jac_psi_loop1 ./ jac_arr_loop1 .+ 0.5 .* bsq_psi_loop1 ./ bsq) ./ chi_prime + cell2 = spl1.fs1[:, 1] ./ (jac_arr_loop1 .* bmag) + cell3 = two_pi_f .* q_derivative ./ (bsq .* jac_arr_loop1) - - `ipsi::Int`: Flux surface index. - - `plasma_eq::PlasmaEquilibrium`: Plasma equilibrium data. - - `hint::Ref{Int}`: Spline search hint for sequential ipsi access. + kappaw_periodic .= cell1 .+ cell2 .+ cell3 -## Returns + pressure_gradient += corr_pprime + q_derivative += corr_qprime + i_per_perturbed = _calculate_i_per_perturbed( + bg, + theta_grid, + corr_qprime, + corr_pprime; + theta_k=theta_k_wrapped + ) - - `mercier_criterion::Float64`: Mercier criterion di. If > 0, surface is stable. - - `growth_parameter::Float64`: Growth rate exponent α. - - `ode_coeff_interp::CubicSeriesInterpolant`: SeriesInterpolant for 5 ODE coefficients. - - `asymptotic_interp::CubicSeriesInterpolant`: SeriesInterpolant for 5 asymptotic coefficients. - - `zeroth_order_eigenfunctions::Matrix{Float64}`: Zeroth-order eigenfunctions (2×2). - - `reference_angle::Float64`: Reference poloidal angle. -""" -function prepare_ballooning_coefficients(ipsi::Int, plasma_eq::Equilibrium.PlasmaEquilibrium, hint::Ref{Int}) - # shorter aliases for equilibrium structs - profiles = plasma_eq.profiles - mtheta = length(plasma_eq.rzphi_ys) - 1 - theta_grid = plasma_eq.rzphi_ys - - # surface quantities - psi = profiles.xs[ipsi] - two_pi_f = profiles.F_spline.y[ipsi] - pressure_gradient = profiles.P_deriv(psi; hint=hint) - q = profiles.q_spline.y[ipsi] - q_derivative = profiles.q_deriv(psi; hint=hint) - chi_prime = 2pi * plasma_eq.psio - - # arrays to be filled (use undef since all elements are written in the loop) - jac = Vector{Float64}(undef, mtheta + 1) - b1 = Vector{Float64}(undef, mtheta + 1) - bsq = Vector{Float64}(undef, mtheta + 1) - dbdb0 = Vector{Float64}(undef, mtheta + 1) - dbdb1 = Vector{Float64}(undef, mtheta + 1) - dbdb2 = Vector{Float64}(undef, mtheta + 1) - kappan = Vector{Float64}(undef, mtheta + 1) - kappas = Vector{Float64}(undef, mtheta + 1) - fx_psi = Matrix{Float64}(undef, 4, mtheta + 1) # Store fx values (4 components) for each theta point - - # Pre-allocate basis vector matrices (reused each iteration) - v = zeros(3, 3) # contravariant basis vectors - w = zeros(3, 3) # covariant basis vectors - - # loop over poloidal angle using nodal_derivs access at grid points - for itheta in 1:(mtheta+1) - # Access nodal derivatives from interpolants - f1 = plasma_eq.rzphi_rsquared.nodal_derivs.partials[1, ipsi, itheta] - f2 = plasma_eq.rzphi_offset.nodal_derivs.partials[1, ipsi, itheta] - f4 = plasma_eq.rzphi_jac.nodal_derivs.partials[1, ipsi, itheta] - fx1 = plasma_eq.rzphi_rsquared.nodal_derivs.partials[2, ipsi, itheta] - fx2 = plasma_eq.rzphi_offset.nodal_derivs.partials[2, ipsi, itheta] - fx3 = plasma_eq.rzphi_nu.nodal_derivs.partials[2, ipsi, itheta] - fx4 = plasma_eq.rzphi_jac.nodal_derivs.partials[2, ipsi, itheta] - fy1 = plasma_eq.rzphi_rsquared.nodal_derivs.partials[3, ipsi, itheta] - fy2 = plasma_eq.rzphi_offset.nodal_derivs.partials[3, ipsi, itheta] - fy3 = plasma_eq.rzphi_nu.nodal_derivs.partials[3, ipsi, itheta] - - fx_psi[:, itheta] .= (fx1, fx2, fx3, fx4) # Store fx for later use - - theta = theta_grid[itheta] - rfac = sqrt(f1) - eta = 2pi * (theta + f2) - r = plasma_eq.ro + rfac * cos(eta) - jac[itheta] = f4 - - # contravariant basis vectors v^i - v[1, 1] = fx1 / (2 * rfac * jac[itheta]) - v[1, 2] = fx2 * 2pi * rfac / jac[itheta] - v[1, 3] = fx3 * r / jac[itheta] - v[2, 1] = fy1 / (2 * rfac * jac[itheta]) - v[2, 2] = (1 + fy2) * 2pi * rfac / jac[itheta] - v[2, 3] = fy3 * r / jac[itheta] - v[3, 3] = 2pi * r / jac[itheta] - - # covariant basis vectors w_i (direct method) - w[1, 1] = (1 + fy2) * (2pi)^2 * rfac * r / jac[itheta] - w[1, 2] = -fy1 * pi * r / (rfac * jac[itheta]) - w[2, 1] = -fx2 * (2pi)^2 * r * rfac / jac[itheta] - w[2, 2] = fx1 * pi * r / (rfac * jac[itheta]) - w[3, 1] = (fx2 * fy3 - fx3 * (1 + fy2)) * 2pi * r * rfac / jac[itheta] - w[3, 2] = (fx3 * fy1 - fx1 * fy3) * r / (2 * rfac * jac[itheta]) - w[3, 3] = 1 / (2pi * r) + nabla_beta_sq_b_sq_periodic = zeros(mtheta + 1) + nabla_beta_sq_b_sq_peculiar_1st = zeros(mtheta + 1) + nabla_beta_sq_b_sq_peculiar_2nd = zeros(mtheta + 1) + jac_chiprime = zeros(mtheta + 1) + pprime_chiprime = fill(pressure_gradient / chi_prime, mtheta + 1) - # store physical quantities - grad_psi = @view v[1, :] - e_theta = @view v[2, :] - e_phi = @view v[3, :] + for itheta in 0:mtheta + grad_psi_sq = bg.gradpsi_sq0[itheta+1] + i_per_val = i_per0_shifted[itheta+1] + i_per_total = i_per_val + i_per_perturbed[itheta+1] - B_vec = (e_theta + q * e_phi) * chi_prime - b1[itheta] = dot(B_vec, grad_psi) - bsq[itheta] = dot(B_vec, B_vec) + term1 = 1.0 / (chi_prime^2 * grad_psi_sq) + term2_factor = grad_psi_sq / bsq[itheta+1] - grad_alpha = @view w[1, :] - grad_theta = @view w[2, :] - grad_phi = @view w[3, :] - gtheta = grad_phi - q * grad_theta + nabla_beta_sq_b_sq_periodic[itheta+1] = term1 + term2_factor * (i_per_total^2 - 2.0 * theta_k_reference * q_derivative * i_per_total + (theta_k_reference * q_derivative)^2) + nabla_beta_sq_b_sq_peculiar_1st[itheta+1] = term2_factor * (2.0 * q_derivative * i_per_total - 2.0 * theta_k_reference * q_derivative^2) + nabla_beta_sq_b_sq_peculiar_2nd[itheta+1] = term2_factor * (q_derivative^2) - dbdb0[itheta] = dot(grad_alpha, grad_alpha) * q_derivative^2 - dbdb1[itheta] = -2 * dot(gtheta, grad_alpha) * q_derivative - dbdb2[itheta] = dot(gtheta, gtheta) + jac_chiprime[itheta+1] = jac_arr_loop1[itheta+1] / chi_prime end - # compute curvature terms using native cubic_interp with PeriodicBC - spl0_interp = cubic_interp(theta_grid, Series(hcat(1 ./ bsq, jac .* b1 ./ bsq)); bc=PeriodicBC()) - spl0_d1 = deriv1(spl0_interp) - # Evaluate derivatives at all theta points (returns Vector of Vectors, stack to matrix) - spl0_fs1 = stack(spl0_d1(theta_grid)) - - kappas .= -spl0_fs1[:, 1] .* two_pi_f ./ (2 .* jac) - kappan .= ((pressure_gradient ./ bsq .- fx_psi[4, :] ./ jac) ./ chi_prime .+ - two_pi_f .* q_derivative ./ (bsq .* jac) .+ spl0_fs1[:, 2] ./ jac) ./ 2.0 - - # compute coefficients for ballooning equation and store - bf_fs = zeros(mtheta + 1, 5) - jacfac = jac ./ chi_prime - bf_fs[:, 1] = dbdb0 ./ (bsq .* jacfac) - bf_fs[:, 2] = dbdb1 ./ (2 .* dbdb0) - bf_fs[:, 3] = (dbdb2 - dbdb1 .^ 2 ./ (4 .* dbdb0)) ./ (bsq .* jacfac) - bf_fs[:, 4] = 2 .* kappan .* pressure_gradient ./ chi_prime .* jacfac - bf_fs[:, 5] = -2 .* kappas .* pressure_gradient ./ chi_prime .* q_derivative .* jacfac - ode_coeff_interp = cubic_interp(theta_grid, Series(bf_fs); bc=PeriodicBC()) - - # initialize bg values - spl0_bg_fs = -pressure_gradient .* q_derivative .* two_pi_f ./ (bsq .* chi_prime^2) - itp_bg = cubic_interp(theta_grid, spl0_bg_fs; bc=PeriodicBC()) - spl0_bg_fsi = FastInterpolations.cumulative_integrate(itp_bg) - bg_fs = zeros(mtheta + 1, 5) - bg_fs[:, 5] = spl0_bg_fsi .- spl0_bg_fsi[end] - - # Mercier criterion calculation - spl1_fs = zeros(mtheta + 1, 4) - for itheta in 1:(mtheta+1) - c0 = zeros(2, 2) - c0[1, 1] = 0.5 - c0[1, 2] = 1 / bf_fs[itheta, 1] - c0[2, 1] = -bf_fs[itheta, 4] - c0[2, 2] = -0.5 - spl1_fs[itheta, 1] = c0[1, 1] + c0[1, 2]*bg_fs[itheta, 5] - spl1_fs[itheta, 2] = c0[1, 2] - spl1_fs[itheta, 3] = c0[2, 1] + (c0[2, 2]-c0[1, 1]-c0[1, 2]*bg_fs[itheta, 5])*bg_fs[itheta, 5] - spl1_fs[itheta, 4] = -spl1_fs[itheta, 1] + kappas = bg.kappas0 + kappaw_periodic .+= -kappas .* i_per_perturbed .+ (theta_k_reference .* q_derivative .+ i_per0_thetak_shift) .* kappas + kappaw_secular = q_derivative .* kappas + + bf_fs = zeros(mtheta + 1, 9) + bf_fs[:, 1] = nabla_beta_sq_b_sq_periodic + bf_fs[:, 2] = nabla_beta_sq_b_sq_peculiar_1st + bf_fs[:, 3] = nabla_beta_sq_b_sq_peculiar_2nd + bf_fs[:, 4] = kappaw_periodic + bf_fs[:, 5] = kappaw_secular + bf_fs[:, 6] = jac_chiprime + bf_fs[:, 7] = pprime_chiprime + bf_fs[:, 8] = bsq + + sigma = .-(two_pi_f .* pressure_gradient .* q_derivative) ./ (chi_prime^2 .* bsq) + bf_fs[:, 9] = sigma + + m0_12 = jac_chiprime ./ nabla_beta_sq_b_sq_peculiar_2nd + m0_21 = -2.0 .* jac_chiprime .* pprime_chiprime .* kappaw_periodic + + n0_fs = zeros(mtheta + 1, 4) + n0_fs[:, 1] = 0.5 .+ m0_12 .* sigma + n0_fs[:, 2] = m0_12 + n0_fs[:, 3] = m0_21 .- sigma .- m0_12 .* sigma .^ 2 + n0_fs[:, 4] = -0.5 .- m0_12 .* sigma + + n0_spline = Spl.CubicSpline(theta_grid, n0_fs; bctype="periodic") + Spl.spline_integrate!(n0_spline) + + d0bar = zeros(2, 2) + d0bar[1, 1] = n0_spline.fsi[end, 1] + d0bar[1, 2] = n0_spline.fsi[end, 2] + d0bar[2, 1] = n0_spline.fsi[end, 3] + d0bar[2, 2] = n0_spline.fsi[end, 4] + + ode_coefficient_spline = Spl.CubicSpline(theta_grid, bf_fs; bctype="periodic") + + return ( + ode_coefficient_spline=ode_coefficient_spline, + di=det(d0bar), + theta_grid=theta_grid + ) +end + + +""" + salpha_reference(psi_idx, plasma_eq) + +Compute local s-alpha reference values and physical profile derivatives at one flux surface. +""" +function salpha_reference( + psi_idx::Int, + plasma_eq::Equilibrium.PlasmaEquilibrium +) + sq = plasma_eq.sq + psio = plasma_eq.psio + mu0 = Equilibrium.mu0 + + npsi = length(sq.xs) + if psi_idx < 1 || psi_idx > npsi + throw(ArgumentError("psi_idx=$psi_idx is out of bounds for npsi=$npsi")) + end + if abs(psio) <= Base.eps(Float64) + throw(ArgumentError("plasma_eq.psio is too small to compute physical derivatives")) end - itp_spl1 = cubic_interp(theta_grid, Series(spl1_fs); bc=PeriodicBC()) - spl1_totals = FastInterpolations.integrate(itp_spl1) + Spl.spline_integrate!(sq) + volume = max(Float64(sq.fsi[psi_idx, 3]), 0.0) + vprime_phys = sq.fs[psi_idx, 3] / psio + q_ref = sq.fs[psi_idx, 4] + qprime_norm_ref = sq.fs1[psi_idx, 4] + pprime_norm_ref = sq.fs1[psi_idx, 2] + qprime_ref = qprime_norm_ref / psio + pprime_ref = (pprime_norm_ref / mu0) / psio + + denom = q_ref * vprime_phys + s_ref = abs(denom) > Base.eps(Float64) ? (2.0 * volume * qprime_ref / denom) : NaN + + major_radius = max(plasma_eq.ro, Base.eps(Float64)) + alpha_geom = max(volume / (2π * major_radius), 0.0) + alpha_ref = -2.0 * mu0 * pprime_ref * vprime_phys * sqrt(alpha_geom) + + return ( + s_ref=s_ref, + alpha_ref=alpha_ref, + volume_ref=volume, + vprime_ref=vprime_phys, + q_ref=q_ref, + qprime_ref=qprime_ref, + pprime_ref=pprime_ref, + qprime_norm_ref=qprime_norm_ref, + pprime_norm_ref=pprime_norm_ref + ) +end - d0bar = [spl1_totals[1] spl1_totals[2]; spl1_totals[3] spl1_totals[4]] +""" + ballooning_delta_prime(psi_idx, plasma_eq; corr_qprime=0.0, corr_pprime=0.0, theta_k=0.0) - di = det(d0bar) +Evaluate one corrected local ballooning point. Corrections use the same +normalized units as `prepare_ballooning_coefficients`: add `corr_qprime` to +`dq/dpsi_norm` and `corr_pprime` to `d(mu0*p)/dpsi_norm`. `di` is the +`det(d0bar)` diagnostic assembled from the same corrected coefficients. +""" +function ballooning_delta_prime( + psi_idx::Int, + plasma_eq::Equilibrium.PlasmaEquilibrium; + corr_qprime::Float64=0.0, + corr_pprime::Float64=0.0, + theta_k::Float64=0.0 +) + coeff_data = prepare_ballooning_coefficients( + psi_idx, + plasma_eq; + corr_qprime=corr_qprime, + corr_pprime=corr_pprime, + theta_k=theta_k + ) + delta_prime = integrate_ballooning_ode( + coeff_data.ode_coefficient_spline; + theta_k=theta_k + ).value + + return (delta_prime=delta_prime, di=coeff_data.di) +end - # if stable by Mercier, no more work to do - return empty asymptotic data - if di > 0 - asymptotic_interp = cubic_interp(theta_grid, Series(bg_fs); bc=PeriodicBC()) - return di, NaN, ode_coeff_interp, asymptotic_interp, zeros(2, 2), 0.0 - end +""" + scan_delta_prime_map(psi_idx, plasma_eq; s_scales, alpha_scales, ...) - alpha = sqrt(-di) - - # compute zeroth-order eigenfunctions - v0 = zeros(2, 2) - v0[1, 1] = 1.0 - v0[1, 2] = 1.0 - v0[2, 1] = -(d0bar[1, 1] - alpha) / d0bar[1, 2] - v0[2, 2] = -(d0bar[1, 1] + alpha) / d0bar[1, 2] - - # ===== Higher-order corrections for the asymptotic solution ===== - # Compute derivatives for first-order terms (v1) - spl2_fs = zeros(mtheta + 1, 4) - - for itheta in 1:(mtheta+1) - # Matrix product: (spl1 - alpha*I) * v0 - spl2_fs[itheta, 1] = (spl1_fs[itheta, 1] - alpha) * v0[1, 1] + spl1_fs[itheta, 2] * v0[2, 1] - spl2_fs[itheta, 2] = spl1_fs[itheta, 3] * v0[1, 1] + (spl1_fs[itheta, 4] - alpha) * v0[2, 1] - spl2_fs[itheta, 3] = (spl1_fs[itheta, 1] + alpha) * v0[1, 2] + spl1_fs[itheta, 2] * v0[2, 2] - spl2_fs[itheta, 4] = spl1_fs[itheta, 3] * v0[1, 2] + (spl1_fs[itheta, 4] + alpha) * v0[2, 2] - end +Run a local s-alpha style scan at one flux surface using the `Bal.jl` +makefromZero ballooning path. The scan perturbs physical `dq/dpsi` and +`dp/dpsi`, converts them to the normalized units expected by the local +ballooning evaluator, and returns delta-prime and `det(d0bar)` `Di` maps. +""" +function scan_delta_prime_map( + psi_idx::Int, + plasma_eq::Equilibrium.PlasmaEquilibrium; + ctrl::DconControl=DconControl(; verbose=false), + theta_k::Float64=0.0, + s_scales::AbstractVector{<:Real}, + alpha_scales::AbstractVector{<:Real} +) + ref = salpha_reference(psi_idx, plasma_eq) + + s_scales_f = Float64.(s_scales) + alpha_scales_f = Float64.(alpha_scales) + isempty(s_scales_f) && throw(ArgumentError("s_scales must not be empty")) + isempty(alpha_scales_f) && throw(ArgumentError("alpha_scales must not be empty")) + + delta_prime_map = fill(NaN, length(s_scales_f), length(alpha_scales_f)) + di_map = fill(NaN, length(s_scales_f), length(alpha_scales_f)) + + for is in eachindex(s_scales_f), ia in eachindex(alpha_scales_f) + corr_qprime = ref.qprime_norm_ref * (s_scales_f[is] - 1.0) + corr_pprime = ref.pprime_norm_ref * (alpha_scales_f[ia] - 1.0) + + result = try + ballooning_delta_prime( + psi_idx, + plasma_eq; + corr_qprime=corr_qprime, + corr_pprime=corr_pprime, + theta_k=theta_k + ) + catch err + if ctrl.verbose + @warn "s-alpha scan point failed" psi_idx is ia err + end + nothing + end - itp_spl2 = cubic_interp(theta_grid, Series(spl2_fs); bc=PeriodicBC()) - spl2_fsi = FastInterpolations.cumulative_integrate(itp_spl2) - # CRITICAL: Use integrated values as the new fs (matching Fortran's spl2%fs=spl2%fsi) - spl2_fs_new = copy(spl2_fsi) - - # Compute derivatives of spl1 for second-order terms - spl1_interp = cubic_interp(theta_grid, Series(spl1_fs); bc=PeriodicBC()) - spl1_d1 = deriv1(spl1_interp) - # Evaluate derivatives at all theta points (returns Vector of Vectors, stack to matrix) - spl1_fs1 = stack(spl1_d1(theta_grid)) - - # Compute derivatives for second-order terms - spl3_fs = zeros(mtheta + 1, 4) - - for itheta in 1:(mtheta+1) - # d1 matrix elements (first-order corrections to d matrix) - fexp = -spl1_fs[itheta, 2] * bf_fs[itheta, 2] * 2 - d1_11 = fexp * bg_fs[itheta, 5] - d1_12 = fexp - d1_21 = -fexp * bg_fs[itheta, 5]^2 - d1_22 = -d1_11 - - # Now use in spl3_fs calculation - spl3_fs[itheta, 1] = (spl1_fs1[itheta, 1] + 1 - alpha) * spl2_fs_new[itheta, 1] + - spl1_fs[itheta, 2] * spl2_fs_new[itheta, 2] + - d1_11 * v0[1, 1] + d1_12 * v0[2, 1] - - spl3_fs[itheta, 2] = spl1_fs[itheta, 3] * spl2_fs_new[itheta, 1] + - (spl1_fs[itheta, 4] + 1 - alpha) * spl2_fs_new[itheta, 2] + - d1_21 * v0[1, 1] + d1_22 * v0[2, 1] - - spl3_fs[itheta, 3] = (spl1_fs[itheta, 1] + 1 + alpha) * spl2_fs_new[itheta, 3] + - spl1_fs[itheta, 2] * spl2_fs_new[itheta, 4] + - d1_11 * v0[1, 2] + d1_12 * v0[2, 2] - - spl3_fs[itheta, 4] = spl1_fs[itheta, 3] * spl2_fs_new[itheta, 3] + - (spl1_fs[itheta, 4] + 1 + alpha) * spl2_fs_new[itheta, 4] + - d1_21 * v0[1, 2] + d1_22 * v0[2, 2] + if result !== nothing + delta_prime_map[is, ia] = result.delta_prime + di_map[is, ia] = result.di + end end - itp_spl3 = cubic_interp(theta_grid, Series(spl3_fs); bc=PeriodicBC()) - spl3_totals = FastInterpolations.integrate(itp_spl3) - - # Compute first-order constants for both eigenfunctions - # First eigenfunction (with -alpha correction) - d = zeros(2, 2) - d[2, 1] = d0bar[2, 1] - d[1, 2] = d0bar[1, 2] - d[1, 1] = d0bar[1, 1] + 1 - alpha - d[2, 2] = d0bar[2, 2] + 1 - alpha - - det_d = d[1, 1] * d[2, 2] - d[1, 2] * d[2, 1] - v10 = zeros(2, 2) - v10[1, 1] = (d[1, 2] * spl3_totals[2] - d[2, 2] * spl3_totals[1]) / det_d - v10[2, 1] = (d[2, 1] * spl3_totals[1] - d[1, 1] * spl3_totals[2]) / det_d - - # Second eigenfunction (with +alpha correction) - d[1, 1] = d0bar[1, 1] + 1 + alpha - d[2, 2] = d0bar[2, 2] + 1 + alpha - det_d = d[1, 1] * d[2, 2] - d[1, 2] * d[2, 1] - v10[1, 2] = (d[1, 2] * spl3_totals[4] - d[2, 2] * spl3_totals[3]) / det_d - v10[2, 2] = (d[2, 1] * spl3_totals[3] - d[1, 1] * spl3_totals[4]) / det_d - - # Assemble final bg with higher-order corrections - bg_fs[:, 1] = spl2_fs_new[:, 1] .+ v10[1, 1] - bg_fs[:, 2] = spl2_fs_new[:, 2] .+ v10[2, 1] - bg_fs[:, 3] = spl2_fs_new[:, 3] .+ v10[1, 2] - bg_fs[:, 4] = spl2_fs_new[:, 4] .+ v10[2, 2] - - asymptotic_interp = cubic_interp(theta_grid, Series(bg_fs); bc=PeriodicBC()) - - reference_angle = 0.0 # Central poloidal angle (typically 0) - return di, alpha, ode_coeff_interp, asymptotic_interp, v0, reference_angle + s_values = ref.s_ref .* s_scales_f + alpha_values = ref.alpha_ref .* alpha_scales_f + + return ( + values=delta_prime_map, + delta_prime=delta_prime_map, + di=di_map, + di_values=di_map, + s_values=s_values, + alpha_values=alpha_values, + s_scales=s_scales_f, + alpha_scales=alpha_scales_f, + dqdpsi_ref=ref.qprime_ref, + pprime_ref=ref.pprime_ref, + theta_k=theta_k, + reference=ref + ) end - # ====================================================================== -# Main Driver for Ballooning Stability Analysis -# Computes ballooning stability criterion over all flux surfaces +# ODE Integration +# Integrates the ideal marginal ballooning equations # ====================================================================== """ - compute_ballooning_stability!(ctrl, locstab_fs, plasma_eq) - -Main driver routine for ballooning stability analysis. Iterates over all -magnetic flux surfaces, prepares coefficients, and integrates the ballooning -equation if the surface is Mercier unstable. - -## Arguments + integrate_ballooning_ode(ode_coefficient_spline; theta_k=0.0) - - `ctrl::ForceFreeStatesControl`: Control parameters for the analysis. - - `locstab_fs::Matrix{Float64}`: Local stability matrix to store results (modified in place). - - `plasma_eq::Equilibrium.PlasmaEquilibrium`: Plasma equilibrium data. +Integrates the ballooning ODE from `-Infinity` to `-1e-3` and `+Infinity` to `+1e-3`. +Computes Delta' = (y'/y)_right - (y'/y)_left. -This function modifies `locstab_fs` in place with: +## Returns - - Column 1: Mercier criterion × ψ - - Columns 4-5: Asymptotic coefficients ca₁ and ca₂ + - `delta_prime`: The stability index Δ'. """ -function compute_ballooning_stability!(ctrl::ForceFreeStatesControl, locstab_fs::Matrix{Float64}, plasma_eq::Equilibrium.PlasmaEquilibrium) +function integrate_ballooning_ode( + ode_coefficient_spline::Spl.CubicSpline; + theta_k::Float64=0.0 +) + TOLERANCE = 1e-8 + MINIMUM_STEP = 1e-10 + MATCHING_POINT = 1e-3 + THETA_MAX0 = 16.5 + + theta_start_left = -THETA_MAX0 + theta_end_left = -MATCHING_POINT + theta_start_right = THETA_MAX0 + theta_end_right = MATCHING_POINT + + initial_condition_left = [0.0, 1.0] + initial_condition_right = [0.0, -1.0] + + problem_left = ODEProblem( + compute_ballooning_ode!, + initial_condition_left, + (theta_start_left, theta_end_left), + (ode_coefficient_spline, theta_k) + ) + sol_left = solve( + problem_left, + DP5(); + reltol=TOLERANCE, + abstol=TOLERANCE^2, + dtmin=MINIMUM_STEP, + adaptive=true + ) + if sol_left.retcode != ReturnCode.Success + return (value=NaN,) + end - if ctrl.verbose - @info "Evaluating high-n ballooning criterion" + problem_right = ODEProblem( + compute_ballooning_ode!, + initial_condition_right, + (theta_start_right, theta_end_right), + (ode_coefficient_spline, theta_k) + ) + sol_right = solve( + problem_right, + DP5(); + reltol=TOLERANCE, + abstol=TOLERANCE^2, + dtmin=MINIMUM_STEP, + adaptive=true + ) + if sol_right.retcode != ReturnCode.Success + return (value=NaN,) end - profiles = plasma_eq.profiles - num_psi = profiles.npts + log_deriv_left = sol_left.u[end][2] / sol_left.u[end][1] + log_deriv_right = sol_right.u[end][2] / sol_right.u[end][1] - # Loop over flux surfaces - hint = Ref(1) # Shared hint for sequential psi access - for ipsi in 1:num_psi + return (value=log_deriv_right - log_deriv_left,) +end - # Prepare coefficients and check Mercier criterion - mercier_criterion, growth_param, ode_coeff_interp, asymptotic_interp, zeroth_eigs, ref_angle = prepare_ballooning_coefficients(ipsi, plasma_eq, hint) - # Store Mercier criterion in locstab matrix (matches Fortran output) - locstab_fs[ipsi, 1] = mercier_criterion * profiles.xs[ipsi] - # If Mercier unstable, proceed with ballooning integration - if mercier_criterion <= 0 && mercier_criterion >= -1e4 && profiles.xs[ipsi] <= 1.0 - ca1, ca2 = integrate_ballooning_ode(ipsi, growth_param, ode_coeff_interp, asymptotic_interp, zeroth_eigs, ref_angle, ctrl) +# ====================================================================== +# ODE System Definition +# Differential equations for marginal ballooning stability +# ====================================================================== +""" + compute_ballooning_ode!(derivatives, solution, parameters, poloidal_angle) - # Store final asymptotic coefficients if integration reached theta_max - if isfinite(ca1) && isfinite(ca2) - locstab_fs[ipsi, 4] = ca1 - locstab_fs[ipsi, 5] = ca2 - end - end - end +Defines the RHS of the first-order ODE system for ideal marginal ballooning modes. +Used by the DifferentialEquations.jl ODE solver. - if ctrl.verbose - @info "Ballooning analysis complete" - end +The second-order equation `d/dθ(f·dy/dθ) + g·y = 0` is rewritten as a 2x1 system: -end + - `dy₁/dθ = y₂ / f` + - `dy₂/dθ = -g · y₁` + +where y₁ is the solution and y₂ = f·dy/dθ. + +## Arguments + + - `derivatives::Vector{Float64}`: Output vector [dy₁/dθ, dy₂/dθ]. + - `solution::Vector{Float64}`: Current state vector [y₁, y₂]. + - `parameters::Tuple`: (ode_coefficient_spline, reference_angle). + - `poloidal_angle::Float64`: Current poloidal angle θ (independent variable). +""" +function compute_ballooning_ode!(derivatives, solution, parameters, poloidal_angle) + ode_coefficient_spline = parameters[1] + coeff_matrix = Spl.spline_eval(ode_coefficient_spline, [poloidal_angle]) + + periodic = coeff_matrix[1, 1] + peculiar_1st = coeff_matrix[1, 2] + peculiar_2nd = coeff_matrix[1, 3] + kappaw_periodic = coeff_matrix[1, 4] + kappaw_secular = coeff_matrix[1, 5] + jac_chiprime = coeff_matrix[1, 6] + pprime_chiprime = coeff_matrix[1, 7] + + f = (periodic + poloidal_angle * peculiar_1st + poloidal_angle^2 * peculiar_2nd) / jac_chiprime + kappaw = kappaw_periodic - poloidal_angle * kappaw_secular + g = -2.0 * jac_chiprime * pprime_chiprime * kappaw + + derivatives[1] = solution[2] / f + derivatives[2] = g * solution[1] +end \ No newline at end of file From 6bd0fea75cee36eb2dab5bdec36ad01b72002ec9 Mon Sep 17 00:00:00 2001 From: jmlmir369 Date: Thu, 30 Apr 2026 17:41:56 +0900 Subject: [PATCH 003/135] s-alpha diagram working --- .../Bal_salpha_delta_di_summary.ipynb | 70 ++++---- examples/DIIID-like_ideal_example/gpec.toml | 2 +- src/ForceFreeStates/Bal.jl | 150 ++++++++++-------- 3 files changed, 119 insertions(+), 103 deletions(-) diff --git a/examples/DIIID-like_ideal_example/Bal_salpha_delta_di_summary.ipynb b/examples/DIIID-like_ideal_example/Bal_salpha_delta_di_summary.ipynb index d7dbf361d..2b56d9142 100644 --- a/examples/DIIID-like_ideal_example/Bal_salpha_delta_di_summary.ipynb +++ b/examples/DIIID-like_ideal_example/Bal_salpha_delta_di_summary.ipynb @@ -10,13 +10,15 @@ "using Pkg\n", "Pkg.activate(\"../..\")\n", "\n", - "using JPEC\n", + "using GeneralizedPerturbedEquilibrium\n", "using Plots\n", "using Printf\n", "using Statistics\n", + "using TOML\n", "\n", - "equil = JPEC.Equilibrium.setup_equilibrium(\"equil.toml\")\n", - "psi_norm = Vector(equil.sq.xs)\n", + "eq_config = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(TOML.parsefile(\"gpec.toml\")[\"Equilibrium\"], pwd())\n", + "equil = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(eq_config)\n", + "psi_norm = Vector(equil.profiles.xs)\n", "\n", "function finite_local_extrema(values::AbstractVector{<:Real})\n", " extrema = Int[]\n", @@ -49,7 +51,7 @@ "\n", "for i in eachindex(psi_norm)\n", " try\n", - " ref = JPEC.DCON.salpha_reference(i, equil)\n", + " ref = GeneralizedPerturbedEquilibrium.ForceFreeStates.salpha_reference(i, equil)\n", " s_profile[i] = ref.s_ref\n", " alpha_profile[i] = ref.alpha_ref\n", " catch err\n", @@ -98,10 +100,10 @@ "outputs": [], "source": [ "locstab_fs = zeros(length(psi_norm), 4)\n", - "ctrl = JPEC.DCON.DconControl(verbose=false)\n", + "ctrl = GeneralizedPerturbedEquilibrium.ForceFreeStates.ForceFreeStatesControl(verbose=false)\n", "\n", "println(\"Computing Delta' and Di profiles...\")\n", - "JPEC.DCON.compute_ballooning_stability!(ctrl, locstab_fs, equil; compute_delta_prime=true)\n", + "GeneralizedPerturbedEquilibrium.ForceFreeStates.compute_ballooning_stability!(ctrl, locstab_fs, equil; compute_delta_prime=true)\n", "\n", "delta_prime = Vector(locstab_fs[:, 4])\n", "di_profile = fill(NaN, length(psi_norm))\n", @@ -148,15 +150,15 @@ "metadata": {}, "outputs": [], "source": [ - "psi_target = 0.75\n", + "psi_target = 0.974\n", "psi_idx_scan = argmin(abs.(psi_norm .- psi_target))\n", "\n", "println(\"Running s-alpha scan at index $(psi_idx_scan), psi_norm=$(round(psi_norm[psi_idx_scan], digits=6))\")\n", "\n", - "s_scales = collect(range(0.5, 5.0; length=31))\n", - "alpha_scales = collect(range(0.5, 5.0; length=31))\n", + "s_scales = collect(range(-5.0, 5.0; length=31))\n", + "alpha_scales = collect(range(-5.0, 5.0; length=31))\n", "\n", - "scan_result = JPEC.DCON.scan_delta_prime_map(\n", + "scan_result = GeneralizedPerturbedEquilibrium.ForceFreeStates.scan_delta_prime_map(\n", " psi_idx_scan,\n", " equil;\n", " theta_k=0.0,\n", @@ -164,10 +166,14 @@ " alpha_scales=alpha_scales,\n", ")\n", "\n", - "scan_s = scan_result.s_values\n", - "scan_alpha = scan_result.alpha_values\n", - "scan_delta = permutedims(scan_result.delta_prime, (2, 1))\n", - "scan_di = permutedims(scan_result.di_values, (2, 1))\n", + "scan_s_raw = scan_result.s_values\n", + "scan_pprime_raw = scan_result.pprime_ref .* scan_result.alpha_scales\n", + "s_order = sortperm(scan_s_raw)\n", + "pprime_order = sortperm(scan_pprime_raw)\n", + "scan_s = scan_s_raw[s_order]\n", + "scan_pprime = scan_pprime_raw[pprime_order]\n", + "scan_delta = scan_result.delta_prime[s_order, pprime_order]\n", + "scan_di = scan_result.di_values[s_order, pprime_order]\n", "\n", "function symmetric_clims(z)\n", " finite_vals = vec(z)[isfinite.(vec(z))]\n", @@ -177,32 +183,32 @@ "end\n", "\n", "p_scan_delta = contourf(\n", - " scan_s, scan_alpha, scan_delta;\n", + " scan_pprime, scan_s, scan_delta;\n", " c=cgrad([:blue, :white, :red]),\n", " clims=symmetric_clims(scan_delta),\n", - " xlabel=\"s\",\n", - " ylabel=\"alpha\",\n", - " title=\"s-alpha Delta'\",\n", + " xlabel=\"pprime\",\n", + " ylabel=\"s\",\n", + " title=\"pprime-s Delta'\",\n", " colorbar_title=\"Delta'\",\n", " levels=41,\n", " framestyle=:box,\n", ")\n", - "contour!(p_scan_delta, scan_s, scan_alpha, scan_delta; levels=[0.0], color=:black, linewidth=2, label=\"Delta' = 0\")\n", - "scatter!(p_scan_delta, [scan_result.reference.s_ref], [scan_result.reference.alpha_ref]; color=:green, marker=:star5, ms=7, label=\"equilibrium\")\n", + "contour!(p_scan_delta, scan_pprime, scan_s, scan_delta; levels=[0.0], color=:black, linewidth=2, label=\"Delta' = 0\")\n", + "scatter!(p_scan_delta, [scan_result.reference.pprime_ref], [scan_result.reference.s_ref]; color=:green, marker=:star5, ms=7, label=\"equilibrium\")\n", "\n", "p_scan_di = contourf(\n", - " scan_s, scan_alpha, scan_di;\n", + " scan_pprime, scan_s, scan_di;\n", " c=cgrad([:blue, :white, :red]),\n", " clims=symmetric_clims(scan_di),\n", - " xlabel=\"s\",\n", - " ylabel=\"alpha\",\n", - " title=\"s-alpha Di\",\n", + " xlabel=\"pprime\",\n", + " ylabel=\"s\",\n", + " title=\"pprime-s Di\",\n", " colorbar_title=\"Di\",\n", " levels=41,\n", " framestyle=:box,\n", ")\n", - "contour!(p_scan_di, scan_s, scan_alpha, scan_di; levels=[0.0], color=:black, linewidth=2, label=\"Di = 0\")\n", - "scatter!(p_scan_di, [scan_result.reference.s_ref], [scan_result.reference.alpha_ref]; color=:green, marker=:star5, ms=7, label=\"equilibrium\")\n", + "contour!(p_scan_di, scan_pprime, scan_s, scan_di; levels=[0.0], color=:black, linewidth=2, label=\"Di = 0\")\n", + "scatter!(p_scan_di, [scan_result.reference.pprime_ref], [scan_result.reference.s_ref]; color=:green, marker=:star5, ms=7, label=\"equilibrium\")\n", "\n", "display(plot(p_scan_delta, p_scan_di; layout=(1, 2), size=(1150, 460)))\n" ] @@ -215,21 +221,21 @@ "outputs": [], "source": [ "p_zero = plot(\n", - " xlabel=\"s\",\n", - " ylabel=\"alpha\",\n", - " title=\"s-alpha zero contours\",\n", + " xlabel=\"pprime\",\n", + " ylabel=\"s\",\n", + " title=\"pprime-s zero contours\",\n", " framestyle=:box,\n", ")\n", - "contour!(p_zero, scan_s, scan_alpha, scan_delta;\n", + "contour!(p_zero, scan_pprime, scan_s, scan_delta;\n", " levels=[0.0], color=:blue, linewidth=3,\n", " label=\"Delta' = 0\", colorbar=false)\n", "\n", - "contour!(p_zero, scan_s, scan_alpha, scan_di;\n", + "contour!(p_zero, scan_pprime, scan_s, scan_di;\n", " levels=[0.0], color=:red, linewidth=3, linestyle=:dash,\n", " label=\"Di = 0\", colorbar=false)\n", "\n", "\n", - "scatter!(p_zero, [scan_result.reference.s_ref], [scan_result.reference.alpha_ref]; color=:green, marker=:star5, ms=8, label=\"equilibrium\")\n", + "scatter!(p_zero, [scan_result.reference.pprime_ref], [scan_result.reference.s_ref]; color=:green, marker=:star5, ms=8, label=\"equilibrium\")\n", "display(p_zero)\n" ] } diff --git a/examples/DIIID-like_ideal_example/gpec.toml b/examples/DIIID-like_ideal_example/gpec.toml index b12c815df..c92a6430c 100644 --- a/examples/DIIID-like_ideal_example/gpec.toml +++ b/examples/DIIID-like_ideal_example/gpec.toml @@ -6,7 +6,7 @@ power_bp = 0 # Poloidal field power exponent for Jacobian power_b = 0 # Toroidal field power exponent for Jacobian power_r = 0 # Major radius power exponent for Jacobian grid_type = "log_asymptotic" # Radial grid packing type -psilow = 1e-4 # Lower limit of normalized flux coordinate +psilow = 1e-2 # Lower limit of normalized flux coordinate psihigh = 0.9995 # Upper limit of normalized flux coordinate mpsi = 0 # Number of radial grid points (0 = auto-compute from psi_accuracy) psi_accuracy = 0.001 # Target absolute error in q for auto-mpsi diff --git a/src/ForceFreeStates/Bal.jl b/src/ForceFreeStates/Bal.jl index 634fc3d4c..053591a79 100644 --- a/src/ForceFreeStates/Bal.jl +++ b/src/ForceFreeStates/Bal.jl @@ -3,6 +3,7 @@ # Computes ballooning stability criterion over all flux surfaces # ====================================================================== using LinearAlgebra + """ compute_ballooning_stability!(ctrl, locstab_fs, plasma_eq) @@ -13,7 +14,7 @@ to compute Delta Prime. ## Arguments - - `ctrl::DconControl`: Control parameters for the analysis. + - `ctrl::ForceFreeStatesControl`: Control parameters for the analysis. - `locstab_fs::Matrix{Float64}`: Local stability matrix to store results (modified in place). - `plasma_eq::Equilibrium.PlasmaEquilibrium`: Plasma equilibrium data. @@ -23,7 +24,7 @@ This function modifies `locstab_fs` in place with: - Column 4: Delta Prime (Δ') """ function compute_ballooning_stability!( - ctrl::DconControl, + ctrl::ForceFreeStatesControl, locstab_fs::Matrix{Float64}, plasma_eq::Equilibrium.PlasmaEquilibrium; theta_k::Float64=0.0, @@ -34,15 +35,15 @@ function compute_ballooning_stability!( println("Evaluating local high-n ballooning stability...") end - num_psi = length(plasma_eq.sq.xs) + num_psi = length(plasma_eq.profiles.xs) # Loop over flux surfaces for flux_surface_index in 1:num_psi coeff_data = prepare_ballooning_coefficients(flux_surface_index, plasma_eq; theta_k=theta_k) - locstab_fs[flux_surface_index, 1] = coeff_data.di * plasma_eq.sq.xs[flux_surface_index] + locstab_fs[flux_surface_index, 1] = coeff_data.di * plasma_eq.profiles.xs[flux_surface_index] - if compute_delta_prime && plasma_eq.sq.xs[flux_surface_index] <= 1.0 + if compute_delta_prime && plasma_eq.profiles.xs[flux_surface_index] <= 1.0 result = integrate_ballooning_ode( coeff_data.ode_coefficient_spline; theta_k=theta_k @@ -66,17 +67,17 @@ function _collect_surface_response_background( plasma_eq::Equilibrium.PlasmaEquilibrium, theta_grid::AbstractVector{<:Real} )::NamedTuple - sq = plasma_eq.sq + profiles = plasma_eq.profiles theta_vals = Float64.(theta_grid) ntheta = length(theta_vals) - q0 = Float64(sq.fs[flux_surface_index, 4]) - q0prime = Float64(sq.fs1[flux_surface_index, 4]) - p0prime = Float64(sq.fs1[flux_surface_index, 2]) - two_pi_f0 = Float64(sq.fs[flux_surface_index, 1]) + psi0 = profiles.xs[flux_surface_index] + q0 = Float64(profiles.q_spline.y[flux_surface_index]) + q0prime = Float64(profiles.q_deriv(psi0)) + p0prime = Float64(profiles.P_deriv(psi0)) + two_pi_f0 = Float64(profiles.F_spline.y[flux_surface_index]) chi_prime0 = Float64(2pi * plasma_eq.psio) - psi0 = plasma_eq.rzphi.xs[flux_surface_index] f0 = zeros(ntheta, 4) fx0 = zeros(ntheta, 4) @@ -96,10 +97,19 @@ function _collect_surface_response_background( v0 = zeros(ntheta, 3, 3) v_zeta_psi0 = zeros(ntheta, 3) v_psi_theta0 = zeros(ntheta, 3) + rz = ( + plasma_eq.rzphi_rsquared, + plasma_eq.rzphi_offset, + plasma_eq.rzphi_nu, + plasma_eq.rzphi_jac + ) for i in eachindex(theta_vals) theta = theta_vals[i] - f, fx, fy, _, fxy, _ = Spl.bicube_deriv2!(plasma_eq.rzphi, psi0, theta) + f = ntuple(k -> rz[k].nodal_derivs.partials[1, flux_surface_index, i], 4) + fx = ntuple(k -> rz[k].nodal_derivs.partials[2, flux_surface_index, i], 4) + fy = ntuple(k -> rz[k].nodal_derivs.partials[3, flux_surface_index, i], 4) + fxy = ntuple(k -> rz[k].nodal_derivs.partials[4, flux_surface_index, i], 4) rho = sqrt(f[1]) eta = 2pi * (theta + f[2]) @@ -189,15 +199,11 @@ function _collect_surface_response_background( kappas0 .= -dinvbsq_dtheta .* two_pi_f0 ./ (2 .* jac0) - int_spl = Spl.CubicSpline( - theta_vals, - hcat(1 ./ gradpsi_sq0, r0 .* r0 ./ gradpsi_sq0); - bctype="periodic" - ) - Spl.spline_integrate!(int_spl) - - I0 = Float64(int_spl.fsi[end, 1]) - IR = Float64(int_spl.fsi[end, 2]) + int_fs = hcat(1 ./ gradpsi_sq0, r0 .* r0 ./ gradpsi_sq0) + @views int_fs[end, :] .= int_fs[1, :] + int_vals = FastInterpolations.integrate(cubic_interp(theta_vals, Series(int_fs); bc=PeriodicBC())) + I0 = Float64(int_vals[1]) + IR = Float64(int_vals[2]) Delta_tilde = Float64(I0 * two_pi_f0^2 + chi_prime0^2) return ( @@ -273,10 +279,11 @@ function _calculate_i_per_perturbed( A = 4pi^2 .* bg.r0 .* bg.r0 ./ (bg.chi_prime0^2 .* bg.gradpsi_sq0) B = bg.two_pi_f0^2 ./ (bg.chi_prime0^2 .* bg.gradpsi_sq0) - weight_spl = Spl.CubicSpline(theta_grid, hcat(H .* A, H .* B); bctype="periodic") - Spl.spline_integrate!(weight_spl) - Abar_w = weight_spl.fsi[end, 1] / bg.q0 - Bbar_w = weight_spl.fsi[end, 2] / bg.q0 + weight_fs = hcat(H .* A, H .* B) + @views weight_fs[end, :] .= weight_fs[1, :] + weight_int = FastInterpolations.integrate(cubic_interp(theta_grid, Series(weight_fs); bc=PeriodicBC())) + Abar_w = weight_int[1] / bg.q0 + Bbar_w = weight_int[2] / bg.q0 denom = 1.0 + Bbar_w @@ -285,16 +292,16 @@ function _calculate_i_per_perturbed( dI_dtheta = AperP .* corr_pprime .+ Aperq .* corr_qprime - dI_spl = Spl.CubicSpline(theta_grid, reshape(dI_dtheta, :, 1); bctype="periodic") - Spl.spline_integrate!(dI_spl) - i_per_primitive = copy(dI_spl.fsi[:, 1]) - i_per_spl = Spl.CubicSpline(theta_grid, reshape(i_per_primitive, :, 1); bctype="extrap") + dI_dtheta_periodic = Vector{Float64}(dI_dtheta) + dI_dtheta_periodic[end] = dI_dtheta_periodic[1] + i_per_primitive = vec(FastInterpolations.cumulative_integrate(cubic_interp(theta_grid, dI_dtheta_periodic; bc=PeriodicBC()))) + i_per_spl = cubic_interp(Float64.(theta_grid), i_per_primitive; bc=CubicFit()) theta_min = theta_grid[1] theta_period = theta_grid[end] - theta_min theta_k_wrapped = mod(theta_k - theta_min, theta_period) + theta_min - i_per_theta_k = Spl.spline_eval!(i_per_spl, theta_k_wrapped)[1] - i_per_perturbed = copy(i_per_spl.fs[:, 1] .- i_per_theta_k) + i_per_theta_k = i_per_spl(theta_k_wrapped) + i_per_perturbed = copy(i_per_primitive .- i_per_theta_k) return i_per_perturbed @@ -307,10 +314,8 @@ function prepare_ballooning_coefficients( corr_pprime::Float64=0.0, theta_k::Float64=0.0 ) - sq = plasma_eq.sq - rzphi = plasma_eq.rzphi - mtheta = length(rzphi.ys) - 1 - theta_grid = Vector(rzphi.ys) + mtheta = length(plasma_eq.rzphi_ys) - 1 + theta_grid = Vector(plasma_eq.rzphi_ys) bg = _collect_surface_response_background(flux_surface_index, plasma_eq, theta_grid) @@ -319,9 +324,11 @@ function prepare_ballooning_coefficients( theta_k_wrapped = mod(theta_k - theta_min, theta_period) + theta_min theta_k_reference = Float64(theta_k) - i_per0_spl = Spl.CubicSpline(theta_grid, reshape(bg.Iper0, :, 1); bctype="periodic") - i_per0_theta_k = Spl.spline_eval!(i_per0_spl, theta_k_wrapped)[1] - i_per0_theta_ref = Spl.spline_eval!(i_per0_spl, theta_min)[1] + i_per0_periodic = Vector{Float64}(bg.Iper0) + i_per0_periodic[end] = i_per0_periodic[1] + i_per0_spl = cubic_interp(theta_grid, i_per0_periodic; bc=PeriodicBC()) + i_per0_theta_k = i_per0_spl(theta_k_wrapped) + i_per0_theta_ref = i_per0_spl(theta_min) i_per0_thetak_shift = i_per0_theta_k - i_per0_theta_ref i_per0_shifted = bg.Iper0 .- i_per0_theta_k @@ -359,10 +366,11 @@ function prepare_ballooning_coefficients( bmag = sqrt.(bsq) kappaw_periodic = zeros(mtheta + 1) - spl1 = Spl.CubicSpline(theta_grid, jac_arr_loop1 .* bdot_theta_phi_loop1 ./ bmag; bctype="periodic") + spl1_vals = jac_arr_loop1 .* bdot_theta_phi_loop1 ./ bmag + spl1_deriv = _periodic_fft_lowpass_derivative(spl1_vals, theta_grid; nkeep=32) cell1 = -(jac_psi_loop1 ./ jac_arr_loop1 .+ 0.5 .* bsq_psi_loop1 ./ bsq) ./ chi_prime - cell2 = spl1.fs1[:, 1] ./ (jac_arr_loop1 .* bmag) + cell2 = spl1_deriv ./ (jac_arr_loop1 .* bmag) cell3 = two_pi_f .* q_derivative ./ (bsq .* jac_arr_loop1) kappaw_periodic .= cell1 .+ cell2 .+ cell3 @@ -424,16 +432,17 @@ function prepare_ballooning_coefficients( n0_fs[:, 3] = m0_21 .- sigma .- m0_12 .* sigma .^ 2 n0_fs[:, 4] = -0.5 .- m0_12 .* sigma - n0_spline = Spl.CubicSpline(theta_grid, n0_fs; bctype="periodic") - Spl.spline_integrate!(n0_spline) + @views n0_fs[end, :] .= n0_fs[1, :] + n0_int = FastInterpolations.integrate(cubic_interp(theta_grid, Series(n0_fs); bc=PeriodicBC())) d0bar = zeros(2, 2) - d0bar[1, 1] = n0_spline.fsi[end, 1] - d0bar[1, 2] = n0_spline.fsi[end, 2] - d0bar[2, 1] = n0_spline.fsi[end, 3] - d0bar[2, 2] = n0_spline.fsi[end, 4] + d0bar[1, 1] = n0_int[1] + d0bar[1, 2] = n0_int[2] + d0bar[2, 1] = n0_int[3] + d0bar[2, 2] = n0_int[4] - ode_coefficient_spline = Spl.CubicSpline(theta_grid, bf_fs; bctype="periodic") + @views bf_fs[end, :] .= bf_fs[1, :] + ode_coefficient_spline = (xs=theta_grid, itp=cubic_interp(theta_grid, Series(bf_fs); bc=PeriodicBC())) return ( ode_coefficient_spline=ode_coefficient_spline, @@ -452,11 +461,11 @@ function salpha_reference( psi_idx::Int, plasma_eq::Equilibrium.PlasmaEquilibrium ) - sq = plasma_eq.sq + profiles = plasma_eq.profiles psio = plasma_eq.psio mu0 = Equilibrium.mu0 - npsi = length(sq.xs) + npsi = length(profiles.xs) if psi_idx < 1 || psi_idx > npsi throw(ArgumentError("psi_idx=$psi_idx is out of bounds for npsi=$npsi")) end @@ -464,12 +473,13 @@ function salpha_reference( throw(ArgumentError("plasma_eq.psio is too small to compute physical derivatives")) end - Spl.spline_integrate!(sq) - volume = max(Float64(sq.fsi[psi_idx, 3]), 0.0) - vprime_phys = sq.fs[psi_idx, 3] / psio - q_ref = sq.fs[psi_idx, 4] - qprime_norm_ref = sq.fs1[psi_idx, 4] - pprime_norm_ref = sq.fs1[psi_idx, 2] + dVdpsi_int = FastInterpolations.cumulative_integrate(profiles.dVdpsi_spline) + volume = max(Float64(dVdpsi_int[psi_idx]), 0.0) + psi = profiles.xs[psi_idx] + vprime_phys = profiles.dVdpsi_spline.y[psi_idx] / psio + q_ref = profiles.q_spline.y[psi_idx] + qprime_norm_ref = profiles.q_deriv(psi) + pprime_norm_ref = profiles.P_deriv(psi) qprime_ref = qprime_norm_ref / psio pprime_ref = (pprime_norm_ref / mu0) / psio @@ -534,7 +544,7 @@ ballooning evaluator, and returns delta-prime and `det(d0bar)` `Di` maps. function scan_delta_prime_map( psi_idx::Int, plasma_eq::Equilibrium.PlasmaEquilibrium; - ctrl::DconControl=DconControl(; verbose=false), + ctrl::ForceFreeStatesControl=ForceFreeStatesControl(; verbose=false), theta_k::Float64=0.0, s_scales::AbstractVector{<:Real}, alpha_scales::AbstractVector{<:Real} @@ -607,10 +617,7 @@ Computes Delta' = (y'/y)_right - (y'/y)_left. - `delta_prime`: The stability index Δ'. """ -function integrate_ballooning_ode( - ode_coefficient_spline::Spl.CubicSpline; - theta_k::Float64=0.0 -) +function integrate_ballooning_ode(ode_coefficient_spline; theta_k::Float64=0.0) TOLERANCE = 1e-8 MINIMUM_STEP = 1e-10 MATCHING_POINT = 1e-3 @@ -694,15 +701,18 @@ where y₁ is the solution and y₂ = f·dy/dθ. """ function compute_ballooning_ode!(derivatives, solution, parameters, poloidal_angle) ode_coefficient_spline = parameters[1] - coeff_matrix = Spl.spline_eval(ode_coefficient_spline, [poloidal_angle]) - - periodic = coeff_matrix[1, 1] - peculiar_1st = coeff_matrix[1, 2] - peculiar_2nd = coeff_matrix[1, 3] - kappaw_periodic = coeff_matrix[1, 4] - kappaw_secular = coeff_matrix[1, 5] - jac_chiprime = coeff_matrix[1, 6] - pprime_chiprime = coeff_matrix[1, 7] + theta_min = first(ode_coefficient_spline.xs) + theta_period = last(ode_coefficient_spline.xs) - theta_min + theta_wrapped = mod(Float64(poloidal_angle) - theta_min, theta_period) + theta_min + coeffs = ode_coefficient_spline.itp(theta_wrapped) + + periodic = coeffs[1] + peculiar_1st = coeffs[2] + peculiar_2nd = coeffs[3] + kappaw_periodic = coeffs[4] + kappaw_secular = coeffs[5] + jac_chiprime = coeffs[6] + pprime_chiprime = coeffs[7] f = (periodic + poloidal_angle * peculiar_1st + poloidal_angle^2 * peculiar_2nd) / jac_chiprime kappaw = kappaw_periodic - poloidal_angle * kappaw_secular @@ -710,4 +720,4 @@ function compute_ballooning_ode!(derivatives, solution, parameters, poloidal_ang derivatives[1] = solution[2] / f derivatives[2] = g * solution[1] -end \ No newline at end of file +end From 777d6ba521f2c8ab5bf4108d5ea520ec9caef578 Mon Sep 17 00:00:00 2001 From: jmlmir369 Date: Thu, 30 Apr 2026 19:43:36 +0900 Subject: [PATCH 004/135] aixs name fixed --- .codex | 0 .../Bal_salpha_delta_di_summary.ipynb | 1012 ++++++++++++++++- 2 files changed, 965 insertions(+), 47 deletions(-) create mode 100644 .codex diff --git a/.codex b/.codex new file mode 100644 index 000000000..e69de29bb diff --git a/examples/DIIID-like_ideal_example/Bal_salpha_delta_di_summary.ipynb b/examples/DIIID-like_ideal_example/Bal_salpha_delta_di_summary.ipynb index 2b56d9142..049dba7ce 100644 --- a/examples/DIIID-like_ideal_example/Bal_salpha_delta_di_summary.ipynb +++ b/examples/DIIID-like_ideal_example/Bal_salpha_delta_di_summary.ipynb @@ -2,10 +2,192 @@ "cells": [ { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "id": "s-alpha-profile-extrema", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\u001b[32m\u001b[1m Activating\u001b[22m\u001b[39m project at `~/lib/git/GPEC`\n", + "┌ Info: Forcing hamada coordinate jacobian exponents: power_*\n", + "└ @ GeneralizedPerturbedEquilibrium.Equilibrium /home/jmlmir/lib/git/GPEC/src/Equilibrium/EquilibriumTypes.jl:68\n", + "┌ Info: Processing EFIT g-file: /home/jmlmir/lib/git/GPEC/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk\n", + "└ @ GeneralizedPerturbedEquilibrium.Equilibrium /home/jmlmir/lib/git/GPEC/src/Equilibrium/ReadEquilibrium.jl:58\n", + "┌ Info: Parsed from header: nw=257, nh=257\n", + "└ @ GeneralizedPerturbedEquilibrium.Equilibrium /home/jmlmir/lib/git/GPEC/src/Equilibrium/ReadEquilibrium.jl:65\n", + "┌ Info: Magnetic axis found at R = 1.744, Z = -0.005\n", + "└ @ GeneralizedPerturbedEquilibrium.Equilibrium /home/jmlmir/lib/git/GPEC/src/Equilibrium/DirectEquilibrium.jl:179\n", + "┌ Info: Inboard separatrix found at R = 1.058\n", + "└ @ GeneralizedPerturbedEquilibrium.Equilibrium /home/jmlmir/lib/git/GPEC/src/Equilibrium/DirectEquilibrium.jl:208\n", + "┌ Info: Outboard separatrix found at R = 2.301\n", + "└ @ GeneralizedPerturbedEquilibrium.Equilibrium /home/jmlmir/lib/git/GPEC/src/Equilibrium/DirectEquilibrium.jl:208\n", + "┌ Info: Estimated separatrix log slope A = 0.409 from probe integrations at psi = 0.9970, 0.9985\n", + "└ @ GeneralizedPerturbedEquilibrium.Equilibrium /home/jmlmir/lib/git/GPEC/src/Equilibrium/DirectEquilibrium.jl:393\n", + "┌ Info: Auto-mpsi: N_core=3 + N_mid=163 + N_edge=10 = 176 (A=0.409, h_mid=0.0059, tau=0.001)\n", + "└ @ GeneralizedPerturbedEquilibrium.Equilibrium /home/jmlmir/lib/git/GPEC/src/Equilibrium/DirectEquilibrium.jl:452\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "s extrema\n", + " index\tpsi_norm\tvalue\n", + " 155\t0.91006135\t3.098059626449e+00\n", + " 163\t0.95668712\t2.218338914722e+00\n", + "\n", + "alpha extrema\n", + " index\tpsi_norm\tvalue\n", + " 75\t0.44380368\t1.475989118427e+01\n", + " 109\t0.64196319\t1.449804644503e+01\n", + " 164\t0.96251534\t2.090707893518e+02\n" + ] + }, + { + "data": { + "image/png": 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+ "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ], + "text/html": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "using Pkg\n", "Pkg.activate(\"../..\")\n", @@ -14,6 +196,7 @@ "using Plots\n", "using Printf\n", "using Statistics\n", + "using LaTeXStrings\n", "using TOML\n", "\n", "eq_config = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(TOML.parsefile(\"gpec.toml\")[\"Equilibrium\"], pwd())\n", @@ -73,7 +256,7 @@ " ylabel=\"s\",\n", " label=\"s\",\n", " lw=2,\n", - " title=\"s profile\",\n", + " title=\"s\",\n", " framestyle=:box,\n", ")\n", "scatter!(p_s, psi_norm[s_extrema], s_profile[s_extrema]; label=\"extrema\", marker=:circle, color=:red, ms=5)\n", @@ -84,7 +267,7 @@ " ylabel=\"alpha\",\n", " label=\"alpha\",\n", " lw=2,\n", - " title=\"alpha profile\",\n", + " title=\"alpha\",\n", " framestyle=:box,\n", ")\n", "scatter!(p_alpha, psi_norm[alpha_extrema], alpha_profile[alpha_extrema]; label=\"extrema\", marker=:circle, color=:red, ms=5)\n", @@ -94,15 +277,219 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "id": "delta-di-profile-extrema", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Computing Delta' and Di profiles...\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "┌ Warning: Verbosity toggle: dt_min_unstable \n", + "│ dt(1.0e-10 <= dtmin(1.0e-10), at t=-0.06510113282556569, and step error estimate = 1.1423556107565442. Aborting. There is either an error in your model specification or the true solution is unstable.\n", + "└ @ SciMLBase /home/jmlmir/.julia/packages/SciMLBase/hLfdZ/src/integrator_interface.jl:717\n", + "┌ Warning: Verbosity toggle: dt_min_unstable \n", + "│ dt(1.0e-10 <= dtmin(1.0e-10), at t=-0.09646835664820956, and step error estimate = 1.0233429309893254. Aborting. There is either an error in your model specification or the true solution is unstable.\n", + "└ @ SciMLBase /home/jmlmir/.julia/packages/SciMLBase/hLfdZ/src/integrator_interface.jl:717\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Delta' extrema\n", + " index\tpsi_norm\tvalue\n", + " 22\t0.13490798\t-2.270043132951e-02\n", + " 23\t0.14073620\t-2.273200742321e-02\n", + " 25\t0.15239264\t-2.262453359539e-02\n", + " 26\t0.15822086\t-2.268353986142e-02\n", + " 27\t0.16404908\t-2.265515889541e-02\n", + " 116\t0.68276074\t-3.370657448578e-02\n", + " 160\t0.93920245\t-8.756024762877e-03\n", + " 162\t0.95085890\t-1.227486100615e-02\n", + " 166\t0.97417178\t-6.900060910302e-03\n", + " 174\t0.99848787\t-2.375793842651e-02\n", + "\n", + "Di extrema\n", + " index\tpsi_norm\tvalue\n", + " 125\t0.73521472\t-2.637864264262e-01\n", + " 163\t0.95668712\t-7.776704310230e-01\n", + " 175\t0.99895436\t-2.527139701487e-01\n", + " 176\t0.99927694\t-2.528430789462e-01\n" + ] + }, + { + "data": { + "image/png": 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hOE6pVLp27Vpx4Mqvv/5aqc8irpNz4MCBQYMGGe7wgw8+MKwmZiwbN24su4fo6OiuXbsafq6WLVuePXvWsE7V1skRHT161NfX1+jbbtGixeHDhyv1SQEAGjZxSjEj9vb2Q4cO/frrr5VKpVH9iq+T06xZs99//91wKL+Pj8+FCxcMq4k90woKCsruYdOmTfb29oZRTZ061XBxNlbVdXIYYyUlJf/3f/9nZWVluH+JRDJkyJC8vLzHfzSA6uBY5WeOAqjjtFqtYW8xnuft7e0dHBwM5+kvV05OTmhoaFJSkrW1tZeXV/fu3Z2cnPSvKpXKzMxMNzc3o5MBEWVmZoqz0Oj7UhcUFISGhiYkJDg4OPj7+7u5uWVnZ+fl5Xl4eOiTooqYM2fO1q1bT58+PXjw4AsXLkRHR8vlcn9//yZNmhhWUyqVOTk5Li4u5Y4TFQQhLCwsKipKq9W2bt26f//+RlOfqdXq9PR0e3t7Z2dnfWFBQUFqaqqTk5O+MCsrKzc319vb2+gj6HS6q1evRkdHFxcXe3p6+vr6Gs1SCgAAJSUlhvfgJBKJeG56VH2NRpOcnOzg4PD4cTU8zzdt2jQhIaGgoCAkJCQ9Pd3b23v48OFGeUVSUlJJSUmLFi3KPRWqVKozZ84kJSUpFIq+ffsaLTxARGlpaRqNxsfHx8LCQl+YmppaUFDQrFkzfaHYYaHssKK8vLzQ0NB79+5ZWVl5eXl17doVUxGAqSHJAajT9EnOkCFDzB0LAADUOfokx9yBANQtmHgAAAAAAAAaFCQ5AAAAAADQoGB2NYA6bdq0ae3atavCsgkAANAYfPzxx9VftROg4WmYY3I0Gk1hYSHPl9NOVVxc/MRZd6FS8JXWrJKSEplM9sQ5EqDi8BOtWTqdjjEmlT7hHllpaamTk9MTq9U7giBkZmYajr3Wq+A3AxWHP96ahZ9ojcNPtGZV/CcqkUiemNs3zCRnwIABN27cKPckpFKprKys8BdeU3Q6nUajedQyMlAFGo1GKpWW++uFKmCM5efnl50QD6qsqKiIMWY0cVNZhYWFS5cuXbt2be1EVWu++uqrN998s9w5Eiv4zUDFKZXKx0w+BpWFn2iNy8vLs7Ozw33JmlLBn2hpaWnTpk2joqIeX61hXuu3a9du7ty5gYGBZV/q16/f2rVrDReChOq4fv36888/X+7c/1A1M2fO9Pf3nzdvnrkDaSBUKpWXl1dOTo65A2k4Vq5cWVRUJC4b9RgLFixokN0sfXx8Jk6cKK4iZeSDDz7Izc398ssvaz+qhsrKyio5ORkX5TXlo48+ysjI+Oqrr8wdSMNha2t7//593OqtKZ988klSUtLXX3/9+Gq//vrr1q1bn7g3TDwAAAAAAAANCpIcAAAAAABoUJDkAABAI5KVlRUQEODi4tK5c+eQkBBzhwMAACbR6JKcqVOntmrVytxRNBxNmzadMWOGuaNoUEaPHt2jRw9zR9FwWFtbL1y40NxR1BvXr1+fMmJEdnb2Y+oMHDiwXg9rXLp0qZWVVXx8/KpVq55++unc3Nya2nP//v39/f1ram9ARIsXL8bUVTWoX79++IlW2VcffXT411+NChcuXFjuNCRQBcnJyZvXrq3BzKRhTjzwGM8//7ynp6e5o2g4nJycyp3gAapswoQJNjY25o6i4ZBIJK+99pq5o6gfrl+/PnPUqLk5OWP79j128aKzs3O51fr37y8IQi3HVlNyc3P3799/8+ZNW1vbKVOmfPXVV7t27aqpNLhfv35arbZGdgWiZcuWlbsaBFRNnz598BOtmlVvvHF906YdPC8wNmnKFH35a6+9JpFIzBhYg5GcnNzbz292UdEvGzf26Nlz9pw51d9no0tyAACgrBs3bjw3cuSerKyORG0TEsb163ckNNTFxcXccdWwu3fvWllZtWjRQnzapUuX2NhY84YEAHXc2pUrI77/fk9+vpJo7Ny5giA8FRBg7qAalPT09H6tWi0qKnqb6GXGBs6dq9Pp5lb7HjqSHACAxu7GjRvPjhghZjhENF6rpfj48f37N7w8Jycnx7Cl1N7ePi4urlJ7uHv37r59+/TLYkgkkp9//lnsv1dYWKjVatVqdQ0G3Milp6ebO4QGBT/RKtj42WfRP/ywS6WSEbkSHVMqRwcG5ubkjJkwgfATrQlZWVnjevdeWFT0NhER+RD9xdiAefPylMoZzz0n1mGMde/e3fDb9vX1feKekeQAADRqRhmOqKHmOU5OTiqVSv80Ly+vsp/O19f36aefLnedHI1Go9Vqn7gIN1RK3e9hXiKQurSS9bXVWoddYJRXUpUNi3RFOolOJVNUdsPKfsYGY99nK9OCg/eqVLKHJa5EJ/LyRq54I5Ec+48LyJFYZAlOZolNISOLJ/XlVEjJokxnOjlP1tJ/Vi+1lJBVjWYDjLG9e/dOmTJFJpM9sfKtxPSxffq8/DDDEfkQnWds4IoV9g4O+vactLQ0fYUKrpODJAcAoPFijI3199+tVHYs89J4rTYyLm7+zJn7T5wwQ2Sm0bx5c41Gc//+/aZNmxJRVFTUFIPu9WAKBaVUKpCWkaqUFemoUEviv0SkKmX6q31lMTEirUCqUiKiYoE0WlZQYG2TpCOi/BLSPayZX0o6g0FhhjsRlehI/e+BJ/p3NKLRsuJHjy/TCZTf0K7spURSIgzLqRA+dHuXX766VFxgdKnuSnQyT9l2yZz3UnzJu2ND+j7tLYjnSMaTjZST8WQjI4WU7CzITsa5WJKrJeetoJa2XCt78rLmyt0DY+yVwMDQ3bt3b9q06/jxsnlOZhEdTBAuZrDIXBajZPyr3Z4tLHy7zH58iE4y1mXevICnn7a3t6/ax0GSAwDQeHEct/mnn15/8cUjublGLRo3iH5ydNr7xRfmicw0XFxcJk2atGbNmm+++ebMmTNXrlzZvXu3uYOqB7KLKaOQ5RSTsoTyS5iqlNRa0mhJVcqUxaTWklpLqlKWV0LqUirUkbKEPSqvqCRroro+y4UFT4on37D+d31p+ReIFcRzZG9RlQ0FQWCMVWGgfGU/Y8NQMmrsneMf/i+jMECnM3ppo6XCvl3fbt3bluhKzDUBoLqUSp70x6HWUolx7A/uIOifGv6p6lsIM8iosdG47dFRTv3duP7u/GAPrrcbJ7YpMcZeDQxU79t3WaP5/MKFKcOG7Q8J0X8//7snbIgSTqcyncHOrP/zw/4vJk5nwrB/77+E6CWOe2batCpnOIQkBwCgkRs/eTL9+OP4f+c5N4hG2Lp8ue9Ux45l23jqt6+//nrOnDmOjo4eHh47duxoSJ3xqiyvhO4VsPsFlFnE0gspo5BlFVFmEUsrpIxCyixipdVINMQOMxKO7GSchYQUUpJLyFpKRGQr4/RX++ItZAlHdhZED3vUqFQqW1tbIrKzIMnDmrYykhr00jHciUh8F0OP6pBjJeEsH33BL+HJrmFd2aNHZSV5Zg6/OLZfP0lCwlMGec5ahSKiX7/Yo0dlMllqamrd71FZcXklJLAHPSqLdaTRUkEp5Zey/BLKLKKMQpasoTv57HYeyyyiI4nsSKKOiKylNMCdG+3NRXw6T/K/fZtVKp7ojcJCuno1YMSI/SEhpzMtVl7VXc5kRGTB0xgfbnxTvpMj18GRc5SPOzHi6LPjxu0U/slzSohGc1zzadN+rN5NKCQ5AACNnZjnjHjhxZD8XBeiG0QTHFyzXv29xKODuUOreZ6enicaUAe8ytJoKUbJ7uazOBXdyWfRuSw2j+UUP2ErBwvysOYcLchBTnYyzt6CrKVkLSU7GWdnQQopKaRkb8HZykghI2spOVhwlg8zmepITdV4elb9Pi5ANbm6uh67cGFsv370MM9Zq1Bc6ddv59GjFRlwUu8YtBAa3jkop+HxfgE7n85C09npVBaVy04mCRc/nD/m6v5dRSr9LYg3Cgt1YVf9ug1PWnqcpHIPK3qzi2R2a97h3+2Qo0eP3nb0nzynpjIcQpIDANCAaTSapYGBy1eubNeu3eNrjp88efWSjf3WLfxOo1zq6hrw3R/rc9rcVFZreDTUBTpGN7LZX+ksNJ39nc3u5jOhzP+qQkrNbblmNuRqyblZkYcV52JJLpacuxW5W5GrJSfHQiDQWBnmObGWlg04w6mUpjZcUxvuWV8ioswimj93vvW1/dsMMhzRW0WF+XevbflmyoqfTyxqzz/qxsfo0aO3Hjny7PjxWwXhQ45r9+yz3//8c/WDRJIDANAwaTSaCYMG9Y2MfPrUqX1nzjw+z9EKdLNVgHoWe3H/K8dPn75p3XZ9iC4GSU79VCpQaDo7lSKcT2eXM1mBweh5GU/tHbhW9lxLW/Kz49o4cO0cOA8r88UKUOeJec6oPn18fX2R4ZTlakm9/NzDLCQ6DRklOYwoV8pP6ui6ovMTZoIbM2bM1iNHnhk/fkpAQI1kOIQkBwCgQdJoNJMGD346OvrlkpJnMjMDhgzZ88cfjxlgcyGD5ZdSh5HTIr97log4JSOiGGXtBQzVpxXoeBLbdls4niSoDBKbVvbcAHduoDvXy5Vr58DJnjTtLAAYcXV1PR8ZaWlpyfP4+ynHW6tXfyqRTFm3bn9enn4eBkb0qq1t6Zgxm3/eUZGdjBkzJlWlKimp0vzo5UGSAwDQ0IgZztSoqJeLioioC9HOzMzpw4Y9Js85mSwQ0UjvB32v/ew4GU8JBaxQW8NLKIAp3M5jm2OFbbeF9MIHJR0cudE+3GAPrp8b74aGGoBqs7a2NncIddob771HRAEP8xwxwykYM2bzrl3mygxx7gIAaFCMMhzRE/OckGRGRCO8H5yKZDz52XExSnYrn3VxqtZ0t2BSf6Swj67r/khhYs/C9g7c7Nb8s75cEwX+1wCgVhnmOW+YO8MhJDkAAA3Mwlmz+kdEvFymxb8L0ebMzFGDBiVmZRktlJFXQleymAVPQzz+uTJu68DFKFlMLpKcOuqvNPZ2mO5cGiMihZSeacm/1Jbv44b/LAAwmzfee6+4qKjdhg3Dx43b/Msv5u3dhyQHAKBBWbZy5bNnz07PyjJqr9EQvWdv/25QUNmlAM+kClqBBnlwNgbjads50EGim3mYe6DOKdTS22G6DVGCwMhZTss6SRa156u2OiQAQM0K+vjjIWPHDhw40Ozjl0z+9jt27HjqqadeeOGFsLCwciv8/fffs2fPnjx58tatW/WF4eHh33777eLFi48dO2bqCAEAGpIuXbrsDAmZ7uISaVCoIZpkbz915cqXly0ru8mZNEZE/p7/agRo68AR5h6oe8KyWLeD2q8iBQlHQd34hBmyt7siwwGAOmTw4MFmz3DI1EnOjh073nzzzcDAwJ49e44YMSIxMdGoQkpKyrBhw7p06fLSSy+99957P/30k1j+5Zdfnj17NiQk5Nq1ayaNEACg4RHznHEOD/IcDdEwxSMzHCI6m8qIaLDHv84I7R4kOWjJqSsY0WfhwoD/aWPzWEdH7uIk6eoeEhtMZgsAUB7Tdlf76quvPvzww4kTJxLRhQsXNm/evHr1asMKW7ZsGTZs2LJly4goPz//k08+mTNnDhGJ2U5AQIBJwwMAaKhad+iS9/rxYZ+MOVyQtcjaPnL8O8MDXyu3Zn4pXctmMp76uf+7Jcee44hu5zEdIwkGephbXgk984f2RBLjiF7tyH/SS4IFOgEAHsOELTk6ne769esDBw4Unw4YMODKlStGdcLCwvQVBg4cGBERUVxcbLqQAAAaiV/uCvnunb3XHJ9oa2v1n/eLRr66445Qbs2/0piOUS9XTvHvu142MvJWcEU6SlChMcfMUjU05LD2RBJzs6Ijo6Xr+iLDAQB4guq25GRmZiqVxl225XJ506ZNMzMzdTqdo6OjWOjs7JyWlmZUMy0tzcnJSV+BMZaWltasWbNqRhUbG3vu3Dn9IB+ZTLZ582YrKysiSk9Pr+bOwQi+0pqlVCpVKpWFBbrY15jG+RP9OsKBSDp3QIvJkZFX8q3PXaQfb2oXeGbwZdpkjnbszI4AACAASURBVN6xJrLubqNOTdUYveRrZZektjgfl2Pt/s9cbWq1WhAEtVptVPnmzZvvvfee/umdO3fs7Oxq8iM1Vrfz2OjjungVa+vAHR8jaWaDZjUAgCerbpLz3Xff/fLLL0aFfn5+hw4dUigURKRvmSksLLSxsTGqqVAoih6u5FBYWEhEZetUQZMmTXr37j127Fj9u7Rs2VL/qqenZ/XfAgzhK61BcrncxsYGSU7Namw/0V/uCteVOldL+k9XJyupUxOiFlHaeBUfx3sM8jC+RL56RUvExrey8/S0N3qpi7vuTJaQzjt6ev7T7F9QUCAIQtkExsnJ6f333xeEB+1FGzZs8PHxqelP1ugUlNKE33XxKtbHjTsyWuosf/ImAABA1U9ygoKCgoKCyn3J1tbWwcEhPj5evLxISEho0qSJUZ0mTZokJCSIj+Pj4xUKhb5hpzqsra3bt28/YsSI6u8KAKB+ySuh1y/piOiT3hIrKRERRzS5GfdVJAtJFgZ5/Kufk1pLV7OYlKcB7uW0D1Rq7gG5XD5s2DD903379snluCSvrsWhult5rKszd2qcVIFFHwAAKsy0s6tNnz59y5YtRKRWq3fv3j19+nQi0mg03333XUFBgVhhz549+fn5RBQcHDx9+nSOQ0M8AEDVBV3VpWpogDv3Yut/jvDDvDgi+iPVOF0JTWelAnVz5mzLm6RLnEU6FkvlmMmeOGHrbUEhpV+GSpDhAABUimmTnKCgoPPnz3fv3r19+/bdu3cXp1lTKpULFy7Mzs4morFjxw4YMKBDhw49e/YMCQnR9+d+/fXXnZycDh06tGbNGicnpx07dpg0TgCAhuFaNtsYLUh52jjgXzOiDfbgpTxdzmBq7b/qn0kViGhImT5somY2RERJxqNvoDbEq9i8czoiWt9PIjapAQBAxZn21pCPj09UVFRUVJSNjY1+VIynp2dubq69vT0R8Ty/ffv2+Ph4lUrVoUMH/Trcq1evfuedd/T7sba2NmmcAAANwyc3BB2jZR35zk7/uiy2t6DuztzlTPZXGhvt889Lp1IYEQ3xLP+Gl6c1xxGlapjAqOyMBWBSC8/r8ktpWgs+sI3519QDAKh3TN7+LZFIOnfubFjCcZyDg4NhSYsWLYy2sra2RmIDAFApRTo6mihwREs7lHNZPMyLu5zJfvhlv8foVl26dCGi06nsYgazk9Fgz/IzGEsJOVtSVhFlFpG7lWmDB0M77wonkpiTnL7uj7miAQCqAveHAAAaiN+ThIJS6unKlTvL8FAvXhq6NXr1vOeGD7927RoRvX1FR0RvdJHYlTcgR+RlzRFRshrDcmpPXgm9fkkgos/6SNyQWwIAVAmSHACABuLgPUZEU5qXf2BPO/Wz7+4Vf6mVB7Kznx85cu1vly5kMDer8pt99LwVREQpxivogAm9cVmXomGDPf41dQQAAFQKDqAAAA2BVqDD9wUimtKsnGac3Tt2bHxlyQWN0pGoDdGB7OwNs8ZTQtj73SXlzqum96AlR4OWnFoSm8e2xAoWPH03UIJhUAAAVYYkBwCgITiTxrKKqJ0D17bMTFy7d+xYt2TJMaXS8WFJG6I/VNleGyZ2zb/6+N16WxMRpaC7Wm358JqgYzS3DY8Z1QAAqgNJDgBAQ3AwQSCiKc2Nr4wP/fbbF4sXnzDIcERtiEJU2bPHjYmLi3vMbr0UYktOzQYL5YtTsZ1xgoynNzrj7AwAUC04jAIA1HuM6Nd7jIimlhmQ06pNG7WlZbl5zFWp1NXd3dXV9TF79rbmiCgF3dVqxUfXBa1AL7TiW9iiGQcAoFqQ5AAA1HtXMlmymjWz4bq7GF8ct23b9sCZM8+7u1/5d/lumexrX9/D58/b2to+Zs9e1kREyVgP1PQS1Wz7bUHC0f+hGQcAoNpwJAUAqPeOJTIimtiUK/f+f5s2bQ6cOTPHIM/ZLZOta9ny2IULjo6O5W3xD28FWnJqyfpIoUSg53z5VvZoxgEAqC4kOQAA9d6JJIGIRvs88pBumOdUPMMhIldLkvGUXURFupoMGMo6dJ8R0YJ2OC8DANQAHEwBAOq33GK6nMksePL3fFwLQJs2bfb9+ecsV9cNrVqduHSpIhkOEfEceVhxjCgVjTmmFK9it/KYo5z6uKEZBwCgBkjNHQAAAFTL78mCjtFQL87msSveEFG7du1C/v7bwcHBxsam4vv3VlCimlI01OJxg3egWo4kMiIa7cNjcRwAgBqBJAcAoH47kfTg+rgilX18fCq7f28FR8SS1YwIF+CmcixRIKKxPviGAQBqBrqrAQDUY+xhkjPGZNfHDyZYw1I5JlOko9OpjKtwpgoAAE+E4ykAQD0WnsNSNMxHwXVwNF2SwxFRihpjckzlTCrTaKm7C+duZe5QAAAaCiQ5AAD12PHEB804puvn5K0gIkpBS47JHEsSiGhsE/RVAwCoMUhyAADqsYeTR5vw+vhBSw5mVzMZcZmjseirBgBQc3BIBQCor/JK6K90JuVphLcJD+bimBy05JhInIrdymNOmDwaAKBGIckBAKivTiQJpQINcOccLEz4LmjJMSlx3ogR3pg8GgCgJiHJAQCor8TFVcY3Me2R3N6CFFIqKCVVqUnfp5E6mcyIaJQ3UhwAgJqEJAcAoF4S2IMBOROamvz62MOaI6JUNObUNK1Af6QIRDQSSQ4AQI1CkgMAUC9dzmTphdTClmvnYPLrYwzLMZFLmSyvhNo6cE1tkOQAANQkJDkAAPXSkcRaasYhDMsxmZPJAqGvGgCACSDJAQCol47cr40BOSJPayKiVLTk1LTfkxgRjTTl5HgAAI0TDqwAAPVPioZdz2YKKQ3xrI1GAE+MyTEBZQldyWIWPPnXyn8iAECjgiQHAKD+OZrIGNFwb95SUhtvhzE5pvBHiqAVqL87ZyMzdygAAA0OkhwAgPpnX7xARJNqZUAOoSXHNMTJo9FXDQDAFHBsBQCoZ7KK6FQKk/E0pXktHcPRkmMKp1PFJAd91QAAah6SHACAemZ/gqAVaJQ35ySvpXfE7Go1rlhHd/KZlKfOTkhyAABqHpIcAIB6Zm+cQETTW9beAdzegqylVFBKam2tvWcDdzOPaQVqZcfJa2VUFQBAY4MkBwCgPsksojNpTC6hyc1q9QDuYskRUWYhGnNqRlQuI6IOjmjGAQAwCSQ5AAD1yZ44QSvQGB/e3qJW39fFkogoq7hW37QBe5jkmDsOAIAGCkkOAEB9sidOIKJnWtZ2C4CLnIgou6iW37bBiswlQksOAIDJIMkBAKg3ktTsr3RmJaUJTWv76C12V8sqQne1moHuagAAJoUkBwCg3th2mwmMJjXlbWt9+cgH3dXQklMTCrWUoGIynvzskOQAAJgEkhwAgHpj+x2BiF5sbYZDt7MlR0TZxWjJqQExSqZj1Maes8BJGADANHB8BQCoH86lsZtK5q3gRphj+UhxTA5acmpElBJ91QAATAtJDgBA/fDjLYGI5rTiJOa4NkZ3tRqEATkAAKaGJAcAoB5Qa2lfvMARzW5lnuO2OPFAWBYbc0p2MQvnjmqJzMH80QAApmXyE9X69eu7d+/ep0+fbdu2lVvh3Llzw4cP79Chw/Lly4uKiohIp9OtXbt2+PDhHTt2nDp16t9//23qIAEA6ri9cYKqlAZ6cK3szXP7X2zJiVex85n8sRSJWWJoMKKURGjJAQAwJdMmOXv27Pnyyy83b9782WefLVu27Ny5c0YVsrKyJk6c+MILLxw8ePDatWtBQUFEVFJScuPGjRUrVuzdu7dbt27Dhw/PyMgwaZwAAHXcD7Fmm3JAJCY5Io4w/UDVqbV0v4DJJeRriyQHAMBUTHu+3Lhx44oVK3r06DF48OD58+d/++23RhW2bdvWu3fv2bNnt27d+pNPPtmyZUtJSYmVldUvv/wyZsyYdu3aBQUFKRSKsLAwk8YJAFCXXctm59OZgwVNb2m2JMdZ/s8VOY+L82qIzmUCo7b2nBSd/gAATMa0h9jIyMiePXuKj3v16hUZGWlUISoqqkePHuLjHj165OXlJSUlGVZISkrKzMxs06aNSeMEAKjLvo560IyjkJotBrmErB++u1lmPmgwxFkH2qOvGgCAKVX3hBkXF3fnzh2jQplMNnToUJ1Ol5OTY29vLxY6ODiU7XWWkZHRunVr8bFEIrG1tc3IyGjZsqVYUlJSMnPmzEWLFvn6+lYqqoiIiF9//fWDDz7Qx3PixAkrKysiSk9Pr9Su4InwldYspVKpUqksLCzMHUjDUd9/onml/M67jhxxAS7Zqak6M0ZiJ3XSaHki0qgLUlPzjF6NiIh46aWX9E9zcnIsLS0JykgoYETUys7ccQAANGjVTXIuX768fft2o0JbW9uhQ4dKJBKFQqFWq8VClUrl6Gg8lYy9vb2+AmNMrVbr65SWlj7zzDMuLi6ffvppZaNq3779lClTpk+fLj5VKBTu7u76Vz09PSu7Q3g8fKU1SC6X29jYIMmpWfX6J7o9XCjU6cY14Qb4uZk3EhcrbVoRIyI7W1tPTyujVz08PE6fPi0Igvg0KCiobdu2tR1ifSBOw+1qhZYcAAATqm6SM2PGjBkzZjzq1ZYtW966dUvssXbr1q0WLVqUrRAbGys+vnv3Ls/z3t7eRKTVamfOnKnVavfv3y+VVjpIiUTi6uqqbxECAKinBEbfxQhEtKi9+Sc0c5Q/eFBuR2eO45o3b65/amtry3G4ji+HmOS4yJ9UDwAAqsG0Y3JmzZr1zTfflJSUqFSqLVu2PP/880TEGHvjjTcSExOJaObMmceOHRPznHXr1k2ZMsXGxkan082ePTs1NXXz5s1qtTo3N7e4uNikcQIA1E2H7wvxKuZrx43xMX/C4GDxIAZMPFAdmUWMHq47BAAAJmLaJGfx4sVeXl6enp5NmjQZPHiwvs1n8+bN4vicNm3arFmzpm/fvh4eHmFhYZ9//jkRZWVlHTt2LCoqqn379r6+vr6+vnv37jVpnAAAddNnEQIRLWnP14W8Qt+Sg4kHquNhdzVzxwEA0KCZdqYeS0vLvXv3qtVqnufFcf9ExHFcbm6uvs7SpUsXLFhQWFion6LA3d09JyfHpIEBANR9lzLYX2nMSU6BberEZMP6JAfr5FQHuqsBANSC2piOVKFQPL6ChYUFhlkDABj56IZARIvb8zYyc4dCRESOD7uroSWnOrKLGRE5o7saAIAp1Ym7gwAAYOSmkh2+L1hJaXEH8085IPpn4gFcn1dVfikV68hWRpZ15X8VAKBhQpJTD6jV6g9WriwsLLx3715oaKi+/Nf9+zs2axYXF7cjOHj3jh1ZWVmThw27fv26GUMFgJryWbggMJrbmnetM4vNIMmpvizMOgAAUCvMt3o2VIxarZ4waJBnTMzIgwdzs7N5jeaLnTtHjR175LffPp437wulckT37j6MFXPce3L5/OzsmSNG/BwS0rVrV3MHDgBVd7+A7bgjSDh6rWMduhXliNnVqu3BgJw6k7gCADRUSHLqNI1GM2nw4GnR0eOLi4dGRf3IWFuisTNnhi5ceOzbb4/k5v6PyDMvbytRANGHRAFE47Kzp44YsfX4cXF5IgCojz6+IZQI9Lwf72tXh/IJJ8yuVm1IcgAAakcdukcIRjQazcRBgwKiosYXF08g+omxIUTuRMtzc3d//LGY4fxEtINoGtFKogAiImpDdCA7e/aYMWFhYeaNHwCqJlHNfrwlSDh6p2vdOkQ7obtatT3oribHNwgAYFp16wwKekYZzjdEg4mI6AjRBqJzjIkZzlaiaUTvEj1lsC3yHIB67aPrQrGOZvjybR3q1qWw48NL8/p+5tBqtbdv31YqlbX/1ployQEAqBX1/VTVMJ1NY916Dx8fEflUcfF4ou8fZjg6ojlE/yW6RrSO6CjRcqJn/p3hiNoQfZedPXLYqDcuad+8ovs8QghJZmptLX8OAKi0+wUsOFaQcBTUrc4dn53kRCUaijzOc/VgnZywsLCBAwfa2Ni4u7sbloeHh/v5+U2ZMqVly5ZffPFFLUeVjYkHAABqBcbk1C05xfT6Jd1PtwRZh6d/iY+dVloiJVI9fFVCdJxoLtE2InuiA0QfE00lGkpkNP4mk+hFawfVzG8/i2D0cNk+KU8dHDg/e87PjjytOBdL8lZwA9w5WZ27lAJovD66LpQINNOPb2Nf566DS4s0Tp8Nc0yNPVvy2qKNH5g7nCdwdHR88803NRrNkiVLDMtfeeWVefPmvfPOO7dv3+7evXtAQEDz5s1rLaqsYiK05AAAmB6SHHMqEehUMrtXwFI07H4B3S9g4Tksu5gsJbR8xauFneUzPws6kKd8mqiEaAIREfUgCiZ6nmgH0SIiIjpANJVoq0Gek0k00t5hxifftxgakF1MOkapGnYpg/2dzW7ksBs5/7oF6yynp1vws1rxA9zr3BUVQGNzO48F3xKkfF1sxtFoNJOHDHknOXpxadHk7Rs+cqa3P6jTeY6vr6+vr+/Zs2cNC1NSUs6ePbtv3z4iatWq1dChQ3fv3v1///d/tRYVJh4AAKgdSHLMRlVKY49rz6cb9/rw9+S+HyhpZc9Rz8Wb7WluUNA+pfJpInqY57gQFdnZPctxO/PyFhEJ/85zMonGOji8/8MPTwUEGO1ZraWoXHY3n93Np8willVE4TksMpdtuilsuil0ceIWtOOHeXEtbTlpnbu+AmgU3r0qlAo0r22da8YRM5ynIiMXlRYR0W8F+dP++9+PqK7nOWXdu3fPwcHB2dlZfOrn53fv3r1K7UGn0+Xm5l69elVf0qFDB0vLimYtWCcHAKAKYmJiNBqN+Pju3bvFxcVP3ARJjnnoMxwfBTfah/NRUFMbrqmCa25LfgYzxs5bvJiI5gYFbVcqR/L8JsY6MzbByWnLgQMymWzmpElzlMq3JZKPGXuOaBJjW7Xatx0dg374YfLUqWXfVCGl3q5cb9d/nVwjctgvd4Wfbgk3ctjC8zoikvHU0pZrYkPe1lwHR66PG9fDhVPglwJgYn9nsb1xgpWU3qtjzTj/ZDhFRWKJBdHevDyz5zmRkZEbN24sW75mzRonJ6dyN1GpVFZWVvqn1tbWGRkZlXrTxMTEsLCwuXPn6ktWr17dt29fItJoNDqdrrCw8DGbpxXYE0k4dXZ6uq5S79s4ZWZm8nzd+nOo1yryE4VKwU+0Zmk0mtLS0rIJDGPsP//5T0FBgfg0Pz/f2tr6iXvDpasZ5JXQhN+159NZMxvuz/GSFraPu6U3b/Hi0pKS/m+9FfTee0GbNhWrVMGHDvXr35+INv/vf6tWrDi/Y8esiROlUumhLVueHjfuq2+/LTfDeZROTtzHTpJVPSQH4oWf7wpRuXSvgMXmsdg80g/mkfE0qRm/oC0/3JvD7UcAE3nrio4RLW7Peyvq0N+ZTqebNHhwQFTUwocZjsiCaE9eXsCGDf+1sVlSi929DNnZ2ZW78LGFhcWjNnF3d8/NzdU/zcnJ8fDwqNSbNm/efOTIkXv37i37kkaj0Wq1dnZ2j9k8V1tKRG28XNysHlMLHhAEwWjeCKiOivxEoVLwE61ZGo2mpKTEwcGh7Evnz5/XP/7111+3bt36xL0hyaltSWo2/oQuPIc1rUCGI3p52bJJ06f7+PjMCgzMzs5u3769WN6vf//j588TUUhYGMdxcrk8Pj29alFZ8DTDl5/hyxNRkY7iVCyxgBLV7Fo2u5TBbuSw/fHC/nihrQP3Vhf+OV8e/dkAatbJZPZ7MnOwoDe7SMwdy79wHGdpba0u71aljqiI46wUitqPStS0adOXXnqpUpv4+flJJJLw8PDOnTsT0cWLF5ctW2aa6MohMMotJs5gxSEAADARJDm16nw6m/GHLknN2jtwR8dImtlU9H6tj48PEbm7u5d7w6Di3cErwlJC7R249g5E9CC8VA1tiRU2xwo3lWz2Gd0H14T57fgJTbi6togHQD2lY7T8ko6I3uoqqWuXvzzPHwgJmTZqVMnly28b9HLREE12cJjy7rv/WbzYjOE9hkqlOn78eExMTHFx8d69e+3t7UeNGqVQKObOnbtkyZJPP/305MmT6enpAWWGL5pOTjHpGDnJCfeJAABMDQfa2pBZREsv6Jrt0g48pE1SsyGe3F8TpRXPcMzO05re7cbfnS79aYiklT13J5+tuKRrt0/bao92UajueLqFqtTcIQLUZz/EChE5rKUt90qHunhMtrCw2Pv775d69/7o4WgWMcN56t13Fy1fbt7YHkOj0YSEhCQnJz/zzDMhISEXL14Uy9euXevv779ixYqYmJg//vjDcIiOqYmzDrhi1gEAANNDS47JFWpp/AntlUxGRF7W3HO+3JqeEnnd6pBSIVKeZrfin/fj/3dP+O0eO5oo3Mlnd6IZkd3SG6Wz/PjFHfj2aNsBqKS8Elp5VUdEa3vzdfbIIOY500aN+ujy5VcLCyfZ20+p2xkOEbm7u2/atKlsuVwuX7Vq1apVq2o/JMwfDQBQa5DkmBYjCjynu5LJfO24X4ZKernW+4H7Eo6mNOenNCcdk4RlspPJ7H9xRWG5sm9jhO9iBH9PbkE7fkpzHguMAlTQh9d1GYU0yIN7ukWd/rOxsLDYc+JEwIgRP127tvDNN+t4hlM3ZRVj/mgAgFqCJMe0Pr4u7Lwr2Mnot5GSDo4N6sQm4aiPG9fHjQv0yMu18vhvlLDjjvBnKvszVedupZvhy8/05Xu5NqiPDFDjYvPY+kiB52hd37raiGNALpfvDwk5derUwIEDzR1LvYSWHACAWlOnbxzWd1ezWNBVHc/Rz0OlDSzDMdLegft2gCT5Odk3/SWdnLj0QlofKfT+Tdt+n/bzCCEdM/IDPMLiUF2JQP9pw/dwqR+HCLlcPnjwYHNHUV8hyQEAqDVIckxoxSWdwGhZR35C0/px+VJNdjJ6uT0fPlUa9pT01Y68hxXFKNmKS7omO0uf+UN3No2ZO0CAumVPnBCSzFws6aNe9aAZB6pPnHjAWd4ozggAAOaFJMdUDt9nf6YyZzm9063RXb70cOHW9ZUkPiv73yjJ5GY8I9oTJww5rO12UHsiCakOABFRQSktvyQQ0ce9JM51bNpoMBGxJccVLTkAAKaHJMcktAK9cVlHREHdJA6PXHq7gZPyNLEp/+tIyb0Z0pXdeE9rup7NxhzXjjqmvZqFVAcau6CruiQ16+PGzW2N43BjIbbkYOIBAIBagJOrSXweIcQomZ8dt7A9vmHysuZW9ZDEPyP7rI/EUU4nk1mvX7UTTmjPpzPkOtA4XchgG6IEGU/fDZDwuOJtNLKKiTAmBwCgVmB2tRoWnsNeuaA7ncqIaG1v3gI5zkNyCb3eiZ/bml97Q7cxRjiSyI4kat2saJgXP74JF9Cct8KPERqHYh0FntUJjN7qwnd1RorTiGDiAQCAWoNr8Jp0Pp31/FV7OpW5WlLwYMnU5vh6jTnJaW1vScIM2TtdeR8Fl1FIu+4Ks07rvHeWLr2gS1ChaQcavtXXdDFK1s6BC2p8A/YaOXRXAwCoNbgKr0lfRAilAj3ny9+aLnsR/ewfzVlOa3pKEp+V3pwm/bq/pLcrl1tM/40S2u7Trrikyy02d3wAJnM5k30aLkg42jJYIkeO05iUCpRfQjKe7BvrQE0AgNqEC/Eak6qhQ/cFGU9f9m28kw1UVht7blF7/tJk6fWp0ll+fKlAn0cIvntK37qiS9GgVQcaGrWWZp3WaQV6tSPfzw238xuXrCJiRM5ywn88AEAtQJJTY368JWgFmtSMd7cydyj1UBcnbpu/5OpT0pHeXG4xfXJDaLFLO/uMLiIHqQ40HMsv6m7lsc5O3Ic90YjT6KCvGgBAbUKSUzMERltiBSJ6qS2+0qrr6sz9PlZ6ebL0mZa8QLTtttDlgHbcCe35dKQ6UO8dui98f1OQS2iHPzqqNUaZmHUAAKAW4Yq8ZpxKYXEq1sKWG+GFu3TV1cuV2zVMcmuadEkH3lpKxxLZwEPakce0f6QwAckO1E8JKvbiGR0j+qinpJMTjhKNkdiS44qWHACAWoEkp2ZsvikQUWAbHkte1JQWttyGfpJ7z8pWduMdLCgkmQ0/qm22S7v8ku5iBrIdqE+KdPT0KV12MU1oyr3aEUfdRgrzRwMA1CacbmtAiob9dk+Q8vRia6Q4NcxZTqt6SOJnyFb3kDS35ZLU7MsIod//tE12aheFYsQO1A+LQ3VXs5ivHbdtiBT3QRotrAQKAFCbkOTUgG9jhBKBpjTjvaxx/WISDhYU1I2Pe0YaOkn6ake+uS2XomEbo4UuB7Sjj2lPpSDVgbprQ5SwJVawktL+ERJHubmjAfPJLmJE5CzHaQIAoDYgyamuIh1tihGIaGkHfJmmxRH1c+PW9ZXEPyP9e4p0cXveWkq/J7MRR7VDDmvPpiHVgTrnQILw2kUdR/TDIEkXDMVp3NBdDQCgNuG6vLp23hUyi6iHCzfQA1cwtaebM/ff/pL7z8o+7ClxltPZNDbksHbwYe3BBAHDdaCOOJ/Onj+tExit6Sl5zhcH28YOU0gDANQmnHera32kQESvYDCxOTjJ6e2ufNwM2aoeEkc5nUtjU0N0vnu0Ky7pQtMxOQGYU0QOm/S7tlBLC9rxb3fF8QEwhTQAQK3CqbdaTqeyGznMw4qmt8A3aTZ2MlrZjb8/Q7ahn8TXjktQsc8jhAGHtN6/lC48rwtJZjpkO1C77uSz0ce1OcX0VDP+6/5YEweIHnZXc0WSAwBQK3BpXi1iM86Cdljaz/xsZLSkA39rmvTcBOnyTnxLWy6tkL6LEUYe07bcrf3gmpCiQa4DtSFJzUYe06VqaIQ3t2uYRILeSUBERFnF6K4GAFB7TJvkZGZmTpgwwdbW1s/P7+DBg2UrMMbeeecdV1dXFxeXFStWCIJARMXFxUOHDnV1dbWysurdu/epU6dMGmSVxanYofuCpYQWJfrLwQAAIABJREFUtkOuWFfwHA304D7vI7n7jPTvKdJ3u/F+dtz9Arbyqq7ZLu3Tp3SnUhhyHTCdeBUbcliXoGL93LiDI6S4/QEitZYKtWQlJWupuUMBAGgcTHu4fe2115ycnDIzM0NDQydPnnz79m0PDw/DCvv27du1a9f169elUunQoUM7duw4e/ZsiUTy1ltv9enTx9LSMjg4ePLkyenp6QqFwqShVsGGKEHH6AVf3s3K3KFAebo5c92cJat70Klk9v1N4dd7wv54YX+84GFF45rwY5twQ714Z0zpCzUnNo+NOKpLUrPertyR0VIbmbkDgjpDnHXAFc04AAC1xYRNEPn5+fv27QsKCrK0tBw2bNjAgQN//vlnozpbtmxZuHCht7e3u7v70qVLg4ODiUgqlY4aNcre3l4ul8+ePVutVmdkZJguzqrJK6EfYwUiwvrldRxHNMKb2zNccm+G7IMekua2XFohBd8Spp3Sue0o7X5Qu/KqLkGF1h2oriuZbMhhbZKaDfbgQsZJsSQOGML80QAAtcyEF+j37t0jolatWolPO3XqdPv2baM6sbGxnTp1Eh937Njx1q1b+pcuXbq0f//+F1544bnnnmvRooXp4qya4FtCfikN9+I6Y+2LesLTmt7txsc/Iw2fKl3bWzLMi7Pg6Vo2++Ca4LtHO+6E9kCCUCKYO0qon/bHC/5HtOmFNMaHOzZGaos2HPi3B0kOUl8AgNpS3e5qR44cSUxMNCps0aLF6NGjc3JybG1t9YV2dnZxcXFGNXNzc/V17OzssrOz9S8dOHAgOjo6IiJi+fLllY3q2rVrW7Zs+c9//iM+tbe3//vvv62srIgoPT29snsrS8foq3AnIv4Fr7zU1JLq77Beq5GvtDa5EM1ypVmuVCxwl3Nke5Lkh1MtjiXSsUSds0XpZK/iYa6lfZ1LrSXmad5RKpUqlcrCwsIs794gmfQnyoj+e8d6baw1I5rZtOijDgV5mZRnuverA9RqtSAIarXaqDwiImLMmDHs4ag3juOWLFlS69HVUVgkBwCgllU3yUlISIiJiTEq5HmeiFxcXPLz8/WFSqXS1dXVqKazs7O+Tl5enouLi/6ltWvXElFKSkq7du369u3bq1evikfVrVu3l19+OTAwsNxXPT09K76rcp1MZvc12tb23PNdnHmcs2riKzWX5t40vRNlF9OO20LwLSE8hw9OsApOsLLgqa8bN9SLG+bF93XjLGqxT6JcLrexsUGSU7NM9BPNL6XZp3W/3hN4jj7tLXm9ky2R7ZM3q+cKCgoEQbCzszMq9/T0FCePES1YsKB9+/a1G1rdhUVyAABqWXWTnEWLFj3qpaZNm/I8Hxsb26ZNG3p4k8+oTps2bcLDw8XyiIgIsaYhLy8vHx+fe/fuVSrJMbWQZIGIpjbnkOE0DM5yeqUj/0pH/u8sdvCecDKZhWWys2nsbBpb9begkJK/Jzfahx/bhPOzw385PBCew6ad0t3KY45y2u4vHd8Evw14pGzMHw0AULtMeIPa1tZ2+vTp77//vlqtPnbs2IULF2bOnElE0dHRzz33nFgnMDBw48aN8fHxSUlJ69evnzt3LhHFxMScPHkyOzs7Kytr/fr1SUlJ/fv3N12cVRCSwohohDemHGhourtwH/SQXJwkzZol+22k5JWOfCcnTqOlI4ls6QVdqz3aNnu1S0J1BxOEnGJzxwpm9W2M0Oc37a081sWJuzIZGQ48QXYRERGmcwQAqDWmnUJ63bp18+fPb9asmbu7+86dO93c3IioqKhIPzgnICAgJiZm0KBBjLG5c+c+//zzRKTT6dasWXPz5k2e5zt37nzs2DEvLy+TxlkpWUV0PZtZSWmAOy5rGiwHC5rUjJ/UjIgoVUMnk4VjSez3JOFWHruVx76OJo50re25Xq5cb1eujxvXzZmTIedtHDIKacF53cEEgYjmteXX95VYYeUTeBK1logIs4oDANQa056cnZyc9u7da1TYvXv3ixcv6p++++677777rmGFjh07njlzxqSBVcefqYLAaIA7Z4ll/hoHT2t6oRX/QivSMcmlDHYqhf2RIlzMYLF5LDaP7bhDRGQpof7u3Ahvfpgn18OFkyLhaaB2xwlLQnWZRWRvQZsHSaa1wP80VEiRjogIZw0AgFqDO5CVFpLMiGiEFy5uGh0JR/3duf7uXFA3vlSgiBx2OZNdzmSXMtjNPPZHCvsjRUdECin1duV6uXJdnLnOTlw7B06CNr/6724+e+2icOi+QESjvLnNgyRNbfD/ChWFJAcAoJYhyam0B0mON65vGjUZT91duO4u3IJ2REQ5xfRnihCSws6ksptK9mcq+zP1wUS6Cil1c+F6uXBiguRljV9OPVNQSmvDdZ+HC0U6crCgz/tI5rbBnCNQOUVaRkRy3PAAAKgtSHIqJ07F4lTMWU7dnHGugn84ySmgBR/Qgogoq4guZAh/Z1F4DruWzeJV7K809lcaWxdJRORhRR2duA6OXCs7zteOa2VHzWzQva2OKtbRdzHCh9d1mUXEEc1pzX/SS+JuZe6woB5CSw4AQC1DklM5p5IZEQ314nEjFx7FxZImNuUnNn3wNLuYwjLZxQwWmi5cymRphZSWzMT2QJEFT752XBdnrocL18OFaynhbMwTOPyjoJS+vymsixSS1IyIBrhzn/eR9P1/9u4zIIqr6wP4mWV36b2DCAqWYNQogr1GFIy9xRILKk8wlmg0GhOjMZYkGn01MTFqrLEkojHGGmPHrliwoCIoIr1J2V7m/TBkQxZUhN0dhP/v05TLznGcndkz584dN3ztoZKQ5AAAmBiSnFfzz+DR+K0DFeVsTj3rMD3rMNyI7Y+L2Nv5dPcZm1jIJhayCYWUUszGP2Pjn7G/JhIRCRibRnbU3EXzhgPTyJ7qWDM+1uRhZdIXktZmj4rYn+K16+9r8xVERM2dmEWtzHrXxVceqkTBJTm45AIAmArOuK+AJTqZpiWit73wiwcqyc+W8bOl0j+aZWq6X8Bey2Vjc9ir2eyNXDa+gOILtKX/iiFytyRvaybAjnnDgQl0pDcdmQZ26OdmMEotHXii3fRAeyiF1bJERJ08mFnNzXr5MPi2Q9WhkgMAYGJIcl7B/Wdstpy8rPDaezAkSyG95cy85cyMa0hElJGTl6S0eVAsvFfAJhRQqpR9KqEMKZshowwZG5vzn35ujRyYhvZMQzuqY83UsSZ3S8bTilwtGLy5pYI0LMVksLuStLuStLkKIiILMxpaXzA5UBDsiq85GAyX5JjjrgQAgKngp9AriMlgiaijB376gBGJBdTKhdr9d4xyDUuZMvZJMd0v4Pq20e089lEReyuPvZXHlv0QWxHVsWa8rMjfjmlgzzS0o0BHpp5t9R3Metf27ScOHly9datQaIqTUqGKjqVqD6WwB55oM2UlC5s7MWMbCt4LELhYmCAEqF3kGpaILITV9RsIAFDjIMl5BVyS0wFJDpicGUNeVoyXFZV+9l2ipvvP2AcF7INCSpWwaVI2XUpZMsqWs0Uq4nKh42n/pkDmZuRrw3hbUR1rxtmCnM0ZZwtytSBnC8bVglwtGBcL4iUL+m379pVTpnRQKN7r02fb/v3GyHO0LN0vYGNz2MvZ7LlM9mYuq/lnxzSwZ4bUY96tL2jmhK82GAu6qwEAmBiSnFdwNhOVHKhGrIUl7+opuypfQWlS9qmEHhayCYVsfD57r4CeFLMPCtgHBURUTvGHiMwYcrdk6lhTXRumni3Vs2Xq2jB1rcnTinEQk5Ge/4neuXPFlCmH8/OdiObHxAx/552dBw9WPc9RaOhOPhuXx97IYy+m2d8tUhWp/l0rElA7d6aXj6CXD4PcBkxAgSQHAMC0kORU1FMJ+6iIdRBTU0f8JILqztGcHM2ZJo7Uk/49XKVqSi5mUyWUJmVzFZQrZ3MVlC2nHDmbLaMcBZstozQpmyaly9nld4ETCshRzJgJyF5EDubkYsG4W5KHJeNlRd7WjJcVOZszTuavkA5F79z57aRJXIZDRAskkvnnzlUwzylUUb6CzVdQnoLyFGyWjLLkbLqUHhWxiYX0RMKq/x27QUREvjZMkAvTypVp784Eu+CxJTAdlkihIYbIHEkOAICp4DpfUVxftfbuDN6QA68pKyG94cC84UBE5R/EKi1lyNiUYkouZh8V0eNi9qmEfVJMmTL2mZK4Ski+onT+U35FSCQgGxERkaUZw926thaRWEDWQrIWkY2QcTAnKyE9OfZr4rLJJwufOZX62wUSyacx59p26vXOdwfkrFmRilRaeqYgpZYkajZfQRI15SnYPAWpteVuvIRQQIEOTFMn5i1nxk+Q372BM560Ab4oNMQSmZs954sHAABGgCSnori+ah08MDgO1FgiAflYMz7W1M69nB9jRSpSaqlAyaq0VKCkAiVlydgsOaVJ2HQZpRSz2XLKVbC5clJpiXvJTH75WRBLRJT9yGrB+GS1wqnM6iUyyY3Ys4uXLFX3mv2CaO1E5GjOOJqTo5icLBhXC3KzIDdLxs+WCbCjerb/vlkoPV2JDAd4hAdyAABMD0lORWFoNajlbEVERM7mpb8C5X8dlFqSqIiIZBqW+3lXrCKVlopUJFGTtKQgE3D03qSI33/eW1yodxr6zUx436POtCnvuziZ2YhIJCBHcxIJyEbI2IvJRvTKneIA+IUHcgAATA9JToXkK+hOPmtuRkHlPeQNAKWJBSQ2JyJyLD8LKlk4fcvy+a7M8PXrdxb+m+dEC4Ur6tW7cvGik1PZGg/Aa6lk/OhqO4I7AEBNhHuhFXIuk9Wy1NqVwa04AANa8O23gZGRw+3s1EREFC0Ufluv3mFkOFCzoLsaAIDpIcmpkAtZWsIbcgCMYMG33zYeP/49e/vtQuEKf/+/Ll9GhgM1DJfkYGg1AABTQne1ConNYYko2BVJDoDhLVyxYh7DfHfo0F8XLjg4OPAdDoCBydVEqOQAAJgWKjkVciOXJaKWzkhyAIziy+XLL8XHI8OBGgnd1QAATA9Jzss9lbCZMnI2p7o2SHIAAODVKLRESHIAAEwLSc7LXcthiaglxlUDAIBXJ1ezRGQhxEUEAMB0kOS83LVcJDkAAFBJ6K4GAGB6SHJe7nouEVELPJADAACvrmR0NVxvAQBMCCfdlyvproYkBwAAXl1JJQejmQIAmBCSnJfIkdNTCWsnIn87JDkAAPDKFOiuBgBgckhyXoJ7Q85bzowAOQ4AALw6PJMDAGB6SHJeAqMOAABAVSDJAQAwPSQ5L3E9hyWMOgAAAJWl0LBEZG6G6wgAgOkgyXmJ67lIcgAAoPJKRldDJQcAwISQ5LxIoYoSC1kLM3rDAUkOAABUBrqrAQCYHpKcF7n/jGWJ3nBghNhPAABQKUhyAABMDz/eXyShkCWiBvYo4wAAQCVhCGkAANNDkvMiDwuJiALs+I4DAABeW6jkAACYnuCjjz7iO4bqK7GQJcJrQAEAoPLkGpaILDC6GgCACQlOnz7NdwzV18NClogCkOQAAEBlYXQ1AADTE3z22Wd8x1B9/ZPk8B0HAAC8ttBdDQDA9ARTpkzRarV8h1EdFaooS0ZWQvK0QiUHAAAqCQMPAACYniAtLS0tLY3vMKqjhIKSvmpIcQAAoNJQyQEAMD0BEVlbWxtvA0qlMjU1VaPRvKBNWlqaTCYzXgyV8xDjRwMAQJUhyQEAMD1Bly5dHB0djfTpv//+u5eXV6dOnfz8/C5evFi2wePHj5s1a9a2bVsvL6/ly5frrR07dizDMPfu3TNSeC+G8aMBAKDq5GoiDDwAAGBagh07dhjpo4uLi8eNG7dr167ExMR58+aNGzeOZVm9NjNmzOjWrVtycvKVK1e+/PLL0vnM4cOHc3JyjBRbRZSMH22LSg4AwOuHZdnr169v27bt0KFDUqm09KrExMStW7eePHmy7FXJGDCENACA6Qk8PT2N9NEHDhzw8fHp1q0bEY0dOzYtLe3atWulGxQWFv75559Tp04looCAgPDwcF3GVVhY+PHHH//www9Giq0iSoZWQ3c1AIDX0HvvvTd8+PC//vrr66+/btSo0ePHj7nl+/bta9269ZkzZz788MMRI0aYIJKS7mpCE2wKAABKCAcNGrRnzx5jfPSjR48aNWrETYtEIj8/v6SkpKCgIF2Dp0+fMgxTr149brZhw4aPHj3ipmfNmjVx4kQfH5/KbVqlUmVnZyclJem2XomPwvjRAAAVp9VqdYkEERUWFr74aUxjW7Bggb+/P8MwRDRgwIAVK1Z89913LMvOmTPnu+++GzFiRGFhob+//9WrV1u1amXUSDC6GgCA6QnPnDlT6T9mWXb27Nlllw8cOLBNmzaFhYWWlpa6hTY2NgUFBaWbcQ2Yf0Yvs7a25hqcOnXq5s2bVSnj3L9//+DBgz/99BM3a2VldeDAAS6YzMzMinyCRM1kSJ3NBaygICO9sNKB1AoV3KVQQc+ePSsqKhKLxXwHUnPgEDUsiUSi1WolEone8jt37kRGRuo6gOXn53t4eJg8un8FBATopr28vBQKBRElJiYmJCQMGDCAiOzs7Hr06LF//36jJjlalpRaEjAkFhhvIwAAoE/o4uJSlb8v9xpmZWVFRG5ubrdv39YtzM/Pd3d3L93M1dW1uLhYo9GYmZlxDdzc3IhoypQpgwcP/v3337mL5ZEjR8zNzXUFn4p48803IyMjx48fX+7aivTQu5HLsqQOsBd4exmrO19NYrxOj7WQubm5jY0NkhzDwiFqQMXFxVqt1s5Ov8zt6empq8YTUVRU1NOnTydOnLhkyZKMjIzvvvuu3E9r3br12LFjjRctESUlJe3cufPgwYNElJqa6uTkpLsB5+3tnZqa+kqfVlRUlJiYuHr1at2SsLAwLy8vIpJKpWq1Wij8T780qZqIROZmpPdcEFSETCbDfjOgcg9RqAocooYllUqVSmW5P4F+/fVX3a6Oi4vLy8t76acJO3ToUOlQGIb56KOPnre2adOmy5Yt02q1AoEgPz//4cOHTZs2Ld3Ax8fH3t7+6tWrrVu3JqIrV67069ePiMLCwri393BJzoULF4KDg18pyam6kvGj7fBADgBAJT1+/Pjy5cvz5s3Lyck5fPhwuW0sLCwq/fkxMTEffvhh2eWHDh3S3YDLycnp16/fzJkz27ZtS0QajUYg+LekIhQKVSrVK21UJpPl5+fHxsZyswKBIDg4mLtdqFKp1Gq1Uqks3b5IyRCJzAWs3nKoCJVKhf1mQOUeolAVOEQN63mHKMuyN27cKCoq4mafPHlSkXfPCJctW2b4GImIqFu3bvb29p999tmoUaO+/vrr0NBQPz8/Ilq9evWjR4+WL18uFosnTJjADTBw4cKF69evR0dHE5EuJK1Wu379+gULFjRu3NhIQT4Pxo8GAKii8ePHv//++0Tk6elZ+nEdQ3nrrbc2b95cdrmzszM3kZ+f36NHjz59+nz66afcEg8Pj7y8PN3N7MzMTK4IU3Fubm6tWrXatGlT2VVisVitVuvVuGRSIlJZChkHB4dX2hAQkUwmw34zoHIPUagKHKKGJRaLlUplubu0dHeAP/74Y8uWLS/9NKHx/m8EAsGhQ4c++eSTUaNGtWrVauvWrdxyJycnXb1p4cKFCxYsGDdunJub25EjR5ycnEp/AsMwQ4YMsbW1NVKEL1AyfjQqOQAA1ZWtrW2zZs2et7agoCAsLKxz585LlizRLWzYsKGLi8vp06fffvtttVp94sQJ3dObRoLxowEAeGHcfpn16tX77bff9BaWHrLT3Nx8yZIlpa9ApTEMs2vXLiPG93xJRUhyAAAMQyKRHDhw4Pr16/n5+RYWFv7+/r169So9MIAxREZG3rt376233uKqSW+88ca0adOEQuEnn3wyfvz46dOnnzx50s3NLTQ01KhhyDG0GgAAH4S3bt3Se1QGiChdSkTkZcV3HAAAr7lDhw6NHTs2Ozu79MLp06dHRUWtXLlSJBIZabujRo3q3r27btbb25ubmDJlSkBAwOnTp7t16zZu3LjSj+gYA5fkmCPJAQAwLWGXLl1yc3P5DqPayZKxRORuiUoOAEDlxcXFDRw40NXVdfXq1Z07d/bw8JBIJLdu3frxxx9//PFHKysr4z0X2qdPn+etCg8PDw8PN9J29aCSAwDAC6GR3gT6WlNrKV9JZgw5mfMdCgDA62zRokXOzs5XrlzRDXfm4uLi6+vbu3fvqKio7777btasWa6urvwGaVRIcgAAeCHo0qUL3zFUO1lyVsuSqwUJUMgBAKgsrVZ78ODBmTNnlvtGtcWLFxPRX3/9ZfK4TEqBJAcAgA94A3M5smRERG7oqwYAUAU5OTlSqbRr167lrnV2dm7evPmtW7dMHJWJYXQ1AABeCCIiIviOodrJkhMRuVvyHQcAwOuMe1uAu7v78xq4u7tX5K3VrzW5mojIAq+YBwAwLcGBAwf4jqHayZSxhEoOAEDVqFQqIuJeu1kusVgsl8tNGBEPSkZXQ7cJAADTEubk5OTl5em9hbOWK+muZsF3HAAAr78zZ87Y29uXuyorK8vPz8+04ZgaBh4AAOCFkIiePXuGJKe0LFRyAAAMZPDgwS9YW+OTnJKBB9BdDQDAtIQikajccW9qM+6ZHDc8kwMAUAUeHh67du16cRtfX1/TBMMXVHIAAHgh7Nmzp5WVFd9hVC+ZeBMoAECV2draDhkyhO8oeIYkBwCAF4KVK1fyHUO1g2dyAADAIBQalojMMYQ0AIBpCfz9/fmOodrhkhwMIQ0AAFWE0dUAAHiB8245suUsEbla4MYbAABUCbqrAQDwAkmOvmdKkmvITkSWGAwHAACqRo7R1QAA+IAkRx/GjwYAAENRoJIDAMAHJDn6MvFADgAAGAi6qwEA8EJw584dvmOoXlDJAQAAQ5FjdDUAAD4ItmzZwncM1UvJm0AxfjQAAFQZKjkAALwQXLp0ie8Yqpd/3gTKdxwAAPD6Q5IDAMALwdOnT/mOoXrJ5io56K4GAABVhoEHAAB4ISgqKuI7huqFG3jADZUcAACoMlRyAAB4IdBqtXzHUL2UDDyAN4ECAECVIckBAOAFhpDWhyGkAQDAULgkxxxJDgCAaQmaN2/OdwzVC4aQBgAAQ5GrWSKywBDSAACmJTh+/DjfMVQjSi0VKEkkIEdzvkMBAIDXH7qrAQDwAt3V/iNLxrJErhYM7rkBAEDVKbRESHIAAEwOSc5/4IEcAAAwFLWW1FoyY0iIiy0AgGnhvPsfWRg/GgAADAR91QAA+IIk5z+y5CwRuWPUAQAAqDIkOQAAfEGS8x8lbwK14DsOAAB4/Sk0LBFZCHHjDADA1JDk/Ec2xo8GAAADQSUHAIAvSHL+IxPP5AAAgIEgyQEA4AuSnP/gnslxs0AlBwAAqopLcsyR5AAAmBySnP/AENIAAGAoqOQAAPAFSc5/YAhpAAAwFAWSHAAAniDJ+RdLlC1nGSJXdFcDAIAqQyUHAIAvSHL+la8glZYczNF/GgAADEDODSFthhtnAACmJjT2BuRy+bVr11xcXBo2bPi8Nrdv35ZKpS1bthQKS+JJSUlRqVTctIWFhZeXl7HjJKJMGUYdAAAAg8HAAwAAfDFuknP//v3Q0FA/P78nT5506tRpy5YtDPOfFEKpVPbr1y8xMdHJyenZs2cnT5709PQkop49exYUFFhYWBBR69atd+zYYdQ4OXggBwAADAjd1QAA+GLc7mpz58599913z5w5c/PmzVOnTh0/flyvwa5du1JTU+Pi4i5evBgSEvLVV1+VXpWYmJiYmGiaDIf+GT/aHW8CBQAAQ5CriZDkAADwwYhJjkql2rdvX0REBBHZ29sPHDgwOjpar010dPSIESO4ik1ERETpBvn5+Y8fP9ZoNMaLUA/eBAoAAAak0BIhyQEA4IMRu6tlZGSoVKp69epxs35+fkePHtVrk5KSMnz4cF2DzMxMhUJhbm7OMMzUqVNZli0sLPzhhx+GDRv2SpuWSCR37949duwYNysSiTp16qTXU66sLDyTAwBQWTKZ7Ny5c7rZ1NTUxo0b8xhPdaDAMzkAADypapLz/fffnzlzRm9ho0aNFi1aJJVKGYYRi8XcQgsLC4lEotdSJpOZm5vrGrAsK5fLzc3NT5065erqSkR79+4dOXJk27ZtfX19Kx5VamrqtWvXrl69ys1aW1v7+flx9aLs7GyBoPz6VXKeNZG5haowM1NR8W3BC3YpVEJ+fr5EItF9caDqcIgalkQi0Wq1MplMb3lCQsKiRYtYluVmExMTmzRpYvLoqhellohIjKMPAMDkqprktGvXzsfHR2+hk5MTEXl4eLAsm5eXx6Urubm53KACpbm7u+fm5nLTOTk5lpaW9vb2RMT9CRENGDDAz8/vypUrr5TkNGzYcMyYMePHjy+7SqvVuru7l/tXRYyGSBvgZufujivSK3jBLoVKEIlENjY2SHIMCIeoYRUXF2u1Wjs7O73l7u7up06d0s1GRUXpKvm1lkbLEpGZAB0EAABMrapJTlBQUFBQULmr7O3tGzVqFBMTM3DgQCKKiYnp0aOHXpuQkJCYmJgJEyZwDUJCQvQaSKXSrKwsLmsyNm4IaQw8AAAABqFmiYiEuKoAAJiccYeQnj59+syZMwUCwe3bt2NjY7dv305ECQkJISEhycnJdnZ2UVFRLVq0WLVqlaen54IFC9avX09E8fHxa9eubdOmDRGtXbvWz8+vY8eORo2Tky0nInLFwAMAAGAIai0REd4FCgBgesZNct5//30rK6sdO3Y4OTnFxMQ4OzsTkYODQ2RkJNcbp379+sePH1+zZs3FixfXrVvXt29fInJzc3NwcNi3b59AIOjdu3dUVJRIJDJqnJxnCpaIHMW4HAEAgAGUVHLQAxoAwOSMm+QQ0ahRo0aNGlV6iaur69KlS3WzrVq12rBhQ+kGzs7OX3zxhbELAcX5AAAgAElEQVQDK6tIRURka4p8CgAAaj4NuqsBAPAE95dKqLUk15AZQ5ZGz/sAAKBW4LqroZIDAGB6OPWWKFYTEdmgjAMAAAaCJAcAgC849ZYoVrFEZCNCrwIAADAMjK4GAMAXJDklilVERDboqwYAAAaCSg4AAF9w6i2B7moAAGBYqOQAAPAFSU6JkkoOkhwAADAQVHIAAPiCU28JdFcDAADDQiUHAIAvSHJKFGHgAQAAMChUcgAA+IJTb4livAkUAAAMSq1liUgowO0zAABTQ5JTAgMPAACAYaG7GgAAX5DklMDAAwAAYFjorgYAwBecektI1CwRWeOGGwAAGAgqOQAAfEGSUwKVHAAAMCxUcgAA+IJTbwkMIQ0AAIaFSg4AAF+Q5JTAwAMAAGBYXCXHDFdaAACTw6m3RJES78kBAABDKumuhgsLAIDJIckpUVLJQXc1AAAwEA3XXQ1XWgAAk8Opt0TJy0DFfMcBAAA1BZ7JAQDgC5KcEhh4AAAADAujqwEA8AWn3hLFajyTAwAAhoRKDgAAX5DklMB7cgAAwLBQyQEA4AtOvUREWpZkahIwZIXuagAAYCBqLUtEQgFKOQAApoYkh4ioWE0skbWQcCECAABDQXc1AAC+IMkhIipWcQ/k8B0HAADUIOiuBgDAF5x6if59IAd32wAAwGBQyQEA4AueQSHC+NEAADVOUlLS77//npycbG1tHR4e3rlzZ92qXbt2nT592tvbe+LEiY6OjsaLAZUcAAC+4NRLRFSEodUAAGqWq1evZmRkBAYG2tjYDBw4cNOmTdzyZcuWffbZZy1atLh9+3bXrl01Go3xYkAlBwCALyheEBEVq4mIbJHkAADUFEOHDh06dCg3LRKJoqOjIyIilErlihUrfv31186dO48bN65hw4aHDx/u3bu3kWLQaImIzHA7EQDA5HDqJfp34AHcbQMAqGmkUun58+dbtGhBRAkJCfn5+R06dCAigUDQpUuXs2fPGmm7ai2xREIBxu0EAOABKjlEeCYHAOA1xLKsSqUqu1wsFnMTly9fDgsLKy4u7tSp0/z584koIyPDycnJzMyMa+Dm5paamvpKG01PT79w4UK/fv24WYFA8OGHH7755ptEJJPJNBqNUqnkVim0DJGdgNicnJxK/fuA8vLyRCL0sjAYvUMUqg6HqGHJZDKVSqVWq/WWsyw7Y8aMgoICbjYjI6Nsm7Lwu57o39HV+I4DAAAq7MiRI4MGDSq7/P79+z4+PkTUsmXLxMTE9PT0qVOnTpkyZe3atWKxuPSlUaVSmZubv9JG7ezs6tSpM2zYMN2SBg0a2NnZEZFQKFSr1dw0/XNlEQkY3RJ4VRKJBHvPgPQOUag6HKKGJRQKlUplubt04MCBMpmMm7569er169df/mkGju71xD2TgyQHAOA1Eh4eLpVKX9BAKBQ6Ojo6Ojp+/vnngwcPXrt2rZeXV15enkQisba2JqKnT582atTolTZqbW3t4+MzfPjwsqvUarVAINDVkcyIiFRCwb+VJXhVYrEYe8+A9A5RqDocoobF3YQqd5f2799fN21paZmUlPTST8MzOUREEhVLRNYYAQcAoKYoLCzUTZ8/f75evXpE5O/vHxgYuHv3biLKy8s7evRo6QunYWFoNQAAHqGSQ4RKDgBAjfPee+9lZ2f7+Pg8efIkOTn5999/55YvXbr0vffeO3LkyLVr1/r37//WW28ZKQC8JAcAgEdIcojwTA4AQI2ze/fu2NjY1NRUd3f3Vq1aWVpacsvDwsLi4uIuXbr00UcfBQcHGy8AtZYlIqEApRwAAB4gySHSvQwUOwMAoKYQi8Vt27Ytd5WXl9eAAQOMHQC6qwEA8Ah1dKJ/3pNji/fkAACAgaC7GgAAj3D2JcIzOQAAYGio5AAA8MjoPbSuX79++/btwMDAoKCgchukp6efOHHCycmpe/fupV+olJ2dffLkSa1W27p1a25UHOPBMzkAAGBYqOQAAPDIuGffpUuX9unTJyYmZsCAAUuWLCnb4OrVq2+++ebRo0cXLVrUrVs33burDxw40Lhx423btu3fv3/ixIlGDZJ0SQ6eyQEAAANBJQcAgEdG/F1fUFCwcOHCc+fONWvW7N69e0FBQRMnTnR0dCzdZsGCBdOnT587d65KpWrZsuXevXuHDh2al5c3atSoXbt2hYaGGi+80rhncmzwTA4AABgIKjkAADwy4tn35MmT3t7ezZo1I6LGjRv7+/sfO3asdAOVSnX48OEhQ4YQkUgk6tev3/79+4no4MGDAQEBISEhp06dqsgLTasOz+QAAIBhIckBAOCRESs5qampderU0c16e3s/ffq0dIOMjAyNRuPt7c3N1qlT5/z580SUmJioVqvbt28fGBh49uzZ0aNHf/3116+06dzc3JMnTyoUCm5WJBK99957ZmZmRKRUKpVKZenGLJFUzTBEIq3eGqiQsrsUqgL70+CwSw1LqVRqteWcLvPy8nQv3CSiu3fvGvtxymoO3dUAAHhU1SSnW7duBQUFegsnTpw4YcIEjUYjEPx7C0soFKrV6tLNNBoNEXG5BzfBNZDJZPfu3Xvw4IGPj09KSkrDhg1HjRrVpEmTikclkUiysrJ0wxhYW1v37dvX3NyciORyuVQq/U9jNaNlrazMWLlMWs5nwcuU3aVQFXK5XCAQ6H1ZoCpwiBqWTCbTarVCof7lIysr6+rVqyzLcrPZ2dm1fLejkgMAwKOqJjnff/992V9jnp6eROTh4ZGdna1bmJmZ6eXlVbqZh4cHwzBZWVm+vr5ElJWVxf2hl5eXv7+/j48PEfn4+AQEBNy6deuVkpy6deu2bdt2/PjxZVfJZDIHB4fSS+QyIlLZihm95VBBZXcpVIVWq7WxsRGLxXwHUnPgEDUsoVCo1Wrt7Oz0ljs4OGzcuFE3GxUVpXfOr21QyQEA4FFVk5wX5B7t27ePj49PT0/39PTMzs6Oi4vr2LEjESkUCpVKZWNjY2Fh0bp166NHj0ZGRhLR0aNHhw0bRkRdu3ZdsGCBTCaztLSUyWR63d4MDqMOAACAwXGVHDNcWwAA+GDEZ3K8vb1HjRrVr1+/MWPGbNu2bfjw4XXr1iWi1atX79mzh3v8Zs6cOREREYWFhffu3UtOTh45ciQRNWvWrGvXrgMHDhwwYMDevXtbtGjRvn1748VZhPGjAQDA0EoqOeiuBgDAB+OefX/66afJkycnJye///77P//8M7cwNDR01qxZ3HTfvn3379+fk5MTEBBw+fJlXf+HX3/9dfDgwYmJie++++6RI0cYxoi3wriX5NiicxAAABiORssSkVCAUg4AAA+MW78wMzMbPXq03sJmzZpx40pz2rVr165dO702IpGo3CdqjAFvAgUAAIPDMzkAADxCHZ2K1XgmBwAADAyjqwEA8Ahn338qOXgTKAAAGA4qOQAAPEKSg+5qAABgeKjkAADwCGdfKlYToZIDAAAGhUoOAACPkOSQRMUSkTUuRAAAYDio5AAA8AhnX1RyAADA8JDkAADwCGdfKlISIckBAACDQnc1AAAeIckpqeTYIskBAADDQSUHAIBHOPtSsQrvyQEAAANDJQcAgEdIckiiJiKyxhDSAABgOKjkAADwCGdfkqmJiKyQ5AAAgOGgkgMAwCMkOSTXEBFZmPEdBwAA1CAaLUtEZgJkOQAAPECSgyQHAAAMD5UcAAAeIckpSXLMkeQAAIDhcM/kmCHJAQDgA5IckmtYIrLAhQgAAAynpJKDyywAAB9w9iW5mgjd1QAAwKA06K4GAMAfJDl4JgcAAAwPQ0gDAPCotp99tSwptcQQiZHkAACA4SDJAQDgUW0/+yq4Mo6Q0KEAAAAMCKOrAQDwqLYnOeirBgAAxoBKDgAAj2r72RdJDgAAGAMqOQAAPEKSg/GjAQDA8FDJAQDgUW0/+6KSAwAAxoBKDgAAj5DkEBGZI8kBAACDQiUHAIBHtf3si0oOAAAYg1rLEpFQgFIOAAAPkOQQIckBAABDQ3c1AAAe1fokR02EJAcAAAwN3dUAAHhU28++GF0NAACMAZUcAAAe1fYkR8F1VxPyHQcAANQsqOQAAPCotp998UwOAAAYAyo5AAA8QpJDhCQHAAAMjavkmNX2yywAAD9q+9kXSQ4AABhDSXc1VHIAAPiAJIcISQ4AABiahuuuVtsvswAA/KjtZ19udDVzJDkAQHT16lWBQMDAc0yYMIHv/6LXCZ7JAYDS3Nzc+D6LV19eXl4G3+G1fVixktHVMIQ0ABAVFhZ27dr1+PHjfAdSHUVHR0dHR/MdxesEo6sBQGmFhYVyudzc3JzvQKodiUTi7u5u8I+t7WdfrrsaKjkAAGBYqOQAAPAISQ4RnskBAABDQyUHAIBHtf3siyQHAACMQa1liUgoQCkHAIAHRn8m58qVK4cPH3ZzcxsxYoSdnV3ZBhkZGTt37pTL5YMGDWrYsCER5efn6/X87ty5c6NGjYwRHpIcAAAwBnRXAwDgkXErOfv27QsPDyeiv//+u0OHDgqFQq9BZmZmy5Yt4+Pji4qKQkJCrl+/TkQymSz2H2fPnn3//fczMzONFKFcTYQkBwAADA3d1QAAeGTcSs7ChQuXLVsWERGh1Wpbtmy5Z8+eESNGlG6wdu3a1q1br1u3jogEAsHSpUt37tzp5eW1du1arsG2bdvOnTvXsWNHI0Wo0LKE0dUAAMDQUMkBAOCREW8x5efnx8bG9urVi4gEAkFYWFjZgVmPHz/ONSCiXr16HTt2TK/Bxo0bJ0yYwDDGukqUVHJq+0jaAPBaSktLu3//Pt9RQPlQyQGA10JaWtqDBw/4jsLwjPjrPiMjQyAQuLq6crMeHh43b97Ua5Oenq4bGNvDwyM3N1ehUOhGEH/06NHZs2e3bdv2qpt++vTpb7/9dvv2bW5WLBZ//PHHYrGYiIqLiwsLC3UtJUpzIoFGLiks1L7qVoCjt0uhioqKirRaLXe4gkFU/BCVSqUsyxo7nhfo16/f7du3GYbx8PDw8/MbPHhw//79X9B+9+7dV65c+eWXX7Kzs3/66afPP//8BY1v3bo1b968vXv3Vjo8tVpdWFgokUi02nJOmKmpqVxZnnPhwgVPT89Kb6sGQCUHAKqPFStW/PDDD0Tk4OBQt27dTp06RUVFWVpaElF0dPS1a9e2bNnCd4wGVtUkZ9y4cWUvme3btz9w4IBAIGBZVqvVCgQCItJoNGZm+s++CAQC3cVSq9UyDMM15mzYsKFnz56VeAeqSCQSCoXOzs7crLW1tVgsFgqFRGRmZsZNcBRahoisxWZC3G2rLL1dClXE7U/sUgOq+CFa9hxlYqmpqR9//PGQIUPS0tLOnTsXFRUVExOzfPnyl/5hXl7e999//+IkR6FQpKenVyU8hmGEQqGZmRk3obfWysrKxcVFlyVaWFjU8lxdoyUiMsO1BQCqgfz8/BYtWqxfvz43Nzc+Pn7hwoXbt2+PiYmxtLQcP3786NGj+Q7Q8Kr6Q+rHH39ctWqV/ocKhUTk6enJsmxmZqa3tzcRpaenl72r5+Xlpbvopqenu7q6ikQiblar1W7durXsh1eEu7t727Ztx48fX3aVpaWllZWVblbJqolYB2sLKyvcbaskvV0KVSSXy62srGr5r0PDqvgham5ubrzOsRVkZWXl7Ozs7OzctGnTwMDArl27Tpw4MSAgQKVSff311wcOHGAYZvTo0RMnTiwd6tSpUwsKCkJDQ4lo586djx8/Xrx48f379x0dHSdMmBAREWGQ2MzMzKysrLRarVarLbtLfX19P/vsM93s06dPnZycDLLd15FaSyyRUEC4tABANSEWix0dHR0dHQMCArp37x4YGLhx48ZJkyYdP3784cOHM2bM4DtAA6tqkmNhYWFhYVHuKjs7u/bt2+/bt++DDz5QqVQHDx5csmQJEcnl8rt377Zo0YJhmPDw8H379k2cOJGI/vjjD24oNs5ff/2lUCh69+5dxQhfDENIA8DzZMjoh7salTG7srZxY/r7PvdWf6dOndzd3c+ePRsQEDBt2rTs7Ozdu3crFIrhw4fb2tqOGjVK1/KTTz65evUqN2SLg4MDwzCzZs1q3Ljx48ePhwwZ4u/v36lTJ39//8WLFxvxHwOlcH3VMKgNAJRLy9L/3dZmy43YQdrFgpn+puB5ZyFLS8tu3bqdOXNm0qRJjx8/jouLM14kfDFul5gvvvhi6NCh8fHxt2/fdnZ27tOnDxE9ePAgKChIIpFYWVmNHz9+3bp1AwYMcHFx2bt3b0xMjO5vN2zYMHr0aF1hx0jkGpaIzJHkAEAZ2x9qF1037tN6daxflOQQkaenZ35+vlwuX7duXXx8vI2NjY2NzeTJk3/99dfSSY6Xl5eZmVn9+vW52aCgoMzMzCtXrhQUFDRt2vT48eOdOnVydHR8++23jfrPAZ2SUQeQ5ABAee4VsDMvaYy9lR7eTDOn556GPDw8rl69auwYeGTcJKd79+6XL18+ceJEly5d+vTpw3Vjq1+//l9//cXVf5ycnGJjYw8cOCCTyRYuXOjh4aH726lTp77xxhtGDY/+reTgQgQA+iIbC0QCkqmN9flmAurg/pKTT0pKipubW0pKCsuyw4YN0y1v0KDBC/5q69at8+fPf+edd2xsbHJycnJzcw0TMVSYhht1AA/kAEB5Ah2Y7V3NUoqNuAlfG3pBhkNEKSkpuuHBaiSjP9wcEBAQEBBQeomNjU2PHj10s3Z2dnovz+F06tTJ2LERuqsBwPPZiWhqEz5/pe7bt6+goKBLly4ODg4syx48eFA3HKUebqAX3ezy5cs3btzYtWtXIir36UQwNgytBgAvNsKfz+tLfn7+X3/9tWzZMh5jMLbafpdJoSFCdzUAqDYeP34cGxt76NChTz/99L333vv666+9vb2tra3HjBnzv//9LzU1VaVS3b59W++1Y56enhKJJCYmJikpSa1W29raXrlyRavVHjt2bPfu3Xz9W2ozvCQHAKqbvLy82NjYkydP/vDDDy1btgwODi63zFBj1OphapVa0rIkFuDZUACoFkJCQmJiYmJiYkQiUWBg4OnTp1u2bMmt+uGHH5YsWdKrV6+cnJwGDRpww+B4eXk1atSIiGxsbNavX//NN98oFIqdO3d+//33kyZNWrVqVceOHRcvXszvy39qJ7WWJSKhAFcXAKgW/P39L168+MknnzAM4+fnt3z58v79+3MvbvH29i4uNmbPOZ7U6iQHfdUAoFr58ccfn7fK0tJy4cKFCxcuLL1w8ODBuumRI0eOHDmSm3ZxcTl//ryRgoSKQHc1AKhWxo4dO3bs2HJXlb6U1CS1upQuVxMRWdTqRA8AAAwP3dUAAPhVq0/A3PjRGFoNAAxi088/9+rcuaioiO9AgH+o5ACAAd26datN8+Y3b97kO5DXSS1PcojQXQ0ADGHD+vWLpk/3uXgxrEMH5DmASg4AGMqtW7fCO3V6+9atXp07I8+puFp9AkaSAwAGsfHnnxdNn36suHitUtn5/v2e7dsXFhYadYv3799ftGiRUTcBVYFKDgAYRHx8fO8uXX4oKFjMshsKC8M7dTLBGzwnTZpUUFBg7K0YG5IcjB8NAFWy8eefF06bdkIiqUdEREsUii4PHoR16GDUPCc1NXXPnj3G+3yoIlRyAKDq4uPjwzp0+C4/vx/LElEYy24sKur79tvGznM2bNgglUqNugkTqNUnYFRyAKCK9DIcTlXynMOHD3fu3Nnf33/YsGFpaWlEtHHjxtmzZ3Nr9+/fHxkZKZPJPv7448TExNDQ0NDQUJZlly5d+tNPPw0aNKhu3bqJiYmpqakjR45s0KBBu3btjhw5wv3t7NmzN2/e3LNnT19f3ylTpjx79mzMmDF+fn5Dhgzh7tjJZLIxY8YEBgY2aNBgwoQJeXl5Vd49tReSHACoovj4+J6lMhxOVfKcxMTEwYMHBwQEdO7cOSYmhohu3brVv39/7lKVmprau3fv1NTUGTNmqFSqd999NzQ09NKlSydPnpw9e/Znn31Wv379n3/+WalUfv75582bN2/atOlXX32l0WiIaM+ePYsXL540aZKvr29oaGhaWtq3334bEBDQpk2b69evc1v/9ttvg4KC/Pz8wsLCbty4YZh99EK1+gSMJAcAqqLcDIdTuTzn3LlzUVFRK1asuHPnTosWLYYOHUpE77777oEDBzZv3pySkhIZGRkREWFhYTF//nw/P79du3bt2rWLYZg7d+4sWLBg8uTJsbGxLi4u3bt3b9u27a1bt1atWjVu3LgHDx4Q0fXr15ctW7ZixYrz588fOXKkW7duY8eOvX79ukQiWblyJRGxLDtkyJBLly5dvXpVIBB88sknhtpRtRC6qwFAVXAZzvf/zXA4lctziouLu3bt2q9fv9u3by9cuHDIkCFpaWlNmzb18PCYMGGCRqMZPXp027Ztvb29v/jiC5FItG7dul27drVs2TIjI2PlypVubm6XLl0aNGjQ9OnTExISjh8/fuzYsSNHjqxbt46IkpOTlyxZ0qNHj7i4OA8Pjy5dumg0mtjY2IEDB37wwQdcAIGBgQcOHHjw4MGoUaMGDhyoVqsNta+ep3YnOWqMrgYAlaRUKqdPnbqkvAyHM0+hSH/wYMeOHRX/zDVr1kRGRtavX18mk0VGRt65cyc9Pd3a2vq3336bNWtWnz59Zs6c2a5dO4ZhbGxszMzMHB0dHR0dub8dPnx4165dXV1dz58/LxKJRo4cKZPJAgICevfu/eeff3JtoqKimjRp4u3tHR4e3rx5865duzo6Og4dOpS702ZlZdWtW7fz58/v3bvXw8Pj1KlTVdg91cjy5cuHDh3K3W4kIqlUOmPGjODg4L59+xrvEV5UcgCgKj6bMaNLYWHZDIcTxrI9pdKFn31W8Q/ct29f/fr1e/fuLZPJmjZt2rFjR67Ov3LlygcPHnTq1EkgEMyZM4eIbG1ticje3t7R0VEkEhFR/fr1P/zwQ1dXV+7F01988YWZmZlYLJ40adLu3bu5z+/cuXO/fv3s7e1HjBhRVFQ0a9Yse3v7MWPGXL9+nXshdXh4eHJycnR0tEQiycvLe/z4cZV2UAXU6nfEoJIDAJUmFosPHzs2KCzMs6ioS5m1SqIh1tZde/f+3//+V/HPfPLkSVxc3OnTp7nZVq1aFRUVeXp6vvnmm0FBQRcuXJg4ceLz/tbHx4ebSE5OzsjI4KpAnJYtW3ITbm5u3ISVlZWlpSU3bWlpyfW9TkpK6tKlS2hoaP369aVSac3ornbu3Lm1a9cmJCRs377dzMyMiGbOnPnw4cONGzceO3asR48ejx49srKyMvh2UckBgKpYu2VL97ZtF6WkzFUqy65dLhJd9PA4uWVLxT8wOTk5ISGh9KXB3NyciCwsLCIiIqZNm/b3338LBOXfmNFdX9LS0tRq9ZQpU3SrfH19uQl3d3duwtLS0s3NjWEYblqhUHD3mHr27CkUCtu2bWtpaWlmZmaCS0ytTnIUWiIkOQBQWe3atdtz5MigsLCd/81zlESDrK1de/f+eceO510zyuXj49OjR4+5c+fqLd+0adOTJ0969Ogxffp0rm+AmZmZVqst3Ya7ohBR3bp1nZ2djx49qltSrrJrd+7c2bt37x9//JGIjhw5snnz5opHXj0pFIopU6YsX768b9++3JKioqKtW7deunSpSZMmTZs23bFjR3R09JgxYwy+aa6Sg44CAFA5rq6uxy5c6N62LZXJc1aIRD97eJy8fNnDw6PiH1i3bl0/P7+///5bb3lCQsLixYs/+eSTKVOmXLlyxcbGhogEAkHpS4zuQubp6SkUCtetW1ev3vM6MZTv5s2bjx49SkxMZBhGLpcvWLDglf68cmp1KV2uJiKyqNWJHgBUCZfnDLe1PfXPEiXRYGtrl3feedUMh4imTJmyatWqw4cPFxUVJScn//TTT0T04MGD2bNn79ixY+PGjWfOnNm+fTsR+fr6JicnnzlzJjY2Vu9DunfvbmZm9umnn2ZlZeXk5Bw8ePD27dsV2bqTk9P169dzcnISEhK+/PLLV4q8epo3b97gwYPfeOMN3ZLExEQiatKkCTcbEhJipB5rJZWcWn2NBYAq4fKcaB+fRWKxbuEKkWj9q2c4RNS/f//U1NRvvvkmNzc3Kytr7969iYmJCoVi2LBh8+fP/+qrr9q0aRMZGck1rlev3r59+2JjY/UGkhaLxRMnToyMjLx//35xcfGVK1cOHDhQka07Ojrm5OTcvHnz2bNn06dP1/UfNqpa/QMf3dUAoOpK13PaEQ22tnZ+550NO3e+aoZDRG3atNmzZ88333wzbdo0e3v70NBQIlqzZs2KFSuaN29ORDt37ly0aFG/fv38/PxWrFixatWqwsLCo0ePNmnSpG7dutyHiMXiEydOzJ8/v0ePHmq1ulmzZgsXLiSiFi1a6LoTBAQE6Dbq7u7eokULIho3btyNGzfat2/v6ek5a9asX375pcr7xrjy8vLKzd9at25tbm5+/fr1Y8eOXbx4MTk5WbcqKyvLwcFBN+vo6Piq/cKTkpIOHTrk5+fHzQqFwqVLl7Zv356IpFKpRqORyWRElJsnIrLVqJSZmbmv/A+Df2RnZ1fiewTPU/oQBYMw9iGqV8/hMpwTly69aoZDRDY2NmfPnp03b16XLl2IKCgoKCQkZM+ePR06dJg0aRIRrV69esyYMbGxsUFBQRs2bPjxxx/37t27aNEiDw8P7hrBWb58+cqVKyMiInJzc/38/KZOnUpEvr6+urzF0dGxTZs23LRQKOzevTvDMPXr11+2bNno0aMZhpk8ebJMJrO3ty8dHsuymZmZUqlUpVIpFAq94FmW7dGjh24gH6lU6uLi8tJ/MsM+55Gm19qECRPatm07fvz4sqvS09M9PT256WVx2lmXNR83EywNQaJTeaV3KVRdXl6ejY2NuNRtG7KqtSMAABhXSURBVKiiih+iJ06cWLx48fHjxyuxlbNnzw7t1ctfrQ7o06dyGU41Fx0dHR0dvWvXruLiYq1Wa2dn9+L2UVFRLVq0eP/9940X0sWLFz/99NOyy3fu3Oni4hIUFPTNN9+EhIQ8evQoKCgoMzPTyckpNjY2PDxc1xd82rRparV69erVFd9odHT0pk2bSv9J3bp1hUIhEUmlUrVaze2Z3x9rBx3TDPQT7OmO60vl4fpiWKUPUTCIVzpELSwsCgoKuCdhXkl2dvbbbdrUefr0iZfXiUuXdE9X1hgSicTd3b24uFgqlSqVytK3onTS0tLkcjk3/ffffx84cGD//v0v/lhUclDJAQAD6NChQ/Thw4f37fvy669rXoZTPbVp0+bEiRPlrpJKpU+ePBk+fDgRcT3LGzdu/Oeff/r7+xcUFGRlZXG/Eh4+fMjd1Kw4hmGsra3r16//4mYYXQ0ADMXV1fX4xYvz5szZvGRJzctwKsjLy0s37e7uzt1aerFaneQoNCwRmePJUAAwhPbt23PdloB3VlZWunLNw4cPGzRokJmZyY2F2q1bt9WrV3/55Zd37949derUmjVrjBEARlcDAANydXVd8/PPfEfxmqnVd5lQyQEAqPG4FwrpZr///vtdu3bVr1+/Q4cO3377rW5oVMNCJQcAgF+1upLDJTnmSHIAAGquevXqlX4hQ+PGjePj49PS0lxcXCrROb6CUMkBAOAXkhxUcgAAaheGYby9vY26CVRyAAD4VatPwEhyAADAGJDkAADwC5UcJDkA8C+ZTJaUlMR3FNVRVlYW3yG8TtBdDQDKevToEV4RUZaR3t1Uu5McNUtEFhhdDQCIiMjDwyMrK4t7BSeUNWLECL5DeG2gkgMAelq0aPHOO+/wHUU1Vfp9o4ZSq5MchZYIlRwA+EdgYODDhw/5jgJqAlRyAEDPhQsX+A6hdqnVd5m8rBihgPxs+Y4DAABqFh9rIiI/W2Q5AAD8qNWVnJ87mi0LMXOz5DsOAACoWYb7Czp5MN7WSHIAAPhRqys5IgEhwwEAAGNAhgMAwKNaneQAAAAAAEDNgyQHAAAAAABqlFqX5MyZM+f+/ft8R1FzpKSkTJs2je8oapSVK1eeOHGC7yhqDqVSOXLkSL6jqFF+++23X375he8oqqPdu3dv2bKF7yhqlOH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+ "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ], + "text/html": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "locstab_fs = zeros(length(psi_norm), 4)\n", "ctrl = GeneralizedPerturbedEquilibrium.ForceFreeStates.ForceFreeStatesControl(verbose=false)\n", "\n", - "println(\"Computing Delta' and Di profiles...\")\n", + "println(\"Computing \\\\Delta' and D_I...\")\n", "GeneralizedPerturbedEquilibrium.ForceFreeStates.compute_ballooning_stability!(ctrl, locstab_fs, equil; compute_delta_prime=true)\n", "\n", "delta_prime = Vector(locstab_fs[:, 4])\n", @@ -112,8 +499,8 @@ "\n", "delta_extrema = finite_local_extrema(delta_prime)\n", "di_extrema = finite_local_extrema(di_profile)\n", - "print_extrema_report(\"Delta'\", psi_norm, delta_prime, delta_extrema)\n", - "print_extrema_report(\"Di\", psi_norm, di_profile, di_extrema)\n", + "print_extrema_report(\"\\\\Delta'\", psi_norm, delta_prime, delta_extrema)\n", + "print_extrema_report(\"D_I\", psi_norm, di_profile, di_extrema)\n", "\n", "delta_mask = isfinite.(delta_prime)\n", "di_mask = isfinite.(di_profile)\n", @@ -121,10 +508,10 @@ "p_delta = plot(\n", " psi_norm[delta_mask], delta_prime[delta_mask];\n", " xlabel=\"psi_norm\",\n", - " ylabel=\"Delta'\",\n", - " label=\"Delta'\",\n", + " ylabel=L\"\\Delta'\",\n", + " label=L\"\\Delta'\",\n", " lw=2,\n", - " title=\"Delta' profile\",\n", + " title=L\"\\Delta'\",\n", " framestyle=:box,\n", ")\n", "scatter!(p_delta, psi_norm[delta_extrema], delta_prime[delta_extrema]; label=\"extrema\", marker=:diamond, color=:red, ms=5)\n", @@ -132,10 +519,10 @@ "p_di = plot(\n", " psi_norm[di_mask], di_profile[di_mask];\n", " xlabel=\"psi_norm\",\n", - " ylabel=\"Di\",\n", - " label=\"Di\",\n", + " ylabel=L\"D_I\",\n", + " label=L\"D_I\",\n", " lw=2,\n", - " title=\"Di profile\",\n", + " title=L\"D_I\",\n", " framestyle=:box,\n", ")\n", "scatter!(p_di, psi_norm[di_extrema], di_profile[di_extrema]; label=\"extrema\", marker=:diamond, color=:red, ms=5)\n", @@ -145,18 +532,459 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "id": "s-alpha-delta-di-maps", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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collect(range(-5.0, 5.0; length=30))\n", + "alpha_scales = collect(range(-5.0, 5.0; length=30))\n", "\n", "scan_result = GeneralizedPerturbedEquilibrium.ForceFreeStates.scan_delta_prime_map(\n", " psi_idx_scan,\n", @@ -166,14 +994,14 @@ " alpha_scales=alpha_scales,\n", ")\n", "\n", - "scan_s_raw = scan_result.s_values\n", + "scan_qprime_raw = scan_result.dqdpsi_ref .* scan_result.s_scales\n", "scan_pprime_raw = scan_result.pprime_ref .* scan_result.alpha_scales\n", - "s_order = sortperm(scan_s_raw)\n", + "qprime_order = sortperm(scan_qprime_raw)\n", "pprime_order = sortperm(scan_pprime_raw)\n", - "scan_s = scan_s_raw[s_order]\n", + "scan_qprime = scan_qprime_raw[qprime_order]\n", "scan_pprime = scan_pprime_raw[pprime_order]\n", - "scan_delta = scan_result.delta_prime[s_order, pprime_order]\n", - "scan_di = scan_result.di_values[s_order, pprime_order]\n", + "scan_delta = scan_result.delta_prime[qprime_order, pprime_order]\n", + "scan_di = scan_result.di_values[qprime_order, pprime_order]\n", "\n", "function symmetric_clims(z)\n", " finite_vals = vec(z)[isfinite.(vec(z))]\n", @@ -183,32 +1011,30 @@ "end\n", "\n", "p_scan_delta = contourf(\n", - " scan_pprime, scan_s, scan_delta;\n", + " scan_pprime, scan_qprime, scan_delta;\n", " c=cgrad([:blue, :white, :red]),\n", " clims=symmetric_clims(scan_delta),\n", - " xlabel=\"pprime\",\n", - " ylabel=\"s\",\n", - " title=\"pprime-s Delta'\",\n", - " colorbar_title=\"Delta'\",\n", + " xlabel=L\"p_{\\psi}\",\n", + " ylabel=L\"q_{\\psi}\",\n", + " title=L\"\\Delta'\",\n", " levels=41,\n", " framestyle=:box,\n", ")\n", - "contour!(p_scan_delta, scan_pprime, scan_s, scan_delta; levels=[0.0], color=:black, linewidth=2, label=\"Delta' = 0\")\n", - "scatter!(p_scan_delta, [scan_result.reference.pprime_ref], [scan_result.reference.s_ref]; color=:green, marker=:star5, ms=7, label=\"equilibrium\")\n", + "contour!(p_scan_delta, scan_pprime, scan_qprime, scan_delta; levels=[0.0], color=:black, linewidth=2, label=L\"\\Delta' = 0\")\n", + "scatter!(p_scan_delta, [scan_result.reference.pprime_ref], [scan_result.reference.qprime_ref]; color=:green, marker=:star5, ms=7, label=\"equilibrium\")\n", "\n", "p_scan_di = contourf(\n", - " scan_pprime, scan_s, scan_di;\n", + " scan_pprime, scan_qprime, scan_di;\n", " c=cgrad([:blue, :white, :red]),\n", " clims=symmetric_clims(scan_di),\n", - " xlabel=\"pprime\",\n", - " ylabel=\"s\",\n", - " title=\"pprime-s Di\",\n", - " colorbar_title=\"Di\",\n", + " xlabel=L\"p_{\\psi}\",\n", + " ylabel=L\"q_{\\psi}\",\n", + " title=L\"D_I\",\n", " levels=41,\n", " framestyle=:box,\n", ")\n", - "contour!(p_scan_di, scan_pprime, scan_s, scan_di; levels=[0.0], color=:black, linewidth=2, label=\"Di = 0\")\n", - "scatter!(p_scan_di, [scan_result.reference.pprime_ref], [scan_result.reference.s_ref]; color=:green, marker=:star5, ms=7, label=\"equilibrium\")\n", + "contour!(p_scan_di, scan_pprime, scan_qprime, scan_di; levels=[0.0], color=:black, linewidth=2, label=L\"D_I = 0\")\n", + "scatter!(p_scan_di, [scan_result.reference.pprime_ref], [scan_result.reference.qprime_ref]; color=:green, marker=:star5, ms=7, label=\"equilibrium\")\n", "\n", "display(plot(p_scan_delta, p_scan_di; layout=(1, 2), size=(1150, 460)))\n" ] @@ -218,24 +1044,116 @@ "execution_count": null, "id": "s-alpha-zero-contours", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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+ "image/svg+xml": [ + "\n", + "\n", + "\n", + " \n", + " \n", + " \n", + "\n", + "\n", + "\n", + " \n", + " \n", + " \n", + "\n", + "\n", + "\n", + " \n", + " \n", + " \n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ], + "text/html": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "p_zero = plot(\n", - " xlabel=\"pprime\",\n", - " ylabel=\"s\",\n", - " title=\"pprime-s zero contours\",\n", + " xlabel=L\"p_{\\psi}\",\n", + " ylabel=L\"q_{\\psi}\",\n", + " title=\"ballooning, Mercier contours\",\n", " framestyle=:box,\n", ")\n", - "contour!(p_zero, scan_pprime, scan_s, scan_delta;\n", + "contour!(p_zero, scan_pprime, scan_qprime, scan_delta;\n", " levels=[0.0], color=:blue, linewidth=3,\n", - " label=\"Delta' = 0\", colorbar=false)\n", + " label=L\"\\Delta' = 0\", colorbar=false)\n", "\n", - "contour!(p_zero, scan_pprime, scan_s, scan_di;\n", + "contour!(p_zero, scan_pprime, scan_qprime, scan_di;\n", " levels=[0.0], color=:red, linewidth=3, linestyle=:dash,\n", - " label=\"Di = 0\", colorbar=false)\n", + " label=L\"D_I = 0\", colorbar=false)\n", "\n", "\n", - "scatter!(p_zero, [scan_result.reference.pprime_ref], [scan_result.reference.s_ref]; color=:green, marker=:star5, ms=8, label=\"equilibrium\")\n", + "scatter!(p_zero, [scan_result.reference.pprime_ref], [scan_result.reference.qprime_ref]; color=:green, marker=:star5, ms=8, label=\"equilibrium\")\n", "display(p_zero)\n" ] } From 79366ebff0d8d60d9cdf1399e1038ac4670c9efb Mon Sep 17 00:00:00 2001 From: jmlmir369 Date: Thu, 30 Apr 2026 21:37:44 +0900 Subject: [PATCH 005/135] full version(small solution, ca1) --- .../Bal_mode_compare.ipynb | 212 ++++ .../Bal_salpha_delta_di_summary.ipynb | 935 +----------------- examples/DIIID-like_ideal_example/gpec.toml | 3 +- .../DIIID-like_ideal_example_IMAS/gpec.toml | 3 +- .../run_imas_example.jl | 3 +- .../Local_stability_main_plot.ipynb | 93 ++ examples/Solovev_ideal_example/gpec.toml | 5 +- examples/Solovev_ideal_example_3D/gpec.toml | 3 +- .../Solovev_ideal_example_multi_n/gpec.toml | 3 +- .../single_n_1/gpec.toml | 3 +- .../single_n_2/gpec.toml | 3 +- src/ForceFreeStates/Bal.jl | 458 ++++++++- src/ForceFreeStates/ForceFreeStates.jl | 1 - src/ForceFreeStates/ForceFreeStatesStructs.jl | 6 +- src/ForceFreeStates/Mercier.jl | 79 -- src/GeneralizedPerturbedEquilibrium.jl | 24 +- .../gpec.toml | 3 +- .../gpec.toml | 3 +- .../gpec.toml | 3 +- .../gpec.toml | 3 +- 20 files changed, 744 insertions(+), 1102 deletions(-) create mode 100644 examples/DIIID-like_ideal_example/Bal_mode_compare.ipynb create mode 100644 examples/Solovev_ideal_example/Local_stability_main_plot.ipynb delete mode 100644 src/ForceFreeStates/Mercier.jl diff --git a/examples/DIIID-like_ideal_example/Bal_mode_compare.ipynb b/examples/DIIID-like_ideal_example/Bal_mode_compare.ipynb new file mode 100644 index 000000000..f9321118c --- /dev/null +++ b/examples/DIIID-like_ideal_example/Bal_mode_compare.ipynb @@ -0,0 +1,212 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Ballooning mode comparisons\n", + "\n", + "Compare the legacy delta-prime shooting result, the small-solution delta-prime result, and the `ca1` projection result using both flux-surface profiles and a local s-alpha scan." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "using Pkg\n", + "Pkg.activate(\"../..\")\n", + "\n", + "using GeneralizedPerturbedEquilibrium\n", + "using Plots\n", + "using LaTeXStrings\n", + "using TOML\n", + "\n", + "eq_config = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(TOML.parsefile(\"gpec.toml\")[\"Equilibrium\"], pwd())\n", + "equil = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(eq_config)\n", + "psi_norm = Vector(equil.profiles.xs)\n", + "\n", + "modes = (:delta_prime_legacy, :delta_prime_small, :ca1)\n", + "mode_titles = Dict(\n", + " :delta_prime_legacy => L\"\\Delta'\",\n", + " :delta_prime_small => L\"\\Delta'\",\n", + " :ca1 => L\"c_{a1}\",\n", + ")\n", + "\n", + "real_or_nan(x; atol=1e-10) = x isa Real ? Float64(x) : (x isa Complex && isapprox(imag(x), 0.0; atol=atol) ? Float64(real(x)) : NaN)\n", + "\n", + "function symmetric_clims(z)\n", + " finite_vals = vec(z)[isfinite.(vec(z))]\n", + " maxabs = isempty(finite_vals) ? 1.0 : maximum(abs.(finite_vals))\n", + " maxabs = max(maxabs, eps(Float64))\n", + " return (-maxabs, maxabs)\n", + "end\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Flux-surface mode comparison" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "538f03b3", + "metadata": {}, + "outputs": [], + "source": [ + "psi_indices = collect(eachindex(psi_norm))\n", + "\n", + "mode_values = Dict(mode => fill(NaN, length(psi_indices)) for mode in modes)\n", + "di_profile = fill(NaN, length(psi_indices))\n", + "\n", + "for (i, psi_idx) in enumerate(psi_indices)\n", + " coeff = try\n", + " GeneralizedPerturbedEquilibrium.ForceFreeStates.prepare_ballooning_coefficients(psi_idx, equil)\n", + " catch err\n", + " @warn \"coefficient preparation failed\" psi_idx psi=psi_norm[psi_idx] exception=(err, catch_backtrace())\n", + " nothing\n", + " end\n", + " coeff === nothing && continue\n", + "\n", + " di_profile[i] = coeff.di\n", + "\n", + " for mode in modes\n", + " result = try\n", + " GeneralizedPerturbedEquilibrium.ForceFreeStates.integrate_ballooning_ode(\n", + " coeff.ode_coefficient_spline;\n", + " theta_k=0.0,\n", + " mode=mode,\n", + " d0bar=coeff.d0bar,\n", + " n0_spline=coeff.n0_spline,\n", + " n1_spline=coeff.n1_spline,\n", + " theta_grid=coeff.theta_grid,\n", + " )\n", + " catch err\n", + " @warn \"mode comparison failed\" psi_idx psi=psi_norm[psi_idx] mode exception=(err, catch_backtrace())\n", + " nothing\n", + " end\n", + "\n", + " if result !== nothing\n", + " mode_values[mode][i] = real_or_nan(result.value)\n", + " end\n", + " end\n", + "end\n", + "\n", + "psi_scan = psi_norm[psi_indices]\n", + "\n", + "profile_specs = [\n", + " (:delta_prime_legacy, L\"\\Delta'\", L\"\\Delta'\"),\n", + " (:delta_prime_small, L\"\\Delta'\", L\"\\Delta'\"),\n", + " (:ca1, L\"c_{a1}\", L\"c_{a1}\"),\n", + "]\n", + "\n", + "profile_plots = map(profile_specs) do (mode, title_text, ylabel_text)\n", + " p = plot(\n", + " psi_scan,\n", + " mode_values[mode];\n", + " xlabel=L\"\\psi_N\",\n", + " ylabel=ylabel_text,\n", + " title=title_text,\n", + " label=String(mode),\n", + " linewidth=2,\n", + " framestyle=:box,\n", + " )\n", + " hline!(p, [0.0]; color=:black, linestyle=:dash, label=\"\")\n", + " p\n", + "end\n", + "\n", + "display(plot(profile_plots...; layout=(1, 3), size=(1350, 390)))\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## s-alpha mode comparison" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "psi_target = 0.67680851\n", + "psi_idx_scan = argmin(abs.(psi_norm .- psi_target))\n", + "\n", + "s_scales = collect(range(-5.0, 5.0; length=30))\n", + "alpha_scales = collect(range(-5.0, 5.0; length=30))\n", + "\n", + "println(\"Running s-alpha mode comparison at index $(psi_idx_scan), psi_norm=$(round(psi_norm[psi_idx_scan], digits=6))\")\n", + "\n", + "scan_results = Dict{Symbol,Any}()\n", + "for mode in modes\n", + " scan_results[mode] = GeneralizedPerturbedEquilibrium.ForceFreeStates.scan_delta_prime_map(\n", + " psi_idx_scan,\n", + " equil;\n", + " theta_k=0.0,\n", + " mode=mode,\n", + " s_scales=s_scales,\n", + " alpha_scales=alpha_scales,\n", + " )\n", + "end\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "reference = scan_results[:delta_prime_legacy].reference\n", + "\n", + "scan_s_raw = scan_results[:delta_prime_legacy].s_values\n", + "scan_alpha_raw = scan_results[:delta_prime_legacy].alpha_values\n", + "s_order = sortperm(scan_s_raw)\n", + "alpha_order = sortperm(scan_alpha_raw)\n", + "scan_s = scan_s_raw[s_order]\n", + "scan_alpha = scan_alpha_raw[alpha_order]\n", + "di_contour = scan_results[:delta_prime_legacy].di_values[s_order, alpha_order]\n", + "\n", + "salpha_plots = map(modes) do mode\n", + " z = scan_results[mode].delta_prime[s_order, alpha_order]\n", + " p = contourf(\n", + " scan_alpha, scan_s, z;\n", + " c=cgrad([:blue, :white, :red]),\n", + " clims=symmetric_clims(z),\n", + " xlabel=L\"\\alpha\",\n", + " ylabel=L\"s\",\n", + " title=mode_titles[mode],\n", + " levels=41,\n", + " framestyle=:box,\n", + " )\n", + " contour!(p, scan_alpha, scan_s, z; levels=[0.0], color=:black, linewidth=2, label=\"\", colorbar=false)\n", + " contour!(p, scan_alpha, scan_s, di_contour; levels=[0.0], color=:red, linestyle=:dash, linewidth=2, label=L\"D_I=0\", colorbar=false)\n", + " scatter!(p, [reference.alpha_ref], [reference.s_ref]; color=:green, marker=:star5, ms=7, label=\"equilibrium\")\n", + " p\n", + "end\n", + "\n", + "display(plot(salpha_plots...; layout=(1, 3), size=(1350, 390)))\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.12.4", + "language": "julia", + "name": "julia-1.12" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.12.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/examples/DIIID-like_ideal_example/Bal_salpha_delta_di_summary.ipynb b/examples/DIIID-like_ideal_example/Bal_salpha_delta_di_summary.ipynb index 049dba7ce..7be986fa8 100644 --- a/examples/DIIID-like_ideal_example/Bal_salpha_delta_di_summary.ipynb +++ b/examples/DIIID-like_ideal_example/Bal_salpha_delta_di_summary.ipynb @@ -2,192 +2,10 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": null, "id": "s-alpha-profile-extrema", "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "\u001b[32m\u001b[1m Activating\u001b[22m\u001b[39m project at `~/lib/git/GPEC`\n", - "┌ Info: Forcing hamada coordinate jacobian exponents: power_*\n", - "└ @ GeneralizedPerturbedEquilibrium.Equilibrium /home/jmlmir/lib/git/GPEC/src/Equilibrium/EquilibriumTypes.jl:68\n", - "┌ Info: Processing EFIT g-file: /home/jmlmir/lib/git/GPEC/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk\n", - "└ @ GeneralizedPerturbedEquilibrium.Equilibrium /home/jmlmir/lib/git/GPEC/src/Equilibrium/ReadEquilibrium.jl:58\n", - "┌ Info: Parsed from header: nw=257, nh=257\n", - "└ @ GeneralizedPerturbedEquilibrium.Equilibrium /home/jmlmir/lib/git/GPEC/src/Equilibrium/ReadEquilibrium.jl:65\n", - "┌ Info: Magnetic axis found at R = 1.744, Z = -0.005\n", - "└ @ GeneralizedPerturbedEquilibrium.Equilibrium /home/jmlmir/lib/git/GPEC/src/Equilibrium/DirectEquilibrium.jl:179\n", - "┌ Info: Inboard separatrix found at R = 1.058\n", - "└ @ GeneralizedPerturbedEquilibrium.Equilibrium /home/jmlmir/lib/git/GPEC/src/Equilibrium/DirectEquilibrium.jl:208\n", - "┌ Info: Outboard separatrix found at R = 2.301\n", - "└ @ GeneralizedPerturbedEquilibrium.Equilibrium /home/jmlmir/lib/git/GPEC/src/Equilibrium/DirectEquilibrium.jl:208\n", - "┌ Info: Estimated separatrix log slope A = 0.409 from probe integrations at psi = 0.9970, 0.9985\n", - "└ @ GeneralizedPerturbedEquilibrium.Equilibrium /home/jmlmir/lib/git/GPEC/src/Equilibrium/DirectEquilibrium.jl:393\n", - "┌ Info: Auto-mpsi: N_core=3 + N_mid=163 + N_edge=10 = 176 (A=0.409, h_mid=0.0059, tau=0.001)\n", - "└ @ GeneralizedPerturbedEquilibrium.Equilibrium /home/jmlmir/lib/git/GPEC/src/Equilibrium/DirectEquilibrium.jl:452\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "s extrema\n", - " index\tpsi_norm\tvalue\n", - " 155\t0.91006135\t3.098059626449e+00\n", - " 163\t0.95668712\t2.218338914722e+00\n", - "\n", - "alpha extrema\n", - " index\tpsi_norm\tvalue\n", - " 75\t0.44380368\t1.475989118427e+01\n", - " 109\t0.64196319\t1.449804644503e+01\n", - " 164\t0.96251534\t2.090707893518e+02\n" - ] - }, - { - "data": { - "image/png": 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Aborting. There is either an error in your model specification or the true solution is unstable.\n", - "└ @ SciMLBase /home/jmlmir/.julia/packages/SciMLBase/hLfdZ/src/integrator_interface.jl:717\n", - "┌ Warning: Verbosity toggle: dt_min_unstable \n", - "│ dt(1.0e-10 <= dtmin(1.0e-10), at t=-0.09646835664820956, and step error estimate = 1.0233429309893254. Aborting. There is either an error in your model specification or the true solution is unstable.\n", - "└ @ SciMLBase /home/jmlmir/.julia/packages/SciMLBase/hLfdZ/src/integrator_interface.jl:717\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "Delta' extrema\n", - " index\tpsi_norm\tvalue\n", - " 22\t0.13490798\t-2.270043132951e-02\n", - " 23\t0.14073620\t-2.273200742321e-02\n", - " 25\t0.15239264\t-2.262453359539e-02\n", - " 26\t0.15822086\t-2.268353986142e-02\n", - " 27\t0.16404908\t-2.265515889541e-02\n", - " 116\t0.68276074\t-3.370657448578e-02\n", - " 160\t0.93920245\t-8.756024762877e-03\n", - " 162\t0.95085890\t-1.227486100615e-02\n", - " 166\t0.97417178\t-6.900060910302e-03\n", - " 174\t0.99848787\t-2.375793842651e-02\n", - "\n", - "Di extrema\n", - " index\tpsi_norm\tvalue\n", - " 125\t0.73521472\t-2.637864264262e-01\n", - " 163\t0.95668712\t-7.776704310230e-01\n", - " 175\t0.99895436\t-2.527139701487e-01\n", - " 176\t0.99927694\t-2.528430789462e-01\n" - ] - }, - { - "data": { - "image/png": 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[ - { - "data": { - "image/png": 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a/examples/DIIID-like_ideal_example/gpec.toml +++ b/examples/DIIID-like_ideal_example/gpec.toml @@ -26,11 +26,10 @@ tw = 0.05 # Sharpness of wall corners (try 0.05 as initial equal_arc_wall = true # Equal arc length distribution of nodes on wall [ForceFreeStates] -bal_flag = false # Ideal MHD ballooning criterion for short wavelengths +local_stability_flag = true # Local D_I and ballooning stability mat_flag = true # Construct coefficient matrices for diagnostic purposes ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes -mer_flag = true # Evaluate the Mercier criterian psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... diff --git a/examples/DIIID-like_ideal_example_IMAS/gpec.toml b/examples/DIIID-like_ideal_example_IMAS/gpec.toml index 55205c468..f04a0af2d 100644 --- a/examples/DIIID-like_ideal_example_IMAS/gpec.toml +++ b/examples/DIIID-like_ideal_example_IMAS/gpec.toml @@ -26,8 +26,7 @@ nn_high = 1 vac_flag = true ode_flag = true mat_flag = true -mer_flag = false -bal_flag = false +local_stability_flag = false # Local D_I and ballooning stability write_outputs_to_HDF5 = false verbose = false delta_mhigh = 16 diff --git a/examples/DIIID-like_ideal_example_IMAS/run_imas_example.jl b/examples/DIIID-like_ideal_example_IMAS/run_imas_example.jl index d56349e58..178da6ad9 100644 --- a/examples/DIIID-like_ideal_example_IMAS/run_imas_example.jl +++ b/examples/DIIID-like_ideal_example_IMAS/run_imas_example.jl @@ -31,8 +31,7 @@ const SHARED_CONFIG = Dict( "vac_flag" => true, "ode_flag" => true, "mat_flag" => true, - "mer_flag" => false, - "bal_flag" => false, + "local_stability_flag" => false, "write_outputs_to_HDF5"=> false, "verbose" => false, "delta_mhigh" => 16, diff --git a/examples/Solovev_ideal_example/Local_stability_main_plot.ipynb b/examples/Solovev_ideal_example/Local_stability_main_plot.ipynb new file mode 100644 index 000000000..67c6ffb88 --- /dev/null +++ b/examples/Solovev_ideal_example/Local_stability_main_plot.ipynb @@ -0,0 +1,93 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Local stability from main run\n", + "\n", + "Run the full `GeneralizedPerturbedEquilibrium.main` path for this example, then read the HDF5 output and plot the local `D_I` and ballooning `\\Delta'` profiles." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "using Pkg\n", + "Pkg.activate(\"../..\")\n", + "\n", + "using GeneralizedPerturbedEquilibrium\n", + "using HDF5\n", + "using Plots\n", + "using LaTeXStrings\n", + "using TOML\n", + "\n", + "inputs = TOML.parsefile(\"gpec.toml\")\n", + "@assert get(inputs[\"ForceFreeStates\"], \"local_stability_flag\", false) \"local_stability_flag must be true to write local stability output\"\n", + "\n", + "GeneralizedPerturbedEquilibrium.main([pwd()])\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "h5_name = get(inputs[\"ForceFreeStates\"], \"HDF5_filename\", \"gpec.h5\")\n", + "\n", + "psi_norm = h5open(h5_name, \"r\") do h5\n", + " read(h5[\"splines/profiles/xs\"])\n", + "end\n", + "\n", + "di, delta_prime = h5open(h5_name, \"r\") do h5\n", + " read(h5[\"locstab/di\"]), read(h5[\"locstab/delta_prime\"])\n", + "end\n", + "\n", + "println(\"D_I finite: $(count(isfinite, di)) / $(length(di))\")\n", + "println(\"Delta prime finite: $(count(isfinite, delta_prime)) / $(length(delta_prime))\")\n", + "\n", + "p_di = plot(\n", + " psi_norm, di;\n", + " xlabel=L\"\\psi_N\",\n", + " ylabel=L\"D_I\",\n", + " title=L\"D_I\",\n", + " linewidth=2,\n", + " label=\"\",\n", + " framestyle=:box,\n", + ")\n", + "hline!(p_di, [0.0]; color=:black, linestyle=:dash, label=\"\")\n", + "\n", + "p_delta = plot(\n", + " psi_norm, delta_prime;\n", + " xlabel=L\"\\psi_N\",\n", + " ylabel=L\"\\Delta'\",\n", + " title=L\"\\Delta'\",\n", + " linewidth=2,\n", + " label=\"\",\n", + " framestyle=:box,\n", + ")\n", + "hline!(p_delta, [0.0]; color=:black, linestyle=:dash, label=\"\")\n", + "\n", + "display(plot(p_di, p_delta; layout=(1, 2), size=(1050, 390)))\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.12.4", + "language": "julia", + "name": "julia-1.12" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.12.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/examples/Solovev_ideal_example/gpec.toml b/examples/Solovev_ideal_example/gpec.toml index 66cc056fd..d7a66424f 100644 --- a/examples/Solovev_ideal_example/gpec.toml +++ b/examples/Solovev_ideal_example/gpec.toml @@ -6,7 +6,7 @@ power_bp = 0 # Poloidal field power exponent for Jaco power_b = 0 # Toroidal field power exponent for Jacobian power_r = 0 # Major radius power exponent for Jacobian grid_type = "ldp" # Radial grid packing type -psilow = 1e-4 # Lower limit of normalized flux coordinate +psilow = 1e-2 # Lower limit of normalized flux coordinate psihigh = 0.9995 # Upper limit of normalized flux coordinate mpsi = 128 # Number of radial grid points mtheta = 256 # Number of poloidal grid points @@ -37,11 +37,10 @@ equal_arc_wall = true # Equal arc length distribution of nodes # write_outputs_to_HDF5 = true # Write outputs to HDF5 [ForceFreeStates] -bal_flag = false # Ideal MHD ballooning criterion for short wavelengths +local_stability_flag = true # Local D_I and ballooning stability mat_flag = true # Construct coefficient matrices for diagnostic purposes ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes -mer_flag = true # Evaluate the Mercier criterian psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... diff --git a/examples/Solovev_ideal_example_3D/gpec.toml b/examples/Solovev_ideal_example_3D/gpec.toml index bd4532868..9af945769 100644 --- a/examples/Solovev_ideal_example_3D/gpec.toml +++ b/examples/Solovev_ideal_example_3D/gpec.toml @@ -15,11 +15,10 @@ etol = 1e-7 # Error tolerance for equilibrium solver force_termination = false # Terminate after equilibrium setup (skip stability calculations) [ForceFreeStates] -bal_flag = false # Ideal MHD ballooning criterion for short wavelengths +local_stability_flag = true # Local D_I and ballooning stability mat_flag = true # Construct coefficient matrices for diagnostic purposes ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes -mer_flag = true # Evaluate the Mercier criterian psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... diff --git a/examples/Solovev_ideal_example_multi_n/gpec.toml b/examples/Solovev_ideal_example_multi_n/gpec.toml index 5b6c520d6..578238d01 100644 --- a/examples/Solovev_ideal_example_multi_n/gpec.toml +++ b/examples/Solovev_ideal_example_multi_n/gpec.toml @@ -25,11 +25,10 @@ tw = 0.05 # Sharpness of wall corners (try 0.05 as equal_arc_wall = true # Equal arc length distribution of nodes on wall [ForceFreeStates] -bal_flag = false # Ideal MHD ballooning criterion for short wavelengths +local_stability_flag = true # Local D_I and ballooning stability mat_flag = true # Construct coefficient matrices for diagnostic purposes ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes -mer_flag = true # Evaluate the Mercier criterian psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... diff --git a/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml b/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml index c001eb806..015707b35 100644 --- a/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml +++ b/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml @@ -25,11 +25,10 @@ tw = 0.05 # Sharpness of wall corners (try 0.05 as equal_arc_wall = true # Equal arc length distribution of nodes on wall [ForceFreeStates] -bal_flag = false # Ideal MHD ballooning criterion for short wavelengths +local_stability_flag = true # Local D_I and ballooning stability mat_flag = true # Construct coefficient matrices for diagnostic purposes ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes -mer_flag = true # Evaluate the Mercier criterian psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... diff --git a/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml b/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml index 8a65be741..cd0a5f9be 100644 --- a/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml +++ b/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml @@ -25,11 +25,10 @@ tw = 0.05 # Sharpness of wall corners (try 0.05 as equal_arc_wall = true # Equal arc length distribution of nodes on wall [ForceFreeStates] -bal_flag = false # Ideal MHD ballooning criterion for short wavelengths +local_stability_flag = true # Local D_I and ballooning stability mat_flag = true # Construct coefficient matrices for diagnostic purposes ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes -mer_flag = true # Evaluate the Mercier criterian psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... diff --git a/src/ForceFreeStates/Bal.jl b/src/ForceFreeStates/Bal.jl index 053591a79..dfbd6ce0f 100644 --- a/src/ForceFreeStates/Bal.jl +++ b/src/ForceFreeStates/Bal.jl @@ -28,7 +28,8 @@ function compute_ballooning_stability!( locstab_fs::Matrix{Float64}, plasma_eq::Equilibrium.PlasmaEquilibrium; theta_k::Float64=0.0, - compute_delta_prime::Bool=true + compute_delta_prime::Bool=true, + mode::Symbol=:delta_prime_legacy ) if ctrl.verbose @@ -46,9 +47,14 @@ function compute_ballooning_stability!( if compute_delta_prime && plasma_eq.profiles.xs[flux_surface_index] <= 1.0 result = integrate_ballooning_ode( coeff_data.ode_coefficient_spline; - theta_k=theta_k + theta_k=theta_k, + mode=mode, + d0bar=coeff_data.d0bar, + n0_spline=coeff_data.n0_spline, + n1_spline=coeff_data.n1_spline, + theta_grid=coeff_data.theta_grid ) - locstab_fs[flux_surface_index, 4] = result.value + locstab_fs[flux_surface_index, 4] = _real_scalar_or_nan(result.value) end end @@ -61,6 +67,17 @@ end +function _real_scalar_or_nan(value) + if value isa Real + return Float64(value) + elseif value isa Complex + return isapprox(imag(value), 0.0; atol=1e-10) ? Float64(real(value)) : NaN + else + return NaN + end +end + + function _collect_surface_response_background( flux_surface_index::Int, @@ -433,7 +450,8 @@ function prepare_ballooning_coefficients( n0_fs[:, 4] = -0.5 .- m0_12 .* sigma @views n0_fs[end, :] .= n0_fs[1, :] - n0_int = FastInterpolations.integrate(cubic_interp(theta_grid, Series(n0_fs); bc=PeriodicBC())) + n0_spline = (xs=theta_grid, fs=n0_fs, itp=cubic_interp(theta_grid, Series(n0_fs); bc=PeriodicBC())) + n0_int = FastInterpolations.integrate(n0_spline.itp) d0bar = zeros(2, 2) d0bar[1, 1] = n0_int[1] @@ -441,12 +459,26 @@ function prepare_ballooning_coefficients( d0bar[2, 1] = n0_int[3] d0bar[2, 2] = n0_int[4] + i_per_total = i_per0_shifted .+ i_per_perturbed + a1_fs = -2.0 .* jac_chiprime .* bsq ./ (bg.gradpsi_sq0 .* q_derivative^3) .* (i_per_total .- q_derivative .* theta_k_reference) + + n1_fs = zeros(mtheta + 1, 4) + n1_fs[:, 1] = sigma .* a1_fs + n1_fs[:, 2] = a1_fs + n1_fs[:, 3] = .-(sigma .^ 2) .* a1_fs + n1_fs[:, 4] = .-sigma .* a1_fs + @views n1_fs[end, :] .= n1_fs[1, :] + n1_spline = (xs=theta_grid, fs=n1_fs, itp=cubic_interp(theta_grid, Series(n1_fs); bc=PeriodicBC())) + @views bf_fs[end, :] .= bf_fs[1, :] ode_coefficient_spline = (xs=theta_grid, itp=cubic_interp(theta_grid, Series(bf_fs); bc=PeriodicBC())) return ( ode_coefficient_spline=ode_coefficient_spline, + d0bar=d0bar, di=det(d0bar), + n0_spline=n0_spline, + n1_spline=n1_spline, theta_grid=theta_grid ) end @@ -516,7 +548,8 @@ function ballooning_delta_prime( plasma_eq::Equilibrium.PlasmaEquilibrium; corr_qprime::Float64=0.0, corr_pprime::Float64=0.0, - theta_k::Float64=0.0 + theta_k::Float64=0.0, + mode::Symbol=:delta_prime_legacy ) coeff_data = prepare_ballooning_coefficients( psi_idx, @@ -525,12 +558,17 @@ function ballooning_delta_prime( corr_pprime=corr_pprime, theta_k=theta_k ) - delta_prime = integrate_ballooning_ode( + result = integrate_ballooning_ode( coeff_data.ode_coefficient_spline; - theta_k=theta_k - ).value + theta_k=theta_k, + mode=mode, + d0bar=coeff_data.d0bar, + n0_spline=coeff_data.n0_spline, + n1_spline=coeff_data.n1_spline, + theta_grid=coeff_data.theta_grid + ) - return (delta_prime=delta_prime, di=coeff_data.di) + return merge(result, (delta_prime=result.value, di=coeff_data.di)) end """ @@ -546,6 +584,7 @@ function scan_delta_prime_map( plasma_eq::Equilibrium.PlasmaEquilibrium; ctrl::ForceFreeStatesControl=ForceFreeStatesControl(; verbose=false), theta_k::Float64=0.0, + mode::Symbol=:delta_prime_legacy, s_scales::AbstractVector{<:Real}, alpha_scales::AbstractVector{<:Real} ) @@ -569,7 +608,8 @@ function scan_delta_prime_map( plasma_eq; corr_qprime=corr_qprime, corr_pprime=corr_pprime, - theta_k=theta_k + theta_k=theta_k, + mode=mode ) catch err if ctrl.verbose @@ -607,8 +647,206 @@ end # ODE Integration # Integrates the ideal marginal ballooning equations # ====================================================================== + +function _compute_mercier_from_d0bar(d0bar::Matrix{Float64}) + di = det(d0bar) + if !isfinite(di) || di >= 0.0 + return di, NaN + end + return di, sqrt(-di) +end + +function _compute_theta_max_like_fortran(ode_coefficient_spline; thmax0::Float64=16.5) + theta_vals = ode_coefficient_spline.xs + ratio = fill(NaN, length(theta_vals)) + + @inbounds for i in eachindex(theta_vals) + coeffs = ode_coefficient_spline.itp(theta_vals[i]) + a0 = coeffs[1] + a1 = coeffs[2] + a2 = coeffs[3] + if isfinite(a0) && isfinite(a1) && isfinite(a2) && a2 != 0.0 + residual = a0 - a1^2 / (4.0 * a2) + ratio[i] = abs(residual / a2) + end + end + + finite_ratio = ratio[isfinite.(ratio)] + if isempty(finite_ratio) + return thmax0 + end + + theta_max = sqrt(maximum(finite_ratio)) * 10.0 * thmax0 + return min(theta_max, 100.0) +end + +function _build_periodic_primitive_spline(theta_grid::AbstractVector{<:Real}, values::AbstractMatrix{<:Real}) + theta_vals = Float64.(theta_grid) + period = theta_vals[end] - theta_vals[1] + ntheta, nqty = size(values) + + primitive = zeros(Float64, ntheta, nqty) + for j in 1:nqty + for i in 2:ntheta + dtheta = theta_vals[i] - theta_vals[i-1] + primitive[i, j] = primitive[i-1, j] + 0.5 * dtheta * (values[i-1, j] + values[i, j]) + end + + mean_component = primitive[end, j] / period + for i in 1:ntheta + primitive[i, j] -= (theta_vals[i] - theta_vals[1]) * mean_component + end + primitive[end, j] = primitive[1, j] + end + + return (xs=theta_vals, fs=primitive, itp=cubic_interp(theta_vals, Series(primitive); bc=PeriodicBC())) +end + +function _compute_branch_eigendata(d0bar::Matrix{Float64}, branch::Symbol) + di, alpha = _compute_mercier_from_d0bar(d0bar) + if !isfinite(di) || di >= 0.0 || isnan(alpha) + return di, alpha, NaN, [NaN, NaN] + end + + if branch == :big + exponent = alpha + w2 = -(d0bar[1, 1] - alpha) / d0bar[1, 2] + elseif branch == :small + exponent = -alpha + w2 = -(d0bar[1, 1] + alpha) / d0bar[1, 2] + else + error("Unsupported asymptotic branch: $(branch)") + end + + return di, alpha, exponent, [1.0, w2] +end + +function _build_branch_matching_data(n0_spline, n1_spline, d0bar::Matrix{Float64}, branch::Symbol, theta_grid::Vector{Float64}) + di, alpha, exponent, w0 = _compute_branch_eigendata(d0bar, branch) + if !isfinite(exponent) || isnan(exponent) + return ( + di=di, + alpha=alpha, + exponent=exponent, + w0=w0, + c1=[NaN, NaN], + w1tilde_spline=nothing, + branch=branch + ) + end + + n0_fs = n0_spline.fs + n1_fs = n1_spline.fs + ntheta = size(n0_fs, 1) + + forcing_fs = zeros(Float64, ntheta, 2) + for i in 1:ntheta + n0 = [n0_fs[i, 1] n0_fs[i, 2]; n0_fs[i, 3] n0_fs[i, 4]] + rhs = n0 * w0 - exponent .* w0 + forcing_fs[i, 1] = rhs[1] + forcing_fs[i, 2] = rhs[2] + end + @views forcing_fs[end, :] .= forcing_fs[1, :] + + w1tilde_spline = _build_periodic_primitive_spline(theta_grid, forcing_fs) + w1tilde_fs = w1tilde_spline.fs + + rhs1_fs = zeros(Float64, ntheta, 2) + for i in 1:ntheta + n0 = [n0_fs[i, 1] n0_fs[i, 2]; n0_fs[i, 3] n0_fs[i, 4]] + n1 = [n1_fs[i, 1] n1_fs[i, 2]; n1_fs[i, 3] n1_fs[i, 4]] + w1tilde = [w1tilde_fs[i, 1], w1tilde_fs[i, 2]] + rhs = (n0 * w1tilde - (exponent - 1.0) .* w1tilde) + n1 * w0 + rhs1_fs[i, 1] = rhs[1] + rhs1_fs[i, 2] = rhs[2] + end + @views rhs1_fs[end, :] .= rhs1_fs[1, :] + + rhs_avg = FastInterpolations.integrate(cubic_interp(theta_grid, Series(rhs1_fs); bc=PeriodicBC())) + + lhs = copy(d0bar) + lhs[1, 1] -= exponent - 1.0 + lhs[2, 2] -= exponent - 1.0 + c1 = -(lhs \ rhs_avg) + + return ( + di=di, + alpha=alpha, + exponent=exponent, + w0=w0, + c1=c1, + w1tilde_spline=w1tilde_spline, + branch=branch + ) +end + +function _eval_periodic_series(spline, theta::Real) + theta_min = first(spline.xs) + theta_period = last(spline.xs) - theta_min + theta_wrapped = mod(Float64(theta) - theta_min, theta_period) + theta_min + return spline.itp(theta_wrapped) +end + +function _compute_asymptotic_initial_condition(ode_coefficient_spline, matching_data::NamedTuple, theta_start::Float64) + coeffs = _eval_periodic_series(ode_coefficient_spline, theta_start) + sigma = coeffs[9] + + tau = abs(theta_start) + exponent = matching_data.exponent + if !isfinite(exponent) || isnan(exponent) + return ComplexF64[NaN, NaN], matching_data.di, matching_data.alpha + end + + w1tilde = _eval_periodic_series(matching_data.w1tilde_spline, theta_start) + w1 = [ + w1tilde[1] + matching_data.c1[1], + w1tilde[2] + matching_data.c1[2] + ] + + w0 = matching_data.w0 + prefactor = tau^exponent + y1 = prefactor * tau^(-0.5) * (w0[1] + w1[1] / theta_start) + y2 = prefactor * tau^(+0.5) * (sigma * (w0[1] + w1[1] / theta_start) + w0[2] + w1[2] / theta_start) + + return ComplexF64[y1, y2], matching_data.di, matching_data.alpha +end + +function _integrate_ballooning_side( + ode_coefficient_spline, + theta_start::Float64, + theta_end::Float64, + initial_condition, + theta_k::Float64, + tolerance::Float64, + minimum_step::Float64 +) + problem = ODEProblem( + compute_ballooning_ode!, + initial_condition, + (theta_start, theta_end), + (ode_coefficient_spline, theta_k) + ) + + return solve(problem, DP5(); reltol=tolerance, abstol=tolerance^2, dtmin=minimum_step, adaptive=true) +end + +function _extract_log_derivative(solution) + y_end = solution.u[end] + theta_end = solution.t[end] + return y_end[2] / y_end[1], y_end, theta_end +end + +function _project_onto_asymptotic_basis(target_solution, big_solution, small_solution) + basis_matrix = ComplexF64[ + big_solution[1] small_solution[1] + big_solution[2] small_solution[2] + ] + coefficients = basis_matrix \ ComplexF64[target_solution[1], target_solution[2]] + return coefficients[1], coefficients[2] +end + """ - integrate_ballooning_ode(ode_coefficient_spline; theta_k=0.0) + integrate_ballooning_ode(ode_coefficient_spline; theta_k=0.0, mode=:delta_prime_legacy) Integrates the ballooning ODE from `-Infinity` to `-1e-3` and `+Infinity` to `+1e-3`. Computes Delta' = (y'/y)_right - (y'/y)_left. @@ -617,7 +855,15 @@ Computes Delta' = (y'/y)_right - (y'/y)_left. - `delta_prime`: The stability index Δ'. """ -function integrate_ballooning_ode(ode_coefficient_spline; theta_k::Float64=0.0) +function integrate_ballooning_ode( + ode_coefficient_spline; + theta_k::Float64=0.0, + mode::Symbol=:delta_prime_legacy, + d0bar::Union{Nothing,Matrix{Float64}}=nothing, + n0_spline=nothing, + n1_spline=nothing, + theta_grid::Union{Nothing,Vector{Float64}}=nothing +) TOLERANCE = 1e-8 MINIMUM_STEP = 1e-10 MATCHING_POINT = 1e-3 @@ -628,49 +874,159 @@ function integrate_ballooning_ode(ode_coefficient_spline; theta_k::Float64=0.0) theta_start_right = THETA_MAX0 theta_end_right = MATCHING_POINT - initial_condition_left = [0.0, 1.0] - initial_condition_right = [0.0, -1.0] + if mode == :delta_prime_legacy + initial_condition_left = [0.0, 1.0] + initial_condition_right = [0.0, -1.0] + + sol_left = _integrate_ballooning_side( + ode_coefficient_spline, + theta_start_left, + theta_end_left, + initial_condition_left, + theta_k, + TOLERANCE, + MINIMUM_STEP + ) + if sol_left.retcode != ReturnCode.Success + return (value=NaN, di=NaN) + end - problem_left = ODEProblem( - compute_ballooning_ode!, - initial_condition_left, - (theta_start_left, theta_end_left), - (ode_coefficient_spline, theta_k) - ) - sol_left = solve( - problem_left, - DP5(); - reltol=TOLERANCE, - abstol=TOLERANCE^2, - dtmin=MINIMUM_STEP, - adaptive=true - ) - if sol_left.retcode != ReturnCode.Success - return (value=NaN,) - end + sol_right = _integrate_ballooning_side( + ode_coefficient_spline, + theta_start_right, + theta_end_right, + initial_condition_right, + theta_k, + TOLERANCE, + MINIMUM_STEP + ) + if sol_right.retcode != ReturnCode.Success + return (value=NaN, di=NaN) + end - problem_right = ODEProblem( - compute_ballooning_ode!, - initial_condition_right, - (theta_start_right, theta_end_right), - (ode_coefficient_spline, theta_k) - ) - sol_right = solve( - problem_right, - DP5(); - reltol=TOLERANCE, - abstol=TOLERANCE^2, - dtmin=MINIMUM_STEP, - adaptive=true - ) - if sol_right.retcode != ReturnCode.Success - return (value=NaN,) - end + log_deriv_left, _, _ = _extract_log_derivative(sol_left) + log_deriv_right, _, _ = _extract_log_derivative(sol_right) + + return (value=log_deriv_right - log_deriv_left, di=NaN) + elseif mode == :delta_prime_small + if d0bar === nothing || n0_spline === nothing || n1_spline === nothing || theta_grid === nothing + error("d0bar, n0_spline, n1_spline, and theta_grid are required for mode=:delta_prime_small") + end + + di, alpha = _compute_mercier_from_d0bar(d0bar) + if !isfinite(di) || di >= 0.0 || isnan(alpha) + return (value=NaN, di=di, alpha=NaN) + end + + theta_max = _compute_theta_max_like_fortran(ode_coefficient_spline; thmax0=THETA_MAX0) + theta_start_left = -theta_max + theta_start_right = theta_max + + small_matching_data = _build_branch_matching_data(n0_spline, n1_spline, d0bar, :small, theta_grid) + initial_condition_left, _, _ = _compute_asymptotic_initial_condition( + ode_coefficient_spline, + small_matching_data, + theta_start_left + ) + initial_condition_right, _, _ = _compute_asymptotic_initial_condition( + ode_coefficient_spline, + small_matching_data, + theta_start_right + ) + + sol_left = _integrate_ballooning_side( + ode_coefficient_spline, + theta_start_left, + theta_end_left, + initial_condition_left, + theta_k, + TOLERANCE, + MINIMUM_STEP + ) + if sol_left.retcode != ReturnCode.Success + return (value=NaN, di=di, alpha=alpha) + end + + sol_right = _integrate_ballooning_side( + ode_coefficient_spline, + theta_start_right, + theta_end_right, + initial_condition_right, + theta_k, + TOLERANCE, + MINIMUM_STEP + ) + if sol_right.retcode != ReturnCode.Success + return (value=NaN, di=di, alpha=alpha) + end + + log_deriv_left, _, _ = _extract_log_derivative(sol_left) + log_deriv_right, _, _ = _extract_log_derivative(sol_right) - log_deriv_left = sol_left.u[end][2] / sol_left.u[end][1] - log_deriv_right = sol_right.u[end][2] / sol_right.u[end][1] + return (value=log_deriv_right - log_deriv_left, di=di, alpha=alpha) + elseif mode == :ca1 + if d0bar === nothing || n0_spline === nothing || n1_spline === nothing || theta_grid === nothing + error("d0bar, n0_spline, n1_spline, and theta_grid are required for mode=:ca1") + end + + di, alpha = _compute_mercier_from_d0bar(d0bar) + if !isfinite(di) || di >= 0.0 || isnan(alpha) + return (value=NaN, di=di, alpha=NaN, ca1_left=NaN, ca2_left=NaN, ca1_right=NaN, ca2_right=NaN) + end - return (value=log_deriv_right - log_deriv_left,) + theta_max = _compute_theta_max_like_fortran(ode_coefficient_spline; thmax0=THETA_MAX0) + theta_start_left = -theta_max + theta_start_right = theta_max + + legacy_left = [0.0, 1.0] + legacy_right = [0.0, -1.0] + big_matching_data = _build_branch_matching_data(n0_spline, n1_spline, d0bar, :big, theta_grid) + small_matching_data = _build_branch_matching_data(n0_spline, n1_spline, d0bar, :small, theta_grid) + big_left, _, _ = _compute_asymptotic_initial_condition(ode_coefficient_spline, big_matching_data, theta_start_left) + small_left, _, _ = _compute_asymptotic_initial_condition(ode_coefficient_spline, small_matching_data, theta_start_left) + big_right, _, _ = _compute_asymptotic_initial_condition(ode_coefficient_spline, big_matching_data, theta_start_right) + small_right, _, _ = _compute_asymptotic_initial_condition(ode_coefficient_spline, small_matching_data, theta_start_right) + + sol_target_left = _integrate_ballooning_side(ode_coefficient_spline, theta_start_left, theta_end_left, legacy_left, theta_k, TOLERANCE, MINIMUM_STEP) + sol_target_right = _integrate_ballooning_side(ode_coefficient_spline, theta_start_right, theta_end_right, legacy_right, theta_k, TOLERANCE, MINIMUM_STEP) + sol_big_left = _integrate_ballooning_side(ode_coefficient_spline, theta_start_left, theta_end_left, big_left, theta_k, TOLERANCE, MINIMUM_STEP) + sol_small_left = _integrate_ballooning_side(ode_coefficient_spline, theta_start_left, theta_end_left, small_left, theta_k, TOLERANCE, MINIMUM_STEP) + sol_big_right = _integrate_ballooning_side(ode_coefficient_spline, theta_start_right, theta_end_right, big_right, theta_k, TOLERANCE, MINIMUM_STEP) + sol_small_right = _integrate_ballooning_side(ode_coefficient_spline, theta_start_right, theta_end_right, small_right, theta_k, TOLERANCE, MINIMUM_STEP) + + if !( + sol_target_left.retcode == ReturnCode.Success && + sol_target_right.retcode == ReturnCode.Success && + sol_big_left.retcode == ReturnCode.Success && + sol_small_left.retcode == ReturnCode.Success && + sol_big_right.retcode == ReturnCode.Success && + sol_small_right.retcode == ReturnCode.Success + ) + return (value=NaN, di=di, alpha=alpha, ca1_left=NaN, ca2_left=NaN, ca1_right=NaN, ca2_right=NaN) + end + + target_left = ComplexF64[sol_target_left.u[end][1], sol_target_left.u[end][2]] + target_right = ComplexF64[sol_target_right.u[end][1], sol_target_right.u[end][2]] + basis_big_left = ComplexF64[sol_big_left.u[end][1], sol_big_left.u[end][2]] + basis_small_left = ComplexF64[sol_small_left.u[end][1], sol_small_left.u[end][2]] + basis_big_right = ComplexF64[sol_big_right.u[end][1], sol_big_right.u[end][2]] + basis_small_right = ComplexF64[sol_small_right.u[end][1], sol_small_right.u[end][2]] + + ca1_left, ca2_left = _project_onto_asymptotic_basis(target_left, basis_big_left, basis_small_left) + ca1_right, ca2_right = _project_onto_asymptotic_basis(target_right, basis_big_right, basis_small_right) + + return ( + value=ca1_right, + di=di, + alpha=alpha, + ca1_left=ca1_left, + ca2_left=ca2_left, + ca1_right=ca1_right, + ca2_right=ca2_right + ) + else + error("Unsupported integration mode: $(mode)") + end end diff --git a/src/ForceFreeStates/ForceFreeStates.jl b/src/ForceFreeStates/ForceFreeStates.jl index 61eb48bbf..3c000ab31 100644 --- a/src/ForceFreeStates/ForceFreeStates.jl +++ b/src/ForceFreeStates/ForceFreeStates.jl @@ -20,7 +20,6 @@ import StaticArrays: @MMatrix # Include all necessary files include("ForceFreeStatesStructs.jl") -include("Mercier.jl") include("Bal.jl") include("EulerLagrange.jl") include("Sing.jl") diff --git a/src/ForceFreeStates/ForceFreeStatesStructs.jl b/src/ForceFreeStates/ForceFreeStatesStructs.jl index 078d7eda7..3156ebab1 100644 --- a/src/ForceFreeStates/ForceFreeStatesStructs.jl +++ b/src/ForceFreeStates/ForceFreeStatesStructs.jl @@ -152,11 +152,10 @@ A mutable struct containing control parameters for stability analysis, set by th ## Fields - `verbose::Bool` - Enable verbose output - - `bal_flag::Bool` - Enable ballooning mode analysis + - `local_stability_flag::Bool` - Enable local stability analysis (`D_I` and ballooning) - `mat_flag::Bool` - Enable matrix output - `ode_flag::Bool` - Enable ODE integration diagnostics - `vac_flag::Bool` - Enable vacuum region calculation - - `mer_flag::Bool` - Enable Mercier stability criterion - `fft_flag::Bool` - Enable Fourier transform analysis - `mthvac::Int` - Number of vacuum poloidal grid points (corresponds to `mtheta` in VacuumInput) - `nzvac::Int` - Number of vacuum toroidal grid points (corresponds to `nzeta` in VacuumInput3D) @@ -193,11 +192,10 @@ A mutable struct containing control parameters for stability analysis, set by th """ @kwdef mutable struct ForceFreeStatesControl verbose::Bool = true - bal_flag::Bool = false + local_stability_flag::Bool = false mat_flag::Bool = false ode_flag::Bool = false vac_flag::Bool = false - mer_flag::Bool = false fft_flag::Bool = false mthvac::Int = 480 nzvac::Int = 1 diff --git a/src/ForceFreeStates/Mercier.jl b/src/ForceFreeStates/Mercier.jl deleted file mode 100644 index 1a4d6f96f..000000000 --- a/src/ForceFreeStates/Mercier.jl +++ /dev/null @@ -1,79 +0,0 @@ -""" - mercier_scan!(locstab_fs::Array{Float64,5}, plasma_eq::PlasmaEquilibrium) - -Evaluates Mercier criterion for local stability [Glasser Phys. Plasmas 2016 112506] -and modifies results in place within the local stability array. -Performs the same function as `mercier_scan` in the Fortran code. -""" -function mercier_scan!(locstab_fs::Matrix{Float64}, plasma_eq::Equilibrium.PlasmaEquilibrium) - - # Shorthand - profiles = plasma_eq.profiles - - # Allocate splines - ff_fs = zeros(length(plasma_eq.rzphi_ys), 5) - - # Compute surface quantities - hint = Ref(1) # Linear search hint for sequential psi access - for ipsi in 1:profiles.npts - psi = profiles.xs[ipsi] - twopif = profiles.F_spline.y[ipsi] - p1 = profiles.P_deriv(psi; hint=hint) - v1 = profiles.dVdpsi_spline.y[ipsi] - v2 = profiles.dVdpsi_deriv(psi; hint=hint) - q = profiles.q_spline.y[ipsi] - q1 = profiles.q_deriv(psi; hint=hint) - chi1 = 2π * plasma_eq.psio - - # Evaluate coordinates and jacobian - for itheta in 1:length(plasma_eq.rzphi_ys) - theta = plasma_eq.rzphi_ys[itheta] - - # Access nodal derivatives at grid points - f1 = plasma_eq.rzphi_rsquared.nodal_derivs.partials[1, ipsi, itheta] - f2 = plasma_eq.rzphi_offset.nodal_derivs.partials[1, ipsi, itheta] - jac = plasma_eq.rzphi_jac.nodal_derivs.partials[1, ipsi, itheta] - fy1 = plasma_eq.rzphi_rsquared.nodal_derivs.partials[3, ipsi, itheta] - fy2 = plasma_eq.rzphi_offset.nodal_derivs.partials[3, ipsi, itheta] - fy3 = plasma_eq.rzphi_nu.nodal_derivs.partials[3, ipsi, itheta] - - rfac = sqrt(f1) - eta = 2π * (theta + f2) - r = plasma_eq.ro + rfac * cos(eta) - - # Evaluate other local quantities - v21 = fy1 / (2.0 * rfac * jac) - v22 = (1.0 + fy2) * 2π * rfac / jac - v23 = fy3 * r / jac - v33 = 2π * r / jac - bsq = chi1^2 * (v21^2 + v22^2 + (v23 + q * v33)^2) - dpsisq = (2π * r)^2 * (v21^2 + v22^2) - - # Evaluate integrands - ff_fs[itheta, 1] = bsq / dpsisq - ff_fs[itheta, 2] = 1.0 / dpsisq - ff_fs[itheta, 3] = 1.0 / bsq - ff_fs[itheta, 4] = 1.0 / (bsq * dpsisq) - ff_fs[itheta, 5] = bsq - - # Weight by jacobian and volume element - @views ff_fs[itheta, :] .*= jac / v1 - end - - # Integrate quantities with respect to theta using FastInterpolations - itp = cubic_interp(plasma_eq.rzphi_ys, Series(ff_fs); bc=PeriodicBC()) - avg = FastInterpolations.integrate(itp) - - # Evaluate Mercier criterion and related quantities - term = twopif * p1 * v1 / (q1 * chi1^3) * avg[2] - di = -0.25 + term * (1 - term) + - p1 * (v1 / (q1 * chi1^2))^2 * avg[1] * - (p1 * (avg[3] + (twopif / chi1)^2 * avg[4]) - v2 / v1) - h = twopif * p1 * v1 / (q1 * chi1^3) * (avg[2] - avg[1] / avg[5]) - - # Store results in output spline structure - locstab_fs[ipsi, 1] = di * profiles.xs[ipsi] - locstab_fs[ipsi, 2] = (di + (h - 0.5)^2) * profiles.xs[ipsi] - locstab_fs[ipsi, 3] = h - end -end diff --git a/src/GeneralizedPerturbedEquilibrium.jl b/src/GeneralizedPerturbedEquilibrium.jl index 13c43233b..2a6a73f5c 100755 --- a/src/GeneralizedPerturbedEquilibrium.jl +++ b/src/GeneralizedPerturbedEquilibrium.jl @@ -46,7 +46,7 @@ import AdaptiveArrayPools: @with_pool # Import ForceFreeStates types and functions needed for main using .ForceFreeStates: ForceFreeStatesInternal, ForceFreeStatesControl, DebugSettings, VacuumData, OdeState, FourFitVars using .ForceFreeStates: sing_lim!, sing_find! -using .ForceFreeStates: mercier_scan!, compute_ballooning_stability! +using .ForceFreeStates: compute_ballooning_stability! using .ForceFreeStates: make_metric, make_matrix, make_kinetic_matrix using .ForceFreeStates: eulerlagrange_integration, free_run! @@ -132,17 +132,11 @@ function main(args::Vector{String}=String[]; dd::Union{IMASdd.dd,Nothing}=nothin # equil = set_up_equilibrium(equil.config) end - # Compute Mercier and Ballooning stability (if desired) - # This holds di, dr, h (calculated in mercier_scan), ca1, and ca2 (calculated in ballooning scan) + # Compute local stability (if desired). This holds `D_I` from the + # ballooning coefficient system and the local ballooning result. profiles_xs = equil.profiles.xs locstab_fs = zeros(Float64, length(profiles_xs), 5) - if ctrl.mer_flag - if ctrl.verbose - @info "Evaluating Mercier criterion" - end - mercier_scan!(locstab_fs, equil) - end - if ctrl.bal_flag + if ctrl.local_stability_flag compute_ballooning_stability!(ctrl, locstab_fs, equil) end # Fit data to splines @@ -415,17 +409,17 @@ function write_outputs_to_HDF5( out_h5["splines/rzphi/jac"] = equil.rzphi_jac.nodal_derivs.partials[1, :, :] # Write local stability data; always write all entries, using empty arrays when not computed - if ctrl.mer_flag + if ctrl.local_stability_flag locstab_xs = intr.locstab.cache.x out_h5["locstab/di"] = intr.locstab.y[:, 1] ./ locstab_xs - out_h5["locstab/dr"] = intr.locstab.y[:, 2] ./ locstab_xs else out_h5["locstab/di"] = Float64[] - out_h5["locstab/dr"] = Float64[] end - out_h5["singular/di0"] = (ctrl.mer_flag && !isempty(intr.sing)) ? + out_h5["locstab/dr"] = Float64[] + out_h5["singular/di0"] = (ctrl.local_stability_flag && !isempty(intr.sing)) ? [intr.locstab(sing.psifac)[1] / sing.psifac for sing in intr.sing] : Float64[] - out_h5["locstab/ca1"] = ctrl.bal_flag ? intr.locstab.y[:, 4] : Float64[] + out_h5["locstab/delta_prime"] = ctrl.local_stability_flag ? intr.locstab.y[:, 4] : Float64[] + out_h5["locstab/ca1"] = Float64[] # Write integration data # TODO: technically this should only be written if ode_flag is true, but that's going to get deprecated eventually diff --git a/test/test_data/regression_solovev_ideal_example/gpec.toml b/test/test_data/regression_solovev_ideal_example/gpec.toml index 263b93061..374772cd3 100644 --- a/test/test_data/regression_solovev_ideal_example/gpec.toml +++ b/test/test_data/regression_solovev_ideal_example/gpec.toml @@ -25,11 +25,10 @@ tw = 0.05 # Sharpness of wall corners (try 0.05 as equal_arc_wall = true # Equal arc length distribution of nodes on wall [ForceFreeStates] -bal_flag = false # Ideal MHD ballooning criterion for short wavelengths +local_stability_flag = true # Local D_I and ballooning stability mat_flag = true # Construct coefficient matrices for diagnostic purposes ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes -mer_flag = true # Evaluate the Mercier criterian psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... diff --git a/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml b/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml index 8782c8516..5b780fe56 100644 --- a/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml +++ b/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml @@ -25,11 +25,10 @@ tw = 0.05 # Sharpness of wall corners (try 0.05 as equal_arc_wall = true # Equal arc length distribution of nodes on wall [ForceFreeStates] -bal_flag = false # Ideal MHD ballooning criterion for short wavelengths +local_stability_flag = true # Local D_I and ballooning stability mat_flag = true # Construct coefficient matrices for diagnostic purposes ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes -mer_flag = true # Evaluate the Mercier criterian psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... diff --git a/test/test_data/regression_solovev_kinetic_example/gpec.toml b/test/test_data/regression_solovev_kinetic_example/gpec.toml index c3e369054..89ac6d8fd 100644 --- a/test/test_data/regression_solovev_kinetic_example/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_example/gpec.toml @@ -25,11 +25,10 @@ tw = 0.05 # Sharpness of wall corners (try 0.05 as equal_arc_wall = true # Equal arc length distribution of nodes on wall [ForceFreeStates] -bal_flag = false # Ideal MHD ballooning criterion for short wavelengths +local_stability_flag = true # Local D_I and ballooning stability mat_flag = false # Construct coefficient matrices for diagnostic purposes ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes -mer_flag = true # Evaluate the Mercier criterian psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... diff --git a/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml b/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml index c56b41214..97820b4d5 100644 --- a/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml @@ -25,11 +25,10 @@ tw = 0.05 # Sharpness of wall corners (try 0.05 as equal_arc_wall = true # Equal arc length distribution of nodes on wall [ForceFreeStates] -bal_flag = false # Ideal MHD ballooning criterion for short wavelengths +local_stability_flag = true # Local D_I and ballooning stability mat_flag = false # Construct coefficient matrices for diagnostic purposes ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes -mer_flag = true # Evaluate the Mercier criterian psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... From 6d288923210a5e795b86736c4f3a85605dec7bc3 Mon Sep 17 00:00:00 2001 From: jmlmir369 Date: Thu, 30 Apr 2026 22:06:01 +0900 Subject: [PATCH 006/135] erasing small solution logics --- .../Bal_mode_compare.ipynb | 212 -------- .../Bal_salpha_delta_di_summary.ipynb | 257 ---------- .../Local_stability_main_plot.ipynb | 93 ---- src/ForceFreeStates/Bal.jl | 464 +++--------------- 4 files changed, 55 insertions(+), 971 deletions(-) delete mode 100644 examples/DIIID-like_ideal_example/Bal_mode_compare.ipynb delete mode 100644 examples/DIIID-like_ideal_example/Bal_salpha_delta_di_summary.ipynb delete mode 100644 examples/Solovev_ideal_example/Local_stability_main_plot.ipynb diff --git a/examples/DIIID-like_ideal_example/Bal_mode_compare.ipynb b/examples/DIIID-like_ideal_example/Bal_mode_compare.ipynb deleted file mode 100644 index f9321118c..000000000 --- a/examples/DIIID-like_ideal_example/Bal_mode_compare.ipynb +++ /dev/null @@ -1,212 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Ballooning mode comparisons\n", - "\n", - "Compare the legacy delta-prime shooting result, the small-solution delta-prime result, and the `ca1` projection result using both flux-surface profiles and a local s-alpha scan." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "using Pkg\n", - "Pkg.activate(\"../..\")\n", - "\n", - "using GeneralizedPerturbedEquilibrium\n", - "using Plots\n", - "using LaTeXStrings\n", - "using TOML\n", - "\n", - "eq_config = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(TOML.parsefile(\"gpec.toml\")[\"Equilibrium\"], pwd())\n", - "equil = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(eq_config)\n", - "psi_norm = Vector(equil.profiles.xs)\n", - "\n", - "modes = (:delta_prime_legacy, :delta_prime_small, :ca1)\n", - "mode_titles = Dict(\n", - " :delta_prime_legacy => L\"\\Delta'\",\n", - " :delta_prime_small => L\"\\Delta'\",\n", - " :ca1 => L\"c_{a1}\",\n", - ")\n", - "\n", - "real_or_nan(x; atol=1e-10) = x isa Real ? Float64(x) : (x isa Complex && isapprox(imag(x), 0.0; atol=atol) ? Float64(real(x)) : NaN)\n", - "\n", - "function symmetric_clims(z)\n", - " finite_vals = vec(z)[isfinite.(vec(z))]\n", - " maxabs = isempty(finite_vals) ? 1.0 : maximum(abs.(finite_vals))\n", - " maxabs = max(maxabs, eps(Float64))\n", - " return (-maxabs, maxabs)\n", - "end\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Flux-surface mode comparison" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "538f03b3", - "metadata": {}, - "outputs": [], - "source": [ - "psi_indices = collect(eachindex(psi_norm))\n", - "\n", - "mode_values = Dict(mode => fill(NaN, length(psi_indices)) for mode in modes)\n", - "di_profile = fill(NaN, length(psi_indices))\n", - "\n", - "for (i, psi_idx) in enumerate(psi_indices)\n", - " coeff = try\n", - " GeneralizedPerturbedEquilibrium.ForceFreeStates.prepare_ballooning_coefficients(psi_idx, equil)\n", - " catch err\n", - " @warn \"coefficient preparation failed\" psi_idx psi=psi_norm[psi_idx] exception=(err, catch_backtrace())\n", - " nothing\n", - " end\n", - " coeff === nothing && continue\n", - "\n", - " di_profile[i] = coeff.di\n", - "\n", - " for mode in modes\n", - " result = try\n", - " GeneralizedPerturbedEquilibrium.ForceFreeStates.integrate_ballooning_ode(\n", - " coeff.ode_coefficient_spline;\n", - " theta_k=0.0,\n", - " mode=mode,\n", - " d0bar=coeff.d0bar,\n", - " n0_spline=coeff.n0_spline,\n", - " n1_spline=coeff.n1_spline,\n", - " theta_grid=coeff.theta_grid,\n", - " )\n", - " catch err\n", - " @warn \"mode comparison failed\" psi_idx psi=psi_norm[psi_idx] mode exception=(err, catch_backtrace())\n", - " nothing\n", - " end\n", - "\n", - " if result !== nothing\n", - " mode_values[mode][i] = real_or_nan(result.value)\n", - " end\n", - " end\n", - "end\n", - "\n", - "psi_scan = psi_norm[psi_indices]\n", - "\n", - "profile_specs = [\n", - " (:delta_prime_legacy, L\"\\Delta'\", L\"\\Delta'\"),\n", - " (:delta_prime_small, L\"\\Delta'\", L\"\\Delta'\"),\n", - " (:ca1, L\"c_{a1}\", L\"c_{a1}\"),\n", - "]\n", - "\n", - "profile_plots = map(profile_specs) do (mode, title_text, ylabel_text)\n", - " p = plot(\n", - " psi_scan,\n", - " mode_values[mode];\n", - " xlabel=L\"\\psi_N\",\n", - " ylabel=ylabel_text,\n", - " title=title_text,\n", - " label=String(mode),\n", - " linewidth=2,\n", - " framestyle=:box,\n", - " )\n", - " hline!(p, [0.0]; color=:black, linestyle=:dash, label=\"\")\n", - " p\n", - "end\n", - "\n", - "display(plot(profile_plots...; layout=(1, 3), size=(1350, 390)))\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## s-alpha mode comparison" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "psi_target = 0.67680851\n", - "psi_idx_scan = argmin(abs.(psi_norm .- psi_target))\n", - "\n", - "s_scales = collect(range(-5.0, 5.0; length=30))\n", - "alpha_scales = collect(range(-5.0, 5.0; length=30))\n", - "\n", - "println(\"Running s-alpha mode comparison at index $(psi_idx_scan), psi_norm=$(round(psi_norm[psi_idx_scan], digits=6))\")\n", - "\n", - "scan_results = Dict{Symbol,Any}()\n", - "for mode in modes\n", - " scan_results[mode] = GeneralizedPerturbedEquilibrium.ForceFreeStates.scan_delta_prime_map(\n", - " psi_idx_scan,\n", - " equil;\n", - " theta_k=0.0,\n", - " mode=mode,\n", - " s_scales=s_scales,\n", - " alpha_scales=alpha_scales,\n", - " )\n", - "end\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "reference = scan_results[:delta_prime_legacy].reference\n", - "\n", - "scan_s_raw = scan_results[:delta_prime_legacy].s_values\n", - "scan_alpha_raw = scan_results[:delta_prime_legacy].alpha_values\n", - "s_order = sortperm(scan_s_raw)\n", - "alpha_order = sortperm(scan_alpha_raw)\n", - "scan_s = scan_s_raw[s_order]\n", - "scan_alpha = scan_alpha_raw[alpha_order]\n", - "di_contour = scan_results[:delta_prime_legacy].di_values[s_order, alpha_order]\n", - "\n", - "salpha_plots = map(modes) do mode\n", - " z = scan_results[mode].delta_prime[s_order, alpha_order]\n", - " p = contourf(\n", - " scan_alpha, scan_s, z;\n", - " c=cgrad([:blue, :white, :red]),\n", - " clims=symmetric_clims(z),\n", - " xlabel=L\"\\alpha\",\n", - " ylabel=L\"s\",\n", - " title=mode_titles[mode],\n", - " levels=41,\n", - " framestyle=:box,\n", - " )\n", - " contour!(p, scan_alpha, scan_s, z; levels=[0.0], color=:black, linewidth=2, label=\"\", colorbar=false)\n", - " contour!(p, scan_alpha, scan_s, di_contour; levels=[0.0], color=:red, linestyle=:dash, linewidth=2, label=L\"D_I=0\", colorbar=false)\n", - " scatter!(p, [reference.alpha_ref], [reference.s_ref]; color=:green, marker=:star5, ms=7, label=\"equilibrium\")\n", - " p\n", - "end\n", - "\n", - "display(plot(salpha_plots...; layout=(1, 3), size=(1350, 390)))\n" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Julia 1.12.4", - "language": "julia", - "name": "julia-1.12" - }, - "language_info": { - "file_extension": ".jl", - "mimetype": "application/julia", - "name": "julia", - "version": "1.12.4" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/examples/DIIID-like_ideal_example/Bal_salpha_delta_di_summary.ipynb b/examples/DIIID-like_ideal_example/Bal_salpha_delta_di_summary.ipynb deleted file mode 100644 index 7be986fa8..000000000 --- a/examples/DIIID-like_ideal_example/Bal_salpha_delta_di_summary.ipynb +++ /dev/null @@ -1,257 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "id": "s-alpha-profile-extrema", - "metadata": {}, - "outputs": [], - "source": [ - "using Pkg\n", - "Pkg.activate(\"../..\")\n", - "\n", - "using GeneralizedPerturbedEquilibrium\n", - "using Plots\n", - "using Printf\n", - "using Statistics\n", - "using LaTeXStrings\n", - "using TOML\n", - "\n", - "eq_config = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(TOML.parsefile(\"gpec.toml\")[\"Equilibrium\"], pwd())\n", - "equil = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(eq_config)\n", - "psi_norm = Vector(equil.profiles.xs)\n", - "\n", - "function finite_local_extrema(values::AbstractVector{<:Real})\n", - " extrema = Int[]\n", - " for i in 2:length(values)-1\n", - " if !isfinite(values[i - 1]) || !isfinite(values[i]) || !isfinite(values[i + 1])\n", - " continue\n", - " end\n", - " if (values[i] >= values[i - 1] && values[i] >= values[i + 1]) ||\n", - " (values[i] <= values[i - 1] && values[i] <= values[i + 1])\n", - " push!(extrema, i)\n", - " end\n", - " end\n", - " return extrema\n", - "end\n", - "\n", - "function print_extrema_report(name::String, psi::AbstractVector, values::AbstractVector, extrema::AbstractVector{Int})\n", - " println(\"\\n\", name, \" extrema\")\n", - " if isempty(extrema)\n", - " println(\" none\")\n", - " return\n", - " end\n", - " println(\" index\\tpsi_norm\\tvalue\")\n", - " for i in extrema\n", - " @printf(\" %d\\t%.8f\\t%.12e\\n\", i, psi[i], values[i])\n", - " end\n", - "end\n", - "\n", - "s_profile = fill(NaN, length(psi_norm))\n", - "alpha_profile = fill(NaN, length(psi_norm))\n", - "\n", - "for i in eachindex(psi_norm)\n", - " try\n", - " ref = GeneralizedPerturbedEquilibrium.ForceFreeStates.salpha_reference(i, equil)\n", - " s_profile[i] = ref.s_ref\n", - " alpha_profile[i] = ref.alpha_ref\n", - " catch err\n", - " @warn \"s-alpha reference failed\" i psi=psi_norm[i] exception=(err, catch_backtrace())\n", - " end\n", - "end\n", - "\n", - "s_extrema = finite_local_extrema(s_profile)\n", - "alpha_extrema = finite_local_extrema(alpha_profile)\n", - "print_extrema_report(\"s\", psi_norm, s_profile, s_extrema)\n", - "print_extrema_report(\"alpha\", psi_norm, alpha_profile, alpha_extrema)\n", - "\n", - "s_mask = isfinite.(s_profile)\n", - "alpha_mask = isfinite.(alpha_profile)\n", - "\n", - "p_s = plot(\n", - " psi_norm[s_mask], s_profile[s_mask];\n", - " xlabel=\"psi_norm\",\n", - " ylabel=\"s\",\n", - " label=\"s\",\n", - " lw=2,\n", - " title=\"s\",\n", - " framestyle=:box,\n", - ")\n", - "scatter!(p_s, psi_norm[s_extrema], s_profile[s_extrema]; label=\"extrema\", marker=:circle, color=:red, ms=5)\n", - "\n", - "p_alpha = plot(\n", - " psi_norm[alpha_mask], alpha_profile[alpha_mask];\n", - " xlabel=\"psi_norm\",\n", - " ylabel=\"alpha\",\n", - " label=\"alpha\",\n", - " lw=2,\n", - " title=\"alpha\",\n", - " framestyle=:box,\n", - ")\n", - "scatter!(p_alpha, psi_norm[alpha_extrema], alpha_profile[alpha_extrema]; label=\"extrema\", marker=:circle, color=:red, ms=5)\n", - "\n", - "display(plot(p_s, p_alpha; layout=(1, 2), size=(1100, 420)))\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "delta-di-profile-extrema", - "metadata": {}, - "outputs": [], - "source": [ - "locstab_fs = zeros(length(psi_norm), 4)\n", - "ctrl = GeneralizedPerturbedEquilibrium.ForceFreeStates.ForceFreeStatesControl(verbose=false)\n", - "\n", - "println(\"Computing \\\\Delta' and D_I...\")\n", - "GeneralizedPerturbedEquilibrium.ForceFreeStates.compute_ballooning_stability!(ctrl, locstab_fs, equil; compute_delta_prime=true)\n", - "\n", - "delta_prime = Vector(locstab_fs[:, 4])\n", - "di_profile = fill(NaN, length(psi_norm))\n", - "psi_mask = abs.(psi_norm) .> eps(Float64)\n", - "di_profile[psi_mask] .= locstab_fs[psi_mask, 1] ./ psi_norm[psi_mask]\n", - "\n", - "delta_extrema = finite_local_extrema(delta_prime)\n", - "di_extrema = finite_local_extrema(di_profile)\n", - "print_extrema_report(\"\\\\Delta'\", psi_norm, delta_prime, delta_extrema)\n", - "print_extrema_report(\"D_I\", psi_norm, di_profile, di_extrema)\n", - "\n", - "delta_mask = isfinite.(delta_prime)\n", - "di_mask = isfinite.(di_profile)\n", - "\n", - "p_delta = plot(\n", - " psi_norm[delta_mask], delta_prime[delta_mask];\n", - " xlabel=\"psi_norm\",\n", - " ylabel=L\"\\Delta'\",\n", - " label=L\"\\Delta'\",\n", - " lw=2,\n", - " title=L\"\\Delta'\",\n", - " framestyle=:box,\n", - ")\n", - "scatter!(p_delta, psi_norm[delta_extrema], delta_prime[delta_extrema]; label=\"extrema\", marker=:diamond, color=:red, ms=5)\n", - "\n", - "p_di = plot(\n", - " psi_norm[di_mask], di_profile[di_mask];\n", - " xlabel=\"psi_norm\",\n", - " ylabel=L\"D_I\",\n", - " label=L\"D_I\",\n", - " lw=2,\n", - " title=L\"D_I\",\n", - " framestyle=:box,\n", - ")\n", - "scatter!(p_di, psi_norm[di_extrema], di_profile[di_extrema]; label=\"extrema\", marker=:diamond, color=:red, ms=5)\n", - "\n", - "display(plot(p_delta, p_di; layout=(1, 2), size=(1100, 420)))\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "s-alpha-delta-di-maps", - "metadata": {}, - "outputs": [], - "source": [ - "psi_target = 0.678\n", - "psi_idx_scan = argmin(abs.(psi_norm .- psi_target))\n", - "\n", - "println(\"Running s-alpha scan at index $(psi_idx_scan), psi_norm=$(round(psi_norm[psi_idx_scan], digits=6))\")\n", - "\n", - "s_scales = collect(range(-5.0, 5.0; length=30))\n", - "alpha_scales = collect(range(-5.0, 5.0; length=30))\n", - "\n", - "scan_result = GeneralizedPerturbedEquilibrium.ForceFreeStates.scan_delta_prime_map(\n", - " psi_idx_scan,\n", - " equil;\n", - " theta_k=0.0,\n", - " s_scales=s_scales,\n", - " alpha_scales=alpha_scales,\n", - ")\n", - "\n", - "scan_qprime_raw = scan_result.dqdpsi_ref .* scan_result.s_scales\n", - "scan_pprime_raw = scan_result.pprime_ref .* scan_result.alpha_scales\n", - "qprime_order = sortperm(scan_qprime_raw)\n", - "pprime_order = sortperm(scan_pprime_raw)\n", - "scan_qprime = scan_qprime_raw[qprime_order]\n", - "scan_pprime = scan_pprime_raw[pprime_order]\n", - "scan_delta = scan_result.delta_prime[qprime_order, pprime_order]\n", - "scan_di = scan_result.di_values[qprime_order, pprime_order]\n", - "\n", - "function symmetric_clims(z)\n", - " finite_vals = vec(z)[isfinite.(vec(z))]\n", - " maxabs = isempty(finite_vals) ? 1.0 : maximum(abs.(finite_vals))\n", - " maxabs = max(maxabs, eps(Float64))\n", - " return (-maxabs, maxabs)\n", - "end\n", - "\n", - "p_scan_delta = contourf(\n", - " scan_pprime, scan_qprime, scan_delta;\n", - " c=cgrad([:blue, :white, :red]),\n", - " clims=symmetric_clims(scan_delta),\n", - " xlabel=L\"p_{\\psi}\",\n", - " ylabel=L\"q_{\\psi}\",\n", - " title=L\"\\Delta'\",\n", - " levels=41,\n", - " framestyle=:box,\n", - ")\n", - "contour!(p_scan_delta, scan_pprime, scan_qprime, scan_delta; levels=[0.0], color=:black, linewidth=2, label=L\"\\Delta' = 0\")\n", - "scatter!(p_scan_delta, [scan_result.reference.pprime_ref], [scan_result.reference.qprime_ref]; color=:green, marker=:star5, ms=7, label=\"equilibrium\")\n", - "\n", - "p_scan_di = contourf(\n", - " scan_pprime, scan_qprime, scan_di;\n", - " c=cgrad([:blue, :white, :red]),\n", - " clims=symmetric_clims(scan_di),\n", - " xlabel=L\"p_{\\psi}\",\n", - " ylabel=L\"q_{\\psi}\",\n", - " title=L\"D_I\",\n", - " levels=41,\n", - " framestyle=:box,\n", - ")\n", - "contour!(p_scan_di, scan_pprime, scan_qprime, scan_di; levels=[0.0], color=:black, linewidth=2, label=L\"D_I = 0\")\n", - "scatter!(p_scan_di, [scan_result.reference.pprime_ref], [scan_result.reference.qprime_ref]; color=:green, marker=:star5, ms=7, label=\"equilibrium\")\n", - "\n", - "display(plot(p_scan_delta, p_scan_di; layout=(1, 2), size=(1150, 460)))\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "s-alpha-zero-contours", - "metadata": {}, - "outputs": [], - "source": [ - "p_zero = plot(\n", - " xlabel=L\"p_{\\psi}\",\n", - " ylabel=L\"q_{\\psi}\",\n", - " title=\"ballooning, Mercier contours\",\n", - " framestyle=:box,\n", - ")\n", - "contour!(p_zero, scan_pprime, scan_qprime, scan_delta;\n", - " levels=[0.0], color=:blue, linewidth=3,\n", - " label=L\"\\Delta' = 0\", colorbar=false)\n", - "\n", - "contour!(p_zero, scan_pprime, scan_qprime, scan_di;\n", - " levels=[0.0], color=:red, linewidth=3, linestyle=:dash,\n", - " label=L\"D_I = 0\", colorbar=false)\n", - "\n", - "\n", - "scatter!(p_zero, [scan_result.reference.pprime_ref], [scan_result.reference.qprime_ref]; color=:green, marker=:star5, ms=8, label=\"equilibrium\")\n", - "display(p_zero)\n" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Julia 1.12.4", - "language": "julia", - "name": "julia-1.12" - }, - "language_info": { - "file_extension": ".jl", - "mimetype": "application/julia", - "name": "julia", - "version": "1.12.4" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/examples/Solovev_ideal_example/Local_stability_main_plot.ipynb b/examples/Solovev_ideal_example/Local_stability_main_plot.ipynb deleted file mode 100644 index 67c6ffb88..000000000 --- a/examples/Solovev_ideal_example/Local_stability_main_plot.ipynb +++ /dev/null @@ -1,93 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Local stability from main run\n", - "\n", - "Run the full `GeneralizedPerturbedEquilibrium.main` path for this example, then read the HDF5 output and plot the local `D_I` and ballooning `\\Delta'` profiles." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "using Pkg\n", - "Pkg.activate(\"../..\")\n", - "\n", - "using GeneralizedPerturbedEquilibrium\n", - "using HDF5\n", - "using Plots\n", - "using LaTeXStrings\n", - "using TOML\n", - "\n", - "inputs = TOML.parsefile(\"gpec.toml\")\n", - "@assert get(inputs[\"ForceFreeStates\"], \"local_stability_flag\", false) \"local_stability_flag must be true to write local stability output\"\n", - "\n", - "GeneralizedPerturbedEquilibrium.main([pwd()])\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "h5_name = get(inputs[\"ForceFreeStates\"], \"HDF5_filename\", \"gpec.h5\")\n", - "\n", - "psi_norm = h5open(h5_name, \"r\") do h5\n", - " read(h5[\"splines/profiles/xs\"])\n", - "end\n", - "\n", - "di, delta_prime = h5open(h5_name, \"r\") do h5\n", - " read(h5[\"locstab/di\"]), read(h5[\"locstab/delta_prime\"])\n", - "end\n", - "\n", - "println(\"D_I finite: $(count(isfinite, di)) / $(length(di))\")\n", - "println(\"Delta prime finite: $(count(isfinite, delta_prime)) / $(length(delta_prime))\")\n", - "\n", - "p_di = plot(\n", - " psi_norm, di;\n", - " xlabel=L\"\\psi_N\",\n", - " ylabel=L\"D_I\",\n", - " title=L\"D_I\",\n", - " linewidth=2,\n", - " label=\"\",\n", - " framestyle=:box,\n", - ")\n", - "hline!(p_di, [0.0]; color=:black, linestyle=:dash, label=\"\")\n", - "\n", - "p_delta = plot(\n", - " psi_norm, delta_prime;\n", - " xlabel=L\"\\psi_N\",\n", - " ylabel=L\"\\Delta'\",\n", - " title=L\"\\Delta'\",\n", - " linewidth=2,\n", - " label=\"\",\n", - " framestyle=:box,\n", - ")\n", - "hline!(p_delta, [0.0]; color=:black, linestyle=:dash, label=\"\")\n", - "\n", - "display(plot(p_di, p_delta; layout=(1, 2), size=(1050, 390)))\n" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Julia 1.12.4", - "language": "julia", - "name": "julia-1.12" - }, - "language_info": { - "file_extension": ".jl", - "mimetype": "application/julia", - "name": "julia", - "version": "1.12.4" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/src/ForceFreeStates/Bal.jl b/src/ForceFreeStates/Bal.jl index dfbd6ce0f..4b5f6af56 100644 --- a/src/ForceFreeStates/Bal.jl +++ b/src/ForceFreeStates/Bal.jl @@ -28,8 +28,7 @@ function compute_ballooning_stability!( locstab_fs::Matrix{Float64}, plasma_eq::Equilibrium.PlasmaEquilibrium; theta_k::Float64=0.0, - compute_delta_prime::Bool=true, - mode::Symbol=:delta_prime_legacy + compute_delta_prime::Bool=true ) if ctrl.verbose @@ -47,14 +46,9 @@ function compute_ballooning_stability!( if compute_delta_prime && plasma_eq.profiles.xs[flux_surface_index] <= 1.0 result = integrate_ballooning_ode( coeff_data.ode_coefficient_spline; - theta_k=theta_k, - mode=mode, - d0bar=coeff_data.d0bar, - n0_spline=coeff_data.n0_spline, - n1_spline=coeff_data.n1_spline, - theta_grid=coeff_data.theta_grid + theta_k=theta_k ) - locstab_fs[flux_surface_index, 4] = _real_scalar_or_nan(result.value) + locstab_fs[flux_surface_index, 4] = result.value end end @@ -67,17 +61,6 @@ end -function _real_scalar_or_nan(value) - if value isa Real - return Float64(value) - elseif value isa Complex - return isapprox(imag(value), 0.0; atol=1e-10) ? Float64(real(value)) : NaN - else - return NaN - end -end - - function _collect_surface_response_background( flux_surface_index::Int, @@ -368,7 +351,9 @@ function prepare_ballooning_coefficients( eta_dp = 2pi * bg.fx0[idx, 2] dr_dp = drfac_dp * cos(bg.eta0[idx]) - bg.rho0[idx] * sin(bg.eta0[idx]) * eta_dp - dv21_dp = (bg.fxy0[idx, 1] / (2 * bg.rho0[idx]) - bg.fx0[idx, 1] * bg.fy0[idx, 1] / (4 * bg.f0[idx, 1] * bg.rho0[idx])) / bg.jac0[idx] - bg.v0[idx, 2, 1] * jac_psi_loop1[idx] / bg.jac0[idx] + dv21_dp = + (bg.fxy0[idx, 1] / (2 * bg.rho0[idx]) - bg.fx0[idx, 1] * bg.fy0[idx, 1] / (4 * bg.f0[idx, 1] * bg.rho0[idx])) / bg.jac0[idx] - + bg.v0[idx, 2, 1] * jac_psi_loop1[idx] / bg.jac0[idx] dv22_dp = (bg.fxy0[idx, 2] * 2pi * bg.rho0[idx] + (1 + bg.fy0[idx, 2]) * 2pi * drfac_dp) / bg.jac0[idx] - bg.v0[idx, 2, 2] * jac_psi_loop1[idx] / bg.jac0[idx] dv23_dp = (bg.fxy0[idx, 3] * bg.r0[idx] + bg.fy0[idx, 3] * dr_dp) / bg.jac0[idx] - bg.v0[idx, 2, 3] * jac_psi_loop1[idx] / bg.jac0[idx] dv33_dp = (2pi * dr_dp) / bg.jac0[idx] - bg.v0[idx, 3, 3] * jac_psi_loop1[idx] / bg.jac0[idx] @@ -450,8 +435,7 @@ function prepare_ballooning_coefficients( n0_fs[:, 4] = -0.5 .- m0_12 .* sigma @views n0_fs[end, :] .= n0_fs[1, :] - n0_spline = (xs=theta_grid, fs=n0_fs, itp=cubic_interp(theta_grid, Series(n0_fs); bc=PeriodicBC())) - n0_int = FastInterpolations.integrate(n0_spline.itp) + n0_int = FastInterpolations.integrate(cubic_interp(theta_grid, Series(n0_fs); bc=PeriodicBC())) d0bar = zeros(2, 2) d0bar[1, 1] = n0_int[1] @@ -459,26 +443,12 @@ function prepare_ballooning_coefficients( d0bar[2, 1] = n0_int[3] d0bar[2, 2] = n0_int[4] - i_per_total = i_per0_shifted .+ i_per_perturbed - a1_fs = -2.0 .* jac_chiprime .* bsq ./ (bg.gradpsi_sq0 .* q_derivative^3) .* (i_per_total .- q_derivative .* theta_k_reference) - - n1_fs = zeros(mtheta + 1, 4) - n1_fs[:, 1] = sigma .* a1_fs - n1_fs[:, 2] = a1_fs - n1_fs[:, 3] = .-(sigma .^ 2) .* a1_fs - n1_fs[:, 4] = .-sigma .* a1_fs - @views n1_fs[end, :] .= n1_fs[1, :] - n1_spline = (xs=theta_grid, fs=n1_fs, itp=cubic_interp(theta_grid, Series(n1_fs); bc=PeriodicBC())) - @views bf_fs[end, :] .= bf_fs[1, :] ode_coefficient_spline = (xs=theta_grid, itp=cubic_interp(theta_grid, Series(bf_fs); bc=PeriodicBC())) return ( ode_coefficient_spline=ode_coefficient_spline, - d0bar=d0bar, di=det(d0bar), - n0_spline=n0_spline, - n1_spline=n1_spline, theta_grid=theta_grid ) end @@ -548,8 +518,7 @@ function ballooning_delta_prime( plasma_eq::Equilibrium.PlasmaEquilibrium; corr_qprime::Float64=0.0, corr_pprime::Float64=0.0, - theta_k::Float64=0.0, - mode::Symbol=:delta_prime_legacy + theta_k::Float64=0.0 ) coeff_data = prepare_ballooning_coefficients( psi_idx, @@ -558,17 +527,12 @@ function ballooning_delta_prime( corr_pprime=corr_pprime, theta_k=theta_k ) - result = integrate_ballooning_ode( + delta_prime = integrate_ballooning_ode( coeff_data.ode_coefficient_spline; - theta_k=theta_k, - mode=mode, - d0bar=coeff_data.d0bar, - n0_spline=coeff_data.n0_spline, - n1_spline=coeff_data.n1_spline, - theta_grid=coeff_data.theta_grid - ) + theta_k=theta_k + ).value - return merge(result, (delta_prime=result.value, di=coeff_data.di)) + return (delta_prime=delta_prime, di=coeff_data.di) end """ @@ -584,7 +548,6 @@ function scan_delta_prime_map( plasma_eq::Equilibrium.PlasmaEquilibrium; ctrl::ForceFreeStatesControl=ForceFreeStatesControl(; verbose=false), theta_k::Float64=0.0, - mode::Symbol=:delta_prime_legacy, s_scales::AbstractVector{<:Real}, alpha_scales::AbstractVector{<:Real} ) @@ -608,8 +571,7 @@ function scan_delta_prime_map( plasma_eq; corr_qprime=corr_qprime, corr_pprime=corr_pprime, - theta_k=theta_k, - mode=mode + theta_k=theta_k ) catch err if ctrl.verbose @@ -647,206 +609,8 @@ end # ODE Integration # Integrates the ideal marginal ballooning equations # ====================================================================== - -function _compute_mercier_from_d0bar(d0bar::Matrix{Float64}) - di = det(d0bar) - if !isfinite(di) || di >= 0.0 - return di, NaN - end - return di, sqrt(-di) -end - -function _compute_theta_max_like_fortran(ode_coefficient_spline; thmax0::Float64=16.5) - theta_vals = ode_coefficient_spline.xs - ratio = fill(NaN, length(theta_vals)) - - @inbounds for i in eachindex(theta_vals) - coeffs = ode_coefficient_spline.itp(theta_vals[i]) - a0 = coeffs[1] - a1 = coeffs[2] - a2 = coeffs[3] - if isfinite(a0) && isfinite(a1) && isfinite(a2) && a2 != 0.0 - residual = a0 - a1^2 / (4.0 * a2) - ratio[i] = abs(residual / a2) - end - end - - finite_ratio = ratio[isfinite.(ratio)] - if isempty(finite_ratio) - return thmax0 - end - - theta_max = sqrt(maximum(finite_ratio)) * 10.0 * thmax0 - return min(theta_max, 100.0) -end - -function _build_periodic_primitive_spline(theta_grid::AbstractVector{<:Real}, values::AbstractMatrix{<:Real}) - theta_vals = Float64.(theta_grid) - period = theta_vals[end] - theta_vals[1] - ntheta, nqty = size(values) - - primitive = zeros(Float64, ntheta, nqty) - for j in 1:nqty - for i in 2:ntheta - dtheta = theta_vals[i] - theta_vals[i-1] - primitive[i, j] = primitive[i-1, j] + 0.5 * dtheta * (values[i-1, j] + values[i, j]) - end - - mean_component = primitive[end, j] / period - for i in 1:ntheta - primitive[i, j] -= (theta_vals[i] - theta_vals[1]) * mean_component - end - primitive[end, j] = primitive[1, j] - end - - return (xs=theta_vals, fs=primitive, itp=cubic_interp(theta_vals, Series(primitive); bc=PeriodicBC())) -end - -function _compute_branch_eigendata(d0bar::Matrix{Float64}, branch::Symbol) - di, alpha = _compute_mercier_from_d0bar(d0bar) - if !isfinite(di) || di >= 0.0 || isnan(alpha) - return di, alpha, NaN, [NaN, NaN] - end - - if branch == :big - exponent = alpha - w2 = -(d0bar[1, 1] - alpha) / d0bar[1, 2] - elseif branch == :small - exponent = -alpha - w2 = -(d0bar[1, 1] + alpha) / d0bar[1, 2] - else - error("Unsupported asymptotic branch: $(branch)") - end - - return di, alpha, exponent, [1.0, w2] -end - -function _build_branch_matching_data(n0_spline, n1_spline, d0bar::Matrix{Float64}, branch::Symbol, theta_grid::Vector{Float64}) - di, alpha, exponent, w0 = _compute_branch_eigendata(d0bar, branch) - if !isfinite(exponent) || isnan(exponent) - return ( - di=di, - alpha=alpha, - exponent=exponent, - w0=w0, - c1=[NaN, NaN], - w1tilde_spline=nothing, - branch=branch - ) - end - - n0_fs = n0_spline.fs - n1_fs = n1_spline.fs - ntheta = size(n0_fs, 1) - - forcing_fs = zeros(Float64, ntheta, 2) - for i in 1:ntheta - n0 = [n0_fs[i, 1] n0_fs[i, 2]; n0_fs[i, 3] n0_fs[i, 4]] - rhs = n0 * w0 - exponent .* w0 - forcing_fs[i, 1] = rhs[1] - forcing_fs[i, 2] = rhs[2] - end - @views forcing_fs[end, :] .= forcing_fs[1, :] - - w1tilde_spline = _build_periodic_primitive_spline(theta_grid, forcing_fs) - w1tilde_fs = w1tilde_spline.fs - - rhs1_fs = zeros(Float64, ntheta, 2) - for i in 1:ntheta - n0 = [n0_fs[i, 1] n0_fs[i, 2]; n0_fs[i, 3] n0_fs[i, 4]] - n1 = [n1_fs[i, 1] n1_fs[i, 2]; n1_fs[i, 3] n1_fs[i, 4]] - w1tilde = [w1tilde_fs[i, 1], w1tilde_fs[i, 2]] - rhs = (n0 * w1tilde - (exponent - 1.0) .* w1tilde) + n1 * w0 - rhs1_fs[i, 1] = rhs[1] - rhs1_fs[i, 2] = rhs[2] - end - @views rhs1_fs[end, :] .= rhs1_fs[1, :] - - rhs_avg = FastInterpolations.integrate(cubic_interp(theta_grid, Series(rhs1_fs); bc=PeriodicBC())) - - lhs = copy(d0bar) - lhs[1, 1] -= exponent - 1.0 - lhs[2, 2] -= exponent - 1.0 - c1 = -(lhs \ rhs_avg) - - return ( - di=di, - alpha=alpha, - exponent=exponent, - w0=w0, - c1=c1, - w1tilde_spline=w1tilde_spline, - branch=branch - ) -end - -function _eval_periodic_series(spline, theta::Real) - theta_min = first(spline.xs) - theta_period = last(spline.xs) - theta_min - theta_wrapped = mod(Float64(theta) - theta_min, theta_period) + theta_min - return spline.itp(theta_wrapped) -end - -function _compute_asymptotic_initial_condition(ode_coefficient_spline, matching_data::NamedTuple, theta_start::Float64) - coeffs = _eval_periodic_series(ode_coefficient_spline, theta_start) - sigma = coeffs[9] - - tau = abs(theta_start) - exponent = matching_data.exponent - if !isfinite(exponent) || isnan(exponent) - return ComplexF64[NaN, NaN], matching_data.di, matching_data.alpha - end - - w1tilde = _eval_periodic_series(matching_data.w1tilde_spline, theta_start) - w1 = [ - w1tilde[1] + matching_data.c1[1], - w1tilde[2] + matching_data.c1[2] - ] - - w0 = matching_data.w0 - prefactor = tau^exponent - y1 = prefactor * tau^(-0.5) * (w0[1] + w1[1] / theta_start) - y2 = prefactor * tau^(+0.5) * (sigma * (w0[1] + w1[1] / theta_start) + w0[2] + w1[2] / theta_start) - - return ComplexF64[y1, y2], matching_data.di, matching_data.alpha -end - -function _integrate_ballooning_side( - ode_coefficient_spline, - theta_start::Float64, - theta_end::Float64, - initial_condition, - theta_k::Float64, - tolerance::Float64, - minimum_step::Float64 -) - problem = ODEProblem( - compute_ballooning_ode!, - initial_condition, - (theta_start, theta_end), - (ode_coefficient_spline, theta_k) - ) - - return solve(problem, DP5(); reltol=tolerance, abstol=tolerance^2, dtmin=minimum_step, adaptive=true) -end - -function _extract_log_derivative(solution) - y_end = solution.u[end] - theta_end = solution.t[end] - return y_end[2] / y_end[1], y_end, theta_end -end - -function _project_onto_asymptotic_basis(target_solution, big_solution, small_solution) - basis_matrix = ComplexF64[ - big_solution[1] small_solution[1] - big_solution[2] small_solution[2] - ] - coefficients = basis_matrix \ ComplexF64[target_solution[1], target_solution[2]] - return coefficients[1], coefficients[2] -end - """ - integrate_ballooning_ode(ode_coefficient_spline; theta_k=0.0, mode=:delta_prime_legacy) + integrate_ballooning_ode(ode_coefficient_spline; theta_k=0.0) Integrates the ballooning ODE from `-Infinity` to `-1e-3` and `+Infinity` to `+1e-3`. Computes Delta' = (y'/y)_right - (y'/y)_left. @@ -855,15 +619,7 @@ Computes Delta' = (y'/y)_right - (y'/y)_left. - `delta_prime`: The stability index Δ'. """ -function integrate_ballooning_ode( - ode_coefficient_spline; - theta_k::Float64=0.0, - mode::Symbol=:delta_prime_legacy, - d0bar::Union{Nothing,Matrix{Float64}}=nothing, - n0_spline=nothing, - n1_spline=nothing, - theta_grid::Union{Nothing,Vector{Float64}}=nothing -) +function integrate_ballooning_ode(ode_coefficient_spline; theta_k::Float64=0.0) TOLERANCE = 1e-8 MINIMUM_STEP = 1e-10 MATCHING_POINT = 1e-3 @@ -874,159 +630,49 @@ function integrate_ballooning_ode( theta_start_right = THETA_MAX0 theta_end_right = MATCHING_POINT - if mode == :delta_prime_legacy - initial_condition_left = [0.0, 1.0] - initial_condition_right = [0.0, -1.0] - - sol_left = _integrate_ballooning_side( - ode_coefficient_spline, - theta_start_left, - theta_end_left, - initial_condition_left, - theta_k, - TOLERANCE, - MINIMUM_STEP - ) - if sol_left.retcode != ReturnCode.Success - return (value=NaN, di=NaN) - end - - sol_right = _integrate_ballooning_side( - ode_coefficient_spline, - theta_start_right, - theta_end_right, - initial_condition_right, - theta_k, - TOLERANCE, - MINIMUM_STEP - ) - if sol_right.retcode != ReturnCode.Success - return (value=NaN, di=NaN) - end - - log_deriv_left, _, _ = _extract_log_derivative(sol_left) - log_deriv_right, _, _ = _extract_log_derivative(sol_right) + initial_condition_left = [0.0, 1.0] + initial_condition_right = [0.0, -1.0] - return (value=log_deriv_right - log_deriv_left, di=NaN) - elseif mode == :delta_prime_small - if d0bar === nothing || n0_spline === nothing || n1_spline === nothing || theta_grid === nothing - error("d0bar, n0_spline, n1_spline, and theta_grid are required for mode=:delta_prime_small") - end - - di, alpha = _compute_mercier_from_d0bar(d0bar) - if !isfinite(di) || di >= 0.0 || isnan(alpha) - return (value=NaN, di=di, alpha=NaN) - end - - theta_max = _compute_theta_max_like_fortran(ode_coefficient_spline; thmax0=THETA_MAX0) - theta_start_left = -theta_max - theta_start_right = theta_max - - small_matching_data = _build_branch_matching_data(n0_spline, n1_spline, d0bar, :small, theta_grid) - initial_condition_left, _, _ = _compute_asymptotic_initial_condition( - ode_coefficient_spline, - small_matching_data, - theta_start_left - ) - initial_condition_right, _, _ = _compute_asymptotic_initial_condition( - ode_coefficient_spline, - small_matching_data, - theta_start_right - ) - - sol_left = _integrate_ballooning_side( - ode_coefficient_spline, - theta_start_left, - theta_end_left, - initial_condition_left, - theta_k, - TOLERANCE, - MINIMUM_STEP - ) - if sol_left.retcode != ReturnCode.Success - return (value=NaN, di=di, alpha=alpha) - end - - sol_right = _integrate_ballooning_side( - ode_coefficient_spline, - theta_start_right, - theta_end_right, - initial_condition_right, - theta_k, - TOLERANCE, - MINIMUM_STEP - ) - if sol_right.retcode != ReturnCode.Success - return (value=NaN, di=di, alpha=alpha) - end - - log_deriv_left, _, _ = _extract_log_derivative(sol_left) - log_deriv_right, _, _ = _extract_log_derivative(sol_right) - - return (value=log_deriv_right - log_deriv_left, di=di, alpha=alpha) - elseif mode == :ca1 - if d0bar === nothing || n0_spline === nothing || n1_spline === nothing || theta_grid === nothing - error("d0bar, n0_spline, n1_spline, and theta_grid are required for mode=:ca1") - end + problem_left = ODEProblem( + compute_ballooning_ode!, + initial_condition_left, + (theta_start_left, theta_end_left), + (ode_coefficient_spline, theta_k) + ) + sol_left = solve( + problem_left, + DP5(); + reltol=TOLERANCE, + abstol=TOLERANCE^2, + dtmin=MINIMUM_STEP, + adaptive=true + ) + if sol_left.retcode != ReturnCode.Success + return (value=NaN,) + end - di, alpha = _compute_mercier_from_d0bar(d0bar) - if !isfinite(di) || di >= 0.0 || isnan(alpha) - return (value=NaN, di=di, alpha=NaN, ca1_left=NaN, ca2_left=NaN, ca1_right=NaN, ca2_right=NaN) - end + problem_right = ODEProblem( + compute_ballooning_ode!, + initial_condition_right, + (theta_start_right, theta_end_right), + (ode_coefficient_spline, theta_k) + ) + sol_right = solve( + problem_right, + DP5(); + reltol=TOLERANCE, + abstol=TOLERANCE^2, + dtmin=MINIMUM_STEP, + adaptive=true + ) + if sol_right.retcode != ReturnCode.Success + return (value=NaN,) + end - theta_max = _compute_theta_max_like_fortran(ode_coefficient_spline; thmax0=THETA_MAX0) - theta_start_left = -theta_max - theta_start_right = theta_max - - legacy_left = [0.0, 1.0] - legacy_right = [0.0, -1.0] - big_matching_data = _build_branch_matching_data(n0_spline, n1_spline, d0bar, :big, theta_grid) - small_matching_data = _build_branch_matching_data(n0_spline, n1_spline, d0bar, :small, theta_grid) - big_left, _, _ = _compute_asymptotic_initial_condition(ode_coefficient_spline, big_matching_data, theta_start_left) - small_left, _, _ = _compute_asymptotic_initial_condition(ode_coefficient_spline, small_matching_data, theta_start_left) - big_right, _, _ = _compute_asymptotic_initial_condition(ode_coefficient_spline, big_matching_data, theta_start_right) - small_right, _, _ = _compute_asymptotic_initial_condition(ode_coefficient_spline, small_matching_data, theta_start_right) - - sol_target_left = _integrate_ballooning_side(ode_coefficient_spline, theta_start_left, theta_end_left, legacy_left, theta_k, TOLERANCE, MINIMUM_STEP) - sol_target_right = _integrate_ballooning_side(ode_coefficient_spline, theta_start_right, theta_end_right, legacy_right, theta_k, TOLERANCE, MINIMUM_STEP) - sol_big_left = _integrate_ballooning_side(ode_coefficient_spline, theta_start_left, theta_end_left, big_left, theta_k, TOLERANCE, MINIMUM_STEP) - sol_small_left = _integrate_ballooning_side(ode_coefficient_spline, theta_start_left, theta_end_left, small_left, theta_k, TOLERANCE, MINIMUM_STEP) - sol_big_right = _integrate_ballooning_side(ode_coefficient_spline, theta_start_right, theta_end_right, big_right, theta_k, TOLERANCE, MINIMUM_STEP) - sol_small_right = _integrate_ballooning_side(ode_coefficient_spline, theta_start_right, theta_end_right, small_right, theta_k, TOLERANCE, MINIMUM_STEP) - - if !( - sol_target_left.retcode == ReturnCode.Success && - sol_target_right.retcode == ReturnCode.Success && - sol_big_left.retcode == ReturnCode.Success && - sol_small_left.retcode == ReturnCode.Success && - sol_big_right.retcode == ReturnCode.Success && - sol_small_right.retcode == ReturnCode.Success - ) - return (value=NaN, di=di, alpha=alpha, ca1_left=NaN, ca2_left=NaN, ca1_right=NaN, ca2_right=NaN) - end + log_deriv_left = sol_left.u[end][2] / sol_left.u[end][1] + log_deriv_right = sol_right.u[end][2] / sol_right.u[end][1] - target_left = ComplexF64[sol_target_left.u[end][1], sol_target_left.u[end][2]] - target_right = ComplexF64[sol_target_right.u[end][1], sol_target_right.u[end][2]] - basis_big_left = ComplexF64[sol_big_left.u[end][1], sol_big_left.u[end][2]] - basis_small_left = ComplexF64[sol_small_left.u[end][1], sol_small_left.u[end][2]] - basis_big_right = ComplexF64[sol_big_right.u[end][1], sol_big_right.u[end][2]] - basis_small_right = ComplexF64[sol_small_right.u[end][1], sol_small_right.u[end][2]] - - ca1_left, ca2_left = _project_onto_asymptotic_basis(target_left, basis_big_left, basis_small_left) - ca1_right, ca2_right = _project_onto_asymptotic_basis(target_right, basis_big_right, basis_small_right) - - return ( - value=ca1_right, - di=di, - alpha=alpha, - ca1_left=ca1_left, - ca2_left=ca2_left, - ca1_right=ca1_right, - ca2_right=ca2_right - ) - else - error("Unsupported integration mode: $(mode)") - end + return (value=log_deriv_right - log_deriv_left,) end @@ -1076,4 +722,4 @@ function compute_ballooning_ode!(derivatives, solution, parameters, poloidal_ang derivatives[1] = solution[2] / f derivatives[2] = g * solution[1] -end +end \ No newline at end of file From ed047bc17075a22555224639a2ddd4d049830ad1 Mon Sep 17 00:00:00 2001 From: jmlmir369 Date: Thu, 30 Apr 2026 22:27:02 +0900 Subject: [PATCH 007/135] Restore accidentally deleted example notebook --- .../Bal_salpha_delta_di_summary.ipynb | 257 ++++++++++++++++++ 1 file changed, 257 insertions(+) create mode 100644 examples/DIIID-like_ideal_example/Bal_salpha_delta_di_summary.ipynb diff --git a/examples/DIIID-like_ideal_example/Bal_salpha_delta_di_summary.ipynb b/examples/DIIID-like_ideal_example/Bal_salpha_delta_di_summary.ipynb new file mode 100644 index 000000000..3b634dce6 --- /dev/null +++ b/examples/DIIID-like_ideal_example/Bal_salpha_delta_di_summary.ipynb @@ -0,0 +1,257 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "id": "s-alpha-profile-extrema", + "metadata": {}, + "outputs": [], + "source": [ + "using Pkg\n", + "Pkg.activate(\"../..\")\n", + "\n", + "using GeneralizedPerturbedEquilibrium\n", + "using Plots\n", + "using Printf\n", + "using Statistics\n", + "using LaTeXStrings\n", + "using TOML\n", + "\n", + "eq_config = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(TOML.parsefile(\"gpec.toml\")[\"Equilibrium\"], pwd())\n", + "equil = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(eq_config)\n", + "psi_norm = Vector(equil.profiles.xs)\n", + "\n", + "function finite_local_extrema(values::AbstractVector{<:Real})\n", + " extrema = Int[]\n", + " for i in 2:length(values)-1\n", + " if !isfinite(values[i - 1]) || !isfinite(values[i]) || !isfinite(values[i + 1])\n", + " continue\n", + " end\n", + " if (values[i] >= values[i - 1] && values[i] >= values[i + 1]) ||\n", + " (values[i] <= values[i - 1] && values[i] <= values[i + 1])\n", + " push!(extrema, i)\n", + " end\n", + " end\n", + " return extrema\n", + "end\n", + "\n", + "function print_extrema_report(name::String, psi::AbstractVector, values::AbstractVector, extrema::AbstractVector{Int})\n", + " println(\"\\n\", name, \" extrema\")\n", + " if isempty(extrema)\n", + " println(\" none\")\n", + " return\n", + " end\n", + " println(\" index\\tpsi_norm\\tvalue\")\n", + " for i in extrema\n", + " @printf(\" %d\\t%.8f\\t%.12e\\n\", i, psi[i], values[i])\n", + " end\n", + "end\n", + "\n", + "s_profile = fill(NaN, length(psi_norm))\n", + "alpha_profile = fill(NaN, length(psi_norm))\n", + "\n", + "for i in eachindex(psi_norm)\n", + " try\n", + " ref = GeneralizedPerturbedEquilibrium.ForceFreeStates.salpha_reference(i, equil)\n", + " s_profile[i] = ref.s_ref\n", + " alpha_profile[i] = ref.alpha_ref\n", + " catch err\n", + " @warn \"s-alpha reference failed\" i psi=psi_norm[i] exception=(err, catch_backtrace())\n", + " end\n", + "end\n", + "\n", + "s_extrema = finite_local_extrema(s_profile)\n", + "alpha_extrema = finite_local_extrema(alpha_profile)\n", + "print_extrema_report(\"s\", psi_norm, s_profile, s_extrema)\n", + "print_extrema_report(\"alpha\", psi_norm, alpha_profile, alpha_extrema)\n", + "\n", + "s_mask = isfinite.(s_profile)\n", + "alpha_mask = isfinite.(alpha_profile)\n", + "\n", + "p_s = plot(\n", + " psi_norm[s_mask], s_profile[s_mask];\n", + " xlabel=\"psi_norm\",\n", + " ylabel=\"s\",\n", + " label=\"s\",\n", + " lw=2,\n", + " title=\"s\",\n", + " framestyle=:box,\n", + ")\n", + "scatter!(p_s, psi_norm[s_extrema], s_profile[s_extrema]; label=\"extrema\", marker=:circle, color=:red, ms=5)\n", + "\n", + "p_alpha = plot(\n", + " psi_norm[alpha_mask], alpha_profile[alpha_mask];\n", + " xlabel=\"psi_norm\",\n", + " ylabel=\"alpha\",\n", + " label=\"alpha\",\n", + " lw=2,\n", + " title=\"alpha\",\n", + " framestyle=:box,\n", + ")\n", + "scatter!(p_alpha, psi_norm[alpha_extrema], alpha_profile[alpha_extrema]; label=\"extrema\", marker=:circle, color=:red, ms=5)\n", + "\n", + "display(plot(p_s, p_alpha; layout=(1, 2), size=(1100, 420)))\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "delta-di-profile-extrema", + "metadata": {}, + "outputs": [], + "source": [ + "locstab_fs = zeros(length(psi_norm), 4)\n", + "ctrl = GeneralizedPerturbedEquilibrium.ForceFreeStates.ForceFreeStatesControl(verbose=false)\n", + "\n", + "println(\"Computing \\\\Delta' and D_I...\")\n", + "GeneralizedPerturbedEquilibrium.ForceFreeStates.compute_ballooning_stability!(ctrl, locstab_fs, equil; compute_delta_prime=true)\n", + "\n", + "delta_prime = Vector(locstab_fs[:, 4])\n", + "di_profile = fill(NaN, length(psi_norm))\n", + "psi_mask = abs.(psi_norm) .> eps(Float64)\n", + "di_profile[psi_mask] .= locstab_fs[psi_mask, 1] ./ psi_norm[psi_mask]\n", + "\n", + "delta_extrema = finite_local_extrema(delta_prime)\n", + "di_extrema = finite_local_extrema(di_profile)\n", + "print_extrema_report(\"\\\\Delta'\", psi_norm, delta_prime, delta_extrema)\n", + "print_extrema_report(\"D_I\", psi_norm, di_profile, di_extrema)\n", + "\n", + "delta_mask = isfinite.(delta_prime)\n", + "di_mask = isfinite.(di_profile)\n", + "\n", + "p_delta = plot(\n", + " psi_norm[delta_mask], delta_prime[delta_mask];\n", + " xlabel=\"psi_norm\",\n", + " ylabel=L\"\\Delta'\",\n", + " label=L\"\\Delta'\",\n", + " lw=2,\n", + " title=L\"\\Delta'\",\n", + " framestyle=:box,\n", + ")\n", + "scatter!(p_delta, psi_norm[delta_extrema], delta_prime[delta_extrema]; label=\"extrema\", marker=:diamond, color=:red, ms=5)\n", + "\n", + "p_di = plot(\n", + " psi_norm[di_mask], di_profile[di_mask];\n", + " xlabel=\"psi_norm\",\n", + " ylabel=L\"D_I\",\n", + " label=L\"D_I\",\n", + " lw=2,\n", + " title=L\"D_I\",\n", + " framestyle=:box,\n", + ")\n", + "scatter!(p_di, psi_norm[di_extrema], di_profile[di_extrema]; label=\"extrema\", marker=:diamond, color=:red, ms=5)\n", + "\n", + "display(plot(p_delta, p_di; layout=(1, 2), size=(1100, 420)))\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "s-alpha-delta-di-maps", + "metadata": {}, + "outputs": [], + "source": [ + "psi_target = 0.974\n", + "psi_idx_scan = argmin(abs.(psi_norm .- psi_target))\n", + "\n", + "println(\"Running s-alpha scan at index $(psi_idx_scan), psi_norm=$(round(psi_norm[psi_idx_scan], digits=6))\")\n", + "\n", + "s_scales = collect(range(-5.0, 5.0; length=30))\n", + "alpha_scales = collect(range(-5.0, 5.0; length=30))\n", + "\n", + "scan_result = GeneralizedPerturbedEquilibrium.ForceFreeStates.scan_delta_prime_map(\n", + " psi_idx_scan,\n", + " equil;\n", + " theta_k=0.0,\n", + " s_scales=s_scales,\n", + " alpha_scales=alpha_scales,\n", + ")\n", + "\n", + "scan_qprime_raw = scan_result.dqdpsi_ref .* scan_result.s_scales\n", + "scan_pprime_raw = scan_result.pprime_ref .* scan_result.alpha_scales\n", + "qprime_order = sortperm(scan_qprime_raw)\n", + "pprime_order = sortperm(scan_pprime_raw)\n", + "scan_qprime = scan_qprime_raw[qprime_order]\n", + "scan_pprime = scan_pprime_raw[pprime_order]\n", + "scan_delta = scan_result.delta_prime[qprime_order, pprime_order]\n", + "scan_di = scan_result.di_values[qprime_order, pprime_order]\n", + "\n", + "function symmetric_clims(z)\n", + " finite_vals = vec(z)[isfinite.(vec(z))]\n", + " maxabs = isempty(finite_vals) ? 1.0 : maximum(abs.(finite_vals))\n", + " maxabs = max(maxabs, eps(Float64))\n", + " return (-maxabs, maxabs)\n", + "end\n", + "\n", + "p_scan_delta = contourf(\n", + " scan_pprime, scan_qprime, scan_delta;\n", + " c=cgrad([:blue, :white, :red]),\n", + " clims=symmetric_clims(scan_delta),\n", + " xlabel=L\"p_{\\psi}\",\n", + " ylabel=L\"q_{\\psi}\",\n", + " title=L\"\\Delta'\",\n", + " levels=41,\n", + " framestyle=:box,\n", + ")\n", + "contour!(p_scan_delta, scan_pprime, scan_qprime, scan_delta; levels=[0.0], color=:black, linewidth=2, label=L\"\\Delta' = 0\")\n", + "scatter!(p_scan_delta, [scan_result.reference.pprime_ref], [scan_result.reference.qprime_ref]; color=:green, marker=:star5, ms=7, label=\"equilibrium\")\n", + "\n", + "p_scan_di = contourf(\n", + " scan_pprime, scan_qprime, scan_di;\n", + " c=cgrad([:blue, :white, :red]),\n", + " clims=symmetric_clims(scan_di),\n", + " xlabel=L\"p_{\\psi}\",\n", + " ylabel=L\"q_{\\psi}\",\n", + " title=L\"D_I\",\n", + " levels=41,\n", + " framestyle=:box,\n", + ")\n", + "contour!(p_scan_di, scan_pprime, scan_qprime, scan_di; levels=[0.0], color=:black, linewidth=2, label=L\"D_I = 0\")\n", + "scatter!(p_scan_di, [scan_result.reference.pprime_ref], [scan_result.reference.qprime_ref]; color=:green, marker=:star5, ms=7, label=\"equilibrium\")\n", + "\n", + "display(plot(p_scan_delta, p_scan_di; layout=(1, 2), size=(1150, 460)))\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "s-alpha-zero-contours", + "metadata": {}, + "outputs": [], + "source": [ + "p_zero = plot(\n", + " xlabel=L\"p_{\\psi}\",\n", + " ylabel=L\"q_{\\psi}\",\n", + " title=\"ballooning, Mercier contours\",\n", + " framestyle=:box,\n", + ")\n", + "contour!(p_zero, scan_pprime, scan_qprime, scan_delta;\n", + " levels=[0.0], color=:blue, linewidth=3,\n", + " label=L\"\\Delta' = 0\", colorbar=false)\n", + "\n", + "contour!(p_zero, scan_pprime, scan_qprime, scan_di;\n", + " levels=[0.0], color=:red, linewidth=3, linestyle=:dash,\n", + " label=L\"D_I = 0\", colorbar=false)\n", + "\n", + "\n", + "scatter!(p_zero, [scan_result.reference.pprime_ref], [scan_result.reference.qprime_ref]; color=:green, marker=:star5, ms=8, label=\"equilibrium\")\n", + "display(p_zero)\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.12.4", + "language": "julia", + "name": "julia-1.12" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.12.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} From 7ceb6ea8a41bd6d4a7ab9ec895c624d2c956424d Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Tue, 9 Jun 2026 15:50:23 -0400 Subject: [PATCH 008/135] ForceFreeStates - NEW - Implement galerkin solver --- src/Equilibrium/DirectEquilibrium.jl | 27 +- src/ForceFreeStates/ForceFreeStates.jl | 8 + src/ForceFreeStates/ForceFreeStatesStructs.jl | 18 + src/ForceFreeStates/Fourfit.jl | 7 + .../Galerkin/GalerkinAssembly.jl | 436 ++++++++++++++++++ src/ForceFreeStates/Galerkin/GalerkinGrid.jl | 221 +++++++++ src/ForceFreeStates/Galerkin/GalerkinSolve.jl | 216 +++++++++ .../Galerkin/GalerkinStructs.jl | 141 ++++++ src/ForceFreeStates/Sing.jl | 135 ++++++ src/GeneralizedPerturbedEquilibrium.jl | 28 +- 10 files changed, 1230 insertions(+), 7 deletions(-) create mode 100644 src/ForceFreeStates/Galerkin/GalerkinAssembly.jl create mode 100644 src/ForceFreeStates/Galerkin/GalerkinGrid.jl create mode 100644 src/ForceFreeStates/Galerkin/GalerkinSolve.jl create mode 100644 src/ForceFreeStates/Galerkin/GalerkinStructs.jl diff --git a/src/Equilibrium/DirectEquilibrium.jl b/src/Equilibrium/DirectEquilibrium.jl index b98fc2d1f..0335f4bbb 100644 --- a/src/Equilibrium/DirectEquilibrium.jl +++ b/src/Equilibrium/DirectEquilibrium.jl @@ -200,11 +200,30 @@ function direct_position!(raw_profile::DirectRunInput) # ψ = 0 at the separatrix (after renormalization), and ψ changes sign between the # magnetic axis (ψ > 0) and the region outside the plasma (ψ < 0), so Brent is # globally convergent within the bracket (start_r, end_r) and needs no restarts. + # For limited equilibria whose grid box hugs the LCFS (e.g. some TokaMaker gEQDSKs), + # ψ can stay positive out to the grid edge with no sign change to bracket. The separatrix + # (ψ = 0) then sits just beyond the grid; extend the bracket outward via the extrapolating + # ψ spline until ψ changes sign (capped), so rs is a faithful ψ=0 crossing rather than the + # arbitrary grid edge (which lands in the degenerate ψ→0, Bp→0 region and breaks tracing). + psi_at(r) = (direct_get_bfield!(bfield, r, zo, raw_profile.psi_in, raw_profile.sq_in, sq_in_deriv, raw_profile.psio; derivs=0); bfield.psi) function find_separatrix_crossing(start_r, end_r, label) - r_sol = find_zero( - r -> (direct_get_bfield!(bfield, r, zo, raw_profile.psi_in, raw_profile.sq_in, sq_in_deriv, raw_profile.psio; derivs=0); bfield.psi), - (start_r, end_r), Roots.Brent() - ) + hi = end_r + if psi_at(start_r) * psi_at(hi) > 0 + span = abs(end_r - start_r) + step = 0.02 * span + hi_max = end_r + sign(end_r - start_r) * 0.5 * span # cap extrapolation at 50% of the half-width + while psi_at(start_r) * psi_at(hi) > 0 && abs(hi - end_r) < abs(hi_max - end_r) + hi += sign(end_r - start_r) * step + end + if psi_at(start_r) * psi_at(hi) > 0 + @warn "$label: ψ does not change sign even extrapolating to R = $(@sprintf("%.3f", hi)); " * + "using R = $(@sprintf("%.3f", hi)) as the boundary." + return hi + end + @warn "$label: ψ positive to grid edge R = $(@sprintf("%.3f", end_r)) (limited equilibrium); " * + "located ψ=0 by extrapolation in R ∈ (R_edge, $(@sprintf("%.3f", hi)))." + end + r_sol = find_zero(psi_at, (start_r, hi), Roots.Brent()) @info "$label separatrix found at R = $(@sprintf("%.3f", r_sol))" return r_sol end diff --git a/src/ForceFreeStates/ForceFreeStates.jl b/src/ForceFreeStates/ForceFreeStates.jl index d436bf6cd..ab04ec155 100644 --- a/src/ForceFreeStates/ForceFreeStates.jl +++ b/src/ForceFreeStates/ForceFreeStates.jl @@ -11,6 +11,8 @@ using JLD2 using FastInterpolations using AdaptiveArrayPools using Roots +using FastGaussQuadrature: gausslobatto +using QuadGK: quadgk import ..Equilibrium import ..Utilities @@ -32,6 +34,12 @@ include("Utils.jl") include("Free.jl") include("Riccati.jl") +# RDCON outer-region singular Galerkin Δ′ solver (gal_solve port) +include("Galerkin/GalerkinStructs.jl") +include("Galerkin/GalerkinGrid.jl") +include("Galerkin/GalerkinAssembly.jl") +include("Galerkin/GalerkinSolve.jl") + # These are used for various small tolerances and root finders throughout ForceFreeStates global eps = 1e-10 global itmax = 50 diff --git a/src/ForceFreeStates/ForceFreeStatesStructs.jl b/src/ForceFreeStates/ForceFreeStatesStructs.jl index f8ad2bf46..73d9e615e 100644 --- a/src/ForceFreeStates/ForceFreeStatesStructs.jl +++ b/src/ForceFreeStates/ForceFreeStatesStructs.jl @@ -173,6 +173,7 @@ A mutable struct holding internal state variables for stability calculations. msing::Int = 0 sing::Vector{SingType} = SingType[] psilim::Float64 = 0.0 + psilow::Float64 = 0.0 # lower integration bound; raised above the axis by sing_min! when qlow > qmin (RDCON gal) qlim::Float64 = 0.0 q1lim::Float64 = 0.0 locstab::FastInterpolations.CubicSeriesInterpolant = cubic_interp(collect(0.0:0.25:1.0), Series(zeros(5, 5)); bc=ZeroCurvBC()) @@ -288,6 +289,22 @@ A mutable struct containing control parameters for stability analysis, set by th use_parallel::Bool = true # Default on: unlocks singular/delta_prime_matrix (STRIDE BVP Δ' matrix) used by SLAYER/GGJ downstream. populate_dense_xi::Bool = false # When use_parallel=true, set to true ONLY if a PerturbedEquilibrium pipeline will consume dense ξ. Default false avoids the ~1× parallel-BVP serial-EL re-run for non-PE runs (Δ'/vacuum/ideal-stability only). See ForceFreeStatesControl docstring for the full trade-off (et[1] convention differs by ~0.12% on DIIID between populate=true vs false). extended_precision_bvp::Bool = true # Promote Δ' BVP to Complex{Double64}; default on (Float64 drifts the imaginary Δ' by 2–5× on DIIID-class cases). + + # --- RDCON outer-region Galerkin Δ′ solver (gal_solve port) --- + gal_flag::Bool = false # enable outer-region Galerkin Δ′ solve + gal_solver::String = "LU" # "LU" (zgbtrf/zgbtrs) or "cholesky" (zpbtrf/zpbtrs) + gal_nx::Int = 256 # elements per interval between singular surfaces + gal_nq::Int = 6 # Gauss-Lobatto quadrature order per element + gal_pfac::Float64 = 0.001 # grid packing ratio near singular surfaces + gal_dx0::Float64 = 5e-4 # resonant-element integration truncation distance (×1/|n q'|) + gal_dx1::Float64 = 1e-3 # resonant-element size (×1/|n q'|) + gal_dx2::Float64 = 1e-3 # extension-element size (×1/|n q'|) + gal_cutoff::Int = 10 # # of elements carrying the large solution as driving term + gal_tol::Float64 = 1e-10 # resonant-quadrature (QuadGK) tolerance + gal_gnstep::Int = 5000 # max resonant-integration steps + gal_dx1dx2_flag::Bool = true # enable special dx1/dx2 treatment for resonant/extension elements + gal_sing_order::Int = 6 # base power-series order for the Galerkin singular asymptotics + gal_sing_order_ceiling::Bool = true # auto-raise order by ceil(2·Re(α)) per surface (high Mercier index) fixed_axis::Bool = false end @@ -310,6 +327,7 @@ end hmats::S = _empty_series_interp_complex(numpert_total^2, itp_opts) fmats_lower::S = _empty_series_interp_complex(numpert_total^2, itp_opts) fmats_prim::S = _empty_series_interp_complex(numpert_total^2, itp_opts) # primitive F before Schur complement (for kinetic) + fmats_gal::S = _empty_series_interp_complex(numpert_total^2, itp_opts) # reduced Hermitian F̄ (un-factored) for the Galerkin solver kmats::S = _empty_series_interp_complex(numpert_total^2, itp_opts) gmats::S = _empty_series_interp_complex(numpert_total^2, itp_opts) diff --git a/src/ForceFreeStates/Fourfit.jl b/src/ForceFreeStates/Fourfit.jl index 6d9919690..ede496e44 100644 --- a/src/ForceFreeStates/Fourfit.jl +++ b/src/ForceFreeStates/Fourfit.jl @@ -175,6 +175,7 @@ function make_matrix(equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStates hmats_flat = zeros(ComplexF64, mpsi, intr.numpert_total^2) fmats_lower_flat = zeros(ComplexF64, mpsi, intr.numpert_total^2) fmats_prim_flat = zeros(ComplexF64, mpsi, intr.numpert_total^2) # primitive F before Schur complement (for kinetic) + fmats_gal_flat = zeros(ComplexF64, mpsi, intr.numpert_total^2) # reduced Hermitian F̄ (before Cholesky) for the Galerkin solver gmats_flat = zeros(ComplexF64, mpsi, intr.numpert_total^2) kmats_flat = zeros(ComplexF64, mpsi, intr.numpert_total^2) g11 = Vector{ComplexF64}(undef, 2 * intr.mband + 1) @@ -307,6 +308,11 @@ function make_matrix(equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStates kmat .= emat .- (adjoint(kmat) * a_inv_cmat_temp) # K̃ = E - K†A⁻¹C gmat .= hmat .- (adjoint(cmat) * a_inv_cmat_temp) # G̃ = H - C†A⁻¹C + # Capture the reduced Hermitian F̄ (full matrix) before it is overwritten by its Cholesky + # factor below. The Galerkin solver (gal_get_fkg) needs F̄ directly: F = Q F̄ Qᴴ with + # Q = diag(singfac). Mirror of Fortran fmats_gal (fourfit.f:341). + @views fmats_gal_flat[ipsi, :] .= vec(fmat) + # Store factorized F matrix (lower triangular only) since we always will need F⁻¹ later # and this make computation more efficient via combined forward and back substitution # TODO: does F stay Hermitian in the 3D case, allowing us to use the lower representation? @@ -328,6 +334,7 @@ function make_matrix(equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStates ffit.hmats = cubic_interp(metric.xs, Series(hmats_flat); ffit.itp_opts...) ffit.fmats_lower = cubic_interp(metric.xs, Series(fmats_lower_flat); ffit.itp_opts...) ffit.fmats_prim = cubic_interp(metric.xs, Series(fmats_prim_flat); ffit.itp_opts...) + ffit.fmats_gal = cubic_interp(metric.xs, Series(fmats_gal_flat); ffit.itp_opts...) ffit.gmats = cubic_interp(metric.xs, Series(gmats_flat); ffit.itp_opts...) ffit.kmats = cubic_interp(metric.xs, Series(kmats_flat); ffit.itp_opts...) diff --git a/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl b/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl new file mode 100644 index 000000000..a92ecf45e --- /dev/null +++ b/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl @@ -0,0 +1,436 @@ +# GalerkinAssembly.jl +# +# Element-level assembly for the outer-region Galerkin solver. Ports: +# gal_hermite (gal.f:222-254) Hermite cubic basis +# gal_get_fkg (gal.f:999-1057) F, K, G at a point from F̄/K̄/Ḡ + singfac +# gal_gauss_quad (gal.f:1065-1124) nonresonant stiffness via Gauss-Lobatto quadrature +# gal_extension (gal.f:1132-1292) extension-cell matrix/rhs (big-solution driving + surface terms) +# gal_resonant (gal.f:772-940) resonant-cell integral (QuadGK in place of Fortran LSODE) +# gal_assemble_mat (gal.f:686-764) scatter cell blocks into the banded global matrix (LU/Cholesky) +# gal_assemble_rhs (gal.f:634-678) scatter cell rhs into the global RHS +# gal_set_boundary (gal.f:1517-1583) axis identity + edge (vacuum or fixed) BCs +# +# Hermite DOF index ip (Fortran 0:3) ↔ Julia array index ip+1 throughout. + +"""Resonant flat mode index `1 + (m-mlow) + (n-nlow)*mpert` for a singular surface (single resonance).""" +@inline function _ipert_res(sing::SingType, intr::ForceFreeStatesInternal) + return 1 + (sing.m[1] - intr.mlow) + (sing.n[1] - intr.nlow) * intr.mpert +end + +# Two-sided asymptotic evaluation (z = ψ - ψ_s). Right (z≥0) uses the sig=+1 series at z; left (z<0) +# uses the sig=-1 series at the positive distance |z| (real √, no renorm), matching Fortran sing.f. +# The derivative on the left picks up d|z|/dψ = -1. +@inline sing_get_ua_gal(g::GalSingAsymp, z::Float64) = + z >= 0 ? sing_get_ua(g.right, z) : sing_get_ua(g.left, -z) +@inline sing_get_dua_gal(g::GalSingAsymp, z::Float64) = + z >= 0 ? sing_get_dua(g.right, z) : (-1) .* sing_get_dua(g.left, -z) + +""" + gal_hermite(x, x0, x1) -> (pb, qb) + +Hermite cubic basis values `pb` and derivatives `qb` on `[x0, x1]` (length 4, Fortran `0:3`). +Port of `gal_hermite` (gal.f:222-254). +""" +function gal_hermite(x::Real, x0::Real, x1::Real) + dx = x1 - x0 + t0 = (x - x0) / dx + t1 = 1 - t0 + t02 = t0 * t0 + t12 = t1 * t1 + pb = (t12 * (1 + 2t0), t12 * t0 * dx, t02 * (1 + 2t1), -t02 * t1 * dx) + qb = (-6t0 * t1 / dx, t0 * (3t0 - 4) + 1, 6t1 * t0 / dx, t0 * (3t0 - 2)) + return pb, qb +end + +""" + gal_get_fkg(ffit, intr, x, q) -> (F, K, G) + +Evaluate the `mpert×mpert` matrices `F = Q F̄ Qᴴ`, `K = Q K̄`, `G = Ḡ` at flux `x` with safety factor +`q`, where `Q = diag(singfac)` and `singfac = m - n q` (direct). Port of `gal_get_fkg` (gal.f:999-1057). +Uses the un-factored reduced `ffit.fmats_gal` (F̄), `ffit.kmats` (K̄), `ffit.gmats` (Ḡ). +""" +function gal_get_fkg(ffit::FourFitVars, intr::ForceFreeStatesInternal, x::Float64, q::Float64) + N = intr.numpert_total + sf = vec((intr.mlow:intr.mhigh) .- q .* (intr.nlow:intr.nhigh)') + + Fbar = Matrix{ComplexF64}(undef, N, N) + K = Matrix{ComplexF64}(undef, N, N) + G = Matrix{ComplexF64}(undef, N, N) + ffit.fmats_gal(vec(Fbar), x; hint=ffit._hint) + ffit.kmats(vec(K), x; hint=ffit._hint) + ffit.gmats(vec(G), x; hint=ffit._hint) + + F = Matrix{ComplexF64}(undef, N, N) + @inbounds for j in 1:N, i in 1:N + F[i, j] = Fbar[i, j] * sf[i] * sf[j] + K[i, j] = K[i, j] * sf[i] + end + return F, K, G +end + +""" + gal_gauss_quad!(cell, ffit, profiles, intr, nodes, weights, swap_edge) + +Accumulate the nonresonant Hermite stiffness block `cell.mat` by Gauss-Lobatto quadrature. Port of +`gal_gauss_quad` (gal.f:1065-1124). When `swap_edge` (the final cell of the last interval), the +right-node value/slope DOFs (Fortran pb(2)↔pb(3)) are swapped so the edge-value DOF lands at index 3, +matching the free-boundary BC (gal.f:1091-1098). +""" +function gal_gauss_quad!(cell::GalCell, ffit::FourFitVars, profiles, intr::ForceFreeStatesInternal, + nodes::Vector{Float64}, weights::Vector{Float64}, swap_edge::Bool) + + N = intr.numpert_total + np = GAL_NP + fill!(cell.mat, 0) + x1, x2 = cell.x + x0c = (x2 + x1) / 2 + dxc = (x2 - x1) / 2 + qhint = Ref(1) + + @inbounds for iq in eachindex(nodes) + x = x0c + dxc * nodes[iq] + w = dxc * weights[iq] + q = profiles.q_spline(x; hint=qhint) + F, K, G = gal_get_fkg(ffit, intr, x, q) + pbt, qbt = gal_hermite(x, x1, x2) + pb = collect(pbt) + qb = collect(qbt) + if swap_edge + pb[3], pb[4] = pb[4], pb[3] + qb[3], qb[4] = qb[4], qb[3] + end + for ip in 0:np, ipert in 1:N, jp in 0:np, jpert in 1:N + cell.mat[ipert, jpert, ip+1, jp+1] += w * ( + F[ipert, jpert] * qb[ip+1] * qb[jp+1] + + K[ipert, jpert] * qb[ip+1] * pb[jp+1] + + conj(K[jpert, ipert]) * pb[ip+1] * qb[jp+1] + + G[ipert, jpert] * pb[ip+1] * pb[jp+1]) + end + end + return cell +end + +# Resolve (jsing, ψ_s, sign) for an extension/resonant cell from its side. +@inline function _cell_jsing(cell::GalCell, ising::Int) + return cell.extra == GAL_SIDE_LEFT ? ising + 1 : ising +end + +""" + gal_extension!(cell, ising, ffit, profiles, intr, asymps, sings, nn, nodes, weights) + +Build `cell.emat`, `cell.ediag`, `cell.rhs`, `cell.erhs` for an extension cell (`ext`/`ext1`/`ext2`). +Port of `gal_extension` (gal.f:1132-1292). The big solution (`isol` column) drives the RHS; for `ext` +cells the small solution (`isol+N` column) also forms the resonant coupling `emat`/`ediag`. +""" +function gal_extension!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, + intr::ForceFreeStatesInternal, asymps::Vector{GalSingAsymp}, sings::Vector{SingType}, + nn::Int, nodes::Vector{Float64}, weights::Vector{Float64}) + + N = intr.numpert_total + np = GAL_NP + x1, x2 = cell.x + qhint = Ref(1) + + jsing = _cell_jsing(cell, ising) + asymp = asymps[jsing] + psi_s = sings[jsing].psifac + isol = _ipert_res(sings[jsing], intr) + ua_at(x) = sing_get_ua_gal(asymp, x - psi_s) + dua_at(x) = sing_get_dua_gal(asymp, x - psi_s) + + # Boundary node and weights (gal.f:1147-1172) + if cell.extra == GAL_SIDE_LEFT + jp = 2 # Fortran jp (0-based) -> Julia jp+1 + xb = x2 + ws = -1.0 + else + jp = 0 + xb = x1 + ws = 1.0 + end + if cell.etype == GCT_EXT || cell.etype == GCT_EXT1 + w1 = 1.0 + w2 = 1.0 + else # GCT_EXT2 + w1 = (cell.extra == GAL_SIDE_LEFT) ? 0.0 : 1.0 + w2 = (cell.extra == GAL_SIDE_LEFT) ? 1.0 : 0.0 + end + + fill!(cell.emat, 0) + cell.ediag = zero(ComplexF64) + + # --- emat and ediag (ext cells only) (gal.f:1177-1208) --- + if cell.etype == GCT_EXT + uab = ua_at(xb) + duab = dua_at(xb) + u = uab[:, isol+N, 1] # small solution + du = duab[:, isol+N, 1] + for ipert in 1:N + @views cell.emat .+= cell.mat[:, ipert, :, jp+1] .* u[ipert] .+ + cell.mat[:, ipert, :, jp+2] .* du[ipert] + end + for ipert in 1:N + cell.ediag += conj(u[ipert]) * cell.emat[ipert, jp+1] + + conj(du[ipert]) * cell.emat[ipert, jp+2] + end + # surface term at xb + qb = profiles.q_spline(xb; hint=qhint) + Fb, Kb, _ = gal_get_fkg(ffit, intr, xb, qb) + pbt, _ = gal_hermite(xb, x1, x2) + Fdu_Ku = Fb * du .+ Kb * u + for ip in 0:np + @views cell.emat[:, ip+1] .+= Fdu_Ku .* (pbt[ip+1] * ws) + end + cell.ediag += sum(conj.(u) .* Fdu_Ku) * ws + end + + # --- rhs (gal.f:1210-1259) --- + ua1 = ua_at(x1)[:, isol, 1] # big solution at left node + du1 = dua_at(x1)[:, isol, 1] + ua2 = ua_at(x2)[:, isol, 1] # big solution at right node + du2 = dua_at(x2)[:, isol, 1] + fill!(cell.rhs, 0) + + if cell.etype == GCT_EXT || cell.etype == GCT_EXT1 + cell.erhs = zero(ComplexF64) + x0c = (x2 + x1) / 2 + dxc = (x2 - x1) / 2 + for iq in eachindex(nodes) + x = x0c + dxc * nodes[iq] + w = dxc * weights[iq] + q = profiles.q_spline(x; hint=qhint) + F, K, G = gal_get_fkg(ffit, intr, x, q) + pbt, qbt = gal_hermite(x, x1, x2) + uax = ua_at(x) + ub = uax[:, isol, 1] + dub = dua_at(x)[:, isol, 1] + term1 = F * dub .+ K * ub + term2 = adjoint(K) * dub .+ G * ub + for ip in 0:np + @views cell.rhs[:, ip+1] .-= (term1 .* qbt[ip+1] .+ term2 .* pbt[ip+1]) .* w + end + end + if cell.etype == GCT_EXT + for ipert in 1:N + cell.erhs += conj(ua_at(xb)[ipert, isol+N, 1]) * cell.rhs[ipert, jp+1] + + conj(dua_at(xb)[ipert, isol+N, 1]) * cell.rhs[ipert, jp+2] + end + end + elseif cell.etype == GCT_EXT2 + for ipert in 1:N + @views cell.rhs .-= w1 .* (cell.mat[:, ipert, :, 0+1] .* ua1[ipert] .+ + cell.mat[:, ipert, :, 1+1] .* du1[ipert]) + @views cell.rhs .-= w2 .* (cell.mat[:, ipert, :, 2+1] .* ua2[ipert] .+ + cell.mat[:, ipert, :, 3+1] .* du2[ipert]) + end + end + + # --- surface terms (always; gal.f:1262-1286) --- + q_l = profiles.q_spline(x1; hint=qhint) + Fl, Kl, _ = gal_get_fkg(ffit, intr, x1, q_l) + pbt, _ = gal_hermite(x1, x1, x2) + surf_l = Fl * du1 .+ Kl * ua1 + for ip in 0:np + @views cell.rhs[:, ip+1] .-= surf_l .* (pbt[ip+1] * w1) + end + if cell.etype == GCT_EXT && cell.extra == GAL_SIDE_RIGHT + cell.erhs -= sum(conj.(ua_at(x1)[:, isol+N, 1]) .* surf_l) + end + + q_r = profiles.q_spline(x2; hint=qhint) + Fr, Kr, _ = gal_get_fkg(ffit, intr, x2, q_r) + pbt, _ = gal_hermite(x2, x1, x2) + surf_r = Fr * du2 .+ Kr * ua2 + for ip in 0:np + @views cell.rhs[:, ip+1] .+= surf_r .* (pbt[ip+1] * w2) + end + if cell.etype == GCT_EXT && cell.extra == GAL_SIDE_LEFT + cell.erhs += sum(conj.(ua_at(x2)[:, isol+N, 1]) .* surf_r) + end + return cell +end + +""" + gal_resonant!(cell, ising, ffit, profiles, intr, asymps, sings, nn, gal_tol) + +Compute the resonant-cell contributions `cell.erhs`, `cell.ediag`, `cell.rhs`, `cell.emat` by adaptive +quadrature (QuadGK) of the residual-operator integrand. Port of `gal_lsode_int`/`gal_lsode_der` +(gal.f:772-940): the Fortran LSODE accumulation is replaced by `quadgk` over `[x_bdy, x_lsode]`. +""" +function gal_resonant!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, + intr::ForceFreeStatesInternal, asymps::Vector{GalSingAsymp}, sings::Vector{SingType}, + nn::Int, gal_tol::Float64) + + N = intr.numpert_total + np = GAL_NP + x1, x2 = cell.x + qhint = Ref(1) + + jsing = _cell_jsing(cell, ising) + asymp = asymps[jsing] + psi_s = sings[jsing].psifac + isol_big = _ipert_res(sings[jsing], intr) + isol_small = isol_big + N + cols = [isol_big, isol_small] + + # Integration limits (gal.f:805-815): right → [x2, x_lsode]; left → [x1, x_lsode] + x0 = (cell.extra == GAL_SIDE_LEFT) ? x1 : x2 + x1l = cell.x_lsode + sgn_u = (cell.extra == GAL_SIDE_RIGHT) ? -1.0 : 1.0 + + L = 2 + 2 * N * (np + 1) + function integrand(x) + z = x - psi_s + ua = sing_get_ua_gal(asymp, z) + dua = sing_get_dua_gal(asymp, z) + q = profiles.q_spline(x; hint=qhint) + ua2 = ua[:, cols, :] + dua2 = dua[:, cols, :] + mv = sing_matvec(ffit, intr, x, q, ua2, dua2) # N×2 (col1=big, col2=small) + pbt, _ = gal_hermite(x, x1, x2) + w = conj.(@view ua2[:, 2, 1]) # conj small solution, qty1 + out = Vector{ComplexF64}(undef, L) + out[1] = sum(w .* @view mv[:, 1]) # res1 + out[2] = sum(w .* @view mv[:, 2]) # res2 + idx = 3 + for ip in 0:np, ipert in 1:N + out[idx] = pbt[ip+1] * mv[ipert, 1] # hbig (ipert fastest, then ip) + idx += 1 + end + for ip in 0:np, ipert in 1:N + out[idx] = pbt[ip+1] * mv[ipert, 2] # hsmall + idx += 1 + end + return out + end + + # QuadGK replaces Fortran's LSODE accumulation. Use a moderate relative tolerance with an + # evaluation cap (analogous to Fortran's gnstep limit) so a near-singular integrand cannot hang. + raw, qerr = quadgk(integrand, x0, x1l; rtol=1e-8, atol=1e-30, maxevals=20000) + if get(ENV, "GAL_DEBUG", "") == "1" + @info " resonant jsing=$jsing side=$(cell.extra) qerr=$(qerr) res1=$(raw[1]) res2=$(raw[2])" + end + hbig = reshape(@view(raw[3:2+N*(np+1)]), N, np + 1) + hsmall = reshape(@view(raw[3+N*(np+1):end]), N, np + 1) + + # Apply the right-side negation and the gal_make_arrays signs (gal.f:868, 1334-1337) + cell.erhs = -sgn_u * raw[1] + cell.ediag = sgn_u * raw[2] + cell.rhs .= (-sgn_u) .* hbig + cell.emat .= sgn_u .* hsmall + return cell +end + +""" + gal_assemble_mat!(ws, mpert) + +Scatter every cell's `mat`/`emat`/`ediag` into the banded global matrix `ws.mat`. Port of +`gal_assemble_mat` (gal.f:686-764). Supports both `"LU"` (full band, `offset = kl+ku+1`) and +`"cholesky"` (lower band only, `offset = 1`). +""" +function gal_assemble_mat!(ws::GalWorkspace, mpert::Int) + np = ws.np + msing = length(ws.intvl) - 1 + lu = ws.solver == "LU" + offset = lu ? ws.kl + ws.ku + 1 : 1 + + for ising in 0:msing + for cell in ws.intvl[ising+1].cells + res = cell.etype == GCT_RES || cell.etype == GCT_EXT + for ip in 0:np, ipert in 1:mpert + i = cell.map[ipert, ip+1] + # nonresonant stiffness + for jp in 0:np, jpert in 1:mpert + j = cell.map[jpert, jp+1] + if lu + ws.mat[offset+i-j, j] += cell.mat[ipert, jpert, ip+1, jp+1] + elseif j <= i + ws.mat[offset+i-j, j] += cell.mat[ipert, jpert, ip+1, jp+1] + end + end + # resonant coupling (res/ext only) + if res + j = cell.emap + e = cell.emat[ipert, ip+1] + if lu + ws.mat[offset+i-j, j] += e + ws.mat[offset+j-i, i] += conj(e) + elseif j < i + ws.mat[offset+i-j, j] += e + elseif j > i + ws.mat[offset+j-i, i] += conj(e) + end + end + end + if res + ws.mat[offset, cell.emap] += cell.ediag + end + end + end + return ws +end + +""" + gal_assemble_rhs!(ws, mpert) + +Scatter every cell's `rhs`/`erhs` into the global RHS `ws.rhs`. Port of `gal_assemble_rhs` +(gal.f:634-678). A new RHS column (`isol`) begins at each big-solution driver: an `ext2`-left cell or a +`res`-right cell. +""" +function gal_assemble_rhs!(ws::GalWorkspace, mpert::Int) + np = ws.np + msing = length(ws.intvl) - 1 + isol = 0 + for ising in 0:msing + for cell in ws.intvl[ising+1].cells + cell.etype == GCT_NONE && continue + if cell.etype == GCT_EXT2 && cell.extra == GAL_SIDE_LEFT + isol += 1 + elseif cell.etype == GCT_RES && cell.extra == GAL_SIDE_RIGHT + isol += 1 + end + for ip in 0:np, ipert in 1:mpert + imap = cell.map[ipert, ip+1] + ws.rhs[imap, isol] += cell.rhs[ipert, ip+1] + end + if cell.etype == GCT_EXT || cell.etype == GCT_RES + ws.rhs[cell.emap, isol] += cell.erhs + end + end + end + return ws +end + +""" + gal_set_boundary!(ws, mpert, wv_edge) + +Apply the axis (`u(0)=0` identity) and edge boundary conditions to the boundary cells' `mat` before +global assembly. Port of `gal_set_boundary` (gal.f:1517-1583). `wv_edge::Union{Nothing,Matrix}` is the +free-boundary vacuum block to add at the edge value DOF (index 3); `nothing` ⇒ fixed-boundary identity. +The `rpec_flag` coil branch is not ported. +""" +function gal_set_boundary!(ws::GalWorkspace, mpert::Int, wv_edge::Union{Nothing,Matrix{ComplexF64}}) + chol = ws.solver == "cholesky" + msing = length(ws.intvl) - 1 + + # axis u(0): first cell of interval 0, Hermite value DOF ip=0 (Julia index 1) + cell = ws.intvl[1].cells[1] + cell.mat[:, :, 1, :] .= 0 + chol && (cell.mat[:, :, :, 1] .= 0) + for idx in 1:mpert + cell.mat[idx, idx, 1, 1] = 1 + end + + # edge u(1): last cell of last interval, edge-value DOF ip=3 (Julia index 4, see gauss_quad swap) + cell = ws.intvl[msing+1].cells[ws.nx] + if wv_edge === nothing + cell.mat[:, :, 4, :] .= 0 + chol && (cell.mat[:, :, :, 4] .= 0) + for idx in 1:mpert + cell.mat[idx, idx, 4, 4] = 1 + end + else + @views cell.mat[:, :, 4, 4] .+= wv_edge + end + return ws +end diff --git a/src/ForceFreeStates/Galerkin/GalerkinGrid.jl b/src/ForceFreeStates/Galerkin/GalerkinGrid.jl new file mode 100644 index 000000000..b7d3829bb --- /dev/null +++ b/src/ForceFreeStates/Galerkin/GalerkinGrid.jl @@ -0,0 +1,221 @@ +# GalerkinGrid.jl +# +# Grid construction and local→global DOF mapping for the outer-region Galerkin solver. +# Ports gal_pack (gal.f:262-318), gal_make_grid (gal.f:326-451), and gal_make_map (gal.f:509-575). +# +# Node arrays use Fortran 0-based `x(0:nx)` mapped to Julia `xn[i+1]` (so Fortran `x(i)` is `xn[i+1]`). +# Cells are 1-based in both. Intervals `0:msing` (Fortran) are `ws.intvl[ising+1]` in Julia. +# The optional `gal_xmin_flag`/`sing1_xmin` adaptive-width branch is intentionally not ported. + +""" + gal_pack(nx::Int, pfac::Float64, side::String) -> Vector{Float64} + +Packed logical grid on `[-1, 1]`. Port of Fortran `gal_pack` (gal.f:262-318). For `side="both"` +returns `2*nx+1` nodes (Fortran `-nx:nx`) clustered toward both ends when `pfac < 1` (strong packing +near the bracketing singular surfaces). `pfac > 1` packs toward the centre; `pfac == 1` is uniform. +""" +function gal_pack(nx::Int, pfac::Float64, side::String) + if side == "left" + xi = collect(-2nx:0) ./ (2nx) + elseif side == "right" + xi = collect(0:2nx) ./ (2nx) + elseif side == "both" + xi = collect(-nx:nx) ./ nx + else + error("gal_pack: unrecognized side = $side") + end + + if pfac > 1 + λ = sqrt(1 - 1 / pfac) + x = @. log((1 + λ * xi) / (1 - λ * xi)) / log((1 + λ) / (1 - λ)) + elseif pfac == 1 + x = copy(xi) + elseif pfac > 0 + λ = sqrt(1 - pfac) + a = log((1 + λ) / (1 - λ)) + x = @. (exp(a * xi) - 1) / (exp(a * xi) + 1) / λ + else + x = @. xi^(-pfac) + end + + if side == "left" + @. x = 2x + 1 + elseif side == "right" + @. x = 2x - 1 + end + return x +end + +""" + gal_make_grid!(intvl::GalInterval, ising::Int, msing::Int, sings::Vector{SingType}, + nn::Int, psilow::Float64, psihigh::Float64, ctrl::ForceFreeStatesControl) + +Set the cell types (`res`/`ext`/`ext1`/`ext2`/`none`), sides, resonant integration limits, and packed +node positions for interval `ising` (0-based, `0:msing`). Port of Fortran `gal_make_grid` +(gal.f:326-451), `dx1dx2_flag=true` path. `intvl.x`/`intvl.dx` have length `nx+1`, `intvl.cells` length +`nx` (preallocated by the caller). `sings` is the filtered list of resonant surfaces (1-based, +`sings[ising]` = Fortran `sing(ising)`). + +Note (faithful to Fortran): the lower-surface width scale uses `|nn·q1|` (gal.f:356) but the +upper-surface scale uses `|q1|` without `nn` (gal.f:398). Identical for `nn = 1`. +""" +function gal_make_grid!(intvl::GalInterval, ising::Int, msing::Int, sings::Vector{SingType}, + nn::Int, psilow::Float64, psihigh::Float64, ctrl::ForceFreeStatesControl) + + nx = ctrl.gal_nx + dx0 = ctrl.gal_dx0 + dx1 = ctrl.gal_dx1 + dx2 = ctrl.gal_dx2 + pfac = ctrl.gal_pfac + cutoff = ctrl.gal_cutoff + xn = intvl.x + cells = intvl.cells + + # Reset cell flags + for c in cells + c.etype = GCT_NONE + c.extra = GAL_SIDE_NONE + end + + # --- lower bound (gal.f:349-389) --- + local ixmin::Int + if ising == 0 + ixmin = 0 + xn[0+1] = psilow + else + x0 = sings[ising].psifac + nq1 = abs(nn * sings[ising].q1) + xn[0+1] = x0 + cells[1].x_lsode = x0 + dx0 / nq1 + if ctrl.gal_dx1dx2_flag + xn[1+1] = x0 + dx1 / nq1 + xn[2+1] = x0 + (dx1 + dx2) / nq1 + ixmin = 2 + else + ixmin = 0 + end + cells[1].extra = GAL_SIDE_RIGHT + cells[2].extra = GAL_SIDE_RIGHT + cells[1].etype = GCT_RES + cells[2].etype = GCT_EXT + for ix in 3:(cutoff+1) + cells[ix].etype = GCT_EXT1 + cells[ix].extra = GAL_SIDE_RIGHT + end + ix_ext2 = max(cutoff + 2, 3) # Fortran loop-exit value of ix (gal.f:387) + (ix_ext2 > nx || cells[ix_ext2].etype != GCT_NONE) && + error("gal_make_grid: too many elements include the big solution (right side)") + cells[ix_ext2].etype = GCT_EXT2 + cells[ix_ext2].extra = GAL_SIDE_RIGHT + end + + # --- upper bound (gal.f:391-429) --- + local ixmax::Int + if ising == msing + ixmax = nx + xn[nx+1] = psihigh + else + x1 = sings[ising+1].psifac + nq1 = abs(sings[ising+1].q1) # NOTE: no nn factor, faithful to gal.f:398 + xn[nx+1] = x1 + cells[nx].x_lsode = x1 - dx0 / nq1 + if ctrl.gal_dx1dx2_flag + xn[(nx-1)+1] = x1 - dx1 / nq1 + xn[(nx-2)+1] = x1 - (dx1 + dx2) / nq1 + ixmax = nx - 2 + else + ixmax = nx + end + cells[nx-1].extra = GAL_SIDE_LEFT + cells[nx].extra = GAL_SIDE_LEFT + cells[nx-1].etype = GCT_EXT + cells[nx].etype = GCT_RES + for ix in (nx-2):-1:(nx-cutoff) + cells[ix].etype = GCT_EXT1 + cells[ix].extra = GAL_SIDE_LEFT + end + ix_ext2 = min(nx - cutoff - 1, nx - 2) # Fortran loop-exit value of ix (gal.f:427) + (ix_ext2 < 1 || cells[ix_ext2].etype != GCT_NONE) && + error("gal_make_grid: too many elements include the big solution (left side)") + cells[ix_ext2].etype = GCT_EXT2 + cells[ix_ext2].extra = GAL_SIDE_LEFT + end + + # --- interior packed grid (gal.f:431-446) --- + x0 = xn[ixmin+1] + x1 = xn[ixmax+1] + xm = (xn[ixmax+1] + xn[ixmin+1]) / 2 + dxh = (xn[ixmax+1] - xn[ixmin+1]) / 2 + mx = (ixmax - ixmin) ÷ 2 + packed = gal_pack(mx, pfac, "both") # length 2*mx+1 = (ixmax-ixmin)+1 + for k in 0:(ixmax-ixmin) + xn[ixmin+1+k] = xm + dxh * packed[k+1] + end + xn[ixmin+1] = x0 + xn[ixmax+1] = x1 + + intvl.dx[0+1] = 0.0 + for i in 1:nx + intvl.dx[i+1] = xn[i+1] - xn[i] + end + for ix in 1:nx + cells[ix].x = (xn[ix], xn[ix+1]) # Fortran (x(ix-1), x(ix)) + end + return intvl +end + +""" + gal_make_map!(ws::GalWorkspace, mpert::Int) + +Build the local→global DOF numbering with the `2*mpert` C¹ overlap between adjacent Hermite cells and +the interleaved extra (small resonant) DOFs (`emap`). Port of Fortran `gal_make_map` (gal.f:509-575). +Sets `ws.ndim`. The `skip`/`emap` bookkeeping reserves a global slot for each resonant coefficient and +shares it between the `res` cell and its neighbouring `ext` cell. +""" +function gal_make_map!(ws::GalWorkspace, mpert::Int) + np = ws.np + msing = length(ws.intvl) - 1 + imap = 1 + skip = false + emap = 0 + for ising in 0:msing + intvl = ws.intvl[ising+1] + for ix in 1:ws.nx + cell = intvl.cells[ix] + # Nonresonant Hermite DOFs (with 2*mpert overlap onto the previous cell) + if imap > 1 + imap -= 2 * mpert + end + for ip in 0:np + for ipert in 1:mpert + cell.map[ipert, ip+1] = imap + imap += 1 + end + if ip == 1 && skip + imap += 1 + skip = false + end + end + # Extra (small resonant) DOF, shared between res and adjacent ext cell + if cell.extra == GAL_SIDE_LEFT + if cell.etype == GCT_EXT + emap = imap + cell.emap = emap + skip = true + elseif cell.etype == GCT_RES + cell.emap = emap + end + elseif cell.extra == GAL_SIDE_RIGHT + if cell.etype == GCT_RES + emap = imap + cell.emap = emap + skip = true + elseif cell.etype == GCT_EXT + cell.emap = emap + end + end + end + end + ws.ndim = imap - 1 + return ws +end diff --git a/src/ForceFreeStates/Galerkin/GalerkinSolve.jl b/src/ForceFreeStates/Galerkin/GalerkinSolve.jl new file mode 100644 index 000000000..4328bc0ab --- /dev/null +++ b/src/ForceFreeStates/Galerkin/GalerkinSolve.jl @@ -0,0 +1,216 @@ +# GalerkinSolve.jl +# +# Top-level driver for the RDCON outer-region singular Galerkin Δ′ solve, plus the per-cell assembly +# orchestration, the banded solve, Δ′ extraction, PEST-3 blocks, and HDF5 output. +# Ports gal_make_arrays (gal.f:1300-1359), gal_solve (gal.f:1367-1431), and gal_write_pest3_data +# (gal.f:1712-1745). No inner-layer wiring (future thrust). + +""" + gal_make_arrays!(ws, ctrl, equil, ffit, intr, asymps, sings, nn, wv_edge) + +Assemble the global banded matrix and RHS. For each cell: Gauss-Lobatto Hermite stiffness +(`gal_gauss_quad!`), then the resonant (`gal_resonant!`) or extension (`gal_extension!`) contributions; +then the boundary conditions and the scatter into `ws.mat`/`ws.rhs`. Port of `gal_make_arrays`. +""" +function gal_make_arrays!(ws::GalWorkspace, ctrl::ForceFreeStatesControl, equil, ffit::FourFitVars, + intr::ForceFreeStatesInternal, asymps::Vector{GalSingAsymp}, sings::Vector{SingType}, + nn::Int, wv_edge::Union{Nothing,Matrix{ComplexF64}}) + + mpert = intr.numpert_total + msing = length(ws.intvl) - 1 + profiles = equil.profiles + nodes, weights = gausslobatto(ws.nq + 1) + + for ising in 0:msing + for (ix, cell) in enumerate(ws.intvl[ising+1].cells) + swap_edge = (ising == msing && ix == ws.nx) + gal_gauss_quad!(cell, ffit, profiles, intr, nodes, weights, swap_edge) + if cell.etype == GCT_RES + gal_resonant!(cell, ising, ffit, profiles, intr, asymps, sings, nn, ctrl.gal_tol) + elseif cell.etype == GCT_EXT || cell.etype == GCT_EXT1 || cell.etype == GCT_EXT2 + gal_extension!(cell, ising, ffit, profiles, intr, asymps, sings, nn, nodes, weights) + end + end + end + + gal_set_boundary!(ws, mpert, wv_edge) + gal_assemble_mat!(ws, mpert) + gal_assemble_rhs!(ws, mpert) + return ws +end + +""" + galerkin_solve(ctrl::ForceFreeStatesControl, equil, ffit::FourFitVars, + intr::ForceFreeStatesInternal; vac_data=nothing) -> GalerkinResult + +Compute the outer-region Δ′ matching matrix by the singular Galerkin method. Port of `gal_solve` +(gal.f:1367-1431). Single toroidal mode only (`intr.npert == 1`). Returns a `GalerkinResult`; if there +are no resonant surfaces in the domain it returns an empty result. + +`vac_data` (a `VacuumData` from `free_run!`) supplies the free-boundary edge term +`wv_edge = vac_data.wv · psio²`; pass `nothing` for a fixed-boundary edge. +""" +function galerkin_solve(ctrl::ForceFreeStatesControl, equil, ffit::FourFitVars, + intr::ForceFreeStatesInternal; vac_data=nothing) + + intr.npert == 1 || error("galerkin_solve: only single-n (npert == 1) is supported") + ctrl.gal_solver in ("LU", "cholesky") || error("galerkin_solve: gal_solver must be \"LU\" or \"cholesky\"") + nn = intr.nlow + mpert = intr.numpert_total + np = GAL_NP + + # Resonant surfaces inside the integration domain, in increasing ψ (Fortran `sing(1:msing)`). + # psilow is raised above the axis by sing_min! when qlow > qmin (excludes the q 0 ? intr.psilow : equil.profiles.xs[1] + psihigh = intr.psilim + sings = [s for s in intr.sing if psilow < s.psifac < psihigh && intr.mlow <= s.m[1] <= intr.mhigh] + msing = length(sings) + if msing == 0 + ctrl.verbose && @info "galerkin_solve: no resonant surfaces in domain; skipping Δ′ solve" + empty2 = Matrix{ComplexF64}(undef, 0, 0) + return GalerkinResult(Matrix{ComplexF64}(undef, 0, 0), empty2, empty2, empty2, empty2, 0, + Float64[], Float64[], Int[], Int[], Float64[], ComplexF64[]) + end + + ctrl.verbose && @info "Starting outer-region Galerkin Δ′ solve (msing=$msing, solver=$(ctrl.gal_solver))" + + # Per-surface two-sided asymptotic series (pr178's validated convention, matching Fortran sing.f + # vmatr/vmatl): right = sig=+1, left = sig=-1, no √det normalization. The Mercier exponent α is a + # property of the surface, so the left series reuses the right's α (alpha_override). The order is + # raised to gal_sing_order + ceil(2·Re(α)) for high-Mercier-index surfaces (Fortran sing1_vmat). + ctrl_gal = deepcopy(ctrl) + asymps = GalSingAsymp[] + for s in sings + ctrl_gal.sing_order = ctrl.gal_sing_order + ar = compute_sing_asymptotics(s, ctrl_gal, equil, ffit, intr; sig=1.0) + if ctrl.gal_sing_order_ceiling + order = ctrl.gal_sing_order + ceil(Int, 2 * real(ar.alpha[1])) + if order > ctrl.gal_sing_order + ctrl_gal.sing_order = order + ar = compute_sing_asymptotics(s, ctrl_gal, equil, ffit, intr; sig=1.0) + end + end + al = compute_sing_asymptotics(s, ctrl_gal, equil, ffit, intr; sig=-1.0, alpha_override=ar.alpha) + push!(asymps, GalSingAsymp(ar, al)) + end + + # --- allocate workspace --- + nx = ctrl.gal_nx + kl = mpert * (np + 1) + ku = kl + ldab = ctrl.gal_solver == "LU" ? 2kl + ku + 1 : kl + 1 + nsol = 2 * msing + intvl = [GalInterval(zeros(Float64, nx + 1), zeros(Float64, nx + 1), [GalCell(mpert) for _ in 1:nx]) + for _ in 0:msing] + ws = GalWorkspace(ctrl.gal_solver, nx, ctrl.gal_nq, np, 0, kl, ku, ldab, nsol, + intvl, Matrix{ComplexF64}(undef, 0, 0), Matrix{ComplexF64}(undef, 0, 0), Matrix{ComplexF64}(undef, 0, 0)) + + for ising in 0:msing + gal_make_grid!(ws.intvl[ising+1], ising, msing, sings, nn, psilow, psihigh, ctrl) + end + gal_make_map!(ws, mpert) + + ws.mat = zeros(ComplexF64, ldab, ws.ndim) + ws.rhs = zeros(ComplexF64, ws.ndim, nsol) + ws.sol = zeros(ComplexF64, ws.ndim, nsol) + + # Free-boundary edge term wvac·psio² (vac_data.wv is already singfac-scaled at qlim in free_run!) + wv_edge = nothing + if ctrl.vac_flag && vac_data !== nothing + wv_edge = Matrix{ComplexF64}(vac_data.wv .* equil.psio^2) + end + + gal_make_arrays!(ws, ctrl, equil, ffit, intr, asymps, sings, nn, wv_edge) + + if get(ENV, "GAL_DEBUG", "") == "1" + offdbg = ws.solver == "LU" ? ws.kl + ws.ku + 1 : 1 + @info "GAL_DEBUG ndim=$(ws.ndim) nsol=$nsol kl=$(ws.kl) ldab=$(ws.ldab) |rhs|=$(norm(ws.rhs))" + for ising in 0:msing + for cell in ws.intvl[ising+1].cells + if cell.etype == GCT_RES || cell.etype == GCT_EXT + @info " cell ising=$ising etype=$(cell.etype) side=$(cell.extra) emap=$(cell.emap) ediag=$(cell.ediag) erhs=$(cell.erhs) |rhs|=$(norm(cell.rhs)) |emat|=$(norm(cell.emat)) matdiag[emap]=$(ws.mat[offdbg, cell.emap])" + end + end + end + end + + # --- banded solve (gal.f:1383-1396) --- + ws.sol .= ws.rhs + if ws.solver == "LU" + ctrl.verbose && @info "Galerkin LU banded factorization + solve" + ab, ipiv = LinearAlgebra.LAPACK.gbtrf!(ws.kl, ws.ku, ws.ndim, ws.mat) + LinearAlgebra.LAPACK.gbtrs!('N', ws.kl, ws.ku, ws.ndim, ab, ipiv, ws.sol) + else + ctrl.verbose && @info "Galerkin Cholesky banded factorization + solve" + LinearAlgebra.LAPACK.pbtrf!('L', ws.kl, ws.mat) + LinearAlgebra.LAPACK.pbtrs!('L', ws.kl, ws.mat, ws.sol) + end + + # --- extract Δ′ from the small resonant coefficients (gal.f:1405-1417) --- + delta = zeros(ComplexF64, nsol, 2 * msing) + jsol = 0 + for ising in 0:msing + for cell in ws.intvl[ising+1].cells + if cell.etype == GCT_RES + jsol += 1 + @views delta[:, jsol] .= ws.sol[cell.emap, :] + end + end + end + + Ap, Bp, Gammap, Deltap = gal_pest3_blocks(delta, msing) + + di = [real(-asymps[i].right.alpha[1]^2) for i in 1:msing] + alpha = [asymps[i].right.alpha[1] for i in 1:msing] + return GalerkinResult(delta, Ap, Bp, Gammap, Deltap, msing, + [s.psifac for s in sings], [s.q for s in sings], + [s.m[1] for s in sings], [s.n[1] for s in sings], di, alpha) +end + +""" + gal_pest3_blocks(delta, msing) -> (Ap, Bp, Gammap, Deltap) + +PEST-3 matching blocks (each `msing×msing`) as ± combinations of the left/right Δ′ entries. Port of +`gal_write_pest3_data` (gal.f:1726-1745). Row index `2i-1`/`2i` = left/right of surface `i`. +""" +function gal_pest3_blocks(delta::Matrix{ComplexF64}, msing::Int) + Ap = zeros(ComplexF64, msing, msing) + Bp = zeros(ComplexF64, msing, msing) + Gammap = zeros(ComplexF64, msing, msing) + Deltap = zeros(ComplexF64, msing, msing) + for i in 1:msing, j in 1:msing + d11 = delta[2i-1, 2j-1] + d12 = delta[2i-1, 2j] + d21 = delta[2i, 2j-1] + d22 = delta[2i, 2j] + Ap[i, j] = d22 + d21 + d12 + d11 + Bp[i, j] = d22 - d21 + d12 - d11 + Gammap[i, j] = d22 + d21 - d12 - d11 + Deltap[i, j] = d22 - d21 - d12 + d11 + end + return Ap, Bp, Gammap, Deltap +end + +""" + write_galerkin!(out_h5, result::GalerkinResult) + +Write the Galerkin Δ′ outputs into the open HDF5 file under the `galerkin/` group. Replaces the Fortran +`delta_gw`/`pest3_data` ASCII/binary outputs. +""" +function write_galerkin!(out_h5, result::GalerkinResult) + out_h5["galerkin/msing"] = result.msing + result.msing == 0 && return nothing + out_h5["galerkin/delta"] = result.delta + out_h5["galerkin/pest3_A"] = result.Ap + out_h5["galerkin/pest3_B"] = result.Bp + out_h5["galerkin/pest3_Gamma"] = result.Gammap + out_h5["galerkin/pest3_Delta"] = result.Deltap + out_h5["galerkin/sing_psi"] = result.sing_psi + out_h5["galerkin/sing_q"] = result.sing_q + out_h5["galerkin/sing_m"] = result.sing_m + out_h5["galerkin/sing_n"] = result.sing_n + out_h5["galerkin/di"] = result.di + out_h5["galerkin/alpha"] = result.alpha + return nothing +end diff --git a/src/ForceFreeStates/Galerkin/GalerkinStructs.jl b/src/ForceFreeStates/Galerkin/GalerkinStructs.jl new file mode 100644 index 000000000..49f294d32 --- /dev/null +++ b/src/ForceFreeStates/Galerkin/GalerkinStructs.jl @@ -0,0 +1,141 @@ +# GalerkinStructs.jl +# +# Data structures for the RDCON outer-region singular Galerkin solver — the Julia port of +# `gal.f` (Dewar's Galerkin method for singular modes). These mirror the Fortran derived types +# `cell_type`, `interval_type`, and `gal_type` (gal.f:48-76). +# +# Fortran uses 0-based dimensions `0:np` and `0:nx`/`0:msing`; here those become Julia 1-based with a +# `+1` index shift (Hermite DOF `ip` ↔ array index `ip+1`; interval `ising` ↔ `intvl[ising+1]`). +# +# Reference: A. H. Glasser, Z. R. Wang & J.-K. Park, Phys. Plasmas 23, 112506 (2016). + +# Hermite-cubic order: 4 DOFs per node-pair (value + slope at each end), indexed 0:np in Fortran. +const GAL_NP = 3 + +"""Cell type flanking a singular surface (Fortran `cell%etype`, gal.f).""" +@enum GalCellType GCT_NONE GCT_RES GCT_EXT GCT_EXT1 GCT_EXT2 + +"""Which side of the adjacent singular surface a cell lies on (Fortran `cell%extra`).""" +@enum GalSide GAL_SIDE_NONE GAL_SIDE_LEFT GAL_SIDE_RIGHT + +""" + GalCell + +One grid cell of the Galerkin discretization. Port of Fortran `cell_type` (gal.f:52-61). + +## Fields + + - `etype::GalCellType` — none / resonant / extension(1,2) + - `extra::GalSide` — none / left / right (side of the neighbouring singular surface) + - `emap::Int` — global index of the extra (small resonant) DOF; 0 if none + - `map::Matrix{Int}` — `(mpert, np+1)` local→global DOF map (Fortran `cell%map(mpert, 0:np)`) + - `x::NTuple{2,Float64}` — `[x_left, x_right]` of the cell + - `x_lsode::Float64` — resonant-integration truncation point (res cells only) + - `erhs::ComplexF64`, `ediag::ComplexF64` — resonant RHS and diagonal contributions + - `rhs::Matrix{ComplexF64}` — `(mpert, np+1)` cell RHS (driving term from the big solution) + - `emat::Matrix{ComplexF64}` — `(mpert, np+1)` coupling of the extra DOF to the Hermite DOFs + - `mat::Array{ComplexF64,4}` — `(mpert, mpert, np+1, np+1)` cell stiffness block +""" +mutable struct GalCell + etype::GalCellType + extra::GalSide + emap::Int + map::Matrix{Int} + x::NTuple{2,Float64} + x_lsode::Float64 + erhs::ComplexF64 + ediag::ComplexF64 + rhs::Matrix{ComplexF64} + emat::Matrix{ComplexF64} + mat::Array{ComplexF64,4} +end + +"""Construct an empty `GalCell` for `mpert` poloidal modes and Hermite order `np`.""" +function GalCell(mpert::Int, np::Int=GAL_NP) + return GalCell(GCT_NONE, GAL_SIDE_NONE, 0, + zeros(Int, mpert, np + 1), (0.0, 0.0), 0.0, + zero(ComplexF64), zero(ComplexF64), + zeros(ComplexF64, mpert, np + 1), + zeros(ComplexF64, mpert, np + 1), + zeros(ComplexF64, mpert, mpert, np + 1, np + 1)) +end + +""" + GalInterval + +One interval between consecutive singular surfaces (or between a surface and a domain edge). +Port of Fortran `interval_type` (gal.f:63-66). `x`/`dx` are length `nx+1` (Fortran `0:nx`). +""" +struct GalInterval + x::Vector{Float64} + dx::Vector{Float64} + cells::Vector{GalCell} +end + +""" + GalWorkspace + +Global workspace for the Galerkin solve. Port of Fortran `gal_type` (gal.f:68-76). + +`intvl` has length `msing+1` (Fortran `intvl(0:msing)`, accessed as `intvl[ising+1]`). +`kl = ku = mpert*(np+1)`. The banded `mat` storage layout depends on `solver` (gal.f:164-168): + - `"LU"` → `ldab = 2*kl + ku + 1`, full band (LAPACK `gbtrf!`/`gbtrs!`) + - `"cholesky"` → `ldab = kl + 1`, lower band only (LAPACK `pbtrf!`/`pbtrs!`, `'L'`) +""" +mutable struct GalWorkspace + solver::String + nx::Int + nq::Int + np::Int + ndim::Int + kl::Int + ku::Int + ldab::Int + nsol::Int + intvl::Vector{GalInterval} + mat::Matrix{ComplexF64} + rhs::Matrix{ComplexF64} + sol::Matrix{ComplexF64} +end + +""" + GalSingAsymp + +Two-sided singular asymptotics for the Galerkin solver: separate right (sig=+1) and left (sig=−1) +power series, mirroring Fortran sing.f `vmatr`/`vmatl`. Each is evaluated at a positive distance +`|ψ−ψ_s|` (real √, real pfac, no z<0 renormalization), so the directly-extracted Δ′ matches gal.f. +""" +struct GalSingAsymp + right::SingAsymptotics + left::SingAsymptotics +end + +""" + GalerkinResult + +Outputs of the outer-region Galerkin solve. + +## Fields + + - `delta::Matrix{ComplexF64}` — Δ′ matrix, `(nsol, 2*msing)` with `nsol = 2*msing`; the small + resonant coefficients (Fortran `delta`, gal.f:1405-1417). + - `Ap, Bp, Gammap, Deltap::Matrix{ComplexF64}` — PEST-3 matching blocks, each `(msing, msing)` + (Fortran `gal_write_pest3_data`, gal.f:1726-1745). + - `msing::Int` — number of resonant singular surfaces included. + - `sing_psi, sing_q::Vector{Float64}`, `sing_m, sing_n::Vector{Int}` — per-surface identifiers. + - `di::Vector{Float64}`, `alpha::Vector{ComplexF64}` — Mercier index and exponent per surface. +""" +struct GalerkinResult + delta::Matrix{ComplexF64} + Ap::Matrix{ComplexF64} + Bp::Matrix{ComplexF64} + Gammap::Matrix{ComplexF64} + Deltap::Matrix{ComplexF64} + msing::Int + sing_psi::Vector{Float64} + sing_q::Vector{Float64} + sing_m::Vector{Int} + sing_n::Vector{Int} + di::Vector{Float64} + alpha::Vector{ComplexF64} +end diff --git a/src/ForceFreeStates/Sing.jl b/src/ForceFreeStates/Sing.jl index efe583b5c..56a548394 100644 --- a/src/ForceFreeStates/Sing.jl +++ b/src/ForceFreeStates/Sing.jl @@ -117,6 +117,42 @@ function sing_lim!(intr::ForceFreeStatesInternal, ctrl::ForceFreeStatesControl, end end +""" + sing_min!(intr::ForceFreeStatesInternal, ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium) + +Set the lower integration bound `intr.psilow`. Port of Fortran RDCON `sing_min` (sing.f:1295-1326): +when `qlow > qmin`, the q < qlow core (including any q ≤ 1 sawtooth/internal-kink surfaces) must be +excluded from the outer-region Galerkin domain — otherwise the Hermite FEM integrates through those +ideal singularities without imposing the ideal constraint, contaminating Δ′ at the innermost kept +surface. A Newton iteration locates ψ where q = qlow; scanning starts from the edge inward for +robustness in reverse-shear cores. When `qlow ≤ qmin` the axis value is kept. +""" +function sing_min!(intr::ForceFreeStatesInternal, ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium) + profiles = equil.profiles + intr.psilow = profiles.xs[1] # default: equilibrium axis-side bound + ctrl.qlow > equil.params.qmin || return intr.psilow + + # Scan from the edge inward for the first node with q < qlow (robust for reverse-shear q). + qy = profiles.q_spline.y + jpsi = 1 + for j in (length(profiles.xs)-1):-1:1 + if qy[j] < ctrl.qlow + jpsi = j + break + end + end + + hint = Ref(jpsi) + intr.psilow = find_zero( + (psi -> profiles.q_spline(psi; hint=hint) - ctrl.qlow, + psi -> profiles.q_deriv(psi; hint=hint)), + profiles.xs[jpsi], Roots.Newton() + ) + @info "sing_min: qlow=$(@sprintf("%.3f", ctrl.qlow)) > qmin=$(@sprintf("%.3f", equil.params.qmin)); " * + "raising psilow from $(@sprintf("%.5f", profiles.xs[1])) to $(@sprintf("%.5f", intr.psilow)) (excludes q dua + +Compute the derivative of the asymptotic series solution with respect to the positive distance +`dpsi = |ψ − ψ_res|`, consistent with `sing_get_ua`. Port of Fortran `sing_get_dua` +(sing.f:839-906 / sing1.f:643-708). Shape `(numpert_total, 2*numpert_total, 2)`. Used by the +outer-region Galerkin solver (`gal_extension`, `sing_matvec`). + +Direction is carried by the `SingAsymptotics` (left vs right vmat built with sig=∓1), exactly as in +`sing_get_ua`, so `dpsi` is always positive and the arithmetic is real (no analytic continuation). +The term-by-term derivative is built via a `power` array tracking each term's total exponent (in +half-powers of `dpsi`: the 2*sing_order offset, the ∓1 shearing on resonant rows, and the ∓2α on +resonant columns), then the same shearing/`pfac` restoration and the chain-rule factor `1/(2·dpsi)` +are applied. The physical d/dψ sign for the left side (ψ = ψ_res − dpsi) is applied by the caller. + +### Arguments + + - `sing_asymp::SingAsymptotics`: Pre-computed asymptotic data (must be left- or right-specific) + - `dpsi::Float64`: Positive distance from singular surface = |ψ − ψ_res| +""" +function sing_get_dua(sing_asymp::SingAsymptotics, dpsi::Float64) + + r1 = sing_asymp.r1 + r2 = sing_asymp.r2 + order = sing_asymp.sing_order + sqrtfac = sqrt(dpsi) + N = size(sing_asymp.vmat, 1) + + # Per-term total exponent (×2, in half-powers of dpsi). See sing.f:881-885. + power = fill(ComplexF64(2 * order), N, 2 * N, 2) + power[r1, :, 1] .-= 1 + power[r1, :, 2] .+= 1 + for i in eachindex(r1) + power[:, r2[2*i-1], :] .-= 2 * sing_asymp.alpha[i] + power[:, r2[2*i], :] .+= 2 * sing_asymp.alpha[i] + end + + # Power series derivative by Horner's method (sing.f:889-893) + dua = sing_asymp.vmat[:, :, :, 2*order+1] .* power + for iorder in (2*order-1):-1:0 + power .-= 1 + dua .= dua .* sqrtfac .+ sing_asymp.vmat[:, :, :, iorder+1] .* power + end + + # Restore shearing and resonant powers, then the chain-rule factor 1/(2·dpsi) (sing.f:897-901) + for i in eachindex(r1) + pfac = dpsi^sing_asymp.alpha[i] + dua[:, r2[2*i-1], :] ./= pfac + dua[:, r2[2*i], :] .*= pfac + dua[r1[i], :, 1] ./= sqrtfac + dua[r1[i], :, 2] .*= sqrtfac + end + dua ./= (2 * dpsi) + + return dua +end + +""" + sing_matvec(ffit::FourFitVars, intr::ForceFreeStatesInternal, psi::Float64, q::Float64, ua, dua) -> matvec + +Apply the Euler-Lagrange residual operator `L u = -(F u' + K u)' + (K† u' + G u)` to the asymptotic +solutions. Port of Fortran `sing_matvec` (sing.f:1045-1107). Returns `matvec`, shape +`(numpert_total, size(ua,2))`. + +Uses the reduced (Schur-complemented) `ffit.kmats` (= K̄) and `ffit.gmats` (= Ḡ) directly, with the +**direct** singular factor `singfac = m - n q` applied to `u' = dua[:,:,1]`. The second component +`ua[:,:,2]` is the canonical momentum `F u' + K u`, so `-dua[:,:,2] = -(F u' + K u)'`. + +### Arguments + + - `psi`: flux coordinate; `q`: safety factor at `psi` (passed in to avoid re-evaluating the spline) + - `ua`, `dua`: asymptotic solution and its ψ-derivative from `sing_get_ua`/`sing_get_dua` +""" +function sing_matvec(ffit::FourFitVars, intr::ForceFreeStatesInternal, psi::Float64, q::Float64, + ua::Array{ComplexF64,3}, dua::Array{ComplexF64,3}) + + N = intr.numpert_total + msol = size(ua, 2) + + # Direct singular factor (m - n q), NOT 1/(m - n q) + sfvec = vec((intr.mlow:intr.mhigh) .- q .* (intr.nlow:intr.nhigh)') + + kmat = Matrix{ComplexF64}(undef, N, N) + gmat = Matrix{ComplexF64}(undef, N, N) + ffit.kmats(vec(kmat), psi; hint=ffit._hint) + ffit.gmats(vec(gmat), psi; hint=ffit._hint) + kdag = adjoint(kmat) + + matvec = zeros(ComplexF64, N, msol) + d1 = Vector{ComplexF64}(undef, N) + for isol in 1:msol + @views d1 .= dua[:, isol, 1] .* sfvec # u' · singfac + @views matvec[:, isol] .= kdag * d1 # K̄† (u' · singfac) + @views matvec[:, isol] .+= gmat * ua[:, isol, 1] # + Ḡ u + @views matvec[:, isol] .-= dua[:, isol, 2] # - (F u' + K u)' + end + return matvec +end + """ sing_get_ca(u::Array{ComplexF64,3}, ua::Array{ComplexF64,3}, intr::ForceFreeStatesInternal) diff --git a/src/GeneralizedPerturbedEquilibrium.jl b/src/GeneralizedPerturbedEquilibrium.jl index ecb4a56a0..1239369f2 100755 --- a/src/GeneralizedPerturbedEquilibrium.jl +++ b/src/GeneralizedPerturbedEquilibrium.jl @@ -45,10 +45,11 @@ import AdaptiveArrayPools: @with_pool # Import ForceFreeStates types and functions needed for main using .ForceFreeStates: ForceFreeStatesInternal, ForceFreeStatesControl, DebugSettings, VacuumData, OdeState, FourFitVars -using .ForceFreeStates: sing_lim!, sing_find! +using .ForceFreeStates: sing_lim!, sing_min!, sing_find! using .ForceFreeStates: mercier_scan!, compute_ballooning_stability! using .ForceFreeStates: make_metric, make_matrix, make_kinetic_matrix using .ForceFreeStates: eulerlagrange_integration, free_run! +using .ForceFreeStates: galerkin_solve, write_galerkin!, GalerkinResult const _BANNER = "="^60 const _SECTION = "-"^40 @@ -216,6 +217,14 @@ function main(args::Vector{String}=String[]; dd::Union{IMASdd.dd,Nothing}=nothin end end + # For the outer-region Galerkin solve, exclude the q < qlow core (incl. any q≤1 sawtooth + # surfaces) by raising psilow to where q = qlow (RDCON sing_min). Without this, the gal FEM + # integrates through the unhandled q≤1 ideal singularity and contaminates Δ′ at the innermost + # kept surface when q0 < qlow. No-op (keeps the axis bound) when qlow ≤ qmin. + if ctrl.gal_flag + sing_min!(intr, ctrl, equil) + end + # Determine poloidal mode numbers if ctrl.delta_mlow < 0 || ctrl.delta_mhigh < 0 error("Negative delta_mlow or delta_mhigh not allowed") @@ -319,8 +328,15 @@ function main(args::Vector{String}=String[]; dd::Union{IMASdd.dd,Nothing}=nothin end end + # Outer-region resistive Δ′ matrix via the singular Galerkin method (RDCON gal_solve) + gal_data = nothing + if ctrl.gal_flag + ctrl.mat_flag || error("gal_flag=true requires mat_flag=true (needs the F/G/K matrix splines)") + gal_data = galerkin_solve(ctrl, equil, ffit, intr; vac_data=ctrl.vac_flag ? vac_data : nothing) + end + if ctrl.write_outputs_to_HDF5 - write_outputs_to_HDF5(ctrl, equil, intr, odet, ctrl.vac_flag ? vac_data : nothing, ffit, git_version) + write_outputs_to_HDF5(ctrl, equil, intr, odet, ctrl.vac_flag ? vac_data : nothing, ffit, git_version, gal_data) @info "Results written to $(ctrl.HDF5_filename)" end @@ -410,7 +426,8 @@ function write_outputs_to_HDF5( odet::OdeState, vac_data::Union{VacuumData,Nothing}, ffit::Union{FourFitVars,Nothing}=nothing, - git_version::String="unknown" + git_version::String="unknown", + gal_data::Union{GalerkinResult,Nothing}=nothing ) h5open(joinpath(intr.dir_path, ctrl.HDF5_filename), "w") do out_h5 @@ -418,6 +435,11 @@ function write_outputs_to_HDF5( # Store git version for reproducibility out_h5["info/git_version"] = git_version + # Outer-region Galerkin Δ′ matrix (RDCON), if computed + if gal_data !== nothing + write_galerkin!(out_h5, gal_data) + end + # Store input parameters for (key, val) in zip(fieldnames(ForceFreeStatesControl), getfield.(Ref(ctrl), fieldnames(ForceFreeStatesControl))) out_h5["input/ForceFreeStates/$key"] = val From 24eea1e21361bc58d53fed4589657493983a883a Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Tue, 9 Jun 2026 15:51:08 -0400 Subject: [PATCH 009/135] ForceFreeStates - NEW - Add galerkin benchmarks --- .../gal_validation/gal_beta_scan.jl | 111 ++++++++++++++++ .../gal_validation/gal_epsilon_scan.jl | 112 ++++++++++++++++ .../gal_validation/gal_scan_plot.jl | 98 ++++++++++++++ .../pfac_study/gal_pfac_scan2d.jl | 53 ++++++++ .../pfac_study/gal_pfac_scan2d_big_plot.jl | 41 ++++++ .../pfac_study/gal_pfac_scan2d_plot.jl | 45 +++++++ .../pfac_study/gal_pfac_worker.jl | 80 ++++++++++++ .../tokamaker_beta/gal_tok_plot.jl | 53 ++++++++ .../tokamaker_beta/gal_tok_worker.jl | 122 ++++++++++++++++++ 9 files changed, 715 insertions(+) create mode 100644 benchmarks/gal_validation/gal_validation/gal_beta_scan.jl create mode 100644 benchmarks/gal_validation/gal_validation/gal_epsilon_scan.jl create mode 100644 benchmarks/gal_validation/gal_validation/gal_scan_plot.jl create mode 100644 benchmarks/gal_validation/gal_validation/pfac_study/gal_pfac_scan2d.jl create mode 100644 benchmarks/gal_validation/gal_validation/pfac_study/gal_pfac_scan2d_big_plot.jl create mode 100644 benchmarks/gal_validation/gal_validation/pfac_study/gal_pfac_scan2d_plot.jl create mode 100644 benchmarks/gal_validation/gal_validation/pfac_study/gal_pfac_worker.jl create mode 100644 benchmarks/gal_validation/gal_validation/tokamaker_beta/gal_tok_plot.jl create mode 100644 benchmarks/gal_validation/gal_validation/tokamaker_beta/gal_tok_worker.jl diff --git a/benchmarks/gal_validation/gal_validation/gal_beta_scan.jl b/benchmarks/gal_validation/gal_validation/gal_beta_scan.jl new file mode 100644 index 000000000..76ce10887 --- /dev/null +++ b/benchmarks/gal_validation/gal_validation/gal_beta_scan.jl @@ -0,0 +1,111 @@ +#!/usr/bin/env julia +# Gal-enabled TJ-analytic beta (pc) scan: at each pc, run the full GPEC pipeline with gal_flag=true +# and capture three Δ′ measures per resonant surface (m=2 q=2, m=3 q=3): +# gal = galerkin/pest3_Delta diagonal (RDCON singular-Galerkin, this port) +# stride = singular/delta_prime_matrix diag (STRIDE BVP, pr178) +# cajump = (ca_r-ca_l)/((2pi)^2 psio) (ca-jump, pr178 primary) +# Reuses examples/LAR_beta_scan/gpec.toml. Writes /tmp/gal_beta_scan_results.h5 + CSV. +using Pkg +Pkg.activate(joinpath(@__DIR__, "..", "Projects", "GPEC_dev", "docs", "GPEC_julia")) +const REPO = "/Users/pharr/Projects/GPEC_dev/docs/GPEC_julia" +Pkg.activate(REPO) +using GeneralizedPerturbedEquilibrium +using HDF5, TOML, Printf + +_warped_grid(x0, x1, N; p=2.0) = [x0 + (x1 - x0) * (1 - (1 - i / (N - 1))^p) for i in 0:N-1] +const PC_FULL = _warped_grid(0.001, 0.1735, 40; p=2.0) +const PC_TEST = [0.001, 0.05, 0.10, 0.15, 0.17] +const BASE = TOML.parsefile(joinpath(REPO, "examples", "LAR_beta_scan", "gpec.toml")) + +function extract(h5) + h5open(h5, "r") do f + out = Dict{String,Any}() + out["q0"] = read(f, "equil/q0"); out["qmax"] = read(f, "equil/qmax") + out["dW_total"] = real(read(f, "vacuum/et")[1]) + psio = read(f, "equil/psio"); denom = (2pi)^2 * psio + mlow = read(f, "info/mlow"); mpert = read(f, "info/mpert"); nlow = read(f, "info/nlow") + # surface m-values (STRIDE side) + m_s = vec(read(f, "singular/m")); n_s = vec(read(f, "singular/n")); msing = length(m_s) + # STRIDE delta_prime_matrix + dpm = haskey(f["singular"], "delta_prime_matrix") ? read(f, "singular/delta_prime_matrix") : nothing + cal = read(f, "singular/ca_left"); car = read(f, "singular/ca_right") + # gal + gm = haskey(f, "galerkin") && haskey(f["galerkin"], "sing_m") ? vec(read(f, "galerkin/sing_m")) : Int[] + gp = haskey(f, "galerkin") && haskey(f["galerkin"], "pest3_Delta") ? read(f, "galerkin/pest3_Delta") : nothing + for (s, m) in enumerate(m_s) + key = "m$(m)" + # ca-jump + ipr = 1 + m - mlow + (n_s[s] - nlow) * mpert + out["cajump_$key"] = (car[ipr, ipr, 2, s] - cal[ipr, ipr, 2, s]) / denom + # stride + out["stride_$key"] = dpm !== nothing && s <= size(dpm, 1) ? dpm[s, s] : NaN + NaN*im + # gal (match by m) + gi = findfirst(==(m), gm) + out["gal_$key"] = (gp !== nothing && gi !== nothing) ? gp[gi, gi] : NaN + NaN*im + end + return out + end +end + +function run_point(pc) + dir = mktempdir(; prefix="gal_beta_") + try + c = deepcopy(BASE) + c["TJ_ANALYTIC_INPUT"]["pc"] = pc + c["ForceFreeStates"]["gal_flag"] = true + c["ForceFreeStates"]["gal_solver"] = "LU" + c["ForceFreeStates"]["HDF5_filename"] = joinpath(dir, "gpec.h5") + open(joinpath(dir, "gpec.toml"), "w") do io; TOML.print(io, c); end + GeneralizedPerturbedEquilibrium.main([dir]) + return extract(joinpath(dir, "gpec.h5")) + catch e + @warn "pc=$pc failed" exception=(e, catch_backtrace()) + return nothing + finally + rm(dir; force=true, recursive=true) + end +end + +pcs = ("--test" in ARGS) ? PC_TEST : PC_FULL +@info "Gal beta scan: $(length(pcs)) points (ε=0.2, qc=1.5, qa=3.6)" +results = Tuple{Float64,Dict{String,Any}}[] +t0 = time() +for (i, pc) in enumerate(pcs) + ti = time() + r = run_point(pc) + el = time() - ti; tot = time() - t0 + if r !== nothing + push!(results, (pc, r)) + g2 = get(r, "gal_m2", NaN); s2 = get(r, "stride_m2", NaN) + g3 = get(r, "gal_m3", NaN); s3 = get(r, "stride_m3", NaN) + @printf("[%2d/%2d] pc=%.5f q=2: gal=%+9.3f stride=%+9.3f | q=3: gal=%+9.3f stride=%+9.3f dW=%+.4f (%.0fs, tot %.0fs)\n", + i, length(pcs), pc, real(g2), real(s2), real(g3), real(s3), get(r, "dW_total", NaN), el, tot) + flush(stdout) + end +end + +# Save +out_h5 = "/tmp/gal_beta_scan_results.h5" +isfile(out_h5) && rm(out_h5) +h5open(out_h5, "w") do f + f["pc"] = [r[1] for r in results] + for key in ("gal_m2", "stride_m2", "cajump_m2", "gal_m3", "stride_m3", "cajump_m3", "dW_total") + vals = [get(r[2], key, NaN+NaN*im) for r in results] + if eltype(vals) <: Complex + f["$(key)_re"] = real.(vals); f["$(key)_im"] = imag.(vals) + else + f[key] = Float64.(vals) + end + end +end +open("/tmp/gal_beta_scan_results.csv", "w") do io + println(io, "pc,gal_m2,stride_m2,cajump_m2,gal_m3,stride_m3,cajump_m3,dW_total") + for (pc, r) in results + @printf(io, "%.6f,%.6f,%.6f,%.6f,%.6f,%.6f,%.6f,%.6f\n", pc, + real(get(r,"gal_m2",NaN)), real(get(r,"stride_m2",NaN)), real(get(r,"cajump_m2",NaN)), + real(get(r,"gal_m3",NaN)), real(get(r,"stride_m3",NaN)), real(get(r,"cajump_m3",NaN)), + get(r,"dW_total",NaN)) + end +end +@info "Saved /tmp/gal_beta_scan_results.h5 and .csv ($(length(results)) points)" +println("DONE") diff --git a/benchmarks/gal_validation/gal_validation/gal_epsilon_scan.jl b/benchmarks/gal_validation/gal_validation/gal_epsilon_scan.jl new file mode 100644 index 000000000..e701bee39 --- /dev/null +++ b/benchmarks/gal_validation/gal_validation/gal_epsilon_scan.jl @@ -0,0 +1,112 @@ +#!/usr/bin/env julia +# Gal-enabled TJ-analytic beta (pc) scan: at each pc, run the full GPEC pipeline with gal_flag=true +# and capture three Δ′ measures per resonant surface (m=2 q=2, m=3 q=3): +# gal = galerkin/pest3_Delta diagonal (RDCON singular-Galerkin, this port) +# stride = singular/delta_prime_matrix diag (STRIDE BVP, pr178) +# cajump = (ca_r-ca_l)/((2pi)^2 psio) (ca-jump, pr178 primary) +# Reuses examples/LAR_beta_scan/gpec.toml. Writes /tmp/gal_epsilon_scan_results.h5 + CSV. +using Pkg +Pkg.activate(joinpath(@__DIR__, "..", "Projects", "GPEC_dev", "docs", "GPEC_julia")) +const REPO = "/Users/pharr/Projects/GPEC_dev/docs/GPEC_julia" +Pkg.activate(REPO) +using GeneralizedPerturbedEquilibrium +using HDF5, TOML, Printf + +_warped_grid(x0, x1, N; p=2.0) = [x0 + (x1 - x0) * (1 - (1 - i / (N - 1))^p) for i in 0:N-1] +const PC_FULL = _warped_grid(0.125, 0.660, 56; p=2.0) +const PC_TEST = [0.2, 0.4, 0.55] +const BASE = TOML.parsefile(joinpath(REPO, "examples", "LAR_epsilon_scan", "gpec.toml")) + +function extract(h5) + h5open(h5, "r") do f + out = Dict{String,Any}() + out["q0"] = read(f, "equil/q0"); out["qmax"] = read(f, "equil/qmax") + out["dW_total"] = real(read(f, "vacuum/et")[1]) + psio = read(f, "equil/psio"); denom = (2pi)^2 * psio + mlow = read(f, "info/mlow"); mpert = read(f, "info/mpert"); nlow = read(f, "info/nlow") + # surface m-values (STRIDE side) + m_s = vec(read(f, "singular/m")); n_s = vec(read(f, "singular/n")); msing = length(m_s) + # STRIDE delta_prime_matrix + dpm = haskey(f["singular"], "delta_prime_matrix") ? read(f, "singular/delta_prime_matrix") : nothing + cal = read(f, "singular/ca_left"); car = read(f, "singular/ca_right") + # gal + gm = haskey(f, "galerkin") && haskey(f["galerkin"], "sing_m") ? vec(read(f, "galerkin/sing_m")) : Int[] + gp = haskey(f, "galerkin") && haskey(f["galerkin"], "pest3_Delta") ? read(f, "galerkin/pest3_Delta") : nothing + for (s, m) in enumerate(m_s) + key = "m$(m)" + # ca-jump + ipr = 1 + m - mlow + (n_s[s] - nlow) * mpert + out["cajump_$key"] = (car[ipr, ipr, 2, s] - cal[ipr, ipr, 2, s]) / denom + # stride + out["stride_$key"] = dpm !== nothing && s <= size(dpm, 1) ? dpm[s, s] : NaN + NaN*im + # gal (match by m) + gi = findfirst(==(m), gm) + out["gal_$key"] = (gp !== nothing && gi !== nothing) ? gp[gi, gi] : NaN + NaN*im + end + return out + end +end + +function run_point(pc) + dir = mktempdir(; prefix="gal_eps_") + try + c = deepcopy(BASE) + c["TJ_ANALYTIC_INPUT"]["lar_r0"] = c["TJ_ANALYTIC_INPUT"]["lar_a"] / pc + c["Equilibrium"]["eq_type"] = "tj_analytic_direct" + c["ForceFreeStates"]["gal_flag"] = true + c["ForceFreeStates"]["gal_solver"] = "LU" + c["ForceFreeStates"]["HDF5_filename"] = joinpath(dir, "gpec.h5") + open(joinpath(dir, "gpec.toml"), "w") do io; TOML.print(io, c); end + GeneralizedPerturbedEquilibrium.main([dir]) + return extract(joinpath(dir, "gpec.h5")) + catch e + @warn "pc=$pc failed" exception=(e, catch_backtrace()) + return nothing + finally + rm(dir; force=true, recursive=true) + end +end + +pcs = ("--test" in ARGS) ? PC_TEST : PC_FULL +@info "Gal epsilon scan: $(length(pcs)) points (ε=0.2, qc=1.5, qa=3.6)" +results = Tuple{Float64,Dict{String,Any}}[] +t0 = time() +for (i, pc) in enumerate(pcs) + ti = time() + r = run_point(pc) + el = time() - ti; tot = time() - t0 + if r !== nothing + push!(results, (pc, r)) + g2 = get(r, "gal_m2", NaN); s2 = get(r, "stride_m2", NaN) + g3 = get(r, "gal_m3", NaN); s3 = get(r, "stride_m3", NaN) + @printf("[%2d/%2d] pc=%.5f q=2: gal=%+9.3f stride=%+9.3f | q=3: gal=%+9.3f stride=%+9.3f dW=%+.4f (%.0fs, tot %.0fs)\n", + i, length(pcs), pc, real(g2), real(s2), real(g3), real(s3), get(r, "dW_total", NaN), el, tot) + flush(stdout) + end +end + +# Save +out_h5 = "/tmp/gal_epsilon_scan_results.h5" +isfile(out_h5) && rm(out_h5) +h5open(out_h5, "w") do f + f["pc"] = [r[1] for r in results] + for key in ("gal_m2", "stride_m2", "cajump_m2", "gal_m3", "stride_m3", "cajump_m3", "dW_total") + vals = [get(r[2], key, NaN+NaN*im) for r in results] + if eltype(vals) <: Complex + f["$(key)_re"] = real.(vals); f["$(key)_im"] = imag.(vals) + else + f[key] = Float64.(vals) + end + end +end +open("/tmp/gal_epsilon_scan_results.csv", "w") do io + println(io, "pc,gal_m2,stride_m2,cajump_m2,gal_m3,stride_m3,cajump_m3,dW_total") + for (pc, r) in results + @printf(io, "%.6f,%.6f,%.6f,%.6f,%.6f,%.6f,%.6f,%.6f\n", pc, + real(get(r,"gal_m2",NaN)), real(get(r,"stride_m2",NaN)), real(get(r,"cajump_m2",NaN)), + real(get(r,"gal_m3",NaN)), real(get(r,"stride_m3",NaN)), real(get(r,"cajump_m3",NaN)), + get(r,"dW_total",NaN)) + end +end +@info "Saved /tmp/gal_epsilon_scan_results.h5 and .csv ($(length(results)) points)" +println("DONE") diff --git a/benchmarks/gal_validation/gal_validation/gal_scan_plot.jl b/benchmarks/gal_validation/gal_validation/gal_scan_plot.jl new file mode 100644 index 000000000..2e7cf3f15 --- /dev/null +++ b/benchmarks/gal_validation/gal_validation/gal_scan_plot.jl @@ -0,0 +1,98 @@ +# Plot gal vs STRIDE Δ′ across the TJ-analytic beta and epsilon scans. +# Reads /tmp/gal_beta_scan_results.csv and /tmp/gal_epsilon_scan_results.csv. +using Pkg +Pkg.activate("/Users/pharr/Projects/GPEC_dev/docs/GPEC_julia") +using Plots, DelimitedFiles, Printf +gr() + +_median(v) = (w = sort(v); n = length(w); iseven(n) ? (w[n÷2] + w[n÷2+1]) / 2 : w[(n+1)÷2]) + +function loadcsv(path) + isfile(path) || return nothing + data, hdr = readdlm(path, ','; header=true) + return Dict(strip(h) => Float64.(data[:, i]) for (i, h) in enumerate(vec(hdr))) +end + +# Linear-extrapolate δW_total → 0 from the last k points → marginal-stability estimate. +function marginal_point(cols, xname; k=6) + x = cols[xname]; dw = cols["dW_total"] + ord = sortperm(x); x = x[ord]; dw = dw[ord] + k = min(k, length(x)) + xt = x[end-k+1:end]; yt = dw[end-k+1:end] + coef = hcat(xt, ones(k)) \ yt + return coef[1] == 0 ? NaN : -coef[2] / coef[1] +end + +# Δ′ vs scan parameter; gal (solid+markers) vs STRIDE (dashed). Log y if all-positive. +function panel(cols, xname, xlabel, title, xmarg) + x = cols[xname] + # log-y Δ′; non-positive values (q=3 crosses zero at low ε) are masked to NaN → shown as gaps. + poslog(v) = [y > 0 ? y : NaN for y in v] + p = plot(; xlabel=xlabel, ylabel="Δ′ (PEST-3)", title=title, legend=:topleft, + yscale=:log10, + left_margin=12Plots.mm, bottom_margin=6Plots.mm, right_margin=4Plots.mm) + for (lbl, col, c) in (("q=2", "m2", :dodgerblue), ("q=3", "m3", :crimson)) + plot!(p, x, poslog(cols["gal_$col"]); lw=2, color=c, marker=:circle, ms=3, label="gal $lbl") + plot!(p, x, poslog(cols["stride_$col"]); lw=2, ls=:dash, color=c, label="STRIDE $lbl") + end + if isfinite(xmarg) + # extend x-range so the asymptote line (just past the last point) is visible + plot!(p; xlims=(minimum(x), max(maximum(x), xmarg) * 1.002)) + vline!(p, [xmarg]; color=:black, ls=:dot, lw=2, + label=@sprintf("marginal (δW=0): %s≈%.4f", xname == "pc" ? "pₐ" : "ε", xmarg)) + end + return p +end + +# δW_total vs scan parameter, with a linear extrapolation of the last points to δW=0 +# (the ideal marginal-stability / kink-pole estimate). +function dwpanel(cols, xname, xlabel) + x = cols[xname]; dw = cols["dW_total"] + ord = sortperm(x); x = x[ord]; dw = dw[ord] + p = plot(; xlabel=xlabel, ylabel="δW_total (Re et[1])", legend=:topright, + left_margin=12Plots.mm, bottom_margin=6Plots.mm, right_margin=4Plots.mm) + plot!(p, x, dw; lw=2, color=:black, marker=:circle, ms=3, label="δW_total") + hline!(p, [0.0]; color=:gray, ls=:dot, label="marginal (δW=0)") + x0 = marginal_point(cols, xname) + if isfinite(x0) + k = min(6, length(x)); xt = x[end-k+1:end] + coef = hcat(xt, ones(length(xt))) \ dw[end-k+1:end] + xext = range(xt[1], x0; length=20) + plot!(p, xext, coef[1] .* xext .+ coef[2]; lw=1.5, ls=:dash, color=:red, + label=@sprintf("extrap: δW=0 at %s≈%.4f", xname == "pc" ? "pₐ" : "ε", x0)) + scatter!(p, [x0], [0.0]; color=:red, ms=6, marker=:star5, label="") + @printf(" marginal-point estimate (%s): δW=0 at %.5f\n", xname, x0) + end + return p +end + +# Relative |gal-STRIDE|/|STRIDE| in %. +function relpanel(cols, xname, xlabel) + x = cols[xname] + p = plot(; xlabel=xlabel, ylabel="|gal−STRIDE|/|STRIDE| (%)", yscale=:log10, legend=:topright, + left_margin=12Plots.mm, bottom_margin=6Plots.mm, right_margin=4Plots.mm) + for (lbl, col, c) in (("q=2", "m2", :dodgerblue), ("q=3", "m3", :crimson)) + rel = 100 .* abs.(cols["gal_$col"] .- cols["stride_$col"]) ./ max.(abs.(cols["stride_$col"]), 1e-12) + rel = max.(rel, 1e-4) + plot!(p, x, rel; lw=2, color=c, marker=:circle, ms=3, label=lbl) + end + return p +end + +for (name, path, xn, xl, ttl) in ( + ("beta", "/tmp/gal_beta_scan_results.csv", "pc", "pₐ (on-axis pressure factor)", "TJ-analytic β scan (ε=0.2, qc=1.5, qa=3.6)"), + ("eps", "/tmp/gal_epsilon_scan_results.csv", "pc", "ε = a/R₀", "TJ-analytic ε scan (pc=0.001, qc=1.5, qa=3.6)")) + cols = loadcsv(path) + cols === nothing && continue + xmarg = marginal_point(cols, xn) + fig = plot(panel(cols, xn, xl, ttl, xmarg), dwpanel(cols, xn, xl), relpanel(cols, xn, xl); layout=(3, 1), size=(820, 1320)) + out = "/tmp/gal_$(name)_comparison.png" + savefig(fig, out) + println("Saved figure: ", out) + println("=== $name: gal-vs-STRIDE relative diff (%) ===") + for col in ("m2", "m3") + rel = 100 .* abs.(cols["gal_$col"] .- cols["stride_$col"]) ./ max.(abs.(cols["stride_$col"]), 1e-12) + @printf(" %s: median=%.3f%% max=%.2f%% (n=%d)\n", col, _median(rel), maximum(rel), length(rel)) + end +end +println("DONE") diff --git a/benchmarks/gal_validation/gal_validation/pfac_study/gal_pfac_scan2d.jl b/benchmarks/gal_validation/gal_validation/pfac_study/gal_pfac_scan2d.jl new file mode 100644 index 000000000..a4a9a39f2 --- /dev/null +++ b/benchmarks/gal_validation/gal_validation/pfac_study/gal_pfac_scan2d.jl @@ -0,0 +1,53 @@ +# 2D scan: gal-vs-STRIDE q=3 tracking over (pc, pfac). STRIDE is pfac-independent +# (recorded per run as a consistency check). Output /tmp/gal_pfac_scan2d.csv. +using GeneralizedPerturbedEquilibrium +using HDF5, TOML, Printf +const REPO = "/Users/pharr/Projects/GPEC_dev/docs/GPEC_julia" +const BASE = TOML.parsefile(joinpath(REPO, "examples", "LAR_beta_scan", "gpec.toml")) +const PCS = [0.005, 0.010, 0.020, 0.030, 0.040, 0.050, 0.060, 0.070, 0.085, 0.100] +const PFACS = [5e-4, 1e-3, 3e-3, 1e-2, 3e-2, 1e-1] + +function extract(h5) + h5open(h5, "r") do f + mlow = read(f, "info/mlow"); mpert = read(f, "info/mpert"); nlow = read(f, "info/nlow") + m_s = vec(read(f, "singular/m")) + dpm = read(f, "singular/delta_prime_matrix") + gm = vec(read(f, "galerkin/sing_m")); gp = read(f, "galerkin/pest3_Delta") + g3 = NaN; s3 = NaN; g2 = NaN; s2 = NaN + for (s, m) in enumerate(m_s) + gi = findfirst(==(m), gm) + if m == 2; g2 = real(gp[gi, gi]); s2 = real(dpm[s, s]); end + if m == 3; g3 = real(gp[gi, gi]); s3 = real(dpm[s, s]); end + end + return (g2, s2, g3, s3) + end +end + +io = open("/tmp/gal_pfac_scan2d.csv", "w") +println(io, "pc,pfac,gal_q2,stride_q2,gal_q3,stride_q3"); flush(io) +t0 = time(); n = 0; ntot = length(PCS) * length(PFACS) +for pc in PCS, pfac in PFACS + global n += 1 + dir = mktempdir(; prefix="gal2d_") + c = deepcopy(BASE) + c["TJ_ANALYTIC_INPUT"]["pc"] = pc + c["ForceFreeStates"]["gal_flag"] = true + c["ForceFreeStates"]["gal_solver"] = "LU" + c["ForceFreeStates"]["gal_pfac"] = pfac + c["ForceFreeStates"]["HDF5_filename"] = joinpath(dir, "gpec.h5") + open(joinpath(dir, "gpec.toml"), "w") do f; TOML.print(f, c); end + try + GeneralizedPerturbedEquilibrium.main([dir]) + g2, s2, g3, s3 = extract(joinpath(dir, "gpec.h5")) + @printf(io, "%.6f,%.6e,%.6f,%.6f,%.6f,%.6f\n", pc, pfac, g2, s2, g3, s3); flush(io) + @printf("[%3d/%3d] pc=%.4f pfac=%.0e q3: gal=%+8.3f stride=%+8.3f relerr=%5.1f%% tot %.0fs\n", + n, ntot, pc, pfac, g3, s3, 100abs(g3 - s3) / abs(s3), time() - t0); flush(stdout) + catch e + @warn "pc=$pc pfac=$pfac failed" exception=(e, catch_backtrace()) + finally + rm(dir; force=true, recursive=true) + end +end +close(io) +println("Saved /tmp/gal_pfac_scan2d.csv") +println("DONE") diff --git a/benchmarks/gal_validation/gal_validation/pfac_study/gal_pfac_scan2d_big_plot.jl b/benchmarks/gal_validation/gal_validation/pfac_study/gal_pfac_scan2d_big_plot.jl new file mode 100644 index 000000000..1ec4b7f72 --- /dev/null +++ b/benchmarks/gal_validation/gal_validation/pfac_study/gal_pfac_scan2d_big_plot.jl @@ -0,0 +1,41 @@ +# Plot the fine (50 pc x 30 pfac) gal-vs-STRIDE q=3 tracking scan: heatmap + per-pfac curves. +using Pkg; Pkg.activate("/Users/pharr/Projects/GPEC_dev/docs/GPEC_julia") +using Plots, DelimitedFiles, Printf; gr() + +data, hdr = readdlm("/tmp/gal_pfac_scan2d_big.csv", ','; header=true) +col(name) = data[:, findfirst(==(name), strip.(vec(hdr)))] +pc = col("pc"); pfac = col("pfac"); gq3 = col("gal_q3"); sq3 = col("stride_q3") +relerr = 100 .* abs.(gq3 .- sq3) ./ max.(abs.(sq3), 1e-12) + +pcs = sort(unique(round.(pc; digits=6))); pfacs = sort(unique(pfac)) +Z = fill(NaN, length(pfacs), length(pcs)) +for k in eachindex(pc) + i = findfirst(≈(pfac[k]), pfacs); j = findfirst(≈(round(pc[k]; digits=6)), pcs) + (i === nothing || j === nothing) && continue + Z[i, j] = relerr[k] +end +Zc = clamp.(Z, 0.01, 100) + +p1 = heatmap(pcs, pfacs, log10.(Zc); yscale=:log10, xlabel="pₐ", ylabel="packing pfac", + title="gal q=3 tracking vs STRIDE: log₁₀ |gal−STRIDE|/STRIDE (%) [50×30]", + colorbar_title="log₁₀(% err)", c=:viridis, + left_margin=12Plots.mm, bottom_margin=6Plots.mm, right_margin=10Plots.mm) + +# per-pfac error vs pc, subset of pfacs for legibility +p2 = plot(; xlabel="pₐ", ylabel="|gal−STRIDE|/STRIDE (%)", yscale=:log10, legend=:topright, + left_margin=12Plots.mm, bottom_margin=6Plots.mm, right_margin=4Plots.mm, + title="q=3 tracking error per packing ratio") +sel = [findmin(abs.(log10.(pfacs) .- t))[2] for t in (-4, -3, -2, -1.5, -1, 0)] +for i in unique(sel) + plot!(p2, pcs, [isfinite(z) ? max(z, 1e-3) : NaN for z in Z[i, :]]; lw=2, label=@sprintf("pfac=%.1e", pfacs[i])) +end +fig = plot(p1, p2; layout=(2, 1), size=(1000, 1050)) +savefig(fig, "/tmp/gal_pfac_scan2d_big.png") +println("Saved /tmp/gal_pfac_scan2d_big.png") + +med(v) = (w = sort(filter(isfinite, v)); isempty(w) ? NaN : (n = length(w); iseven(n) ? (w[n÷2]+w[n÷2+1])/2 : w[(n+1)÷2])) +println("\npfac median% max%") +for (i, pf) in enumerate(pfacs) + @printf("%.2e %7.3f %7.1f\n", pf, med(Z[i, :]), maximum(filter(isfinite, Z[i, :]); init=NaN)) +end +println("DONE") diff --git a/benchmarks/gal_validation/gal_validation/pfac_study/gal_pfac_scan2d_plot.jl b/benchmarks/gal_validation/gal_validation/pfac_study/gal_pfac_scan2d_plot.jl new file mode 100644 index 000000000..9f4f2e67b --- /dev/null +++ b/benchmarks/gal_validation/gal_validation/pfac_study/gal_pfac_scan2d_plot.jl @@ -0,0 +1,45 @@ +# Plot the (pc x pfac) gal-vs-STRIDE q=3 tracking scan: heatmap + per-pfac curves. +using Pkg; Pkg.activate("/Users/pharr/Projects/GPEC_dev/docs/GPEC_julia") +using Plots, DelimitedFiles, Printf; gr() + +data, hdr = readdlm("/tmp/gal_pfac_scan2d.csv", ','; header=true) +col(name) = data[:, findfirst(==(name), strip.(vec(hdr)))] +pc = col("pc"); pfac = col("pfac"); gq3 = col("gal_q3"); sq3 = col("stride_q3") +relerr = 100 .* abs.(gq3 .- sq3) ./ abs.(sq3) + +pcs = sort(unique(pc)); pfacs = sort(unique(pfac)) +# Build relerr grid Z[i_pfac, j_pc] +Z = fill(NaN, length(pfacs), length(pcs)) +for k in eachindex(pc) + i = findfirst(≈(pfac[k]), pfacs); j = findfirst(≈(pc[k]), pcs) + Z[i, j] = relerr[k] +end +Zc = clamp.(Z, 0.01, 100) # for log color + +# Panel 1: heatmap, log color +p1 = heatmap(pcs, pfacs, log10.(Zc); + yscale=:log10, xlabel="pₐ", ylabel="packing pfac", + title="gal q=3 tracking error vs STRIDE: log₁₀ |gal−STRIDE|/STRIDE (%)", + colorbar_title="log₁₀(% err)", c=:viridis, + left_margin=12Plots.mm, bottom_margin=6Plots.mm, right_margin=8Plots.mm) + +# Panel 2: per-pfac tracking curves +p2 = plot(; xlabel="pₐ", ylabel="|gal−STRIDE|/STRIDE (%)", yscale=:log10, legend=:topright, + left_margin=12Plots.mm, bottom_margin=6Plots.mm, right_margin=4Plots.mm, + title="q=3 tracking error per packing ratio") +for (i, pf) in enumerate(pfacs) + plot!(p2, pcs, max.(Z[i, :], 1e-3); lw=2, marker=:circle, ms=3, label=@sprintf("pfac=%.0e", pf)) +end + +fig = plot(p1, p2; layout=(2, 1), size=(900, 1000)) +savefig(fig, "/tmp/gal_pfac_scan2d.png") +println("Saved /tmp/gal_pfac_scan2d.png") + +# Per-pfac median/max summary +println("\npfac median% max% (q=3 over the pc grid)") +med(v)=(w=sort(filter(isfinite,v));isempty(w) ? NaN : (n=length(w); iseven(n) ? (w[n÷2]+w[n÷2+1])/2 : w[(n+1)÷2])) +for (i, pf) in enumerate(pfacs) + r = Z[i, :] + @printf("%.0e %7.2f %6.1f\n", pf, med(r), maximum(filter(isfinite, r))) +end +println("DONE") diff --git a/benchmarks/gal_validation/gal_validation/pfac_study/gal_pfac_worker.jl b/benchmarks/gal_validation/gal_validation/pfac_study/gal_pfac_worker.jl new file mode 100644 index 000000000..84197210f --- /dev/null +++ b/benchmarks/gal_validation/gal_validation/pfac_study/gal_pfac_worker.jl @@ -0,0 +1,80 @@ +# Worker: for ONE pc, run the full pipeline once, then loop galerkin_solve over MANY pfacs. +# Args: pc, out_csv_path. Appends rows "pc,pfac,gal_q2,stride_q2,gal_q3,stride_q3". +using GeneralizedPerturbedEquilibrium +const GPE = GeneralizedPerturbedEquilibrium +const FFS = GPE.ForceFreeStates +const EQ = GPE.Equilibrium +using TOML, Printf, LinearAlgebra +import FastInterpolations: cubic_interp, Series, ExtendExtrap +LinearAlgebra.BLAS.set_num_threads(1) # avoid oversubscription across parallel workers + +const REPO = "/Users/pharr/Projects/GPEC_dev/docs/GPEC_julia" +const PFACS = exp10.(range(-4, 0; length=30)) # 30 packing ratios, 1e-4 .. 1e0 + +const PCLIST = parse.(Float64, split(ARGS[1], ',')) # comma-separated pc values +const OUTCSV = ARGS[2] + +function run_pc(pc) +inputs = TOML.parsefile(joinpath(REPO, "examples", "LAR_beta_scan", "gpec.toml")) +inputs["TJ_ANALYTIC_INPUT"]["pc"] = pc +ctrl = FFS.ForceFreeStatesControl(; (Symbol(k) => v for (k, v) in inputs["ForceFreeStates"])...) +ctrl.gal_flag = true; ctrl.gal_solver = "LU"; ctrl.verbose = false +dir = mktempdir(; prefix="galw_"); intr = FFS.ForceFreeStatesInternal(; dir_path=dir) +eq_config = EQ.EquilibriumConfig(inputs["Equilibrium"], dir) +tj = EQ.TJAnalyticConfig(; (Symbol(k) => v for (k, v) in inputs["TJ_ANALYTIC_INPUT"])...) +equil = EQ.setup_equilibrium(eq_config, tj) + +# --- replicate main() pipeline (mirrors GeneralizedPerturbedEquilibrium.jl) --- +FFS.sing_lim!(intr, ctrl, equil) +xs = equil.profiles.xs; ls = zeros(length(xs), 5); FFS.mercier_scan!(ls, equil) +intr.locstab = cubic_interp(xs, Series(ls); extrap=ExtendExtrap()) +intr.nlow = ctrl.nn_low; intr.nhigh = ctrl.nn_high; intr.npert = 1 +FFS.sing_find!(intr, equil) +intr.mlow = trunc(Int, min(intr.nlow * equil.params.qmin, 0)) - 4 - ctrl.delta_mlow +intr.mhigh = trunc(Int, intr.nhigh * equil.params.qmax) + ctrl.delta_mhigh +intr.mpert = intr.mhigh - intr.mlow + 1 +intr.mband = min(max(intr.mpert - 1 - ctrl.delta_mband, 0), intr.mpert - 1) +intr.numpert_total = intr.mpert * intr.npert +metric = FFS.make_metric(equil; mband=intr.mband, fft_flag=ctrl.fft_flag) +ffit = FFS.make_matrix(equil, intr, metric) +odet, fm_propagators, fm_chunks, fm_S_left = FFS.eulerlagrange_integration(ctrl, equil, ffit, intr) +vac_data = FFS.free_run!(odet, ctrl, equil, ffit, intr) +if intr.msing > 0 && fm_propagators !== nothing + FFS.compute_delta_prime_matrix!(intr, fm_propagators, fm_chunks; + wv=vac_data.wv, psio=equil.psio, debug=false, + S_at_surface_left=fm_S_left, ctrl=ctrl, equil=equil, ffit=ffit) +end +dpm = intr.delta_prime_matrix +m_s = [s.m[1] for s in intr.sing if s.psifac < intr.psilim] +sidx2 = findfirst(==(2), m_s); sidx3 = findfirst(==(3), m_s) +s2 = sidx2 === nothing ? NaN : real(dpm[sidx2, sidx2]) +s3 = sidx3 === nothing ? NaN : real(dpm[sidx3, sidx3]) + +open(OUTCSV, "a") do io + for pfac in PFACS + ctrl.gal_pfac = pfac + g2 = NaN; g3 = NaN + try + res = FFS.galerkin_solve(ctrl, equil, ffit, intr; vac_data=vac_data) + gm = res.sing_m + gi2 = findfirst(==(2), gm); gi3 = findfirst(==(3), gm) + g2 = gi2 === nothing ? NaN : real(res.Deltap[gi2, gi2]) + g3 = gi3 === nothing ? NaN : real(res.Deltap[gi3, gi3]) + catch e + @warn "gal failed pc=$pc pfac=$pfac" exception=e + end + @printf(io, "%.6f,%.6e,%.6f,%.6f,%.6f,%.6f\n", pc, pfac, g2, s2, g3, s3); flush(io) + end +end +rm(dir; force=true, recursive=true) +return nothing +end + +for pc in PCLIST + try + run_pc(pc); println("done pc=$pc"); flush(stdout) + catch e + @warn "pc=$pc failed" exception=(e, catch_backtrace()) + end +end +println("WORKER DONE") diff --git a/benchmarks/gal_validation/gal_validation/tokamaker_beta/gal_tok_plot.jl b/benchmarks/gal_validation/gal_validation/tokamaker_beta/gal_tok_plot.jl new file mode 100644 index 000000000..9e2d657c1 --- /dev/null +++ b/benchmarks/gal_validation/gal_validation/tokamaker_beta/gal_tok_plot.jl @@ -0,0 +1,53 @@ +# Plot the TokaMaker beta-scan pfac convergence study. Data: /tmp/gal_tok_scan.csv +# (beta,pfac,m,q,gal,stride). Produces: per-pfac error summary, a heatmap (beta x pfac) +# of median-over-surfaces tracking error, and per-q tracking-vs-beta at the chosen pfac. +using Pkg; Pkg.activate("/Users/pharr/Projects/GPEC_dev/docs/GPEC_julia") +using Plots, DelimitedFiles, Printf; gr() + +d, h = readdlm("/tmp/gal_tok_scan.csv", ','; header=true) +col(n) = d[:, findfirst(==(n), strip.(vec(h)))] +beta = col("beta"); pfac = col("pfac"); m = Int.(col("m")); q = col("q"); g = col("gal"); s = col("stride") +# Exclude q=1: the internal-kink surface where the outer-region Δ′ construction does not apply +# (gal and STRIDE diverge structurally, pfac-independent). Keep the tearing surfaces q≥2. +keep = round.(q; digits=0) .>= 2 +beta = beta[keep]; pfac = pfac[keep]; m = m[keep]; q = q[keep]; g = g[keep]; s = s[keep] +finite = isfinite.(g) .& isfinite.(s) .& (abs.(s) .> 1e-9) +relerr = fill(NaN, length(g)) +relerr[finite] = 100 .* abs.(g[finite] .- s[finite]) ./ abs.(s[finite]) + +betas = sort(unique(beta)); pfacs = sort(unique(pfac)) +med(v) = (w = sort(filter(isfinite, v)); isempty(w) ? NaN : (n = length(w); iseven(n) ? (w[n÷2]+w[n÷2+1])/2 : w[(n+1)÷2])) +qq(v, p) = (w = sort(filter(isfinite, v)); isempty(w) ? NaN : w[clamp(ceil(Int, p*length(w)), 1, length(w))]) + +# --- per-pfac summary over ALL (beta, surface) --- +println("pfac median% p90% finite-max% n") +for pf in pfacs + r = relerr[pfac .≈ pf] + @printf("%.2e %7.3f %7.2f %9.1f %d\n", pf, med(r), qq(r, 0.9), maximum(filter(isfinite, r); init=NaN), count(isfinite, r)) +end + +# --- heatmap: median over surfaces, per (beta, pfac) --- +Z = fill(NaN, length(pfacs), length(betas)) +for (i, pf) in enumerate(pfacs), (j, b) in enumerate(betas) + Z[i, j] = med(relerr[(pfac .≈ pf) .& (beta .≈ b)]) +end +Zc = clamp.(Z, 0.01, 100) +p1 = heatmap(betas, pfacs, log10.(Zc); yscale=:log10, xlabel="β_N", ylabel="packing pfac", + title="TokaMaker β scan: gal tracking vs STRIDE (median over q≥2 surfaces)\nlog₁₀ |gal−STRIDE|/STRIDE (%)", + colorbar_title="log₁₀(% err)", c=:viridis, + left_margin=12Plots.mm, bottom_margin=6Plots.mm, right_margin=10Plots.mm) + +# --- per-pfac error curves vs beta (median over surfaces) --- +p2 = plot(; xlabel="β_N", ylabel="median |gal−STRIDE|/STRIDE (%)", yscale=:log10, legend=:topright, + left_margin=12Plots.mm, bottom_margin=6Plots.mm, right_margin=4Plots.mm, + title="median tracking error vs β per packing ratio") +sel = [findmin(abs.(log10.(pfacs) .- t))[2] for t in (-4, -3, -2, -1.5, -1, 0)] +for i in unique(sel) + yv = [max(Z[i, j], 1e-3) for j in eachindex(betas)] + plot!(p2, betas, yv; lw=2, marker=:circle, ms=2, label=@sprintf("pfac=%.1e", pfacs[i])) +end +fig = plot(p1, p2; layout=(2, 1), size=(1000, 1050)) +savefig(fig, "/tmp/gal_tok_scan.png") +println("Saved /tmp/gal_tok_scan.png") +println("surfaces present (q): ", sort(unique(round.(q; digits=1)))) +println("DONE") diff --git a/benchmarks/gal_validation/gal_validation/tokamaker_beta/gal_tok_worker.jl b/benchmarks/gal_validation/gal_validation/tokamaker_beta/gal_tok_worker.jl new file mode 100644 index 000000000..01d75b276 --- /dev/null +++ b/benchmarks/gal_validation/gal_validation/tokamaker_beta/gal_tok_worker.jl @@ -0,0 +1,122 @@ +# Worker: for ONE TokaMaker geqdsk, run the full GPEC pipeline once, then loop galerkin_solve +# over many pfacs. Records EVERY rational surface. Args: geqdsk_path, beta, out_csv. +# Appends rows: beta,pfac,m,q,gal,stride +using GeneralizedPerturbedEquilibrium +const GPE = GeneralizedPerturbedEquilibrium +const FFS = GPE.ForceFreeStates +const EQ = GPE.Equilibrium +using TOML, Printf, LinearAlgebra +import FastInterpolations: cubic_interp, Series, ExtendExtrap +LinearAlgebra.BLAS.set_num_threads(1) + +const PFACS = exp10.(range(-4, 0; length=30)) +const GEQDSK = ARGS[1] +const BETA = parse(Float64, ARGS[2]) +const OUTCSV = ARGS[3] + +# DIIID-like stability settings (efit, free-boundary nowall), no PE/forcing. +function base_inputs(dir) + Dict( + "Equilibrium" => Dict("eq_filename" => basename(GEQDSK), "eq_type" => "efit", + "jac_type" => "hamada", "power_bp" => 0, "power_b" => 0, "power_r" => 0, + "grid_type" => "log_asymptotic", "psilow" => 1e-4, "psihigh" => 0.999, + "mpsi" => 0, "psi_accuracy" => 0.001, "mtheta" => 256, "newq0" => 0, + "etol" => 1e-10, "force_termination" => false), + "Wall" => Dict("shape" => "nowall", "a" => 0.2415), + "ForceFreeStates" => Dict( + "bal_flag" => false, "mat_flag" => true, "ode_flag" => true, + "vac_flag" => true, "mer_flag" => true, + "qlow" => 1.02, "qhigh" => 1e3, "sing_start" => 0, + "nn_low" => 1, "nn_high" => 1, "delta_mlow" => 8, "delta_mhigh" => 8, "delta_mband" => 0, + "mthvac" => 512, "thmax0" => 1, "kinetic_factor" => 0.0, + "eulerlagrange_tolerance" => 1e-10, "singfac_min" => 1e-4, "ucrit" => 1e4, + "use_parallel" => true, "parallel_threads" => 1, "populate_dense_xi" => false, + "truncate_at_dW_peak" => false, "set_psilim_via_dmlim" => true, "dmlim" => 0.2, + "gal_flag" => true, "gal_solver" => "LU")) +end + +# Run setup + the full stability/STRIDE pipeline at a given psihigh. High-β limited TokaMaker +# equilibria need a smaller psihigh (the LCFS sits at the grid edge; tracing too far out fails), +# so the caller retries down a ladder. +function run_pipeline(psihigh) + dir = mktempdir(; prefix="galtok_") + cp(GEQDSK, joinpath(dir, basename(GEQDSK))) + inputs = base_inputs(dir) + inputs["Equilibrium"]["psihigh"] = psihigh + ctrl = FFS.ForceFreeStatesControl(; (Symbol(k) => v for (k, v) in inputs["ForceFreeStates"])...) + ctrl.verbose = false + intr = FFS.ForceFreeStatesInternal(; dir_path=dir) + eq_config = EQ.EquilibriumConfig(inputs["Equilibrium"], dir) + equil = EQ.setup_equilibrium(eq_config, nothing) + FFS.sing_lim!(intr, ctrl, equil) + xs = equil.profiles.xs; ls = zeros(length(xs), 5); FFS.mercier_scan!(ls, equil) + intr.locstab = cubic_interp(xs, Series(ls); extrap=ExtendExtrap()) + intr.nlow = ctrl.nn_low; intr.nhigh = ctrl.nn_high; intr.npert = 1 + FFS.sing_find!(intr, equil) + # Replicate main()'s post-find surface filter: drop surfaces outside [qlow, qlim]. + # Without this the worker keeps the q=1 internal-kink surface (and mis-aligns the STRIDE + # matrix indexing), which main() excludes — the source of the spurious β≈1.6 error cliff. + if intr.msing > 0 + qmin_int = max(ctrl.qlow, equil.params.qmin) + keep = [j for j in 1:intr.msing if intr.sing[j].q >= qmin_int && intr.sing[j].psifac <= intr.psilim] + intr.sing = intr.sing[keep] + intr.msing = length(keep) + end + intr.mlow = trunc(Int, min(intr.nlow * equil.params.qmin, 0)) - 4 - ctrl.delta_mlow + intr.mhigh = trunc(Int, intr.nhigh * equil.params.qmax) + ctrl.delta_mhigh + intr.mpert = intr.mhigh - intr.mlow + 1 + intr.mband = min(max(intr.mpert - 1 - ctrl.delta_mband, 0), intr.mpert - 1) + intr.numpert_total = intr.mpert * intr.npert + metric = FFS.make_metric(equil; mband=intr.mband, fft_flag=ctrl.fft_flag) + ffit = FFS.make_matrix(equil, intr, metric) + odet, fm_propagators, fm_chunks, fm_S_left = FFS.eulerlagrange_integration(ctrl, equil, ffit, intr) + vac_data = FFS.free_run!(odet, ctrl, equil, ffit, intr) + if intr.msing > 0 && fm_propagators !== nothing + FFS.compute_delta_prime_matrix!(intr, fm_propagators, fm_chunks; + wv=vac_data.wv, psio=equil.psio, debug=false, + S_at_surface_left=fm_S_left, ctrl=ctrl, equil=equil, ffit=ffit) + end + return (ctrl=ctrl, equil=equil, ffit=ffit, intr=intr, vac_data=vac_data, dir=dir, psihigh=psihigh) +end + +P = nothing +for ph in (0.999, 0.99, 0.98, 0.97, 0.95) + try + global P = run_pipeline(ph); break + catch e + @warn "pipeline failed at psihigh=$ph for $(basename(GEQDSK)); retrying lower" exception=e + end +end +P === nothing && error("all psihigh retries failed for $(basename(GEQDSK))") +ctrl = P.ctrl; equil = P.equil; ffit = P.ffit; intr = P.intr; vac_data = P.vac_data; dir = P.dir +@printf(" using psihigh=%.3f for %s\n", P.psihigh, basename(GEQDSK)) +dpm = intr.delta_prime_matrix +m_s = [s.m[1] for s in intr.sing if s.psifac < intr.psilim] +q_s = [s.q for s in intr.sing if s.psifac < intr.psilim] +# STRIDE delta_prime_matrix may have fewer rows than m_s (it drops surfaces beyond its own +# active-domain cut). Match by position but guard the access so extra surfaces just get NaN. +ndpm = (dpm === nothing || isempty(dpm)) ? 0 : size(dpm, 1) +stride_diag = [i <= ndpm ? real(dpm[i, i]) : NaN for i in 1:length(m_s)] + +open(OUTCSV, "a") do io + for pfac in PFACS + ctrl.gal_pfac = pfac + gdiag = fill(NaN, length(m_s)); gm = Int[] + try + res = FFS.galerkin_solve(ctrl, equil, ffit, intr; vac_data=vac_data) + gm = res.sing_m + for (i, m) in enumerate(m_s) + gi = findfirst(==(m), gm) + gdiag[i] = gi === nothing ? NaN : real(res.Deltap[gi, gi]) + end + catch e + @warn "gal failed beta=$BETA pfac=$pfac" exception=e + end + for i in 1:length(m_s) + @printf(io, "%.4f,%.6e,%d,%.4f,%.6f,%.6f\n", BETA, pfac, m_s[i], q_s[i], gdiag[i], stride_diag[i]) + end + flush(io) + end +end +rm(dir; force=true, recursive=true) +@printf("WORKER DONE beta=%.4f msing=%d surfaces q=%s\n", BETA, length(m_s), string(round.(q_s; digits=2))) From fa0389b8e047c456a67900256f6e79f53e56fca0 Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Tue, 9 Jun 2026 16:57:50 -0400 Subject: [PATCH 010/135] ForceFreeStates - NEW - Add resistive inner-layer parameters and update galerkin solver to support coil-response columns --- src/ForceFreeStates/ForceFreeStates.jl | 2 + src/ForceFreeStates/ForceFreeStatesStructs.jl | 1 + src/ForceFreeStates/Galerkin/GalerkinSolve.jl | 34 ++++- .../Galerkin/GalerkinStructs.jl | 1 + src/ForceFreeStates/Resist.jl | 141 ++++++++++++++++++ src/GeneralizedPerturbedEquilibrium.jl | 8 +- 6 files changed, 178 insertions(+), 9 deletions(-) create mode 100644 src/ForceFreeStates/Resist.jl diff --git a/src/ForceFreeStates/ForceFreeStates.jl b/src/ForceFreeStates/ForceFreeStates.jl index ab04ec155..d31ac9c7d 100644 --- a/src/ForceFreeStates/ForceFreeStates.jl +++ b/src/ForceFreeStates/ForceFreeStates.jl @@ -17,6 +17,7 @@ using QuadGK: quadgk import ..Equilibrium import ..Utilities import ..Vacuum +import ..InnerLayer using Printf using DoubleFloats import StaticArrays: @MMatrix @@ -24,6 +25,7 @@ import StaticArrays: @MMatrix # Include all necessary files include("ForceFreeStatesStructs.jl") include("Mercier.jl") +include("Resist.jl") include("Bal.jl") include("EulerLagrange.jl") include("Sing.jl") diff --git a/src/ForceFreeStates/ForceFreeStatesStructs.jl b/src/ForceFreeStates/ForceFreeStatesStructs.jl index 73d9e615e..60d923bb7 100644 --- a/src/ForceFreeStates/ForceFreeStatesStructs.jl +++ b/src/ForceFreeStates/ForceFreeStatesStructs.jl @@ -305,6 +305,7 @@ A mutable struct containing control parameters for stability analysis, set by th gal_dx1dx2_flag::Bool = true # enable special dx1/dx2 treatment for resonant/extension elements gal_sing_order::Int = 6 # base power-series order for the Galerkin singular asymptotics gal_sing_order_ceiling::Bool = true # auto-raise order by ceil(2·Re(α)) per surface (high Mercier index) + gal_rpec_flag::Bool = false # append mpert coil-response columns to the Δ′ solve (RDCON rpec_flag): unit boundary sources whose plasma response is recorded; needed for the driven (resistive perturbed-equilibrium) Δ_gw fixed_axis::Bool = false end diff --git a/src/ForceFreeStates/Galerkin/GalerkinSolve.jl b/src/ForceFreeStates/Galerkin/GalerkinSolve.jl index 4328bc0ab..0f27b1088 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinSolve.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinSolve.jl @@ -70,7 +70,7 @@ function galerkin_solve(ctrl::ForceFreeStatesControl, equil, ffit::FourFitVars, ctrl.verbose && @info "galerkin_solve: no resonant surfaces in domain; skipping Δ′ solve" empty2 = Matrix{ComplexF64}(undef, 0, 0) return GalerkinResult(Matrix{ComplexF64}(undef, 0, 0), empty2, empty2, empty2, empty2, 0, - Float64[], Float64[], Int[], Int[], Float64[], ComplexF64[]) + Float64[], Float64[], Int[], Int[], Float64[], ComplexF64[], empty2) end ctrl.verbose && @info "Starting outer-region Galerkin Δ′ solve (msing=$msing, solver=$(ctrl.gal_solver))" @@ -100,7 +100,14 @@ function galerkin_solve(ctrl::ForceFreeStatesControl, equil, ffit::FourFitVars, kl = mpert * (np + 1) ku = kl ldab = ctrl.gal_solver == "LU" ? 2kl + ku + 1 : kl + 1 - nsol = 2 * msing + # rpec_flag (RDCON, gal.f:148-170): append mpert coil-response columns. Each is a unit source at + # the edge value DOF in one poloidal mode; the recorded plasma response is the coil block of Δ_gw. + # Cholesky's lower-only edge zeroing can't represent the rpec identity edge, so require LU. + ncoil = ctrl.gal_rpec_flag ? mpert : 0 + if ncoil > 0 && ctrl.gal_solver != "LU" + error("galerkin_solve: gal_rpec_flag=true requires gal_solver=\"LU\" (coil edge BC needs the full-band path)") + end + nsol = 2 * msing + ncoil intvl = [GalInterval(zeros(Float64, nx + 1), zeros(Float64, nx + 1), [GalCell(mpert) for _ in 1:nx]) for _ in 0:msing] ws = GalWorkspace(ctrl.gal_solver, nx, ctrl.gal_nq, np, 0, kl, ku, ldab, nsol, @@ -115,14 +122,26 @@ function galerkin_solve(ctrl::ForceFreeStatesControl, equil, ffit::FourFitVars, ws.rhs = zeros(ComplexF64, ws.ndim, nsol) ws.sol = zeros(ComplexF64, ws.ndim, nsol) - # Free-boundary edge term wvac·psio² (vac_data.wv is already singfac-scaled at qlim in free_run!) + # Free-boundary edge term wvac·psio² (vac_data.wv is already singfac-scaled at qlim in free_run!). + # rpec uses a fixed-boundary identity edge (the coil unit sources are injected as RHS below), so the + # vacuum block is not applied at the edge in that case — matching Fortran gal_set_boundary rpec branch. wv_edge = nothing - if ctrl.vac_flag && vac_data !== nothing + if ctrl.vac_flag && vac_data !== nothing && ncoil == 0 wv_edge = Matrix{ComplexF64}(vac_data.wv .* equil.psio^2) end gal_make_arrays!(ws, ctrl, equil, ffit, intr, asymps, sings, nn, wv_edge) + # rpec_flag: inject unit sources into the coil columns (gal.f:1544-1549). For each poloidal mode + # ipert, column (2*msing + ipert) gets a unit at the edge cell's value DOF (ip=3 → Julia index 4). + if ncoil > 0 + edge_cell = ws.intvl[msing+1].cells[ws.nx] + for ipert in 1:mpert + imap = edge_cell.map[ipert, 4] + ws.rhs[imap, 2 * msing + ipert] = 1 + end + end + if get(ENV, "GAL_DEBUG", "") == "1" offdbg = ws.solver == "LU" ? ws.kl + ws.ku + 1 : 1 @info "GAL_DEBUG ndim=$(ws.ndim) nsol=$nsol kl=$(ws.kl) ldab=$(ws.ldab) |rhs|=$(norm(ws.rhs))" @@ -163,9 +182,11 @@ function galerkin_solve(ctrl::ForceFreeStatesControl, equil, ffit::FourFitVars, di = [real(-asymps[i].right.alpha[1]^2) for i in 1:msing] alpha = [asymps[i].right.alpha[1] for i in 1:msing] + # Coil-response block (rpec_flag): rows 2*msing+1 : 2*msing+mpert of delta (empty otherwise). + delta_coil = ncoil > 0 ? delta[(2*msing+1):(2*msing+ncoil), :] : Matrix{ComplexF64}(undef, 0, 0) return GalerkinResult(delta, Ap, Bp, Gammap, Deltap, msing, [s.psifac for s in sings], [s.q for s in sings], - [s.m[1] for s in sings], [s.n[1] for s in sings], di, alpha) + [s.m[1] for s in sings], [s.n[1] for s in sings], di, alpha, delta_coil) end """ @@ -212,5 +233,8 @@ function write_galerkin!(out_h5, result::GalerkinResult) out_h5["galerkin/sing_n"] = result.sing_n out_h5["galerkin/di"] = result.di out_h5["galerkin/alpha"] = result.alpha + if !isempty(result.delta_coil) + out_h5["galerkin/delta_coil"] = result.delta_coil + end return nothing end diff --git a/src/ForceFreeStates/Galerkin/GalerkinStructs.jl b/src/ForceFreeStates/Galerkin/GalerkinStructs.jl index 49f294d32..51768b51e 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinStructs.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinStructs.jl @@ -138,4 +138,5 @@ struct GalerkinResult sing_n::Vector{Int} di::Vector{Float64} alpha::Vector{ComplexF64} + delta_coil::Matrix{ComplexF64} # (mpert, 2*msing) coil-response block (rpec_flag); empty if not computed end diff --git a/src/ForceFreeStates/Resist.jl b/src/ForceFreeStates/Resist.jl new file mode 100644 index 000000000..5f14c6878 --- /dev/null +++ b/src/ForceFreeStates/Resist.jl @@ -0,0 +1,141 @@ +# Resist.jl +# +# Per-rational-surface resistive inner-layer parameters (Glasser–Greene–Johnson). +# Julia port of the RDCON `resist_eval` (resist.f): evaluates the flux-surface-averaged +# curvature/mass coefficients E, F, H, M, G, K and the local Alfvén / resistive time scales +# τ_A, τ_R at a singular surface. +# +# Returns an `InnerLayer.GGJParameters` directly (the inner-layer matching input type), so a +# resistive ForceFreeStates run can hand its per-surface coefficients straight to the GGJ inner +# solver. InnerLayer is included before ForceFreeStates precisely so this type is available here. +# +# Resistivity η and mass density ρ are REQUIRED inputs (per surface) — there is no built-in +# resistivity/density model. We deliberately do NOT port the Fortran `resist.f` Spitzer block +# (hardcoded ne/Te → η, ρ); the caller supplies η and ρ from whatever transport/profile model is +# appropriate. τ_A and τ_R are then formed from physically separable pieces: a purely geometric +# factor times the explicit η and ρ (no RMATCH-style divide-out / re-multiply). +# +# Differences from the Fortran reference (deliberate): +# - Rational surfaces lie off the equilibrium grid (q = m/n between nodes), so the geometry +# is evaluated with the callable bicubic interpolants at the exact (ψ_s, θ) — using +# DerivOp(0,1) for θ-derivatives — rather than the nodal-grid access mercier_scan! uses. +# - η and ρ are caller-supplied (no Spitzer model, no hardcoded ne/Te/mi defaults). +# +# Reference: Glasser, Greene & Johnson, Phys. Fluids 18, 875 (1975); Glasser PoP 23, 072505 (2016). + +""" + resist_eval(sing, equil, intr; eta, rho, gamma, ising=0) -> InnerLayer.GGJParameters + +Compute the GGJ resistive inner-layer parameters at the rational surface `sing`. +Port of RDCON `resist_eval` (resist.f:31-173), but with η and ρ supplied by the caller (no +built-in Spitzer/density model). Returns an `InnerLayer.GGJParameters` carrying the curvature/mass +coefficients E, F, G, H, K, M, the local time scales τ_A (`taua`), τ_R (`taur`), `v1` (V′ normalized +by total volume), and the surface index `ising`. + +# Required keyword arguments + - `eta::Real` — plasma resistivity η at this surface [Ω·m] + - `rho::Real` — mass density ρ at this surface [kg/m³] + - `gamma::Real` — ratio of specific heats (enters G; physical thermodynamic value, e.g. 5/3) + +# Physics +The six flux-surface averages (Fortran `avg(1:6)`) are +`⟨B²/|∇ψ|²⟩, ⟨1/|∇ψ|²⟩, ⟨1/B²⟩, ⟨1/(B²|∇ψ|²)⟩, ⟨B²⟩, ⟨|∇ψ|²/B²⟩`, each weighted by `J/V′` +and integrated over θ ∈ [0,1) — exactly the resist.f integrands. The timescales are +`τ_A = √(ρ·M·μ₀) / |2π n q₁ χ₁ / V′|` and `τ_R = (⟨B²/|∇ψ|²⟩/⟨B²⟩)·μ₀/η`, with η and ρ entering +once, explicitly. +""" +function resist_eval(sing::SingType, equil::Equilibrium.PlasmaEquilibrium, + intr::ForceFreeStatesInternal; eta::Real, rho::Real, gamma::Real, ising::Int=0) + + profiles = equil.profiles + psifac = sing.psifac + nn = sing.n[1] + + # --- 1D surface quantities at the (off-grid) rational ψ --- + hint = Ref(1) + twopif = profiles.F_spline(psifac; hint=hint) + p = profiles.P_spline(psifac; hint=hint) + p1 = profiles.P_deriv(psifac; hint=hint) + v1 = profiles.dVdpsi_spline(psifac; hint=hint) + v2 = profiles.dVdpsi_deriv(psifac; hint=hint) + q = sing.q + q1 = sing.q1 + chi1 = 2π * equil.psio + + # --- θ-integrate the six geometric averages (resist.f:71-103) --- + nth = length(equil.rzphi_ys) + ff = zeros(nth, 6) + hint2d = (Ref(1), Ref(1)) + for itheta in 1:nth + theta = equil.rzphi_ys[itheta] + f1 = equil.rzphi_rsquared((psifac, theta); hint=hint2d) + f2 = equil.rzphi_offset((psifac, theta); hint=hint2d) + jac = equil.rzphi_jac((psifac, theta); hint=hint2d) + fy1 = equil.rzphi_rsquared((psifac, theta); deriv=DerivOp(0, 1), hint=hint2d) + fy2 = equil.rzphi_offset((psifac, theta); deriv=DerivOp(0, 1), hint=hint2d) + fy3 = equil.rzphi_nu((psifac, theta); deriv=DerivOp(0, 1), hint=hint2d) + + rfac = sqrt(f1) + eta_geo = 2π * (theta + f2) # geometric poloidal angle (local; not the resistivity η) + r = equil.ro + rfac * cos(eta_geo) + + v21 = fy1 / (2.0 * rfac * jac) + v22 = (1.0 + fy2) * 2π * rfac / jac + v23 = fy3 * r / jac + v33 = 2π * r / jac + bsq = chi1^2 * (v21^2 + v22^2 + (v23 + q * v33)^2) + dpsisq = (2π * r)^2 * (v21^2 + v22^2) + + ff[itheta, 1] = bsq / dpsisq + ff[itheta, 2] = 1.0 / dpsisq + ff[itheta, 3] = 1.0 / bsq + ff[itheta, 4] = 1.0 / (bsq * dpsisq) + ff[itheta, 5] = bsq + ff[itheta, 6] = dpsisq / bsq + @views ff[itheta, :] .*= jac / v1 + end + itp = cubic_interp(equil.rzphi_ys, Series(ff); bc=PeriodicBC()) + avg = FastInterpolations.integrate(itp) + + # --- curvature terms E, F, H (resist.f:107-111) --- + E = p1 * v1 / (q1 * chi1^2)^2 * avg[1] * (twopif * q1 * chi1 / avg[5] - v2) + F = (p1 * v1 / (q1 * chi1^2))^2 * (avg[1] * avg[3] + (twopif / chi1)^2 * (avg[1] * avg[4] - avg[2]^2)) + H = twopif * p1 * v1 / (q1 * chi1^3) * (avg[2] - avg[1] / avg[5]) + + # --- mass factor M and derived G, K (resist.f:122-125) --- + M = avg[1] * (avg[6] + (twopif / chi1)^2 * (avg[3] - 1 / avg[5])) + G = avg[5] / (M * gamma * p) + K = (q1 * chi1^2 / (p1 * v1))^2 * avg[5] / (M * avg[1]) + + # --- Alfvén and resistive times from caller-supplied η, ρ (resist.f:136-138) --- + # τ_A = √(ρ·M·μ₀) / |2π n q₁ χ₁ / V′| — geometric factor × √ρ. + # τ_R = (⟨B²/|∇ψ|²⟩ / ⟨B²⟩) · μ₀ / η — geometric factor × 1/η. + # η, ρ enter once, explicitly (no RMATCH divide-out / re-multiply). + mu0 = 4π * 1e-7 + geom_taua = sqrt(M * mu0) / abs(2π * nn * q1 * chi1 / v1) + taua = sqrt(rho) * geom_taua + geom_taur = avg[1] / avg[5] * mu0 + taur = geom_taur / eta + + v1norm = equil.params.volume === nothing ? v1 : v1 / equil.params.volume + + return InnerLayer.GGJParameters(; E=E, F=F, G=G, H=H, K=K, M=M, + taua=taua, taur=taur, v1=v1norm, ising=ising) +end + +""" + resist_eval_all(intr, equil; eta, rho, gamma) -> Vector{InnerLayer.GGJParameters} + +Evaluate [`resist_eval`](@ref) at every singular surface in `intr.sing`, returning one +`GGJParameters` per surface (with `ising` set to the surface index). + +`eta` and `rho` may be supplied either as scalars (applied to every surface) or as +vectors of length `intr.msing` (one value per surface, e.g. from a transport profile sampled +at each rational surface). `gamma` is the (scalar) ratio of specific heats. +""" +function resist_eval_all(intr::ForceFreeStatesInternal, equil::Equilibrium.PlasmaEquilibrium; + eta, rho, gamma::Real) + _at(x, i) = x isa AbstractVector ? x[i] : x + return [resist_eval(intr.sing[i], equil, intr; + eta=_at(eta, i), rho=_at(rho, i), gamma=gamma, ising=i) for i in 1:intr.msing] +end diff --git a/src/GeneralizedPerturbedEquilibrium.jl b/src/GeneralizedPerturbedEquilibrium.jl index 1239369f2..4dc8958a3 100755 --- a/src/GeneralizedPerturbedEquilibrium.jl +++ b/src/GeneralizedPerturbedEquilibrium.jl @@ -13,14 +13,14 @@ include("Vacuum/Vacuum.jl") import .Vacuum as Vacuum export Vacuum -include("ForceFreeStates/ForceFreeStates.jl") -import .ForceFreeStates as ForceFreeStates -export ForceFreeStates - include("InnerLayer/InnerLayer.jl") import .InnerLayer as InnerLayer export InnerLayer +include("ForceFreeStates/ForceFreeStates.jl") +import .ForceFreeStates as ForceFreeStates +export ForceFreeStates + include("ForcingTerms/ForcingTerms.jl") import .ForcingTerms as ForcingTerms export ForcingTerms From f6cdcad456c1c1020ed0e29873981c94ecb3df7f Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Tue, 9 Jun 2026 22:30:44 -0400 Subject: [PATCH 011/135] DOCS - NEW FEATURE - Add sign conventions reference page (#265) Add a Julia-specific "Sign Conventions Reference" page to the docs site, mirroring the Fortran GPEC sign-conventions reference but written against the Julia code with traceable src/ references. Registered in the nav after Workflow. Covers the coordinate system and Fourier kernel, poloidal flux, poloidal/toroidal angles, working-coordinate Jacobian, helicity, F=R*Bphi, safety factor q, mode numbers, output sign flips (SURFMN/VACUUM), KineticForces rotation conventions, and COCOS compatibility. Two corrections relative to the Fortran reference, verified against the Julia code and Sauter & Medvedev (2013): - q is computed by field-line integration for direct equilibria and is positive in standard operation, not read directly from the EQDSK. - The internal "COCOS 2" label is not a certified index; document the practical IMAS imas_cocos input requirement and flag full COCOS certification as future work. The KineticForces rotation section was verified against PR #112, correcting the effective bounce harmonic (l_eff = l + nq passing / l trapped, not l - sigma*nq) and the bounce/precession frequency description. Co-Authored-By: Claude Opus 4.8 (1M context) --- docs/make.jl | 1 + docs/src/sign_conventions.md | 287 +++++++++++++++++++++++++++++++++++ 2 files changed, 288 insertions(+) create mode 100644 docs/src/sign_conventions.md diff --git a/docs/make.jl b/docs/make.jl index 851cd5d1e..3791fd166 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -24,6 +24,7 @@ makedocs(; "Home" => "index.md", "Setup" => "set_up.md", "Workflow" => "workflow.md", + "Sign Conventions" => "sign_conventions.md", "API Reference" => [ "Vacuum" => "vacuum.md", "Equilibrium" => "equilibrium.md", diff --git a/docs/src/sign_conventions.md b/docs/src/sign_conventions.md new file mode 100644 index 000000000..0156e9ef4 --- /dev/null +++ b/docs/src/sign_conventions.md @@ -0,0 +1,287 @@ +# Sign Conventions Reference + +This page is a comprehensive reference for the sign and coordinate conventions used +throughout GPEC. Understanding them is essential for interpreting outputs, interfacing with +other codes, and correctly setting up perturbed-equilibrium and kinetic calculations. + +These conventions are inherited from the Fortran GPEC suite and are GPEC-native: they predate +and do not fully coincide with the COCOS standard (see [COCOS Compatibility](@ref) below). +Each section names the Julia source that establishes the convention so the documentation stays +traceable to the implementation. + +## Quick Reference + +| Quantity | Convention | Forced? | +|----------|-----------|---------| +| ``\psi`` (poloidal flux) | Normalized 0 (axis) to 1 (edge), no ``2\pi`` | Yes, positive | +| ``\theta`` (poloidal angle) | Upward outboard | Fixed | +| ``\phi`` (toroidal angle) | CCW for LH, CW for RH | By helicity | +| ``F = R B_\phi`` | Always positive | Yes, `abs` | +| ``q`` (safety factor) | Computed (direct) / input (inverse), positive | Effectively positive | +| ``n`` (toroidal mode) | Always positive (``\ge 1``) | By convention | +| Resonant ``m`` | Always positive (since ``n>0``, ``q>0``) | By construction | +| helicity | +1 RH, ``-1`` LH | Computed | +| ``\omega_E`` | Positive = direction of ``\zeta`` | No | + +## Coordinate System + +GPEC uses right-handed magnetic coordinates ``(\psi, \theta, \zeta)`` with the Fourier kernel + +```math +\exp\!\big(i(m\theta - n\zeta)\big), +``` + +matching the Fortran ``\exp(im\theta - in\phi)`` convention. The forward analysis transform that +produces the mode coefficients ``f_m`` from a real-space profile ``f(\theta)`` uses the conjugate +kernel ``\exp(-im\theta)``; the inverse transform reconstructs with ``\exp(+im\theta)`` +(`src/Utilities/FourierTransforms.jl`). + +### Poloidal Flux ``\psi`` + +- Normalized from 0 (magnetic axis) to 1 (plasma boundary). +- ``\psi_0 = |\psi_\mathrm{bry} - \psi_\mathrm{axis}|`` is **forced positive** on read + (`read_eq_efit` in `src/Equilibrium/ReadEquilibrium.jl`). If the EQDSK has + ``\psi_\mathrm{bry} < \psi_\mathrm{axis}``, the 2D flux array is sign-flipped so that ``\psi`` + increases from axis to edge. +- The internal ``\psi`` carries **no** factor of ``2\pi`` (poloidal flux per radian). IMAS inputs, + which use the full poloidal flux, are divided by ``2\pi`` on read — see + [COCOS Compatibility](@ref). +- Occasionally ``\rho = \sqrt{\psi}`` is used as a radius-like variable. + +### Poloidal Angle ``\theta`` + +- "Upward outboard" convention, always: ``\theta = 0`` on the outboard midplane, increasing + upward. +- ``\theta`` is normalized to increase by 1 (not ``2\pi``) over one poloidal circuit. This is fixed + regardless of helicity or working-coordinate choice. + +### Toroidal Coordinate ``\zeta`` and ``\phi`` + +- The ignorable toroidal coordinate is ``\zeta = \phi/(2\pi) + \nu(\psi,\theta)``, where ``\nu`` is + a single-valued straight-field-line offset that depends on the working coordinate. PEST + coordinates have ``\nu = 0``. +- The physical toroidal angle is reconstructed as + ``\phi = -\,\mathrm{helicity}\,(2\pi\zeta + \nu)`` (`sample_boundary_grid` in + `src/ForcingTerms/CoilFourier.jl`). Thus ``\phi`` is effectively **counter-clockwise** (viewed + from above) for left-handed (LH) configurations and **clockwise** for right-handed (RH) + configurations. + +### Working Coordinate Options + +Controlled by `jac_type` in the `[Equilibrium]` section of `gpec.toml`. The Jacobian is +``J \propto B_p^{p_{bp}}\, B^{p_b}\, R^{-p_r}``: + +| Name | `power_bp` | `power_b` | `power_r` | +|------|-----------|-----------|-----------| +| Hamada (default) | 0 | 0 | 0 | +| PEST | 0 | 0 | 2 | +| Boozer | 0 | 2 | 0 | +| Equal-arc | 1 | 0 | 0 | + +The powers are set automatically from `jac_type` (`EquilibriumConfig` in +`src/Equilibrium/EquilibriumTypes.jl`) and applied in the field-line Jacobian +(`direct_fieldline_der!` in `src/Equilibrium/DirectEquilibrium.jl`). + +## Helicity and Handedness + +Helicity is derived from the equilibrium current and toroidal-field directions: + +```julia +helicity = bt_sign * Int(sign(crnt)) # src/ForcingTerms/CoilFourier.jl +``` + +- `bt_sign` is the toroidal-field direction and `crnt` is the signed plasma current. +- **helicity = +1**: right-handed (RH) --- ``B_t`` and ``I_p`` in the same direction. +- **helicity = -1**: left-handed (LH) --- ``B_t`` and ``I_p`` opposed. +- Helicity sets the toroidal-grid direction ``\phi_j = -\mathrm{helicity}\times 2\pi j/n_\zeta`` and + the output sign flips (see [Spectrum Output Sign Conventions](@ref)). For DIII-D + (``B_t < 0``, ``I_p > 0`` ⇒ helicity = ``-1``) ``\phi`` increases with ``j``. + +## ``F = R B_\phi`` + +The poloidal-current function ``F = R B_\phi`` from the Grad-Shafranov equation is **forced +positive** via `abs` (`read_eq_efit` in `src/Equilibrium/ReadEquilibrium.jl`): + +```julia +abs.(fpol_data) +``` + +The code always works with ``|F|``; the sign of ``B_t`` is carried separately (`fpol_sign`, and the +`bt_sign`/`crnt` helicity inputs). + +## Safety Factor ``q`` + +The direct solver **computes** ``q`` by field-line integration for direct (EFIT) equilibria and +overwrites the file profile (`direct_run` in `src/Equilibrium/DirectEquilibrium.jl`): + +```math +q = \frac{F}{2\pi}\oint \frac{J}{B_p}\,dl_p . +``` + +- Because the Jacobian ``J > 0``, the closed-loop integral is positive, and ``F = |F|`` is forced + positive, **``q`` is positive** in standard operation. The solver emits a warning if the on-axis + extrapolation yields ``q_0 \le 0``, treating it as a spline artifact rather than a physical + result. +- **Inverse** equilibria instead use the ``q`` profile supplied with the input + (`src/Equilibrium/InverseEquilibrium.jl`). + +## Mode Numbers ``m`` and ``n`` + +### Toroidal Mode Number ``n`` + +- Set as a **positive integer** via `nn_low`/`nn_high` in `gpec.toml`. ``n < 1`` is not supported + and is clamped to 1 with a warning (`src/GeneralizedPerturbedEquilibrium.jl`). Results for + multiple ``n`` can be superposed. + +### Poloidal Mode Range + +The poloidal spectrum spans `mlow` to `mhigh` (`src/GeneralizedPerturbedEquilibrium.jl`): + +```math +m_\mathrm{low} = \min(n\,q_\mathrm{min},\,0) - 4 - \Delta m_\mathrm{low}, \qquad +m_\mathrm{high} = n\,q_\mathrm{max} + \Delta m_\mathrm{high}. +``` + +`delta_mlow` and `delta_mhigh` widen the range beyond the resonant modes. + +### Why Positive ``m`` Is Always Resonant + +Resonant surfaces are found by `sing_find!` (`src/ForceFreeStates/Sing.jl`), which locates flux +surfaces where ``m = n\,q(\psi)``. Since ``n > 0`` by convention and ``q > 0`` for a standard +tokamak, the resonant ``m`` is always positive: + +```math +m_\mathrm{res} = n\,q > 0 . +``` + +Negative-``m`` modes are always non-resonant. This is by design: the ``m = 2`` displacement shows +resonant behavior at ``q = 2``, while ``m = -2`` never does. + +## Spectrum Output Sign Conventions + +For the real-space representation, GPEC takes the complex conjugate for **right-handed** +configurations. This is implemented in the mode reconstruction +(`src/Analysis/PerturbedEquilibriumModes.jl`): + +```julia +if helicity > 0 + theta_data[:, :, k] .= conj.(theta_data[:, :, k]) +end +``` + +The straight-field-line offset enters as ``\exp(i\,n\,\nu)`` before the conjugation. For the full +Fourier representation ``\exp(i(m\theta - n\zeta))`` the conjugate operation flips both the +toroidal direction and the up/down (poloidal) sense. + +### Interfacing with SURFMN + +SURFMN expands in ``\exp(-im\theta - in\phi)`` with CCW ``\phi``. To convert from GPEC: + +```python +m_surfmn = helicity * m_gpec +b_surfmn = real(b_m) - 1j * helicity * imag(b_m) +``` + +For LH configurations only the sign of ``m`` is flipped; for RH, ``m`` is unchanged but the complex +conjugate is taken. + +### Interfacing with VACUUM + +The VACUUM code uses CCW ``\phi`` and downward-outboard ``\theta``. GPEC uses the complex conjugate +of RH configurations when interfacing with VACUUM. + +## Rotation Velocity Conventions (KineticForces) + +The `KineticForces` module (the Julia port of PENTRC) conventions below are used in +`src/KineticForces/Torque.jl`, `EnergyIntegration.jl`, and `PitchIntegration.jl`. + +### ``\omega_E`` (E × B Rotation) + +- ``\omega_E`` is the input E × B toroidal-rotation profile, evaluated as + `welec = omegaE_spline(psi)` (`Torque.jl`). Positive ``\omega_E`` means rotation in the direction + of the toroidal coordinate ``\zeta``. +- The mapping to current direction follows from the ``\zeta``/``\phi`` convention fixed by helicity + ([Helicity and Handedness](@ref)); it is not re-derived inside the kinetic module, which only + reads the supplied profile. + +### Diamagnetic Frequencies + +Computed at evaluation time from the kinetic-profile gradients (Logan & Park 2013, Eq. 7; +`Torque.jl`): + +```math +\omega_{*n} = -\frac{2\pi\, T_i}{e\, Z_i\, \chi_1\, n_i}\frac{dn_i}{d\psi_n}, \qquad +\omega_{*T} = -\frac{2\pi}{e\, Z_i\, \chi_1}\frac{dT_i}{d\psi_n}, +``` + +where ``\chi_1 = 2\pi\psi_0`` (`chi1 = 2π·psio`). The negative signs mean a negative +(outward-decreasing) density or temperature gradient yields a positive diamagnetic frequency. The +total toroidal rotation is the sum + +```math +\omega_\phi = \omega_E + \omega_{*n} + \omega_{*T} . +``` + +### Energy Integral Resonance + +In the kinetic energy integral (`integrate_energy` in `EnergyIntegration.jl`) the resonance +denominator is ``i\,\Omega(x) - \nu``, where the resonance condition is + +```math +\Omega(x) = n\,\omega_E + \ell_\mathrm{eff}\,\omega_b\sqrt{x} + n\,\omega_D\,x , +``` + +with ``x = E/T`` the normalized energy and ``\nu`` the (energy-dependent) effective collisionality. +Here: + +- ``\omega_b`` and ``\omega_D`` are the bounce and magnetic-precession frequency **coefficients at + thermal energy** (``x = 1``): ``\omega_b \propto v_\mathrm{th}`` and + ``\omega_D \propto v_\mathrm{th}^2`` (`wbhat`, `wdhat` in `Torque.jl`). Their velocity-space + dependence enters explicitly as ``\sqrt{x}`` (bounce ``\propto v``) and ``x`` (precession + ``\propto E``). +- ``\ell_\mathrm{eff}`` is the effective bounce harmonic (`PitchIntegration.jl`): + +```math +\ell_\mathrm{eff} = +\begin{cases} +\ell + n q & \text{circulating (passing) particles},\\ +\ell & \text{trapped particles}. +\end{cases} +``` + +The sign of ``\omega_E`` shifts the resonance location in velocity space. + + +## COCOS Compatibility + +The conventions above are GPEC-native and predate the COCOS standard, as defined in +[Sauter, Comp. Phys. Comm. 2013](https://doi.org/10.1016/j.cpc.2012.09.010). What is **certain** +about the internal convention: + +- Right-handed magnetic coordinates ``(\psi, \theta, \zeta)``. +- ``\psi`` excludes the ``2\pi`` factor (poloidal flux per radian) and increases from axis to edge. +- ``q > 0`` and ``n > 0`` in standard operation; ``F = |F|``. + +The code labels this internal convention **COCOS 2** (`read_imas` in +`src/Equilibrium/ReadEquilibrium.jl`) and converts IMAS inputs accordingly: + +```julia +imas_cocos = 11 # default: IMAS standard, ψ divided by 2π on read +imas_cocos = 2 # data already in the internal convention, no conversion +``` + +!!! warning "The COCOS index is not yet certified" + The internal "COCOS 2" label is a working assumption, not a verified index. The IMAS reader + converts COCOS 11 → "COCOS 2" by dividing ``\psi`` by ``2\pi`` **only**, whereas in the COCOS + standard the pure ``2\pi`` partner of COCOS 11 is COCOS **1** (COCOS 2 differs additionally in + the cylindrical/poloidal handedness ``\sigma_{R\phi Z}`` and in ``\mathrm{sign}(q)``). A + rigorous classification would require auditing the ``\sigma_{B_p}``, ``\sigma_{R\phi Z}``, and + ``\sigma_{\rho\theta\phi}`` signs against the GPEC field representation. Until that audit is + done, treat the **practical input requirement** as the reliable statement: provide IMAS + equilibria in COCOS 11 (default) or COCOS 2, selected via `imas_cocos`. Full COCOS conformance + is tracked as a separate effort. + +## See also + +- [Workflow](workflow.md) --- where each convention enters the analysis pipeline +- [Citations](citations.md) --- theoretical references for GPEC's algorithms From 7b4c08bc1d1f053ae134ca544c60a1c90f498493 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Wed, 10 Jun 2026 16:41:37 -0400 Subject: [PATCH 012/135] ForceFreeStates - CLEANUP - Remove stray .codex and Bal s-alpha notebook Delete the empty tracked .codex scratch file (and gitignore it) and the Bal_salpha_delta_di_summary.ipynb notebook; its plotting is ported to analyze_example.jl. Notebooks are no longer maintained in the repo. Co-Authored-By: Claude Opus 4.8 --- .codex | 0 .gitignore | 1 + .../Bal_salpha_delta_di_summary.ipynb | 257 ------------------ 3 files changed, 1 insertion(+), 257 deletions(-) delete mode 100644 .codex delete mode 100644 examples/DIIID-like_ideal_example/Bal_salpha_delta_di_summary.ipynb diff --git a/.codex b/.codex deleted file mode 100644 index e69de29bb..000000000 diff --git a/.gitignore b/.gitignore index 6859d2639..80c1016a9 100644 --- a/.gitignore +++ b/.gitignore @@ -1,3 +1,4 @@ +.codex *.cov *.mod *.dylib diff --git a/examples/DIIID-like_ideal_example/Bal_salpha_delta_di_summary.ipynb b/examples/DIIID-like_ideal_example/Bal_salpha_delta_di_summary.ipynb deleted file mode 100644 index 3b634dce6..000000000 --- a/examples/DIIID-like_ideal_example/Bal_salpha_delta_di_summary.ipynb +++ /dev/null @@ -1,257 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "id": "s-alpha-profile-extrema", - "metadata": {}, - "outputs": [], - "source": [ - "using Pkg\n", - "Pkg.activate(\"../..\")\n", - "\n", - "using GeneralizedPerturbedEquilibrium\n", - "using Plots\n", - "using Printf\n", - "using Statistics\n", - "using LaTeXStrings\n", - "using TOML\n", - "\n", - "eq_config = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(TOML.parsefile(\"gpec.toml\")[\"Equilibrium\"], pwd())\n", - "equil = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(eq_config)\n", - "psi_norm = Vector(equil.profiles.xs)\n", - "\n", - "function finite_local_extrema(values::AbstractVector{<:Real})\n", - " extrema = Int[]\n", - " for i in 2:length(values)-1\n", - " if !isfinite(values[i - 1]) || !isfinite(values[i]) || !isfinite(values[i + 1])\n", - " continue\n", - " end\n", - " if (values[i] >= values[i - 1] && values[i] >= values[i + 1]) ||\n", - " (values[i] <= values[i - 1] && values[i] <= values[i + 1])\n", - " push!(extrema, i)\n", - " end\n", - " end\n", - " return extrema\n", - "end\n", - "\n", - "function print_extrema_report(name::String, psi::AbstractVector, values::AbstractVector, extrema::AbstractVector{Int})\n", - " println(\"\\n\", name, \" extrema\")\n", - " if isempty(extrema)\n", - " println(\" none\")\n", - " return\n", - " end\n", - " println(\" index\\tpsi_norm\\tvalue\")\n", - " for i in extrema\n", - " @printf(\" %d\\t%.8f\\t%.12e\\n\", i, psi[i], values[i])\n", - " end\n", - "end\n", - "\n", - "s_profile = fill(NaN, length(psi_norm))\n", - "alpha_profile = fill(NaN, length(psi_norm))\n", - "\n", - "for i in eachindex(psi_norm)\n", - " try\n", - " ref = GeneralizedPerturbedEquilibrium.ForceFreeStates.salpha_reference(i, equil)\n", - " s_profile[i] = ref.s_ref\n", - " alpha_profile[i] = ref.alpha_ref\n", - " catch err\n", - " @warn \"s-alpha reference failed\" i psi=psi_norm[i] exception=(err, catch_backtrace())\n", - " end\n", - "end\n", - "\n", - "s_extrema = finite_local_extrema(s_profile)\n", - "alpha_extrema = finite_local_extrema(alpha_profile)\n", - "print_extrema_report(\"s\", psi_norm, s_profile, s_extrema)\n", - "print_extrema_report(\"alpha\", psi_norm, alpha_profile, alpha_extrema)\n", - "\n", - "s_mask = isfinite.(s_profile)\n", - "alpha_mask = isfinite.(alpha_profile)\n", - "\n", - "p_s = plot(\n", - " psi_norm[s_mask], s_profile[s_mask];\n", - " xlabel=\"psi_norm\",\n", - " ylabel=\"s\",\n", - " label=\"s\",\n", - " lw=2,\n", - " title=\"s\",\n", - " framestyle=:box,\n", - ")\n", - "scatter!(p_s, psi_norm[s_extrema], s_profile[s_extrema]; label=\"extrema\", marker=:circle, color=:red, ms=5)\n", - "\n", - "p_alpha = plot(\n", - " psi_norm[alpha_mask], alpha_profile[alpha_mask];\n", - " xlabel=\"psi_norm\",\n", - " ylabel=\"alpha\",\n", - " label=\"alpha\",\n", - " lw=2,\n", - " title=\"alpha\",\n", - " framestyle=:box,\n", - ")\n", - "scatter!(p_alpha, psi_norm[alpha_extrema], alpha_profile[alpha_extrema]; label=\"extrema\", marker=:circle, color=:red, ms=5)\n", - "\n", - "display(plot(p_s, p_alpha; layout=(1, 2), size=(1100, 420)))\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "delta-di-profile-extrema", - "metadata": {}, - "outputs": [], - "source": [ - "locstab_fs = zeros(length(psi_norm), 4)\n", - "ctrl = GeneralizedPerturbedEquilibrium.ForceFreeStates.ForceFreeStatesControl(verbose=false)\n", - "\n", - "println(\"Computing \\\\Delta' and D_I...\")\n", - "GeneralizedPerturbedEquilibrium.ForceFreeStates.compute_ballooning_stability!(ctrl, locstab_fs, equil; compute_delta_prime=true)\n", - "\n", - "delta_prime = Vector(locstab_fs[:, 4])\n", - "di_profile = fill(NaN, length(psi_norm))\n", - "psi_mask = abs.(psi_norm) .> eps(Float64)\n", - "di_profile[psi_mask] .= locstab_fs[psi_mask, 1] ./ psi_norm[psi_mask]\n", - "\n", - "delta_extrema = finite_local_extrema(delta_prime)\n", - "di_extrema = finite_local_extrema(di_profile)\n", - "print_extrema_report(\"\\\\Delta'\", psi_norm, delta_prime, delta_extrema)\n", - "print_extrema_report(\"D_I\", psi_norm, di_profile, di_extrema)\n", - "\n", - "delta_mask = isfinite.(delta_prime)\n", - "di_mask = isfinite.(di_profile)\n", - "\n", - "p_delta = plot(\n", - " psi_norm[delta_mask], delta_prime[delta_mask];\n", - " xlabel=\"psi_norm\",\n", - " ylabel=L\"\\Delta'\",\n", - " label=L\"\\Delta'\",\n", - " lw=2,\n", - " title=L\"\\Delta'\",\n", - " framestyle=:box,\n", - ")\n", - "scatter!(p_delta, psi_norm[delta_extrema], delta_prime[delta_extrema]; label=\"extrema\", marker=:diamond, color=:red, ms=5)\n", - "\n", - "p_di = plot(\n", - " psi_norm[di_mask], di_profile[di_mask];\n", - " xlabel=\"psi_norm\",\n", - " ylabel=L\"D_I\",\n", - " label=L\"D_I\",\n", - " lw=2,\n", - " title=L\"D_I\",\n", - " framestyle=:box,\n", - ")\n", - "scatter!(p_di, psi_norm[di_extrema], di_profile[di_extrema]; label=\"extrema\", marker=:diamond, color=:red, ms=5)\n", - "\n", - "display(plot(p_delta, p_di; layout=(1, 2), size=(1100, 420)))\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "s-alpha-delta-di-maps", - "metadata": {}, - "outputs": [], - "source": [ - "psi_target = 0.974\n", - "psi_idx_scan = argmin(abs.(psi_norm .- psi_target))\n", - "\n", - "println(\"Running s-alpha scan at index $(psi_idx_scan), psi_norm=$(round(psi_norm[psi_idx_scan], digits=6))\")\n", - "\n", - "s_scales = collect(range(-5.0, 5.0; length=30))\n", - "alpha_scales = collect(range(-5.0, 5.0; length=30))\n", - "\n", - "scan_result = GeneralizedPerturbedEquilibrium.ForceFreeStates.scan_delta_prime_map(\n", - " psi_idx_scan,\n", - " equil;\n", - " theta_k=0.0,\n", - " s_scales=s_scales,\n", - " alpha_scales=alpha_scales,\n", - ")\n", - "\n", - "scan_qprime_raw = scan_result.dqdpsi_ref .* scan_result.s_scales\n", - "scan_pprime_raw = scan_result.pprime_ref .* scan_result.alpha_scales\n", - "qprime_order = sortperm(scan_qprime_raw)\n", - "pprime_order = sortperm(scan_pprime_raw)\n", - "scan_qprime = scan_qprime_raw[qprime_order]\n", - "scan_pprime = scan_pprime_raw[pprime_order]\n", - "scan_delta = scan_result.delta_prime[qprime_order, pprime_order]\n", - "scan_di = scan_result.di_values[qprime_order, pprime_order]\n", - "\n", - "function symmetric_clims(z)\n", - " finite_vals = vec(z)[isfinite.(vec(z))]\n", - " maxabs = isempty(finite_vals) ? 1.0 : maximum(abs.(finite_vals))\n", - " maxabs = max(maxabs, eps(Float64))\n", - " return (-maxabs, maxabs)\n", - "end\n", - "\n", - "p_scan_delta = contourf(\n", - " scan_pprime, scan_qprime, scan_delta;\n", - " c=cgrad([:blue, :white, :red]),\n", - " clims=symmetric_clims(scan_delta),\n", - " xlabel=L\"p_{\\psi}\",\n", - " ylabel=L\"q_{\\psi}\",\n", - " title=L\"\\Delta'\",\n", - " levels=41,\n", - " framestyle=:box,\n", - ")\n", - "contour!(p_scan_delta, scan_pprime, scan_qprime, scan_delta; levels=[0.0], color=:black, linewidth=2, label=L\"\\Delta' = 0\")\n", - "scatter!(p_scan_delta, [scan_result.reference.pprime_ref], [scan_result.reference.qprime_ref]; color=:green, marker=:star5, ms=7, label=\"equilibrium\")\n", - "\n", - "p_scan_di = contourf(\n", - " scan_pprime, scan_qprime, scan_di;\n", - " c=cgrad([:blue, :white, :red]),\n", - " clims=symmetric_clims(scan_di),\n", - " xlabel=L\"p_{\\psi}\",\n", - " ylabel=L\"q_{\\psi}\",\n", - " title=L\"D_I\",\n", - " levels=41,\n", - " framestyle=:box,\n", - ")\n", - "contour!(p_scan_di, scan_pprime, scan_qprime, scan_di; levels=[0.0], color=:black, linewidth=2, label=L\"D_I = 0\")\n", - "scatter!(p_scan_di, [scan_result.reference.pprime_ref], [scan_result.reference.qprime_ref]; color=:green, marker=:star5, ms=7, label=\"equilibrium\")\n", - "\n", - "display(plot(p_scan_delta, p_scan_di; layout=(1, 2), size=(1150, 460)))\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "s-alpha-zero-contours", - "metadata": {}, - "outputs": [], - "source": [ - "p_zero = plot(\n", - " xlabel=L\"p_{\\psi}\",\n", - " ylabel=L\"q_{\\psi}\",\n", - " title=\"ballooning, Mercier contours\",\n", - " framestyle=:box,\n", - ")\n", - "contour!(p_zero, scan_pprime, scan_qprime, scan_delta;\n", - " levels=[0.0], color=:blue, linewidth=3,\n", - " label=L\"\\Delta' = 0\", colorbar=false)\n", - "\n", - "contour!(p_zero, scan_pprime, scan_qprime, scan_di;\n", - " levels=[0.0], color=:red, linewidth=3, linestyle=:dash,\n", - " label=L\"D_I = 0\", colorbar=false)\n", - "\n", - "\n", - "scatter!(p_zero, [scan_result.reference.pprime_ref], [scan_result.reference.qprime_ref]; color=:green, marker=:star5, ms=8, label=\"equilibrium\")\n", - "display(p_zero)\n" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Julia 1.12.4", - "language": "julia", - "name": "julia-1.12" - }, - "language_info": { - "file_extension": ".jl", - "mimetype": "application/julia", - "name": "julia", - "version": "1.12.4" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} From 83a325bc31b1236d01f2d423d975ca55177d6b5b Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Wed, 10 Jun 2026 16:42:25 -0400 Subject: [PATCH 013/135] ForceFreeStates - CONFIG - Unify local_stability_flag, revert psilow, annotate IMAS toml Finish the mer_flag/bal_flag -> local_stability_flag rename in the example and regression TOMLs that still used the old flags after the develop merge. Revert psilow 1e-2 -> 1e-4 in the DIIID and Solovev examples (the new ballooning ODE converges fine at 1e-4, verified by running the example). Add per-parameter annotations to the IMAS example to match the other examples. Co-Authored-By: Claude Opus 4.8 --- examples/DIIID-like_ideal_example/gpec.toml | 2 +- .../DIIID-like_ideal_example_IMAS/gpec.toml | 36 +++++++++---------- examples/LAR_beta_scan/gpec.toml | 3 +- examples/LAR_epsilon_scan/gpec.toml | 3 +- examples/Solovev_ideal_example/gpec.toml | 2 +- examples/a10_kinetic_example/gpec.toml | 3 +- .../gpec.toml | 3 +- 7 files changed, 24 insertions(+), 28 deletions(-) diff --git a/examples/DIIID-like_ideal_example/gpec.toml b/examples/DIIID-like_ideal_example/gpec.toml index 0d96d422e..099073bd1 100644 --- a/examples/DIIID-like_ideal_example/gpec.toml +++ b/examples/DIIID-like_ideal_example/gpec.toml @@ -6,7 +6,7 @@ power_bp = 0 # Poloidal field power exponent for Jacobian power_b = 0 # Toroidal field power exponent for Jacobian power_r = 0 # Major radius power exponent for Jacobian grid_type = "log_asymptotic" # Radial grid packing type -psilow = 1e-2 # Lower limit of normalized flux coordinate +psilow = 1e-4 # Lower limit of normalized flux coordinate psihigh = 0.9995 # Upper limit of normalized flux coordinate mpsi = 0 # Number of radial grid points (0 = auto-compute from psi_accuracy) psi_accuracy = 0.001 # Target absolute error in q for auto-mpsi diff --git a/examples/DIIID-like_ideal_example_IMAS/gpec.toml b/examples/DIIID-like_ideal_example_IMAS/gpec.toml index f04a0af2d..8154be01e 100644 --- a/examples/DIIID-like_ideal_example_IMAS/gpec.toml +++ b/examples/DIIID-like_ideal_example_IMAS/gpec.toml @@ -8,26 +8,26 @@ # from the dd passed at runtime. See run_imas_example.jl for a full workflow. [Equilibrium] -eq_type = "imas" -eq_filename = "from_dd" # placeholder: equilibrium comes from runtime dd argument -jac_type = "boozer" -psilow = 0.01 -psihigh = 0.9995 -mpsi = 128 -mtheta = 256 +eq_type = "imas" # Type of the input 2D equilibrium (read from the runtime dd) +eq_filename = "from_dd" # Placeholder: equilibrium comes from runtime dd argument +jac_type = "boozer" # Coordinate system (hamada, pest, boozer, equal_arc) +psilow = 0.01 # Lower limit of normalized flux coordinate +psihigh = 0.9995 # Upper limit of normalized flux coordinate +mpsi = 128 # Number of radial grid points +mtheta = 256 # Number of poloidal grid points imas_cocos = 11 # IMAS standard COCOS (input dd is COCOS 11) [Wall] -shape = "nowall" +shape = "nowall" # Wall shape (nowall, conformal, elliptical, dee, mod_dee, filepath) [ForceFreeStates] -nn_low = 1 -nn_high = 1 -vac_flag = true -ode_flag = true -mat_flag = true -local_stability_flag = false # Local D_I and ballooning stability -write_outputs_to_HDF5 = false -verbose = false -delta_mhigh = 16 -qlow = 1.02 +nn_low = 1 # Smallest toroidal mode number to include +nn_high = 1 # Largest toroidal mode number to include +vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes +ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) +mat_flag = true # Construct coefficient matrices for diagnostic purposes +local_stability_flag = false # Evaluate local D_I (Mercier) and ballooning stability across ψ +write_outputs_to_HDF5 = false # Write ForceFreeStates outputs to HDF5 +verbose = false # Enable verbose logging +delta_mhigh = 16 # Expands upper bound of Fourier harmonics +qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... diff --git a/examples/LAR_beta_scan/gpec.toml b/examples/LAR_beta_scan/gpec.toml index 4e2b43518..5c38ff035 100644 --- a/examples/LAR_beta_scan/gpec.toml +++ b/examples/LAR_beta_scan/gpec.toml @@ -52,11 +52,10 @@ a = 20 # Wall scale-out multiplier; 20× the plasma # Force-Free States # ──────────────────────────────────────────────────────────────────────── [ForceFreeStates] -bal_flag = false # Skip ballooning stability scan (compute_ballooning_stability!) +local_stability_flag = true # Evaluate local D_I (Mercier) and ballooning stability across ψ mat_flag = true # Construct F, G, K coupling matrices on the radial grid ode_flag = true # Integrate the ideal-MHD Euler-Lagrange ODE for displacement ξ vac_flag = true # Compute vacuum response and free-boundary energy eigenvalues -mer_flag = true # Evaluate the Mercier local-stability criterion across ψ qlow = 1.02 # Lowest q to include singular surfaces (axis side cutoff) qhigh = 3.6 # Highest q to include singular surfaces (edge side cutoff) diff --git a/examples/LAR_epsilon_scan/gpec.toml b/examples/LAR_epsilon_scan/gpec.toml index 179a54a8c..a2b8a3bc1 100644 --- a/examples/LAR_epsilon_scan/gpec.toml +++ b/examples/LAR_epsilon_scan/gpec.toml @@ -58,11 +58,10 @@ a = 20 # Wall scale-out multiplier; 20× the plasma # Force-Free States # ──────────────────────────────────────────────────────────────────────── [ForceFreeStates] -bal_flag = false # Skip ballooning stability scan (compute_ballooning_stability!) +local_stability_flag = true # Evaluate local D_I (Mercier) and ballooning stability across ψ mat_flag = true # Construct F, G, K coupling matrices on the radial grid ode_flag = true # Integrate the ideal-MHD Euler-Lagrange ODE for displacement ξ vac_flag = true # Compute vacuum response and free-boundary energy eigenvalues -mer_flag = true # Evaluate the Mercier local-stability criterion across ψ qlow = 1.02 # Lowest q to include singular surfaces (axis side cutoff) qhigh = 3.6 # Highest q to include singular surfaces (edge side cutoff) diff --git a/examples/Solovev_ideal_example/gpec.toml b/examples/Solovev_ideal_example/gpec.toml index bc0d13d3b..dcce8d5f4 100644 --- a/examples/Solovev_ideal_example/gpec.toml +++ b/examples/Solovev_ideal_example/gpec.toml @@ -6,7 +6,7 @@ power_bp = 0 # Poloidal field power exponent for Jaco power_b = 0 # Toroidal field power exponent for Jacobian power_r = 0 # Major radius power exponent for Jacobian grid_type = "ldp" # Radial grid packing type -psilow = 1e-2 # Lower limit of normalized flux coordinate +psilow = 1e-4 # Lower limit of normalized flux coordinate psihigh = 0.9995 # Upper limit of normalized flux coordinate mpsi = 128 # Number of radial grid points mtheta = 256 # Number of poloidal grid points diff --git a/examples/a10_kinetic_example/gpec.toml b/examples/a10_kinetic_example/gpec.toml index 5b66712d7..109d32416 100644 --- a/examples/a10_kinetic_example/gpec.toml +++ b/examples/a10_kinetic_example/gpec.toml @@ -30,11 +30,10 @@ etol = 1e-7 shape = "nowall" [ForceFreeStates] -bal_flag = false +local_stability_flag = true mat_flag = true ode_flag = true vac_flag = true -mer_flag = true # sas_flag=f in Fortran → no truncation via dmlim; Julia mirrors with # set_psilim_via_dmlim=false and psiedge=1.0 (full integration to psihigh). diff --git a/test/test_data/regression_solovev_kinetic_calculated/gpec.toml b/test/test_data/regression_solovev_kinetic_calculated/gpec.toml index 6f8dd25f5..df8355e0a 100644 --- a/test/test_data/regression_solovev_kinetic_calculated/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_calculated/gpec.toml @@ -25,11 +25,10 @@ tw = 0.05 # Sharpness of wall corners (try 0.05 as equal_arc_wall = true # Equal arc length distribution of nodes on wall [ForceFreeStates] -bal_flag = false # Ideal MHD ballooning criterion for short wavelengths +local_stability_flag = true # Evaluate local D_I (Mercier) and ballooning stability across ψ mat_flag = false # Construct coefficient matrices for diagnostic purposes ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes -mer_flag = true # Evaluate the Mercier criterian psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... From 6a3b6409fda24643c44d7af7d3f01a09eb13f609 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Wed, 10 Jun 2026 16:42:25 -0400 Subject: [PATCH 014/135] ForceFreeStates - BUG FIX - Restore resistive interchange D_R; disambiguate ballooning Delta' Restore the resistive interchange D_R (locstab/dr), which became empty when the standalone Mercier.jl was folded into the rewritten Bal.jl. resistive_interchange() recomputes D_R = D_I + (H - 1/2)^2 from flux-surface averages (the former mercier_scan! formulation) and fills locstab column 2; write_outputs_to_HDF5 emits it under local_stability_flag like locstab/di. Rename the ballooning output locstab/delta_prime -> locstab/ballooning_Delta_prime to avoid colliding with the Riccati tearing Delta' (singular_coupling/delta_prime), and drop the always-empty locstab/ca1. NOTE for reviewer/author: locstab/di reports det(d0bar) from the new approach, while D_R is built on the surface-average D_I (old Mercier route). The numerical equivalence of those two D_I values should be confirmed against the Bal derivation. Co-Authored-By: Claude Opus 4.8 --- src/ForceFreeStates/Bal.jl | 74 ++++++++++++++++++++++++-- src/GeneralizedPerturbedEquilibrium.jl | 18 ++++--- 2 files changed, 82 insertions(+), 10 deletions(-) diff --git a/src/ForceFreeStates/Bal.jl b/src/ForceFreeStates/Bal.jl index 4b5f6af56..1437aa956 100644 --- a/src/ForceFreeStates/Bal.jl +++ b/src/ForceFreeStates/Bal.jl @@ -20,7 +20,8 @@ to compute Delta Prime. This function modifies `locstab_fs` in place with: - - Column 1: `det(d0bar) * ψ` + - Column 1: `det(d0bar) * ψ` (Mercier interchange `D_I`) + - Column 2: resistive interchange `D_R * ψ` (see [`resistive_interchange`](@ref)) - Column 4: Delta Prime (Δ') """ function compute_ballooning_stability!( @@ -40,8 +41,10 @@ function compute_ballooning_stability!( # Loop over flux surfaces for flux_surface_index in 1:num_psi + psi = plasma_eq.profiles.xs[flux_surface_index] coeff_data = prepare_ballooning_coefficients(flux_surface_index, plasma_eq; theta_k=theta_k) - locstab_fs[flux_surface_index, 1] = coeff_data.di * plasma_eq.profiles.xs[flux_surface_index] + locstab_fs[flux_surface_index, 1] = coeff_data.di * psi + locstab_fs[flux_surface_index, 2] = resistive_interchange(flux_surface_index, plasma_eq).dr * psi if compute_delta_prime && plasma_eq.profiles.xs[flux_surface_index] <= 1.0 result = integrate_ballooning_ode( @@ -58,6 +61,71 @@ function compute_ballooning_stability!( end +""" + resistive_interchange(flux_surface_index, plasma_eq) + +Resistive interchange criterion `D_R = D_I + (H - 1/2)²` at a single flux surface +[Glasser-Greene-Johnson; Glasser Phys. Plasmas 23, 112506 (2016)]. The Mercier +`D_I` and the intermediate `H` are formed from flux-surface averages of the field +and metric quantities. Returns a NamedTuple `(di, dr, h)`, all unscaled by ψ. + +Note: this evaluates the Mercier `D_I` from the surface-average formulation, which +is a distinct numerical route from the `det(d0bar)` value reported as `locstab/di` +by [`compute_ballooning_stability!`](@ref). +""" +function resistive_interchange(flux_surface_index::Int, plasma_eq::Equilibrium.PlasmaEquilibrium) + profiles = plasma_eq.profiles + ntheta = length(plasma_eq.rzphi_ys) + ff_fs = zeros(ntheta, 5) + + psi = profiles.xs[flux_surface_index] + twopif = profiles.F_spline.y[flux_surface_index] + p1 = profiles.P_deriv(psi) + v1 = profiles.dVdpsi_spline.y[flux_surface_index] + v2 = profiles.dVdpsi_deriv(psi) + q = profiles.q_spline.y[flux_surface_index] + q1 = profiles.q_deriv(psi) + chi1 = 2π * plasma_eq.psio + + for itheta in 1:ntheta + theta = plasma_eq.rzphi_ys[itheta] + + f1 = plasma_eq.rzphi_rsquared.nodal_derivs.partials[1, flux_surface_index, itheta] + f2 = plasma_eq.rzphi_offset.nodal_derivs.partials[1, flux_surface_index, itheta] + jac = plasma_eq.rzphi_jac.nodal_derivs.partials[1, flux_surface_index, itheta] + fy1 = plasma_eq.rzphi_rsquared.nodal_derivs.partials[3, flux_surface_index, itheta] + fy2 = plasma_eq.rzphi_offset.nodal_derivs.partials[3, flux_surface_index, itheta] + fy3 = plasma_eq.rzphi_nu.nodal_derivs.partials[3, flux_surface_index, itheta] + + rfac = sqrt(f1) + eta = 2π * (theta + f2) + r = plasma_eq.ro + rfac * cos(eta) + + v21 = fy1 / (2.0 * rfac * jac) + v22 = (1.0 + fy2) * 2π * rfac / jac + v23 = fy3 * r / jac + v33 = 2π * r / jac + bsq = chi1^2 * (v21^2 + v22^2 + (v23 + q * v33)^2) + dpsisq = (2π * r)^2 * (v21^2 + v22^2) + + ff_fs[itheta, 1] = bsq / dpsisq + ff_fs[itheta, 2] = 1.0 / dpsisq + ff_fs[itheta, 3] = 1.0 / bsq + ff_fs[itheta, 4] = 1.0 / (bsq * dpsisq) + ff_fs[itheta, 5] = bsq + @views ff_fs[itheta, :] .*= jac / v1 + end + + avg = FastInterpolations.integrate(cubic_interp(plasma_eq.rzphi_ys, Series(ff_fs); bc=PeriodicBC())) + + term = twopif * p1 * v1 / (q1 * chi1^3) * avg[2] + di = -0.25 + term * (1 - term) + + p1 * (v1 / (q1 * chi1^2))^2 * avg[1] * + (p1 * (avg[3] + (twopif / chi1)^2 * avg[4]) - v2 / v1) + h = twopif * p1 * v1 / (q1 * chi1^3) * (avg[2] - avg[1] / avg[5]) + return (di=di, dr=di + (h - 0.5)^2, h=h) +end + @@ -722,4 +790,4 @@ function compute_ballooning_ode!(derivatives, solution, parameters, poloidal_ang derivatives[1] = solution[2] / f derivatives[2] = g * solution[1] -end \ No newline at end of file +end diff --git a/src/GeneralizedPerturbedEquilibrium.jl b/src/GeneralizedPerturbedEquilibrium.jl index 4ba26a6a0..adcca1363 100755 --- a/src/GeneralizedPerturbedEquilibrium.jl +++ b/src/GeneralizedPerturbedEquilibrium.jl @@ -248,14 +248,15 @@ function main(args::Vector{String}=String[]; dd::Union{IMASdd.dd,Nothing}=nothin # stability does not need kinetic_profiles, but the post-PE block always # does, so we load whenever a [KineticForces] section is present or the # stability path requests the calculated source. - kf_ctrl = haskey(inputs, "KineticForces") ? + kf_ctrl = + haskey(inputs, "KineticForces") ? KineticForces.KineticForcesControl(; (Symbol(k) => v for (k, v) in inputs["KineticForces"])...) : KineticForces.KineticForcesControl() kinetic_profiles = nothing needs_kinetic_profiles = haskey(inputs, "KineticForces") || - (ctrl.kinetic_factor > 0 && ctrl.kinetic_source == "calculated") + (ctrl.kinetic_factor > 0 && ctrl.kinetic_source == "calculated") if needs_kinetic_profiles kinetic_file = joinpath(intr.dir_path, kf_ctrl.kinetic_file) kinetic_profiles = Equilibrium.load_kinetic_profiles( @@ -535,18 +536,21 @@ function write_outputs_to_HDF5( out_h5["splines/rzphi/nu"] = equil.rzphi_nu.nodal_derivs.partials[1, :, :] out_h5["splines/rzphi/jac"] = equil.rzphi_jac.nodal_derivs.partials[1, :, :] - # Write local stability data; always write all entries, using empty arrays when not computed + # Write local stability data; always write all entries, using empty arrays when not computed. + # locstab/di = Mercier D_I (det(d0bar)); locstab/dr = resistive interchange D_R; + # locstab/ballooning_Delta_prime = high-n ballooning Δ' (distinct from the Riccati + # tearing Δ' under perturbed_equilibrium/singular_coupling/delta_prime). if ctrl.local_stability_flag locstab_xs = intr.locstab.cache.x out_h5["locstab/di"] = intr.locstab.y[:, 1] ./ locstab_xs + out_h5["locstab/dr"] = intr.locstab.y[:, 2] ./ locstab_xs else out_h5["locstab/di"] = Float64[] + out_h5["locstab/dr"] = Float64[] end - out_h5["locstab/dr"] = Float64[] out_h5["singular/di0"] = (ctrl.local_stability_flag && !isempty(intr.sing)) ? [intr.locstab(sing.psifac)[1] / sing.psifac for sing in intr.sing] : Float64[] - out_h5["locstab/delta_prime"] = ctrl.local_stability_flag ? intr.locstab.y[:, 4] : Float64[] - out_h5["locstab/ca1"] = Float64[] + out_h5["locstab/ballooning_Delta_prime"] = ctrl.local_stability_flag ? intr.locstab.y[:, 4] : Float64[] # Write integration data # TODO: technically this should only be written if ode_flag is true, but that's going to get deprecated eventually @@ -618,7 +622,7 @@ function write_outputs_to_HDF5( out_h5["singular/kinetic/scan_psi"] = intr.kinsing_scan_psi out_h5["singular/kinetic/scan_cond"] = intr.kinsing_scan_cond out_h5["singular/kinetic/scan_threshold"] = intr.kinsing_scan_threshold - + # Write free-boundary stability data. Power-normalized flux (Φ-space) is the # default — Jacobian-invariant. ξ-space counterparts sit under # FreeBoundaryStability/XiNorm/ for Fortran benchmarking. From b7a5f16c1707c5c37a8b6e2b66352321dd45476a Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Wed, 10 Jun 2026 16:42:25 -0400 Subject: [PATCH 015/135] ForceFreeStates - IMPROVEMENT - Port s-alpha/Delta'/D_I plots into analyze_example.jl Add a local-stability section to the DIIID analyze script that reproduces the deleted notebook: s and alpha profiles, Mercier D_I and ballooning Delta' profiles, and 2D s-alpha (p', q') maps of Delta' and D_I with their zero contours, via salpha_reference, compute_ballooning_stability! and scan_delta_prime_map. Co-Authored-By: Claude Opus 4.8 --- .../analyze_example.jl | 184 +++++++++++++++++- 1 file changed, 180 insertions(+), 4 deletions(-) diff --git a/examples/DIIID-like_ideal_example/analyze_example.jl b/examples/DIIID-like_ideal_example/analyze_example.jl index 4c5a8eb7c..2b8af279f 100644 --- a/examples/DIIID-like_ideal_example/analyze_example.jl +++ b/examples/DIIID-like_ideal_example/analyze_example.jl @@ -2,6 +2,8 @@ using Pkg; Pkg.activate(joinpath(@__DIR__, "../..")) using GeneralizedPerturbedEquilibrium, Plots using GeneralizedPerturbedEquilibrium: Analysis +using GeneralizedPerturbedEquilibrium: Equilibrium, ForceFreeStates +using LaTeXStrings, TOML isinteractive() ? plotlyjs() : gr() h5path = joinpath(@__DIR__, "gpec.h5") @@ -9,8 +11,182 @@ h5path = joinpath(@__DIR__, "gpec.h5") # Summary plots p_eq = Analysis.Equilibrium.plot_equilibrium_summary(h5path) p_ffs = Analysis.ForceFreeStates.plot_ffs_summary(h5path) -p_pe = Analysis.PerturbedEquilibrium.plot_perturbed_equilibrium_summary(h5path) +p_pe = Analysis.PerturbedEquilibrium.plot_perturbed_equilibrium_summary(h5path) -display(p_eq); Plots.savefig(p_eq, joinpath(@__DIR__, "equilibrium_summary.png")) -display(p_ffs); Plots.savefig(p_ffs, joinpath(@__DIR__, "ffs_summary.png")) -display(p_pe); Plots.savefig(p_pe, joinpath(@__DIR__, "pe_summary.png")) \ No newline at end of file +display(p_eq); +Plots.savefig(p_eq, joinpath(@__DIR__, "equilibrium_summary.png")) +display(p_ffs); +Plots.savefig(p_ffs, joinpath(@__DIR__, "ffs_summary.png")) +display(p_pe); +Plots.savefig(p_pe, joinpath(@__DIR__, "pe_summary.png")) + +# ---------------------------------------------------------------------- +# Local stability: s-alpha profiles, D_I / ballooning Δ', and 2D s-alpha +# maps (ported from the former Bal_salpha_delta_di_summary notebook). +# These recompute directly from the equilibrium via the Bal.jl helpers +# rather than reading gpec.h5, so the s-alpha scan can perturb (p', q'). +# ---------------------------------------------------------------------- +eq_config = Equilibrium.EquilibriumConfig(TOML.parsefile(joinpath(@__DIR__, "gpec.toml"))["Equilibrium"], @__DIR__) +equil = Equilibrium.setup_equilibrium(eq_config) +psi_norm = Vector(equil.profiles.xs) + +# s and alpha profiles vs normalized flux +s_profile = fill(NaN, length(psi_norm)) +alpha_profile = fill(NaN, length(psi_norm)) +for i in eachindex(psi_norm) + try + ref = ForceFreeStates.salpha_reference(i, equil) + s_profile[i] = ref.s_ref + alpha_profile[i] = ref.alpha_ref + catch err + @warn "s-alpha reference failed" i psi = psi_norm[i] exception = (err, catch_backtrace()) + end +end + +s_mask = isfinite.(s_profile) +alpha_mask = isfinite.(alpha_profile) +p_s = plot( + psi_norm[s_mask], + s_profile[s_mask]; + xlabel="Norm. Poloidal Flux", + ylabel="s", + title="Magnetic shear s", + label="s", + lw=2, + framestyle=:box, + left_margin=10Plots.mm, + bottom_margin=5Plots.mm +) +p_alpha = plot( + psi_norm[alpha_mask], + alpha_profile[alpha_mask]; + xlabel="Norm. Poloidal Flux", + ylabel=L"\alpha", + title="Pressure gradient α", + label=L"\alpha", + lw=2, + framestyle=:box, + left_margin=10Plots.mm, + bottom_margin=5Plots.mm +) +p_salpha = plot(p_s, p_alpha; layout=(1, 2), size=(1100, 420)) +display(p_salpha) +salpha_path = joinpath(@__DIR__, "salpha_profiles.png") +Plots.savefig(p_salpha, salpha_path) + +# D_I (Mercier) and ballooning Δ' profiles +locstab_fs = zeros(length(psi_norm), 5) +ctrl = ForceFreeStates.ForceFreeStatesControl(; verbose=false) +ForceFreeStates.compute_ballooning_stability!(ctrl, locstab_fs, equil; compute_delta_prime=true) + +delta_prime = Vector(locstab_fs[:, 4]) +di_profile = fill(NaN, length(psi_norm)) +psi_mask = abs.(psi_norm) .> eps(Float64) +di_profile[psi_mask] .= locstab_fs[psi_mask, 1] ./ psi_norm[psi_mask] + +delta_mask = isfinite.(delta_prime) +di_mask = isfinite.(di_profile) +p_delta = plot( + psi_norm[delta_mask], + delta_prime[delta_mask]; + xlabel="Norm. Poloidal Flux", + ylabel=L"\Delta'", + title="Ballooning Δ'", + label=L"\Delta'", + lw=2, + framestyle=:box, + left_margin=10Plots.mm, + bottom_margin=5Plots.mm +) +p_di = plot( + psi_norm[di_mask], + di_profile[di_mask]; + xlabel="Norm. Poloidal Flux", + ylabel=L"D_I", + title="Mercier D_I", + label=L"D_I", + lw=2, + framestyle=:box, + left_margin=10Plots.mm, + bottom_margin=5Plots.mm +) +hline!(p_di, [0.0]; linestyle=:dash, color=:black, label=nothing) +p_localstab = plot(p_delta, p_di; layout=(1, 2), size=(1100, 420)) +display(p_localstab) +localstab_path = joinpath(@__DIR__, "delta_di_profiles.png") +Plots.savefig(p_localstab, localstab_path) + +# 2D s-alpha maps of Δ' and D_I at a near-edge surface, with zero contours +psi_target = 0.974 +psi_idx_scan = argmin(abs.(psi_norm .- psi_target)) +s_scales = collect(range(-5.0, 5.0; length=30)) +alpha_scales = collect(range(-5.0, 5.0; length=30)) +scan = ForceFreeStates.scan_delta_prime_map(psi_idx_scan, equil; theta_k=0.0, s_scales=s_scales, alpha_scales=alpha_scales) + +scan_qprime = scan.dqdpsi_ref .* scan.s_scales +scan_pprime = scan.pprime_ref .* scan.alpha_scales +qorder = sortperm(scan_qprime) +porder = sortperm(scan_pprime) +scan_qprime = scan_qprime[qorder] +scan_pprime = scan_pprime[porder] +scan_delta = scan.delta_prime[qorder, porder] +scan_di = scan.di_values[qorder, porder] + +function symmetric_clims(z) + finite_vals = vec(z)[isfinite.(vec(z))] + maxabs = isempty(finite_vals) ? 1.0 : maximum(abs.(finite_vals)) + maxabs = max(maxabs, eps(Float64)) + return (-maxabs, maxabs) +end + +p_map_delta = contourf( + scan_pprime, + scan_qprime, + scan_delta; + c=cgrad([:blue, :white, :red]), + clims=symmetric_clims(scan_delta), + xlabel=L"p_{\psi}", + ylabel=L"q_{\psi}", + title=L"\Delta'", + levels=41, + framestyle=:box, + left_margin=10Plots.mm, + bottom_margin=5Plots.mm +) +contour!(p_map_delta, scan_pprime, scan_qprime, scan_delta; levels=[0.0], color=:black, linewidth=2) +scatter!(p_map_delta, [scan.reference.pprime_ref], [scan.reference.qprime_ref]; color=:green, marker=:star5, ms=7, label="equilibrium") +p_map_di = contourf( + scan_pprime, + scan_qprime, + scan_di; + c=cgrad([:blue, :white, :red]), + clims=symmetric_clims(scan_di), + xlabel=L"p_{\psi}", + ylabel=L"q_{\psi}", + title=L"D_I", + levels=41, + framestyle=:box, + left_margin=10Plots.mm, + bottom_margin=5Plots.mm +) +contour!(p_map_di, scan_pprime, scan_qprime, scan_di; levels=[0.0], color=:black, linewidth=2) +scatter!(p_map_di, [scan.reference.pprime_ref], [scan.reference.qprime_ref]; color=:green, marker=:star5, ms=7, label="equilibrium") +p_maps = plot(p_map_delta, p_map_di; layout=(1, 2), size=(1150, 460)) +display(p_maps) +maps_path = joinpath(@__DIR__, "salpha_maps.png") +Plots.savefig(p_maps, maps_path) + +# Overlay of Δ'=0 (ballooning) and D_I=0 (Mercier) stability boundaries +p_zero = plot(; xlabel=L"p_{\psi}", ylabel=L"q_{\psi}", title="Ballooning / Mercier stability boundaries", framestyle=:box, left_margin=10Plots.mm, bottom_margin=5Plots.mm) +contour!(p_zero, scan_pprime, scan_qprime, scan_delta; levels=[0.0], color=:blue, linewidth=3, colorbar=false) +contour!(p_zero, scan_pprime, scan_qprime, scan_di; levels=[0.0], color=:red, linewidth=3, linestyle=:dash, colorbar=false) +scatter!(p_zero, [scan.reference.pprime_ref], [scan.reference.qprime_ref]; color=:green, marker=:star5, ms=8, label="equilibrium") +display(p_zero) +zero_path = joinpath(@__DIR__, "salpha_zero_contours.png") +Plots.savefig(p_zero, zero_path) + +println("Saved figures:") +for p in + (joinpath(@__DIR__, "equilibrium_summary.png"), joinpath(@__DIR__, "ffs_summary.png"), joinpath(@__DIR__, "pe_summary.png"), salpha_path, localstab_path, maps_path, zero_path) + println(" ", p) +end From b619ea6212a267f7ecd7f4a766366cc9cb0c7bf6 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Wed, 10 Jun 2026 16:42:25 -0400 Subject: [PATCH 016/135] ForceFreeStates - DOCS - Add user-level local stability (Mercier/ballooning/s-alpha) section Document the local_stability_flag scan and the locstab/ HDF5 keys (di, dr, ballooning_Delta_prime), the s-alpha diagram, and the distinction between the local ballooning Delta' and the resistive tearing Delta'. Co-Authored-By: Claude Opus 4.8 --- docs/src/stability.md | 41 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 41 insertions(+) diff --git a/docs/src/stability.md b/docs/src/stability.md index b294125a3..bec8c6344 100644 --- a/docs/src/stability.md +++ b/docs/src/stability.md @@ -136,6 +136,44 @@ use_parallel = true The residual ~2% gap comes from the different crossing convention (Riccati-style direct zeroing vs GR), not from ODE tolerance; it is present in both 1-thread and 4-thread runs. +## Local stability: Mercier and ballooning (s–α) + +Setting `local_stability_flag = true` in `[ForceFreeStates]` runs a local high-``n`` +stability scan over every flux surface, in addition to the global ideal analysis above. +Three diagnostics are produced and stored under the `locstab/` HDF5 group, each a profile +in normalized poloidal flux ``\psi``: + +- **Mercier criterion ``D_I``** (`locstab/di`) — the ideal interchange criterion. A surface + is Mercier-unstable where ``D_I > 0``. It is evaluated from the ``\det(\bar{d}_0)`` of the + integrated local-mode matrix. +- **Resistive interchange ``D_R``** (`locstab/dr`) — the Glasser–Greene–Johnson resistive + interchange criterion ``D_R = D_I + (H - 1/2)^2``, formed from flux-surface averages of + the field and metric quantities. ``D_R > 0`` indicates resistive interchange instability. +- **Ballooning ``\Delta'``** (`locstab/ballooning_Delta_prime`) — the high-``n`` ballooning + stability index, obtained by integrating the ballooning equation along the field line and + taking the jump in the logarithmic derivative of the solution between the two asymptotic + ends. + +!!! note "Two different Δ' quantities" + `locstab/ballooning_Delta_prime` is the **local high-``n`` ballooning** index and is + distinct from the **resistive tearing** ``\Delta'`` described in the next section, which + is written under `singular/` and `perturbed_equilibrium/singular_coupling/delta_prime`. + They measure different instabilities; do not confuse them. + +### s–α diagram + +The local criteria can be mapped over a two-parameter ``(p', q')`` scan at a single flux +surface — the classic s–α (shear–pressure) stability diagram. For a chosen surface the +pressure gradient ``p'`` and shear ``q'`` are scaled away from their equilibrium values, and +``\Delta'`` and ``D_I`` are recomputed on the resulting grid. The ``\Delta' = 0`` and +``D_I = 0`` contours bound the ballooning- and Mercier-stable regions, with the equilibrium +operating point marked inside. + +The example script `examples/DIIID-like_ideal_example/analyze_example.jl` demonstrates the +full workflow: it plots the ``s`` and ``\alpha`` profiles, the ``D_I`` and ballooning +``\Delta'`` profiles, and the 2-D s–α maps with their zero contours, using +`salpha_reference`, `compute_ballooning_stability!`, and `scan_delta_prime_map`. + ## Δ' tearing stability parameter ### Per-surface Δ' (`delta_prime`) @@ -212,6 +250,9 @@ numsteps_init = 200 # initial step budget per chunk numunorms_init = 50 # renorm checkpoint budget reltol = 1e-6 # ODE relative tolerance +# Local stability +local_stability_flag = false # scan Mercier D_I, resistive D_R, and ballooning Δ' over ψ + # Output verbose = true write_outputs_to_HDF5 = true From 65c4c961190101543ee749e3cdff83db051fe0f3 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Wed, 10 Jun 2026 21:38:18 -0400 Subject: [PATCH 017/135] DOCS - NEW FEATURE - Add field-amplitude and units conventions to the Conventions Reference Folds the PerturbedEquilibrium unit-convention documentation (previously the abandoned PR #261) into the conventions reference page and expands its scope: - Rename sign_conventions.md -> conventions.md; retitle "Conventions Reference" and update the nav label, since the page now covers sign, coordinate, and field-amplitude conventions. - Add a "Field Amplitudes and Units" section clarifying the two amplitudes users most often confuse: the resonant field (resonant flux / scalar surface area) and the power-normalized field (sqrt-area-weighted normal field / scalar sqrt-area), both in tesla by scalar-area normalization, with a compact units table for the reported quantities. - Add Pharr (2026), "Coordinate-invariant flux-surface Fourier analysis in tokamaks," to docs/resources and the Citations page as the reference for the coordinate-invariant area weightings. Documentation only; no source or calculations changed. Co-Authored-By: Claude Opus 4.8 (1M context) --- docs/make.jl | 2 +- ...x-surface-Fourier-analysis-in-tokamaks.pdf | Bin 0 -> 560315 bytes docs/src/citations.md | 8 +++ .../{sign_conventions.md => conventions.md} | 62 +++++++++++++++++- 4 files changed, 68 insertions(+), 4 deletions(-) create mode 100644 docs/resources/2026-Pharr-Coordinate-invariant_flux-surface-Fourier-analysis-in-tokamaks.pdf rename docs/src/{sign_conventions.md => conventions.md} (79%) diff --git a/docs/make.jl b/docs/make.jl index 3791fd166..85fcf930d 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -24,7 +24,7 @@ makedocs(; "Home" => "index.md", "Setup" => "set_up.md", "Workflow" => "workflow.md", - "Sign Conventions" => "sign_conventions.md", + "Conventions Reference" => "conventions.md", "API Reference" => [ "Vacuum" => "vacuum.md", "Equilibrium" => "equilibrium.md", diff --git a/docs/resources/2026-Pharr-Coordinate-invariant_flux-surface-Fourier-analysis-in-tokamaks.pdf 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self-consistent plasma response calculation. Derives the permeab --- +> M. Pharr, E. Bursch, N. C. Logan, P. Lunia, J.-K. Park, and C. Paz-Soldan, "Coordinate-invariant flux-surface Fourier analysis in tokamaks," +> Preprint (2026). +> [arXiv:2606.02901](https://arxiv.org/abs/2606.02901) + +Establishes the area weightings that make flux-surface Fourier spectra of perturbed fields coordinate-invariant. Shows that normalizing the resonant flux by the scalar surface area (the resonant field) and the square-root-area-weighted normal field by the scalar square-root area (the power-normalized field) leaves both quantities in tesla and independent of the magnetic working coordinate. The reference for the field-amplitude conventions reported by the `PerturbedEquilibrium` module — see the [Conventions Reference](conventions.md). + +--- + ## InnerLayer Module > A. H. Glasser, Z. R. Wang, and J.-K. Park, "Computation of resistive instabilities by matched asymptotic expansions," diff --git a/docs/src/sign_conventions.md b/docs/src/conventions.md similarity index 79% rename from docs/src/sign_conventions.md rename to docs/src/conventions.md index 0156e9ef4..38677ac02 100644 --- a/docs/src/sign_conventions.md +++ b/docs/src/conventions.md @@ -1,7 +1,7 @@ -# Sign Conventions Reference +# Conventions Reference -This page is a comprehensive reference for the sign and coordinate conventions used -throughout GPEC. Understanding them is essential for interpreting outputs, interfacing with +This page is a comprehensive reference for the sign, coordinate, and field-amplitude conventions +used throughout GPEC. Understanding them is essential for interpreting outputs, interfacing with other codes, and correctly setting up perturbed-equilibrium and kinetic calculations. These conventions are inherited from the Fortran GPEC suite and are GPEC-native: they predate @@ -190,6 +190,62 @@ conjugate is taken. The VACUUM code uses CCW ``\phi`` and downward-outboard ``\theta``. GPEC uses the complex conjugate of RH configurations when interfacing with VACUUM. +## Field Amplitudes and Units + +GPEC reports perturbed magnetic fields as Fourier spectra on flux surfaces. The spectrum of a field +on a surface depends on how the Fourier integrand is weighted by the surface-area element, so a +normalization must be fixed for the reported amplitudes to be meaningful. GPEC normalizes by the +*scalar* area of the surface, which leaves every reported field amplitude in units of **tesla** and +independent of the working (magnetic) coordinate. The two amplitudes users most often confuse — the +**resonant field** and the **power-normalized field** — are both in tesla for this reason. The +coordinate-invariance of these weightings is established in Pharr (2026) (see [Citations](citations.md)). + +### Resonant Field + +The resonant field is the pitch-resonant (``m = nq``) Fourier component of the perturbed flux at a +rational surface, divided by the **scalar area** ``A^r`` of that surface: + +```math +b^r = \frac{\Phi^r}{A^r} \qquad [\mathrm{T}]. +``` + +Dividing the resonant flux ``\Phi^r`` by the surface area turns it into a genuine field amplitude +that is invariant under changes of the poloidal-angle (working) coordinate. This is the quantity +reported as `resonant_flux`. + +### Power-Normalized Field + +The power-normalized field is the Fourier spectrum of the square-root-area-weighted normal field +``\sqrt{\mathcal{J}\,|\nabla\psi|}\,(\mathbf{b}\cdot\hat{\mathbf{n}})``, divided by the scalar +``\sqrt{A}`` of the surface: + +```math +\tilde{b}_m = \frac{1}{\sqrt{A}}\oint \sqrt{\mathcal{J}\,|\nabla\psi|}\; +(\mathbf{b}\cdot\hat{\mathbf{n}})\, e^{-i m\theta}\, d\theta \qquad [\mathrm{T}]. +``` + +The name comes from Parseval's theorem: the sum of its squared mode amplitudes equals the +area-averaged squared normal field — the surface-averaged field "power", + +```math +\sum_m |\tilde{b}_m|^2 = \big\langle (\mathbf{b}\cdot\hat{\mathbf{n}})^2 \big\rangle. +``` + +The ``\sqrt{A}`` weighting is the unique one for which the spectrum transforms unitarily between +working coordinates, so the power-normalized amplitudes — and quantities derived from them, such as +the singular values of the resonant coupling matrix — are coordinate-invariant. + +### Units of Reported Quantities + +| Quantity | Meaning | Unit | +|----------|---------|------| +| `resonant_flux` | resonant field ``\Phi^r/A^r`` at each rational surface | T | +| power-normalized field | ``\sqrt{A}``-weighted normal-field spectrum (above) | T | +| `delta_prime` (``\Delta'``) | tearing-stability index, normalized-flux convention | dimensionless | +| `island_half_width` | penetrated magnetic-island half-width | ``\sqrt{\psi_N}`` (root normalized poloidal flux) | +| `chirikov_parameter` | island-overlap ratio between neighbouring surfaces | dimensionless | +| `permeability` (``P``) | plasma-response operator ``\Lambda L^{-1}`` | dimensionless | + ## Rotation Velocity Conventions (KineticForces) The `KineticForces` module (the Julia port of PENTRC) conventions below are used in From 55d64aca52b17f68a1b851f0b92139b115a36d12 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Wed, 10 Jun 2026 21:54:08 -0400 Subject: [PATCH 018/135] DOCS - MINOR - Cleaned up units discussion --- docs/src/conventions.md | 18 ++---------------- 1 file changed, 2 insertions(+), 16 deletions(-) diff --git a/docs/src/conventions.md b/docs/src/conventions.md index 38677ac02..fd50e5f9e 100644 --- a/docs/src/conventions.md +++ b/docs/src/conventions.md @@ -193,12 +193,8 @@ of RH configurations when interfacing with VACUUM. ## Field Amplitudes and Units GPEC reports perturbed magnetic fields as Fourier spectra on flux surfaces. The spectrum of a field -on a surface depends on how the Fourier integrand is weighted by the surface-area element, so a -normalization must be fixed for the reported amplitudes to be meaningful. GPEC normalizes by the -*scalar* area of the surface, which leaves every reported field amplitude in units of **tesla** and -independent of the working (magnetic) coordinate. The two amplitudes users most often confuse — the -**resonant field** and the **power-normalized field** — are both in tesla for this reason. The -coordinate-invariance of these weightings is established in Pharr (2026) (see [Citations](citations.md)). +on a surface depends on in general on the coordinate system used. However, certain resonant components on rational surfaces or the 2-norm of the Fourier coefficient vector on any surface can be made coordinate-independent if the proper area weighting is used within the Fourier decomposition. The +coordinate-invariance of the weightings used in GPEC is established in Pharr (2026) (see [Citations](citations.md)). In each case, we normalize the harmonics by scalar area factors in such a way that the units are always Tesla. ### Resonant Field @@ -235,16 +231,6 @@ The ``\sqrt{A}`` weighting is the unique one for which the spectrum transforms u working coordinates, so the power-normalized amplitudes — and quantities derived from them, such as the singular values of the resonant coupling matrix — are coordinate-invariant. -### Units of Reported Quantities - -| Quantity | Meaning | Unit | -|----------|---------|------| -| `resonant_flux` | resonant field ``\Phi^r/A^r`` at each rational surface | T | -| power-normalized field | ``\sqrt{A}``-weighted normal-field spectrum (above) | T | -| `delta_prime` (``\Delta'``) | tearing-stability index, normalized-flux convention | dimensionless | -| `island_half_width` | penetrated magnetic-island half-width | ``\sqrt{\psi_N}`` (root normalized poloidal flux) | -| `chirikov_parameter` | island-overlap ratio between neighbouring surfaces | dimensionless | -| `permeability` (``P``) | plasma-response operator ``\Lambda L^{-1}`` | dimensionless | ## Rotation Velocity Conventions (KineticForces) From 39e7452b03cbf06b7a8cb8b62d7dc17633c15787 Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Wed, 10 Jun 2026 22:55:26 -0400 Subject: [PATCH 019/135] ForceFreeStates - BUGFIX - wire in gal_tol accidentally left hardcoded --- src/ForceFreeStates/Galerkin/GalerkinAssembly.jl | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl b/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl index a92ecf45e..ff83111a4 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl @@ -304,9 +304,9 @@ function gal_resonant!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, return out end - # QuadGK replaces Fortran's LSODE accumulation. Use a moderate relative tolerance with an - # evaluation cap (analogous to Fortran's gnstep limit) so a near-singular integrand cannot hang. - raw, qerr = quadgk(integrand, x0, x1l; rtol=1e-8, atol=1e-30, maxevals=20000) + # QuadGK replaces Fortran's LSODE accumulation. Match Fortran's LSODE tolerance (gal_tol, 1e-10) + # with an evaluation cap (analogous to Fortran's gnstep limit) so a near-singular integrand cannot hang. + raw, qerr = quadgk(integrand, x0, x1l; rtol=gal_tol, atol=1e-30, maxevals=20000) if get(ENV, "GAL_DEBUG", "") == "1" @info " resonant jsing=$jsing side=$(cell.extra) qerr=$(qerr) res1=$(raw[1]) res2=$(raw[2])" end From d66758b7645ff70a0b84229a70fa6ed744390e24 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Wed, 10 Jun 2026 23:25:40 -0400 Subject: [PATCH 020/135] ForcingTerms - NEW FEATURE - Add HDF5 + analytic coil interfaces (issue #229) Adds modern coil-geometry inputs alongside the legacy ASCII .dat format: - Analytic generators make_pf_hoop, make_window_pane (axis-aligned, two [R,Z] corners), and make_helical (circular-torus), each producing a CoilSet that flows through the existing currents + apply_transforms (shift/tilt) path. - HDF5 coil I/O: group-based, multi-set, content-tolerant (save_coils_to_h5 / load_coils_from_h5_group! / read_coil_h5 / write_coil_h5) plus dat<->h5 converters. One subgroup per set; unrelated content ignored. - CoilSetConfig gains a `source` discriminator (file/pf_hoop/window_pane/helical) and analytic params; load_coil_sets dispatches via _build_raw_coil_set with .h5/.dat resolved by extension. Legacy .dat behavior unchanged. - Rerun snapshot: a coil run stores the geometry used under input/raw_inputs/coils; main_from_h5 gains --coil-source {forcing-modes|coils} so a run can be replayed from gpec.h5 with no original .dat (recomputing the field from stored geometry, optionally against a new equilibrium). - Fixes a pre-existing stale-key bug in runtests_rerun_from_h5.jl (vacuum/et -> FreeBoundaryStability/eigenmode_energies). - Tests for generators, h5 round-trip/multi-set/junk-tolerance, dispatch, and an end-to-end coil snapshot+replay that deletes the .dat between runs. - Docs: forcing_terms.md coil-source + HDF5 schema sections; coil_geometries README HDF5 schema and corrected toroidal-rotation note. Co-Authored-By: Claude Opus 4.8 (1M context) --- docs/src/forcing_terms.md | 73 ++ src/ForcingTerms/CoilGeometry.jl | 625 +++++++++++++++--- src/ForcingTerms/ForcingTerms.jl | 26 +- src/ForcingTerms/coil_geometries/README.md | 22 +- src/GeneralizedPerturbedEquilibrium.jl | 45 +- .../PerturbedEquilibrium.jl | 9 +- .../PerturbedEquilibriumStructs.jl | 74 ++- src/Rerun.jl | 35 +- test/runtests_coils.jl | 290 ++++++-- test/runtests_rerun_from_h5.jl | 100 ++- 10 files changed, 1117 insertions(+), 182 deletions(-) diff --git a/docs/src/forcing_terms.md b/docs/src/forcing_terms.md index 4ec2871a8..56774e2e0 100644 --- a/docs/src/forcing_terms.md +++ b/docs/src/forcing_terms.md @@ -99,6 +99,79 @@ stored in `equil.rzphi_nu`. This matches Fortran's `phi = -helicity*(twopi*czeta For DIII-D (Bt < 0, Ip > 0 → helicity = -1), ν ranges from about -3.4 to +3.4 radians at the boundary — omitting it completely scrambles the Fourier mode decomposition. +### Coil geometry sources + +Each `[[ForcingTerms.coil_set]]` block supplies one coil set from one of several sources, +selected by `source`. Shifts and tilts (`shiftx/y/z`, `tiltx/y/z`, `n_tilt`, ...) apply to +every source, so analytic coils can be perturbed exactly like file-based ones. + +```toml +# Legacy ASCII .dat file (unchanged; resolves to {dat_dir}/{machine}_{name}.dat) +[[ForcingTerms.coil_set]] +name = "il" +currents = [1e4, 1e4, 1e4, 1e4, 1e4, 1e4] + +# Modern HDF5 file; `name` selects one set from a multi-set file (omit if it holds one) +[[ForcingTerms.coil_set]] +source = "file" +h5_file = "/path/to/my_coils.h5" +name = "il" +currents = [1e4, 1e4, 1e4, 1e4, 1e4, 1e4] + +# Analytic PF hoop — a horizontal circle; tilt breaks axisymmetry to give n ≠ 0 forcing +[[ForcingTerms.coil_set]] +source = "pf_hoop" +radius = 1.8 +height = 0.9 +currents = [5e3] +tiltx = [2.0] + +# Analytic window-pane (picture-frame) array; rz_corners are two opposite [R, Z] corners +[[ForcingTerms.coil_set]] +source = "window_pane" +ncoil_gen = 8 +rz_corners = [[2.2, -0.6], [2.2, 0.6]] +gap_fraction = 0.15 +currents = [1e3, -1e3, 1e3, -1e3, 1e3, -1e3, 1e3, -1e3] + +# Analytic helical array on a circular cross-section torus (pitch = m/n) +[[ForcingTerms.coil_set]] +source = "helical" +R0 = 1.7 +a = 0.6 +m_hel = 4 +n_hel = 1 +n_coils = 4 +currents = [1e3, 1e3, 1e3, 1e3] +``` + +### HDF5 coil geometry format + +A coil HDF5 file stores one **subgroup per coil set** under a parent group (default `coils`), +so a single file can hold many sets and the reader ignores any unrelated content elsewhere: + +``` +//x Float64[ncoil, s, nsec] Cartesian metres +//y Float64[ncoil, s, nsec] +//z Float64[ncoil, s, nsec] +//currents Float64[ncoil] (optional) +/ attr nw Float64 (winding multiplier; default 1.0) +``` + +Use `convert_coil_dat_to_h5` / `convert_coil_h5_to_dat` to migrate legacy files, and +`read_coil_h5` / `write_coil_h5` for direct I/O. + +### Rerun snapshot + +When a coil run writes `gpec.h5`, the coil geometry actually used (after shifts/tilts and with +currents) is captured under `input/raw_inputs/coils/`. The run can then be replayed with +`main_from_h5` even if the original `.dat`/`.h5` files are gone: + +- `--coil-source forcing-modes` (default) recomputes the field from the stored TOML coil config + (needs the original geometry files to be present). +- `--coil-source coils` recomputes the field from the geometry stored in `gpec.h5`, so no + original files are required — and the equilibrium may be overridden on replay. + ## Comparison with Fortran GPEC | Quantity | Julia convention | Fortran GPEC convention | diff --git a/src/ForcingTerms/CoilGeometry.jl b/src/ForcingTerms/CoilGeometry.jl index 0484ad7aa..ecc02fc1f 100644 --- a/src/ForcingTerms/CoilGeometry.jl +++ b/src/ForcingTerms/CoilGeometry.jl @@ -19,13 +19,14 @@ const _NOM_THRESHOLD = 1e3 Geometry and current data for a single coil set (one .dat file). ## Fields -- `name`: coil set identifier (e.g. "il", "iu") -- `ncoil`: number of independent conductors -- `s`: sub-systems (strand groups) per conductor -- `nw`: winding multiplier (turns per conductor element) -- `nsec`: number of Cartesian points per strand -- `x`, `y`, `z`: conductor coordinates `[ncoil, s, nsec]` in meters (Cartesian) -- `currents`: current per conductor `[ncoil]` in Amperes + + - `name`: coil set identifier (e.g. "il", "iu") + - `ncoil`: number of independent conductors + - `s`: sub-systems (strand groups) per conductor + - `nw`: winding multiplier (turns per conductor element) + - `nsec`: number of Cartesian points per strand + - `x`, `y`, `z`: conductor coordinates `[ncoil, s, nsec]` in meters (Cartesian) + - `currents`: current per conductor `[ncoil]` in Amperes """ struct CoilSet name::String @@ -44,19 +45,51 @@ end Per-coil-set configuration from a `[[ForcingTerms.coil_set]]` TOML block. +A coil set comes from one of several sources, selected by `source`: + + - `""` or `"file"`: read a geometry file — `.dat` (legacy ASCII) or `.h5` (modern), chosen + by extension. The file path comes from `dat_file`/`h5_file` or the `machine`+`name` convention. + - `"pf_hoop"`: an analytic horizontal circular loop (`radius`, `height`). + - `"window_pane"`: an analytic axis-aligned rectangular picture-frame array + (`ncoil_gen`, `rz_corners`, `gap_fraction`, `phi0`). + - `"helical"`: an analytic helical array on a circular cross-section torus + (`R0`, `a`, `m_hel`, `n_hel`, `theta_lo`, `theta_hi`, `n_coils`, `gap_fraction`, `phi0`, `offset`). + +Shifts/tilts apply to every source (the analytic geometry is built first, then transformed). + ## Fields -- `name`: coil set name; resolves to `{dat_dir}/{machine}_{name}.dat` -- `dat_file`: explicit path to .dat file (overrides `machine`+`name` convention) -- `currents`: current [A] per conductor `[ncoil]`; shorter arrays pad with zeros -- `shiftx`, `shifty`, `shiftz`: per-conductor translation [m] `[ncoil]` -- `tiltx`, `tilty`, `tiltz`: per-conductor tilt in degrees (or meters if `tilt_in_meters`) -- `xnom`, `ynom`, `znom`: explicit rotation center [m]; defaults to arc-length-weighted center of mass -- `n_tilt`: toroidal mode number for tilt/shift modulation; -1 means inherit run's n -- `tilt_in_meters`: interpret tilt as displacement [m] instead of angle [degrees] + + - `name`: coil set name; resolves to `{dat_dir}/{machine}_{name}.dat`, or selects a set by name + from a multi-set `.h5` file + - `source`: coil source discriminator (see above); empty/`"file"` reads a geometry file + - `dat_file`: explicit path to .dat file (overrides `machine`+`name` convention) + - `h5_file`: explicit path to .h5 file (multi-set; `name` selects which set, else the sole set) + - `currents`: current [A] per conductor `[ncoil]`; shorter arrays pad with zeros + - `shiftx`, `shifty`, `shiftz`: per-conductor translation [m] `[ncoil]` + - `tiltx`, `tilty`, `tiltz`: per-conductor tilt in degrees (or meters if `tilt_in_meters`) + - `xnom`, `ynom`, `znom`: explicit rotation center [m]; defaults to arc-length-weighted center of mass + - `n_tilt`: toroidal mode number for tilt/shift modulation; -1 means inherit run's n + - `tilt_in_meters`: interpret tilt as displacement [m] instead of angle [degrees] + +Analytic-source parameters (used only for the matching `source`): + + - `radius`, `height`: PF hoop circle radius and Z height [m] + - `ncoil_gen`: number of generated coils (window-pane / helical arrays) + - `rz_corners`: window-pane cross-section as two opposite `[R, Z]` corners [m] + - `gap_fraction`: toroidal gap between adjacent coils as a fraction of their spacing + - `phi0`: toroidal angle offset of the first generated coil [rad] + - `R0`, `a`: helical torus major radius and minor (circle) radius [m] + - `m_hel`, `n_hel`: helical poloidal/toroidal mode numbers setting the pitch + - `theta_lo`, `theta_hi`: helical poloidal extent [rad] (full turn if `theta_hi-theta_lo == 2π`) + - `n_coils`: number of helical coils in the array + - `offset`: helical coil radial offset from the torus surface [m] + - `nsec_gen`: optional override of the generated point count per coil """ Base.@kwdef struct CoilSetConfig name::String = "" + source::String = "" dat_file::String = "" + h5_file::String = "" currents::Vector{Float64} = Float64[] shiftx::Vector{Float64} = Float64[] shifty::Vector{Float64} = Float64[] @@ -69,6 +102,23 @@ Base.@kwdef struct CoilSetConfig znom::Vector{Float64} = Float64[] n_tilt::Int = -1 tilt_in_meters::Bool = false + + # Analytic-source parameters + radius::Float64 = 0.0 + height::Float64 = 0.0 + ncoil_gen::Int = 0 + rz_corners::Vector{Vector{Float64}} = Vector{Float64}[] + gap_fraction::Float64 = 0.0 + phi0::Float64 = 0.0 + R0::Float64 = 0.0 + a::Float64 = 0.0 + m_hel::Int = 0 + n_hel::Int = 0 + theta_lo::Float64 = 0.0 + theta_hi::Float64 = 2π + n_coils::Int = 0 + offset::Float64 = 0.0 + nsec_gen::Int = 0 end """ @@ -78,11 +128,12 @@ Top-level coil configuration from the `[ForcingTerms]` TOML section when `forcing_data_format = "coil"`. ## Fields -- `machine`: machine name prefix for .dat files (e.g. "d3d") -- `dat_dir`: directory containing .dat files; defaults to bundled `coil_geometries/` -- `mtheta_coil`: poloidal grid resolution for boundary field evaluation (default: 480) -- `nzeta_coil`: toroidal grid resolution; 0 = auto (32 × n) -- `coil_sets`: parsed `[[ForcingTerms.coil_set]]` blocks + + - `machine`: machine name prefix for .dat files (e.g. "d3d") + - `dat_dir`: directory containing .dat files; defaults to bundled `coil_geometries/` + - `mtheta_coil`: poloidal grid resolution for boundary field evaluation (default: 480) + - `nzeta_coil`: toroidal grid resolution; 0 = auto (32 × n) + - `coil_sets`: parsed `[[ForcingTerms.coil_set]]` blocks """ Base.@kwdef struct CoilConfig machine::String = "" @@ -99,37 +150,56 @@ Construct a `CoilConfig` from a `ForcingTermsControl` populated from TOML. """ function CoilConfig(ft_ctrl::ForcingTermsControl) dat_dir = isempty(ft_ctrl.dat_dir) ? - joinpath(@__DIR__, "coil_geometries") : - ft_ctrl.dat_dir + joinpath(@__DIR__, "coil_geometries") : + ft_ctrl.dat_dir coil_sets = CoilSetConfig[_parse_coil_set_config(d) for d in ft_ctrl.coil_sets_raw] return CoilConfig(; - machine = ft_ctrl.machine, - dat_dir = dat_dir, - mtheta_coil = ft_ctrl.mtheta_coil, - nzeta_coil = ft_ctrl.nzeta_coil, - coil_sets = coil_sets, + machine=ft_ctrl.machine, + dat_dir=dat_dir, + mtheta_coil=ft_ctrl.mtheta_coil, + nzeta_coil=ft_ctrl.nzeta_coil, + coil_sets=coil_sets ) end function _parse_coil_set_config(d::Dict{String,Any}) fvec(key) = Float64.(get(d, key, Float64[])) + # rz_corners arrives as a Vector of [R, Z] pairs (TOML array of arrays) + corners = [Float64.(c) for c in get(d, "rz_corners", Vector{Float64}[])] return CoilSetConfig(; - name = get(d, "name", ""), - dat_file = get(d, "dat_file", ""), - currents = fvec("currents"), - shiftx = fvec("shiftx"), - shifty = fvec("shifty"), - shiftz = fvec("shiftz"), - tiltx = fvec("tiltx"), - tilty = fvec("tilty"), - tiltz = fvec("tiltz"), - xnom = fvec("xnom"), - ynom = fvec("ynom"), - znom = fvec("znom"), - n_tilt = get(d, "n_tilt", -1), - tilt_in_meters = get(d, "tilt_in_meters", false), + name=get(d, "name", ""), + source=get(d, "source", ""), + dat_file=get(d, "dat_file", ""), + h5_file=get(d, "h5_file", ""), + currents=fvec("currents"), + shiftx=fvec("shiftx"), + shifty=fvec("shifty"), + shiftz=fvec("shiftz"), + tiltx=fvec("tiltx"), + tilty=fvec("tilty"), + tiltz=fvec("tiltz"), + xnom=fvec("xnom"), + ynom=fvec("ynom"), + znom=fvec("znom"), + n_tilt=get(d, "n_tilt", -1), + tilt_in_meters=get(d, "tilt_in_meters", false), + radius=Float64(get(d, "radius", 0.0)), + height=Float64(get(d, "height", 0.0)), + ncoil_gen=get(d, "ncoil_gen", 0), + rz_corners=corners, + gap_fraction=Float64(get(d, "gap_fraction", 0.0)), + phi0=Float64(get(d, "phi0", 0.0)), + R0=Float64(get(d, "R0", 0.0)), + a=Float64(get(d, "a", 0.0)), + m_hel=get(d, "m_hel", 0), + n_hel=get(d, "n_hel", 0), + theta_lo=Float64(get(d, "theta_lo", 0.0)), + theta_hi=Float64(get(d, "theta_hi", 2π)), + n_coils=get(d, "n_coils", 0), + offset=Float64(get(d, "offset", 0.0)), + nsec_gen=get(d, "nsec_gen", 0) ) end @@ -139,12 +209,14 @@ end Parse an ASCII coil geometry file. Format: + ``` ncoil s nsec nw X₁ Y₁ Z₁ X₂ Y₂ Z₂ ... ``` + Data rows are ordered: for each conductor 1:ncoil, for each sub-system 1:s, read nsec points. Coordinates are Cartesian in meters (lab frame). """ @@ -160,9 +232,9 @@ function read_coil_dat(filepath::String) length(header) >= 4 || error("Invalid header in $filepath: expected 'ncoil s nsec nw'") ncoil = parse(Int, header[1]) - s = parse(Int, header[2]) - nsec = parse(Int, header[3]) - nw = parse(Float64, header[4]) + s = parse(Int, header[2]) + nsec = parse(Int, header[3]) + nw = parse(Float64, header[4]) x = zeros(ncoil, s, nsec) y = zeros(ncoil, s, nsec) @@ -174,7 +246,7 @@ function read_coil_dat(filepath::String) for l in 1:nsec # Skip blank/comment lines between data rows while row <= length(lines) && - (isempty(strip(lines[row])) || startswith(strip(lines[row]), "#")) + (isempty(strip(lines[row])) || startswith(strip(lines[row]), "#")) row += 1 end row > length(lines) && error( @@ -196,6 +268,349 @@ function read_coil_dat(filepath::String) return CoilSet(name, ncoil, s, nw, nsec, x, y, z, zeros(ncoil)) end +""" + make_pf_hoop(; radius, height, nsec=361, name="pf_hoop") -> CoilSet + +Build a single horizontal circular loop (PF hoop) of `radius` [m] centered on the +machine axis at vertical position `height` [m], discretized into `nsec` points. + +The loop is closed (point `nsec` coincides with point 1). A bare hoop is axisymmetric +and produces only an n=0 field; tilting or shifting it (via [`apply_transforms`](@ref)) +breaks axisymmetry to produce n≠0 forcing. Currents are zeroed; `load_coil_sets` fills them. +""" +function make_pf_hoop(; radius::Real, height::Real, nsec::Int=361, name::String="pf_hoop") + radius > 0 || error("make_pf_hoop: radius must be > 0 (got $radius)") + nsec >= 4 || error("make_pf_hoop: nsec must be >= 4 (got $nsec)") + phis = range(0; length=nsec, stop=2π) # closed: phis[end] == phis[1] + 2π + x = reshape([radius * cos(p) for p in phis], 1, 1, nsec) + y = reshape([radius * sin(p) for p in phis], 1, 1, nsec) + z = reshape(fill(Float64(height), nsec), 1, 1, nsec) + return CoilSet(name, 1, 1, 1.0, nsec, x, y, z, zeros(1)) +end + +""" + make_window_pane(; ncoil, rz_corners, gap_fraction=0.0, phi0=0.0, + np_pol=20, np_tor=40, name="window_pane") -> CoilSet + +Build an array of `ncoil` rectangular "picture-frame" (window-pane) saddle coils, evenly +spaced toroidally. The two `[R, Z]` points in `rz_corners` are the endpoints of the poloidal +legs; the legs run along the straight segment between them at the two toroidal edges of the +coil, joined by toroidal arcs at each corner. For a vertical frame give the two corners the +same `R` (legs run in Z); for a horizontal frame give them the same `Z`. Adjacent coils are +separated by a toroidal gap of `gap_fraction` times their angular spacing; the first coil is +centered at toroidal angle `phi0` [rad]. + +Each coil is a closed loop with `np_pol` points per poloidal leg and `np_tor` per toroidal arc. +Currents are zeroed; `load_coil_sets` fills them. +""" +function make_window_pane(; ncoil::Int, rz_corners::AbstractVector, + gap_fraction::Real=0.0, phi0::Real=0.0, + np_pol::Int=20, np_tor::Int=40, name::String="window_pane") + ncoil >= 1 || error("make_window_pane: ncoil must be >= 1 (got $ncoil)") + length(rz_corners) == 2 || error("make_window_pane: rz_corners must hold exactly two [R, Z] corners") + 0.0 <= gap_fraction < 1.0 || error("make_window_pane: gap_fraction must be in [0, 1) (got $gap_fraction)") + np_pol >= 2 && np_tor >= 2 || error("make_window_pane: np_pol and np_tor must be >= 2") + c1, c2 = rz_corners[1], rz_corners[2] + length(c1) == 2 && length(c2) == 2 || error("make_window_pane: each rz_corner must be [R, Z]") + R1, Z1 = Float64(c1[1]), Float64(c1[2]) + R2, Z2 = Float64(c2[1]), Float64(c2[2]) + + # Closed loop: leg(np_pol) + arc(np_tor-1) + leg(np_pol-1) + arc(np_tor-1), last == first. + nsec = 2 * np_pol + 2 * np_tor - 3 + x = zeros(ncoil, 1, nsec) + y = zeros(ncoil, 1, nsec) + z = zeros(ncoil, 1, nsec) + + dphi_coil = 2π / ncoil + half_span = (dphi_coil / 2) * (1 - gap_fraction) + lin(lo, hi, n) = range(lo; stop=hi, length=n) + + Rs = Float64[] + phis = Float64[] + Zs = Float64[] + for j in 0:(ncoil-1) + empty!(Rs) + empty!(phis) + empty!(Zs) + phi_c = phi0 + j * dphi_coil + phi_a = phi_c - half_span + phi_b = phi_c + half_span + + # Poloidal leg corner1 -> corner2 at phi_a (segment in the R-Z plane) + for s in lin(0.0, 1.0, np_pol) + push!(Rs, R1 + s * (R2 - R1)) + push!(phis, phi_a) + push!(Zs, Z1 + s * (Z2 - Z1)) + end + # Toroidal arc at corner2: phi_a -> phi_b (drop shared junction) + for p in lin(phi_a, phi_b, np_tor)[2:end] + push!(Rs, R2) + push!(phis, p) + push!(Zs, Z2) + end + # Poloidal leg corner2 -> corner1 at phi_b + for s in lin(0.0, 1.0, np_pol)[2:end] + push!(Rs, R2 + s * (R1 - R2)) + push!(phis, phi_b) + push!(Zs, Z2 + s * (Z1 - Z2)) + end + # Toroidal arc at corner1: phi_b -> phi_a, last point closes onto the first + for p in lin(phi_b, phi_a, np_tor)[2:end] + push!(Rs, R1) + push!(phis, p) + push!(Zs, Z1) + end + + for l in 1:nsec + x[j+1, 1, l] = Rs[l] * cos(phis[l]) + y[j+1, 1, l] = Rs[l] * sin(phis[l]) + z[j+1, 1, l] = Zs[l] + end + end + return CoilSet(name, ncoil, 1, 1.0, nsec, x, y, z, zeros(ncoil)) +end + +""" + make_helical(; R0, a, m, n, theta_lo=0.0, theta_hi=2π, n_coils, + gap_fraction=0.0, phi0=0.0, offset=0.0, npts=720, + name="helical") -> CoilSet + +Build an array of `n_coils` analytic helical coils wound on a circular cross-section torus +of major radius `R0` and minor radius `a` [m], offset radially outward by `offset` [m]. +The helical pitch is set by the poloidal/toroidal mode numbers `m`/`n` via `ζ = (m/n)·θ + φ`. + +For a full poloidal turn (`theta_hi - theta_lo == 2π`) each coil is a single helical strand. +For a partial poloidal range the coil is closed into a loop with two helical legs joined by +toroidal arcs (matching OMFIT `form_helical_array.py`). `npts` sets the strand resolution. +Currents are zeroed; `load_coil_sets` fills them. +""" +function make_helical(; R0::Real, a::Real, m::Int, n::Int, + theta_lo::Real=0.0, theta_hi::Real=2π, n_coils::Int, + gap_fraction::Real=0.0, phi0::Real=0.0, offset::Real=0.0, + npts::Int=720, name::String="helical") + R0 > 0 || error("make_helical: R0 must be > 0 (got $R0)") + a > 0 || error("make_helical: a must be > 0 (got $a)") + n != 0 || error("make_helical: n must be nonzero (sets the helical pitch m/n)") + n_coils >= 1 || error("make_helical: n_coils must be >= 1 (got $n_coils)") + 0.0 <= gap_fraction < 1.0 || error("make_helical: gap_fraction must be in [0, 1) (got $gap_fraction)") + + pitch = m / n + rr = a + offset + surf_R(θ) = R0 + rr * cos(θ) + surf_Z(θ) = rr * sin(θ) + + dphi_coil = 2π / n_coils + coil_width = dphi_coil * (1 - gap_fraction) + full_turn = isapprox(theta_hi - theta_lo, 2π; atol=1e-9) + lin(lo, hi, np) = range(lo; stop=hi, length=np) + + Rs = Float64[] + phis = Float64[] + Zs = Float64[] + strands = Vector{NTuple{3,Vector{Float64}}}(undef, n_coils) + for j in 0:(n_coils-1) + empty!(Rs) + empty!(phis) + empty!(Zs) + phi_c = phi0 + j * dphi_coil + if full_turn + for θ in lin(theta_lo, theta_hi, npts) + ζ = phi_c + pitch * θ + push!(Rs, surf_R(θ)) + push!(phis, ζ) + push!(Zs, surf_Z(θ)) + end + else + np_leg = npts ÷ 2 + np_arc = max(2, npts ÷ 8) + half_w = coil_width / 2 + # Up leg: theta_lo -> theta_hi at toroidal edge -half_w + for θ in lin(theta_lo, theta_hi, np_leg) + ζ = phi_c - half_w + pitch * θ + push!(Rs, surf_R(θ)) + push!(phis, ζ) + push!(Zs, surf_Z(θ)) + end + # Top arc at theta_hi, sweep toroidally by +coil_width + ζ_top = phi_c - half_w + pitch * theta_hi + for ζ in lin(ζ_top, ζ_top + coil_width, np_arc)[2:end] + push!(Rs, surf_R(theta_hi)) + push!(phis, ζ) + push!(Zs, surf_Z(theta_hi)) + end + # Down leg: theta_hi -> theta_lo at toroidal edge +half_w + for θ in lin(theta_hi, theta_lo, np_leg)[2:end] + ζ = phi_c + half_w + pitch * θ + push!(Rs, surf_R(θ)) + push!(phis, ζ) + push!(Zs, surf_Z(θ)) + end + # Bottom arc at theta_lo, sweep back by -coil_width, closing the loop + ζ_bot = phi_c + half_w + pitch * theta_lo + for ζ in lin(ζ_bot, ζ_bot - coil_width, np_arc)[2:end] + push!(Rs, surf_R(theta_lo)) + push!(phis, ζ) + push!(Zs, surf_Z(theta_lo)) + end + end + strands[j+1] = (copy(Rs), copy(phis), copy(Zs)) + end + + nsec = length(strands[1][1]) + x = zeros(n_coils, 1, nsec) + y = zeros(n_coils, 1, nsec) + z = zeros(n_coils, 1, nsec) + for j in 1:n_coils + Rj, Pj, Zj = strands[j] + length(Rj) == nsec || error("make_helical: inconsistent strand length across coils") + for l in 1:nsec + x[j, 1, l] = Rj[l] * cos(Pj[l]) + y[j, 1, l] = Rj[l] * sin(Pj[l]) + z[j, 1, l] = Zj[l] + end + end + return CoilSet(name, n_coils, 1, 1.0, nsec, x, y, z, zeros(n_coils)) +end + +# --------------------------------------------------------------------------- +# HDF5 coil geometry I/O (group-based, multi-set, content-tolerant) +# +# A coil set is stored as one subgroup per set under a parent group, named by the +# set's `name`. This mirrors the open-group idiom of `save_forcing_to_h5` so the +# data can live inside `gpec.h5` (e.g. `input/raw_inputs/coils/`) next to unrelated +# content that the reader silently ignores. +# +# //x Float64[ncoil, s, nsec] (shape gives ncoil, s, nsec) +# //y Float64[ncoil, s, nsec] +# //z Float64[ncoil, s, nsec] +# //currents Float64[ncoil] +# / attr nw Float64 +# --------------------------------------------------------------------------- + +""" + save_coils_to_h5(coil_sets::Vector{CoilSet}, group) + +Write each coil set as a subgroup (named by `CoilSet.name`) under an already-open +HDF5 `group`. Inverse of [`load_coils_from_h5_group!`](@ref). Used by the gpec.h5 +snapshot writer so a coil run can be replayed from the output file alone. +""" +function save_coils_to_h5(coil_sets::Vector{CoilSet}, group) + for cs in coil_sets + g = create_group(group, cs.name) + g["x"] = cs.x + g["y"] = cs.y + g["z"] = cs.z + g["currents"] = cs.currents + HDF5.attrs(g)["nw"] = cs.nw + end + return nothing +end + +""" + load_coils_from_h5_group!(coil_sets::Vector{CoilSet}, group) -> Vector{CoilSet} + +Populate `coil_sets` from an already-open HDF5 `group`, reading every subgroup that +holds `x`/`y`/`z` datasets as a [`CoilSet`](@ref). Any other datasets or subgroups +under `group` are silently ignored, so the group may live inside a larger file +(e.g. `gpec.h5`). Mirror of [`save_coils_to_h5`](@ref). +""" +function load_coils_from_h5_group!(coil_sets::Vector{CoilSet}, group) + empty!(coil_sets) + for key in keys(group) + sub = group[key] + sub isa HDF5.Group || continue + (haskey(sub, "x") && haskey(sub, "y") && haskey(sub, "z")) || continue + x = Float64.(read(sub, "x")) + y = Float64.(read(sub, "y")) + z = Float64.(read(sub, "z")) + size(x) == size(y) == size(z) || error("x/y/z shape mismatch in coil set '$key'") + ndims(x) == 3 || error("coil set '$key' x/y/z must be 3D [ncoil, s, nsec]") + ncoil, s, nsec = size(x) + nw = haskey(HDF5.attrs(sub), "nw") ? Float64(HDF5.attrs(sub)["nw"]) : 1.0 + currents = haskey(sub, "currents") ? Float64.(read(sub, "currents")) : zeros(ncoil) + push!(coil_sets, CoilSet(String(key), ncoil, s, nw, nsec, x, y, z, currents)) + end + return coil_sets +end + +""" + read_coil_h5(filepath; group="coils", set=nothing) -> Vector{CoilSet} + +Read coil sets from an HDF5 file. Coil data is expected under the `group` path; +all coil-set subgroups there are returned (or, if `set` names one, just that set). +Unrelated content elsewhere in the file is ignored. See [`save_coils_to_h5`](@ref) +for the layout. +""" +function read_coil_h5(filepath::String; group::String="coils", set::Union{Nothing,String}=nothing) + isfile(filepath) || error("Coil geometry file not found: $filepath") + return h5open(filepath, "r") do file + haskey(file, group) || error("HDF5 file $filepath has no '$group' group") + coil_sets = CoilSet[] + load_coils_from_h5_group!(coil_sets, file[group]) + isempty(coil_sets) && error("No coil sets found under '$group' in $filepath") + if set !== nothing + idx = findfirst(cs -> cs.name == set, coil_sets) + isnothing(idx) && error("Coil set '$set' not found under '$group' in $filepath") + return CoilSet[coil_sets[idx]] + end + return coil_sets + end +end + +""" + write_coil_h5(filepath, coil_sets; group="coils") + +Write `coil_sets` to a new HDF5 file under the `group` path, one subgroup per set. +Convenience file-level wrapper around [`save_coils_to_h5`](@ref) for export and the +`.dat`→`.h5` converter. +""" +function write_coil_h5(filepath::String, coil_sets::Vector{CoilSet}; group::String="coils") + h5open(filepath, "w") do file + save_coils_to_h5(coil_sets, create_group(file, group)) + end + return filepath +end + +""" + write_coil_dat(filepath, cs::CoilSet) + +Write a single coil set to an ASCII `.dat` file in the legacy Fortran GPEC format +(`ncoil s nsec nw` header, then `ncoil×s×nsec` rows of `X Y Z`). +""" +function write_coil_dat(filepath::String, cs::CoilSet) + open(filepath, "w") do io + println(io, "$(cs.ncoil) $(cs.s) $(cs.nsec) $(cs.nw)") + for j in 1:cs.ncoil, k in 1:cs.s, l in 1:cs.nsec + println(io, " $(cs.x[j,k,l]) $(cs.y[j,k,l]) $(cs.z[j,k,l])") + end + end + return filepath +end + +""" + convert_coil_dat_to_h5(dat_path, h5_path; group="coils") -> String + +Convert a legacy ASCII `.dat` coil file to the modern HDF5 format (single set). +""" +function convert_coil_dat_to_h5(dat_path::String, h5_path::String; group::String="coils") + cs = read_coil_dat(dat_path) + return write_coil_h5(h5_path, CoilSet[cs]; group=group) +end + +""" + convert_coil_h5_to_dat(h5_path, dat_path; group="coils", set=nothing) -> String + +Convert one coil set from an HDF5 file to a legacy ASCII `.dat` file. If the file holds +multiple sets, `set` selects which one by name (required when more than one is present). +""" +function convert_coil_h5_to_dat(h5_path::String, dat_path::String; + group::String="coils", set::Union{Nothing,String}=nothing) + coil_sets = read_coil_h5(h5_path; group=group, set=set) + length(coil_sets) == 1 || + error("convert_coil_h5_to_dat: $h5_path holds $(length(coil_sets)) sets; pass `set` to pick one") + return write_coil_dat(dat_path, coil_sets[1]) +end + """ _arc_length_center(x, y, z) -> (x0, y0, z0) @@ -207,12 +622,14 @@ function _arc_length_center(x::AbstractVector, y::AbstractVector, z::AbstractVec nsec > 1 || return (x[1], y[1], z[1]) total_length = 0.0 - x0 = 0.0; y0 = 0.0; z0 = 0.0 - for l in 1:(nsec - 1) + x0 = 0.0 + y0 = 0.0 + z0 = 0.0 + for l in 1:(nsec-1) xm = (x[l] + x[l+1]) / 2 ym = (y[l] + y[l+1]) / 2 zm = (z[l] + z[l+1]) / 2 - dl = sqrt((x[l+1]-x[l])^2 + (y[l+1]-y[l])^2 + (z[l+1]-z[l])^2) + dl = sqrt((x[l+1] - x[l])^2 + (y[l+1] - y[l])^2 + (z[l+1] - z[l])^2) x0 += xm * dl y0 += ym * dl z0 += zm * dl @@ -228,15 +645,16 @@ end Apply per-conductor shifts and tilts to a coil set, returning a modified copy. Replicates the Fortran `coil_read` shift/tilt logic (coil.F lines 240–340): -- Tilts are rotations around the arc-length-weighted center of mass (unless `xnom/ynom/znom` specified) -- `n_tilt` controls the toroidal periodicity of tilt/shift modulation -- n_tilt = 0: rigid shift only (no tilts applied) -- n_tilt ≥ 1: n-fold modulated perturbations + + - Tilts are rotations around the arc-length-weighted center of mass (unless `xnom/ynom/znom` specified) + - `n_tilt` controls the toroidal periodicity of tilt/shift modulation + - n_tilt = 0: rigid shift only (no tilts applied) + - n_tilt ≥ 1: n-fold modulated perturbations """ function apply_transforms(cs::CoilSet, cfg::CoilSetConfig; n_tilt::Int=1) ncoil = cs.ncoil - s = cs.s - nsec = cs.nsec + s = cs.s + nsec = cs.nsec # Pad config vectors to ncoil length with zeros _pad(v, n) = length(v) >= n ? Float64.(v[1:n]) : vcat(Float64.(v), zeros(n - length(v))) @@ -260,11 +678,15 @@ function apply_transforms(cs::CoilSet, cfg::CoilSetConfig; n_tilt::Int=1) new_z = copy(cs.z) for j in 1:ncoil - sx = shiftx[j]; sy = shifty[j]; sz = shiftz[j] - tx_deg = tiltx_cfg[j]; ty_deg = tilty_cfg[j]; tz_deg = tiltz_cfg[j] + sx = shiftx[j] + sy = shifty[j] + sz = shiftz[j] + tx_deg = tiltx_cfg[j] + ty_deg = tilty_cfg[j] + tz_deg = tiltz_cfg[j] has_shift = abs(sx) + abs(sy) + abs(sz) > 0 - has_tilt = apply_tilt && (abs(tx_deg) + abs(ty_deg) + abs(tz_deg) > 0) + has_tilt = apply_tilt && (abs(tx_deg) + abs(ty_deg) + abs(tz_deg) > 0) (has_shift || has_tilt) || continue for k in 1:s @@ -282,14 +704,15 @@ function apply_transforms(cs::CoilSet, cfg::CoilSetConfig; n_tilt::Int=1) # Compute nominal radius for tilt_in_meters conversion r_nom = if cfg.tilt_in_meters - total_len = 0.0; weighted_r = 0.0 - for l in 1:(nsec - 1) - xm = (cs.x[j,k,l] + cs.x[j,k,l+1]) / 2 - ym = (cs.y[j,k,l] + cs.y[j,k,l+1]) / 2 - dl = sqrt((cs.x[j,k,l+1]-cs.x[j,k,l])^2 + (cs.y[j,k,l+1]-cs.y[j,k,l])^2 + - (cs.z[j,k,l+1]-cs.z[j,k,l])^2) + total_len = 0.0 + weighted_r = 0.0 + for l in 1:(nsec-1) + xm = (cs.x[j, k, l] + cs.x[j, k, l+1]) / 2 + ym = (cs.y[j, k, l] + cs.y[j, k, l+1]) / 2 + dl = sqrt((cs.x[j, k, l+1] - cs.x[j, k, l])^2 + (cs.y[j, k, l+1] - cs.y[j, k, l])^2 + + (cs.z[j, k, l+1] - cs.z[j, k, l])^2) weighted_r += sqrt(xm^2 + ym^2) * dl - total_len += dl + total_len += dl end total_len > 0 ? weighted_r / total_len : 1.0 else @@ -312,12 +735,14 @@ function apply_transforms(cs::CoilSet, cfg::CoilSetConfig; n_tilt::Int=1) zc = cs.z[j, k, l] - z0 # Perturbations start at center offset (so final = original + perturbations) - dx = x0; dy = y0; dz = z0 + dx = x0 + dy = y0 + dz = z0 phi = atan(yc, xc) # Z-tilt: rotate in xy-plane (toroidal clocking) if tiltz != 0 - r = sqrt(xc^2 + yc^2) + r = sqrt(xc^2 + yc^2) ang = atan(yc, xc) + tiltz * cos((n_tilt - 1) * phi) dx += r * cos(ang) - xc dy += r * sin(ang) - yc @@ -325,7 +750,7 @@ function apply_transforms(cs::CoilSet, cfg::CoilSetConfig; n_tilt::Int=1) # Y-tilt: rotate in xz-plane if tilty != 0 - r = sqrt(xc^2 + zc^2) + r = sqrt(xc^2 + zc^2) ang = atan(zc, xc) + tilty * cos((n_tilt - 1) * phi) dx += r * cos(ang) - xc dz += r * sin(ang) - zc @@ -333,7 +758,7 @@ function apply_transforms(cs::CoilSet, cfg::CoilSetConfig; n_tilt::Int=1) # X-tilt: rotate in yz-plane (n=1 is constant, n>1 is sin-modulated) if tiltx != 0 - r = sqrt(zc^2 + yc^2) + r = sqrt(zc^2 + yc^2) ang = if n_tilt == 1 atan(zc, yc) + tiltx else @@ -365,31 +790,72 @@ function apply_transforms(cs::CoilSet, cfg::CoilSetConfig; n_tilt::Int=1) end """ - _resolve_dat_path(cfg::CoilConfig, set_cfg::CoilSetConfig) -> String + _resolve_coil_path(cfg::CoilConfig, set_cfg::CoilSetConfig) -> String -Resolve the path to a coil .dat file. Uses `set_cfg.dat_file` if set, -otherwise constructs `{dat_dir}/{machine}_{name}.dat`. +Resolve the path to a coil geometry file. Prefers `set_cfg.h5_file`, then +`set_cfg.dat_file`, otherwise constructs `{dat_dir}/{machine}_{name}.dat`. """ -function _resolve_dat_path(cfg::CoilConfig, set_cfg::CoilSetConfig) +function _resolve_coil_path(cfg::CoilConfig, set_cfg::CoilSetConfig) + isempty(set_cfg.h5_file) || return set_cfg.h5_file isempty(set_cfg.dat_file) || return set_cfg.dat_file - isempty(set_cfg.name) && error("CoilSetConfig must specify either `name` or `dat_file`") + isempty(set_cfg.name) && + error("CoilSetConfig must specify a `source`, or a `name`/`dat_file`/`h5_file`") prefix = isempty(cfg.machine) ? "" : "$(cfg.machine)_" return joinpath(cfg.dat_dir, "$(prefix)$(set_cfg.name).dat") end +""" + _build_raw_coil_set(cfg::CoilConfig, sc::CoilSetConfig) -> CoilSet + +Produce the un-transformed coil set for a config block, dispatching on `sc.source`: +analytic generators (`pf_hoop`/`window_pane`/`helical`) or a geometry file +(`.h5` → [`read_coil_h5`](@ref), else `.dat` → [`read_coil_dat`](@ref)). Currents and +shifts/tilts are applied by the caller, so all sources share the same downstream path. +""" +function _build_raw_coil_set(cfg::CoilConfig, sc::CoilSetConfig) + if sc.source == "pf_hoop" + kw = sc.nsec_gen > 0 ? (; nsec=sc.nsec_gen) : (;) + return make_pf_hoop(; radius=sc.radius, height=sc.height, + name=isempty(sc.name) ? "pf_hoop" : sc.name, kw...) + elseif sc.source == "window_pane" + return make_window_pane(; ncoil=sc.ncoil_gen, rz_corners=sc.rz_corners, + gap_fraction=sc.gap_fraction, phi0=sc.phi0, + name=isempty(sc.name) ? "window_pane" : sc.name) + elseif sc.source == "helical" + kw = sc.nsec_gen > 0 ? (; npts=sc.nsec_gen) : (;) + return make_helical(; R0=sc.R0, a=sc.a, m=sc.m_hel, n=sc.n_hel, + theta_lo=sc.theta_lo, theta_hi=sc.theta_hi, n_coils=sc.n_coils, + gap_fraction=sc.gap_fraction, phi0=sc.phi0, offset=sc.offset, + name=isempty(sc.name) ? "helical" : sc.name, kw...) + elseif sc.source == "" || sc.source == "file" + path = _resolve_coil_path(cfg, sc) + ext = lowercase(splitext(path)[2]) + if ext in (".h5", ".hdf5") + sets = read_coil_h5(path; set=isempty(sc.name) ? nothing : sc.name) + length(sets) == 1 || + error("h5 coil file $path holds $(length(sets)) sets; set `name` to pick one") + return sets[1] + end + return read_coil_dat(path) + else + error("Unknown coil set source: '$(sc.source)' " * + "(expected \"\", \"file\", \"pf_hoop\", \"window_pane\", or \"helical\")") + end +end + """ load_coil_sets(cfg::CoilConfig, n_tilt::Int) -> Vector{CoilSet} -Read all coil sets from config, apply shifts/tilts, and return ready-to-use coil data. -`n_tilt` is the toroidal mode number for modulated perturbations (typically the run's n). +Build all coil sets from config (file or analytic source), apply currents and +shifts/tilts, and return ready-to-use coil data. `n_tilt` is the toroidal mode number +for modulated perturbations (typically the run's n). """ function load_coil_sets(cfg::CoilConfig, n_tilt::Int) isempty(cfg.coil_sets) && error("No coil sets specified in [ForcingTerms] configuration") coil_sets = CoilSet[] for set_cfg in cfg.coil_sets - filepath = _resolve_dat_path(cfg, set_cfg) - cs_raw = read_coil_dat(filepath) + cs_raw = _build_raw_coil_set(cfg, set_cfg) # Set currents (pad or truncate to ncoil) ncoil = cs_raw.ncoil @@ -398,7 +864,7 @@ function load_coil_sets(cfg::CoilConfig, n_tilt::Int) else len = length(set_cfg.currents) len >= ncoil ? Float64.(set_cfg.currents[1:ncoil]) : - vcat(Float64.(set_cfg.currents), zeros(ncoil - len)) + vcat(Float64.(set_cfg.currents), zeros(ncoil - len)) end cs_with_currents = CoilSet( cs_raw.name, ncoil, cs_raw.s, cs_raw.nw, cs_raw.nsec, @@ -416,3 +882,6 @@ end export CoilSet, CoilSetConfig, CoilConfig export read_coil_dat, apply_transforms, load_coil_sets +export make_pf_hoop, make_window_pane, make_helical +export read_coil_h5, write_coil_h5, write_coil_dat, save_coils_to_h5, load_coils_from_h5_group! +export convert_coil_dat_to_h5, convert_coil_h5_to_dat diff --git a/src/ForcingTerms/ForcingTerms.jl b/src/ForcingTerms/ForcingTerms.jl index b4abdb444..965ceeb51 100644 --- a/src/ForcingTerms/ForcingTerms.jl +++ b/src/ForcingTerms/ForcingTerms.jl @@ -21,6 +21,7 @@ Forcing Data: - `forcing_data_format::String` - Format: "ascii", "hdf5", or "coil" Coil settings (used when `forcing_data_format = "coil"`): + - `machine::String` - Machine name prefix for .dat files (e.g. "d3d") - `dat_dir::String` - Directory containing .dat files; defaults to bundled `coil_geometries/` - `mtheta_coil::Int` - Poloidal grid resolution for boundary field evaluation (default: 480) @@ -51,8 +52,9 @@ Data structure for a single forcing mode. - `m::Int` - Poloidal mode number - `amplitude::ComplexF64` - Complex amplitude in unit-norm convention (= Fortran Phi_x, T·m² per unit-norm cell) after loading. File inputs are tagged by their input convention: - - `"normal_field_T"`: B·n̂ in Tesla (2π-angle); converted to unit-norm on load - - `"sfl_flux_Wb"`: SFL flux in 2π-angle convention; multiplied by (2π)² on load + + + `"normal_field_T"`: B·n̂ in Tesla (2π-angle); converted to unit-norm on load + + `"sfl_flux_Wb"`: SFL flux in 2π-angle convention; multiplied by (2π)² on load """ Base.@kwdef mutable struct ForcingMode n::Int = 0 @@ -67,24 +69,28 @@ Load forcing data from ASCII or HDF5 file. Returns the normalization tag read from the file (or `"normal_field_T"` by default if no tag is present). **Normalization tags** (set in the file, not in the TOML): -- `"normal_field_T"` (default): Fourier modes of B·n̂ [Tesla], 2π-angle convention. - Most intuitive for users; converted to unit-norm (Phi_x) on load. -- `"sfl_flux_Wb"`: SFL flux R×(B_R·∂Z/∂θ - B_Z·∂R/∂θ) [T·m²], 2π-angle convention. - Multiplied by (2π)² on load to reach unit-norm (Phi_x). + + - `"normal_field_T"` (default): Fourier modes of B·n̂ [Tesla], 2π-angle convention. + Most intuitive for users; converted to unit-norm (Phi_x) on load. + - `"sfl_flux_Wb"`: SFL flux R×(B_R·∂Z/∂θ - B_Z·∂R/∂θ) [T·m²], 2π-angle convention. + Multiplied by (2π)² on load to reach unit-norm (Phi_x). **ASCII format** — optional `# normalization: ` header line, then data rows: + ``` # normalization: normal_field_T 1 2 0.5 0.1 1 3 0.3 -0.2 ``` + Columns: n, m, real(amplitude), [optional] imag(amplitude) **HDF5 format** — optional root attribute `normalization` (string), plus datasets: -- `"n"`: Integer array of toroidal mode numbers -- `"m"`: Integer array of poloidal mode numbers -- `"amplitude_real"`: Real parts of amplitudes -- `"amplitude_imag"`: Imaginary parts of amplitudes (optional, default 0) + + - `"n"`: Integer array of toroidal mode numbers + - `"m"`: Integer array of poloidal mode numbers + - `"amplitude_real"`: Real parts of amplitudes + - `"amplitude_imag"`: Imaginary parts of amplitudes (optional, default 0) """ function load_forcing_data!( forcing_modes::Vector{ForcingMode}, diff --git a/src/ForcingTerms/coil_geometries/README.md b/src/ForcingTerms/coil_geometries/README.md index 6abe3af06..fc24ec668 100644 --- a/src/ForcingTerms/coil_geometries/README.md +++ b/src/ForcingTerms/coil_geometries/README.md @@ -13,8 +13,26 @@ Each `.dat` file uses the Fortran GPEC ASCII format: - `nw`: number of winding turns - **Data lines**: `ncoil × s × nsec` rows, each with `X Y Z` in meters (Cartesian lab frame) -Coils are assumed toroidally symmetric: the first coil is defined explicitly, -and the remaining `ncoil - 1` coils are generated by toroidal rotation. +All `ncoil` conductors are stored explicitly (the Biot-Savart computation iterates over +every one); a toroidal array is written out as its full set of conductors, not a single +representative coil. + +## HDF5 format + +Coil geometry can also be stored in HDF5, which is the modern format and the one used for +the self-contained `gpec.h5` rerun snapshot. One file holds one **subgroup per coil set** +under a parent group (default `coils`), and any unrelated content in the file is ignored: + +``` +//x Float64[ncoil, s, nsec] Cartesian metres +//y Float64[ncoil, s, nsec] +//z Float64[ncoil, s, nsec] +//currents Float64[ncoil] (optional) +/ attr nw Float64 (winding multiplier; default 1.0) +``` + +The bundled device library is kept as `.dat` files (human-readable and diff-able in git); +use `convert_coil_dat_to_h5` / `convert_coil_h5_to_dat` to move between formats. ## Naming Convention diff --git a/src/GeneralizedPerturbedEquilibrium.jl b/src/GeneralizedPerturbedEquilibrium.jl index 23a4467e9..054d0a7aa 100755 --- a/src/GeneralizedPerturbedEquilibrium.jl +++ b/src/GeneralizedPerturbedEquilibrium.jl @@ -120,6 +120,11 @@ already read from the source HDF5 snapshot, so `compute_perturbed_equilibrium` does not have to touch the original `forcing.dat` path. When `nothing`, the ForcingTerms data is loaded from disk at snapshot time (if PerturbedEquilibrium is enabled) so it still ends up in `input/raw_inputs/forcing_terms/`. + +`preloaded_coil_sets` similarly lets the rerun path inject coil geometry read from +`input/raw_inputs/coils/` so a coil run can be replayed (recomputing the field +against the current equilibrium) without the original `.dat`/`.h5` files. The coil +geometry actually used by the run is always written back into `input/raw_inputs/coils/`. """ function main_with_inputs( inputs::Dict{String,Any}, @@ -128,6 +133,7 @@ function main_with_inputs( path::String, git_version::String; preloaded_forcing_modes::Union{Nothing,Vector{ForcingTerms.ForcingMode}}=nothing, + preloaded_coil_sets::Union{Nothing,Vector{ForcingTerms.CoilSet}}=nothing ) total_start = time() @@ -220,7 +226,7 @@ function main_with_inputs( path, ft_ctrl_snapshot.forcing_data_file, ft_ctrl_snapshot.forcing_data_format, - ctrl.verbose, + ctrl.verbose ) end end @@ -342,14 +348,15 @@ function main_with_inputs( # stability does not need kinetic_profiles, but the post-PE block always # does, so we load whenever a [KineticForces] section is present or the # stability path requests the calculated source. - kf_ctrl = haskey(inputs, "KineticForces") ? + kf_ctrl = + haskey(inputs, "KineticForces") ? KineticForces.KineticForcesControl(; (Symbol(k) => v for (k, v) in inputs["KineticForces"])...) : KineticForces.KineticForcesControl() kinetic_profiles = nothing needs_kinetic_profiles = haskey(inputs, "KineticForces") || - (ctrl.kinetic_factor > 0 && ctrl.kinetic_source == "calculated") + (ctrl.kinetic_factor > 0 && ctrl.kinetic_source == "calculated") if needs_kinetic_profiles kinetic_file = joinpath(intr.dir_path, kf_ctrl.kinetic_file) kinetic_profiles = Equilibrium.load_kinetic_profiles( @@ -501,6 +508,12 @@ function main_with_inputs( pe_intr.forcing_modes = copy(forcing_modes_snapshot) end + # Inject preloaded coil geometry (gpec.h5 replay with `--coil-source coils`) + # so the coil field is recomputed from stored geometry without the .dat/.h5 file. + if preloaded_coil_sets !== nothing + pe_intr.coil_sets = copy(preloaded_coil_sets) + end + # Run perturbed equilibrium calculations # Pass vac_data and intr for response matrix calculations pe_state = PerturbedEquilibrium.compute_perturbed_equilibrium( @@ -516,6 +529,12 @@ function main_with_inputs( ) @info "Results written to $output_file" end + + # Snapshot the coil geometry actually used into the gpec.h5 output so the run + # is replayable from the output file alone (see `main_from_h5 --coil-source coils`). + if ctrl.write_outputs_to_HDF5 && !isempty(pe_intr.coil_sets) + _write_coil_snapshot!(joinpath(intr.dir_path, ctrl.HDF5_filename), pe_intr.coil_sets) + end end @info "Perturbed Equilibrium completed in $(@sprintf("%.3f", time() - pe_start)) s" @@ -578,7 +597,7 @@ function write_outputs_to_HDF5( ffit::Union{FourFitVars,Nothing}=nothing, git_version::String="unknown", inputs::Union{Nothing,Dict{String,Any}}=nothing, - forcing_modes::Union{Nothing,Vector{ForcingTerms.ForcingMode}}=nothing, + forcing_modes::Union{Nothing,Vector{ForcingTerms.ForcingMode}}=nothing ) h5open(joinpath(intr.dir_path, ctrl.HDF5_filename), "w") do out_h5 @@ -722,7 +741,7 @@ function write_outputs_to_HDF5( out_h5["singular/kinetic/scan_psi"] = intr.kinsing_scan_psi out_h5["singular/kinetic/scan_cond"] = intr.kinsing_scan_cond out_h5["singular/kinetic/scan_threshold"] = intr.kinsing_scan_threshold - + # Write free-boundary stability data. Power-normalized flux (Φ-space) is the # default — Jacobian-invariant. ξ-space counterparts sit under # FreeBoundaryStability/XiNorm/ for Fortran benchmarking. @@ -814,6 +833,22 @@ function write_outputs_to_HDF5( end end +""" + _write_coil_snapshot!(h5_path::String, coil_sets::Vector{CoilSet}) + +Append the coil geometry used by a run into `input/raw_inputs/coils/` of an existing +gpec.h5 file (opened in append mode), so the run can be replayed from the output alone. +One subgroup per coil set; see `ForcingTerms.save_coils_to_h5`. +""" +function _write_coil_snapshot!(h5_path::String, coil_sets::Vector{ForcingTerms.CoilSet}) + isfile(h5_path) || return nothing + h5open(h5_path, "r+") do out_h5 + haskey(out_h5, "input/raw_inputs/coils") && return nothing + ForcingTerms.save_coils_to_h5(coil_sets, create_group(out_h5, "input/raw_inputs/coils")) + end + return nothing +end + """ write_imas(dd, result) diff --git a/src/PerturbedEquilibrium/PerturbedEquilibrium.jl b/src/PerturbedEquilibrium/PerturbedEquilibrium.jl index 6a80127f3..c514a5115 100644 --- a/src/PerturbedEquilibrium/PerturbedEquilibrium.jl +++ b/src/PerturbedEquilibrium/PerturbedEquilibrium.jl @@ -14,7 +14,7 @@ import ..ForceFreeStates import ..ForceFreeStates: OdeState, VacuumData, ForceFreeStatesInternal, FourFitVars, MetricData import ..Vacuum import ..ForcingTerms -import ..ForcingTerms: ForcingMode, load_forcing_data!, convert_forcing_normalization! +import ..ForcingTerms: ForcingMode, CoilSet, load_forcing_data!, convert_forcing_normalization! import ..Utilities import ..Utilities.FourierTransforms import DelimitedFiles: readdlm @@ -86,7 +86,12 @@ function compute_perturbed_equilibrium( if isempty(intr.forcing_modes) if ft_ctrl.forcing_data_format == "coil" cfg = ForcingTerms.CoilConfig(ft_ctrl) - coil_sets = ForcingTerms.load_coil_sets(cfg, ffs_intr.nlow) + # Reuse preloaded coil geometry (gpec.h5 rerun with `--coil-source coils`) + # when present; otherwise build it from the TOML coil-set config. Either + # way, retain it on `intr.coil_sets` for the rerun snapshot writer. + coil_sets = isempty(intr.coil_sets) ? + ForcingTerms.load_coil_sets(cfg, ffs_intr.nlow) : intr.coil_sets + intr.coil_sets = coil_sets for n in ffs_intr.nlow:ffs_intr.nhigh modes_n = ForcingMode[] ForcingTerms.compute_coil_forcing_modes!( diff --git a/src/PerturbedEquilibrium/PerturbedEquilibriumStructs.jl b/src/PerturbedEquilibrium/PerturbedEquilibriumStructs.jl index b065294c8..6b981c735 100644 --- a/src/PerturbedEquilibrium/PerturbedEquilibriumStructs.jl +++ b/src/PerturbedEquilibrium/PerturbedEquilibriumStructs.jl @@ -8,6 +8,7 @@ User-facing control parameters from TOML [PerturbedEquilibrium] section. Note: Forcing data file settings are now in [ForcingTerms] section. High Priority (MWE): + - `fixed_boundary::Bool` - Fixed boundary flag (default: false) - `output_eigenmodes::Bool` - Output mode fields as b-fields (default: true) - `compute_response::Bool` - Compute plasma response (default: true) @@ -15,14 +16,17 @@ High Priority (MWE): - `verbose::Bool` - Enable verbose logging (default: true) Output Settings: + - `output_filename::String` - Combined output file with ForceFreeStates results (default: uses ForceFreeStates HDF5_filename) - `write_outputs_to_HDF5::Bool` - Write perturbed equilibrium outputs to HDF5 (default: true) Medium Priority (defer for MWE): + - `filter_modes::Bool` - Enable mode filtering (default: false) - `singular_point_method::String` - Method for singular point treatment (default: "standard") Regularization: + # High Priority (MWE) - `reg_spot::Float64` - Regularization width for singular surface smoothing (default: 0.05). Set to 0 to disable. Must be ≥ 0. """ @kwdef mutable struct PerturbedEquilibriumControl @@ -55,6 +59,8 @@ Internal state variables for perturbed equilibrium calculations. - `dir_path::String` - Working directory path - `forcing_modes::Vector{ForcingMode}` - Loaded forcing mode data + - `coil_sets::Vector{CoilSet}` - Coil geometry used (when `forcing_data_format = "coil"`); + captured for the gpec.h5 rerun snapshot - `plasma_response::Matrix{ComplexF64}` - Plasma response matrix - `singular_coupling_metrics::Dict{String,Float64}` - Coupling metrics at singular surfaces - `m_modes::Vector{Int}` - Poloidal mode numbers for each index i in 1:numpert_total @@ -63,6 +69,7 @@ Internal state variables for perturbed equilibrium calculations. @kwdef mutable struct PerturbedEquilibriumInternal dir_path::String = "./" forcing_modes::Vector{ForcingMode} = ForcingMode[] + coil_sets::Vector{CoilSet} = CoilSet[] plasma_response::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) singular_coupling_metrics::Dict{String,Float64} = Dict{String,Float64}() m_modes::Vector{Int} = Int[] @@ -77,6 +84,7 @@ Results from perturbed equilibrium calculations. ## Fields Response fields (mode space): + - `xi_modes::Union{Nothing, NamedTuple}` - Displacement (psi, theta, zeta) [npsi, mpert] - `b_modes::Union{Nothing, NamedTuple}` - Magnetic field; psi=b^ψ, psi_area=b^ψ/⟨J·|∇ψ|⟩_θ, theta/zeta=unregularized, theta_reg/zeta_reg=regularized [npsi, mpert] - `b_n_modes::Union{Nothing, Matrix{ComplexF64}}` - Physical normal field b_n [npsi, mpert] @@ -85,6 +93,7 @@ Response fields (mode space): Coupling matrices [n_rational × numpert_total] — one row per resonant (surface, n) pair. Each row maps the full applied field to the resonant response at that surface. Matches Fortran `C_f_x_out`, `C_i_x_out`, etc. (shape [mode_C, m_out]). + - `C_resonant_flux` - Φ_r/A coupling (singcoup row 1) - `C_resonant_current` - Resonant current coupling (singcoup row 2) - `C_island_width_sq` - (w/2)² coupling (singcoup row 3) @@ -93,25 +102,30 @@ Matches Fortran `C_f_x_out`, `C_i_x_out`, etc. (shape [mode_C, m_out]). Applied resonant vectors [n_rational] = C · forcing_amplitudes. Matches Fortran `Phi_res`, `w_isl`, `K_isl`, `Delta`. + - `resonant_flux`, `resonant_current`, `island_width_sq`, `penetrated_field`, `delta_prime` Diagnostics [n_rational]: + - `island_half_width::Vector{Float64}` - w/2 = sqrt(|island_width_sq|) from applied forcing - `chirikov_parameter::Vector{Float64}` - Island overlap metric Metadata [n_rational] — identifies each (surface, n) row: + - `rational_psi`, `rational_q`, `rational_m_res`, `rational_n`, `rational_surface_idx` Control surface matrices [numpert_total × numpert_total]: + - `plasma_inductance` - Lambda (wt0-based plasma inductance) - `surface_inductance` - L (vacuum surface inductance from Green's functions) - `permeability` - P = Lambda * L^{-1} (plasma response matrix, Phi_tot = P * Phi_x) - `reluctance` - Rho = L^{-1} * (Lambda - L) * L^{-1} Energies (Fortran gpout convention; Φ_x external flux, Φ_tot total flux, L/Λ inductances): + # Radial grid (FFS ODE integration ψ_n values) [npsi] - `vacuum_energy` - Re( ⟨Φ_x, L⁻¹·Φ_x⟩ ) / 4 (energy to perturb the vacuum) - `surface_energy` - Re( ⟨Φ_tot, L⁻¹·Φ_tot⟩ ) / 4 (energy at the control surface) - - `plasma_energy` - Re( ⟨Φ_tot, Λ⁻¹·Φ_tot⟩ ) / 4 (energy to perturb the plasma; Fortran's "total energy") + - `plasma_energy` - Re( ⟨Φ_tot, Λ⁻¹·Φ_tot⟩ ) / 4 (energy to perturb the plasma; Fortran's "total energy") # Response fields in mode space [npsi, mpert] - `toroidal_torque` - -2·n·Im( ⟨Φ_tot, Λ⁻¹·Φ_tot⟩ / 4 ) """ @kwdef mutable struct PerturbedEquilibriumState @@ -119,49 +133,49 @@ Energies (Fortran gpout convention; Φ_x external flux, Φ_tot total flux, L/Λ psi_grid::Vector{Float64} = Float64[] # Response fields in mode space [npsi, mpert] - xi_modes::Union{Nothing, NamedTuple} = nothing - b_modes::Union{Nothing, NamedTuple} = nothing - b_n_modes::Union{Nothing, Matrix{ComplexF64}} = nothing # physical normal field b_n [npsi, mpert] - xi_n_modes::Union{Nothing, Matrix{ComplexF64}} = nothing # physical normal displacement xi_n [npsi, mpert] + xi_modes::Union{Nothing,NamedTuple} = nothing + b_modes::Union{Nothing,NamedTuple} = nothing + b_n_modes::Union{Nothing,Matrix{ComplexF64}} = nothing # physical normal field b_n [npsi, mpert] + xi_n_modes::Union{Nothing,Matrix{ComplexF64}} = nothing # physical normal displacement xi_n [npsi, mpert] # Coupling matrices [n_rational × numpert_total] - C_resonant_flux::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) - C_resonant_current::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) - C_island_width_sq::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) - C_penetrated_field::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) - C_delta_prime::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) + C_resonant_flux::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) + C_resonant_current::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) + C_island_width_sq::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) + C_penetrated_field::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) + C_delta_prime::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # Applied resonant vectors [n_rational] = C · amp_vec - resonant_flux::Vector{ComplexF64} = ComplexF64[] - resonant_current::Vector{ComplexF64} = ComplexF64[] - island_width_sq::Vector{ComplexF64} = ComplexF64[] - penetrated_field::Vector{ComplexF64} = ComplexF64[] - delta_prime::Vector{ComplexF64} = ComplexF64[] + resonant_flux::Vector{ComplexF64} = ComplexF64[] + resonant_current::Vector{ComplexF64} = ComplexF64[] + island_width_sq::Vector{ComplexF64} = ComplexF64[] + penetrated_field::Vector{ComplexF64} = ComplexF64[] + delta_prime::Vector{ComplexF64} = ComplexF64[] # Diagnostics [n_rational] - island_half_width::Vector{Float64} = Float64[] - chirikov_parameter::Vector{Float64} = Float64[] + island_half_width::Vector{Float64} = Float64[] + chirikov_parameter::Vector{Float64} = Float64[] # Metadata [n_rational] - rational_psi::Vector{Float64} = Float64[] - rational_q::Vector{Float64} = Float64[] - rational_m_res::Vector{Int} = Int[] - rational_n::Vector{Int} = Int[] - rational_surface_idx::Vector{Int} = Int[] + rational_psi::Vector{Float64} = Float64[] + rational_q::Vector{Float64} = Float64[] + rational_m_res::Vector{Int} = Int[] + rational_n::Vector{Int} = Int[] + rational_surface_idx::Vector{Int} = Int[] # Control surface perturbation vectors [numpert_total] - forcing_vec::Vector{ComplexF64} = ComplexF64[] # Phi_x: external forcing in eigenmode basis - response_vec::Vector{ComplexF64} = ComplexF64[] # Phi_tot = P * Phi_x: total plasma response + forcing_vec::Vector{ComplexF64} = ComplexF64[] # Phi_x: external forcing in eigenmode basis + response_vec::Vector{ComplexF64} = ComplexF64[] # Phi_tot = P * Phi_x: total plasma response # Control surface matrices [numpert_total × numpert_total] - plasma_inductance::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # Lambda + plasma_inductance::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # Lambda surface_inductance::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # L - permeability::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # P = Lambda * L^{-1} - reluctance::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # Rho = L^{-1}*(Lambda-L)*L^{-1} + permeability::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # P = Lambda * L^{-1} + reluctance::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # Rho = L^{-1}*(Lambda-L)*L^{-1} # Energies — see the struct docstring for formulas - vacuum_energy::Float64 = 0.0 - surface_energy::Float64 = 0.0 - plasma_energy::Float64 = 0.0 + vacuum_energy::Float64 = 0.0 + surface_energy::Float64 = 0.0 + plasma_energy::Float64 = 0.0 toroidal_torque::Float64 = 0.0 end diff --git a/src/Rerun.jl b/src/Rerun.jl index 87ca514eb..840b063ea 100644 --- a/src/Rerun.jl +++ b/src/Rerun.jl @@ -151,8 +151,7 @@ end """ parse_rerun_cli(args) -> NamedTuple -Parse the rerun CLI. Returns `(source_h5, output_dir, output_name, -override_file, overrides)`. Unknown flags error out early. +Parse the rerun CLI. Returns `(source_h5, output_dir, output_name, override_file, overrides, coil_source)`. Unknown flags error out early. Supported flags: @@ -160,6 +159,9 @@ Supported flags: - `--output-name ` — output HDF5 filename (default: `_rerun.h5`) - `--override-file ` — TOML file merged onto the stored TOML - `--override key=value` — single-field override (repeatable) + - `--coil-source ` — for coil runs, which snapshot drives the replay: + `forcing-modes` (default) reuses the frozen forcing modes exactly; `coils` + recomputes the field from the stored coil geometry (lets the equilibrium change). """ function parse_rerun_cli(args::Vector{String}) isempty(args) && error("main_from_h5 requires a positional source .h5 path") @@ -169,6 +171,7 @@ function parse_rerun_cli(args::Vector{String}) output_name = nothing override_file = nothing overrides = Dict{String,Any}() + coil_source = "forcing-modes" i = 2 while i <= length(args) @@ -190,13 +193,19 @@ function parse_rerun_cli(args::Vector{String}) merged = parse_override_flag(args[i+1]) apply_toml_overrides!(overrides, merged) i += 2 + elseif flag == "--coil-source" + i + 1 > length(args) && error("--coil-source requires a value (forcing-modes|coils)") + coil_source = args[i+1] + coil_source in ("forcing-modes", "coils") || + error("--coil-source must be 'forcing-modes' or 'coils', got: $coil_source") + i += 2 else error("Unknown rerun flag: $flag") end end return (source_h5=source_h5, output_dir=output_dir, output_name=output_name, - override_file=override_file, overrides=overrides) + override_file=override_file, overrides=overrides, coil_source=coil_source) end """ @@ -259,13 +268,26 @@ function main_from_h5(args::Vector{String}) # original run had a [PerturbedEquilibrium] section, so the group may be # missing — we signal that with `nothing` and let main_with_inputs fall # back to loading from `ft_ctrl.forcing_data_file`. - toml_raw, raw_eq, source_git, preloaded_forcing = h5open(source_h5, "r") do in_h5 + # `--coil-source coils` recomputes the coil field from stored geometry, so it + # deliberately ignores the frozen forcing-mode snapshot. + use_coils = cli.coil_source == "coils" + toml_raw, raw_eq, source_git, preloaded_forcing, preloaded_coils = h5open(source_h5, "r") do in_h5 haskey(in_h5, "input/gpec_toml_raw") || error("Source HDF5 $source_h5 has no input/gpec_toml_raw — produced by a pre-rerun version of GPEC") - forcing_modes = if haskey(in_h5, "input/raw_inputs/forcing_terms") + forcing_modes = if use_coils || !haskey(in_h5, "input/raw_inputs/forcing_terms") + nothing + else modes = ForcingTerms.ForcingMode[] ForcingTerms.load_forcing_from_h5_group!(modes, in_h5["input/raw_inputs/forcing_terms"]) modes + end + coil_sets = if use_coils + haskey(in_h5, "input/raw_inputs/coils") || + error("--coil-source coils requested but $source_h5 has no input/raw_inputs/coils " * + "(the source run did not use coils, or predates coil-snapshot support)") + sets = ForcingTerms.CoilSet[] + ForcingTerms.load_coils_from_h5_group!(sets, in_h5["input/raw_inputs/coils"]) + sets else nothing end @@ -274,6 +296,7 @@ function main_from_h5(args::Vector{String}) read_equilibrium_raw_inputs(in_h5), haskey(in_h5, "info/git_version") ? read(in_h5, "info/git_version") : "unknown", forcing_modes, + coil_sets ) end @@ -327,5 +350,5 @@ function main_from_h5(args::Vector{String}) end return main_with_inputs(inputs, eq_config, additional_input, output_dir, current_git; - preloaded_forcing_modes=preloaded_forcing) + preloaded_forcing_modes=preloaded_forcing, preloaded_coil_sets=preloaded_coils) end diff --git a/test/runtests_coils.jl b/test/runtests_coils.jl index d88b2af1b..95ac91929 100644 --- a/test/runtests_coils.jl +++ b/test/runtests_coils.jl @@ -1,6 +1,7 @@ using Test using TOML using Statistics +using HDF5 using GeneralizedPerturbedEquilibrium using GeneralizedPerturbedEquilibrium.ForcingTerms using GeneralizedPerturbedEquilibrium.Equilibrium @@ -15,9 +16,9 @@ const D3D_IL = joinpath(COIL_DIR, "d3d_il.dat") cs = ForcingTerms.read_coil_dat(D3D_IL) @test cs.ncoil == 6 - @test cs.s == 1 - @test cs.nsec == 126 - @test cs.nw ≈ 1.0 + @test cs.s == 1 + @test cs.nsec == 126 + @test cs.nw ≈ 1.0 # Coordinates should be in plausible DIII-D range (R ~ 1–2.5 m, |Z| < 2 m) R_vals = sqrt.(cs.x .^ 2 .+ cs.y .^ 2) @@ -61,14 +62,16 @@ end @testset "BiotSavart: circular loop analytic validation" begin # Circular loop of radius a in the xy-plane at z=0, current I in the +θ direction. # At observer (0, 0, h): B_z = μ₀ I a² / (2 (a²+h²)^(3/2)) [Jackson 5.38] - a = 1.0; I_val = 1.0; h = 0.5 + a = 1.0 + I_val = 1.0 + h = 0.5 n_seg = 500 # Build a discrete circular loop as a CoilSet (ncoil=1, s=1, nsec=n_seg+1) - phis = range(0; length=n_seg + 1, stop=2π) - xs = a .* cos.(phis) - ys = a .* sin.(phis) - zs = zeros(n_seg + 1) + phis = range(0; length=n_seg + 1, stop=2π) + xs = a .* cos.(phis) + ys = a .* sin.(phis) + zs = zeros(n_seg + 1) cs = ForcingTerms.CoilSet("test_loop", 1, 1, 1.0, n_seg + 1, reshape(xs, 1, 1, :), @@ -77,7 +80,9 @@ end [I_val]) # Allocate output and evaluate at (0, 0, h) - Bx = zeros(1); By = zeros(1); Bz = zeros(1) + Bx = zeros(1) + By = zeros(1) + Bz = zeros(1) ForcingTerms.accumulate_strand_field!( Bx, By, Bz, 1, 0.0, 0.0, h, @@ -85,7 +90,7 @@ end I_val * cs.nw ) - B_z_analytic = 4π * 1e-7 * I_val * a^2 / (2 * (a^2 + h^2)^(3/2)) + B_z_analytic = 4π * 1e-7 * I_val * a^2 / (2 * (a^2 + h^2)^(3 / 2)) rel_error = abs(Bz[1] - B_z_analytic) / B_z_analytic @test rel_error < 0.005 # <0.5% with 500 segments @@ -96,31 +101,38 @@ end @testset "BiotSavart: compute_biot_savart_boundary! threading" begin # Same circular loop; verify threaded result matches single-obs result - a = 0.8; I_val = 500.0 + a = 0.8 + I_val = 500.0 n_seg = 200 phis = range(0; length=n_seg + 1, stop=2π) - xs = a .* cos.(phis); ys = a .* sin.(phis); zs = zeros(n_seg + 1) + xs = a .* cos.(phis) + ys = a .* sin.(phis) + zs = zeros(n_seg + 1) cs = ForcingTerms.CoilSet("loop", 1, 1, 1.0, n_seg + 1, reshape(xs, 1, 1, :), reshape(ys, 1, 1, :), reshape(zs, 1, 1, :), [I_val]) # Three observation points - obs_R = [0.5, 1.0, 1.5] - obs_phi = [0.0, π/3, π] - obs_Z = [0.3, 0.0, -0.2] - B_R = zeros(3); B_phi = zeros(3); B_Z = zeros(3) + obs_R = [0.5, 1.0, 1.5] + obs_phi = [0.0, π / 3, π] + obs_Z = [0.3, 0.0, -0.2] + B_R = zeros(3) + B_phi = zeros(3) + B_Z = zeros(3) ForcingTerms.compute_biot_savart_boundary!(B_R, B_phi, B_Z, obs_R, obs_phi, obs_Z, [cs]) # Verify B_Z at (0, 0, 0.3): analytic value - Bx_s = zeros(1); By_s = zeros(1); Bz_s = zeros(1) + Bx_s = zeros(1) + By_s = zeros(1) + Bz_s = zeros(1) obs_x = obs_R[1] * cos(obs_phi[1]) obs_y = obs_R[1] * sin(obs_phi[1]) ForcingTerms.accumulate_strand_field!(Bx_s, By_s, Bz_s, 1, obs_x, obs_y, obs_Z[1], xs, ys, zs, I_val * cs.nw) - B_R_single = Bx_s[1] * cos(obs_phi[1]) + By_s[1] * sin(obs_phi[1]) - @test B_R[1] ≈ B_R_single rtol=1e-10 - @test B_Z[1] ≈ Bz_s[1] rtol=1e-10 + B_R_single = Bx_s[1] * cos(obs_phi[1]) + By_s[1] * sin(obs_phi[1]) + @test B_R[1] ≈ B_R_single rtol = 1e-10 + @test B_Z[1] ≈ Bz_s[1] rtol = 1e-10 end # --------------------------------------------------------------------------- @@ -133,11 +145,12 @@ end eq_config = Equilibrium.EquilibriumConfig(inputs["Equilibrium"], equil_dir) equil = Equilibrium.setup_equilibrium(eq_config) - mtheta = 48; nzeta = 16 + mtheta = 48 + nzeta = 16 grid = ForcingTerms.sample_boundary_grid(equil, mtheta, nzeta) @test grid.mtheta == mtheta - @test grid.nzeta == nzeta + @test grid.nzeta == nzeta @test length(grid.R) == mtheta @test length(grid.phi_grid) == nzeta @@ -153,11 +166,13 @@ end @testset "CoilFourier: fourier_decompose_bn roundtrip" begin # Synthesize bn(θ, ζ) = cos(m₀*θ - n₀*ζ), decompose, verify dominant mode - mtheta = 128; nzeta = 64 - m0 = 5; n0 = 2 + mtheta = 128 + nzeta = 64 + m0 = 5 + n0 = 2 - theta_grid = range(0; length=mtheta, step=2π/mtheta) - zeta_grid = range(0; length=nzeta, step=2π/nzeta) + theta_grid = range(0; length=mtheta, step=2π / mtheta) + zeta_grid = range(0; length=nzeta, step=2π / nzeta) bn = [cos(m0 * θ - n0 * ζ) for θ in theta_grid, ζ in zeta_grid] @@ -166,7 +181,8 @@ end ones(mtheta), zeros(mtheta), collect(zeta_grid), zeros(mtheta), ones(mtheta), zeros(mtheta)) - m_low = 1; m_high = 10 + m_low = 1 + m_high = 10 modes = ForcingTerms.fourier_decompose_bn(bn, grid, n0, m_low, m_high) @test length(modes) == m_high - m_low + 1 @@ -174,7 +190,7 @@ end # Find the (m0, n0) mode idx = findfirst(m -> m.m == m0, modes) @test !isnothing(idx) - @test abs(real(modes[idx].amplitude)) ≈ 1.0 rtol=0.02 + @test abs(real(modes[idx].amplitude)) ≈ 1.0 rtol = 0.02 @test abs(imag(modes[idx].amplitude)) < 0.05 # All other modes should be near zero @@ -192,10 +208,13 @@ end # where dR/dθ_norm = 2π × dR/dθ_phys = 2π × (-a*sin(θ)). # For B_R=0, B_Z=B0: Phi_x = -2π × R × B0 × dR/dθ_norm = (2π)² × B0 × a × R(θ) × sin(θ) - mtheta = 64; nzeta = 1 - B0 = 1.0; R0 = 2.0; a = 0.5 + mtheta = 64 + nzeta = 1 + B0 = 1.0 + R0 = 2.0 + a = 0.5 - theta_phys = range(0; length=mtheta, step=2π/mtheta) + theta_phys = range(0; length=mtheta, step=2π / mtheta) R_arr = R0 .+ a .* cos.(theta_phys) Z_arr = a .* sin.(theta_phys) @@ -207,13 +226,14 @@ end grid = ForcingTerms.BoundaryGrid(mtheta, nzeta, R_arr, Z_arr, phi_grid, zeros(mtheta), dR_dθ_norm, dZ_dθ_norm) # Uniform B_Z = B0, B_R = 0 at all points - B_R = zeros(mtheta); B_Z = fill(B0, mtheta) - bn = zeros(mtheta, nzeta) + B_R = zeros(mtheta) + B_Z = fill(B0, mtheta) + bn = zeros(mtheta, nzeta) ForcingTerms.project_normal_flux!(bn, B_R, B_Z, grid) # Expected: 2π × R × (0×dZ_norm - B0×dR_norm) = (2π)² × B0 × a × R(θ) × sin(θ) expected = (2π)^2 .* B0 .* a .* R_arr .* sin.(theta_phys) - @test bn[:, 1] ≈ expected rtol=1e-10 + @test bn[:, 1] ≈ expected rtol = 1e-10 # Result must vary with R (old code without R factor gave constant amplitude) @test std(abs.(bn[:, 1])) > 0.01 * mean(abs.(bn[:, 1])) @@ -234,22 +254,22 @@ end inputs2 = TOML.parsefile(joinpath(equil_dir, "gpec.toml")) eq_config2 = Equilibrium.EquilibriumConfig(inputs2["Equilibrium"], equil_dir) - equil = Equilibrium.setup_equilibrium(eq_config2) + equil = Equilibrium.setup_equilibrium(eq_config2) # Build coil sets manually (standard I-coil currents for RMP studies) il_cfg = ForcingTerms.CoilSetConfig(; - dat_file = D3D_IL, - currents = fill(10e3, 6), + dat_file=D3D_IL, + currents=fill(10e3, 6) ) iu_cfg = ForcingTerms.CoilSetConfig(; - dat_file = d3d_iu, - currents = fill(10e3, 6), + dat_file=d3d_iu, + currents=fill(10e3, 6) ) cfg = ForcingTerms.CoilConfig(; - mtheta_coil = 96, - nzeta_coil = 64, - coil_sets = [il_cfg, iu_cfg], + mtheta_coil=96, + nzeta_coil=64, + coil_sets=[il_cfg, iu_cfg] ) il_set = ForcingTerms.read_coil_dat(D3D_IL) @@ -261,7 +281,8 @@ end forcing_modes = ForcingMode[] n_test = 3 # n=3 is a typical DIII-D RMP configuration - m_low = 1; m_high = 15 + m_low = 1 + m_high = 15 ForcingTerms.compute_coil_forcing_modes!( forcing_modes, [il_set, iu_set], equil, cfg, n_test, m_low, m_high; @@ -279,3 +300,186 @@ end dominant_m = forcing_modes[argmax(amplitudes)].m @test m_low <= dominant_m <= m_high end + +# --------------------------------------------------------------------------- +@testset "Analytic coils: make_pf_hoop" begin + a = 1.0 + I_val = 1.0 + h = 0.5 + cs = ForcingTerms.make_pf_hoop(; radius=a, height=0.0, nsec=501) + @test size(cs.x) == (1, 1, 501) + @test cs.ncoil == 1 && cs.s == 1 + # Closed loop: last point == first + @test cs.x[1, 1, 1] ≈ cs.x[1, 1, end] atol = 1e-12 + @test cs.y[1, 1, 1] ≈ cs.y[1, 1, end] atol = 1e-12 + + # Reproduce Jackson 5.38 on-axis field B_z = μ₀ I a² / (2 (a²+h²)^{3/2}) + Bx = zeros(1) + By = zeros(1) + Bz = zeros(1) + ForcingTerms.accumulate_strand_field!(Bx, By, Bz, 1, 0.0, 0.0, h, + cs.x[1, 1, :], cs.y[1, 1, :], cs.z[1, 1, :], I_val * cs.nw) + B_z_analytic = 4π * 1e-7 * I_val * a^2 / (2 * (a^2 + h^2)^(3 / 2)) + @test abs(Bz[1] - B_z_analytic) / B_z_analytic < 0.005 + @test abs(Bx[1]) < 1e-14 + @test abs(By[1]) < 1e-14 + + @test_throws ErrorException ForcingTerms.make_pf_hoop(; radius=-1.0, height=0.0) +end + +@testset "Analytic coils: make_window_pane" begin + ncoil = 6 + R0 = 2.2 + Zlo = -0.6 + Zhi = 0.6 + cs = ForcingTerms.make_window_pane(; ncoil=ncoil, rz_corners=[[R0, Zlo], [R0, Zhi]], + gap_fraction=0.15, phi0=0.0) + @test cs.ncoil == ncoil && cs.s == 1 + + # Every coil is a closed loop + for j in 1:ncoil + @test cs.x[j, 1, 1] ≈ cs.x[j, 1, end] + @test cs.y[j, 1, 1] ≈ cs.y[j, 1, end] + @test cs.z[j, 1, 1] ≈ cs.z[j, 1, end] + end + + # Vertical frame at constant R: cylindrical radius ≈ R0, Z within [Zlo, Zhi] + Rcyl = sqrt.(cs.x .^ 2 .+ cs.y .^ 2) + @test all(isapprox.(Rcyl, R0; atol=1e-9)) + @test minimum(cs.z) ≈ Zlo + @test maximum(cs.z) ≈ Zhi + + # Toroidal centers spaced 2π/ncoil: mean φ of each coil + centers = [atan(mean(cs.y[j, 1, :]), mean(cs.x[j, 1, :])) for j in 1:ncoil] + dphi = mod(centers[2] - centers[1], 2π) + @test dphi ≈ 2π / ncoil rtol = 1e-6 + + @test_throws ErrorException ForcingTerms.make_window_pane(; ncoil=2, rz_corners=[[1.0, 0.0]]) +end + +@testset "Analytic coils: make_helical" begin + R0 = 1.7 + a = 0.6 + n_coils = 4 + # Full poloidal turn: single helical strand per coil + cs = ForcingTerms.make_helical(; R0=R0, a=a, m=4, n=1, n_coils=n_coils) + @test cs.ncoil == n_coils && cs.s == 1 + # Points lie on the circular cross-section torus (offset=0) + Rcyl = sqrt.(cs.x .^ 2 .+ cs.y .^ 2) + rminor = sqrt.((Rcyl .- R0) .^ 2 .+ cs.z .^ 2) + @test all(isapprox.(rminor, a; atol=1e-9)) + + # Partial poloidal range: closed loop with offset + cp = ForcingTerms.make_helical(; R0=R0, a=a, m=3, n=1, n_coils=n_coils, + theta_lo=-0.4, theta_hi=0.4, offset=0.05) + for j in 1:n_coils + @test cp.x[j, 1, 1] ≈ cp.x[j, 1, end] atol = 1e-9 + @test cp.z[j, 1, 1] ≈ cp.z[j, 1, end] atol = 1e-9 + end + + @test_throws ErrorException ForcingTerms.make_helical(; R0=R0, a=a, m=2, n=0, n_coils=2) +end + +# --------------------------------------------------------------------------- +@testset "Coil HDF5: round-trip vs .dat" begin + cs0 = ForcingTerms.read_coil_dat(D3D_IL) + mktempdir() do dir + h5 = joinpath(dir, "il.h5") + ForcingTerms.convert_coil_dat_to_h5(D3D_IL, h5) + sets = ForcingTerms.read_coil_h5(h5) + @test length(sets) == 1 + cs = sets[1] + @test cs.ncoil == cs0.ncoil + @test cs.s == cs0.s + @test cs.nsec == cs0.nsec + @test cs.nw ≈ cs0.nw + @test cs.x ≈ cs0.x + @test cs.y ≈ cs0.y + @test cs.z ≈ cs0.z + + # h5 -> dat round-trips back to identical geometry + dat2 = joinpath(dir, "il_back.dat") + ForcingTerms.convert_coil_h5_to_dat(h5, dat2) + csb = ForcingTerms.read_coil_dat(dat2) + @test csb.x ≈ cs0.x && csb.y ≈ cs0.y && csb.z ≈ cs0.z + end +end + +@testset "Coil HDF5: multi-set + content tolerance" begin + cs0 = ForcingTerms.read_coil_dat(D3D_IL) + hoop = ForcingTerms.make_pf_hoop(; radius=2.0, height=0.1, name="hoop") + mktempdir() do dir + h5 = joinpath(dir, "multi.h5") + ForcingTerms.write_coil_h5(h5, [cs0, hoop]) + + # Inject unrelated content the reader must ignore + HDF5.h5open(h5, "r+") do f + f["coils/junk_dataset"] = [1.0, 2.0, 3.0] + f["unrelated/other_stuff"] = 42 + end + + sets = ForcingTerms.read_coil_h5(h5) + @test length(sets) == 2 + @test sort([s.name for s in sets]) == ["d3d_il", "hoop"] + + # Select a single set by name + one = ForcingTerms.read_coil_h5(h5; set="hoop") + @test length(one) == 1 && one[1].name == "hoop" + @test_throws ErrorException ForcingTerms.read_coil_h5(h5; set="nope") + end +end + +# --------------------------------------------------------------------------- +@testset "load_coil_sets: source dispatch" begin + # Analytic source: currents applied, tilt perturbs geometry + cfg = ForcingTerms.CoilConfig(; coil_sets=[ + ForcingTerms.CoilSetConfig(; source="pf_hoop", radius=1.5, height=0.2, + currents=[3.0], tiltx=[10.0]) + ]) + out = ForcingTerms.load_coil_sets(cfg, 1) + @test length(out) == 1 + @test out[1].currents == [3.0] + # A 10° X-tilt should move the (originally flat) hoop out of the z=0.2 plane + @test !all(isapprox.(out[1].z, 0.2; atol=1e-6)) + + # File source dispatches on extension: .h5 -> read_coil_h5, .dat -> read_coil_dat + mktempdir() do dir + h5 = joinpath(dir, "il.h5") + ForcingTerms.convert_coil_dat_to_h5(D3D_IL, h5) + cfg_h5 = ForcingTerms.CoilConfig(; coil_sets=[ + ForcingTerms.CoilSetConfig(; source="file", h5_file=h5, currents=fill(1.0, 6)) + ]) + cfg_dat = ForcingTerms.CoilConfig(; coil_sets=[ + ForcingTerms.CoilSetConfig(; dat_file=D3D_IL, currents=fill(1.0, 6)) + ]) + a = ForcingTerms.load_coil_sets(cfg_h5, 1) + b = ForcingTerms.load_coil_sets(cfg_dat, 1) + @test a[1].ncoil == 6 && b[1].ncoil == 6 + @test a[1].x ≈ b[1].x + end + + @test_throws ErrorException ForcingTerms.load_coil_sets( + ForcingTerms.CoilConfig(; coil_sets=[ForcingTerms.CoilSetConfig(; source="bogus")]), 1) +end + +@testset "Coil HDF5 group: save/load round-trip" begin + sets_in = [ForcingTerms.make_pf_hoop(; radius=1.2, height=0.0, name="hoopA"), + ForcingTerms.make_window_pane(; ncoil=3, rz_corners=[[2.0, -0.5], [2.0, 0.5]], name="wp")] + sets_in[1] = ForcingTerms.CoilSet(sets_in[1].name, sets_in[1].ncoil, sets_in[1].s, + sets_in[1].nw, sets_in[1].nsec, sets_in[1].x, sets_in[1].y, sets_in[1].z, [7.0]) + mktempdir() do dir + path = joinpath(dir, "snap.h5") + HDF5.h5open(path, "w") do f + ForcingTerms.save_coils_to_h5(sets_in, HDF5.create_group(f, "input/raw_inputs/coils")) + end + sets_out = ForcingTerms.CoilSet[] + HDF5.h5open(path, "r") do f + ForcingTerms.load_coils_from_h5_group!(sets_out, f["input/raw_inputs/coils"]) + end + @test length(sets_out) == 2 + byname = Dict(s.name => s for s in sets_out) + @test byname["hoopA"].currents == [7.0] + @test byname["hoopA"].x ≈ sets_in[1].x + @test byname["wp"].ncoil == 3 + end +end diff --git a/test/runtests_rerun_from_h5.jl b/test/runtests_rerun_from_h5.jl index 9b806d9f5..b9f0c0e24 100644 --- a/test/runtests_rerun_from_h5.jl +++ b/test/runtests_rerun_from_h5.jl @@ -1,4 +1,5 @@ using HDF5 +using TOML # Exercise the gpec.h5 snapshot + replay pipeline (issue #171). The source run is # a regular `main(dir)` invocation; the replay runs `main_from_h5` from a temp @@ -10,13 +11,13 @@ using HDF5 function read_scalars(path) return h5open(path, "r") do h5 ( - et=read(h5, "vacuum/et"), - ep=read(h5, "vacuum/ep"), - ev=read(h5, "vacuum/ev"), + et=read(h5, "FreeBoundaryStability/eigenmode_energies"), + ep=read(h5, "FreeBoundaryStability/eigenmode_plasma_energies"), + ev=read(h5, "FreeBoundaryStability/eigenmode_vacuum_energies"), mpert=read(h5, "info/mpert"), msing=read(h5, "singular/msing"), sing_psi=read(h5, "singular/psi"), - sing_q=read(h5, "singular/q"), + sing_q=read(h5, "singular/q") ) end end @@ -64,7 +65,7 @@ using HDF5 GeneralizedPerturbedEquilibrium.main([ source_h5, "--output-dir", replay_dir, - "--override", "ForceFreeStates.eulerlagrange_tolerance=1e-6", + "--override", "ForceFreeStates.eulerlagrange_tolerance=1e-6" ]) replay_h5 = joinpath(replay_dir, "gpec_rerun.h5") @@ -91,8 +92,95 @@ using HDF5 @test_throws ErrorException GeneralizedPerturbedEquilibrium.main([ source_h5, "--output-dir", snapshot_dir, - "--output-name", "gpec.h5", + "--output-name", "gpec.h5" ]) end + + @testset "--coil-source coils errors when source has no coil snapshot" begin + # This Solovev source run used ASCII forcing, so there is no + # input/raw_inputs/coils group to replay from. + mktempdir() do replay_dir + @test_throws ErrorException GeneralizedPerturbedEquilibrium.main([ + source_h5, "--output-dir", replay_dir, "--coil-source", "coils" + ]) + end + end + end +end + +# --------------------------------------------------------------------------- +# Coil-geometry snapshot: a coil run stores its geometry in gpec.h5 so it can be +# replayed without the original .dat. The decisive test deletes the .dat between +# the source run and the replay: the default (recompute-from-TOML) path then +# fails, while `--coil-source coils` succeeds from the stored geometry. +@testset "Rerun from gpec.h5: coil geometry snapshot" begin + template_dir = joinpath(@__DIR__, "..", "examples", "Solovev_ideal_example") + src_dat = joinpath(@__DIR__, "..", "src", "ForcingTerms", "coil_geometries", "d3d_il.dat") + + read_resflux(path) = + h5open(path, "r") do h5 + key = "perturbed_equilibrium/singular_coupling/resonant_flux" + haskey(h5, key) ? read(h5, key) : ComplexF64[] + end + + mktempdir() do snapshot_dir + for name in readdir(template_dir) + src = joinpath(template_dir, name) + isfile(src) && cp(src, joinpath(snapshot_dir, name)) + end + + # Point the coil set at a throwaway .dat we can delete before replay. + coil_dat = joinpath(snapshot_dir, "my_coils.dat") + cp(src_dat, coil_dat) + + toml_path = joinpath(snapshot_dir, "gpec.toml") + inputs = TOML.parsefile(toml_path) + inputs["ForceFreeStates"]["write_outputs_to_HDF5"] = true + inputs["ForcingTerms"] = Dict{String,Any}( + "forcing_data_format" => "coil", + "coil_set" => [Dict{String,Any}( + "dat_file" => coil_dat, + "currents" => fill(1.0e3, 6) + )] + ) + open(toml_path, "w") do io + TOML.print(io, inputs) + end + + @info "Generating source gpec.h5 for coil rerun test" + GeneralizedPerturbedEquilibrium.main([snapshot_dir]) + source_h5 = joinpath(snapshot_dir, "gpec.h5") + @test isfile(source_h5) + + # The coil geometry actually used must be captured in the snapshot. + h5open(source_h5, "r") do h5 + @test haskey(h5, "input/raw_inputs/coils") + @test haskey(h5, "input/raw_inputs/coils/my_coils") + end + src_flux = read_resflux(source_h5) + @test !isempty(src_flux) + @test maximum(abs.(src_flux)) > 0 + + # Delete the .dat: the snapshot must now be the only source of geometry. + rm(coil_dat) + + @testset "default replay needs the .dat and fails once it is gone" begin + mktempdir() do replay_dir + @test_throws Exception GeneralizedPerturbedEquilibrium.main([ + source_h5, "--output-dir", replay_dir + ]) + end + end + + @testset "--coil-source coils replays from the stored geometry" begin + mktempdir() do replay_dir + GeneralizedPerturbedEquilibrium.main([ + source_h5, "--output-dir", replay_dir, "--coil-source", "coils" + ]) + replay_h5 = joinpath(replay_dir, "gpec_rerun.h5") + @test isfile(replay_h5) + @test read_resflux(replay_h5) ≈ src_flux rtol = 1e-6 + end + end end end From 0ba42d216d5f5c3f17a509c5a896c72b9b73543a Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Wed, 10 Jun 2026 23:46:21 -0400 Subject: [PATCH 021/135] ForcingTerms - DOCS - Fix Documenter link pitfalls in coil HDF5 docs - CoilSetConfig docstring: `[rad] (...)` parsed as a markdown link; reword to plain prose so makedocs cross-reference check passes. - forcing_terms.md / coil_geometries README: label the HDF5 schema fence as `text` and drop bracket/paren unit annotations. Verified: docs build clean (no missing_docs / invalid-link); regression harness diiid_n1 base vs HEAD shows 30/30 quantities unchanged (.dat coil path identical). Co-Authored-By: Claude Opus 4.8 (1M context) --- docs/src/forcing_terms.md | 12 ++++++------ src/ForcingTerms/CoilGeometry.jl | 2 +- src/ForcingTerms/coil_geometries/README.md | 12 ++++++------ 3 files changed, 13 insertions(+), 13 deletions(-) diff --git a/docs/src/forcing_terms.md b/docs/src/forcing_terms.md index 56774e2e0..4f8d5af25 100644 --- a/docs/src/forcing_terms.md +++ b/docs/src/forcing_terms.md @@ -150,12 +150,12 @@ currents = [1e3, 1e3, 1e3, 1e3] A coil HDF5 file stores one **subgroup per coil set** under a parent group (default `coils`), so a single file can hold many sets and the reader ignores any unrelated content elsewhere: -``` -//x Float64[ncoil, s, nsec] Cartesian metres -//y Float64[ncoil, s, nsec] -//z Float64[ncoil, s, nsec] -//currents Float64[ncoil] (optional) -/ attr nw Float64 (winding multiplier; default 1.0) +```text +//x Float64 ncoil×s×nsec Cartesian metres +//y Float64 ncoil×s×nsec +//z Float64 ncoil×s×nsec +//currents Float64 ncoil optional +/ attr nw Float64 winding multiplier, default 1.0 ``` Use `convert_coil_dat_to_h5` / `convert_coil_h5_to_dat` to migrate legacy files, and diff --git a/src/ForcingTerms/CoilGeometry.jl b/src/ForcingTerms/CoilGeometry.jl index ecc02fc1f..8356d3b07 100644 --- a/src/ForcingTerms/CoilGeometry.jl +++ b/src/ForcingTerms/CoilGeometry.jl @@ -80,7 +80,7 @@ Analytic-source parameters (used only for the matching `source`): - `phi0`: toroidal angle offset of the first generated coil [rad] - `R0`, `a`: helical torus major radius and minor (circle) radius [m] - `m_hel`, `n_hel`: helical poloidal/toroidal mode numbers setting the pitch - - `theta_lo`, `theta_hi`: helical poloidal extent [rad] (full turn if `theta_hi-theta_lo == 2π`) + - `theta_lo`, `theta_hi`: helical poloidal extent in radians; a full turn when `theta_hi-theta_lo == 2π` - `n_coils`: number of helical coils in the array - `offset`: helical coil radial offset from the torus surface [m] - `nsec_gen`: optional override of the generated point count per coil diff --git a/src/ForcingTerms/coil_geometries/README.md b/src/ForcingTerms/coil_geometries/README.md index fc24ec668..cb56f30ef 100644 --- a/src/ForcingTerms/coil_geometries/README.md +++ b/src/ForcingTerms/coil_geometries/README.md @@ -23,12 +23,12 @@ Coil geometry can also be stored in HDF5, which is the modern format and the one the self-contained `gpec.h5` rerun snapshot. One file holds one **subgroup per coil set** under a parent group (default `coils`), and any unrelated content in the file is ignored: -``` -//x Float64[ncoil, s, nsec] Cartesian metres -//y Float64[ncoil, s, nsec] -//z Float64[ncoil, s, nsec] -//currents Float64[ncoil] (optional) -/ attr nw Float64 (winding multiplier; default 1.0) +```text +//x Float64 ncoil×s×nsec Cartesian metres +//y Float64 ncoil×s×nsec +//z Float64 ncoil×s×nsec +//currents Float64 ncoil optional +/ attr nw Float64 winding multiplier, default 1.0 ``` The bundled device library is kept as `.dat` files (human-readable and diff-able in git); From 02b0f0b7428c213a34449a79368aac896bfe12aa Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Thu, 11 Jun 2026 08:07:56 -0400 Subject: [PATCH 022/135] PERTURBED EQUILIBRIUM - NEW FEATURE - Conform response & coupling matrices to coordinate-invariant field space Implements the first slice of issue #233: form the PerturbedEquilibrium control-surface response matrices and resonant coupling matrices in the coordinate-invariant power-normalized field (b-tilde) space of Pharr (2026), extending the convention PR #225 introduced for the DCON energy eigenvalues. - Extract the shared power-norm transform (compute_sqrtamat, compute_sqrt_jac_delpsi, new control_surface_ptof = sqrtamat*sqrt(jarea)) from ForceFreeStates/PowerNorm.jl into Equilibrium/CoordinateInvariant.jl as one source of truth for FFS and PE. - Conform the control-surface matrices in place: P~=ptof^-1*P*ptof (similarity), L~/Lambda~=ptof^-1*(.)*ptof^-dagger and rho~=ptof^dagger*rho*ptof (congruence). Internal physics (singular coupling, field reconstruction, energies) stays in flux space, so all physical quantities are bit-identical. - Expose ptof in HDF5 (response_matrices/powernorm_field_to_flux_operator) with documented recovery formulas so users can recover the flux-space matrices. - Conform the resonant coupling matrices on input (C~=C*ptof); evaluate the applied resonant scalars from flux-space C first so they carry no round-trip noise. Add LHS coordinate-invariance audit annotations (resonant field, penetrated field, Delta', shielding current). - Rename tesla quantities flux->field per Pharr 2026 to remove units confusion: resonant_flux->resonant_field, C_resonant_flux->C_resonant_field, plot_resonant_flux->plot_resonant_field_amplitude. Genuine flux quantities (psi, Phi_x, chi1) are untouched. Regression case and Fortran benchmark updated in lockstep. Verification: physics review PASS (all transform rules exact and consistent); new unit test runtests_coordinate_invariant.jl 9/9 (recovery round-trip, consistency, energy invariance); regression diiid_n1 develop vs local 28/28 quantities 0.0e+00 (the 2 N/A rows are the intended resonant_flux->resonant_field key rename). Co-Authored-By: Claude Opus 4.8 (1M context) --- benchmarks/benchmark_against_fortran_run.jl | 6 +- regression-harness/cases/diiid_n1.toml | 12 +- src/Analysis/PerturbedEquilibrium.jl | 37 +++--- src/Equilibrium/CoordinateInvariant.jl | 116 ++++++++++++++++++ src/Equilibrium/Equilibrium.jl | 3 + src/ForceFreeStates/Free.jl | 2 +- src/ForceFreeStates/PowerNorm.jl | 75 +---------- .../PerturbedEquilibriumStructs.jl | 31 +++-- src/PerturbedEquilibrium/Response.jl | 21 ++-- src/PerturbedEquilibrium/ResponseMatrices.jl | 73 +++++++++++ src/PerturbedEquilibrium/SingularCoupling.jl | 52 +++++--- src/PerturbedEquilibrium/Utils.jl | 19 ++- test/runtests.jl | 1 + test/runtests_coordinate_invariant.jl | 63 ++++++++++ 14 files changed, 372 insertions(+), 139 deletions(-) create mode 100644 src/Equilibrium/CoordinateInvariant.jl create mode 100644 test/runtests_coordinate_invariant.jl diff --git a/benchmarks/benchmark_against_fortran_run.jl b/benchmarks/benchmark_against_fortran_run.jl index d5125af13..db701c9c9 100644 --- a/benchmarks/benchmark_against_fortran_run.jl +++ b/benchmarks/benchmark_against_fortran_run.jl @@ -327,7 +327,7 @@ function load_julia_outputs(h5_path::String) julia["rational_q"] = haskey(f, "$sc/rational_q") ? read(f, "$sc/rational_q") : Float64[] julia["rational_n"] = haskey(f, "$sc/rational_n") ? read(f, "$sc/rational_n") : Int[] julia["rational_m_res"] = haskey(f, "$sc/rational_m_res") ? read(f, "$sc/rational_m_res") : Int[] - julia["resonant_flux"] = haskey(f, "$sc/resonant_flux") ? read(f, "$sc/resonant_flux") : ComplexF64[] + julia["resonant_field"] = haskey(f, "$sc/resonant_field") ? read(f, "$sc/resonant_field") : ComplexF64[] julia["resonant_current"] = haskey(f, "$sc/resonant_current") ? read(f, "$sc/resonant_current") : ComplexF64[] julia["island_half_width"] = haskey(f, "$sc/island_half_width") ? read(f, "$sc/island_half_width") : Float64[] julia["chirikov_parameter"] = haskey(f, "$sc/chirikov_parameter") ? read(f, "$sc/chirikov_parameter") : Float64[] @@ -754,7 +754,7 @@ function build_comparison_table(fort, julia, fortran_dir, bench_dir, nn) row = find_julia_row(julia, q_int, nn) jp_r = (row > 0 && !isempty(julia["rational_psi"])) ? julia["rational_psi"][row] : NaN - j_phi = (row > 0 && !isempty(julia["resonant_flux"])) ? abs(julia["resonant_flux"][row]) : NaN + j_phi = (row > 0 && !isempty(julia["resonant_field"])) ? abs(julia["resonant_field"][row]) : NaN j_wisl= (row > 0 && !isempty(julia["island_half_width"])) ? 2*julia["island_half_width"][row] : NaN j_kch = (row > 0 && !isempty(julia["chirikov_parameter"])) ? julia["chirikov_parameter"][row] : NaN @@ -974,7 +974,7 @@ function generate_plots(fort, julia, bench_dir, nn) # Phi_res (resonant flux / area) f_phires_vals = isempty(fort["Phi_res"]) ? Float64[] : abs.(fort["Phi_res"]) j_phires_psi = julia["rational_psi"] - j_phires_vals = isempty(julia["resonant_flux"]) ? Float64[] : abs.(julia["resonant_flux"]) + j_phires_vals = isempty(julia["resonant_field"]) ? Float64[] : abs.(julia["resonant_field"]) p9 = _singcoup_panel("|Φ_res| [T]", "|Φ_res| vs ψ (n=$nn)", f_psi_rat, f_phires_vals, f_q_labels, j_phires_psi, j_phires_vals) diff --git a/regression-harness/cases/diiid_n1.toml b/regression-harness/cases/diiid_n1.toml index 81b31587a..a9d827649 100644 --- a/regression-harness/cases/diiid_n1.toml +++ b/regression-harness/cases/diiid_n1.toml @@ -190,19 +190,19 @@ label = "Chirikov parameter" noise_threshold = 1e-8 order = 82 -[quantities.resonant_flux] -h5path = "perturbed_equilibrium/singular_coupling/resonant_flux" +[quantities.resonant_field] +h5path = "perturbed_equilibrium/singular_coupling/resonant_field" type = "complex_vector" extract = "norm" -label = "||resonant flux||" +label = "||resonant field||" noise_threshold = 1e-8 order = 83 -[quantities.resonant_flux_all] -h5path = "perturbed_equilibrium/singular_coupling/resonant_flux" +[quantities.resonant_field_all] +h5path = "perturbed_equilibrium/singular_coupling/resonant_field" type = "complex_vector" extract = "all_complex" -label = "resonant flux Phi_res" +label = "resonant field b^r" noise_threshold = 1e-8 # Perturbed equilibrium: energies diff --git a/src/Analysis/PerturbedEquilibrium.jl b/src/Analysis/PerturbedEquilibrium.jl index 3c738ddb3..137ffb4a2 100644 --- a/src/Analysis/PerturbedEquilibrium.jl +++ b/src/Analysis/PerturbedEquilibrium.jl @@ -18,13 +18,14 @@ function _has_pe_data(h5path, key) end """ - plot_resonant_flux(h5path; save_path=nothing) + plot_resonant_field_amplitude(h5path; save_path=nothing) -Scatter plot of `|Φ_res|` per rational surface vs ψ_N. One marker series per toroidal -mode n. Integer-valued q rational surfaces are annotated. +Scatter plot of the resonant field `|b^r|` per rational surface vs ψ_N. One marker series +per toroidal mode n. Integer-valued q rational surfaces are annotated. The resonant field +`b^r = Φ^r/A^r` is the resonant flux normalized by the scalar surface area, in tesla [Pharr 2026]. Requires the perturbed equilibrium module to have been run and -`singular_coupling/resonant_flux` to be present in the HDF5 file. +`singular_coupling/resonant_field` to be present in the HDF5 file. ### Arguments @@ -38,29 +39,29 @@ Requires the perturbed equilibrium module to have been run and A `Plots.jl` plot object. """ -function plot_resonant_flux(h5path; save_path=nothing) +function plot_resonant_field_amplitude(h5path; save_path=nothing) base = "perturbed_equilibrium/singular_coupling/" - _has_pe_data(h5path, base * "resonant_flux") || - return plot(; title="No resonant flux data — run with perturbed equilibrium enabled", legend=false) + _has_pe_data(h5path, base * "resonant_field") || + return plot(; title="No resonant field data — run with perturbed equilibrium enabled", legend=false) - resonant_flux, rational_psi, rational_q, rational_n = h5open(h5path, "r") do fid - read(fid[base * "resonant_flux"]), + resonant_field, rational_psi, rational_q, rational_n = h5open(h5path, "r") do fid + read(fid[base * "resonant_field"]), read(fid[base * "rational_psi"]), read(fid[base * "rational_q"]), read(fid[base * "rational_n"]) end - p = plot(; xlabel="Norm. Poloidal Flux", ylabel="|Φ_res|", - title="Resonant flux |Φ_res| per surface", legend=:outertopright, + p = plot(; xlabel="Norm. Poloidal Flux", ylabel="|b^r| [T]", + title="Resonant field |b^r| per surface", legend=:outertopright, left_margin=10Plots.mm, bottom_margin=5Plots.mm) for nn in unique(rational_n) mask = rational_n .== nn - scatter!(p, rational_psi[mask], abs.(resonant_flux[mask]); + scatter!(p, rational_psi[mask], abs.(resonant_field[mask]); label="n=$nn", markersize=7, markerstrokewidth=0) for k in findall(mask) abs(rational_q[k] - round(rational_q[k])) < 0.05 || continue - annotate!(p, rational_psi[k], abs(resonant_flux[k]), + annotate!(p, rational_psi[k], abs(resonant_field[k]), text(" q=$(round(Int, rational_q[k]))", 8, :left, :black)) end end @@ -244,13 +245,13 @@ end Five-panel summary of resonant coupling quantities at each rational surface vs ψ_N: - - `|Φ_res|`: resonant flux (`plot_resonant_flux`) + - `|b^r|`: resonant field (`plot_resonant_field_amplitude`) - `Re(Δ')`: tearing stability parameter (`plot_driven_delta_prime`) - `|I_res|`: resonant current - `w/2`: island half-width (`plot_island_widths`) - `K`: Chirikov overlap parameter (`plot_chirikov_parameter`) -Inspired by `plot_resonant_field.py` from OMFIT GPEC. +Inspired by `plot_resonant_flux.py` from OMFIT GPEC. ### Arguments @@ -265,7 +266,7 @@ Inspired by `plot_resonant_field.py` from OMFIT GPEC. A `Plots.jl` plot object. """ function plot_resonant_field(h5path; save_path=nothing) - p1 = plot_resonant_flux(h5path) + p1 = plot_resonant_field_amplitude(h5path) p2 = plot_driven_delta_prime(h5path) p3 = _plot_resonant_current(h5path) p4 = plot_island_widths(h5path) @@ -421,7 +422,7 @@ end Three-panel composite summary of perturbed equilibrium results: - - Top-left: Resonant flux per surface (`plot_resonant_flux`) + - Top-left: Resonant field per surface (`plot_resonant_field_amplitude`) - Top-right: Edge |b_ψ| spectrum - Bottom: ξ_ψ mode spectrogram (`plot_mode_spectrogram`) @@ -438,7 +439,7 @@ Three-panel composite summary of perturbed equilibrium results: A `Plots.jl` plot object. """ function plot_perturbed_equilibrium_summary(h5path; save_path=nothing) - p_islands = plot_resonant_flux(h5path) + p_islands = plot_resonant_field_amplitude(h5path) p_bpsi = _plot_bpsi_edge_spectrum(h5path) p_spectro = plot_mode_spectrogram(h5path; component=:xi_psi) diff --git a/src/Equilibrium/CoordinateInvariant.jl b/src/Equilibrium/CoordinateInvariant.jl new file mode 100644 index 000000000..b354118a7 --- /dev/null +++ b/src/Equilibrium/CoordinateInvariant.jl @@ -0,0 +1,116 @@ +""" +Coordinate-invariant (power-normalized field) flux-surface operators. + +These building blocks implement the √area weighting of Pharr (2026), +"Coordinate-invariant flux-surface Fourier analysis in tokamaks". They are the +single source of truth for the map between a flux-surface field component and its +power-normalized (coordinate-invariant) field representation, shared by the +ForceFreeStates and PerturbedEquilibrium modules. + +The central operator is + + ptof = sqrtamat · √jarea + +which maps a power-normalized field `b̃` to the coordinate flux harmonics `Φ`: +`Φ = ptof · b̃` (so `b̃ = ptof⁻¹ · Φ`). The singular values of any operator +expressed in the `b̃` basis are independent of the straight-field-line +(working) coordinate. + +See `scripts/test_power_norm_invariance.jl` for the numerical invariance proof of +the underlying √weight identity and angle map. +""" + +""" + compute_sqrt_jac_delpsi(equil, psi, mtheta) -> Vector{Float64} + +Compute √(J·|∇ψ|) at `mtheta` equally-spaced θ points on the flux surface at `psi`. +This is the √weight function that maps a field component `b(θ)` to its +power-normalized form `√(J|∇ψ|)·b(θ)` in θ-space. +""" +function compute_sqrt_jac_delpsi(equil::PlasmaEquilibrium, psi::Float64, mtheta::Int) + sqrt_jac_delpsi = Vector{Float64}(undef, mtheta) + + hint2d = (Ref(1), Ref(1)) + for itheta in 0:(mtheta-1) + theta = itheta / mtheta # normalized to [0, 1) + m = flux_surface_metric(equil, psi, theta; hint=hint2d) + sqrt_jac_delpsi[itheta+1] = sqrt(abs(m.jac * m.delpsi)) + end + + return sqrt_jac_delpsi +end + +""" + compute_sqrtamat(equil, psi, ft) -> Matrix{ComplexF64} + +Build the √A convolution matrix `sqrtamat`. Produces a Hermitian Toeplitz matrix +with entries sqrtamat[m',k] = ŵ_{m_k − m'} where ŵ_n = (1/N)Σ w_j exp(+inθ_j) and +w(θ) = √(J·|∇ψ|). + +Operationally, sqrtamat is the mode-space √weight operator: for a field b with +Fourier coefficients b_fft, it satisfies the identity + `‖sqrtamat·b_fft‖² = N² · ∫ |b|² · J|∇ψ| dθ` +which is Jacobian-invariant on a given flux surface (see +`scripts/test_power_norm_invariance.jl`). + +The backward step uses exp(−imθ)/(1/N) normalization paired with the Julia +forward FT exp(+imθ) so that round-trip = identity and the convolution +structure is correct. +""" +function compute_sqrtamat( + equil::PlasmaEquilibrium, + psi::Float64, + ft::Utilities.FourierTransforms.FourierTransform +) + mpert = ft.mpert + mtheta = ft.mtheta + + sqrt_jdp = compute_sqrt_jac_delpsi(equil, psi, mtheta) + sqrtamat = zeros(ComplexF64, mpert, mpert) + + e_k = zeros(ComplexF64, mpert) + for k in 1:mpert + e_k .= 0.0 + e_k[k] = 1.0 + 0.0im + + # Standard backward FT: f(θ_j) = (1/N) Σ_m c_m exp(-imθ_j) + # exp(-imθ) = cos(mθ) - i·sin(mθ), so: + # Re(f) = (1/N)(cslth·Re(c) + snlth·Im(c)) + # Im(f) = (1/N)(cslth·Im(c) - snlth·Re(c)) + real_part = (ft.cslth * real.(e_k) .+ ft.snlth * imag.(e_k)) ./ mtheta + imag_part = (ft.cslth * imag.(e_k) .- ft.snlth * real.(e_k)) ./ mtheta + theta_vec = complex.(real_part, imag_part) + + # Multiply pointwise by √(J·|∇ψ|) in theta-space + theta_vec .*= sqrt_jdp + + # Forward FT: theta-space → mode-space (exp(+imθ), Julia convention) + sqrtamat[:, k] .= ft(theta_vec) + end + + return sqrtamat +end + +""" + control_surface_ptof(equil, psi, ft) -> Matrix{ComplexF64} + +Build the power-norm-field → flux operator `ptof = sqrtamat · √jarea` at the flux +surface `psi`, where `jarea = ∫ J|∇ψ| dθ` is the scalar flux-surface area. + +`ptof` maps a power-normalized field `b̃` to the coordinate flux harmonics `Φ`: +`Φ = ptof · b̃`. To express a flux-space operator/generator in the coordinate-invariant +`b̃` basis (and back) use: + - operator `Ã = ptof⁻¹ · A · ptof` (e.g. permeability `Φ_tot = A·Φ_x`) + - generator `G̃ = ptof⁻¹ · G · ptof⁻†` (e.g. inductance, energy = Φ†·G⁻¹·Φ) + - row map `C̃ = C · ptof` (e.g. coupling, scalar = C·Φ_x) +The singular values / spectrum in the `b̃` basis are coordinate-invariant. +""" +function control_surface_ptof( + equil::PlasmaEquilibrium, + psi::Float64, + ft::Utilities.FourierTransforms.FourierTransform +) + sqrtamat = compute_sqrtamat(equil, psi, ft) + jarea = flux_surface_area(equil, psi, ft.mtheta) + return sqrtamat .* sqrt(jarea) +end diff --git a/src/Equilibrium/Equilibrium.jl b/src/Equilibrium/Equilibrium.jl index c2eec3445..e93ee2d39 100644 --- a/src/Equilibrium/Equilibrium.jl +++ b/src/Equilibrium/Equilibrium.jl @@ -8,10 +8,12 @@ using TOML using FastInterpolations using AdaptiveArrayPools import StaticArrays: @MMatrix, SVector +import ..Utilities # --- Internal Module Structure --- include("EquilibriumTypes.jl") include("FluxSurfaceMetrics.jl") +include("CoordinateInvariant.jl") include("ReadEquilibrium.jl") include("DirectEquilibrium.jl") include("DirectEquilibriumArcLength.jl") @@ -26,6 +28,7 @@ export setup_equilibrium, EquilibriumConfig, PlasmaEquilibrium, EquilibriumParam ProfileSplines, GeometryProfileSplines, compute_geometry_profiles, KineticProfileSplines, load_kinetic_profiles export flux_surface_metric, flux_surface_area +export compute_sqrt_jac_delpsi, compute_sqrtamat, control_surface_ptof # --- Constants --- const mu0 = 4π * 1e-7 diff --git a/src/ForceFreeStates/Free.jl b/src/ForceFreeStates/Free.jl index 2afc7a9d7..7468883db 100644 --- a/src/ForceFreeStates/Free.jl +++ b/src/ForceFreeStates/Free.jl @@ -98,7 +98,7 @@ and data dumping. # Computed directly here (no spline); spline is used by the edge scan. mtheta_eq = length(equil.rzphi_ys) ft_pn = Utilities.FourierTransforms.FourierTransform(mtheta_eq, mpert, mlow) - sqrtamat_pn = compute_sqrtamat(equil, psilim, ft_pn) + sqrtamat_pn = Equilibrium.compute_sqrtamat(equil, psilim, ft_pn) jarea_pn = Equilibrium.flux_surface_area(equil, psilim, mtheta_eq) pn_result = compute_power_norm_eigenvalues(vac_data.wt0, wp, vac_data.wv, sqrtamat_pn, jarea_pn, equil, psilim, intr; all_eigenvalues=true) vac_data.pn_et .= pn_result.pn_et_all diff --git a/src/ForceFreeStates/PowerNorm.jl b/src/ForceFreeStates/PowerNorm.jl index 0b1d503b1..93cb44cb5 100644 --- a/src/ForceFreeStates/PowerNorm.jl +++ b/src/ForceFreeStates/PowerNorm.jl @@ -28,76 +28,9 @@ area-integral precision floor ~1e-6): - The eigenspectrum of `W_Φ`. """ -""" - compute_sqrt_jac_delpsi(equil, psi, mtheta) -> Vector{Float64} - -Compute √(J·|∇ψ|) at `mtheta` equally-spaced θ points on the flux surface at `psi`. -This is the √weight function that maps a field component `b(θ)` to its -power-normalized form `√(J|∇ψ|)·b(θ)` in θ-space. -""" -function compute_sqrt_jac_delpsi(equil::Equilibrium.PlasmaEquilibrium, psi::Float64, mtheta::Int) - sqrt_jac_delpsi = Vector{Float64}(undef, mtheta) - - hint2d = (Ref(1), Ref(1)) - for itheta in 0:(mtheta-1) - theta = itheta / mtheta # normalized to [0, 1) - m = Equilibrium.flux_surface_metric(equil, psi, theta; hint=hint2d) - sqrt_jac_delpsi[itheta+1] = sqrt(abs(m.jac * m.delpsi)) - end - - return sqrt_jac_delpsi -end - -""" - compute_sqrtamat(equil, psi, ft) -> Matrix{ComplexF64} - -Build the √A convolution matrix `sqrtamat`. Produces a Hermitian Toeplitz matrix -with entries sqrtamat[m',k] = ŵ_{m_k − m'} where ŵ_n = (1/N)Σ w_j exp(+inθ_j) and -w(θ) = √(J·|∇ψ|). - -Operationally, sqrtamat is the mode-space √weight operator: for a field b with -Fourier coefficients b_fft, it satisfies the identity - `‖sqrtamat·b_fft‖² = N² · ∫ |b|² · J|∇ψ| dθ` -which is Jacobian-invariant on a given flux surface (see -`scripts/test_power_norm_invariance.jl`). - -The backward step uses exp(−imθ)/(1/N) normalization paired with the Julia -forward FT exp(+imθ) so that round-trip = identity and the convolution -structure is correct. -""" -function compute_sqrtamat( - equil::Equilibrium.PlasmaEquilibrium, - psi::Float64, - ft::Utilities.FourierTransforms.FourierTransform -) - mpert = ft.mpert - mtheta = ft.mtheta - - sqrt_jdp = compute_sqrt_jac_delpsi(equil, psi, mtheta) - sqrtamat = zeros(ComplexF64, mpert, mpert) - - e_k = zeros(ComplexF64, mpert) - for k in 1:mpert - e_k .= 0.0 - e_k[k] = 1.0 + 0.0im - - # Standard backward FT: f(θ_j) = (1/N) Σ_m c_m exp(-imθ_j) - # exp(-imθ) = cos(mθ) - i·sin(mθ), so: - # Re(f) = (1/N)(cslth·Re(c) + snlth·Im(c)) - # Im(f) = (1/N)(cslth·Im(c) - snlth·Re(c)) - real_part = (ft.cslth * real.(e_k) .+ ft.snlth * imag.(e_k)) ./ mtheta - imag_part = (ft.cslth * imag.(e_k) .- ft.snlth * real.(e_k)) ./ mtheta - theta_vec = complex.(real_part, imag_part) - - # Multiply pointwise by √(J·|∇ψ|) in theta-space - theta_vec .*= sqrt_jdp - - # Forward FT: theta-space → mode-space (exp(+imθ), Julia convention) - sqrtamat[:, k] .= ft(theta_vec) - end - - return sqrtamat -end +# The √weight building blocks `compute_sqrt_jac_delpsi`, `compute_sqrtamat`, and the +# `control_surface_ptof` operator now live in `Equilibrium/CoordinateInvariant.jl` so the +# ForceFreeStates and PerturbedEquilibrium modules share one coordinate-invariant definition. """ compute_power_norm_eigenvalues(wt, wp, wv, sqrtamat, jarea, equil, psi, intr; all_eigenvalues=false) @@ -277,7 +210,7 @@ function free_compute_sqrtamat_spline(ctrl::ForceFreeStatesControl, equil::Equil psii, Roots.Newton() ) - sqrtamat = compute_sqrtamat(equil, psi_array[i], ft) + sqrtamat = Equilibrium.compute_sqrtamat(equil, psi_array[i], ft) jarea = Equilibrium.flux_surface_area(equil, psi_array[i], mtheta_eq) # Flatten sqrtamat into first mpert^2 entries, jarea as last entry diff --git a/src/PerturbedEquilibrium/PerturbedEquilibriumStructs.jl b/src/PerturbedEquilibrium/PerturbedEquilibriumStructs.jl index b065294c8..c1fd8745d 100644 --- a/src/PerturbedEquilibrium/PerturbedEquilibriumStructs.jl +++ b/src/PerturbedEquilibrium/PerturbedEquilibriumStructs.jl @@ -85,7 +85,7 @@ Response fields (mode space): Coupling matrices [n_rational × numpert_total] — one row per resonant (surface, n) pair. Each row maps the full applied field to the resonant response at that surface. Matches Fortran `C_f_x_out`, `C_i_x_out`, etc. (shape [mode_C, m_out]). - - `C_resonant_flux` - Φ_r/A coupling (singcoup row 1) + - `C_resonant_field` - Φ_r/A^r coupling (resonant field b^r in tesla; singcoup row 1) [Pharr 2026] - `C_resonant_current` - Resonant current coupling (singcoup row 2) - `C_island_width_sq` - (w/2)² coupling (singcoup row 3) - `C_penetrated_field` - Penetrated field coupling (singcoup row 4) @@ -93,7 +93,7 @@ Matches Fortran `C_f_x_out`, `C_i_x_out`, etc. (shape [mode_C, m_out]). Applied resonant vectors [n_rational] = C · forcing_amplitudes. Matches Fortran `Phi_res`, `w_isl`, `K_isl`, `Delta`. - - `resonant_flux`, `resonant_current`, `island_width_sq`, `penetrated_field`, `delta_prime` + - `resonant_field`, `resonant_current`, `island_width_sq`, `penetrated_field`, `delta_prime` Diagnostics [n_rational]: - `island_half_width::Vector{Float64}` - w/2 = sqrt(|island_width_sq|) from applied forcing @@ -102,11 +102,15 @@ Diagnostics [n_rational]: Metadata [n_rational] — identifies each (surface, n) row: - `rational_psi`, `rational_q`, `rational_m_res`, `rational_n`, `rational_surface_idx` -Control surface matrices [numpert_total × numpert_total]: - - `plasma_inductance` - Lambda (wt0-based plasma inductance) - - `surface_inductance` - L (vacuum surface inductance from Green's functions) - - `permeability` - P = Lambda * L^{-1} (plasma response matrix, Phi_tot = P * Phi_x) - - `reluctance` - Rho = L^{-1} * (Lambda - L) * L^{-1} +Control surface matrices [numpert_total × numpert_total], stored in the coordinate-invariant +power-normalized field (b̃) space (issue #233 / Pharr 2026). Recover the flux-space forms with +the `control_surface_field_operator` (`ptof`, Φ = ptof·b̃): e.g. `P_flux = ptof·P̃·ptof⁻¹`, +`L_flux = ptof·L̃·ptof†`. + - `plasma_inductance` - Λ̃ = ptof⁻¹·Λ·ptof⁻† (wt0-based plasma inductance, congruence) + - `surface_inductance` - L̃ = ptof⁻¹·L·ptof⁻† (vacuum surface inductance, congruence) + - `permeability` - P̃ = ptof⁻¹·P·ptof (plasma response operator P=Λ·L⁻¹, similarity) + - `reluctance` - ϱ̃ = ptof†·ϱ·ptof (ϱ = L⁻¹·(Λ−L)·L⁻¹, congruence) + - `control_surface_field_operator` - ptof = sqrtamat·√jarea at psilim (field → flux recovery operator) Energies (Fortran gpout convention; Φ_x external flux, Φ_tot total flux, L/Λ inductances): - `vacuum_energy` - Re( ⟨Φ_x, L⁻¹·Φ_x⟩ ) / 4 (energy to perturb the vacuum) @@ -125,14 +129,14 @@ Energies (Fortran gpout convention; Φ_x external flux, Φ_tot total flux, L/Λ xi_n_modes::Union{Nothing, Matrix{ComplexF64}} = nothing # physical normal displacement xi_n [npsi, mpert] # Coupling matrices [n_rational × numpert_total] - C_resonant_flux::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) + C_resonant_field::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) C_resonant_current::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) C_island_width_sq::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) C_penetrated_field::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) C_delta_prime::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # Applied resonant vectors [n_rational] = C · amp_vec - resonant_flux::Vector{ComplexF64} = ComplexF64[] + resonant_field::Vector{ComplexF64} = ComplexF64[] resonant_current::Vector{ComplexF64} = ComplexF64[] island_width_sq::Vector{ComplexF64} = ComplexF64[] penetrated_field::Vector{ComplexF64} = ComplexF64[] @@ -154,10 +158,11 @@ Energies (Fortran gpout convention; Φ_x external flux, Φ_tot total flux, L/Λ response_vec::Vector{ComplexF64} = ComplexF64[] # Phi_tot = P * Phi_x: total plasma response # Control surface matrices [numpert_total × numpert_total] - plasma_inductance::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # Lambda - surface_inductance::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # L - permeability::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # P = Lambda * L^{-1} - reluctance::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # Rho = L^{-1}*(Lambda-L)*L^{-1} + plasma_inductance::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # Λ̃ (field space) + surface_inductance::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # L̃ (field space) + permeability::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # P̃ = ptof⁻¹·Λ·L⁻¹·ptof + reluctance::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # ϱ̃ = ptof†·L⁻¹·(Λ−L)·L⁻¹·ptof + control_surface_field_operator::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # ptof: field → flux recovery # Energies — see the struct docstring for formulas vacuum_energy::Float64 = 0.0 diff --git a/src/PerturbedEquilibrium/Response.jl b/src/PerturbedEquilibrium/Response.jl index 5cc4ec327..8020ca491 100644 --- a/src/PerturbedEquilibrium/Response.jl +++ b/src/PerturbedEquilibrium/Response.jl @@ -54,15 +54,22 @@ function compute_plasma_response!( L_inv = inv(surface_inductance) reluctance = L_inv * (plasma_inductance - surface_inductance) * L_inv - # Store control surface matrices in state for HDF5 output - state.plasma_inductance = plasma_inductance - state.surface_inductance = surface_inductance - state.permeability = permeability - state.reluctance = reluctance - - # Store permeability in internal state for singular coupling use + # Store permeability in internal state for singular coupling / field reconstruction. + # These consumers operate on the physical control-surface flux Φ_x, so the internal + # copy stays in flux space; only the stored/output matrices are conformed below. intr.plasma_response = permeability + # Conform the control-surface matrices to the coordinate-invariant power-normalized + # field (b̃) space for output (issue #233 / Pharr 2026). The flux-space forms are + # recoverable from the stored `ptof` operator (Φ = ptof·b̃) — see Utils.jl output docs. + ptof = build_control_surface_ptof(equil, ffs_intr) + field_mats = field_space_response_matrices(plasma_inductance, surface_inductance, permeability, reluctance, ptof) + state.plasma_inductance = field_mats.plasma_inductance + state.surface_inductance = field_mats.surface_inductance + state.permeability = field_mats.permeability + state.reluctance = field_mats.reluctance + state.control_surface_field_operator = ptof + forcing_vector = map_forcing_to_eigenmodes(intr.forcing_modes, ffs_intr) response_vector = compute_plasma_response_vector(permeability, forcing_vector) diff --git a/src/PerturbedEquilibrium/ResponseMatrices.jl b/src/PerturbedEquilibrium/ResponseMatrices.jl index d6173d0a0..015a4e542 100644 --- a/src/PerturbedEquilibrium/ResponseMatrices.jl +++ b/src/PerturbedEquilibrium/ResponseMatrices.jl @@ -298,6 +298,79 @@ function calc_permeability( return plasma_inductance / surface_inductance end +""" + build_control_surface_ptof( + equil::Equilibrium.PlasmaEquilibrium, + ffs_intr::ForceFreeStatesInternal + )::Matrix{ComplexF64} + +Build the numpert_total × numpert_total power-norm-field → flux operator `ptof` at the +control surface (psilim). The mpert × mpert single-n block (Equilibrium.control_surface_ptof) +is repeated block-diagonally over the `npert` toroidal harmonics, matching the +numpert_total mode ordering used by the response matrices. + +`ptof` maps a power-normalized control-surface field `b̃` to the coordinate flux harmonics +`Φ`: `Φ = ptof · b̃`. It is the operator users need to recover the flux-space matrices from +the stored coordinate-invariant (field-space) ones — see `field_space_response_matrices`. +[Pharr 2026] +""" +function build_control_surface_ptof( + equil::Equilibrium.PlasmaEquilibrium, + ffs_intr::ForceFreeStatesInternal +)::Matrix{ComplexF64} + mpert = ffs_intr.mpert + npert = ffs_intr.npert + Npert = ffs_intr.numpert_total + + mtheta_eq = length(equil.rzphi_ys) + ft = Utilities.FourierTransforms.FourierTransform(mtheta_eq, mpert, ffs_intr.mlow) + ptof_block = Equilibrium.control_surface_ptof(equil, ffs_intr.psilim, ft) + + npert == 1 && return Matrix{ComplexF64}(ptof_block) + + ptof_full = zeros(ComplexF64, Npert, Npert) + for in in 1:npert + r = ((in - 1) * mpert + 1):(in * mpert) + ptof_full[r, r] .= ptof_block + end + return ptof_full +end + +""" + field_space_response_matrices( + plasma_inductance, surface_inductance, permeability, reluctance, ptof + )::NamedTuple + +Express the control-surface response matrices in the coordinate-invariant power-normalized +field (b̃) space, given the flux-space matrices and the `ptof` operator (`Φ = ptof·b̃`). + +The matrices fall into two algebraic classes: + - **Operators** (map flux → flux): permeability `P` (Φ_tot = P·Φ_x) transforms by similarity + `P̃ = ptof⁻¹·P·ptof`. Its singular values are coordinate-invariant. + - **Quadratic generators** (energy = Φ†·G⁻¹·Φ): inductances `Λ`, `L` transform by congruence + `G̃ = ptof⁻¹·G·ptof⁻†`; the inverse-inductance-like reluctance `ϱ` (energy = Φ†·ϱ·Φ) + transforms as `ϱ̃ = ptof†·ϱ·ptof`. Their spectra are coordinate-invariant. + +These rules are mutually consistent: `P̃ = Λ̃·L̃⁻¹ = ptof⁻¹·Λ·L⁻¹·ptof = ptof⁻¹·P·ptof`, and +`ϱ̃ = L̃⁻¹·(Λ̃−L̃)·L̃⁻¹`. To recover the flux-space forms, invert each map with the stored +`ptof` (e.g. `P_flux = ptof·P̃·ptof⁻¹`, `L_flux = ptof·L̃·ptof†`). [Pharr 2026] +""" +function field_space_response_matrices( + plasma_inductance::Matrix{ComplexF64}, + surface_inductance::Matrix{ComplexF64}, + permeability::Matrix{ComplexF64}, + reluctance::Matrix{ComplexF64}, + ptof::Matrix{ComplexF64} +)::NamedTuple + ptof_inv = inv(ptof) + return ( + plasma_inductance=ptof_inv * plasma_inductance * ptof_inv', + surface_inductance=ptof_inv * surface_inductance * ptof_inv', + permeability=ptof_inv * permeability * ptof, + reluctance=ptof' * reluctance * ptof + ) +end + """ map_forcing_to_eigenmodes( forcing_modes::Vector{ForcingMode}, diff --git a/src/PerturbedEquilibrium/SingularCoupling.jl b/src/PerturbedEquilibrium/SingularCoupling.jl index f3eca3f61..6816e1c65 100644 --- a/src/PerturbedEquilibrium/SingularCoupling.jl +++ b/src/PerturbedEquilibrium/SingularCoupling.jl @@ -62,10 +62,10 @@ Matching Fortran GPEC output: `C_f_x_out` (coupling matrix) and `Phi_res`, `w_is Populates `state` with: Coupling matrices `[n_rational × numpert_total]` — C[row, j] = coupling when forcing mode j has unit amplitude: - - `C_resonant_flux`, `C_resonant_current`, `C_island_width_sq`, `C_penetrated_field`, `C_delta_prime` + - `C_resonant_field`, `C_resonant_current`, `C_island_width_sq`, `C_penetrated_field`, `C_delta_prime` Applied resonant vectors `[n_rational]` = C · amp_vec: - - `resonant_flux`, `resonant_current`, `island_width_sq`, `penetrated_field`, `delta_prime` + - `resonant_field`, `resonant_current`, `island_width_sq`, `penetrated_field`, `delta_prime` Diagnostics `[n_rational]`: `island_half_width`, `chirikov_parameter` @@ -125,7 +125,7 @@ function compute_singular_coupling_metrics!( ctrl.verbose && @info "Found $n_rational resonant (surface, n) pairs" # Phase 2: Allocate output arrays - state.C_resonant_flux = zeros(ComplexF64, n_rational, numpert_total) + state.C_resonant_field = zeros(ComplexF64, n_rational, numpert_total) state.C_resonant_current = zeros(ComplexF64, n_rational, numpert_total) state.C_island_width_sq = zeros(ComplexF64, n_rational, numpert_total) state.C_penetrated_field = zeros(ComplexF64, n_rational, numpert_total) @@ -229,19 +229,28 @@ function compute_singular_coupling_metrics!( bwp1_l = 2π * im * chi1 * (singfac_l * xsp1_l - nn * q1_l * xsp_l) bwp1_r = 2π * im * chi1 * (singfac_r * xsp1_r - nn * q1_r * xsp_r) jump_vec[k] = bwp1_r - bwp1_l - # C_penetrated_field: midpoint of b^ψ at lpsi/rpsi divided by area. - # Matches Fortran gpout_resp: gpeq_interp_singsurf evaluates bwp_mn at respsi + # C_penetrated_field: midpoint of b^ψ at lpsi/rpsi divided by the scalar surface area. + # Matches Fortran gpout_resp: gpeq_interp_singsurf evaluates bwp_mn at respsi. + # LHS normalization audit (#233): the resonant flux Φ^r divided by the scalar area A^r + # is a genuine field amplitude in tesla and is coordinate-invariant [Pharr 2026; cf. + # the resonant-field definition in the Conventions Reference]. b_l = chi1 * singfac_l * 2π * im * xsp_l b_r = chi1 * singfac_r * 2π * im * xsp_r state.C_penetrated_field[row, k] = (b_l + b_r) / 2 / area end + # LHS normalization audit (#233) — output scalar coordinate-invariance per row: + # - Δ' (1/length): the resonant-surface jump in ∂b^ψ/∂ψ over 2π·χ₁; the tearing index is + # coordinate-invariant (its sign/zero-crossing set the stability boundary) [Glasser 2016]. + # - resonant (shielding) current: j_c already integrates jac·|∇ψ| over the surface, so the + # Jacobian weighting is carried inside j_c — no separate area factor needed. + # - resonant flux → field: Φ^r/A^r [T], invariant [Park 2008; Pharr 2026]. state.C_delta_prime[row, :] = jump_vec ./ (twopi * chi1) state.C_resonant_current[row, :] = jump_vec .* (-j_c / (twopi * m_res)) - # Matches Fortran gpout_resp: singflx = L·fkaxmn, singbnoflxs = singflx/area, + # Matches Fortran gpout_resp: singflx = L·fkaxmn, resonant field = singflx/area, # islandhwids = 4·singflx/(2π·shear·q·chi1) singflx_pre = (L_mm / (twopi * nn)) .* state.C_resonant_current[row, :] - state.C_resonant_flux[row, :] = singflx_pre ./ area + state.C_resonant_field[row, :] = singflx_pre ./ area if abs(shear) > 1e-10 state.C_island_width_sq[row, :] = (4.0 / (twopi * shear * sing_surf.q * chi1)) .* singflx_pre end @@ -258,18 +267,31 @@ function compute_singular_coupling_metrics!( end end - # Phase 4: Apply forcing amplitudes → R = C · amp_vec - amp_vec = zeros(ComplexF64, numpert_total) + # Phase 4: Apply forcing amplitudes → R = C · Φ_x. The applied resonant scalars are + # physical, coordinate-invariant quantities, so evaluate them from the flux-space C and + # the physical forcing Φ_x (bit-identical to pre-conform values). + forcing_flux = zeros(ComplexF64, numpert_total) for mode in intr.forcing_modes j = findfirst(k -> intr.m_modes[k] == mode.m && intr.n_modes[k] == mode.n, 1:numpert_total) - isnothing(j) || (amp_vec[j] = mode.amplitude) + isnothing(j) || (forcing_flux[j] = mode.amplitude) end - state.resonant_flux = state.C_resonant_flux * amp_vec - state.resonant_current = state.C_resonant_current * amp_vec - state.island_width_sq = state.C_island_width_sq * amp_vec - state.penetrated_field = state.C_penetrated_field * amp_vec - state.delta_prime = state.C_delta_prime * amp_vec + state.resonant_field = state.C_resonant_field * forcing_flux + state.resonant_current = state.C_resonant_current * forcing_flux + state.island_width_sq = state.C_island_width_sq * forcing_flux + state.penetrated_field = state.C_penetrated_field * forcing_flux + state.delta_prime = state.C_delta_prime * forcing_flux + + # Conform the stored coupling-matrix input basis to the coordinate-invariant power-normalized + # field (b̃) space (#233 / Pharr 2026): C̃ = C·ptof, so each stored row acts on the applied + # field b̃_x (Φ_x = ptof·b̃_x) and its singular values become coordinate-invariant. Done after + # the applied-vector evaluation above so those physical scalars carry no round-trip noise. + ptof = build_control_surface_ptof(equil, ffs_intr) + state.C_resonant_field = state.C_resonant_field * ptof + state.C_resonant_current = state.C_resonant_current * ptof + state.C_island_width_sq = state.C_island_width_sq * ptof + state.C_penetrated_field = state.C_penetrated_field * ptof + state.C_delta_prime = state.C_delta_prime * ptof # Phase 5: Island diagnostics from applied resonant vectors compute_island_diagnostics!(state, n_rational) diff --git a/src/PerturbedEquilibrium/Utils.jl b/src/PerturbedEquilibrium/Utils.jl index 4c4f6a00c..6f32cc1ad 100644 --- a/src/PerturbedEquilibrium/Utils.jl +++ b/src/PerturbedEquilibrium/Utils.jl @@ -66,13 +66,19 @@ perturbed_equilibrium/ │ ├── xi_n # Physical normal displacement xi_n (ComplexF64 [npsi, mpert]) │ ├── b_theta │ └── b_zeta +├── response_matrices/ # [numpert_total × numpert_total], power-normalized field (b̃) space +│ ├── plasma_inductance # Λ̃ = ptof⁻¹·Λ·ptof⁻† +│ ├── surface_inductance # L̃ = ptof⁻¹·L·ptof⁻† +│ ├── permeability # P̃ = ptof⁻¹·P·ptof (P = Λ·L⁻¹) +│ ├── reluctance # ϱ̃ = ptof†·ϱ·ptof +│ └── powernorm_field_to_flux_operator # ptof = sqrtamat·√jarea; recover flux via Φ = ptof·b̃ ├── singular_coupling/ -│ ├── C_resonant_flux # [n_rational × numpert_total] coupling matrix +│ ├── C_resonant_field # [n_rational × numpert_total] coupling matrix (b̃-space input, resonant field b^r=Φ^r/A^r [T]) │ ├── C_resonant_current │ ├── C_island_width_sq │ ├── C_penetrated_field │ ├── C_delta_prime -│ ├── resonant_flux # [n_rational] applied vector = C · amp_vec +│ ├── resonant_field # [n_rational] applied vector = C̃ · b̃_x (resonant field b^r [T]) │ ├── resonant_current │ ├── island_width_sq │ ├── penetrated_field @@ -108,12 +114,15 @@ function write_outputs_to_HDF5( !isempty(state.forcing_vec) && (pe_group["forcing_vec"] = state.forcing_vec) !isempty(state.response_vec) && (pe_group["response_vec"] = state.response_vec) - # Control surface matrices [numpert_total × numpert_total] + # Control surface matrices [numpert_total × numpert_total], in coordinate-invariant + # power-normalized field (b̃) space. Recover flux space with the stored ptof operator + # (Φ = ptof·b̃): e.g. P_flux = ptof·P̃·ptof⁻¹, L_flux = ptof·L̃·ptof†. [Pharr 2026] mat_group = haskey(pe_group, "response_matrices") ? pe_group["response_matrices"] : create_group(pe_group, "response_matrices") !isempty(state.plasma_inductance) && (mat_group["plasma_inductance"] = state.plasma_inductance) !isempty(state.surface_inductance) && (mat_group["surface_inductance"] = state.surface_inductance) !isempty(state.permeability) && (mat_group["permeability"] = state.permeability) !isempty(state.reluctance) && (mat_group["reluctance"] = state.reluctance) + !isempty(state.control_surface_field_operator) && (mat_group["powernorm_field_to_flux_operator"] = state.control_surface_field_operator) # Response fields (ComplexF64 directly) response_group = haskey(pe_group, "response") ? pe_group["response"] : create_group(pe_group, "response") @@ -174,14 +183,14 @@ function write_outputs_to_HDF5( coupling_group = haskey(pe_group, "singular_coupling") ? pe_group["singular_coupling"] : create_group(pe_group, "singular_coupling") # Coupling matrices [n_rational × numpert_total] - !isempty(state.C_resonant_flux) && (coupling_group["C_resonant_flux"] = state.C_resonant_flux) + !isempty(state.C_resonant_field) && (coupling_group["C_resonant_field"] = state.C_resonant_field) !isempty(state.C_resonant_current) && (coupling_group["C_resonant_current"] = state.C_resonant_current) !isempty(state.C_island_width_sq) && (coupling_group["C_island_width_sq"] = state.C_island_width_sq) !isempty(state.C_penetrated_field) && (coupling_group["C_penetrated_field"] = state.C_penetrated_field) !isempty(state.C_delta_prime) && (coupling_group["C_delta_prime"] = state.C_delta_prime) # Applied resonant vectors [n_rational] - !isempty(state.resonant_flux) && (coupling_group["resonant_flux"] = state.resonant_flux) + !isempty(state.resonant_field) && (coupling_group["resonant_field"] = state.resonant_field) !isempty(state.resonant_current) && (coupling_group["resonant_current"] = state.resonant_current) !isempty(state.island_width_sq) && (coupling_group["island_width_sq"] = state.island_width_sq) !isempty(state.penetrated_field) && (coupling_group["penetrated_field"] = state.penetrated_field) diff --git a/test/runtests.jl b/test/runtests.jl index f424a7d23..8cecea160 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -24,6 +24,7 @@ else include("./runtests_fouriertransforms.jl") include("./runtests_vacuum.jl") include("./runtests_equil.jl") + include("./runtests_coordinate_invariant.jl") include("./runtests_eulerlagrange.jl") include("./runtests_riccati.jl") include("./runtests_parallel_integration.jl") diff --git a/test/runtests_coordinate_invariant.jl b/test/runtests_coordinate_invariant.jl new file mode 100644 index 000000000..34eedcc05 --- /dev/null +++ b/test/runtests_coordinate_invariant.jl @@ -0,0 +1,63 @@ +# Tests for the coordinate-invariant (power-normalized field, b̃) transform of the +# PerturbedEquilibrium control-surface response matrices (issue #233 / Pharr 2026). +# +# Verifies the field-space transform rules in +# `PerturbedEquilibrium.field_space_response_matrices` and the recovery-operator +# contract: the flux-space matrices are exactly recoverable from the stored b̃-space +# matrices via the `ptof` operator (Φ = ptof·b̃). + +using Test +using LinearAlgebra +using GeneralizedPerturbedEquilibrium + +const PE = GeneralizedPerturbedEquilibrium.PerturbedEquilibrium + +# Deterministic, well-conditioned synthetic operators (no RNG → reproducible). +function _synthetic_inputs(n::Int) + # ptof: a generic invertible complex operator standing in for sqrtamat·√jarea. + ptof = Matrix{ComplexF64}(undef, n, n) + for i in 1:n, j in 1:n + ptof[i, j] = (1.0 + 0.3 * cospi((i + 2j) / n)) * cis(0.2 * (i - j)) * (i == j ? 1.0 : 0.15) + end + # Hermitian positive-definite inductances (energy generators). + A = [cis(0.1 * (i - j)) / (1 + abs(i - j)) for i in 1:n, j in 1:n] + L = A * A' + n * I # Hermitian PD surface inductance + B = [cis(-0.07 * (i + j)) / (1 + abs(i - j)) for i in 1:n, j in 1:n] + Λ = B * B' + 2n * I # Hermitian PD plasma inductance + return Matrix{ComplexF64}(ptof), Matrix{ComplexF64}(L), Matrix{ComplexF64}(Λ) +end + +@testset "Coordinate-invariant field-space response matrices" begin + n = 6 + ptof, L, Λ = _synthetic_inputs(n) + P = Λ / L # permeability Φ_tot = P·Φ_x + ϱ = inv(L) * (Λ - L) * inv(L) # reluctance + + fm = PE.field_space_response_matrices(Λ, L, P, ϱ, ptof) + + @testset "Recovery operator contract (round-trip to flux space)" begin + # Recover flux space from the stored b̃-space matrices via ptof. + @test ptof * fm.permeability / ptof ≈ P rtol = 1e-10 + @test ptof * fm.surface_inductance * ptof' ≈ L rtol = 1e-10 + @test ptof * fm.plasma_inductance * ptof' ≈ Λ rtol = 1e-10 + @test (ptof') \ fm.reluctance / ptof ≈ ϱ rtol = 1e-10 + end + + @testset "Internal consistency of the transform rules" begin + # P̃ = Λ̃·L̃⁻¹ + @test fm.permeability ≈ fm.plasma_inductance / fm.surface_inductance rtol = 1e-10 + # ϱ̃ = L̃⁻¹·(Λ̃ − L̃)·L̃⁻¹ + L̃inv = inv(fm.surface_inductance) + @test fm.reluctance ≈ L̃inv * (fm.plasma_inductance - fm.surface_inductance) * L̃inv rtol = 1e-10 + end + + @testset "Energy-scalar invariance under conformance" begin + # A physical applied flux Φ and its power-norm counterpart b̃ = ptof⁻¹·Φ + Φ = ComplexF64[cis(0.3k) / k for k in 1:n] + b̃ = ptof \ Φ + # energy = Φ†·L⁻¹·Φ must equal b̃†·L̃⁻¹·b̃ (and likewise for Λ, ϱ) + @test dot(Φ, L \ Φ) ≈ dot(b̃, fm.surface_inductance \ b̃) rtol = 1e-10 + @test dot(Φ, Λ \ Φ) ≈ dot(b̃, fm.plasma_inductance \ b̃) rtol = 1e-10 + @test dot(Φ, ϱ * Φ) ≈ dot(b̃, fm.reluctance * b̃) rtol = 1e-10 + end +end From 5ae65f97b6e100919c0246dbf1bd066e0d1e30e3 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Thu, 11 Jun 2026 14:07:33 -0400 Subject: [PATCH 023/135] RERUN - IMPROVEMENT - Unify input dispatch and address PR review Unify main() so each input source builds a ready (inputs, eq_config, additional_input) and hands it to the renamed main_from_inputs: build_inputs_from_toml and build_inputs_from_h5. This also fixes a latent IMAS bug where main(; dd) never threaded dd into the pipeline body. - equil.toml snapshots are now rerunnable: serialize the built eq_config into inputs[Equilibrium] so gpec_toml_raw is complete (equilibrium_config_to_dict). - parse_override_flag warns instead of silently storing an unparseable value as a String. - Rerun.jl file-level docstring -> comments. - Slim rerun tests to one source + one replay: analytic Solovev replay now diffs all output datasets; direct (EFIT) recovery is checked through the real h5 reader without a pipeline run; override flags and parse logic are covered pipeline-free. Drop the heavy regression-harness rerun cases. - Add an IMAS dd-dispatch regression test. - CLAUDE.md: forbid PR/issue references in source comments. Co-Authored-By: Claude Opus 4.8 (1M context) --- CLAUDE.md | 1 + src/Equilibrium/Equilibrium.jl | 2 +- src/GeneralizedPerturbedEquilibrium.jl | 109 +++++++------- src/Rerun.jl | 61 ++++---- test/runtests_imas.jl | 16 +++ test/runtests_rerun_from_h5.jl | 191 ++++++++++++++++--------- 6 files changed, 233 insertions(+), 147 deletions(-) diff --git a/CLAUDE.md b/CLAUDE.md index e5686ae09..671a8d068 100644 --- a/CLAUDE.md +++ b/CLAUDE.md @@ -617,6 +617,7 @@ Every consultation is bounded — see **Subagent Consultations** under Important - **Documentation coverage** - When adding a new module or submodule with public docstrings, add a corresponding `@autodocs` block in `docs/src/`. Documenter CI will fail with a `missing_docs` error if any exported docstring is not covered. The analysis submodule docs live in `docs/src/analysis.md`. - **Docstrings are rendered as Markdown** - Documenter parses docstrings as CommonMark, so `[text](...)` patterns become hyperlinks and will fail CI with `invalid local link/image` if the target doesn't exist. Common pitfall: unit annotations like `[degrees] (or [m] if ...)` parse as `[degrees](or [m] if ...)` — a broken link. Use plain words (`in degrees`) or backticks (`` `[m]` ``) for unit labels inside docstrings. Same rule for bracketed array-shape hints (`[ncoil]`) followed by parentheses. When in doubt, preview with `julia --project=docs docs/make.jl` before pushing. - **Keep code comments concise** - A comment should be one line where possible. Do not write multi-line block comments explaining the current session's investigation, what was tried, what was wrong before, or why a specific file/path behaves differently. State what the code does and why at a general level. Example of too much detail: a 6-line block explaining that efit_by_inversion uses psilow>0 while CHEASE starts at 0, that the old code was removed, and that spline spikes result. Preferred: `# Replicate Fortran inverse.f: overwrite deta at axis (r²=0) by extrapolating from innermost surfaces.` +- **No PR/issue references in source** - Do not cite specific GitHub PR or issue numbers (e.g. `#171`, `#202`) in source or test comments/docstrings. During dynamic development these references quickly go stale and pollute the code. Just concisely state the objective or what the code does; the git history and PR threads track the provenance. ### Output Files - **Default output**: `gpec.h5` (previously `euler.h5` in older versions) diff --git a/src/Equilibrium/Equilibrium.jl b/src/Equilibrium/Equilibrium.jl index 87006e645..d98bec0e8 100644 --- a/src/Equilibrium/Equilibrium.jl +++ b/src/Equilibrium/Equilibrium.jl @@ -43,7 +43,7 @@ function setup_equilibrium(eq_config::EquilibriumConfig, additional_input=nothin eq_type = eq_config.eq_type - # Rerun path: caller (e.g. main_from_h5) already rebuilt the solver input from + # Rerun path: caller (e.g. build_inputs_from_h5) already rebuilt the solver input from # the stored raw arrays. Bind it onto the current config and skip the reader. if additional_input isa DirectRunInput eq_input = additional_input diff --git a/src/GeneralizedPerturbedEquilibrium.jl b/src/GeneralizedPerturbedEquilibrium.jl index 23a4467e9..8c78c1e7c 100755 --- a/src/GeneralizedPerturbedEquilibrium.jl +++ b/src/GeneralizedPerturbedEquilibrium.jl @@ -61,19 +61,20 @@ const _SECTION = "-"^40 # Rerun snapshot/replay helpers. Depends on the module-level imports above # (HDF5, TOML, Equilibrium, ForcingTerms) and the `_BANNER` constant, so this # include has to come after them but before `main`, which dispatches into -# `main_from_h5` on .h5 inputs. +# `build_inputs_from_h5` on .h5 inputs. include("Rerun.jl") function main(args::Vector{String}=String[]; dd::Union{IMASdd.dd,Nothing}=nothing) - # Parse command line arguments - path = length(args) >= 1 ? args[1] : "./" - - # Rerun dispatch: when the first positional argument is an HDF5 file, treat it as - # a stored snapshot and hand off to the replay entry point. + # Every input source builds a ready `(inputs, eq_config, additional_input)` and hands it to + # `main_from_inputs`: a gpec.toml working directory, an IMAS `dd`, or a gpec.h5 snapshot. if !isempty(args) && endswith(lowercase(args[1]), ".h5") - return main_from_h5(args) + inputs, eq_config, additional_input, path, git_version, preloaded_forcing = build_inputs_from_h5(args) + return main_from_inputs(inputs, eq_config, additional_input, path, git_version; + preloaded_forcing_modes=preloaded_forcing) end + path = length(args) >= 1 ? args[1] : "./" + # Capture git version for reproducibility git_version = try String(readchomp(`git -C $(@__DIR__) describe --tags --always`)) @@ -83,9 +84,20 @@ function main(args::Vector{String}=String[]; dd::Union{IMASdd.dd,Nothing}=nothin @info "\n$_BANNER\n GPEC - Generalized Perturbed Equilibrium Code [$git_version]\n$_BANNER" - # Read input TOML from the working directory and set up the equilibrium. The - # rest of the pipeline is shared with `main_with_inputs` (used by the rerun - # path), which accepts a prebuilt `inputs` dict and equilibrium config. + inputs, eq_config, additional_input = build_inputs_from_toml(path; dd=dd) + return main_from_inputs(inputs, eq_config, additional_input, path, git_version) +end + +""" + build_inputs_from_toml(path; dd=nothing) -> (inputs, eq_config, additional_input) + +Build the pipeline inputs from a working directory containing `gpec.toml`. Returns the +parsed `inputs` dict (made self-contained for the rerun snapshot), the `EquilibriumConfig`, +and the `additional_input` consumed by `setup_equilibrium` — an analytic `*Config` for +TJ/SOL/LAR equilibria, the `dd` data dictionary for IMAS, or `nothing` for file-based +equilibria (efit, chease) that `setup_equilibrium` reads from disk. +""" +function build_inputs_from_toml(path::String; dd::Union{IMASdd.dd,Nothing}=nothing) inputs = TOML.parsefile(joinpath(path, "gpec.toml")) if "Equilibrium" in keys(inputs) @@ -93,6 +105,9 @@ function main(args::Vector{String}=String[]; dd::Union{IMASdd.dd,Nothing}=nothin elseif isfile(joinpath(path, "equil.toml")) @warn "Reading from equil.toml is deprecated. Please move [EQUIL_CONTROL] and [EQUIL_OUTPUT] sections to [Equilibrium] in gpec.toml" eq_config = Equilibrium.EquilibriumConfig(joinpath(path, "equil.toml")) + # Populate [Equilibrium] from the constructed config so the snapshot TOML blob is + # complete and rerunnable — the deprecated equil.toml is not stored in gpec.h5. + inputs["Equilibrium"] = equilibrium_config_to_dict(eq_config) else error("No equilibrium configuration found. Add [Equilibrium] section to gpec.toml") end @@ -102,18 +117,33 @@ function main(args::Vector{String}=String[]; dd::Union{IMASdd.dd,Nothing}=nothin # the snapshot writer emits a self-contained TOML blob. merge_auxiliary_eq_toml!(inputs, eq_config) - return main_with_inputs(inputs, eq_config, nothing, path, git_version) + # Build `additional_input` from embedded TOML sections (analytic equilibria) or from + # the dd keyword argument (IMAS). These are mutually exclusive — an equilibrium is + # either analytic (TJ/SOL/LAR), IMAS-fed, or read from a file (additional_input=nothing). + additional_input = nothing + if eq_config.eq_type in ("tj_analytic", "tj_analytic_direct") && haskey(inputs, "TJ_ANALYTIC_INPUT") + additional_input = Equilibrium.TJAnalyticConfig(inputs["TJ_ANALYTIC_INPUT"]) + elseif eq_config.eq_type == "sol" && haskey(inputs, "SOL_INPUT") + additional_input = Equilibrium.SolovevConfig(inputs["SOL_INPUT"]) + elseif eq_config.eq_type == "lar" && haskey(inputs, "LAR_INPUT") + additional_input = Equilibrium.LargeAspectRatioConfig(inputs["LAR_INPUT"]) + elseif eq_config.eq_type == "imas" + additional_input = dd + end + + return inputs, eq_config, additional_input end """ - main_with_inputs(inputs, eq_config, additional_input, path, git_version; + main_from_inputs(inputs, eq_config, additional_input, path, git_version; preloaded_forcing_modes=nothing) -Shared pipeline body used by both the TOML entry point (`main`) and the rerun -entry point (`main_from_h5`). The caller is responsible for producing a fully -merged `inputs::Dict` and an `EquilibriumConfig`; `additional_input` is forwarded -to `setup_equilibrium` (it may be a prebuilt `DirectRunInput`/`InverseRunInput` -or a `LargeAspectRatioConfig`/`SolovevConfig`, or nothing for the normal path). +Shared pipeline body that every input source funnels into. The caller (one of the +`build_inputs_from_*` builders) is responsible for producing a fully merged +`inputs::Dict`, an `EquilibriumConfig`, and a ready `additional_input` — this body +does no source dispatch of its own. `additional_input` is forwarded directly to +`setup_equilibrium`: a prebuilt `DirectRunInput`/`InverseRunInput` (rerun path), an +analytic `*Config` or IMAS `dd` (TOML path), or `nothing` for file-based equilibria. `preloaded_forcing_modes` lets the rerun path inject a `Vector{ForcingMode}` already read from the source HDF5 snapshot, so `compute_perturbed_equilibrium` @@ -121,7 +151,7 @@ does not have to touch the original `forcing.dat` path. When `nothing`, the ForcingTerms data is loaded from disk at snapshot time (if PerturbedEquilibrium is enabled) so it still ends up in `input/raw_inputs/forcing_terms/`. """ -function main_with_inputs( +function main_from_inputs( inputs::Dict{String,Any}, eq_config::Equilibrium.EquilibriumConfig, additional_input, @@ -143,42 +173,13 @@ function main_with_inputs( # so this body must not re-read them from disk — the rerun has no gpec.toml file. ctrl = ForceFreeStatesControl(; (Symbol(k) => v for (k, v) in inputs["ForceFreeStates"])...) - # Set up equilibrium from gpec.toml or fallback to equil.toml if it exists. - # Analytic equilibria ("tj_analytic", "tj_analytic_direct", "sol", "lar") can - # EITHER point `eq_filename` at a side-car TOML (legacy) OR embed their - # parameters directly in gpec.toml under a top-level section: - # [TJ_ANALYTIC_INPUT], [SOL_INPUT], [LAR_INPUT]. When the embedded section - # is present it takes precedence and the side-car file is not consulted, - # so a run is fully described by a single gpec.toml. + # The builder already resolved `additional_input` (analytic `*Config`, IMAS `dd`, + # prebuilt DirectRunInput/InverseRunInput from a rerun, or `nothing` for file-based + # equilibria). `setup_equilibrium` consumes it directly — no source dispatch here. # - # The TJ-analytic equilibrium follows the profile family of - # R. Fitzpatrick's TJ code (https://github.com/rfitzp/TJ); see - # `Equilibrium.TJAnalyticConfig`. - if "Equilibrium" in keys(inputs) - # Build additional_input from embedded TOML sections (analytic equilibria) or from - # the dd keyword argument (IMAS). These are mutually exclusive at runtime — an - # equilibrium is either analytic (TJ/SOL/LAR) or IMAS-fed or read from a file. - # Skip rebuilding when the caller already supplied a prebuilt solver input: the - # gpec.h5 rerun path passes a DirectRunInput/InverseRunInput that - # setup_equilibrium consumes directly to bypass the file reader. - if additional_input === nothing - if eq_config.eq_type in ("tj_analytic", "tj_analytic_direct") && haskey(inputs, "TJ_ANALYTIC_INPUT") - additional_input = Equilibrium.TJAnalyticConfig(inputs["TJ_ANALYTIC_INPUT"]) - elseif eq_config.eq_type == "sol" && haskey(inputs, "SOL_INPUT") - additional_input = Equilibrium.SolovevConfig(inputs["SOL_INPUT"]) - elseif eq_config.eq_type == "lar" && haskey(inputs, "LAR_INPUT") - additional_input = Equilibrium.LargeAspectRatioConfig(inputs["LAR_INPUT"]) - elseif eq_config.eq_type == "imas" - additional_input = dd - end - end - equil = Equilibrium.setup_equilibrium(eq_config, additional_input) - elseif isfile(joinpath(intr.dir_path, "equil.toml")) - @warn "Reading from equil.toml is deprecated. Please move [EQUIL_CONTROL] and [EQUIL_OUTPUT] sections to [Equilibrium] in gpec.toml" - equil = Equilibrium.setup_equilibrium(joinpath(intr.dir_path, "equil.toml")) - else - error("No equilibrium configuration found. Add [Equilibrium] section to gpec.toml") - end + # The TJ-analytic equilibrium follows the profile family of R. Fitzpatrick's TJ code + # (https://github.com/rfitzp/TJ); see `Equilibrium.TJAnalyticConfig`. + equil = Equilibrium.setup_equilibrium(eq_config, additional_input) @info "Equilibrium construction completed in $(@sprintf("%.3f", time() - equil_start)) s" @@ -494,7 +495,7 @@ function main_with_inputs( pe_intr = PerturbedEquilibrium.PerturbedEquilibriumInternal(; dir_path=intr.dir_path) # Reuse the forcing modes loaded at snapshot time (or injected by - # `main_from_h5`) so the PE compute step never re-reads the original + # `build_inputs_from_h5`) so the PE compute step never re-reads the original # forcing file. `compute_perturbed_equilibrium` short-circuits # `load_forcing_data!` when `pe_intr.forcing_modes` is non-empty. if forcing_modes_snapshot !== nothing diff --git a/src/Rerun.jl b/src/Rerun.jl index 87ca514eb..f50160e55 100644 --- a/src/Rerun.jl +++ b/src/Rerun.jl @@ -1,15 +1,9 @@ -""" - Rerun support: helpers for saving run inputs into gpec.h5 and replaying them. - -This file provides the machinery that backs issue #171: turning a gpec.h5 output -into a self-contained run snapshot that can be rerun from any directory, with -optional overrides, without needing the original g-file / CHEASE / wall / TOML -auxiliary inputs. - -Functions here are included directly into the GeneralizedPerturbedEquilibrium -module (via `include("Rerun.jl")`), so they share its imports (TOML, HDF5, -Equilibrium, ForcingTerms, etc.). -""" +# Rerun support: save a run's inputs into gpec.h5 and replay them. Turns a gpec.h5 output into +# a self-contained snapshot rerunnable from any directory, with optional overrides, without the +# original g-file / CHEASE / wall / auxiliary TOML inputs. +# +# Included directly into the GeneralizedPerturbedEquilibrium module, so these functions share +# its imports (TOML, HDF5, Equilibrium, ForcingTerms, etc.). """ merge_auxiliary_eq_toml!(inputs::Dict{String,Any}, eq_config) @@ -18,7 +12,7 @@ For analytic equilibria (`lar`, `sol`), the equilibrium parameters live in a separate auxiliary TOML referenced by `eq_config.eq_filename` (e.g. `sol.toml` with a `[SOL_INPUT]` section). To make the `gpec.h5` snapshot self-contained, we merge the relevant auxiliary section into the in-memory `inputs` dict under -the same key (`LAR_INPUT` / `SOL_INPUT`). On replay, `main_from_h5` reads these +the same key (`LAR_INPUT` / `SOL_INPUT`). On replay, `build_inputs_from_h5` reads these sections back into a `LargeAspectRatioConfig` / `SolovevConfig` and passes them to `setup_equilibrium` as `additional_input`, bypassing the auxiliary file read entirely. @@ -74,7 +68,7 @@ end read_equilibrium_raw_inputs(in_h5) -> Dict{String,Any} Inverse of `write_equilibrium_raw_inputs!`: read every dataset under -`input/raw_inputs/equilibrium/` into a plain dict. Used by `main_from_h5` +`input/raw_inputs/equilibrium/` into a plain dict. Used by `build_inputs_from_h5` to hydrate a `DirectRunInput` / `InverseRunInput` without any filesystem access. """ @@ -132,8 +126,11 @@ function parse_override_flag(expr::AbstractString) parsed_val = try parsed = TOML.parse("_rerun_override_ = $rhs") parsed["_rerun_override_"] - catch - # Fall back to string if TOML parse fails (e.g., unquoted bare words). + catch e + # Warn instead of silently stringifying a bare word, which would otherwise only fail + # much later where the field expects a number/bool. + @warn "Could not parse --override value as a TOML literal; storing it as a string. " * + "Quote it explicitly if a string was intended." key=lhs value=rhs error=e rhs end @@ -162,7 +159,7 @@ Supported flags: - `--override key=value` — single-field override (repeatable) """ function parse_rerun_cli(args::Vector{String}) - isempty(args) && error("main_from_h5 requires a positional source .h5 path") + isempty(args) && error("build_inputs_from_h5 requires a positional source .h5 path") source_h5 = args[1] output_dir = pwd() @@ -242,14 +239,27 @@ function rebuild_equilibrium_input(eq_config::Equilibrium.EquilibriumConfig, raw end """ - main_from_h5(args::Vector{String}) + equilibrium_config_to_dict(eq_config) -> Dict{String,Any} -Rerun entry point. Parses the rerun-specific CLI flags, reads the snapshot -out of the source HDF5, applies any overrides, and dispatches back into -`main` with the reconstructed inputs. Never touches the source file's -original ingest paths. +Serialize an `EquilibriumConfig` back into a plain dict keyed by field name. Used to +synthesize a complete `[Equilibrium]` section when a run was configured via the deprecated +`equil.toml`, so the gpec.h5 snapshot is self-contained and rerunnable. +""" +function equilibrium_config_to_dict(eq_config::Equilibrium.EquilibriumConfig) + return Dict{String,Any}(String(f) => getfield(eq_config, f) for f in fieldnames(typeof(eq_config))) +end + +""" + build_inputs_from_h5(args::Vector{String}) + -> (inputs, eq_config, additional_input, output_dir, current_git, preloaded_forcing) + +Rerun input builder. Parses the rerun-specific CLI flags, reads the snapshot out of the +source HDF5, applies any overrides, and reconstructs the pipeline inputs — a prebuilt +`DirectRunInput`/`InverseRunInput` for file-based equilibria, or an analytic `*Config` for +LAR/SOL. Never touches the source file's original ingest paths. The returned tuple is fed +straight into `main_from_inputs`. """ -function main_from_h5(args::Vector{String}) +function build_inputs_from_h5(args::Vector{String}) cli = parse_rerun_cli(args) source_h5 = cli.source_h5 isfile(source_h5) || error("Source HDF5 not found: $source_h5") @@ -257,7 +267,7 @@ function main_from_h5(args::Vector{String}) # Pull the stored TOML, raw equilibrium arrays, and (if present) forcing # data out of the source file. Forcing modes are only written when the # original run had a [PerturbedEquilibrium] section, so the group may be - # missing — we signal that with `nothing` and let main_with_inputs fall + # missing — we signal that with `nothing` and let main_from_inputs fall # back to loading from `ft_ctrl.forcing_data_file`. toml_raw, raw_eq, source_git, preloaded_forcing = h5open(source_h5, "r") do in_h5 haskey(in_h5, "input/gpec_toml_raw") || @@ -326,6 +336,5 @@ function main_from_h5(args::Vector{String}) rebuild_equilibrium_input(eq_config, raw_eq) end - return main_with_inputs(inputs, eq_config, additional_input, output_dir, current_git; - preloaded_forcing_modes=preloaded_forcing) + return inputs, eq_config, additional_input, output_dir, current_git, preloaded_forcing end diff --git a/test/runtests_imas.jl b/test/runtests_imas.jl index de801771f..d2afd3091 100644 --- a/test/runtests_imas.jl +++ b/test/runtests_imas.jl @@ -91,6 +91,22 @@ using GeneralizedPerturbedEquilibrium.Equilibrium @test psi_center >= 0.0 # ψ should be non-negative at magnetic axis region end + # An imas run started via `main(; dd)` must thread the dd through to `additional_input`; + # guards against the dispatch silently dropping it. + @testset "main dd dispatch: dd reaches additional_input" begin + dd, _ = make_mock_dd() + mktempdir() do dir + write(joinpath(dir, "gpec.toml"), "[Equilibrium]\neq_type = \"imas\"\nimas_cocos = 11\n") + inputs, eq_config, additional_input = + GeneralizedPerturbedEquilibrium.build_inputs_from_toml(dir; dd=dd) + @test eq_config.eq_type == "imas" + @test additional_input === dd + # Without a dd, an imas config leaves additional_input === nothing. + _, _, no_dd = GeneralizedPerturbedEquilibrium.build_inputs_from_toml(dir) + @test no_dd === nothing + end + end + # Test 4: write_imas — single n, correct metadata and energy_perturbed @testset "write_imas: single n_tor" begin dd = IMASdd.dd() diff --git a/test/runtests_rerun_from_h5.jl b/test/runtests_rerun_from_h5.jl index 9b806d9f5..64c4f429a 100644 --- a/test/runtests_rerun_from_h5.jl +++ b/test/runtests_rerun_from_h5.jl @@ -1,98 +1,157 @@ using HDF5 -# Exercise the gpec.h5 snapshot + replay pipeline (issue #171). The source run is -# a regular `main(dir)` invocation; the replay runs `main_from_h5` from a temp -# directory that contains nothing but the captured gpec.h5, proving that the -# snapshot is self-contained (no auxiliary TOML, no g-file, no forcing data). -@testset "Rerun from gpec.h5" begin - template_dir = joinpath(@__DIR__, "test_data", "regression_solovev_ideal_example") +# Tests for the gpec.h5 snapshot + replay feature, kept deliberately light: exactly one +# full-pipeline source run + one replay (the analytic Solovev path), plus pipeline-free checks +# for direct-equilibrium recovery and the override flags. - function read_scalars(path) - return h5open(path, "r") do h5 - ( - et=read(h5, "vacuum/et"), - ep=read(h5, "vacuum/ep"), - ev=read(h5, "vacuum/ev"), - mpert=read(h5, "info/mpert"), - msing=read(h5, "singular/msing"), - sing_psi=read(h5, "singular/psi"), - sing_q=read(h5, "singular/q"), - ) +# Collect every leaf dataset path under an open HDF5 file, skipping the groups/paths that +# legitimately differ between a source run and its replay (`input/` is re-emitted with the +# rerun's own filename/TOML blob; `info/git_version` reflects the running commit). +function _rerun_leaf_paths(h5) + skip_toplevel = Set(["input"]) + skip_paths = Set(["info/git_version"]) + paths = String[] + function walk(node, prefix) + for k in keys(node) + full = isempty(prefix) ? k : prefix * "/" * k + (isempty(prefix) && k in skip_toplevel) && continue + full in skip_paths && continue + child = node[k] + child isa HDF5.Group ? walk(child, full) : push!(paths, full) end end + walk(h5, "") + return paths +end + +# Count datasets that differ between a source gpec.h5 and its replay. Zero mismatches over the +# whole output is the strongest snapshot drift guard: it fires if any TOML var or IO field is +# added but not threaded through the snapshot + replay path. +function _rerun_dataset_mismatches(source_h5, rerun_h5) + n_compared = 0 + n_mismatched = 0 + h5open(source_h5, "r") do hs + h5open(rerun_h5, "r") do hr + src = Set(_rerun_leaf_paths(hs)) + rer = Set(_rerun_leaf_paths(hr)) + for p in union(src, rer) + n_compared += 1 + if !(p in src) || !(p in rer) || read(hs, p) != read(hr, p) + n_mismatched += 1 + end + end + end + end + return n_compared, n_mismatched +end + +# Analytic (Solovev) equilibrium: the single end-to-end source + replay. The replay runs from a +# temp directory containing nothing but the captured gpec.h5, proving the snapshot is +# self-contained (no auxiliary TOML, g-file, or forcing data), and reproduces the source +# bit-for-bit across every output dataset. +@testset "Rerun from gpec.h5 (analytic Solovev)" begin + template_dir = joinpath(@__DIR__, "test_data", "regression_solovev_ideal_example") - # Copy the regression example into a temp directory and enable HDF5 output - # so the rest of the test can work against a self-contained source snapshot. - # We avoid editing the in-tree fixture (and its shared gpec.toml) directly. mktempdir() do snapshot_dir for name in readdir(template_dir) cp(joinpath(template_dir, name), joinpath(snapshot_dir, name)) end toml_path = joinpath(snapshot_dir, "gpec.toml") - toml_text = read(toml_path, String) - toml_text = replace(toml_text, "write_outputs_to_HDF5 = false" => "write_outputs_to_HDF5 = true") - write(toml_path, toml_text) + write(toml_path, replace(read(toml_path, String), "write_outputs_to_HDF5 = false" => "write_outputs_to_HDF5 = true")) @info "Generating source gpec.h5 for rerun tests" GeneralizedPerturbedEquilibrium.main([snapshot_dir]) source_h5 = joinpath(snapshot_dir, "gpec.h5") @test isfile(source_h5) - source_scalars = read_scalars(source_h5) - @testset "self-contained replay matches source bit-for-bit" begin + @testset "self-contained replay matches source across all datasets" begin mktempdir() do replay_dir - # No gpec.toml, no sol.toml, no g-file in replay_dir — this is - # the hard constraint from issue #171. GeneralizedPerturbedEquilibrium.main([source_h5, "--output-dir", replay_dir]) - replay_h5 = joinpath(replay_dir, "gpec_rerun.h5") @test isfile(replay_h5) - replay_scalars = read_scalars(replay_h5) - - @test replay_scalars.et == source_scalars.et - @test replay_scalars.ep == source_scalars.ep - @test replay_scalars.ev == source_scalars.ev - @test replay_scalars.mpert == source_scalars.mpert - @test replay_scalars.msing == source_scalars.msing - @test replay_scalars.sing_psi == source_scalars.sing_psi - @test replay_scalars.sing_q == source_scalars.sing_q + + n_compared, n_mismatched = _rerun_dataset_mismatches(source_h5, replay_h5) + @test n_compared > 0 + @test n_mismatched == 0 end end - @testset "override changes tolerance without breaking singular structure" begin - mktempdir() do replay_dir - GeneralizedPerturbedEquilibrium.main([ - source_h5, - "--output-dir", replay_dir, - "--override", "ForceFreeStates.eulerlagrange_tolerance=1e-6", - ]) + # `build_inputs_from_h5` reconstructs the run inputs without executing the pipeline, so + # both override flags are covered through the real code path with no extra runs. + @testset "override flags propagate through build_inputs_from_h5" begin + mktempdir() do out_dir + inline = GeneralizedPerturbedEquilibrium.build_inputs_from_h5([source_h5, "--output-dir", out_dir, "--override", "ForceFreeStates.eulerlagrange_tolerance=1e-6"]) + @test inline[1]["ForceFreeStates"]["eulerlagrange_tolerance"] == 1e-6 - replay_h5 = joinpath(replay_dir, "gpec_rerun.h5") - @test isfile(replay_h5) - replay_scalars = read_scalars(replay_h5) - - # Loosening the tolerance should leave the rational-surface - # structure intact and the real eigenvalue unchanged to high - # precision, while the imaginary part (set by integrator - # residuals) is allowed to drift. - @test replay_scalars.mpert == source_scalars.mpert - @test replay_scalars.msing == source_scalars.msing - @test replay_scalars.sing_psi == source_scalars.sing_psi - @test replay_scalars.sing_q == source_scalars.sing_q - @test real(replay_scalars.et[1]) ≈ real(source_scalars.et[1]) rtol = 1e-4 + override_toml = joinpath(out_dir, "overrides.toml") + write(override_toml, "[ForceFreeStates]\neulerlagrange_tolerance = 2e-6\n") + from_file = GeneralizedPerturbedEquilibrium.build_inputs_from_h5([source_h5, "--output-dir", out_dir, "--override-file", override_toml]) + @test from_file[1]["ForceFreeStates"]["eulerlagrange_tolerance"] == 2e-6 end end @testset "rerun refuses to overwrite its own source" begin - # Default output name is `_rerun.h5`, so clobbering only - # happens when the user tries to route the rerun back on top of the - # source file. Exercise the guard by aiming the output at the - # snapshot dir with the source filename. - @test_throws ErrorException GeneralizedPerturbedEquilibrium.main([ - source_h5, - "--output-dir", snapshot_dir, - "--output-name", "gpec.h5", - ]) + # Default output is `_rerun.h5`, so clobbering only happens if the user + # routes the rerun back onto the source file; exercise that guard. + @test_throws ErrorException GeneralizedPerturbedEquilibrium.main([source_h5, "--output-dir", snapshot_dir, "--output-name", "gpec.h5"]) end end end + +# Direct (DIII-D EFIT) equilibrium recovery through the h5 path, without a pipeline run: +# `read_efit` captures the raw arrays, which we round-trip through a temp h5 via the real +# replay reader `read_equilibrium_raw_inputs` and rebuild with `build_direct_from_raw`. The +# rebuilt splines must evaluate bit-for-bit identical to the originals. +@testset "Rerun direct-equilibrium recovery through h5" begin + Equil = GeneralizedPerturbedEquilibrium.Equilibrium + config = Equil.EquilibriumConfig(; + eq_filename=joinpath(@__DIR__, "..", "examples", "DIIID-like_ideal_example", "TkMkr_D3Dlike_Hmode.geqdsk"), + eq_type="efit" + ) + src = Equil.read_efit(config) + @test src isa Equil.DirectRunInput + @test !isempty(src.raw_data) + + mktempdir() do d + h5path = joinpath(d, "raw.h5") + h5open(h5path, "w") do f + for (k, v) in src.raw_data + f["input/raw_inputs/equilibrium/$k"] = v + end + end + raw = h5open(GeneralizedPerturbedEquilibrium.read_equilibrium_raw_inputs, h5path, "r") + rebuilt = Equil.build_direct_from_raw(config, raw) + + @test rebuilt.rmin == src.rmin + @test rebuilt.rmax == src.rmax + @test rebuilt.zmin == src.zmin + @test rebuilt.zmax == src.zmax + @test rebuilt.psio == src.psio + @test rebuilt.bt_sign == src.bt_sign + @test rebuilt.psi_in_xs == src.psi_in_xs + @test rebuilt.psi_in_ys == src.psi_in_ys + + # 2D flux interpolant must evaluate bit-for-bit at interior sample points. + for fr in (0.25, 0.5, 0.75), fz in (0.4, 0.6) + R = src.rmin + fr * (src.rmax - src.rmin) + Z = src.zmin + fz * (src.zmax - src.zmin) + @test rebuilt.psi_in((R, Z)) == src.psi_in((R, Z)) + end + # 1D profile spline likewise. + for frac in (0.1, 0.5, 0.9) + x = src.psi_in_xs[1] + frac * (src.psi_in_xs[end] - src.psi_in_xs[1]) + @test rebuilt.sq_in(x) == src.sq_in(x) + end + end +end + +# `parse_override_flag` (pure): literal typing and the string-fallback warning for bare words. +@testset "parse_override_flag literal typing and warn" begin + pf = GeneralizedPerturbedEquilibrium.parse_override_flag + @test pf("ForceFreeStates.npert=5")["ForceFreeStates"]["npert"] === 5 + @test pf("ForceFreeStates.eulerlagrange_tolerance=1.5e-3")["ForceFreeStates"]["eulerlagrange_tolerance"] === 1.5e-3 + @test pf("ForceFreeStates.kin_flag=true")["ForceFreeStates"]["kin_flag"] === true + + bad = @test_logs (:warn,) pf("ForceFreeStates.mode=blorp") + @test bad["ForceFreeStates"]["mode"] == "blorp" +end From b8e9502613e49d58acc9092c932185f2a626ed43 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Thu, 11 Jun 2026 14:08:52 -0400 Subject: [PATCH 024/135] Analysis - NEW FEATURE - 3D plasma-surface field viz for coils (plot_control_3d analog) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Adds two reusable Analysis.CoilForcing entry points that replicate GPEC's plot_control_3d: - plot_surface_3d(equil; color_by, coil_sets, ...) — the 3D plasma boundary surface, optionally coloured by ANY control-surface output and/or with coils overlaid. One function covers surface-only / +field / +coils / +field+coils; coils-only stays plot_coil_geometry_3d. - control_surface_scalar(equil, modes, n; ...) — inverse-Fourier-transforms spectral modes (b_n, b_n_x, xi_n, …) to a real-space [θ,φ] field, reusing FourierTransforms.inverse and the ν/helicity correction from PerturbedEquilibriumModes (no field recomputation, no Biot-Savart). Conventions: - Shared :RdBu symmetric scale: a blue (+current) coil reads the same colour as the blue (+) field it drives. Sign/handedness chosen and VERIFIED against coil currents so a positive coil produces positive b_n_x directly beneath it (the legacy Python mis-tracks toroidally). - No new Project.toml deps. Coloured 3D surfaces need a PlotlyJS-style backend (already a dep); on GR the tool warns and degrades to an uncoloured surface rather than mis-colouring by Z. Co-Authored-By: Claude Opus 4.8 (1M context) --- src/Analysis/CoilForcing.jl | 342 ++++++++++++++++++++++++++++++------ 1 file changed, 288 insertions(+), 54 deletions(-) diff --git a/src/Analysis/CoilForcing.jl b/src/Analysis/CoilForcing.jl index 22cc30334..e8549e474 100644 --- a/src/Analysis/CoilForcing.jl +++ b/src/Analysis/CoilForcing.jl @@ -4,12 +4,19 @@ Visualization functions for coil geometry and the resulting normal field perturbations on the plasma boundary. +Two 3D entry points cover the common cases: [`plot_coil_geometry_3d`](@ref) draws the coils +alone, and [`plot_surface_3d`](@ref) draws the plasma boundary surface — optionally coloured by +any control-surface field (via [`control_surface_scalar`](@ref)) and/or with coils overlaid — +the Julia analog of GPEC's `plot_control_3d`. The `:RdBu` colour scale is shared, so a blue +(positive-current) coil and a blue (positive) field read identically. + All functions return `Plots.jl` plot objects and accept an optional `save_path` keyword argument to write the figure to disk. """ module CoilForcing using Plots +import ...Utilities.FourierTransforms: FourierTransform, inverse """ plot_coil_geometry_3d(coil_sets; save_path=nothing, kwargs...) @@ -20,45 +27,61 @@ Each coil set is shown with a distinct color; individual conductors are plotted as lines in Cartesian (X, Y, Z) space in meters. ### Arguments -- `coil_sets`: `Vector{CoilSet}` from `ForcingTerms.load_coil_sets` + + - `coil_sets`: `Vector{CoilSet}` from `ForcingTerms.load_coil_sets` ### Keyword arguments -- `save_path`: file path to save the figure (default: `nothing`) -- Any extra kwargs are forwarded to `Plots.plot` + + - `save_path`: file path to save the figure (default: `nothing`) + - Any extra kwargs are forwarded to `Plots.plot` ### Returns + A `Plots.jl` plot object. """ function plot_coil_geometry_3d(coil_sets; save_path=nothing, kwargs...) - # Collect all currents to set a symmetric colorscale centred at zero - all_currents = [I for cs in coil_sets for I in cs.currents] - clim = isempty(all_currents) ? 1.0 : max(maximum(abs, all_currents), eps()) + clim = _current_clim(coil_sets) p = plot(; xlabel="X [m]", ylabel="Y [m]", zlabel="Z [m]", - title="Coil geometry (3D)", legend=false, - camera=(30, 20), kwargs...) + title="Coil geometry (3D)", legend=false, + camera=(30, 20), kwargs...) + + _overlay_coils!(p, coil_sets; clim=clim) + + # Invisible scatter spanning the current range to force the colorbar to appear + scatter!(p, [NaN], [NaN], [NaN]; + zcolor=[0.0], clims=(-clim, clim), color=:RdBu, + colorbar_title="I [A]", markersize=0) + + isnothing(save_path) || savefig(p, save_path) + return p +end + +# Symmetric current colour-limit (centred at zero) for a set of coils. +function _current_clim(coil_sets) + all_currents = [I for cs in coil_sets for I in cs.currents] + return isempty(all_currents) ? 1.0 : max(maximum(abs, all_currents), eps()) +end +""" + _overlay_coils!(p, coil_sets; clim=nothing) + +Draw each conductor of every coil set onto plot `p` as a 3D `path3d` curve, coloured on a +symmetric `:RdBu` scale by its current (positive = blue, negative = red — the same mapping +used for surface fields, so a blue coil and a blue field read identically). +""" +function _overlay_coils!(p, coil_sets; clim=nothing) + cl = isnothing(clim) ? _current_clim(coil_sets) : clim for cs in coil_sets for j in 1:cs.ncoil - I = cs.currents[j] - # Map current to [0,1] on symmetric RdBu scale (blue=positive, red=negative) - t = clamp((I + clim) / (2clim), 0.0, 1.0) + t = clamp((cs.currents[j] + cl) / (2cl), 0.0, 1.0) col = get(cgrad(:RdBu), t) for k in 1:cs.s - xs = view(cs.x, j, k, :) - ys = view(cs.y, j, k, :) - zs = view(cs.z, j, k, :) - plot!(p, xs, ys, zs; seriestype=:path3d, color=col, lw=2, linestyle=:solid) + plot!(p, view(cs.x, j, k, :), view(cs.y, j, k, :), view(cs.z, j, k, :); + seriestype=:path3d, color=col, lw=2, linestyle=:solid, label="") end end end - - # Invisible scatter spanning the current range to force the colorbar to appear - scatter!(p, [NaN], [NaN], [NaN]; - zcolor=[0.0], clims=(-clim, clim), color=:RdBu, - colorbar_title="I [A]", markersize=0) - - isnothing(save_path) || savefig(p, save_path) return p end @@ -71,28 +94,31 @@ Each coil strand is shown as a closed curve in `(R, Z) = (√(X²+Y²), Z)` spac If `equil` is provided, the plasma boundary is overplotted for reference. ### Arguments -- `coil_sets`: `Vector{CoilSet}` from `ForcingTerms.load_coil_sets` + + - `coil_sets`: `Vector{CoilSet}` from `ForcingTerms.load_coil_sets` ### Keyword arguments -- `equil`: optional `PlasmaEquilibrium`; if given, overlays the plasma boundary -- `psi`: flux surface to trace (default: `equil.rzphi_xs[end]`, the outermost grid point) -- `save_path`: file path to save the figure (default: `nothing`) -- Any extra kwargs are forwarded to `Plots.plot` + + - `equil`: optional `PlasmaEquilibrium`; if given, overlays the plasma boundary + - `psi`: flux surface to trace (default: `equil.rzphi_xs[end]`, the outermost grid point) + - `save_path`: file path to save the figure (default: `nothing`) + - Any extra kwargs are forwarded to `Plots.plot` ### Returns + A `Plots.jl` plot object. """ function plot_coil_geometry_rz(coil_sets; equil=nothing, psi=nothing, save_path=nothing, kwargs...) p = plot(; xlabel="R [m]", ylabel="Z [m]", - title="Coil cross-sections (R, Z)", legend=:topright, - aspect_ratio=:equal, kwargs...) + title="Coil cross-sections (R, Z)", legend=:topright, + aspect_ratio=:equal, kwargs...) colors = [:blue, :red, :green, :orange, :purple, :brown, :cyan, :magenta] for (ci, cs) in enumerate(coil_sets) col = colors[mod1(ci, length(colors))] for j in 1:cs.ncoil for k in 1:cs.s - R_strand = sqrt.(view(cs.x, j, k, :).^2 .+ view(cs.y, j, k, :).^2) + R_strand = sqrt.(view(cs.x, j, k, :) .^ 2 .+ view(cs.y, j, k, :) .^ 2) Z_strand = view(cs.z, j, k, :) label = (j == 1 && k == 1) ? cs.name : "" plot!(p, R_strand, Z_strand; label=label, color=col, lw=1.5) @@ -108,12 +134,12 @@ function plot_coil_geometry_rz(coil_sets; equil=nothing, psi=nothing, save_path= Z_bnd = zeros(mtheta_boundary) for (i, θ_sfl) in enumerate(equil.rzphi_ys) r_minor = sqrt(equil.rzphi_rsquared((psi_bnd, θ_sfl); hint=hint2d)) - θ_cyl = 2π * (θ_sfl + equil.rzphi_offset((psi_bnd, θ_sfl); hint=hint2d)) + θ_cyl = 2π * (θ_sfl + equil.rzphi_offset((psi_bnd, θ_sfl); hint=hint2d)) R_bnd[i] = equil.ro + r_minor * cos(θ_cyl) Z_bnd[i] = equil.zo + r_minor * sin(θ_cyl) end plot!(p, [R_bnd; R_bnd[1]], [Z_bnd; Z_bnd[1]]; - label="plasma boundary (ψ=$(round(psi_bnd; digits=3)))", color=:black, lw=2) + label="plasma boundary (ψ=$(round(psi_bnd; digits=3)))", color=:black, lw=2) end isnothing(save_path) || savefig(p, save_path) @@ -129,31 +155,34 @@ Expects the raw Biot-Savart B·n̂ field in Tesla (before `project_normal_flux!` converts to flux). If plotting post-projection data, note units are T·m² not T. ### Arguments -- `bn`: normal field matrix `[mtheta, nzeta]` — typically B·n̂ in Tesla -- `mtheta`: number of poloidal grid points -- `nzeta`: number of toroidal grid points + + - `bn`: normal field matrix `[mtheta, nzeta]` — typically B·n̂ in Tesla + - `mtheta`: number of poloidal grid points + - `nzeta`: number of toroidal grid points ### Keyword arguments -- `n`: toroidal mode number (used for axis label only) -- `save_path`: file path to save the figure (default: `nothing`) -- Any extra kwargs are forwarded to `Plots.heatmap` + + - `n`: toroidal mode number (used for axis label only) + - `save_path`: file path to save the figure (default: `nothing`) + - Any extra kwargs are forwarded to `Plots.heatmap` ### Returns + A `Plots.jl` plot object. """ function plot_bn_contour(bn::Matrix{Float64}, mtheta::Int, nzeta::Int; - n=nothing, save_path=nothing, kwargs...) + n=nothing, save_path=nothing, kwargs...) # Shift rows so θ=0 (outboard midplane) is centred on the y-axis at 0° bn_wrapped = circshift(bn, (mtheta ÷ 2, 0)) - theta_deg = range(-180; step=360.0/mtheta, length=mtheta) - zeta_deg = range(0; step=360.0/nzeta, length=nzeta) + theta_deg = range(-180; step=360.0 / mtheta, length=mtheta) + zeta_deg = range(0; step=360.0 / nzeta, length=nzeta) n_label = isnothing(n) ? "" : " (n=$n)" p = heatmap(zeta_deg, theta_deg, bn_wrapped; - xlabel="zeta [deg]", ylabel="theta [deg]", - ylims=(-180, 180), - title="Normal field bₙ(θ, ζ)$n_label [T]", - color=:RdBu, kwargs...) + xlabel="zeta [deg]", ylabel="theta [deg]", + ylims=(-180, 180), + title="Normal field bₙ(θ, ζ)$n_label [T]", + color=:RdBu, kwargs...) isnothing(save_path) || savefig(p, save_path) return p @@ -165,15 +194,18 @@ end Plot the Fourier mode spectrum `|bmn|` vs poloidal mode number m as a step line, grouped by n. ### Arguments -- `forcing_modes`: `Vector{ForcingMode}` from `compute_coil_forcing_modes!` + + - `forcing_modes`: `Vector{ForcingMode}` from `compute_coil_forcing_modes!` ### Keyword arguments -- `mlow`, `mhigh`: poloidal mode range for the x-axis (e.g. from ForceFreeStates config); - if provided, sets xlims to span the full stability range even if some modes are zero -- `save_path`: file path to save the figure (default: `nothing`) -- Any extra kwargs are forwarded to `Plots.plot` + + - `mlow`, `mhigh`: poloidal mode range for the x-axis (e.g. from ForceFreeStates config); + if provided, sets xlims to span the full stability range even if some modes are zero + - `save_path`: file path to save the figure (default: `nothing`) + - Any extra kwargs are forwarded to `Plots.plot` ### Returns + A `Plots.jl` plot object. """ function plot_mode_spectrum(forcing_modes; mlow=nothing, mhigh=nothing, save_path=nothing, kwargs...) @@ -181,16 +213,16 @@ function plot_mode_spectrum(forcing_modes; mlow=nothing, mhigh=nothing, save_pat colors = [:blue, :red, :green, :orange, :purple, :brown] p = plot(; xlabel="Poloidal mode m", ylabel="|Φ_x(m,n)| [unit-norm]", - title="Coil forcing mode spectrum", - legend=:topright, kwargs...) + title="Coil forcing mode spectrum", + legend=:topright, kwargs...) for (ni, n) in enumerate(n_vals) modes_n = filter(m -> m.n == n, forcing_modes) sort!(modes_n; by=m -> m.m) m_vals = [m.m for m in modes_n] - amps = abs.([m.amplitude for m in modes_n]) + amps = abs.([m.amplitude for m in modes_n]) col = colors[mod1(ni, length(colors))] - m_ext = [m_vals[1] - 1; m_vals; m_vals[end] + 1] + m_ext = [m_vals[1] - 1; m_vals; m_vals[end] + 1] amp_ext = [0.0; amps; 0.0] plot!(p, m_ext, amp_ext; label="n=$n", color=col, lw=2, seriestype=:steppre) end @@ -205,7 +237,209 @@ function plot_mode_spectrum(forcing_modes; mlow=nothing, mhigh=nothing, save_pat return p end +# Helicity = sign(Bt)·sign(Ip); the SFL→machine toroidal-angle handedness. +function _equil_helicity(equil) + bt = isnothing(equil.params.bt_sign) ? 1 : Int(sign(equil.params.bt_sign)) + ip = isnothing(equil.params.crnt) ? 1 : Int(sign(equil.params.crnt)) + return bt * ip +end + +# Unpack `modes` (a Vector of ForcingMode-like objects filtered to toroidal mode `n`, +# or a `(m_vals, amplitudes)` tuple) into parallel m and complex-amplitude vectors. +function _unpack_modes(modes, n::Int) + if modes isa Tuple + return collect(Int, modes[1]), collect(ComplexF64, modes[2]) + end + sel = [md for md in modes if md.n == n] + isempty(sel) && error("control_surface_scalar: no modes found with n=$n") + return Int[md.m for md in sel], ComplexF64[md.amplitude for md in sel] +end + +""" + control_surface_scalar(equil, modes, n; mtheta=180, nphi=180, psi=nothing, + helicity=nothing) -> Matrix{Float64} + +Inverse-Fourier-transform a spectral control-surface quantity into a real-space `[mtheta, nphi]` +field on the plasma boundary, ready to colour [`plot_surface_3d`](@ref). + +`modes` are complex Fourier amplitudes indexed by poloidal mode `m` for a single toroidal mode +`n` — a `Vector{ForcingMode}` (filtered to `n`) or a `(m_vals, amplitudes)` tuple. The quantity is +arbitrary (e.g. applied normal field `b_n_x`, total `b_n`, displacement `xi_n`); the caller +supplies whichever modes they want to view. + +The transform follows `Analysis.PerturbedEquilibriumModes.modes_to_theta` / `theta_to_thetaphi` +(the gpec.h5 control-surface path): `f(θ) = Σ_m amp_m e^{i m θ}`, the SFL→machine-angle correction +`e^{i n ν(ψ,θ)}` from `equil.rzphi_nu`, then `c(θ,φ) = Re[f(θ) e^{i n φ}]`. + +!!! note "Sign / helicity convention" + + The toroidal handedness and overall sign are chosen so that, for applied coil fields + (`b_n_x`), **a positive coil current produces positive (blue) `b_n_x` directly beneath the + coil** — verified against coil currents on DIII-D (`helicity = sign(Bt)·sign(Ip) > 0`). This + is the opposite handedness from a naive copy of the legacy Python `plot_control_3d`, which + mis-tracks the coil toroidally. Pass `helicity` to override `sign(Bt)·sign(Ip)` if the + field/coil colours disagree for your machine. + +### Keyword arguments + + - `mtheta`, `nphi`: poloidal/toroidal grid resolution + - `psi`: flux surface (default `equil.rzphi_xs[end]`, the boundary) + - `helicity`: override `sign(Bt)·sign(Ip)` +""" +function control_surface_scalar(equil, modes, n::Int; mtheta::Int=180, nphi::Int=180, + psi=nothing, helicity=nothing) + psi_b = isnothing(psi) ? equil.rzphi_xs[end] : Float64(psi) + m_vals, amps = _unpack_modes(modes, n) + m_low, m_high = extrema(m_vals) + mpert = m_high - m_low + 1 + + vec = zeros(ComplexF64, mpert) + for (m, a) in zip(m_vals, amps) + vec[m-m_low+1] = a + end + + # m→θ inverse transform; f[i] is at normalized θ = (i-1)/mtheta + ft = FourierTransform(mtheta, mpert, m_low) + f = inverse(ft, vec) + + # SFL→machine toroidal-angle correction e^{i n ν(ψ,θ)} + hel = isnothing(helicity) ? _equil_helicity(equil) : helicity + hint = (Ref(1), Ref(1)) + for i in 1:mtheta + θ = (i - 1) / mtheta + ν = equil.rzphi_nu((psi_b, θ); hint=hint) + f[i] *= exp(im * n * ν) + end + # Conjugate for the toroidal handedness that makes the field track its source coil; the + # condition is the opposite of the legacy Python (verified empirically, see note above). + hel < 0 && (f = conj.(f)) + + # θ→φ extension: c(θ,φ) = Re[ f(θ) e^{i n φ} ]. The leading − sets the convention that a + # positive coil current drives positive (blue) b_n_x directly beneath the coil. + c = zeros(Float64, mtheta, nphi) + for k in 1:nphi + ph = exp(im * n * (k - 1) * 2π / nphi) + for i in 1:mtheta + c[i, k] = -real(f[i] * ph) + end + end + return c +end + +# Build the closed (θ,φ)→(x,y,z) boundary surface from the equilibrium splines. +# Returns X, Y, Z each [mtheta+1, nphi+1] (wrapped so the torus closes seamlessly). +function _boundary_surface_xyz(equil, mtheta::Int, nphi::Int, psi) + psi_b = isnothing(psi) ? equil.rzphi_xs[end] : Float64(psi) + hint = (Ref(1), Ref(1)) + R = zeros(mtheta) + Z = zeros(mtheta) + for i in 1:mtheta + θ = (i - 1) / mtheta + r_minor = sqrt(equil.rzphi_rsquared((psi_b, θ); hint=hint)) + θ_cyl = 2π * (θ + equil.rzphi_offset((psi_b, θ); hint=hint)) + R[i] = equil.ro + r_minor * cos(θ_cyl) + Z[i] = equil.zo + r_minor * sin(θ_cyl) + end + + X = zeros(mtheta + 1, nphi + 1) + Y = zeros(mtheta + 1, nphi + 1) + Zs = zeros(mtheta + 1, nphi + 1) + for k in 1:(nphi+1) + φ = (k - 1) * 2π / nphi + cφ, sφ = cos(φ), sin(φ) + for i in 1:(mtheta+1) + ii = i <= mtheta ? i : 1 + X[i, k] = R[ii] * cφ + Y[i, k] = R[ii] * sφ + Zs[i, k] = Z[ii] + end + end + return X, Y, Zs +end + +# Wrap a [mtheta, nphi] field to [mtheta+1, nphi+1] to match the closed surface mesh. +_wrap_field(c) = [c[i <= size(c, 1) ? i : 1, k <= size(c, 2) ? k : 1] + for i in 1:(size(c, 1)+1), k in 1:(size(c, 2)+1)] + +""" + plot_surface_3d(equil; color_by=nothing, coil_sets=nothing, mtheta=180, nphi=180, + psi=nothing, clim=nothing, colorbar_title="", title="Plasma boundary", + camera=(35, 25), save_path=nothing, kwargs...) + +Plot the 3D plasma boundary surface, optionally coloured by a control-surface field and/or with +coils overlaid — the Julia analog of GPEC's `plot_control_3d`. + +!!! note "Backend for coloured surfaces" + + Scalar colouring of the closed surface requires a PlotlyJS-style backend (`plotlyjs()`, + already a GPEC dependency); the default GR backend cannot colour a parametric surface by an + independent array and will draw an **uncoloured** surface with a warning. Call `plotlyjs()` + before requesting `color_by`. Coil overlay and uncoloured surfaces work on any backend. + +### Keyword arguments + + - `color_by`: optional real-space `[mtheta, nphi]` scalar (any control-surface output — e.g. from + [`control_surface_scalar`](@ref)). Coloured on a symmetric `:RdBu` scale centred at zero + (positive = blue), matching the coil-current colours. `nothing` draws an uncoloured surface. + - `coil_sets`: optional `Vector{CoilSet}` overlaid as 3D curves (see [`plot_coil_geometry_3d`](@ref)). + - `mtheta`, `nphi`, `psi`: surface grid resolution and flux surface (must match `color_by`). + - `clim`: symmetric colour limit (default `maximum(abs, color_by)`). + - `save_path`: file path to save the figure; extra `kwargs` forward to `Plots.surface`. + +### Returns + +A `Plots.jl` plot object. + + plot_surface_3d(equil, modes, n; coil_sets=nothing, colorbar_title="", kwargs...) + +Convenience method: colour the surface by [`control_surface_scalar(equil, modes, n; …)`](@ref). +""" +function plot_surface_3d(equil; color_by=nothing, coil_sets=nothing, mtheta::Int=180, + nphi::Int=180, psi=nothing, clim=nothing, colorbar_title="", + title="Plasma boundary", camera=(35, 25), save_path=nothing, kwargs...) + X, Y, Z = _boundary_surface_xyz(equil, mtheta, nphi, psi) + + common = (; xlabel="X [m]", ylabel="Y [m]", zlabel="Z [m]", title=title, + legend=false, aspect_ratio=:equal, camera=camera) + + want_color = !isnothing(color_by) + if want_color + size(color_by) == (mtheta, nphi) || + error("color_by must be [mtheta, nphi] = ($mtheta, $nphi), got $(size(color_by))") + # Only PlotlyJS-style backends honour `fill_z` on a closed/parametric surface; GR silently + # colours by Z instead, so warn and degrade rather than show a misleading figure. + if !(backend_name() in (:plotlyjs, :pythonplot, :pyplot)) + @warn "plot_surface_3d: the active Plots backend ($(backend_name())) cannot colour a " * + "parametric 3D surface by a scalar — call `plotlyjs()` first for field-coloured " * + "surfaces. Drawing an uncoloured surface." maxlog = 1 + want_color = false + end + end + + if want_color + cl = isnothing(clim) ? max(maximum(abs, color_by), eps()) : clim + cw = _wrap_field(color_by) + p = surface(X, Y, Z; fill_z=cw, color=:RdBu, clims=(-cl, cl), + colorbar_title=colorbar_title, common..., kwargs...) + else + p = surface(X, Y, Z; color=:grays, alpha=0.5, colorbar=false, common..., kwargs...) + end + + isnothing(coil_sets) || _overlay_coils!(p, coil_sets) + isnothing(save_path) || savefig(p, save_path) + return p +end + +function plot_surface_3d(equil, modes, n::Int; coil_sets=nothing, mtheta::Int=180, + nphi::Int=180, psi=nothing, helicity=nothing, + colorbar_title="", save_path=nothing, kwargs...) + c = control_surface_scalar(equil, modes, n; mtheta=mtheta, nphi=nphi, psi=psi, helicity=helicity) + return plot_surface_3d(equil; color_by=c, coil_sets=coil_sets, mtheta=mtheta, nphi=nphi, + psi=psi, colorbar_title=colorbar_title, save_path=save_path, kwargs...) +end + export plot_coil_geometry_3d, plot_coil_geometry_rz export plot_bn_contour, plot_mode_spectrum +export plot_surface_3d, control_surface_scalar end # module CoilForcing From b58e19c93763d0b75e71dcc77395419c0f87dc84 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Thu, 11 Jun 2026 14:48:24 -0400 Subject: [PATCH 025/135] FFS - WIP - Initial attempt to add BALOO style critical pressure plots This contains good structure: calculate in Bal.jl, output in h5, and helper function plots in Analysis + a use case example in examples. But details need to be improved: second stability boundary inclusion, plot cleanup to show the window properly, etc. --- .../analyze_example.jl | 18 ++- src/Analysis/ForceFreeStates.jl | 53 +++++++++ src/ForceFreeStates/Bal.jl | 109 ++++++++++++++++++ src/GeneralizedPerturbedEquilibrium.jl | 15 ++- 4 files changed, 190 insertions(+), 5 deletions(-) diff --git a/examples/DIIID-like_ideal_example/analyze_example.jl b/examples/DIIID-like_ideal_example/analyze_example.jl index 2b8af279f..9c2f2d2b6 100644 --- a/examples/DIIID-like_ideal_example/analyze_example.jl +++ b/examples/DIIID-like_ideal_example/analyze_example.jl @@ -185,8 +185,22 @@ display(p_zero) zero_path = joinpath(@__DIR__, "salpha_zero_contours.png") Plots.savefig(p_zero, zero_path) +# BALOO-style first ballooning stability boundary: experimental α vs critical α +p_baloo = Analysis.ForceFreeStates.plot_ballooning_alpha_boundary(h5path) +display(p_baloo) +baloo_path = joinpath(@__DIR__, "ballooning_alpha_boundary.png") +Plots.savefig(p_baloo, baloo_path) + println("Saved figures:") -for p in - (joinpath(@__DIR__, "equilibrium_summary.png"), joinpath(@__DIR__, "ffs_summary.png"), joinpath(@__DIR__, "pe_summary.png"), salpha_path, localstab_path, maps_path, zero_path) +for p in ( + joinpath(@__DIR__, "equilibrium_summary.png"), + joinpath(@__DIR__, "ffs_summary.png"), + joinpath(@__DIR__, "pe_summary.png"), + salpha_path, + localstab_path, + maps_path, + zero_path, + baloo_path +) println(" ", p) end diff --git a/src/Analysis/ForceFreeStates.jl b/src/Analysis/ForceFreeStates.jl index 16161bf72..24d095e02 100644 --- a/src/Analysis/ForceFreeStates.jl +++ b/src/Analysis/ForceFreeStates.jl @@ -367,6 +367,59 @@ function plot_delta_prime(h5path; save_path=nothing) return p end +""" + plot_ballooning_alpha_boundary(h5path; save_path=nothing, psi_min=0.0) + +Plot the BALOO-style infinite-n ballooning stability diagram: the experimental +pressure gradient α (solid) and the first stability boundary α_crit (dashed) versus +normalized poloidal flux ψ_N. Surfaces where the experimental α lies above the boundary +are ballooning-unstable. Reads `locstab/psi`, `locstab/alpha`, and +`locstab/alpha_critical` (populated when ForceFreeStates runs with +`local_stability_flag = true`). + +### Arguments + + - `h5path`: Path to a GPEC HDF5 output file (e.g. `"gpec.h5"`) + +### Keyword arguments + + - `save_path`: If provided, save the figure to this path (default: `nothing`) + - `psi_min`: Lower ψ_N axis limit; set near the edge (e.g. `0.9`) to focus on the + pedestal (default: `0.0`) + +### Returns + +A `Plots.jl` plot object. +""" +function plot_ballooning_alpha_boundary(h5path; save_path=nothing, psi_min=0.0) + psi, alpha, alpha_crit = h5open(h5path, "r") do fid + haskey(fid, "locstab/alpha") || return (Float64[], Float64[], Float64[]) + read(fid["locstab/psi"]), read(fid["locstab/alpha"]), read(fid["locstab/alpha_critical"]) + end + + isempty(alpha) && return plot(; title="No local stability data (set local_stability_flag)", legend=false) + + p = plot(; + xlims=(psi_min, 1), + xlabel=L"\psi_N", + ylabel=L"\alpha", + title="Infinite-n ballooning stability", + framestyle=:box, + legend=:topleft, + left_margin=10Plots.mm, + bottom_margin=5Plots.mm + ) + + # Mask non-finite α_crit so always-stable surfaces leave a gap rather than a spike. + exp_mask = isfinite.(alpha) + crit_mask = isfinite.(alpha_crit) + plot!(p, psi[exp_mask], alpha[exp_mask]; lw=2, color=:black, label="Experimental gradient") + plot!(p, psi[crit_mask], alpha_crit[crit_mask]; lw=2, linestyle=:dash, color=:red, label="1st stability boundary") + + isnothing(save_path) || savefig(p, save_path) + return p +end + """ plot_cond_fbar(h5path; save_path=nothing, zoom=false) diff --git a/src/ForceFreeStates/Bal.jl b/src/ForceFreeStates/Bal.jl index 1437aa956..dd82cd133 100644 --- a/src/ForceFreeStates/Bal.jl +++ b/src/ForceFreeStates/Bal.jl @@ -673,6 +673,115 @@ function scan_delta_prime_map( ) end +""" + critical_ballooning_alpha(psi_idx, plasma_eq; theta_k=0.0, max_alpha_scale=8.0, n_scan=24, tol=1e-3) + +First infinite-n ballooning stability boundary at one flux surface: holding the +equilibrium magnetic shear fixed (`corr_qprime = 0`), find the critical pressure +gradient `α` at which the marginal ballooning Δ' first crosses zero as `α` increases +from zero. `α` is linear in `dp/dψ`, so the search is over a scaling of the reference +gradient and the boundary maps directly to `α_crit = α_ref * scale_crit`. + +The `α = 0` (zero pressure gradient) point is ballooning stable; its Δ' sign defines +the stable side, and the first scaling at which Δ' flips away from it is the boundary. + +Returns `(alpha_crit, alpha_scale_crit, found)`. When no crossing exists within +`max_alpha_scale` (always stable, or second-stability access) `alpha_crit = NaN` and +`found = false`. +""" +function critical_ballooning_alpha( + psi_idx::Int, + plasma_eq::Equilibrium.PlasmaEquilibrium; + theta_k::Float64=0.0, + max_alpha_scale::Float64=8.0, + n_scan::Int=24, + tol::Float64=1e-3 +) + ref = salpha_reference(psi_idx, plasma_eq) + + # Δ' as a function of the α scaling at fixed magnetic shear. + delta_at(scale) = ballooning_delta_prime( + psi_idx, + plasma_eq; + corr_qprime=0.0, + corr_pprime=ref.pprime_norm_ref * (scale - 1.0), + theta_k=theta_k + ).delta_prime + + stable_sign = sign(delta_at(0.0)) + if stable_sign == 0.0 + return (alpha_crit=NaN, alpha_scale_crit=NaN, found=false) + end + + # Scan α upward and bracket the first scaling where Δ' leaves the stable side. + prev_scale = 0.0 + lo = NaN + hi = NaN + for k in 1:n_scan + scale = max_alpha_scale * k / n_scan + d = delta_at(scale) + if isfinite(d) && sign(d) != stable_sign + lo = prev_scale + hi = scale + break + end + prev_scale = scale + end + + isnan(hi) && return (alpha_crit=NaN, alpha_scale_crit=NaN, found=false) + + # Bisect the bracket to the requested tolerance. + while (hi - lo) > tol + mid = 0.5 * (lo + hi) + d = delta_at(mid) + if !isfinite(d) || sign(d) == stable_sign + lo = mid + else + hi = mid + end + end + scale_crit = 0.5 * (lo + hi) + + return (alpha_crit=ref.alpha_ref * scale_crit, alpha_scale_crit=scale_crit, found=true) +end + +""" + ballooning_alpha_boundary(ctrl, plasma_eq; theta_k=0.0) + +Profile driver for the BALOO-style ballooning stability diagram. Loops over flux +surfaces returning the experimental pressure gradient `alpha` (from +[`salpha_reference`](@ref)) and the first stability boundary `alpha_critical` (from +[`critical_ballooning_alpha`](@ref)) versus normalized flux `psi`. Surfaces whose +experimental `alpha` exceeds `alpha_critical` are ballooning-unstable. + +Per-surface failures and surfaces with no boundary within range are returned as `NaN`. +""" +function ballooning_alpha_boundary( + ctrl::ForceFreeStatesControl, + plasma_eq::Equilibrium.PlasmaEquilibrium; + theta_k::Float64=0.0 +) + xs = plasma_eq.profiles.xs + npsi = length(xs) + psi = Vector{Float64}(xs) + alpha = fill(NaN, npsi) + alpha_critical = fill(NaN, npsi) + + for i in 1:npsi + xs[i] > 1.0 && continue + try + alpha[i] = salpha_reference(i, plasma_eq).alpha_ref + alpha_critical[i] = critical_ballooning_alpha(i, plasma_eq; theta_k=theta_k).alpha_crit + catch err + if ctrl.verbose + @warn "ballooning alpha boundary failed" psi_idx = i exception = err + end + end + end + + return (psi=psi, alpha=alpha, alpha_critical=alpha_critical) +end + # ====================================================================== # ODE Integration # Integrates the ideal marginal ballooning equations diff --git a/src/GeneralizedPerturbedEquilibrium.jl b/src/GeneralizedPerturbedEquilibrium.jl index adcca1363..e73988b15 100755 --- a/src/GeneralizedPerturbedEquilibrium.jl +++ b/src/GeneralizedPerturbedEquilibrium.jl @@ -50,7 +50,7 @@ import AdaptiveArrayPools: @with_pool # Import ForceFreeStates types and functions needed for main using .ForceFreeStates: ForceFreeStatesInternal, ForceFreeStatesControl, DebugSettings, VacuumData, OdeState, FourFitVars using .ForceFreeStates: sing_lim!, sing_find! -using .ForceFreeStates: compute_ballooning_stability! +using .ForceFreeStates: compute_ballooning_stability!, ballooning_alpha_boundary using .ForceFreeStates: make_metric, make_matrix, make_kinetic_matrix using .ForceFreeStates: find_kinetic_singular_surfaces! using .ForceFreeStates: eulerlagrange_integration, free_run! @@ -163,8 +163,11 @@ function main(args::Vector{String}=String[]; dd::Union{IMASdd.dd,Nothing}=nothin # ballooning coefficient system and the local ballooning result. profiles_xs = equil.profiles.xs locstab_fs = zeros(Float64, length(profiles_xs), 5) + ballooning_boundary = (psi=Float64[], alpha=Float64[], alpha_critical=Float64[]) if ctrl.local_stability_flag compute_ballooning_stability!(ctrl, locstab_fs, equil) + # First ballooning stability boundary (α vs ψ_N) for BALOO-style diagnostics. + ballooning_boundary = ballooning_alpha_boundary(ctrl, equil) end # Fit data to splines intr.locstab = cubic_interp(profiles_xs, Series(locstab_fs); extrap=ExtendExtrap()) @@ -360,7 +363,7 @@ function main(args::Vector{String}=String[]; dd::Union{IMASdd.dd,Nothing}=nothin end if ctrl.write_outputs_to_HDF5 - write_outputs_to_HDF5(ctrl, equil, intr, odet, ctrl.vac_flag ? vac_data : nothing, ffit, git_version) + write_outputs_to_HDF5(ctrl, equil, intr, odet, ctrl.vac_flag ? vac_data : nothing, ffit, git_version; ballooning_boundary=ballooning_boundary) @info "Results written to $(ctrl.HDF5_filename)" end @@ -475,7 +478,8 @@ function write_outputs_to_HDF5( odet::OdeState, vac_data::Union{VacuumData,Nothing}, ffit::Union{FourFitVars,Nothing}=nothing, - git_version::String="unknown" + git_version::String="unknown"; + ballooning_boundary=(psi=Float64[], alpha=Float64[], alpha_critical=Float64[]) ) h5open(joinpath(intr.dir_path, ctrl.HDF5_filename), "w") do out_h5 @@ -552,6 +556,11 @@ function write_outputs_to_HDF5( [intr.locstab(sing.psifac)[1] / sing.psifac for sing in intr.sing] : Float64[] out_h5["locstab/ballooning_Delta_prime"] = ctrl.local_stability_flag ? intr.locstab.y[:, 4] : Float64[] + # First ballooning stability boundary: experimental α vs critical α (BALOO-style). + out_h5["locstab/psi"] = ballooning_boundary.psi + out_h5["locstab/alpha"] = ballooning_boundary.alpha + out_h5["locstab/alpha_critical"] = ballooning_boundary.alpha_critical + # Write integration data # TODO: technically this should only be written if ode_flag is true, but that's going to get deprecated eventually out_h5["integration/nstep"] = odet.step # Number of saved solution snapshots From cfb7bbf3c3849139de9f8a5f0780f7cfe576deef Mon Sep 17 00:00:00 2001 From: nelsonand Date: Thu, 11 Jun 2026 14:15:10 -0600 Subject: [PATCH 026/135] Update to BALOO Stability Plotting --- .../analyze_example.jl | 348 +++++++++--------- src/Analysis/ForceFreeStates.jl | 40 ++ src/ForceFreeStates/Bal.jl | 84 +++++ src/GeneralizedPerturbedEquilibrium.jl | 2 +- 4 files changed, 308 insertions(+), 166 deletions(-) diff --git a/examples/DIIID-like_ideal_example/analyze_example.jl b/examples/DIIID-like_ideal_example/analyze_example.jl index 9c2f2d2b6..85df7d8cf 100644 --- a/examples/DIIID-like_ideal_example/analyze_example.jl +++ b/examples/DIIID-like_ideal_example/analyze_example.jl @@ -20,117 +20,18 @@ Plots.savefig(p_ffs, joinpath(@__DIR__, "ffs_summary.png")) display(p_pe); Plots.savefig(p_pe, joinpath(@__DIR__, "pe_summary.png")) +# BALOO-style first ballooning stability boundary: experimental α vs critical α +p_baloo = Analysis.ForceFreeStates.plot_ballooning_alpha_boundary(h5path) +display(p_baloo) +baloo_path = joinpath(@__DIR__, "ballooning_alpha_boundary.png") +Plots.savefig(p_baloo, baloo_path) + # ---------------------------------------------------------------------- # Local stability: s-alpha profiles, D_I / ballooning Δ', and 2D s-alpha # maps (ported from the former Bal_salpha_delta_di_summary notebook). # These recompute directly from the equilibrium via the Bal.jl helpers # rather than reading gpec.h5, so the s-alpha scan can perturb (p', q'). # ---------------------------------------------------------------------- -eq_config = Equilibrium.EquilibriumConfig(TOML.parsefile(joinpath(@__DIR__, "gpec.toml"))["Equilibrium"], @__DIR__) -equil = Equilibrium.setup_equilibrium(eq_config) -psi_norm = Vector(equil.profiles.xs) - -# s and alpha profiles vs normalized flux -s_profile = fill(NaN, length(psi_norm)) -alpha_profile = fill(NaN, length(psi_norm)) -for i in eachindex(psi_norm) - try - ref = ForceFreeStates.salpha_reference(i, equil) - s_profile[i] = ref.s_ref - alpha_profile[i] = ref.alpha_ref - catch err - @warn "s-alpha reference failed" i psi = psi_norm[i] exception = (err, catch_backtrace()) - end -end - -s_mask = isfinite.(s_profile) -alpha_mask = isfinite.(alpha_profile) -p_s = plot( - psi_norm[s_mask], - s_profile[s_mask]; - xlabel="Norm. Poloidal Flux", - ylabel="s", - title="Magnetic shear s", - label="s", - lw=2, - framestyle=:box, - left_margin=10Plots.mm, - bottom_margin=5Plots.mm -) -p_alpha = plot( - psi_norm[alpha_mask], - alpha_profile[alpha_mask]; - xlabel="Norm. Poloidal Flux", - ylabel=L"\alpha", - title="Pressure gradient α", - label=L"\alpha", - lw=2, - framestyle=:box, - left_margin=10Plots.mm, - bottom_margin=5Plots.mm -) -p_salpha = plot(p_s, p_alpha; layout=(1, 2), size=(1100, 420)) -display(p_salpha) -salpha_path = joinpath(@__DIR__, "salpha_profiles.png") -Plots.savefig(p_salpha, salpha_path) - -# D_I (Mercier) and ballooning Δ' profiles -locstab_fs = zeros(length(psi_norm), 5) -ctrl = ForceFreeStates.ForceFreeStatesControl(; verbose=false) -ForceFreeStates.compute_ballooning_stability!(ctrl, locstab_fs, equil; compute_delta_prime=true) - -delta_prime = Vector(locstab_fs[:, 4]) -di_profile = fill(NaN, length(psi_norm)) -psi_mask = abs.(psi_norm) .> eps(Float64) -di_profile[psi_mask] .= locstab_fs[psi_mask, 1] ./ psi_norm[psi_mask] - -delta_mask = isfinite.(delta_prime) -di_mask = isfinite.(di_profile) -p_delta = plot( - psi_norm[delta_mask], - delta_prime[delta_mask]; - xlabel="Norm. Poloidal Flux", - ylabel=L"\Delta'", - title="Ballooning Δ'", - label=L"\Delta'", - lw=2, - framestyle=:box, - left_margin=10Plots.mm, - bottom_margin=5Plots.mm -) -p_di = plot( - psi_norm[di_mask], - di_profile[di_mask]; - xlabel="Norm. Poloidal Flux", - ylabel=L"D_I", - title="Mercier D_I", - label=L"D_I", - lw=2, - framestyle=:box, - left_margin=10Plots.mm, - bottom_margin=5Plots.mm -) -hline!(p_di, [0.0]; linestyle=:dash, color=:black, label=nothing) -p_localstab = plot(p_delta, p_di; layout=(1, 2), size=(1100, 420)) -display(p_localstab) -localstab_path = joinpath(@__DIR__, "delta_di_profiles.png") -Plots.savefig(p_localstab, localstab_path) - -# 2D s-alpha maps of Δ' and D_I at a near-edge surface, with zero contours -psi_target = 0.974 -psi_idx_scan = argmin(abs.(psi_norm .- psi_target)) -s_scales = collect(range(-5.0, 5.0; length=30)) -alpha_scales = collect(range(-5.0, 5.0; length=30)) -scan = ForceFreeStates.scan_delta_prime_map(psi_idx_scan, equil; theta_k=0.0, s_scales=s_scales, alpha_scales=alpha_scales) - -scan_qprime = scan.dqdpsi_ref .* scan.s_scales -scan_pprime = scan.pprime_ref .* scan.alpha_scales -qorder = sortperm(scan_qprime) -porder = sortperm(scan_pprime) -scan_qprime = scan_qprime[qorder] -scan_pprime = scan_pprime[porder] -scan_delta = scan.delta_prime[qorder, porder] -scan_di = scan.di_values[qorder, porder] function symmetric_clims(z) finite_vals = vec(z)[isfinite.(vec(z))] @@ -139,68 +40,185 @@ function symmetric_clims(z) return (-maxabs, maxabs) end -p_map_delta = contourf( - scan_pprime, - scan_qprime, - scan_delta; - c=cgrad([:blue, :white, :red]), - clims=symmetric_clims(scan_delta), - xlabel=L"p_{\psi}", - ylabel=L"q_{\psi}", - title=L"\Delta'", - levels=41, - framestyle=:box, - left_margin=10Plots.mm, - bottom_margin=5Plots.mm -) -contour!(p_map_delta, scan_pprime, scan_qprime, scan_delta; levels=[0.0], color=:black, linewidth=2) -scatter!(p_map_delta, [scan.reference.pprime_ref], [scan.reference.qprime_ref]; color=:green, marker=:star5, ms=7, label="equilibrium") -p_map_di = contourf( - scan_pprime, - scan_qprime, - scan_di; - c=cgrad([:blue, :white, :red]), - clims=symmetric_clims(scan_di), - xlabel=L"p_{\psi}", - ylabel=L"q_{\psi}", - title=L"D_I", - levels=41, - framestyle=:box, - left_margin=10Plots.mm, - bottom_margin=5Plots.mm -) -contour!(p_map_di, scan_pprime, scan_qprime, scan_di; levels=[0.0], color=:black, linewidth=2) -scatter!(p_map_di, [scan.reference.pprime_ref], [scan.reference.qprime_ref]; color=:green, marker=:star5, ms=7, label="equilibrium") -p_maps = plot(p_map_delta, p_map_di; layout=(1, 2), size=(1150, 460)) -display(p_maps) -maps_path = joinpath(@__DIR__, "salpha_maps.png") -Plots.savefig(p_maps, maps_path) - -# Overlay of Δ'=0 (ballooning) and D_I=0 (Mercier) stability boundaries -p_zero = plot(; xlabel=L"p_{\psi}", ylabel=L"q_{\psi}", title="Ballooning / Mercier stability boundaries", framestyle=:box, left_margin=10Plots.mm, bottom_margin=5Plots.mm) -contour!(p_zero, scan_pprime, scan_qprime, scan_delta; levels=[0.0], color=:blue, linewidth=3, colorbar=false) -contour!(p_zero, scan_pprime, scan_qprime, scan_di; levels=[0.0], color=:red, linewidth=3, linestyle=:dash, colorbar=false) -scatter!(p_zero, [scan.reference.pprime_ref], [scan.reference.qprime_ref]; color=:green, marker=:star5, ms=8, label="equilibrium") -display(p_zero) -zero_path = joinpath(@__DIR__, "salpha_zero_contours.png") -Plots.savefig(p_zero, zero_path) +geqdsk_cases = [ + "TkMkr_D3Dlike_Hmode.geqdsk", +] -# BALOO-style first ballooning stability boundary: experimental α vs critical α -p_baloo = Analysis.ForceFreeStates.plot_ballooning_alpha_boundary(h5path) -display(p_baloo) -baloo_path = joinpath(@__DIR__, "ballooning_alpha_boundary.png") -Plots.savefig(p_baloo, baloo_path) +base_toml = TOML.parsefile(joinpath(@__DIR__, "gpec.toml")) println("Saved figures:") -for p in ( - joinpath(@__DIR__, "equilibrium_summary.png"), - joinpath(@__DIR__, "ffs_summary.png"), - joinpath(@__DIR__, "pe_summary.png"), - salpha_path, - localstab_path, - maps_path, - zero_path, - baloo_path -) +for p in (joinpath(@__DIR__, "equilibrium_summary.png"), joinpath(@__DIR__, "ffs_summary.png"), joinpath(@__DIR__, "pe_summary.png"), baloo_path) println(" ", p) end + +for geqdsk_file in geqdsk_cases + case_label = splitext(basename(geqdsk_file))[1] + println("\n=== Local stability: $case_label ===") + + eq_dict = deepcopy(base_toml["Equilibrium"]) + eq_dict["eq_filename"] = geqdsk_file + eq_config = Equilibrium.EquilibriumConfig(eq_dict, @__DIR__) + equil = Equilibrium.setup_equilibrium(eq_config) + psi_norm = Vector(equil.profiles.xs) + + # s and alpha profiles vs normalized flux + s_profile = fill(NaN, length(psi_norm)) + alpha_profile = fill(NaN, length(psi_norm)) + for i in eachindex(psi_norm) + try + ref = ForceFreeStates.salpha_reference(i, equil) + s_profile[i] = ref.s_ref + alpha_profile[i] = ref.alpha_ref + catch err + @warn "s-alpha reference failed" i psi = psi_norm[i] exception = (err, catch_backtrace()) + end + end + + s_mask = isfinite.(s_profile) + alpha_mask = isfinite.(alpha_profile) + p_s = plot( + psi_norm[s_mask], + s_profile[s_mask]; + xlabel="Norm. Poloidal Flux", + ylabel="s", + title="Magnetic shear s", + label="s", + lw=2, + framestyle=:box, + left_margin=10Plots.mm, + bottom_margin=5Plots.mm + ) + p_alpha = plot( + psi_norm[alpha_mask], + alpha_profile[alpha_mask]; + xlabel="Norm. Poloidal Flux", + ylabel=L"\alpha", + title="Pressure gradient α", + label=L"\alpha", + lw=2, + framestyle=:box, + left_margin=10Plots.mm, + bottom_margin=5Plots.mm + ) + p_salpha = plot(p_s, p_alpha; layout=(1, 2), size=(1100, 420)) + display(p_salpha) + salpha_path = joinpath(@__DIR__, "salpha_profiles_$(case_label).png") + Plots.savefig(p_salpha, salpha_path) + + # D_I (Mercier) and ballooning Δ' profiles + locstab_fs = zeros(length(psi_norm), 5) + ctrl = ForceFreeStates.ForceFreeStatesControl(; verbose=false) + ForceFreeStates.compute_ballooning_stability!(ctrl, locstab_fs, equil; compute_delta_prime=true) + + delta_prime = Vector(locstab_fs[:, 4]) + di_profile = fill(NaN, length(psi_norm)) + psi_mask = abs.(psi_norm) .> eps(Float64) + di_profile[psi_mask] .= locstab_fs[psi_mask, 1] ./ psi_norm[psi_mask] + + delta_mask = isfinite.(delta_prime) + di_mask = isfinite.(di_profile) + p_delta = plot( + psi_norm[delta_mask], + delta_prime[delta_mask]; + xlabel="Norm. Poloidal Flux", + ylabel=L"\Delta'", + title="Ballooning Δ'", + label=L"\Delta'", + lw=2, + framestyle=:box, + left_margin=10Plots.mm, + bottom_margin=5Plots.mm + ) + p_di = plot( + psi_norm[di_mask], + di_profile[di_mask]; + xlabel="Norm. Poloidal Flux", + ylabel=L"D_I", + title="Mercier D_I", + label=L"D_I", + lw=2, + framestyle=:box, + left_margin=10Plots.mm, + bottom_margin=5Plots.mm + ) + hline!(p_di, [0.0]; linestyle=:dash, color=:black, label=nothing) + p_localstab = plot(p_delta, p_di; layout=(1, 2), size=(1100, 420)) + display(p_localstab) + localstab_path = joinpath(@__DIR__, "delta_di_profiles_$(case_label).png") + Plots.savefig(p_localstab, localstab_path) + + # 2D s-alpha maps of Δ' and D_I at a near-edge surface, with zero contours + psi_target = 0.974 + psi_idx_scan = argmin(abs.(psi_norm .- psi_target)) + s_scales = collect(range(-5.0, 5.0; length=30)) + alpha_scales = collect(range(-5.0, 5.0; length=30)) + scan = ForceFreeStates.scan_delta_prime_map(psi_idx_scan, equil; theta_k=0.0, s_scales=s_scales, alpha_scales=alpha_scales) + + scan_qprime = scan.dqdpsi_ref .* scan.s_scales + scan_pprime = scan.pprime_ref .* scan.alpha_scales + qorder = sortperm(scan_qprime) + porder = sortperm(scan_pprime) + scan_qprime = scan_qprime[qorder] + scan_pprime = scan_pprime[porder] + scan_delta = scan.delta_prime[qorder, porder] + scan_di = scan.di_values[qorder, porder] + + p_map_delta = contourf( + scan_pprime, + scan_qprime, + scan_delta; + c=cgrad([:blue, :white, :red]), + clims=symmetric_clims(scan_delta), + xlabel=L"p_{\psi}", + ylabel=L"q_{\psi}", + title=L"\Delta'", + levels=41, + framestyle=:box, + left_margin=10Plots.mm, + bottom_margin=5Plots.mm + ) + contour!(p_map_delta, scan_pprime, scan_qprime, scan_delta; levels=[0.0], color=:black, linewidth=2) + scatter!(p_map_delta, [scan.reference.pprime_ref], [scan.reference.qprime_ref]; color=:green, marker=:star5, ms=7, label="equilibrium") + p_map_di = contourf( + scan_pprime, + scan_qprime, + scan_di; + c=cgrad([:blue, :white, :red]), + clims=symmetric_clims(scan_di), + xlabel=L"p_{\psi}", + ylabel=L"q_{\psi}", + title=L"D_I", + levels=41, + framestyle=:box, + left_margin=10Plots.mm, + bottom_margin=5Plots.mm + ) + contour!(p_map_di, scan_pprime, scan_qprime, scan_di; levels=[0.0], color=:black, linewidth=2) + scatter!(p_map_di, [scan.reference.pprime_ref], [scan.reference.qprime_ref]; color=:green, marker=:star5, ms=7, label="equilibrium") + p_maps = plot(p_map_delta, p_map_di; layout=(1, 2), size=(1150, 460)) + display(p_maps) + maps_path = joinpath(@__DIR__, "salpha_maps_$(case_label).png") + Plots.savefig(p_maps, maps_path) + + # Overlay of Δ'=0 (ballooning) and D_I=0 (Mercier) stability boundaries + p_zero = plot(; xlabel=L"p_{\psi}", ylabel=L"q_{\psi}", title="Ballooning / Mercier stability boundaries", framestyle=:box, left_margin=10Plots.mm, bottom_margin=5Plots.mm) + contour!(p_zero, scan_pprime, scan_qprime, scan_delta; levels=[0.0], color=:blue, linewidth=3, colorbar=false) + contour!(p_zero, scan_pprime, scan_qprime, scan_di; levels=[0.0], color=:red, linewidth=3, linestyle=:dash, colorbar=false) + scatter!(p_zero, [scan.reference.pprime_ref], [scan.reference.qprime_ref]; color=:green, marker=:star5, ms=8, label="equilibrium") + display(p_zero) + zero_path = joinpath(@__DIR__, "salpha_zero_contours_$(case_label).png") + Plots.savefig(p_zero, zero_path) + + # BALOO-style α vs ψ stability boundaries (1st and 2nd) + bnd = ForceFreeStates.ballooning_alpha_boundaries(ctrl, equil) + p_alpha_bnd = Analysis.ForceFreeStates.plot_ballooning_alpha_boundaries(bnd) + display(p_alpha_bnd) + alpha_bnd_path = joinpath(@__DIR__, "alpha_stability_boundary_$(case_label).png") + Plots.savefig(p_alpha_bnd, alpha_bnd_path) + + println(" $salpha_path") + println(" $localstab_path") + println(" $maps_path") + println(" $zero_path") + println(" $alpha_bnd_path") +end diff --git a/src/Analysis/ForceFreeStates.jl b/src/Analysis/ForceFreeStates.jl index 24d095e02..5277c9faa 100644 --- a/src/Analysis/ForceFreeStates.jl +++ b/src/Analysis/ForceFreeStates.jl @@ -573,4 +573,44 @@ function plot_ffs_summary(h5path; save_path=nothing) return p end +""" + plot_ballooning_alpha_boundaries(bnd; save_path=nothing, psi_min=0.0) + +Plot the BALOO-style infinite-n ballooning stability diagram with first and second stability +boundaries: experimental α (solid black), 1st stability boundary α_crit1 (dashed red), and +2nd stability boundary α_crit2 (dashed blue) versus ψ_N. `NaN` entries in the boundary +arrays leave natural gaps over always-stable surfaces without requiring explicit masking. + +### Arguments + + - `bnd`: NamedTuple with fields `psi`, `alpha`, `alpha_critical1`, `alpha_critical2` + (as returned by `ForceFreeStates.ballooning_alpha_boundaries`) + +### Keyword arguments + + - `save_path`: If provided, save the figure to this path (default: `nothing`) + - `psi_min`: Lower ψ_N axis limit (default: `0.0`) + +### Returns + +A `Plots.jl` plot object. +""" +function plot_ballooning_alpha_boundaries(bnd; save_path=nothing, psi_min=0.0) + p = plot(; + xlims=(psi_min, 1), + xlabel=L"\psi_N", + ylabel=L"\alpha", + title="Infinite-n ballooning stability", + framestyle=:box, + legend=:topleft, + left_margin=10Plots.mm, + bottom_margin=5Plots.mm + ) + plot!(p, bnd.psi, bnd.alpha; lw=2, color=:black, label="Experimental gradient") + plot!(p, bnd.psi, bnd.alpha_critical1; lw=2, color=:red, linestyle=:dash, label="1st stability boundary") + plot!(p, bnd.psi, bnd.alpha_critical2; lw=2, color=:blue, linestyle=:dash, label="2nd stability boundary") + isnothing(save_path) || savefig(p, save_path) + return p +end + end # module ForceFreeStates diff --git a/src/ForceFreeStates/Bal.jl b/src/ForceFreeStates/Bal.jl index dd82cd133..a4197ff93 100644 --- a/src/ForceFreeStates/Bal.jl +++ b/src/ForceFreeStates/Bal.jl @@ -782,6 +782,90 @@ function ballooning_alpha_boundary( return (psi=psi, alpha=alpha, alpha_critical=alpha_critical) end +""" + second_critical_ballooning_alpha(psi_idx, plasma_eq, alpha_scale_crit1; max_alpha_scale=8.0, n_scan=20, tol=1e-3) + +Second (upper) ballooning stability boundary at one flux surface via bisection. Starting +above the first crossing at `alpha_scale_crit1` (as returned by [`critical_ballooning_alpha`](@ref)), +scans upward to find where Δ' returns to the stable side. Returns the physical critical α, +or `NaN` if no second crossing exists within `max_alpha_scale`. +""" +function second_critical_ballooning_alpha( + psi_idx::Int, + plasma_eq::Equilibrium.PlasmaEquilibrium, + alpha_scale_crit1::Float64; + max_alpha_scale::Float64=8.0, + n_scan::Int=20, + tol::Float64=1e-3 +) + ref = salpha_reference(psi_idx, plasma_eq) + delta_at(scale) = ballooning_delta_prime( + psi_idx, plasma_eq; corr_qprime=0.0, corr_pprime=ref.pprime_norm_ref * (scale - 1.0) + ).delta_prime + stable_sign = sign(delta_at(0.0)) + stable_sign == 0 && return NaN + lo2 = NaN; hi2 = NaN + prev_scale = alpha_scale_crit1 + for k in 1:n_scan + scale = alpha_scale_crit1 + (max_alpha_scale - alpha_scale_crit1) * k / n_scan + d = delta_at(scale) + if isfinite(d) && sign(d) == stable_sign + lo2 = prev_scale; hi2 = scale; break + end + prev_scale = scale + end + isnan(hi2) && return NaN + while (hi2 - lo2) > tol + mid = 0.5 * (lo2 + hi2) + d = delta_at(mid) + (!isfinite(d) || sign(d) != stable_sign) ? (lo2 = mid) : (hi2 = mid) + end + return ref.alpha_ref * 0.5 * (lo2 + hi2) +end + +""" + ballooning_alpha_boundaries(ctrl, plasma_eq; theta_k=0.0, max_alpha_scale=8.0) + +Profile driver returning the experimental pressure gradient `alpha`, the first stability +boundary `alpha_critical1`, and the second (upper) stability boundary `alpha_critical2` +versus normalized flux `psi`. Calls [`critical_ballooning_alpha`](@ref) and +[`second_critical_ballooning_alpha`](@ref) at each surface. Arrays contain `NaN` where +no boundary exists; plotting these arrays directly leaves natural gaps over always-stable +surfaces without requiring explicit masking. +""" +function ballooning_alpha_boundaries( + ctrl::ForceFreeStatesControl, + plasma_eq::Equilibrium.PlasmaEquilibrium; + theta_k::Float64=0.0, + max_alpha_scale::Float64=8.0 +) + xs = plasma_eq.profiles.xs + npsi = length(xs) + psi = Vector{Float64}(xs) + alpha = fill(NaN, npsi) + alpha_critical1 = fill(NaN, npsi) + alpha_critical2 = fill(NaN, npsi) + + for i in 1:npsi + xs[i] > 1.0 && continue + try + alpha[i] = salpha_reference(i, plasma_eq).alpha_ref + r1 = critical_ballooning_alpha(i, plasma_eq; theta_k=theta_k, max_alpha_scale=max_alpha_scale) + r1.found || continue + alpha_critical1[i] = r1.alpha_crit + alpha_critical2[i] = second_critical_ballooning_alpha( + i, plasma_eq, r1.alpha_scale_crit; max_alpha_scale=max_alpha_scale + ) + catch err + if ctrl.verbose + @warn "ballooning alpha boundaries failed" psi_idx=i exception=err + end + end + end + + return (psi=psi, alpha=alpha, alpha_critical1=alpha_critical1, alpha_critical2=alpha_critical2) +end + # ====================================================================== # ODE Integration # Integrates the ideal marginal ballooning equations diff --git a/src/GeneralizedPerturbedEquilibrium.jl b/src/GeneralizedPerturbedEquilibrium.jl index e73988b15..84b7191cc 100755 --- a/src/GeneralizedPerturbedEquilibrium.jl +++ b/src/GeneralizedPerturbedEquilibrium.jl @@ -50,7 +50,7 @@ import AdaptiveArrayPools: @with_pool # Import ForceFreeStates types and functions needed for main using .ForceFreeStates: ForceFreeStatesInternal, ForceFreeStatesControl, DebugSettings, VacuumData, OdeState, FourFitVars using .ForceFreeStates: sing_lim!, sing_find! -using .ForceFreeStates: compute_ballooning_stability!, ballooning_alpha_boundary +using .ForceFreeStates: compute_ballooning_stability!, ballooning_alpha_boundary, ballooning_alpha_boundaries using .ForceFreeStates: make_metric, make_matrix, make_kinetic_matrix using .ForceFreeStates: find_kinetic_singular_surfaces! using .ForceFreeStates: eulerlagrange_integration, free_run! From c656d371ddda93f6c0110e33040802d387446e8d Mon Sep 17 00:00:00 2001 From: nelsonand Date: Thu, 11 Jun 2026 14:19:33 -0600 Subject: [PATCH 027/135] Some cleanup --- src/Analysis/ForceFreeStates.jl | 9 ++++----- src/ForceFreeStates/Bal.jl | 4 ++-- 2 files changed, 6 insertions(+), 7 deletions(-) diff --git a/src/Analysis/ForceFreeStates.jl b/src/Analysis/ForceFreeStates.jl index 5277c9faa..264f31ce2 100644 --- a/src/Analysis/ForceFreeStates.jl +++ b/src/Analysis/ForceFreeStates.jl @@ -410,11 +410,10 @@ function plot_ballooning_alpha_boundary(h5path; save_path=nothing, psi_min=0.0) bottom_margin=5Plots.mm ) - # Mask non-finite α_crit so always-stable surfaces leave a gap rather than a spike. - exp_mask = isfinite.(alpha) - crit_mask = isfinite.(alpha_crit) - plot!(p, psi[exp_mask], alpha[exp_mask]; lw=2, color=:black, label="Experimental gradient") - plot!(p, psi[crit_mask], alpha_crit[crit_mask]; lw=2, linestyle=:dash, color=:red, label="1st stability boundary") + # NaN entries leave natural gaps over always-stable surfaces; isfinite masking would + # wrongly connect across such gaps with a straight line. + plot!(p, psi, alpha; lw=2, color=:black, label="Experimental gradient") + plot!(p, psi, alpha_crit; lw=2, linestyle=:dash, color=:red, label="1st stability boundary") isnothing(save_path) || savefig(p, save_path) return p diff --git a/src/ForceFreeStates/Bal.jl b/src/ForceFreeStates/Bal.jl index a4197ff93..6c7590403 100644 --- a/src/ForceFreeStates/Bal.jl +++ b/src/ForceFreeStates/Bal.jl @@ -798,6 +798,7 @@ function second_critical_ballooning_alpha( n_scan::Int=20, tol::Float64=1e-3 ) + alpha_scale_crit1 >= max_alpha_scale && return NaN ref = salpha_reference(psi_idx, plasma_eq) delta_at(scale) = ballooning_delta_prime( psi_idx, plasma_eq; corr_qprime=0.0, corr_pprime=ref.pprime_norm_ref * (scale - 1.0) @@ -830,8 +831,7 @@ Profile driver returning the experimental pressure gradient `alpha`, the first s boundary `alpha_critical1`, and the second (upper) stability boundary `alpha_critical2` versus normalized flux `psi`. Calls [`critical_ballooning_alpha`](@ref) and [`second_critical_ballooning_alpha`](@ref) at each surface. Arrays contain `NaN` where -no boundary exists; plotting these arrays directly leaves natural gaps over always-stable -surfaces without requiring explicit masking. +no boundary exists. """ function ballooning_alpha_boundaries( ctrl::ForceFreeStatesControl, From 776be710da6fb8e913192cf050cea3c10c3cdf0b Mon Sep 17 00:00:00 2001 From: nelsonand Date: Thu, 11 Jun 2026 14:31:44 -0600 Subject: [PATCH 028/135] Plot preference --- src/Analysis/ForceFreeStates.jl | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/Analysis/ForceFreeStates.jl b/src/Analysis/ForceFreeStates.jl index 264f31ce2..1774869c2 100644 --- a/src/Analysis/ForceFreeStates.jl +++ b/src/Analysis/ForceFreeStates.jl @@ -606,8 +606,8 @@ function plot_ballooning_alpha_boundaries(bnd; save_path=nothing, psi_min=0.0) bottom_margin=5Plots.mm ) plot!(p, bnd.psi, bnd.alpha; lw=2, color=:black, label="Experimental gradient") - plot!(p, bnd.psi, bnd.alpha_critical1; lw=2, color=:red, linestyle=:dash, label="1st stability boundary") - plot!(p, bnd.psi, bnd.alpha_critical2; lw=2, color=:blue, linestyle=:dash, label="2nd stability boundary") + plot!(p, bnd.psi, bnd.alpha_critical1; lw=2, color=:red, marker=:circle, label="1st stability boundary") + plot!(p, bnd.psi, bnd.alpha_critical2; lw=2, color=:blue, marker=:circle, label="2nd stability boundary") isnothing(save_path) || savefig(p, save_path) return p end From 0e35d1d01f2acc1e03dc9eba37a014d20120170c Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Thu, 11 Jun 2026 17:11:43 -0400 Subject: [PATCH 029/135] RERUN - CLEANUP - Remove deprecated equil.toml fallback from input dispatch equil.toml has been deprecated for a long time and no example or test ships one; gpec.toml [Equilibrium] is the single supported source. Drop the dead fallback branch in build_inputs_from_toml (and the equilibrium_config_to_dict band-aid that was only there to make that path's snapshot rerunnable). The deeper deprecated EquilibriumConfig(path)/setup_equilibrium(path) overloads in the Equilibrium module are left for a separate cleanup. Co-Authored-By: Claude Opus 4.8 (1M context) --- src/GeneralizedPerturbedEquilibrium.jl | 13 ++----------- src/Rerun.jl | 11 ----------- 2 files changed, 2 insertions(+), 22 deletions(-) diff --git a/src/GeneralizedPerturbedEquilibrium.jl b/src/GeneralizedPerturbedEquilibrium.jl index 8c78c1e7c..f01a63f70 100755 --- a/src/GeneralizedPerturbedEquilibrium.jl +++ b/src/GeneralizedPerturbedEquilibrium.jl @@ -100,17 +100,8 @@ equilibria (efit, chease) that `setup_equilibrium` reads from disk. function build_inputs_from_toml(path::String; dd::Union{IMASdd.dd,Nothing}=nothing) inputs = TOML.parsefile(joinpath(path, "gpec.toml")) - if "Equilibrium" in keys(inputs) - eq_config = Equilibrium.EquilibriumConfig(inputs["Equilibrium"], path) - elseif isfile(joinpath(path, "equil.toml")) - @warn "Reading from equil.toml is deprecated. Please move [EQUIL_CONTROL] and [EQUIL_OUTPUT] sections to [Equilibrium] in gpec.toml" - eq_config = Equilibrium.EquilibriumConfig(joinpath(path, "equil.toml")) - # Populate [Equilibrium] from the constructed config so the snapshot TOML blob is - # complete and rerunnable — the deprecated equil.toml is not stored in gpec.h5. - inputs["Equilibrium"] = equilibrium_config_to_dict(eq_config) - else - error("No equilibrium configuration found. Add [Equilibrium] section to gpec.toml") - end + haskey(inputs, "Equilibrium") || error("No [Equilibrium] section in gpec.toml") + eq_config = Equilibrium.EquilibriumConfig(inputs["Equilibrium"], path) # LAR/Solovev carry their parameters in a separate auxiliary TOML referenced # by eq_filename. Merge those parameters into the in-memory `inputs` dict so diff --git a/src/Rerun.jl b/src/Rerun.jl index f50160e55..b3d30d8b9 100644 --- a/src/Rerun.jl +++ b/src/Rerun.jl @@ -238,17 +238,6 @@ function rebuild_equilibrium_input(eq_config::Equilibrium.EquilibriumConfig, raw end end -""" - equilibrium_config_to_dict(eq_config) -> Dict{String,Any} - -Serialize an `EquilibriumConfig` back into a plain dict keyed by field name. Used to -synthesize a complete `[Equilibrium]` section when a run was configured via the deprecated -`equil.toml`, so the gpec.h5 snapshot is self-contained and rerunnable. -""" -function equilibrium_config_to_dict(eq_config::Equilibrium.EquilibriumConfig) - return Dict{String,Any}(String(f) => getfield(eq_config, f) for f in fieldnames(typeof(eq_config))) -end - """ build_inputs_from_h5(args::Vector{String}) -> (inputs, eq_config, additional_input, output_dir, current_git, preloaded_forcing) From cf90fed721bb8826be86161ddd85ff83e5a8ebc7 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Thu, 11 Jun 2026 20:33:40 -0400 Subject: [PATCH 030/135] =?UTF-8?q?Analysis=20-=20BUG=20FIX=20-=20Reconstr?= =?UTF-8?q?uct=20coil=20b=5Fn=5Fx=20in=20machine=20=CF=86=20(not=20SFL=20?= =?UTF-8?q?=CE=B6)=20so=20the=20field=20tracks=20its=20coil?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit control_surface_scalar now extends the SFL Fourier modes to the machine angle via c(θ,φ)=-Re[f(θ)e^{i n ν(θ)}e^{i n·hel·φ}], the exact inverse of fourier_decompose_bn under φ=-hel(2π ζ + ν). The +ν correction un-shears the field into a vertical (square-ish) window-pane band — the prior ζ-based e^{i n φ} left a residual toroidal shear (the 'helical tendrils'). The e^{i n·hel·φ} makes the toroidal tracking robust for either helicity, and the leading − is a documented display orientation giving blue-coil↔blue-surface (verified: +coil → +b_n_x lobe beneath it on DIII-D). Co-Authored-By: Claude Opus 4.8 --- src/Analysis/CoilForcing.jl | 43 +++++++++++++++++++++++-------------- 1 file changed, 27 insertions(+), 16 deletions(-) diff --git a/src/Analysis/CoilForcing.jl b/src/Analysis/CoilForcing.jl index e8549e474..132982276 100644 --- a/src/Analysis/CoilForcing.jl +++ b/src/Analysis/CoilForcing.jl @@ -267,18 +267,22 @@ field on the plasma boundary, ready to colour [`plot_surface_3d`](@ref). arbitrary (e.g. applied normal field `b_n_x`, total `b_n`, displacement `xi_n`); the caller supplies whichever modes they want to view. -The transform follows `Analysis.PerturbedEquilibriumModes.modes_to_theta` / `theta_to_thetaphi` -(the gpec.h5 control-surface path): `f(θ) = Σ_m amp_m e^{i m θ}`, the SFL→machine-angle correction -`e^{i n ν(ψ,θ)}` from `equil.rzphi_nu`, then `c(θ,φ) = Re[f(θ) e^{i n φ}]`. +The transform inverts the SFL Fourier decomposition used by `ForcingTerms.fourier_decompose_bn`: +`f(θ) = Σ_m amp_m e^{i m θ}`, the per-θ correction `e^{i n ν(ψ,θ)}` from `equil.rzphi_nu`, then the +toroidal extension in the **machine angle** `c(θ,φ) = -Re[f(θ) e^{i n·hel·φ}]`. The `e^{i n·hel·φ}` +follows from the SFL→machine map `φ = -hel(2π ζ + ν)` (`ζ` the SFL toroidal angle the modes were +decomposed against); substituting `2π ζ = -hel·φ - ν` is what turns the decomposition's `ζ` +exponential into the `ν` correction times `e^{i n·hel·φ}`. !!! note "Sign / helicity convention" - The toroidal handedness and overall sign are chosen so that, for applied coil fields - (`b_n_x`), **a positive coil current produces positive (blue) `b_n_x` directly beneath the - coil** — verified against coil currents on DIII-D (`helicity = sign(Bt)·sign(Ip) > 0`). This - is the opposite handedness from a naive copy of the legacy Python `plot_control_3d`, which - mis-tracks the coil toroidally. Pass `helicity` to override `sign(Bt)·sign(Ip)` if the - field/coil colours disagree for your machine. + The reconstruction tracks the source coil **toroidally** (the field lobe sits at the coil's φ), + carried by `helicity = sign(Bt)·sign(Ip)` in `e^{i n·hel·φ}` (`equil.rzphi_nu`/`equil.params`). + The leading `-` is a display orientation so that **a positive (blue) coil current reads as a + positive (blue) `b_n_x` lobe beneath it** — GPEC's outward-normal flux is intrinsically negative + there, so the overall sign is the blue-coil↔blue-surface convention while the spatial structure + and magnitude are physical. Pass `helicity` to override `sign(Bt)·sign(Ip)` if the toroidal + tracking is wrong for your machine. ### Keyword arguments @@ -302,7 +306,12 @@ function control_surface_scalar(equil, modes, n::Int; mtheta::Int=180, nphi::Int ft = FourierTransform(mtheta, mpert, m_low) f = inverse(ft, vec) - # SFL→machine toroidal-angle correction e^{i n ν(ψ,θ)} + # SFL→machine toroidal-angle correction e^{i n ν(ψ,θ)}. The modes are decomposed on the SFL + # grid against e^{-i(m θ - n ζ)}, with the machine angle φ = -hel(2π ζ + ν) (see CoilFourier + # `sample_boundary_grid`). Substituting 2π ζ = -hel φ - ν into the inverse turns the ζ + # exponential into e^{i n ν(θ)} e^{i n hel φ}: the per-θ ν enters the field, hel sets the + # toroidal handedness, and the real field reconstructs faithfully — so a positive (blue) coil + # current yields positive (blue) b_n_x directly beneath the coil with no extra sign flip. hel = isnothing(helicity) ? _equil_helicity(equil) : helicity hint = (Ref(1), Ref(1)) for i in 1:mtheta @@ -310,15 +319,17 @@ function control_surface_scalar(equil, modes, n::Int; mtheta::Int=180, nphi::Int ν = equil.rzphi_nu((psi_b, θ); hint=hint) f[i] *= exp(im * n * ν) end - # Conjugate for the toroidal handedness that makes the field track its source coil; the - # condition is the opposite of the legacy Python (verified empirically, see note above). - hel < 0 && (f = conj.(f)) - # θ→φ extension: c(θ,φ) = Re[ f(θ) e^{i n φ} ]. The leading − sets the convention that a - # positive coil current drives positive (blue) b_n_x directly beneath the coil. + # θ→φ extension in the machine angle: c(θ,φ) = -Re[ f(θ) e^{i n hel φ} ]. The reconstruction + # tracks the source coil toroidally (the lobe sits at the coil's φ); the leading − is a display + # orientation that makes a positive (blue) coil current read as a positive (blue) b_n_x lobe + # beneath it. GPEC's outward-normal flux is intrinsically negative there, so this overall sign + # is the blue-coil↔blue-surface convention — the spatial structure and magnitude are physical. + # It is a constant flip (not helicity-dependent): the normal-projection sign is set by geometry, + # while hel only carries the toroidal handedness, already in the exponential. c = zeros(Float64, mtheta, nphi) for k in 1:nphi - ph = exp(im * n * (k - 1) * 2π / nphi) + ph = exp(im * n * hel * (k - 1) * 2π / nphi) for i in 1:mtheta c[i, k] = -real(f[i] * ph) end From 378cb4c8c608cd520e568be94fb4a2a3d178914f Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Thu, 11 Jun 2026 20:34:34 -0400 Subject: [PATCH 031/135] PERTURBED EQUILIBRIUM - CLEANUP - Standardize field terminology to Pharr 2026 weighting language MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Pharr (2026) names the three normal-field Fourier decompositions by the area weight applied to the FT integrand, all in tesla: bare b (normal field), b-bar (full-area weighted), b-tilde (square-root-area weighted). "Power-normalized" was a Parseval property, not Pharr's term, and is not intuitive. This pass conforms all code, h5 keys, comments, docstrings, and regression labels to the weighting language. - b-tilde "power-normalized field" -> "root-area-weighted field" everywhere (CoordinateInvariant.jl, RootAreaWeighted.jl, PE Response/ResponseMatrices/Structs/Utils). h5 key powernorm_field_to_flux_operator -> rootarea_field_to_flux_operator. - Resonant/penetrated b-bar fields -> "area-weighted field": resonant_field -> resonant_area_weighted_field (+ C_, penetrated_ variants) across struct fields, h5 keys, doc-tree, Analysis plot fn, Fortran benchmark, and the diiid_n1 regression case. - psi_area -> b_psi_area_weighted: it is b^psi/ (the gpout_xbnormal normal field, tesla), not the surface area — the old name was misleading. - Kill "Power Normalized" in FFS: prose + regression labels (4 cases) -> "root-area- weighted"; internal pn_* -> rootA_*; compute_power_norm_eigenvalues -> compute_rootarea_eigenvalues; PowerNorm.jl -> RootAreaWeighted.jl. The h5 dataset/group structure (eigenmode_energies, XiNorm) is term-neutral and unchanged. - Add docs/src/field_conventions.md: authoritative b/b-bar/b-tilde <-> English <-> h5 table with an admonition prompting #267's conventions page to conform on merge. Verification: package loads; runtests_coordinate_invariant 9/9; docs build clean (field_conventions renders, no missing_docs/cross_reference errors); regression diiid_n1 develop vs local 28/28 quantities 0.0e+00 (pure rename — the 2 N/A rows are the resonant_field -> resonant_area_weighted_field key rename, value bit-identical). Co-Authored-By: Claude Opus 4.8 (1M context) --- benchmarks/benchmark_against_fortran_run.jl | 8 +- docs/make.jl | 1 + docs/src/field_conventions.md | 59 +++++++++++++ regression-harness/cases/diiid_n1.toml | 28 +++---- regression-harness/cases/solovev_multi_n.toml | 12 +-- regression-harness/cases/solovev_n1.toml | 16 ++-- src/Analysis/PerturbedEquilibrium.jl | 44 +++++----- src/Equilibrium/CoordinateInvariant.jl | 12 +-- src/ForceFreeStates/EulerLagrange.jl | 10 +-- src/ForceFreeStates/ForceFreeStates.jl | 2 +- src/ForceFreeStates/ForceFreeStatesStructs.jl | 40 ++++----- src/ForceFreeStates/Free.jl | 34 ++++---- .../{PowerNorm.jl => RootAreaWeighted.jl} | 84 +++++++++---------- src/GeneralizedPerturbedEquilibrium.jl | 28 +++---- .../FieldReconstruction.jl | 4 +- .../PerturbedEquilibriumStructs.jl | 18 ++-- src/PerturbedEquilibrium/Response.jl | 2 +- src/PerturbedEquilibrium/ResponseMatrices.jl | 6 +- src/PerturbedEquilibrium/SingularCoupling.jl | 26 +++--- src/PerturbedEquilibrium/Utils.jl | 28 +++---- 20 files changed, 261 insertions(+), 201 deletions(-) create mode 100644 docs/src/field_conventions.md rename src/ForceFreeStates/{PowerNorm.jl => RootAreaWeighted.jl} (69%) diff --git a/benchmarks/benchmark_against_fortran_run.jl b/benchmarks/benchmark_against_fortran_run.jl index db701c9c9..a6252214e 100644 --- a/benchmarks/benchmark_against_fortran_run.jl +++ b/benchmarks/benchmark_against_fortran_run.jl @@ -327,7 +327,7 @@ function load_julia_outputs(h5_path::String) julia["rational_q"] = haskey(f, "$sc/rational_q") ? read(f, "$sc/rational_q") : Float64[] julia["rational_n"] = haskey(f, "$sc/rational_n") ? read(f, "$sc/rational_n") : Int[] julia["rational_m_res"] = haskey(f, "$sc/rational_m_res") ? read(f, "$sc/rational_m_res") : Int[] - julia["resonant_field"] = haskey(f, "$sc/resonant_field") ? read(f, "$sc/resonant_field") : ComplexF64[] + julia["resonant_area_weighted_field"] = haskey(f, "$sc/resonant_area_weighted_field") ? read(f, "$sc/resonant_area_weighted_field") : ComplexF64[] julia["resonant_current"] = haskey(f, "$sc/resonant_current") ? read(f, "$sc/resonant_current") : ComplexF64[] julia["island_half_width"] = haskey(f, "$sc/island_half_width") ? read(f, "$sc/island_half_width") : Float64[] julia["chirikov_parameter"] = haskey(f, "$sc/chirikov_parameter") ? read(f, "$sc/chirikov_parameter") : Float64[] @@ -337,7 +337,7 @@ function load_julia_outputs(h5_path::String) julia["forcing_vec"] = haskey(f, "$pe/forcing_vec") ? read(f, "$pe/forcing_vec") : ComplexF64[] julia["response_vec"] = haskey(f, "$pe/response_vec") ? read(f, "$pe/response_vec") : ComplexF64[] julia["b_n"] = haskey(f, "$pe/response/b_n") ? read(f, "$pe/response/b_n") : Matrix{ComplexF64}(undef, 0, 0) - julia["Jbgradpsi"] = haskey(f, "$pe/response/psi_area") ? read(f, "$pe/response/psi_area") : Matrix{ComplexF64}(undef, 0, 0) + julia["Jbgradpsi"] = haskey(f, "$pe/response/b_psi_area_weighted") ? read(f, "$pe/response/b_psi_area_weighted") : Matrix{ComplexF64}(undef, 0, 0) julia["xi_psi"] = haskey(f, "$pe/response/xi_psi") ? read(f, "$pe/response/xi_psi") : Matrix{ComplexF64}(undef, 0, 0) julia["xi_n"] = haskey(f, "$pe/response/xi_n") ? read(f, "$pe/response/xi_n") : Matrix{ComplexF64}(undef, 0, 0) julia["clebsch_psi1"] = haskey(f, "$pe/response/clebsch_psi1") ? read(f, "$pe/response/clebsch_psi1") : Matrix{ComplexF64}(undef, 0, 0) @@ -754,7 +754,7 @@ function build_comparison_table(fort, julia, fortran_dir, bench_dir, nn) row = find_julia_row(julia, q_int, nn) jp_r = (row > 0 && !isempty(julia["rational_psi"])) ? julia["rational_psi"][row] : NaN - j_phi = (row > 0 && !isempty(julia["resonant_field"])) ? abs(julia["resonant_field"][row]) : NaN + j_phi = (row > 0 && !isempty(julia["resonant_area_weighted_field"])) ? abs(julia["resonant_area_weighted_field"][row]) : NaN j_wisl= (row > 0 && !isempty(julia["island_half_width"])) ? 2*julia["island_half_width"][row] : NaN j_kch = (row > 0 && !isempty(julia["chirikov_parameter"])) ? julia["chirikov_parameter"][row] : NaN @@ -974,7 +974,7 @@ function generate_plots(fort, julia, bench_dir, nn) # Phi_res (resonant flux / area) f_phires_vals = isempty(fort["Phi_res"]) ? Float64[] : abs.(fort["Phi_res"]) j_phires_psi = julia["rational_psi"] - j_phires_vals = isempty(julia["resonant_field"]) ? Float64[] : abs.(julia["resonant_field"]) + j_phires_vals = isempty(julia["resonant_area_weighted_field"]) ? Float64[] : abs.(julia["resonant_area_weighted_field"]) p9 = _singcoup_panel("|Φ_res| [T]", "|Φ_res| vs ψ (n=$nn)", f_psi_rat, f_phires_vals, f_q_labels, j_phires_psi, j_phires_vals) diff --git a/docs/make.jl b/docs/make.jl index fbbbb3725..ffe5452a9 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -24,6 +24,7 @@ makedocs(; "Home" => "index.md", "Setup" => "set_up.md", "Workflow" => "workflow.md", + "Field Conventions" => "field_conventions.md", "API Reference" => [ "Vacuum" => "vacuum.md", "Equilibrium" => "equilibrium.md", diff --git a/docs/src/field_conventions.md b/docs/src/field_conventions.md new file mode 100644 index 000000000..601153034 --- /dev/null +++ b/docs/src/field_conventions.md @@ -0,0 +1,59 @@ +# Field Conventions + +GPEC reports perturbed magnetic fields on flux surfaces as Fourier spectra. Following +Pharr (2026), *Coordinate-invariant flux-surface Fourier analysis in tokamaks* (see +[Citations](citations.md)), there are three Fourier decompositions of the normal field, +**all in field units (tesla)**, distinguished only by the **area weight applied to the +Fourier integrand**. This page is the authoritative in-repository source for how those +three quantities are named — in prose, in code, and in the HDF5 output. + +!!! note "Authoritative field terminology" + These names are canonical for the Julia GPEC codebase. The standalone Conventions + Reference page (added by a separate documentation effort) should review and conform to + the terminology in the table below — in particular, use **"root-area-weighted field"** + rather than "power-normalized field", since "power-normalized" is a Parseval *property* + and is not the term used by Pharr (2026). + +## The three field amplitudes + +| Pharr symbol | FT integrand weight ``W`` | English name | HDF5 token | +|---|---|---|---| +| ``b`` (bare) | ``1`` | **normal field** | `b_n` | +| ``\bar b`` (bar) | ``\mathcal{J}\,\lvert\nabla\psi\rvert`` | **area-weighted field** | `area` | +| ``\tilde b`` (tilde) | ``\sqrt{\mathcal{J}\,\lvert\nabla\psi\rvert}`` | **root-area-weighted field** | `root_area` | + +All three carry units of tesla because each integral is divided by the appropriate power of +the coordinate-invariant scalar surface area ``A``: + +```math +b_m = \oint (\mathbf{b}\cdot\hat{\mathbf n})\, e^{-i m\theta}\, d\theta, \qquad +\bar b_m = \frac{1}{A}\oint \mathcal{J}\lvert\nabla\psi\rvert\,(\mathbf{b}\cdot\hat{\mathbf n})\, e^{-i m\theta}\, d\theta, \qquad +\tilde b_m = \frac{1}{\sqrt{A}}\oint \sqrt{\mathcal{J}\lvert\nabla\psi\rvert}\,(\mathbf{b}\cdot\hat{\mathbf n})\, e^{-i m\theta}\, d\theta . +``` + +Only the **square-root-area weighting** ``\tilde b`` transforms unitarily between working +coordinates, so its 2-norm (and quantities derived from it, such as the singular values of +the resonant coupling matrix) are coordinate-invariant. The **full-area weighting** +``\bar b`` is coordinate-invariant for the pitch-resonant ``m = nq`` harmonic on a rational +surface — the **resonant area-weighted field** ``\bar b^{\,r} = \Phi^r/A^r``. + +## Where each appears in GPEC output + +- **`b_n`** — the bare normal field ``\mathbf{b}\cdot\hat{\mathbf n}`` (and the area-weighted + radial field `b_psi_area_weighted`), under `perturbed_equilibrium/response/`. +- **`resonant_area_weighted_field`** / **`C_resonant_area_weighted_field`** — the resonant + area-weighted field ``\bar b^{\,r}`` and its coupling matrix, under + `perturbed_equilibrium/singular_coupling/`. The sibling `penetrated_area_weighted_field` + follows the same convention. +- **Root-area-weighted (``\tilde b``) space** — the control-surface response matrices + (`permeability`, `reluctance`, `plasma_inductance`, `surface_inductance`) are stored in + this coordinate-invariant space under `perturbed_equilibrium/response_matrices/`; the + `rootarea_field_to_flux_operator` recovers the flux-space forms. The + coordinate-invariant ideal-MHD energies written by the stability stage + (`FreeBoundaryStability/eigenmode_energies`) are likewise obtained through the + root-area-weighted transform. + +## See also + +- [Citations](citations.md) — Pharr (2026) and the other theoretical references. +- [Perturbed Equilibrium](perturbed_equilibrium.md) — where these quantities are produced. diff --git a/regression-harness/cases/diiid_n1.toml b/regression-harness/cases/diiid_n1.toml index a9d827649..36f7a7eef 100644 --- a/regression-harness/cases/diiid_n1.toml +++ b/regression-harness/cases/diiid_n1.toml @@ -3,12 +3,12 @@ name = "diiid_n1" description = "DIII-D-like equilibrium, n=1, ideal + perturbed equilibrium" example_dir = "examples/DIIID-like_ideal_example" -# Energies — leading eigenvalues at the final truncation (psilim). eigenmode_* are now power-normalized (Φ-space, Jacobian-invariant); ξ-space counterparts live under FreeBoundaryStability/XiNorm/ and are not tracked. +# Energies — leading eigenvalues at the final truncation (psilim). eigenmode_* are now root-area-weighted (Φ-space, Jacobian-invariant); ξ-space counterparts live under FreeBoundaryStability/XiNorm/ and are not tracked. [quantities.et_real] h5path = "FreeBoundaryStability/eigenmode_energies" type = "complex_vector" extract = "real_first" -label = "Power Normalized total energy Re(et[1])" +label = "root-area-weighted total energy Re(et[1])" noise_threshold = 1e-10 order = 10 @@ -16,7 +16,7 @@ order = 10 h5path = "FreeBoundaryStability/eigenmode_energies" type = "complex_vector" extract = "imag_first" -label = "Power Normalized total energy Im(et[1])" +label = "root-area-weighted total energy Im(et[1])" noise_threshold = 1e-10 order = 11 @@ -24,7 +24,7 @@ order = 11 h5path = "FreeBoundaryStability/eigenmode_plasma_energies" type = "complex_vector" extract = "real_first" -label = "Power Normalized plasma energy Re(ep[1])" +label = "root-area-weighted plasma energy Re(ep[1])" noise_threshold = 1e-10 order = 12 @@ -32,7 +32,7 @@ order = 12 h5path = "FreeBoundaryStability/eigenmode_vacuum_energies" type = "complex_vector" extract = "real_first" -label = "Power Normalized vacuum energy Re(ev[1])" +label = "root-area-weighted vacuum energy Re(ev[1])" noise_threshold = 1e-10 order = 13 @@ -49,7 +49,7 @@ order = 14 h5path = "FreeBoundaryStability/eigenmode_plasma_energies" type = "complex_vector" extract = "all_complex" -label = "Power Normalized plasma energy (all)" +label = "root-area-weighted plasma energy (all)" noise_threshold = 1e-10 order = 20 @@ -57,7 +57,7 @@ order = 20 h5path = "FreeBoundaryStability/eigenmode_vacuum_energies" type = "complex_vector" extract = "all_complex" -label = "Power Normalized vacuum energy (all)" +label = "root-area-weighted vacuum energy (all)" noise_threshold = 1e-10 order = 21 @@ -65,7 +65,7 @@ order = 21 h5path = "FreeBoundaryStability/eigenmode_energies" type = "complex_vector" extract = "all_complex" -label = "Power Normalized total energy (all)" +label = "root-area-weighted total energy (all)" noise_threshold = 1e-10 order = 22 @@ -190,19 +190,19 @@ label = "Chirikov parameter" noise_threshold = 1e-8 order = 82 -[quantities.resonant_field] -h5path = "perturbed_equilibrium/singular_coupling/resonant_field" +[quantities.resonant_area_weighted_field] +h5path = "perturbed_equilibrium/singular_coupling/resonant_area_weighted_field" type = "complex_vector" extract = "norm" -label = "||resonant field||" +label = "||resonant area-weighted field||" noise_threshold = 1e-8 order = 83 -[quantities.resonant_field_all] -h5path = "perturbed_equilibrium/singular_coupling/resonant_field" +[quantities.resonant_area_weighted_field_all] +h5path = "perturbed_equilibrium/singular_coupling/resonant_area_weighted_field" type = "complex_vector" extract = "all_complex" -label = "resonant field b^r" +label = "resonant area-weighted field b^r" noise_threshold = 1e-8 # Perturbed equilibrium: energies diff --git a/regression-harness/cases/solovev_multi_n.toml b/regression-harness/cases/solovev_multi_n.toml index f002bd01d..864d1269a 100644 --- a/regression-harness/cases/solovev_multi_n.toml +++ b/regression-harness/cases/solovev_multi_n.toml @@ -3,12 +3,12 @@ name = "solovev_multi_n" description = "Solovev analytical equilibrium, multi-n, ideal stability" example_dir = "examples/Solovev_ideal_example_multi_n" -# Energies — leading eigenvalues at the final truncation (psilim). eigenmode_* are now power-normalized (Φ-space, Jacobian-invariant); ξ-space counterparts live under FreeBoundaryStability/XiNorm/ and are not tracked. +# Energies — leading eigenvalues at the final truncation (psilim). eigenmode_* are now root-area-weighted (Φ-space, Jacobian-invariant); ξ-space counterparts live under FreeBoundaryStability/XiNorm/ and are not tracked. [quantities.et_real] h5path = "FreeBoundaryStability/eigenmode_energies" type = "complex_vector" extract = "real_first" -label = "Power Normalized total energy Re(et[1])" +label = "root-area-weighted total energy Re(et[1])" noise_threshold = 1e-10 order = 10 @@ -16,7 +16,7 @@ order = 10 h5path = "FreeBoundaryStability/eigenmode_energies" type = "complex_vector" extract = "imag_first" -label = "Power Normalized total energy Im(et[1])" +label = "root-area-weighted total energy Im(et[1])" noise_threshold = 1e-10 order = 11 @@ -33,7 +33,7 @@ order = 14 h5path = "FreeBoundaryStability/eigenmode_plasma_energies" type = "complex_vector" extract = "all_complex" -label = "Power Normalized plasma energy (all)" +label = "root-area-weighted plasma energy (all)" noise_threshold = 1e-10 order = 20 @@ -41,7 +41,7 @@ order = 20 h5path = "FreeBoundaryStability/eigenmode_vacuum_energies" type = "complex_vector" extract = "all_complex" -label = "Power Normalized vacuum energy (all)" +label = "root-area-weighted vacuum energy (all)" noise_threshold = 1e-10 order = 21 @@ -49,7 +49,7 @@ order = 21 h5path = "FreeBoundaryStability/eigenmode_energies" type = "complex_vector" extract = "all_complex" -label = "Power Normalized total energy (all)" +label = "root-area-weighted total energy (all)" noise_threshold = 1e-10 order = 22 diff --git a/regression-harness/cases/solovev_n1.toml b/regression-harness/cases/solovev_n1.toml index 04332c6d9..fa5a7923c 100644 --- a/regression-harness/cases/solovev_n1.toml +++ b/regression-harness/cases/solovev_n1.toml @@ -3,12 +3,12 @@ name = "solovev_n1" description = "Solovev analytical equilibrium, n=1, ideal stability" example_dir = "examples/Solovev_ideal_example" -# Energies — leading eigenvalues at the final truncation (psilim). eigenmode_* are now power-normalized (Φ-space, Jacobian-invariant); ξ-space counterparts live under FreeBoundaryStability/XiNorm/ and are not tracked. +# Energies — leading eigenvalues at the final truncation (psilim). eigenmode_* are now root-area-weighted (Φ-space, Jacobian-invariant); ξ-space counterparts live under FreeBoundaryStability/XiNorm/ and are not tracked. [quantities.et_real] h5path = "FreeBoundaryStability/eigenmode_energies" type = "complex_vector" extract = "real_first" -label = "Power Normalized total energy Re(et[1])" +label = "root-area-weighted total energy Re(et[1])" noise_threshold = 1e-10 order = 10 @@ -16,7 +16,7 @@ order = 10 h5path = "FreeBoundaryStability/eigenmode_energies" type = "complex_vector" extract = "imag_first" -label = "Power Normalized total energy Im(et[1])" +label = "root-area-weighted total energy Im(et[1])" noise_threshold = 1e-10 order = 11 @@ -24,7 +24,7 @@ order = 11 h5path = "FreeBoundaryStability/eigenmode_plasma_energies" type = "complex_vector" extract = "real_first" -label = "Power Normalized plasma energy Re(ep[1])" +label = "root-area-weighted plasma energy Re(ep[1])" noise_threshold = 1e-10 order = 12 @@ -32,7 +32,7 @@ order = 12 h5path = "FreeBoundaryStability/eigenmode_vacuum_energies" type = "complex_vector" extract = "real_first" -label = "Power Normalized vacuum energy Re(ev[1])" +label = "root-area-weighted vacuum energy Re(ev[1])" noise_threshold = 1e-10 order = 13 @@ -49,7 +49,7 @@ order = 14 h5path = "FreeBoundaryStability/eigenmode_plasma_energies" type = "complex_vector" extract = "all_complex" -label = "Power Normalized plasma energy (all)" +label = "root-area-weighted plasma energy (all)" noise_threshold = 1e-10 order = 20 @@ -57,7 +57,7 @@ order = 20 h5path = "FreeBoundaryStability/eigenmode_vacuum_energies" type = "complex_vector" extract = "all_complex" -label = "Power Normalized vacuum energy (all)" +label = "root-area-weighted vacuum energy (all)" noise_threshold = 1e-10 order = 21 @@ -65,7 +65,7 @@ order = 21 h5path = "FreeBoundaryStability/eigenmode_energies" type = "complex_vector" extract = "all_complex" -label = "Power Normalized total energy (all)" +label = "root-area-weighted total energy (all)" noise_threshold = 1e-10 order = 22 diff --git a/src/Analysis/PerturbedEquilibrium.jl b/src/Analysis/PerturbedEquilibrium.jl index 137ffb4a2..f1219a2e9 100644 --- a/src/Analysis/PerturbedEquilibrium.jl +++ b/src/Analysis/PerturbedEquilibrium.jl @@ -18,14 +18,14 @@ function _has_pe_data(h5path, key) end """ - plot_resonant_field_amplitude(h5path; save_path=nothing) + plot_resonant_area_weighted_field_amplitude(h5path; save_path=nothing) -Scatter plot of the resonant field `|b^r|` per rational surface vs ψ_N. One marker series -per toroidal mode n. Integer-valued q rational surfaces are annotated. The resonant field +Scatter plot of the resonant area-weighted field `|b^r|` per rational surface vs ψ_N. One marker series +per toroidal mode n. Integer-valued q rational surfaces are annotated. The resonant area-weighted field `b^r = Φ^r/A^r` is the resonant flux normalized by the scalar surface area, in tesla [Pharr 2026]. Requires the perturbed equilibrium module to have been run and -`singular_coupling/resonant_field` to be present in the HDF5 file. +`singular_coupling/resonant_area_weighted_field` to be present in the HDF5 file. ### Arguments @@ -39,29 +39,29 @@ Requires the perturbed equilibrium module to have been run and A `Plots.jl` plot object. """ -function plot_resonant_field_amplitude(h5path; save_path=nothing) +function plot_resonant_area_weighted_field_amplitude(h5path; save_path=nothing) base = "perturbed_equilibrium/singular_coupling/" - _has_pe_data(h5path, base * "resonant_field") || - return plot(; title="No resonant field data — run with perturbed equilibrium enabled", legend=false) + _has_pe_data(h5path, base * "resonant_area_weighted_field") || + return plot(; title="No resonant area-weighted field data — run with perturbed equilibrium enabled", legend=false) - resonant_field, rational_psi, rational_q, rational_n = h5open(h5path, "r") do fid - read(fid[base * "resonant_field"]), + resonant_area_weighted_field, rational_psi, rational_q, rational_n = h5open(h5path, "r") do fid + read(fid[base * "resonant_area_weighted_field"]), read(fid[base * "rational_psi"]), read(fid[base * "rational_q"]), read(fid[base * "rational_n"]) end p = plot(; xlabel="Norm. Poloidal Flux", ylabel="|b^r| [T]", - title="Resonant field |b^r| per surface", legend=:outertopright, + title="Resonant area-weighted field |b^r| per surface", legend=:outertopright, left_margin=10Plots.mm, bottom_margin=5Plots.mm) for nn in unique(rational_n) mask = rational_n .== nn - scatter!(p, rational_psi[mask], abs.(resonant_field[mask]); + scatter!(p, rational_psi[mask], abs.(resonant_area_weighted_field[mask]); label="n=$nn", markersize=7, markerstrokewidth=0) for k in findall(mask) abs(rational_q[k] - round(rational_q[k])) < 0.05 || continue - annotate!(p, rational_psi[k], abs(resonant_field[k]), + annotate!(p, rational_psi[k], abs(resonant_area_weighted_field[k]), text(" q=$(round(Int, rational_q[k]))", 8, :left, :black)) end end @@ -241,11 +241,11 @@ function plot_driven_delta_prime(h5path; save_path=nothing) end """ - plot_resonant_field(h5path; save_path=nothing) + plot_resonant_area_weighted_field(h5path; save_path=nothing) Five-panel summary of resonant coupling quantities at each rational surface vs ψ_N: - - `|b^r|`: resonant field (`plot_resonant_field_amplitude`) + - `|b^r|`: resonant area-weighted field (`plot_resonant_area_weighted_field_amplitude`) - `Re(Δ')`: tearing stability parameter (`plot_driven_delta_prime`) - `|I_res|`: resonant current - `w/2`: island half-width (`plot_island_widths`) @@ -265,8 +265,8 @@ Inspired by `plot_resonant_flux.py` from OMFIT GPEC. A `Plots.jl` plot object. """ -function plot_resonant_field(h5path; save_path=nothing) - p1 = plot_resonant_field_amplitude(h5path) +function plot_resonant_area_weighted_field(h5path; save_path=nothing) + p1 = plot_resonant_area_weighted_field_amplitude(h5path) p2 = plot_driven_delta_prime(h5path) p3 = _plot_resonant_current(h5path) p4 = plot_island_widths(h5path) @@ -343,7 +343,7 @@ Inspired by `plot_spectrograms.py` from OMFIT GPEC. - `component`: Response field component to plot; one of `:xi_psi`, `:b_psi`, `:b_theta`, `:b_zeta` (default: `:xi_psi`). `:b_psi` reads the area-normalized - `psi_area` dataset. + `b_psi_area_weighted` dataset. - `save_path`: If provided, save the figure to this path (default: `nothing`) ### Returns @@ -353,7 +353,7 @@ A `Plots.jl` plot object. function plot_mode_spectrogram(h5path; component=:xi_psi, save_path=nothing) comp_map = Dict( :xi_psi => "xi_psi", - :b_psi => "psi_area", # area-normalized b^ψ + :b_psi => "b_psi_area_weighted", # area-normalized b^ψ :b_theta => "b_theta", :b_zeta => "b_zeta", ) @@ -422,7 +422,7 @@ end Three-panel composite summary of perturbed equilibrium results: - - Top-left: Resonant field per surface (`plot_resonant_field_amplitude`) + - Top-left: Resonant area-weighted field per surface (`plot_resonant_area_weighted_field_amplitude`) - Top-right: Edge |b_ψ| spectrum - Bottom: ξ_ψ mode spectrogram (`plot_mode_spectrogram`) @@ -439,7 +439,7 @@ Three-panel composite summary of perturbed equilibrium results: A `Plots.jl` plot object. """ function plot_perturbed_equilibrium_summary(h5path; save_path=nothing) - p_islands = plot_resonant_field_amplitude(h5path) + p_islands = plot_resonant_area_weighted_field_amplitude(h5path) p_bpsi = _plot_bpsi_edge_spectrum(h5path) p_spectro = plot_mode_spectrogram(h5path; component=:xi_psi) @@ -453,11 +453,11 @@ end # Internal helper — |b_psi(m)| spectrum at the outermost psi surface function _plot_bpsi_edge_spectrum(h5path) base = "perturbed_equilibrium/response/" - _has_pe_data(h5path, base * "psi_area") || + _has_pe_data(h5path, base * "b_psi_area_weighted") || return plot(; title="No b_psi data — run with perturbed equilibrium enabled", legend=false) data, mlow, mhigh = h5open(h5path, "r") do fid - read(fid[base * "psi_area"]), + read(fid[base * "b_psi_area_weighted"]), read(fid["info/mlow"]), read(fid["info/mhigh"]) end diff --git a/src/Equilibrium/CoordinateInvariant.jl b/src/Equilibrium/CoordinateInvariant.jl index b354118a7..1e6cffdfc 100644 --- a/src/Equilibrium/CoordinateInvariant.jl +++ b/src/Equilibrium/CoordinateInvariant.jl @@ -1,17 +1,17 @@ """ -Coordinate-invariant (power-normalized field) flux-surface operators. +Coordinate-invariant (root-area-weighted field) flux-surface operators. These building blocks implement the √area weighting of Pharr (2026), "Coordinate-invariant flux-surface Fourier analysis in tokamaks". They are the single source of truth for the map between a flux-surface field component and its -power-normalized (coordinate-invariant) field representation, shared by the +root-area-weighted (coordinate-invariant) field representation, shared by the ForceFreeStates and PerturbedEquilibrium modules. The central operator is ptof = sqrtamat · √jarea -which maps a power-normalized field `b̃` to the coordinate flux harmonics `Φ`: +which maps a root-area-weighted field `b̃` to the coordinate flux harmonics `Φ`: `Φ = ptof · b̃` (so `b̃ = ptof⁻¹ · Φ`). The singular values of any operator expressed in the `b̃` basis are independent of the straight-field-line (working) coordinate. @@ -25,7 +25,7 @@ the underlying √weight identity and angle map. Compute √(J·|∇ψ|) at `mtheta` equally-spaced θ points on the flux surface at `psi`. This is the √weight function that maps a field component `b(θ)` to its -power-normalized form `√(J|∇ψ|)·b(θ)` in θ-space. +root-area-weighted form `√(J|∇ψ|)·b(θ)` in θ-space. """ function compute_sqrt_jac_delpsi(equil::PlasmaEquilibrium, psi::Float64, mtheta::Int) sqrt_jac_delpsi = Vector{Float64}(undef, mtheta) @@ -94,10 +94,10 @@ end """ control_surface_ptof(equil, psi, ft) -> Matrix{ComplexF64} -Build the power-norm-field → flux operator `ptof = sqrtamat · √jarea` at the flux +Build the root-area-weighted field → flux operator `ptof = sqrtamat · √jarea` at the flux surface `psi`, where `jarea = ∫ J|∇ψ| dθ` is the scalar flux-surface area. -`ptof` maps a power-normalized field `b̃` to the coordinate flux harmonics `Φ`: +`ptof` maps a root-area-weighted field `b̃` to the coordinate flux harmonics `Φ`: `Φ = ptof · b̃`. To express a flux-space operator/generator in the coordinate-invariant `b̃` basis (and back) use: - operator `Ã = ptof⁻¹ · A · ptof` (e.g. permeability `Φ_tot = A·Φ_x`) diff --git a/src/ForceFreeStates/EulerLagrange.jl b/src/ForceFreeStates/EulerLagrange.jl index c124479d7..daa373376 100644 --- a/src/ForceFreeStates/EulerLagrange.jl +++ b/src/ForceFreeStates/EulerLagrange.jl @@ -939,7 +939,7 @@ function findmax_dW_edge!(odet::OdeState, ctrl::ForceFreeStatesControl, equil::E # Create a rough spline for wv matrix between psiedge -> psilim so we can approximate dW es.wvmat = free_compute_wv_spline(ctrl, equil, intr) - # Pre-compute sqrtamat + jarea spline for power-normalized eigenvalues + # Pre-compute sqrtamat + jarea spline for root-area-weighted eigenvalues es.sqrtamat_spline = free_compute_sqrtamat_spline(ctrl, equil, intr) # Loop with compact index j into EdgeScanState; ODE index is edge_start + j - 1. @@ -954,10 +954,10 @@ function findmax_dW_edge!(odet::OdeState, ctrl::ForceFreeStatesControl, equil::E es.plasma_energy[j] = result.plasma_energy es.vacuum_energy[j] = result.vacuum_energy es.vacuum_eigenvalue[j] = result.vacuum_eigenvalue - es.pn_total_eigenvalue[j] = result.pn_total_eigenvalue - es.pn_plasma_energy[j] = result.pn_plasma_energy - es.pn_vacuum_energy[j] = result.pn_vacuum_energy - es.pn_vacuum_eigenvalue[j] = result.pn_vacuum_eigenvalue + es.rootA_total_eigenvalue[j] = result.rootA_total_eigenvalue + es.rootA_plasma_energy[j] = result.rootA_plasma_energy + es.rootA_vacuum_energy[j] = result.rootA_vacuum_energy + es.rootA_vacuum_eigenvalue[j] = result.rootA_vacuum_eigenvalue catch e e isa LinearAlgebra.SingularException || rethrow() end diff --git a/src/ForceFreeStates/ForceFreeStates.jl b/src/ForceFreeStates/ForceFreeStates.jl index 4af40c716..a9d90ef0d 100644 --- a/src/ForceFreeStates/ForceFreeStates.jl +++ b/src/ForceFreeStates/ForceFreeStates.jl @@ -30,7 +30,7 @@ include("FixedKineticMatrices.jl") include("Kinetic.jl") include("FixedBoundaryStability.jl") include("Utils.jl") -include("PowerNorm.jl") +include("RootAreaWeighted.jl") include("Free.jl") include("Riccati.jl") diff --git a/src/ForceFreeStates/ForceFreeStatesStructs.jl b/src/ForceFreeStates/ForceFreeStatesStructs.jl index 852d8893e..4f9602296 100644 --- a/src/ForceFreeStates/ForceFreeStatesStructs.jl +++ b/src/ForceFreeStates/ForceFreeStatesStructs.jl @@ -388,8 +388,8 @@ Populated in `Free.jl`. - `wt0::Array{ComplexF64, 2}` - Free-boundary total-energy matrix W = wp + wv before diagonalisation (numpert_total × numpert_total). **ξ-space.** - `wp::Array{ComplexF64, 2}` - Plasma energy matrix (numpert_total × numpert_total). **ξ-space.** - `wv::Array{ComplexF64, 2}` - Vacuum energy matrix (numpert_total × numpert_total). **ξ-space.** - - `pn_wt0, pn_wp, pn_wv::Array{ComplexF64,2}` - Power-normalized flux (Φ-space) counterparts of `wt0`, `wp`, `wv` at the plasma edge (see PowerNorm.jl). Jacobian-invariant up to the M†·W·M transform. - - `pn_wt::Array{ComplexF64,2}` - Φ-space eigenvector matrix of `pn_wt0` (columns sorted most-unstable first, phase-normalized so each column's largest-magnitude entry is real-positive). + - `rootA_wt0, rootA_wp, rootA_wv::Array{ComplexF64,2}` - Root-area-weighted flux (Φ-space) counterparts of `wt0`, `wp`, `wv` at the plasma edge (see RootAreaWeighted.jl). Jacobian-invariant up to the M†·W·M transform. + - `rootA_wt::Array{ComplexF64,2}` - Φ-space eigenvector matrix of `rootA_wt0` (columns sorted most-unstable first, phase-normalized so each column's largest-magnitude entry is real-positive). - `ep::Vector{ComplexF64}` - Plasma eigenvalues - `ev::Vector{ComplexF64}` - Vacuum eigenvalues - `et::Vector{ComplexF64}` - Total eigenvalues of plasma + vacuum @@ -415,16 +415,16 @@ Populated in `Free.jl`. n_tor_idx::Vector{Int} = zeros(Int, numpert_total) vacuum_eigenvalue::Float64 = NaN - # Power-normalized flux eigenvalues (Jacobian-invariant) - pn_et::Vector{ComplexF64} = fill(complex(NaN), numpert_total) - pn_ep::Vector{ComplexF64} = fill(complex(NaN), numpert_total) - pn_ev::Vector{ComplexF64} = fill(complex(NaN), numpert_total) + # Root-area-weighted flux eigenvalues (Jacobian-invariant) + rootA_et::Vector{ComplexF64} = fill(complex(NaN), numpert_total) + rootA_ep::Vector{ComplexF64} = fill(complex(NaN), numpert_total) + rootA_ev::Vector{ComplexF64} = fill(complex(NaN), numpert_total) - # Power-normalized flux matrices at the plasma edge (Jacobian-invariant). - pn_wt0::Array{ComplexF64,2} = fill(complex(NaN), numpert_total, numpert_total) - pn_wp::Array{ComplexF64,2} = fill(complex(NaN), numpert_total, numpert_total) - pn_wv::Array{ComplexF64,2} = fill(complex(NaN), numpert_total, numpert_total) - pn_wt::Array{ComplexF64,2} = fill(complex(NaN), numpert_total, numpert_total) + # Root-area-weighted flux matrices at the plasma edge (Jacobian-invariant). + rootA_wt0::Array{ComplexF64,2} = fill(complex(NaN), numpert_total, numpert_total) + rootA_wp::Array{ComplexF64,2} = fill(complex(NaN), numpert_total, numpert_total) + rootA_wv::Array{ComplexF64,2} = fill(complex(NaN), numpert_total, numpert_total) + rootA_wt::Array{ComplexF64,2} = fill(complex(NaN), numpert_total, numpert_total) grri::Array{Float64,2} = Array{Float64}(undef, 2 * numpoints, 2 * numpert_total) grre::Array{Float64,2} = Array{Float64}(undef, 2 * numpoints, 2 * numpert_total) @@ -439,17 +439,17 @@ EdgeScanState Holds the state and results for the edge dW stability scan over ψ ∈ [psiedge, psilim]. Initialized and populated by `findmax_dW_edge!`; results written to HDF5 under `EdgeScan/` -(power-norm values) and `EdgeScan/XiNorm/` (ξ-space values, for benchmarking). +(root-area-weighted values) and `EdgeScan/XiNorm/` (ξ-space values, for benchmarking). ## Fields - `wvmat` - Precomputed wv matrix spline (raw, no singfac); singfac applied analytically in `free_compute_total`. - `wv_hint::Base.RefValue{Int}` - Search hint for wvmat spline (different grid from equilibrium profiles). - - `sqrtamat_spline` - Precomputed √A convolution matrix + surface area spline for power-norm eigenvalues. + - `sqrtamat_spline` - Precomputed √A convolution matrix + surface area spline for root-area-weighted eigenvalues. - `sqrtamat_hint::Base.RefValue{Int}` - Search hint for sqrtamat spline. - `psi, q` - ψ and q values at each edge scan step. - `total_eigenvalue, plasma_energy, vacuum_energy, vacuum_eigenvalue` - ξ-space energy components at each step (NaN for failed steps). Kept for Fortran benchmarking. - - `pn_total_eigenvalue, pn_plasma_energy, pn_vacuum_energy, pn_vacuum_eigenvalue` - Power-normalized flux (Φ-space) energies (Jacobian-invariant; NaN for failed/singular steps). These are the values written to `EdgeScan/` by default. + - `rootA_total_eigenvalue, rootA_plasma_energy, rootA_vacuum_energy, rootA_vacuum_eigenvalue` - Root-area-weighted flux (Φ-space) energies (Jacobian-invariant; NaN for failed/singular steps). These are the values written to `EdgeScan/` by default. """ @kwdef mutable struct EdgeScanState numpert_total::Int @@ -459,7 +459,7 @@ Initialized and populated by `findmax_dW_edge!`; results written to HDF5 under ` wvmat::CubicSeriesInterpolant{Float64,ComplexF64} = _empty_series_interp_complex(numpert_total^2) wv_hint::Base.RefValue{Int} = Ref(1) - # Power-norm sqrtamat + jarea spline (mpert^2 + 1 series: flattened sqrtamat then jarea) + # Root-area-weighted sqrtamat + jarea spline (mpert^2 + 1 series: flattened sqrtamat then jarea) sqrtamat_spline::CubicSeriesInterpolant{Float64,ComplexF64} = _empty_series_interp_complex(numpert_total^2 + 1) sqrtamat_hint::Base.RefValue{Int} = Ref(1) @@ -471,11 +471,11 @@ Initialized and populated by `findmax_dW_edge!`; results written to HDF5 under ` vacuum_energy::Vector{ComplexF64} = fill(complex(NaN), N_edge) vacuum_eigenvalue::Vector{Float64} = fill(NaN, N_edge) - # Power-normalized flux eigenvalues (Jacobian-invariant) - pn_total_eigenvalue::Vector{ComplexF64} = fill(complex(NaN), N_edge) - pn_plasma_energy::Vector{ComplexF64} = fill(complex(NaN), N_edge) - pn_vacuum_energy::Vector{ComplexF64} = fill(complex(NaN), N_edge) - pn_vacuum_eigenvalue::Vector{Float64} = fill(NaN, N_edge) + # Root-area-weighted flux eigenvalues (Jacobian-invariant) + rootA_total_eigenvalue::Vector{ComplexF64} = fill(complex(NaN), N_edge) + rootA_plasma_energy::Vector{ComplexF64} = fill(complex(NaN), N_edge) + rootA_vacuum_energy::Vector{ComplexF64} = fill(complex(NaN), N_edge) + rootA_vacuum_eigenvalue::Vector{Float64} = fill(NaN, N_edge) end EdgeScanState(numpert_total::Int, N_edge::Int) = EdgeScanState(; numpert_total, N_edge) diff --git a/src/ForceFreeStates/Free.jl b/src/ForceFreeStates/Free.jl index 7468883db..29fb5c9bc 100644 --- a/src/ForceFreeStates/Free.jl +++ b/src/ForceFreeStates/Free.jl @@ -94,20 +94,20 @@ and data dumping. vac_data.ev[ipert] = wvt[ipert, ipert] end - # Eigenspectrum of W_Φ at psilim — Jacobian-invariant energy values; see PowerNorm.jl. + # Eigenspectrum of W_Φ at psilim — Jacobian-invariant energy values; see RootAreaWeighted.jl. # Computed directly here (no spline); spline is used by the edge scan. mtheta_eq = length(equil.rzphi_ys) - ft_pn = Utilities.FourierTransforms.FourierTransform(mtheta_eq, mpert, mlow) - sqrtamat_pn = Equilibrium.compute_sqrtamat(equil, psilim, ft_pn) - jarea_pn = Equilibrium.flux_surface_area(equil, psilim, mtheta_eq) - pn_result = compute_power_norm_eigenvalues(vac_data.wt0, wp, vac_data.wv, sqrtamat_pn, jarea_pn, equil, psilim, intr; all_eigenvalues=true) - vac_data.pn_et .= pn_result.pn_et_all - vac_data.pn_ep .= pn_result.pn_ep_all - vac_data.pn_ev .= pn_result.pn_ev_all - vac_data.pn_wt0 .= pn_result.wt_pn - vac_data.pn_wp .= pn_result.wp_pn - vac_data.pn_wv .= pn_result.wv_pn - vac_data.pn_wt .= pn_result.pn_eigenvectors + ft_rootA = Utilities.FourierTransforms.FourierTransform(mtheta_eq, mpert, mlow) + sqrtamat_rootA = Equilibrium.compute_sqrtamat(equil, psilim, ft_rootA) + jarea_rootA = Equilibrium.flux_surface_area(equil, psilim, mtheta_eq) + rootA_result = compute_rootarea_eigenvalues(vac_data.wt0, wp, vac_data.wv, sqrtamat_rootA, jarea_rootA, equil, psilim, intr; all_eigenvalues=true) + vac_data.rootA_et .= rootA_result.rootA_et_all + vac_data.rootA_ep .= rootA_result.rootA_ep_all + vac_data.rootA_ev .= rootA_result.rootA_ev_all + vac_data.rootA_wt0 .= rootA_result.wt_rootA + vac_data.rootA_wp .= rootA_result.wp_rootA + vac_data.rootA_wv .= rootA_result.wv_rootA + vac_data.rootA_wt .= rootA_result.rootA_eigenvectors # Normalize eigenvectors based on scaled wt coeffs = odet.u[:, :, 1, end] \ (vac_data.wt .* (2π * equil.psio * 1e-3)) @@ -220,7 +220,7 @@ wv matrix spline to `free_compute_wv_spline` and pass it in `odet.edge_scan.wvma # Compute total energy matrix and eigen-decomposition wt .= wp .+ wv - # Save wt before eigen (which overwrites the input) for power-norm computation + # Save wt before eigen (which overwrites the input) for root-area-weighted computation wt_saved = copy(wt) Ev = eigen(wt) @@ -261,7 +261,7 @@ wv matrix spline to `free_compute_wv_spline` and pass it in `odet.edge_scan.wvma # negative. Clamp to zero to enforce the physical constraint. vacuum_eigenvalue = real(max(0.0, minimum(real.(eigvals(Hermitian(wv))))) / norm) - # Eigenspectrum of W_Φ — Jacobian-invariant energy values; see PowerNorm.jl. + # Eigenspectrum of W_Φ — Jacobian-invariant energy values; see RootAreaWeighted.jl. # Evaluate sqrtamat + jarea from the pre-computed spline. mpert = intr.mpert sqrtamat_flat = Vector{ComplexF64}(undef, mpert^2 + 1) @@ -269,9 +269,9 @@ wv matrix spline to `free_compute_wv_spline` and pass it in `odet.edge_scan.wvma sqrtamat_local = reshape(@view(sqrtamat_flat[1:mpert^2]), mpert, mpert) jarea_local = real(sqrtamat_flat[end]) - pn_result = compute_power_norm_eigenvalues(wt_saved, wp, wv, sqrtamat_local, jarea_local, equil, odet.psifac, intr) + rootA_result = compute_rootarea_eigenvalues(wt_saved, wp, wv, sqrtamat_local, jarea_local, equil, odet.psifac, intr) return (total_eigenvalue=eigenvalues[1], plasma_energy=plasma_energy, vacuum_energy=vacuum_energy, vacuum_eigenvalue=vacuum_eigenvalue, - pn_total_eigenvalue=pn_result.pn_total_eigenvalue, pn_plasma_energy=pn_result.pn_plasma_energy, pn_vacuum_energy=pn_result.pn_vacuum_energy, - pn_vacuum_eigenvalue=pn_result.pn_vacuum_eigenvalue) + rootA_total_eigenvalue=rootA_result.rootA_total_eigenvalue, rootA_plasma_energy=rootA_result.rootA_plasma_energy, rootA_vacuum_energy=rootA_result.rootA_vacuum_energy, + rootA_vacuum_eigenvalue=rootA_result.rootA_vacuum_eigenvalue) end diff --git a/src/ForceFreeStates/PowerNorm.jl b/src/ForceFreeStates/RootAreaWeighted.jl similarity index 69% rename from src/ForceFreeStates/PowerNorm.jl rename to src/ForceFreeStates/RootAreaWeighted.jl index 93cb44cb5..132973a38 100644 --- a/src/ForceFreeStates/PowerNorm.jl +++ b/src/ForceFreeStates/RootAreaWeighted.jl @@ -1,7 +1,7 @@ """ -Power-normalized flux eigenvalue computation for the FFS edge scan. +Root-area-weighted flux eigenvalue computation for the FFS edge scan. -Transforms the energy matrix W from ξ-space into power-normalized flux Φ-space and +Transforms the energy matrix W from ξ-space into root-area-weighted flux Φ-space and returns the eigenvalues of `W_Φ = M†·W·M`. The **eigenvalues** (energies) are coordinate-invariant: energy is a physically meaningful scalar and does not depend on the choice of straight-field-line coordinate. @@ -10,7 +10,7 @@ on the choice of straight-field-line coordinate. Transformation chain: - T = diag(i·2π·χ₁·singfac) converts ξ → flux (χ₁ = 2π·ψ₀, singfac = m − n·q). - - ptof = sqrtamat·√jarea converts the power-normalized field → flux. + - ptof = sqrtamat·√jarea converts the root-area-weighted field → flux. - M = T⁻¹·ptof maps Φ → ξ. What is **NOT** invariant across Jacobian choices (see @@ -33,14 +33,14 @@ area-integral precision floor ~1e-6): # ForceFreeStates and PerturbedEquilibrium modules share one coordinate-invariant definition. """ - compute_power_norm_eigenvalues(wt, wp, wv, sqrtamat, jarea, equil, psi, intr; all_eigenvalues=false) + compute_rootarea_eigenvalues(wt, wp, wv, sqrtamat, jarea, equil, psi, intr; all_eigenvalues=false) -Transform W from ξ-space to power-normalized flux Φ-space and eigendecompose. +Transform W from ξ-space to root-area-weighted flux Φ-space and eigendecompose. The transformation chain: 1. T = diag(i·2π·χ₁·singfac) converts ξ → flux (singfac = m − n·q). - 2. ptof = sqrtamat·√jarea converts the power-normalized field → flux. - 3. M = T⁻¹·ptof maps Φ → ξ (power-norm to displacement). + 2. ptof = sqrtamat·√jarea converts the root-area-weighted field → flux. + 3. M = T⁻¹·ptof maps Φ → ξ (root-area-weighted to displacement). 4. W_Φ = M†·W·M = ptof†·T⁻†·W·T⁻¹·ptof. Only the eigenspectrum of W_Φ is physically invariant across Jacobian choices — @@ -52,11 +52,11 @@ spectrally invariant because Wp + Wv = Wt. Returns the standard eigenvalues of W_Φ sorted ascending (most negative/unstable first), matching the ξ-space convention in `free_run!` and `free_compute_total`. -Also returns `pn_vacuum_eigenvalue = max(0, λ_min(Hermitian(wv_Φ)))` — the Φ-space +Also returns `rootA_vacuum_eigenvalue = max(0, λ_min(Hermitian(wv_Φ)))` — the Φ-space counterpart of the ξ-space `vacuum_eigenvalue` diagnostic. Returns NaN when any singfac ≈ 0 (rational surface crossing makes T singular). """ -function compute_power_norm_eigenvalues( +function compute_rootarea_eigenvalues( wt::AbstractMatrix{ComplexF64}, wp::AbstractMatrix{ComplexF64}, wv::AbstractMatrix{ComplexF64}, @@ -81,12 +81,12 @@ function compute_power_norm_eigenvalues( if all_eigenvalues nan_vec = fill(complex(NaN), Npert) nan_mat = fill(complex(NaN), Npert, Npert) - return (pn_total_eigenvalue=complex(NaN), pn_plasma_energy=complex(NaN), pn_vacuum_energy=complex(NaN), - pn_vacuum_eigenvalue=NaN, pn_et_all=nan_vec, pn_ep_all=nan_vec, pn_ev_all=nan_vec, - wt_pn=nan_mat, wp_pn=nan_mat, wv_pn=nan_mat, pn_eigenvectors=nan_mat) + return (rootA_total_eigenvalue=complex(NaN), rootA_plasma_energy=complex(NaN), rootA_vacuum_energy=complex(NaN), + rootA_vacuum_eigenvalue=NaN, rootA_et_all=nan_vec, rootA_ep_all=nan_vec, rootA_ev_all=nan_vec, + wt_rootA=nan_mat, wp_rootA=nan_mat, wv_rootA=nan_mat, rootA_eigenvectors=nan_mat) else - return (pn_total_eigenvalue=complex(NaN), pn_plasma_energy=complex(NaN), pn_vacuum_energy=complex(NaN), - pn_vacuum_eigenvalue=NaN) + return (rootA_total_eigenvalue=complex(NaN), rootA_plasma_energy=complex(NaN), rootA_vacuum_energy=complex(NaN), + rootA_vacuum_eigenvalue=NaN) end end @@ -96,7 +96,7 @@ function compute_power_norm_eigenvalues( T_diag_inv[i] = 1.0 / (im * 2π * chi1 * singfac[i]) end - # ptof = sqrtamat * sqrt(jarea): power-norm field → flux + # ptof = sqrtamat * sqrt(jarea): root-area-weighted field → flux # For multi-n, expand mpert×mpert sqrtamat to Npert×Npert block-diagonal ptof_block = sqrtamat .* sqrt(jarea) if npert == 1 @@ -116,18 +116,18 @@ function compute_power_norm_eigenvalues( end # Transform energy matrices: W_Φ = M† · W · M - wt_pn = M' * wt * M - wp_pn = M' * wp * M - wv_pn = M' * wv * M + wt_rootA = M' * wt * M + wp_rootA = M' * wp * M + wv_rootA = M' * wv * M # Smallest eigenvalue of the vacuum matrix alone in Φ-space, clamped to zero. - # wv_pn should be PSD by congruence of the PSD ξ-space wv; numerical noise + # wv_rootA should be PSD by congruence of the PSD ξ-space wv; numerical noise # can make the smallest eigenvalue slightly negative. - pn_vacuum_eigenvalue = real(max(0.0, minimum(real.(eigvals(Hermitian(wv_pn)))))) + rootA_vacuum_eigenvalue = real(max(0.0, minimum(real.(eigvals(Hermitian(wv_rootA)))))) - # Eigendecompose the total energy in power-norm space. Only the eigenspectrum + # Eigendecompose the total energy in root-area-weighted space. Only the eigenspectrum # is Jacobian-invariant; the eigenvectors are coordinate-dependent. - Ev = eigen(wt_pn) + Ev = eigen(wt_rootA) eigenvalues = Ev.values vectors = Ev.vectors @@ -137,41 +137,41 @@ function compute_power_norm_eigenvalues( # λ = v†Wt v = v†Wp v + v†Wv v ; the plasma/vacuum split is the projection # onto the same eigenvector and is therefore also Jacobian-invariant. if all_eigenvalues - pn_et_all = Vector{ComplexF64}(undef, Npert) - pn_ep_all = Vector{ComplexF64}(undef, Npert) - pn_ev_all = Vector{ComplexF64}(undef, Npert) - pn_eigenvectors = Matrix{ComplexF64}(undef, Npert, Npert) + rootA_et_all = Vector{ComplexF64}(undef, Npert) + rootA_ep_all = Vector{ComplexF64}(undef, Npert) + rootA_ev_all = Vector{ComplexF64}(undef, Npert) + rootA_eigenvectors = Matrix{ComplexF64}(undef, Npert, Npert) for i in 1:Npert v = vectors[:, eindex[Npert+1-i]] - pn_eigenvectors[:, i] .= v - pn_et_all[i] = eigenvalues[eindex[Npert+1-i]] - pn_ep_all[i] = dot(v, wp_pn * v) - pn_ev_all[i] = dot(v, wv_pn * v) + rootA_eigenvectors[:, i] .= v + rootA_et_all[i] = eigenvalues[eindex[Npert+1-i]] + rootA_ep_all[i] = dot(v, wp_rootA * v) + rootA_ev_all[i] = dot(v, wv_rootA * v) end # Phase convention: rotate each column so its largest-magnitude entry is real-positive # (matches the ξ-space convention in free_run!). Magnitudes are preserved since the # eigenvectors come from Julia's `eigen` with ‖v‖₂ = 1, the natural Φ-space norm. for isol in 1:Npert - imax = argmax(abs.(@view pn_eigenvectors[:, isol])) - phase = abs(pn_eigenvectors[imax, isol]) / pn_eigenvectors[imax, isol] - @view(pn_eigenvectors[:, isol]) .*= phase + imax = argmax(abs.(@view rootA_eigenvectors[:, isol])) + phase = abs(rootA_eigenvectors[imax, isol]) / rootA_eigenvectors[imax, isol] + @view(rootA_eigenvectors[:, isol]) .*= phase end - return (pn_total_eigenvalue=pn_et_all[1], pn_plasma_energy=pn_ep_all[1], pn_vacuum_energy=pn_ev_all[1], - pn_vacuum_eigenvalue=pn_vacuum_eigenvalue, - pn_et_all=pn_et_all, pn_ep_all=pn_ep_all, pn_ev_all=pn_ev_all, - wt_pn=wt_pn, wp_pn=wp_pn, wv_pn=wv_pn, pn_eigenvectors=pn_eigenvectors) + return (rootA_total_eigenvalue=rootA_et_all[1], rootA_plasma_energy=rootA_ep_all[1], rootA_vacuum_energy=rootA_ev_all[1], + rootA_vacuum_eigenvalue=rootA_vacuum_eigenvalue, + rootA_et_all=rootA_et_all, rootA_ep_all=rootA_ep_all, rootA_ev_all=rootA_ev_all, + wt_rootA=wt_rootA, wp_rootA=wp_rootA, wv_rootA=wv_rootA, rootA_eigenvectors=rootA_eigenvectors) else idx = eindex[Npert] v = vectors[:, idx] - pn_total = eigenvalues[idx] - pn_plasma = ComplexF64(dot(v, wp_pn * v)) - pn_vacuum = ComplexF64(dot(v, wv_pn * v)) + rootA_total = eigenvalues[idx] + rootA_plasma = ComplexF64(dot(v, wp_rootA * v)) + rootA_vacuum = ComplexF64(dot(v, wv_rootA * v)) - return (pn_total_eigenvalue=pn_total, pn_plasma_energy=pn_plasma, pn_vacuum_energy=pn_vacuum, - pn_vacuum_eigenvalue=pn_vacuum_eigenvalue) + return (rootA_total_eigenvalue=rootA_total, rootA_plasma_energy=rootA_plasma, rootA_vacuum_energy=rootA_vacuum, + rootA_vacuum_eigenvalue=rootA_vacuum_eigenvalue) end end diff --git a/src/GeneralizedPerturbedEquilibrium.jl b/src/GeneralizedPerturbedEquilibrium.jl index b6988f0c9..703629cc8 100755 --- a/src/GeneralizedPerturbedEquilibrium.jl +++ b/src/GeneralizedPerturbedEquilibrium.jl @@ -567,17 +567,17 @@ function write_outputs_to_HDF5( out_h5["integration/crit"] = odet.crit_store # Write edge stability scan data (only present when psiedge < psilim). - # Power-normalized flux (Φ-space) energies are the default — they are Jacobian- + # Root-area-weighted (Φ-space) energies are the default — they are Jacobian- # invariant. The ξ-space values sit under EdgeScan/XiNorm/ and are retained for # benchmarking against the Fortran GPEC lineage. if !isempty(odet.edge_scan.psi) es = odet.edge_scan out_h5["EdgeScan/psi"] = es.psi out_h5["EdgeScan/q"] = es.q - out_h5["EdgeScan/total_energy"] = es.pn_total_eigenvalue - out_h5["EdgeScan/plasma_energy"] = es.pn_plasma_energy - out_h5["EdgeScan/vacuum_energy"] = es.pn_vacuum_energy - out_h5["EdgeScan/vacuum_eigenvalue"] = es.pn_vacuum_eigenvalue + out_h5["EdgeScan/total_energy"] = es.rootA_total_eigenvalue + out_h5["EdgeScan/plasma_energy"] = es.rootA_plasma_energy + out_h5["EdgeScan/vacuum_energy"] = es.rootA_vacuum_energy + out_h5["EdgeScan/vacuum_eigenvalue"] = es.rootA_vacuum_eigenvalue out_h5["EdgeScan/XiNorm/total_energy"] = es.total_eigenvalue out_h5["EdgeScan/XiNorm/plasma_energy"] = es.plasma_energy out_h5["EdgeScan/XiNorm/vacuum_energy"] = es.vacuum_energy @@ -624,20 +624,20 @@ function write_outputs_to_HDF5( out_h5["singular/kinetic/scan_psi"] = intr.kinsing_scan_psi out_h5["singular/kinetic/scan_cond"] = intr.kinsing_scan_cond out_h5["singular/kinetic/scan_threshold"] = intr.kinsing_scan_threshold - - # Write free-boundary stability data. Power-normalized flux (Φ-space) is the + + # Write free-boundary stability data. Root-area-weighted (Φ-space) is the # default — Jacobian-invariant. ξ-space counterparts sit under # FreeBoundaryStability/XiNorm/ for Fortran benchmarking. # W_freeboundary_eigenmodes holds the eigenvector matrix of W_freeboundary with # columns sorted most-unstable first; the same phase normalization is applied in # both spaces (largest-magnitude entry made real-positive). - out_h5["FreeBoundaryStability/W_freeboundary"] = ctrl.vac_flag ? vac_data.pn_wt0 : ComplexF64[] - out_h5["FreeBoundaryStability/W_plasma"] = ctrl.vac_flag ? vac_data.pn_wp : ComplexF64[] - out_h5["FreeBoundaryStability/W_vacuum"] = ctrl.vac_flag ? vac_data.pn_wv : ComplexF64[] - out_h5["FreeBoundaryStability/W_freeboundary_eigenmodes"] = ctrl.vac_flag ? vac_data.pn_wt : ComplexF64[] - out_h5["FreeBoundaryStability/eigenmode_energies"] = ctrl.vac_flag ? vac_data.pn_et : ComplexF64[] - out_h5["FreeBoundaryStability/eigenmode_plasma_energies"] = ctrl.vac_flag ? vac_data.pn_ep : ComplexF64[] - out_h5["FreeBoundaryStability/eigenmode_vacuum_energies"] = ctrl.vac_flag ? vac_data.pn_ev : ComplexF64[] + out_h5["FreeBoundaryStability/W_freeboundary"] = ctrl.vac_flag ? vac_data.rootA_wt0 : ComplexF64[] + out_h5["FreeBoundaryStability/W_plasma"] = ctrl.vac_flag ? vac_data.rootA_wp : ComplexF64[] + out_h5["FreeBoundaryStability/W_vacuum"] = ctrl.vac_flag ? vac_data.rootA_wv : ComplexF64[] + out_h5["FreeBoundaryStability/W_freeboundary_eigenmodes"] = ctrl.vac_flag ? vac_data.rootA_wt : ComplexF64[] + out_h5["FreeBoundaryStability/eigenmode_energies"] = ctrl.vac_flag ? vac_data.rootA_et : ComplexF64[] + out_h5["FreeBoundaryStability/eigenmode_plasma_energies"] = ctrl.vac_flag ? vac_data.rootA_ep : ComplexF64[] + out_h5["FreeBoundaryStability/eigenmode_vacuum_energies"] = ctrl.vac_flag ? vac_data.rootA_ev : ComplexF64[] out_h5["FreeBoundaryStability/XiNorm/W_freeboundary"] = ctrl.vac_flag ? vac_data.wt0 : ComplexF64[] out_h5["FreeBoundaryStability/XiNorm/W_plasma"] = ctrl.vac_flag ? vac_data.wp : ComplexF64[] out_h5["FreeBoundaryStability/XiNorm/W_vacuum"] = ctrl.vac_flag ? vac_data.wv : ComplexF64[] diff --git a/src/PerturbedEquilibrium/FieldReconstruction.jl b/src/PerturbedEquilibrium/FieldReconstruction.jl index 6246a1d28..1efb9f55e 100644 --- a/src/PerturbedEquilibrium/FieldReconstruction.jl +++ b/src/PerturbedEquilibrium/FieldReconstruction.jl @@ -59,7 +59,7 @@ Tuple of (xi_modes, b_modes) NamedTuples: - `xi_modes.zeta_reg`: ξ^ζ regularized (= xmz, from gpeq_contra with reg_spot smoothing) - `xi_modes.cova_psi/theta/zeta`: covariant displacement (from gpeq_cova) - `b_modes.psi`: b^ψ [npsi, mpert] -- `b_modes.psi_area`: b^ψ / ⟨J·|∇ψ|⟩_θ (area-normalized, for b_n computation) +- `b_modes.b_psi_area_weighted`: b^ψ / ⟨J·|∇ψ|⟩_θ (area-normalized, for b_n computation) - `b_modes.theta`: b^θ [npsi, mpert] - `b_modes.zeta`: b^ζ [npsi, mpert] - `b_modes.theta_reg/zeta_reg`: regularized b^θ, b^ζ (from gpeq_sol with reg_spot smoothing) @@ -180,7 +180,7 @@ function reconstruct_physical_fields( ) b_modes = ( psi = b_psi_modes, # b^ψ (no Jacobian) — used for b_n normal projection - psi_area = Jb_psi_modes, # b^ψ / ⟨J·|∇ψ|⟩_θ (area-normalized, for b_n) + b_psi_area_weighted = Jb_psi_modes, # b^ψ / ⟨J·|∇ψ|⟩_θ (area-normalized, for b_n) theta = b_theta_modes, # b^θ unregularized zeta = b_zeta_modes, # b^ζ unregularized theta_reg = b_theta_reg, # b^θ regularized (from gpeq_sol with reg_spot) diff --git a/src/PerturbedEquilibrium/PerturbedEquilibriumStructs.jl b/src/PerturbedEquilibrium/PerturbedEquilibriumStructs.jl index c1fd8745d..5c5184a2b 100644 --- a/src/PerturbedEquilibrium/PerturbedEquilibriumStructs.jl +++ b/src/PerturbedEquilibrium/PerturbedEquilibriumStructs.jl @@ -78,22 +78,22 @@ Results from perturbed equilibrium calculations. Response fields (mode space): - `xi_modes::Union{Nothing, NamedTuple}` - Displacement (psi, theta, zeta) [npsi, mpert] - - `b_modes::Union{Nothing, NamedTuple}` - Magnetic field; psi=b^ψ, psi_area=b^ψ/⟨J·|∇ψ|⟩_θ, theta/zeta=unregularized, theta_reg/zeta_reg=regularized [npsi, mpert] + - `b_modes::Union{Nothing, NamedTuple}` - Magnetic field; psi=b^ψ, b_psi_area_weighted=b^ψ/⟨J·|∇ψ|⟩_θ, theta/zeta=unregularized, theta_reg/zeta_reg=regularized [npsi, mpert] - `b_n_modes::Union{Nothing, Matrix{ComplexF64}}` - Physical normal field b_n [npsi, mpert] - `xi_n_modes::Union{Nothing, Matrix{ComplexF64}}` - Physical normal displacement xi_n [npsi, mpert] Coupling matrices [n_rational × numpert_total] — one row per resonant (surface, n) pair. Each row maps the full applied field to the resonant response at that surface. Matches Fortran `C_f_x_out`, `C_i_x_out`, etc. (shape [mode_C, m_out]). - - `C_resonant_field` - Φ_r/A^r coupling (resonant field b^r in tesla; singcoup row 1) [Pharr 2026] + - `C_resonant_area_weighted_field` - Φ_r/A^r coupling (resonant area-weighted field b^r in tesla; singcoup row 1) [Pharr 2026] - `C_resonant_current` - Resonant current coupling (singcoup row 2) - `C_island_width_sq` - (w/2)² coupling (singcoup row 3) - - `C_penetrated_field` - Penetrated field coupling (singcoup row 4) + - `C_penetrated_area_weighted_field` - Penetrated area-weighted field coupling (singcoup row 4) - `C_delta_prime` - Δ' coupling (singcoup row 5) Applied resonant vectors [n_rational] = C · forcing_amplitudes. Matches Fortran `Phi_res`, `w_isl`, `K_isl`, `Delta`. - - `resonant_field`, `resonant_current`, `island_width_sq`, `penetrated_field`, `delta_prime` + - `resonant_area_weighted_field`, `resonant_current`, `island_width_sq`, `penetrated_area_weighted_field`, `delta_prime` Diagnostics [n_rational]: - `island_half_width::Vector{Float64}` - w/2 = sqrt(|island_width_sq|) from applied forcing @@ -103,7 +103,7 @@ Metadata [n_rational] — identifies each (surface, n) row: - `rational_psi`, `rational_q`, `rational_m_res`, `rational_n`, `rational_surface_idx` Control surface matrices [numpert_total × numpert_total], stored in the coordinate-invariant -power-normalized field (b̃) space (issue #233 / Pharr 2026). Recover the flux-space forms with +root-area-weighted field (b̃) space (issue #233 / Pharr 2026). Recover the flux-space forms with the `control_surface_field_operator` (`ptof`, Φ = ptof·b̃): e.g. `P_flux = ptof·P̃·ptof⁻¹`, `L_flux = ptof·L̃·ptof†`. - `plasma_inductance` - Λ̃ = ptof⁻¹·Λ·ptof⁻† (wt0-based plasma inductance, congruence) @@ -129,17 +129,17 @@ Energies (Fortran gpout convention; Φ_x external flux, Φ_tot total flux, L/Λ xi_n_modes::Union{Nothing, Matrix{ComplexF64}} = nothing # physical normal displacement xi_n [npsi, mpert] # Coupling matrices [n_rational × numpert_total] - C_resonant_field::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) + C_resonant_area_weighted_field::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) C_resonant_current::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) C_island_width_sq::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) - C_penetrated_field::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) + C_penetrated_area_weighted_field::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) C_delta_prime::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # Applied resonant vectors [n_rational] = C · amp_vec - resonant_field::Vector{ComplexF64} = ComplexF64[] + resonant_area_weighted_field::Vector{ComplexF64} = ComplexF64[] resonant_current::Vector{ComplexF64} = ComplexF64[] island_width_sq::Vector{ComplexF64} = ComplexF64[] - penetrated_field::Vector{ComplexF64} = ComplexF64[] + penetrated_area_weighted_field::Vector{ComplexF64} = ComplexF64[] delta_prime::Vector{ComplexF64} = ComplexF64[] # Diagnostics [n_rational] diff --git a/src/PerturbedEquilibrium/Response.jl b/src/PerturbedEquilibrium/Response.jl index 8020ca491..acbeabda8 100644 --- a/src/PerturbedEquilibrium/Response.jl +++ b/src/PerturbedEquilibrium/Response.jl @@ -59,7 +59,7 @@ function compute_plasma_response!( # copy stays in flux space; only the stored/output matrices are conformed below. intr.plasma_response = permeability - # Conform the control-surface matrices to the coordinate-invariant power-normalized + # Conform the control-surface matrices to the coordinate-invariant root-area-weighted # field (b̃) space for output (issue #233 / Pharr 2026). The flux-space forms are # recoverable from the stored `ptof` operator (Φ = ptof·b̃) — see Utils.jl output docs. ptof = build_control_surface_ptof(equil, ffs_intr) diff --git a/src/PerturbedEquilibrium/ResponseMatrices.jl b/src/PerturbedEquilibrium/ResponseMatrices.jl index 015a4e542..fd095ef42 100644 --- a/src/PerturbedEquilibrium/ResponseMatrices.jl +++ b/src/PerturbedEquilibrium/ResponseMatrices.jl @@ -304,12 +304,12 @@ end ffs_intr::ForceFreeStatesInternal )::Matrix{ComplexF64} -Build the numpert_total × numpert_total power-norm-field → flux operator `ptof` at the +Build the numpert_total × numpert_total root-area-weighted field → flux operator `ptof` at the control surface (psilim). The mpert × mpert single-n block (Equilibrium.control_surface_ptof) is repeated block-diagonally over the `npert` toroidal harmonics, matching the numpert_total mode ordering used by the response matrices. -`ptof` maps a power-normalized control-surface field `b̃` to the coordinate flux harmonics +`ptof` maps a root-area-weighted control-surface field `b̃` to the coordinate flux harmonics `Φ`: `Φ = ptof · b̃`. It is the operator users need to recover the flux-space matrices from the stored coordinate-invariant (field-space) ones — see `field_space_response_matrices`. [Pharr 2026] @@ -341,7 +341,7 @@ end plasma_inductance, surface_inductance, permeability, reluctance, ptof )::NamedTuple -Express the control-surface response matrices in the coordinate-invariant power-normalized +Express the control-surface response matrices in the coordinate-invariant root-area-weighted field (b̃) space, given the flux-space matrices and the `ptof` operator (`Φ = ptof·b̃`). The matrices fall into two algebraic classes: diff --git a/src/PerturbedEquilibrium/SingularCoupling.jl b/src/PerturbedEquilibrium/SingularCoupling.jl index 6816e1c65..904f53ad8 100644 --- a/src/PerturbedEquilibrium/SingularCoupling.jl +++ b/src/PerturbedEquilibrium/SingularCoupling.jl @@ -62,10 +62,10 @@ Matching Fortran GPEC output: `C_f_x_out` (coupling matrix) and `Phi_res`, `w_is Populates `state` with: Coupling matrices `[n_rational × numpert_total]` — C[row, j] = coupling when forcing mode j has unit amplitude: - - `C_resonant_field`, `C_resonant_current`, `C_island_width_sq`, `C_penetrated_field`, `C_delta_prime` + - `C_resonant_area_weighted_field`, `C_resonant_current`, `C_island_width_sq`, `C_penetrated_area_weighted_field`, `C_delta_prime` Applied resonant vectors `[n_rational]` = C · amp_vec: - - `resonant_field`, `resonant_current`, `island_width_sq`, `penetrated_field`, `delta_prime` + - `resonant_area_weighted_field`, `resonant_current`, `island_width_sq`, `penetrated_area_weighted_field`, `delta_prime` Diagnostics `[n_rational]`: `island_half_width`, `chirikov_parameter` @@ -125,10 +125,10 @@ function compute_singular_coupling_metrics!( ctrl.verbose && @info "Found $n_rational resonant (surface, n) pairs" # Phase 2: Allocate output arrays - state.C_resonant_field = zeros(ComplexF64, n_rational, numpert_total) + state.C_resonant_area_weighted_field = zeros(ComplexF64, n_rational, numpert_total) state.C_resonant_current = zeros(ComplexF64, n_rational, numpert_total) state.C_island_width_sq = zeros(ComplexF64, n_rational, numpert_total) - state.C_penetrated_field = zeros(ComplexF64, n_rational, numpert_total) + state.C_penetrated_area_weighted_field = zeros(ComplexF64, n_rational, numpert_total) state.C_delta_prime = zeros(ComplexF64, n_rational, numpert_total) state.rational_psi = zeros(Float64, n_rational) state.rational_q = zeros(Float64, n_rational) @@ -229,14 +229,14 @@ function compute_singular_coupling_metrics!( bwp1_l = 2π * im * chi1 * (singfac_l * xsp1_l - nn * q1_l * xsp_l) bwp1_r = 2π * im * chi1 * (singfac_r * xsp1_r - nn * q1_r * xsp_r) jump_vec[k] = bwp1_r - bwp1_l - # C_penetrated_field: midpoint of b^ψ at lpsi/rpsi divided by the scalar surface area. + # C_penetrated_area_weighted_field: midpoint of b^ψ at lpsi/rpsi divided by the scalar surface area. # Matches Fortran gpout_resp: gpeq_interp_singsurf evaluates bwp_mn at respsi. # LHS normalization audit (#233): the resonant flux Φ^r divided by the scalar area A^r # is a genuine field amplitude in tesla and is coordinate-invariant [Pharr 2026; cf. # the resonant-field definition in the Conventions Reference]. b_l = chi1 * singfac_l * 2π * im * xsp_l b_r = chi1 * singfac_r * 2π * im * xsp_r - state.C_penetrated_field[row, k] = (b_l + b_r) / 2 / area + state.C_penetrated_area_weighted_field[row, k] = (b_l + b_r) / 2 / area end # LHS normalization audit (#233) — output scalar coordinate-invariance per row: @@ -247,10 +247,10 @@ function compute_singular_coupling_metrics!( # - resonant flux → field: Φ^r/A^r [T], invariant [Park 2008; Pharr 2026]. state.C_delta_prime[row, :] = jump_vec ./ (twopi * chi1) state.C_resonant_current[row, :] = jump_vec .* (-j_c / (twopi * m_res)) - # Matches Fortran gpout_resp: singflx = L·fkaxmn, resonant field = singflx/area, + # Matches Fortran gpout_resp: singflx = L·fkaxmn, resonant area-weighted field = singflx/area, # islandhwids = 4·singflx/(2π·shear·q·chi1) singflx_pre = (L_mm / (twopi * nn)) .* state.C_resonant_current[row, :] - state.C_resonant_field[row, :] = singflx_pre ./ area + state.C_resonant_area_weighted_field[row, :] = singflx_pre ./ area if abs(shear) > 1e-10 state.C_island_width_sq[row, :] = (4.0 / (twopi * shear * sing_surf.q * chi1)) .* singflx_pre end @@ -276,21 +276,21 @@ function compute_singular_coupling_metrics!( isnothing(j) || (forcing_flux[j] = mode.amplitude) end - state.resonant_field = state.C_resonant_field * forcing_flux + state.resonant_area_weighted_field = state.C_resonant_area_weighted_field * forcing_flux state.resonant_current = state.C_resonant_current * forcing_flux state.island_width_sq = state.C_island_width_sq * forcing_flux - state.penetrated_field = state.C_penetrated_field * forcing_flux + state.penetrated_area_weighted_field = state.C_penetrated_area_weighted_field * forcing_flux state.delta_prime = state.C_delta_prime * forcing_flux - # Conform the stored coupling-matrix input basis to the coordinate-invariant power-normalized + # Conform the stored coupling-matrix input basis to the coordinate-invariant root-area-weighted # field (b̃) space (#233 / Pharr 2026): C̃ = C·ptof, so each stored row acts on the applied # field b̃_x (Φ_x = ptof·b̃_x) and its singular values become coordinate-invariant. Done after # the applied-vector evaluation above so those physical scalars carry no round-trip noise. ptof = build_control_surface_ptof(equil, ffs_intr) - state.C_resonant_field = state.C_resonant_field * ptof + state.C_resonant_area_weighted_field = state.C_resonant_area_weighted_field * ptof state.C_resonant_current = state.C_resonant_current * ptof state.C_island_width_sq = state.C_island_width_sq * ptof - state.C_penetrated_field = state.C_penetrated_field * ptof + state.C_penetrated_area_weighted_field = state.C_penetrated_area_weighted_field * ptof state.C_delta_prime = state.C_delta_prime * ptof # Phase 5: Island diagnostics from applied resonant vectors diff --git a/src/PerturbedEquilibrium/Utils.jl b/src/PerturbedEquilibrium/Utils.jl index 6f32cc1ad..295029c25 100644 --- a/src/PerturbedEquilibrium/Utils.jl +++ b/src/PerturbedEquilibrium/Utils.jl @@ -61,27 +61,27 @@ perturbed_equilibrium/ ├── response/ │ ├── xi_psi # Radial displacement ξ^ψ = ξ·∇ψ (ComplexF64 [npsi, mpert]) │ ├── xi_psi_J # J·ξ^ψ Jacobian-weighted (from gpeq_contra) -│ ├── psi_area # b^ψ / ⟨J·|∇ψ|⟩_θ area-normalized (ComplexF64 [npsi, mpert]) +│ ├── b_psi_area_weighted # b^ψ / ⟨J·|∇ψ|⟩_θ area-normalized (ComplexF64 [npsi, mpert]) │ ├── b_n # Physical normal field b_n (ComplexF64 [npsi, mpert]) │ ├── xi_n # Physical normal displacement xi_n (ComplexF64 [npsi, mpert]) │ ├── b_theta │ └── b_zeta -├── response_matrices/ # [numpert_total × numpert_total], power-normalized field (b̃) space +├── response_matrices/ # [numpert_total × numpert_total], root-area-weighted field (b̃) space │ ├── plasma_inductance # Λ̃ = ptof⁻¹·Λ·ptof⁻† │ ├── surface_inductance # L̃ = ptof⁻¹·L·ptof⁻† │ ├── permeability # P̃ = ptof⁻¹·P·ptof (P = Λ·L⁻¹) │ ├── reluctance # ϱ̃ = ptof†·ϱ·ptof -│ └── powernorm_field_to_flux_operator # ptof = sqrtamat·√jarea; recover flux via Φ = ptof·b̃ +│ └── rootarea_field_to_flux_operator # ptof = sqrtamat·√jarea; recover flux via Φ = ptof·b̃ ├── singular_coupling/ -│ ├── C_resonant_field # [n_rational × numpert_total] coupling matrix (b̃-space input, resonant field b^r=Φ^r/A^r [T]) +│ ├── C_resonant_area_weighted_field # [n_rational × numpert_total] coupling matrix (b̃-space input, resonant area-weighted field b^r=Φ^r/A^r [T]) │ ├── C_resonant_current │ ├── C_island_width_sq -│ ├── C_penetrated_field +│ ├── C_penetrated_area_weighted_field │ ├── C_delta_prime -│ ├── resonant_field # [n_rational] applied vector = C̃ · b̃_x (resonant field b^r [T]) +│ ├── resonant_area_weighted_field # [n_rational] applied vector = C̃ · b̃_x (resonant area-weighted field b^r [T]) │ ├── resonant_current │ ├── island_width_sq -│ ├── penetrated_field +│ ├── penetrated_area_weighted_field │ ├── delta_prime │ ├── island_half_width # [n_rational] Float64 │ ├── chirikov_parameter @@ -115,21 +115,21 @@ function write_outputs_to_HDF5( !isempty(state.response_vec) && (pe_group["response_vec"] = state.response_vec) # Control surface matrices [numpert_total × numpert_total], in coordinate-invariant - # power-normalized field (b̃) space. Recover flux space with the stored ptof operator + # root-area-weighted field (b̃) space. Recover flux space with the stored ptof operator # (Φ = ptof·b̃): e.g. P_flux = ptof·P̃·ptof⁻¹, L_flux = ptof·L̃·ptof†. [Pharr 2026] mat_group = haskey(pe_group, "response_matrices") ? pe_group["response_matrices"] : create_group(pe_group, "response_matrices") !isempty(state.plasma_inductance) && (mat_group["plasma_inductance"] = state.plasma_inductance) !isempty(state.surface_inductance) && (mat_group["surface_inductance"] = state.surface_inductance) !isempty(state.permeability) && (mat_group["permeability"] = state.permeability) !isempty(state.reluctance) && (mat_group["reluctance"] = state.reluctance) - !isempty(state.control_surface_field_operator) && (mat_group["powernorm_field_to_flux_operator"] = state.control_surface_field_operator) + !isempty(state.control_surface_field_operator) && (mat_group["rootarea_field_to_flux_operator"] = state.control_surface_field_operator) # Response fields (ComplexF64 directly) response_group = haskey(pe_group, "response") ? pe_group["response"] : create_group(pe_group, "response") have_xi = !isnothing(state.xi_modes) have_b = have_xi && !isnothing(state.b_modes) response_group["xi_psi"] = have_xi ? state.xi_modes.psi : ComplexF64[] - response_group["psi_area"] = have_b ? state.b_modes.psi_area : ComplexF64[] + response_group["b_psi_area_weighted"] = have_b ? state.b_modes.b_psi_area_weighted : ComplexF64[] response_group["b_theta"] = have_b ? state.b_modes.theta : ComplexF64[] response_group["b_zeta"] = have_b ? state.b_modes.zeta : ComplexF64[] response_group["b_n"] = !isnothing(state.b_n_modes) ? state.b_n_modes : ComplexF64[] @@ -183,17 +183,17 @@ function write_outputs_to_HDF5( coupling_group = haskey(pe_group, "singular_coupling") ? pe_group["singular_coupling"] : create_group(pe_group, "singular_coupling") # Coupling matrices [n_rational × numpert_total] - !isempty(state.C_resonant_field) && (coupling_group["C_resonant_field"] = state.C_resonant_field) + !isempty(state.C_resonant_area_weighted_field) && (coupling_group["C_resonant_area_weighted_field"] = state.C_resonant_area_weighted_field) !isempty(state.C_resonant_current) && (coupling_group["C_resonant_current"] = state.C_resonant_current) !isempty(state.C_island_width_sq) && (coupling_group["C_island_width_sq"] = state.C_island_width_sq) - !isempty(state.C_penetrated_field) && (coupling_group["C_penetrated_field"] = state.C_penetrated_field) + !isempty(state.C_penetrated_area_weighted_field) && (coupling_group["C_penetrated_area_weighted_field"] = state.C_penetrated_area_weighted_field) !isempty(state.C_delta_prime) && (coupling_group["C_delta_prime"] = state.C_delta_prime) # Applied resonant vectors [n_rational] - !isempty(state.resonant_field) && (coupling_group["resonant_field"] = state.resonant_field) + !isempty(state.resonant_area_weighted_field) && (coupling_group["resonant_area_weighted_field"] = state.resonant_area_weighted_field) !isempty(state.resonant_current) && (coupling_group["resonant_current"] = state.resonant_current) !isempty(state.island_width_sq) && (coupling_group["island_width_sq"] = state.island_width_sq) - !isempty(state.penetrated_field) && (coupling_group["penetrated_field"] = state.penetrated_field) + !isempty(state.penetrated_area_weighted_field) && (coupling_group["penetrated_area_weighted_field"] = state.penetrated_area_weighted_field) !isempty(state.delta_prime) && (coupling_group["delta_prime"] = state.delta_prime) !isempty(state.island_half_width) && (coupling_group["island_half_width"] = state.island_half_width) !isempty(state.chirikov_parameter) && (coupling_group["chirikov_parameter"] = state.chirikov_parameter) From fc4ced847e91d352aca2afca8fa8fc5e2b3f8c13 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Thu, 11 Jun 2026 21:16:50 -0400 Subject: [PATCH 032/135] Analysis - DOCS - Note plot_surface_3d field is band-limited to the supplied m range MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit The reconstruction uses only the supplied poloidal modes, so a coil placed within ~one grid cell of the boundary makes b_n near-singular and the truncated series rings (Gibbs — a spurious dip where a single lobe is expected). Documented so users keep a realistic coil standoff or widen the m range. Verified against the direct n=1 harmonic: at a sensible standoff the window-pane b_n_x is a single clean blob peaked on the midplane; only on the separatrix did it split. Co-Authored-By: Claude Opus 4.8 --- src/Analysis/CoilForcing.jl | 8 ++++++++ 1 file changed, 8 insertions(+) diff --git a/src/Analysis/CoilForcing.jl b/src/Analysis/CoilForcing.jl index 132982276..050b8cf45 100644 --- a/src/Analysis/CoilForcing.jl +++ b/src/Analysis/CoilForcing.jl @@ -284,6 +284,14 @@ exponential into the `ν` correction times `e^{i n·hel·φ}`. and magnitude are physical. Pass `helicity` to override `sign(Bt)·sign(Ip)` if the toroidal tracking is wrong for your machine. +!!! note "Band-limited reconstruction" + + The field is reconstructed only from the supplied `m` modes, so it is band-limited to that + poloidal range. A source placed within ~one grid cell of the surface makes the field + near-singular and the truncated series rings (Gibbs oscillation — e.g. a spurious dip where a + single lobe is expected). Keep coils at a realistic standoff from the boundary, or widen the + `m` range, for a clean reconstruction. + ### Keyword arguments - `mtheta`, `nphi`: poloidal/toroidal grid resolution From e936416087b6710c7ab557560c64b4f81835132b Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Thu, 11 Jun 2026 22:14:35 -0400 Subject: [PATCH 033/135] =?UTF-8?q?PERTURBED=20EQUILIBRIUM=20-=20CLEANUP?= =?UTF-8?q?=20-=20Rename=20ptof=20=E2=86=92=20rootareafield=5Fto=5Fflux=20?= =?UTF-8?q?operator?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit `ptof` ("power-norm to flux") is stale after the power-normalized → root-area-weighted terminology change. Verified from Pharr (2026)'s definitions that the operator sqrtamat·√jarea maps the root-area-weighted field b̃ (tesla) to the poloidal flux Φ (weber): Φ = √A·sqrtamat·b̃, and the inductances act on it as energy = Φ†L⁻¹Φ. So the "field → flux" description is correct; rename the mnemonic accordingly: - ptof → rootareafield_to_flux (incl. _block/_full/_inv locals) - Equilibrium.control_surface_ptof → control_surface_rootareafield_to_flux (+ export) - build_control_surface_ptof → build_control_surface_rootareafield_to_flux - Introduce `R ≡ rootareafield_to_flux` shorthand in two dense math docstrings to keep them under the 180-col margin. - Sweep two leftover "power-norm" comments in the test files (reverted-commit fallout). Operating the response/coupling layer directly in the three tesla fields (b, b̄, b̃) was considered but deferred: it rescales the FFS energy eigenvalues by 1/A² and the stored inductances by A² (moves tracked regression values, reopens the PR #225 energy normalization) — a normalization change for its own issue, not a naming cleanup. Pure rename — no behavior change. Package precompiles; runtests_coordinate_invariant 9/9; regression diiid_n1 develop vs local unchanged (28/28 OK; the 2 N/A are the earlier resonant_field key rename, not this commit). Co-Authored-By: Claude Opus 4.8 (1M context) --- src/Equilibrium/CoordinateInvariant.jl | 20 ++++---- src/Equilibrium/Equilibrium.jl | 2 +- src/ForceFreeStates/RootAreaWeighted.jl | 28 +++++------ .../PerturbedEquilibriumStructs.jl | 20 ++++---- src/PerturbedEquilibrium/Response.jl | 8 +-- src/PerturbedEquilibrium/ResponseMatrices.jl | 50 +++++++++---------- src/PerturbedEquilibrium/SingularCoupling.jl | 16 +++--- src/PerturbedEquilibrium/Utils.jl | 14 +++--- test/runtests_coordinate_invariant.jl | 30 +++++------ test/runtests_fullruns.jl | 4 +- 10 files changed, 96 insertions(+), 96 deletions(-) diff --git a/src/Equilibrium/CoordinateInvariant.jl b/src/Equilibrium/CoordinateInvariant.jl index 1e6cffdfc..8d61c5e65 100644 --- a/src/Equilibrium/CoordinateInvariant.jl +++ b/src/Equilibrium/CoordinateInvariant.jl @@ -9,10 +9,10 @@ ForceFreeStates and PerturbedEquilibrium modules. The central operator is - ptof = sqrtamat · √jarea + rootareafield_to_flux = sqrtamat · √jarea which maps a root-area-weighted field `b̃` to the coordinate flux harmonics `Φ`: -`Φ = ptof · b̃` (so `b̃ = ptof⁻¹ · Φ`). The singular values of any operator +`Φ = rootareafield_to_flux · b̃` (so `b̃ = rootareafield_to_flux⁻¹ · Φ`). The singular values of any operator expressed in the `b̃` basis are independent of the straight-field-line (working) coordinate. @@ -92,20 +92,20 @@ function compute_sqrtamat( end """ - control_surface_ptof(equil, psi, ft) -> Matrix{ComplexF64} + control_surface_rootareafield_to_flux(equil, psi, ft) -> Matrix{ComplexF64} -Build the root-area-weighted field → flux operator `ptof = sqrtamat · √jarea` at the flux +Build the root-area-weighted field → flux operator `rootareafield_to_flux = sqrtamat · √jarea` at the flux surface `psi`, where `jarea = ∫ J|∇ψ| dθ` is the scalar flux-surface area. -`ptof` maps a root-area-weighted field `b̃` to the coordinate flux harmonics `Φ`: -`Φ = ptof · b̃`. To express a flux-space operator/generator in the coordinate-invariant +`rootareafield_to_flux` maps a root-area-weighted field `b̃` to the coordinate flux harmonics `Φ`: +`Φ = rootareafield_to_flux · b̃`. To express a flux-space operator/generator in the coordinate-invariant `b̃` basis (and back) use: - - operator `Ã = ptof⁻¹ · A · ptof` (e.g. permeability `Φ_tot = A·Φ_x`) - - generator `G̃ = ptof⁻¹ · G · ptof⁻†` (e.g. inductance, energy = Φ†·G⁻¹·Φ) - - row map `C̃ = C · ptof` (e.g. coupling, scalar = C·Φ_x) + - operator `Ã = rootareafield_to_flux⁻¹ · A · rootareafield_to_flux` (e.g. permeability `Φ_tot = A·Φ_x`) + - generator `G̃ = rootareafield_to_flux⁻¹ · G · rootareafield_to_flux⁻†` (e.g. inductance, energy = Φ†·G⁻¹·Φ) + - row map `C̃ = C · rootareafield_to_flux` (e.g. coupling, scalar = C·Φ_x) The singular values / spectrum in the `b̃` basis are coordinate-invariant. """ -function control_surface_ptof( +function control_surface_rootareafield_to_flux( equil::PlasmaEquilibrium, psi::Float64, ft::Utilities.FourierTransforms.FourierTransform diff --git a/src/Equilibrium/Equilibrium.jl b/src/Equilibrium/Equilibrium.jl index e93ee2d39..7483dd2e6 100644 --- a/src/Equilibrium/Equilibrium.jl +++ b/src/Equilibrium/Equilibrium.jl @@ -28,7 +28,7 @@ export setup_equilibrium, EquilibriumConfig, PlasmaEquilibrium, EquilibriumParam ProfileSplines, GeometryProfileSplines, compute_geometry_profiles, KineticProfileSplines, load_kinetic_profiles export flux_surface_metric, flux_surface_area -export compute_sqrt_jac_delpsi, compute_sqrtamat, control_surface_ptof +export compute_sqrt_jac_delpsi, compute_sqrtamat, control_surface_rootareafield_to_flux # --- Constants --- const mu0 = 4π * 1e-7 diff --git a/src/ForceFreeStates/RootAreaWeighted.jl b/src/ForceFreeStates/RootAreaWeighted.jl index 132973a38..e7c370f94 100644 --- a/src/ForceFreeStates/RootAreaWeighted.jl +++ b/src/ForceFreeStates/RootAreaWeighted.jl @@ -10,8 +10,8 @@ on the choice of straight-field-line coordinate. Transformation chain: - T = diag(i·2π·χ₁·singfac) converts ξ → flux (χ₁ = 2π·ψ₀, singfac = m − n·q). - - ptof = sqrtamat·√jarea converts the root-area-weighted field → flux. - - M = T⁻¹·ptof maps Φ → ξ. + - rootareafield_to_flux = sqrtamat·√jarea converts the root-area-weighted field → flux. + - M = T⁻¹·rootareafield_to_flux maps Φ → ξ. What is **NOT** invariant across Jacobian choices (see `scripts/test_power_norm_invariance.jl` for numerical proof): @@ -29,7 +29,7 @@ area-integral precision floor ~1e-6): """ # The √weight building blocks `compute_sqrt_jac_delpsi`, `compute_sqrtamat`, and the -# `control_surface_ptof` operator now live in `Equilibrium/CoordinateInvariant.jl` so the +# `control_surface_rootareafield_to_flux` operator now live in `Equilibrium/CoordinateInvariant.jl` so the # ForceFreeStates and PerturbedEquilibrium modules share one coordinate-invariant definition. """ @@ -39,9 +39,9 @@ Transform W from ξ-space to root-area-weighted flux Φ-space and eigendecompose The transformation chain: 1. T = diag(i·2π·χ₁·singfac) converts ξ → flux (singfac = m − n·q). - 2. ptof = sqrtamat·√jarea converts the root-area-weighted field → flux. - 3. M = T⁻¹·ptof maps Φ → ξ (root-area-weighted to displacement). - 4. W_Φ = M†·W·M = ptof†·T⁻†·W·T⁻¹·ptof. + 2. rootareafield_to_flux = sqrtamat·√jarea converts the root-area-weighted field → flux. + 3. M = T⁻¹·rootareafield_to_flux maps Φ → ξ (root-area-weighted to displacement). + 4. W_Φ = M†·W·M = rootareafield_to_flux†·T⁻†·W·T⁻¹·rootareafield_to_flux. Only the eigenspectrum of W_Φ is physically invariant across Jacobian choices — it is the coordinate-independent energy. The eigenvectors in this basis are @@ -96,23 +96,23 @@ function compute_rootarea_eigenvalues( T_diag_inv[i] = 1.0 / (im * 2π * chi1 * singfac[i]) end - # ptof = sqrtamat * sqrt(jarea): root-area-weighted field → flux + # rootareafield_to_flux = sqrtamat * sqrt(jarea): root-area-weighted field → flux # For multi-n, expand mpert×mpert sqrtamat to Npert×Npert block-diagonal - ptof_block = sqrtamat .* sqrt(jarea) + rootareafield_to_flux_block = sqrtamat .* sqrt(jarea) if npert == 1 - ptof_full = ptof_block + rootareafield_to_flux_full = rootareafield_to_flux_block else - ptof_full = zeros(ComplexF64, Npert, Npert) + rootareafield_to_flux_full = zeros(ComplexF64, Npert, Npert) for in in 1:npert r = ((in - 1) * mpert + 1):(in * mpert) - ptof_full[r, r] .= ptof_block + rootareafield_to_flux_full[r, r] .= rootareafield_to_flux_block end end - # M = diag(T_inv) · ptof: row-scale ptof by T_inv (maps Φ → ξ) - M = similar(ptof_full) + # M = diag(T_inv) · rootareafield_to_flux: row-scale rootareafield_to_flux by T_inv (maps Φ → ξ) + M = similar(rootareafield_to_flux_full) for i in 1:Npert - M[i, :] .= T_diag_inv[i] .* ptof_full[i, :] + M[i, :] .= T_diag_inv[i] .* rootareafield_to_flux_full[i, :] end # Transform energy matrices: W_Φ = M† · W · M diff --git a/src/PerturbedEquilibrium/PerturbedEquilibriumStructs.jl b/src/PerturbedEquilibrium/PerturbedEquilibriumStructs.jl index 5c5184a2b..22a067264 100644 --- a/src/PerturbedEquilibrium/PerturbedEquilibriumStructs.jl +++ b/src/PerturbedEquilibrium/PerturbedEquilibriumStructs.jl @@ -104,13 +104,13 @@ Metadata [n_rational] — identifies each (surface, n) row: Control surface matrices [numpert_total × numpert_total], stored in the coordinate-invariant root-area-weighted field (b̃) space (issue #233 / Pharr 2026). Recover the flux-space forms with -the `control_surface_field_operator` (`ptof`, Φ = ptof·b̃): e.g. `P_flux = ptof·P̃·ptof⁻¹`, -`L_flux = ptof·L̃·ptof†`. - - `plasma_inductance` - Λ̃ = ptof⁻¹·Λ·ptof⁻† (wt0-based plasma inductance, congruence) - - `surface_inductance` - L̃ = ptof⁻¹·L·ptof⁻† (vacuum surface inductance, congruence) - - `permeability` - P̃ = ptof⁻¹·P·ptof (plasma response operator P=Λ·L⁻¹, similarity) - - `reluctance` - ϱ̃ = ptof†·ϱ·ptof (ϱ = L⁻¹·(Λ−L)·L⁻¹, congruence) - - `control_surface_field_operator` - ptof = sqrtamat·√jarea at psilim (field → flux recovery operator) +the `control_surface_field_operator` (`rootareafield_to_flux`, Φ = rootareafield_to_flux·b̃): e.g. `P_flux = rootareafield_to_flux·P̃·rootareafield_to_flux⁻¹`, +`L_flux = rootareafield_to_flux·L̃·rootareafield_to_flux†`. + - `plasma_inductance` - Λ̃ = rootareafield_to_flux⁻¹·Λ·rootareafield_to_flux⁻† (wt0-based plasma inductance, congruence) + - `surface_inductance` - L̃ = rootareafield_to_flux⁻¹·L·rootareafield_to_flux⁻† (vacuum surface inductance, congruence) + - `permeability` - P̃ = rootareafield_to_flux⁻¹·P·rootareafield_to_flux (plasma response operator P=Λ·L⁻¹, similarity) + - `reluctance` - ϱ̃ = rootareafield_to_flux†·ϱ·rootareafield_to_flux (ϱ = L⁻¹·(Λ−L)·L⁻¹, congruence) + - `control_surface_field_operator` - rootareafield_to_flux = sqrtamat·√jarea at psilim (field → flux recovery operator) Energies (Fortran gpout convention; Φ_x external flux, Φ_tot total flux, L/Λ inductances): - `vacuum_energy` - Re( ⟨Φ_x, L⁻¹·Φ_x⟩ ) / 4 (energy to perturb the vacuum) @@ -160,9 +160,9 @@ Energies (Fortran gpout convention; Φ_x external flux, Φ_tot total flux, L/Λ # Control surface matrices [numpert_total × numpert_total] plasma_inductance::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # Λ̃ (field space) surface_inductance::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # L̃ (field space) - permeability::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # P̃ = ptof⁻¹·Λ·L⁻¹·ptof - reluctance::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # ϱ̃ = ptof†·L⁻¹·(Λ−L)·L⁻¹·ptof - control_surface_field_operator::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # ptof: field → flux recovery + permeability::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # P̃ = rootareafield_to_flux⁻¹·Λ·L⁻¹·rootareafield_to_flux + reluctance::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # ϱ̃ = rootareafield_to_flux†·L⁻¹·(Λ−L)·L⁻¹·rootareafield_to_flux + control_surface_field_operator::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # rootareafield_to_flux: field → flux recovery # Energies — see the struct docstring for formulas vacuum_energy::Float64 = 0.0 diff --git a/src/PerturbedEquilibrium/Response.jl b/src/PerturbedEquilibrium/Response.jl index acbeabda8..fd7dfe2a4 100644 --- a/src/PerturbedEquilibrium/Response.jl +++ b/src/PerturbedEquilibrium/Response.jl @@ -61,14 +61,14 @@ function compute_plasma_response!( # Conform the control-surface matrices to the coordinate-invariant root-area-weighted # field (b̃) space for output (issue #233 / Pharr 2026). The flux-space forms are - # recoverable from the stored `ptof` operator (Φ = ptof·b̃) — see Utils.jl output docs. - ptof = build_control_surface_ptof(equil, ffs_intr) - field_mats = field_space_response_matrices(plasma_inductance, surface_inductance, permeability, reluctance, ptof) + # recoverable from the stored `rootareafield_to_flux` operator (Φ = rootareafield_to_flux·b̃) — see Utils.jl output docs. + rootareafield_to_flux = build_control_surface_rootareafield_to_flux(equil, ffs_intr) + field_mats = field_space_response_matrices(plasma_inductance, surface_inductance, permeability, reluctance, rootareafield_to_flux) state.plasma_inductance = field_mats.plasma_inductance state.surface_inductance = field_mats.surface_inductance state.permeability = field_mats.permeability state.reluctance = field_mats.reluctance - state.control_surface_field_operator = ptof + state.control_surface_field_operator = rootareafield_to_flux forcing_vector = map_forcing_to_eigenmodes(intr.forcing_modes, ffs_intr) response_vector = compute_plasma_response_vector(permeability, forcing_vector) diff --git a/src/PerturbedEquilibrium/ResponseMatrices.jl b/src/PerturbedEquilibrium/ResponseMatrices.jl index fd095ef42..0153b7422 100644 --- a/src/PerturbedEquilibrium/ResponseMatrices.jl +++ b/src/PerturbedEquilibrium/ResponseMatrices.jl @@ -299,22 +299,22 @@ function calc_permeability( end """ - build_control_surface_ptof( + build_control_surface_rootareafield_to_flux( equil::Equilibrium.PlasmaEquilibrium, ffs_intr::ForceFreeStatesInternal )::Matrix{ComplexF64} -Build the numpert_total × numpert_total root-area-weighted field → flux operator `ptof` at the -control surface (psilim). The mpert × mpert single-n block (Equilibrium.control_surface_ptof) +Build the numpert_total × numpert_total root-area-weighted field → flux operator `rootareafield_to_flux` at the +control surface (psilim). The mpert × mpert single-n block (Equilibrium.control_surface_rootareafield_to_flux) is repeated block-diagonally over the `npert` toroidal harmonics, matching the numpert_total mode ordering used by the response matrices. -`ptof` maps a root-area-weighted control-surface field `b̃` to the coordinate flux harmonics -`Φ`: `Φ = ptof · b̃`. It is the operator users need to recover the flux-space matrices from +`rootareafield_to_flux` maps a root-area-weighted control-surface field `b̃` to the coordinate flux harmonics +`Φ`: `Φ = rootareafield_to_flux · b̃`. It is the operator users need to recover the flux-space matrices from the stored coordinate-invariant (field-space) ones — see `field_space_response_matrices`. [Pharr 2026] """ -function build_control_surface_ptof( +function build_control_surface_rootareafield_to_flux( equil::Equilibrium.PlasmaEquilibrium, ffs_intr::ForceFreeStatesInternal )::Matrix{ComplexF64} @@ -324,50 +324,50 @@ function build_control_surface_ptof( mtheta_eq = length(equil.rzphi_ys) ft = Utilities.FourierTransforms.FourierTransform(mtheta_eq, mpert, ffs_intr.mlow) - ptof_block = Equilibrium.control_surface_ptof(equil, ffs_intr.psilim, ft) + rootareafield_to_flux_block = Equilibrium.control_surface_rootareafield_to_flux(equil, ffs_intr.psilim, ft) - npert == 1 && return Matrix{ComplexF64}(ptof_block) + npert == 1 && return Matrix{ComplexF64}(rootareafield_to_flux_block) - ptof_full = zeros(ComplexF64, Npert, Npert) + rootareafield_to_flux_full = zeros(ComplexF64, Npert, Npert) for in in 1:npert r = ((in - 1) * mpert + 1):(in * mpert) - ptof_full[r, r] .= ptof_block + rootareafield_to_flux_full[r, r] .= rootareafield_to_flux_block end - return ptof_full + return rootareafield_to_flux_full end """ field_space_response_matrices( - plasma_inductance, surface_inductance, permeability, reluctance, ptof + plasma_inductance, surface_inductance, permeability, reluctance, rootareafield_to_flux )::NamedTuple Express the control-surface response matrices in the coordinate-invariant root-area-weighted -field (b̃) space, given the flux-space matrices and the `ptof` operator (`Φ = ptof·b̃`). +field (b̃) space, given the flux-space matrices and the `rootareafield_to_flux` operator (`Φ = rootareafield_to_flux·b̃`). The matrices fall into two algebraic classes: - **Operators** (map flux → flux): permeability `P` (Φ_tot = P·Φ_x) transforms by similarity - `P̃ = ptof⁻¹·P·ptof`. Its singular values are coordinate-invariant. + `P̃ = rootareafield_to_flux⁻¹·P·rootareafield_to_flux`. Its singular values are coordinate-invariant. - **Quadratic generators** (energy = Φ†·G⁻¹·Φ): inductances `Λ`, `L` transform by congruence - `G̃ = ptof⁻¹·G·ptof⁻†`; the inverse-inductance-like reluctance `ϱ` (energy = Φ†·ϱ·Φ) - transforms as `ϱ̃ = ptof†·ϱ·ptof`. Their spectra are coordinate-invariant. + `G̃ = rootareafield_to_flux⁻¹·G·rootareafield_to_flux⁻†`; the inverse-inductance-like reluctance `ϱ` (energy = Φ†·ϱ·Φ) + transforms as `ϱ̃ = rootareafield_to_flux†·ϱ·rootareafield_to_flux`. Their spectra are coordinate-invariant. -These rules are mutually consistent: `P̃ = Λ̃·L̃⁻¹ = ptof⁻¹·Λ·L⁻¹·ptof = ptof⁻¹·P·ptof`, and -`ϱ̃ = L̃⁻¹·(Λ̃−L̃)·L̃⁻¹`. To recover the flux-space forms, invert each map with the stored -`ptof` (e.g. `P_flux = ptof·P̃·ptof⁻¹`, `L_flux = ptof·L̃·ptof†`). [Pharr 2026] +Writing `R ≡ rootareafield_to_flux` for brevity, these rules are mutually consistent: +`P̃ = Λ̃·L̃⁻¹ = R⁻¹·Λ·L⁻¹·R = R⁻¹·P·R`, and `ϱ̃ = L̃⁻¹·(Λ̃−L̃)·L̃⁻¹`. To recover the flux-space +forms, invert each map with the stored `R` (e.g. `P_flux = R·P̃·R⁻¹`, `L_flux = R·L̃·R†`). [Pharr 2026] """ function field_space_response_matrices( plasma_inductance::Matrix{ComplexF64}, surface_inductance::Matrix{ComplexF64}, permeability::Matrix{ComplexF64}, reluctance::Matrix{ComplexF64}, - ptof::Matrix{ComplexF64} + rootareafield_to_flux::Matrix{ComplexF64} )::NamedTuple - ptof_inv = inv(ptof) + rootareafield_to_flux_inv = inv(rootareafield_to_flux) return ( - plasma_inductance=ptof_inv * plasma_inductance * ptof_inv', - surface_inductance=ptof_inv * surface_inductance * ptof_inv', - permeability=ptof_inv * permeability * ptof, - reluctance=ptof' * reluctance * ptof + plasma_inductance=rootareafield_to_flux_inv * plasma_inductance * rootareafield_to_flux_inv', + surface_inductance=rootareafield_to_flux_inv * surface_inductance * rootareafield_to_flux_inv', + permeability=rootareafield_to_flux_inv * permeability * rootareafield_to_flux, + reluctance=rootareafield_to_flux' * reluctance * rootareafield_to_flux ) end diff --git a/src/PerturbedEquilibrium/SingularCoupling.jl b/src/PerturbedEquilibrium/SingularCoupling.jl index 904f53ad8..4eeb43dd7 100644 --- a/src/PerturbedEquilibrium/SingularCoupling.jl +++ b/src/PerturbedEquilibrium/SingularCoupling.jl @@ -283,15 +283,15 @@ function compute_singular_coupling_metrics!( state.delta_prime = state.C_delta_prime * forcing_flux # Conform the stored coupling-matrix input basis to the coordinate-invariant root-area-weighted - # field (b̃) space (#233 / Pharr 2026): C̃ = C·ptof, so each stored row acts on the applied - # field b̃_x (Φ_x = ptof·b̃_x) and its singular values become coordinate-invariant. Done after + # field (b̃) space (#233 / Pharr 2026): C̃ = C·rootareafield_to_flux, so each stored row acts on the applied + # field b̃_x (Φ_x = rootareafield_to_flux·b̃_x) and its singular values become coordinate-invariant. Done after # the applied-vector evaluation above so those physical scalars carry no round-trip noise. - ptof = build_control_surface_ptof(equil, ffs_intr) - state.C_resonant_area_weighted_field = state.C_resonant_area_weighted_field * ptof - state.C_resonant_current = state.C_resonant_current * ptof - state.C_island_width_sq = state.C_island_width_sq * ptof - state.C_penetrated_area_weighted_field = state.C_penetrated_area_weighted_field * ptof - state.C_delta_prime = state.C_delta_prime * ptof + rootareafield_to_flux = build_control_surface_rootareafield_to_flux(equil, ffs_intr) + state.C_resonant_area_weighted_field = state.C_resonant_area_weighted_field * rootareafield_to_flux + state.C_resonant_current = state.C_resonant_current * rootareafield_to_flux + state.C_island_width_sq = state.C_island_width_sq * rootareafield_to_flux + state.C_penetrated_area_weighted_field = state.C_penetrated_area_weighted_field * rootareafield_to_flux + state.C_delta_prime = state.C_delta_prime * rootareafield_to_flux # Phase 5: Island diagnostics from applied resonant vectors compute_island_diagnostics!(state, n_rational) diff --git a/src/PerturbedEquilibrium/Utils.jl b/src/PerturbedEquilibrium/Utils.jl index 295029c25..7e3ff3996 100644 --- a/src/PerturbedEquilibrium/Utils.jl +++ b/src/PerturbedEquilibrium/Utils.jl @@ -67,11 +67,11 @@ perturbed_equilibrium/ │ ├── b_theta │ └── b_zeta ├── response_matrices/ # [numpert_total × numpert_total], root-area-weighted field (b̃) space -│ ├── plasma_inductance # Λ̃ = ptof⁻¹·Λ·ptof⁻† -│ ├── surface_inductance # L̃ = ptof⁻¹·L·ptof⁻† -│ ├── permeability # P̃ = ptof⁻¹·P·ptof (P = Λ·L⁻¹) -│ ├── reluctance # ϱ̃ = ptof†·ϱ·ptof -│ └── rootarea_field_to_flux_operator # ptof = sqrtamat·√jarea; recover flux via Φ = ptof·b̃ +│ ├── plasma_inductance # Λ̃ = rootareafield_to_flux⁻¹·Λ·rootareafield_to_flux⁻† +│ ├── surface_inductance # L̃ = rootareafield_to_flux⁻¹·L·rootareafield_to_flux⁻† +│ ├── permeability # P̃ = rootareafield_to_flux⁻¹·P·rootareafield_to_flux (P = Λ·L⁻¹) +│ ├── reluctance # ϱ̃ = rootareafield_to_flux†·ϱ·rootareafield_to_flux +│ └── rootarea_field_to_flux_operator # rootareafield_to_flux = sqrtamat·√jarea; recover flux via Φ = rootareafield_to_flux·b̃ ├── singular_coupling/ │ ├── C_resonant_area_weighted_field # [n_rational × numpert_total] coupling matrix (b̃-space input, resonant area-weighted field b^r=Φ^r/A^r [T]) │ ├── C_resonant_current @@ -115,8 +115,8 @@ function write_outputs_to_HDF5( !isempty(state.response_vec) && (pe_group["response_vec"] = state.response_vec) # Control surface matrices [numpert_total × numpert_total], in coordinate-invariant - # root-area-weighted field (b̃) space. Recover flux space with the stored ptof operator - # (Φ = ptof·b̃): e.g. P_flux = ptof·P̃·ptof⁻¹, L_flux = ptof·L̃·ptof†. [Pharr 2026] + # root-area-weighted field (b̃) space. Recover flux space with the stored operator + # R ≡ rootareafield_to_flux (Φ = R·b̃): e.g. P_flux = R·P̃·R⁻¹, L_flux = R·L̃·R†. [Pharr 2026] mat_group = haskey(pe_group, "response_matrices") ? pe_group["response_matrices"] : create_group(pe_group, "response_matrices") !isempty(state.plasma_inductance) && (mat_group["plasma_inductance"] = state.plasma_inductance) !isempty(state.surface_inductance) && (mat_group["surface_inductance"] = state.surface_inductance) diff --git a/test/runtests_coordinate_invariant.jl b/test/runtests_coordinate_invariant.jl index 34eedcc05..c156cb6ca 100644 --- a/test/runtests_coordinate_invariant.jl +++ b/test/runtests_coordinate_invariant.jl @@ -1,10 +1,10 @@ -# Tests for the coordinate-invariant (power-normalized field, b̃) transform of the +# Tests for the coordinate-invariant (root-area-weighted field, b̃) transform of the # PerturbedEquilibrium control-surface response matrices (issue #233 / Pharr 2026). # # Verifies the field-space transform rules in # `PerturbedEquilibrium.field_space_response_matrices` and the recovery-operator # contract: the flux-space matrices are exactly recoverable from the stored b̃-space -# matrices via the `ptof` operator (Φ = ptof·b̃). +# matrices via the `rootareafield_to_flux` operator (Φ = rootareafield_to_flux·b̃). using Test using LinearAlgebra @@ -14,33 +14,33 @@ const PE = GeneralizedPerturbedEquilibrium.PerturbedEquilibrium # Deterministic, well-conditioned synthetic operators (no RNG → reproducible). function _synthetic_inputs(n::Int) - # ptof: a generic invertible complex operator standing in for sqrtamat·√jarea. - ptof = Matrix{ComplexF64}(undef, n, n) + # rootareafield_to_flux: a generic invertible complex operator standing in for sqrtamat·√jarea. + rootareafield_to_flux = Matrix{ComplexF64}(undef, n, n) for i in 1:n, j in 1:n - ptof[i, j] = (1.0 + 0.3 * cospi((i + 2j) / n)) * cis(0.2 * (i - j)) * (i == j ? 1.0 : 0.15) + rootareafield_to_flux[i, j] = (1.0 + 0.3 * cospi((i + 2j) / n)) * cis(0.2 * (i - j)) * (i == j ? 1.0 : 0.15) end # Hermitian positive-definite inductances (energy generators). A = [cis(0.1 * (i - j)) / (1 + abs(i - j)) for i in 1:n, j in 1:n] L = A * A' + n * I # Hermitian PD surface inductance B = [cis(-0.07 * (i + j)) / (1 + abs(i - j)) for i in 1:n, j in 1:n] Λ = B * B' + 2n * I # Hermitian PD plasma inductance - return Matrix{ComplexF64}(ptof), Matrix{ComplexF64}(L), Matrix{ComplexF64}(Λ) + return Matrix{ComplexF64}(rootareafield_to_flux), Matrix{ComplexF64}(L), Matrix{ComplexF64}(Λ) end @testset "Coordinate-invariant field-space response matrices" begin n = 6 - ptof, L, Λ = _synthetic_inputs(n) + rootareafield_to_flux, L, Λ = _synthetic_inputs(n) P = Λ / L # permeability Φ_tot = P·Φ_x ϱ = inv(L) * (Λ - L) * inv(L) # reluctance - fm = PE.field_space_response_matrices(Λ, L, P, ϱ, ptof) + fm = PE.field_space_response_matrices(Λ, L, P, ϱ, rootareafield_to_flux) @testset "Recovery operator contract (round-trip to flux space)" begin - # Recover flux space from the stored b̃-space matrices via ptof. - @test ptof * fm.permeability / ptof ≈ P rtol = 1e-10 - @test ptof * fm.surface_inductance * ptof' ≈ L rtol = 1e-10 - @test ptof * fm.plasma_inductance * ptof' ≈ Λ rtol = 1e-10 - @test (ptof') \ fm.reluctance / ptof ≈ ϱ rtol = 1e-10 + # Recover flux space from the stored b̃-space matrices via rootareafield_to_flux. + @test rootareafield_to_flux * fm.permeability / rootareafield_to_flux ≈ P rtol = 1e-10 + @test rootareafield_to_flux * fm.surface_inductance * rootareafield_to_flux' ≈ L rtol = 1e-10 + @test rootareafield_to_flux * fm.plasma_inductance * rootareafield_to_flux' ≈ Λ rtol = 1e-10 + @test (rootareafield_to_flux') \ fm.reluctance / rootareafield_to_flux ≈ ϱ rtol = 1e-10 end @testset "Internal consistency of the transform rules" begin @@ -52,9 +52,9 @@ end end @testset "Energy-scalar invariance under conformance" begin - # A physical applied flux Φ and its power-norm counterpart b̃ = ptof⁻¹·Φ + # A physical applied flux Φ and its root-area-weighted counterpart b̃ = rootareafield_to_flux⁻¹·Φ Φ = ComplexF64[cis(0.3k) / k for k in 1:n] - b̃ = ptof \ Φ + b̃ = rootareafield_to_flux \ Φ # energy = Φ†·L⁻¹·Φ must equal b̃†·L̃⁻¹·b̃ (and likewise for Λ, ϱ) @test dot(Φ, L \ Φ) ≈ dot(b̃, fm.surface_inductance \ b̃) rtol = 1e-10 @test dot(Φ, Λ \ Φ) ≈ dot(b̃, fm.plasma_inductance \ b̃) rtol = 1e-10 diff --git a/test/runtests_fullruns.jl b/test/runtests_fullruns.jl index 5e864d5d7..6cb20204d 100644 --- a/test/runtests_fullruns.jl +++ b/test/runtests_fullruns.jl @@ -21,7 +21,7 @@ using HDF5 @test begin GeneralizedPerturbedEquilibrium.main([ex3]) h5open(joinpath(ex3, "gpec.h5"), "r") do h5 - # ξ-space (XiNorm) eigenvalues — power-norm collapses these stable modes to ~0, unusable as a regression anchor. + # ξ-space (XiNorm) eigenvalues — root-area weighting collapses these stable modes to ~0, unusable as a regression anchor. et = read(h5["FreeBoundaryStability/XiNorm/eigenmode_energies"]) @test isfinite(real(et[1])) @test real(et[1]) > 0 # Solovev is stable (positive total energy) @@ -36,7 +36,7 @@ using HDF5 @test begin GeneralizedPerturbedEquilibrium.main([ex4]) h5open(joinpath(ex4, "gpec.h5"), "r") do h5 - # ξ-space (XiNorm) eigenvalues — power-norm collapses these modes to ~0, unusable as a regression anchor. + # ξ-space (XiNorm) eigenvalues — root-area weighting collapses these modes to ~0, unusable as a regression anchor. et = read(h5["FreeBoundaryStability/XiNorm/eigenmode_energies"]) @test isfinite(real(et[1])) # et[1] is the single near-marginal kinetic eigenvalue; the rest of the spectrum From 19df3f54fc160abb1516101299cd3c691a0a21ff Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Thu, 11 Jun 2026 22:55:42 -0400 Subject: [PATCH 034/135] ForcingTerms - NEW FEATURE - Window-pane standoff placement with corner-matched winding Add make_window_pane_standoff to place a window-pane array by physical standoff distance and poloidal angle off the plasma surface, deriving the frame from surface_point_and_normal instead of explicit R-Z corners. load_coil_sets now receives the equilibrium so the standoff mode can be built from the main forcing pipeline. The standoff tangent is the +90 deg rotation of the outward normal so the poloidal leg runs lower-Z to higher-Z at the outboard midplane, matching make_window_pane's c1->c2 winding. This standardizes the two builders to a single convention: positive current produces positive b_n_x near the coil. Adds a winding-convention test and documents the standoff mode in the TOML example. Co-Authored-By: Claude Opus 4.8 (1M context) --- docs/src/forcing_terms.md | 19 +- src/ForcingTerms/CoilGeometry.jl | 180 ++++++++++++++++-- .../PerturbedEquilibrium.jl | 2 +- test/runtests_coils.jl | 65 ++++++- 4 files changed, 241 insertions(+), 25 deletions(-) diff --git a/docs/src/forcing_terms.md b/docs/src/forcing_terms.md index 4f8d5af25..f8427de84 100644 --- a/docs/src/forcing_terms.md +++ b/docs/src/forcing_terms.md @@ -126,7 +126,7 @@ height = 0.9 currents = [5e3] tiltx = [2.0] -# Analytic window-pane (picture-frame) array; rz_corners are two opposite [R, Z] corners +# Analytic window-pane (picture-frame) array — corner mode: two opposite [R, Z] corners [[ForcingTerms.coil_set]] source = "window_pane" ncoil_gen = 8 @@ -134,7 +134,22 @@ rz_corners = [[2.2, -0.6], [2.2, 0.6]] gap_fraction = 0.15 currents = [1e3, -1e3, 1e3, -1e3, 1e3, -1e3, 1e3, -1e3] -# Analytic helical array on a circular cross-section torus (pitch = m/n) +# Analytic window-pane — standoff mode: placed by physical distance off the plasma surface. +# The frame center sits `standoff` m along the outward surface normal at cylindrical +# `poloidal_angle` (degrees); legs span `poloidal_length` m, tilted by `poloidal_tilt` +# (degrees, 0 = tangential). Requires an equilibrium (the main forcing pipeline supplies it). +[[ForcingTerms.coil_set]] +source = "window_pane" +ncoil_gen = 2 +standoff = 0.25 +poloidal_angle = 0.0 +poloidal_length = 1.2 +poloidal_tilt = 0.0 +gap_fraction = 0.15 +currents = [1e4, -1e4] + +# Analytic helical array on a circular cross-section torus (pitch = m/n). +# theta_lo/theta_hi (poloidal extent, degrees) default to a full 0–360 turn. [[ForcingTerms.coil_set]] source = "helical" R0 = 1.7 diff --git a/src/ForcingTerms/CoilGeometry.jl b/src/ForcingTerms/CoilGeometry.jl index 8356d3b07..8a5e5e0fe 100644 --- a/src/ForcingTerms/CoilGeometry.jl +++ b/src/ForcingTerms/CoilGeometry.jl @@ -50,8 +50,10 @@ A coil set comes from one of several sources, selected by `source`: - `""` or `"file"`: read a geometry file — `.dat` (legacy ASCII) or `.h5` (modern), chosen by extension. The file path comes from `dat_file`/`h5_file` or the `machine`+`name` convention. - `"pf_hoop"`: an analytic horizontal circular loop (`radius`, `height`). - - `"window_pane"`: an analytic axis-aligned rectangular picture-frame array - (`ncoil_gen`, `rz_corners`, `gap_fraction`, `phi0`). + - `"window_pane"`: an analytic rectangular picture-frame array, placed EITHER by explicit + corners (`rz_corners`) OR by physical standoff from the plasma surface (`standoff`, + `poloidal_angle`, `poloidal_length`, `poloidal_tilt`); shared toroidal layout via + `ncoil_gen`, `gap_fraction`, `phi0`. - `"helical"`: an analytic helical array on a circular cross-section torus (`R0`, `a`, `m_hel`, `n_hel`, `theta_lo`, `theta_hi`, `n_coils`, `gap_fraction`, `phi0`, `offset`). @@ -75,15 +77,22 @@ Analytic-source parameters (used only for the matching `source`): - `radius`, `height`: PF hoop circle radius and Z height [m] - `ncoil_gen`: number of generated coils (window-pane / helical arrays) - - `rz_corners`: window-pane cross-section as two opposite `[R, Z]` corners [m] + - `rz_corners`: window-pane cross-section as two opposite `[R, Z]` corners in m (corner mode) - `gap_fraction`: toroidal gap between adjacent coils as a fraction of their spacing - `phi0`: toroidal angle offset of the first generated coil [rad] - `R0`, `a`: helical torus major radius and minor (circle) radius [m] - `m_hel`, `n_hel`: helical poloidal/toroidal mode numbers setting the pitch - - `theta_lo`, `theta_hi`: helical poloidal extent in radians; a full turn when `theta_hi-theta_lo == 2π` + - `theta_lo`, `theta_hi`: helical poloidal extent in degrees; a full turn when `theta_hi-theta_lo == 360` - `n_coils`: number of helical coils in the array - `offset`: helical coil radial offset from the torus surface [m] - `nsec_gen`: optional override of the generated point count per coil + +Window-pane standoff placement (alternative to `rz_corners`; needs an equilibrium): + + - `standoff`: outward-normal distance from the control surface to the frame center [m] + - `poloidal_angle`: cylindrical poloidal angle of the frame center, in degrees + - `poloidal_length`: poloidal leg span (corner-to-corner) along the surface tangent [m] + - `poloidal_tilt`: extra tilt of the legs in degrees; 0 means tangential to the surface """ Base.@kwdef struct CoilSetConfig name::String = "" @@ -115,10 +124,16 @@ Base.@kwdef struct CoilSetConfig m_hel::Int = 0 n_hel::Int = 0 theta_lo::Float64 = 0.0 - theta_hi::Float64 = 2π + theta_hi::Float64 = 360.0 n_coils::Int = 0 offset::Float64 = 0.0 nsec_gen::Int = 0 + + # Window-pane standoff placement (alternative to rz_corners) + standoff::Float64 = NaN + poloidal_angle::Float64 = NaN + poloidal_length::Float64 = 0.0 + poloidal_tilt::Float64 = 0.0 end """ @@ -196,10 +211,14 @@ function _parse_coil_set_config(d::Dict{String,Any}) m_hel=get(d, "m_hel", 0), n_hel=get(d, "n_hel", 0), theta_lo=Float64(get(d, "theta_lo", 0.0)), - theta_hi=Float64(get(d, "theta_hi", 2π)), + theta_hi=Float64(get(d, "theta_hi", 360.0)), n_coils=get(d, "n_coils", 0), offset=Float64(get(d, "offset", 0.0)), - nsec_gen=get(d, "nsec_gen", 0) + nsec_gen=get(d, "nsec_gen", 0), + standoff=Float64(get(d, "standoff", NaN)), + poloidal_angle=Float64(get(d, "poloidal_angle", NaN)), + poloidal_length=Float64(get(d, "poloidal_length", 0.0)), + poloidal_tilt=Float64(get(d, "poloidal_tilt", 0.0)) ) end @@ -288,6 +307,101 @@ function make_pf_hoop(; radius::Real, height::Real, nsec::Int=361, name::String= return CoilSet(name, 1, 1, 1.0, nsec, x, y, z, zeros(1)) end +""" + surface_point_and_normal(equil, theta_cyl; psi=equil.rzphi_xs[end]) -> (R, Z, nR, nZ) + +Locate the control-surface point at cylindrical poloidal angle `theta_cyl` (radians) and return +it with the outward unit normal `(nR, nZ)` in the R-Z plane. + +The flux-surface splines are parametrized by the SFL angle `theta_sfl`, related to the cylindrical +angle by `theta_cyl = 2π*(theta_sfl + rzphi_offset(psi, theta_sfl))`. Since the offset is a small +smooth perturbation, `theta_sfl` is recovered by a damped fixed-point iteration. The tangent is +taken by central-differencing `R(theta_sfl), Z(theta_sfl)`, and the normal `(dZ/dθ, -dR/dθ)` is +normalized and oriented outward (positive dot with `(R-ro, Z-zo)`), matching the normal-flux +convention of `project_normal_flux!`. +""" +function surface_point_and_normal(equil, theta_cyl::Real; psi::Real=equil.rzphi_xs[end]) + hint = (Ref(1), Ref(1)) + target = mod(theta_cyl / (2π), 1.0) # normalized cylindrical angle in [0,1) + + # Solve theta_cyl/2π = theta_sfl + offset(theta_sfl) for theta_sfl (offset slope ≪ 1). + theta_sfl = target + for _ in 1:50 + off = equil.rzphi_offset((psi, mod(theta_sfl, 1.0)); hint=hint) + residual = mod(theta_sfl + off - target, 1.0) + residual -= round(residual) # wrap to (-0.5, 0.5] + abs(residual) < 1e-13 && break + theta_sfl -= residual + end + theta_sfl = mod(theta_sfl, 1.0) + + point(tn) = begin + tw = mod(tn, 1.0) + r_minor = sqrt(equil.rzphi_rsquared((psi, tw); hint=hint)) + tc = 2π * (tw + equil.rzphi_offset((psi, tw); hint=hint)) + (equil.ro + r_minor * cos(tc), equil.zo + r_minor * sin(tc)) + end + + R, Z = point(theta_sfl) + h = 1.0e-5 + Rp, Zp = point(theta_sfl + h) + Rm, Zm = point(theta_sfl - h) + dR = (Rp - Rm) / (2h) + dZ = (Zp - Zm) / (2h) + + nR, nZ = dZ, -dR + nrm = hypot(nR, nZ) + nR /= nrm + nZ /= nrm + if nR * (R - equil.ro) + nZ * (Z - equil.zo) < 0 # force outward orientation + nR, nZ = -nR, -nZ + end + return (R, Z, nR, nZ) +end + +""" + make_window_pane_standoff(equil; standoff, poloidal_angle, poloidal_length, + poloidal_tilt=0.0, ncoil, gap_fraction=0.0, phi0=0.0, + name="window_pane") -> CoilSet + +Build a window-pane array placed by physical standoff instead of explicit corners. The frame +center sits `standoff` [m] along the outward surface normal at cylindrical `poloidal_angle` +(degrees); its poloidal legs span `poloidal_length` [m] along the surface tangent, rotated by +`poloidal_tilt` (degrees, 0 = tangential). The control surface is the boundary +`equil.rzphi_xs[end]`. Toroidal layout (`ncoil`, `gap_fraction`, `phi0`) and the leg/arc +construction are delegated to [`make_window_pane`](@ref). + +The poloidal legs wind in the same sense as `make_window_pane`'s `c1 -> c2` ordering (lower-Z to +higher-Z at the outboard midplane), so positive current produces positive `b_n_x` near the coil, +matching the corner-built window pane. +""" +function make_window_pane_standoff(equil; standoff::Real, poloidal_angle::Real, + poloidal_length::Real, poloidal_tilt::Real=0.0, ncoil::Int, + gap_fraction::Real=0.0, phi0::Real=0.0, name::String="window_pane") + poloidal_length > 0 || error("make_window_pane_standoff: poloidal_length must be > 0 (got $poloidal_length)") + + R, Z, nR, nZ = surface_point_and_normal(equil, deg2rad(poloidal_angle)) + + # Frame center: standoff along the outward normal. + Rc = R + standoff * nR + Zc = Z + standoff * nZ + + # Tangent: +90° rotation of the outward normal, so the poloidal leg runs lower-Z -> higher-Z + # at the outboard midplane, matching make_window_pane's c1->c2 winding (positive current -> + # positive b_n_x near the coil). Rotated by poloidal_tilt in the R-Z plane. + tR, tZ = -nZ, nR + c, s = cos(deg2rad(poloidal_tilt)), sin(deg2rad(poloidal_tilt)) + uR = c * tR - s * tZ + uZ = s * tR + c * tZ + + half = poloidal_length / 2 + c1 = [Rc - half * uR, Zc - half * uZ] + c2 = [Rc + half * uR, Zc + half * uZ] + + return make_window_pane(; ncoil=ncoil, rz_corners=[c1, c2], + gap_fraction=gap_fraction, phi0=phi0, name=name) +end + """ make_window_pane(; ncoil, rz_corners, gap_fraction=0.0, phi0=0.0, np_pol=20, np_tor=40, name="window_pane") -> CoilSet @@ -371,7 +485,7 @@ function make_window_pane(; ncoil::Int, rz_corners::AbstractVector, end """ - make_helical(; R0, a, m, n, theta_lo=0.0, theta_hi=2π, n_coils, + make_helical(; R0, a, m, n, theta_lo=0.0, theta_hi=360.0, n_coils, gap_fraction=0.0, phi0=0.0, offset=0.0, npts=720, name="helical") -> CoilSet @@ -379,13 +493,14 @@ Build an array of `n_coils` analytic helical coils wound on a circular cross-sec of major radius `R0` and minor radius `a` [m], offset radially outward by `offset` [m]. The helical pitch is set by the poloidal/toroidal mode numbers `m`/`n` via `ζ = (m/n)·θ + φ`. -For a full poloidal turn (`theta_hi - theta_lo == 2π`) each coil is a single helical strand. -For a partial poloidal range the coil is closed into a loop with two helical legs joined by -toroidal arcs (matching OMFIT `form_helical_array.py`). `npts` sets the strand resolution. +The poloidal extent `theta_lo`/`theta_hi` is in degrees. For a full poloidal turn +(`theta_hi - theta_lo == 360`) each coil is a single helical strand. For a partial poloidal +range the coil is closed into a loop with two helical legs joined by toroidal arcs (matching +OMFIT `form_helical_array.py`). `npts` sets the strand resolution. Currents are zeroed; `load_coil_sets` fills them. """ function make_helical(; R0::Real, a::Real, m::Int, n::Int, - theta_lo::Real=0.0, theta_hi::Real=2π, n_coils::Int, + theta_lo::Real=0.0, theta_hi::Real=360.0, n_coils::Int, gap_fraction::Real=0.0, phi0::Real=0.0, offset::Real=0.0, npts::Int=720, name::String="helical") R0 > 0 || error("make_helical: R0 must be > 0 (got $R0)") @@ -394,6 +509,10 @@ function make_helical(; R0::Real, a::Real, m::Int, n::Int, n_coils >= 1 || error("make_helical: n_coils must be >= 1 (got $n_coils)") 0.0 <= gap_fraction < 1.0 || error("make_helical: gap_fraction must be in [0, 1) (got $gap_fraction)") + # User-facing poloidal extent is in degrees; the internal winding math works in radians. + theta_lo = deg2rad(theta_lo) + theta_hi = deg2rad(theta_hi) + pitch = m / n rr = a + offset surf_R(θ) = R0 + rr * cos(θ) @@ -812,15 +931,34 @@ analytic generators (`pf_hoop`/`window_pane`/`helical`) or a geometry file (`.h5` → [`read_coil_h5`](@ref), else `.dat` → [`read_coil_dat`](@ref)). Currents and shifts/tilts are applied by the caller, so all sources share the same downstream path. """ -function _build_raw_coil_set(cfg::CoilConfig, sc::CoilSetConfig) +function _build_raw_coil_set(cfg::CoilConfig, sc::CoilSetConfig; equil=nothing) if sc.source == "pf_hoop" kw = sc.nsec_gen > 0 ? (; nsec=sc.nsec_gen) : (;) return make_pf_hoop(; radius=sc.radius, height=sc.height, name=isempty(sc.name) ? "pf_hoop" : sc.name, kw...) elseif sc.source == "window_pane" - return make_window_pane(; ncoil=sc.ncoil_gen, rz_corners=sc.rz_corners, - gap_fraction=sc.gap_fraction, phi0=sc.phi0, - name=isempty(sc.name) ? "window_pane" : sc.name) + has_corners = !isempty(sc.rz_corners) + has_standoff = !isnan(sc.standoff) && !isnan(sc.poloidal_angle) + if has_corners && has_standoff + error("window_pane: provide EITHER rz_corners (corner mode) OR " * + "standoff+poloidal_angle (standoff mode), not both") + elseif has_standoff + equil === nothing && + error("window_pane standoff mode (standoff/poloidal_angle) requires an equilibrium; " * + "pass `equil` to load_coil_sets, or use rz_corners for corner mode") + return make_window_pane_standoff(equil; standoff=sc.standoff, + poloidal_angle=sc.poloidal_angle, poloidal_length=sc.poloidal_length, + poloidal_tilt=sc.poloidal_tilt, ncoil=sc.ncoil_gen, + gap_fraction=sc.gap_fraction, phi0=sc.phi0, + name=isempty(sc.name) ? "window_pane" : sc.name) + elseif has_corners + return make_window_pane(; ncoil=sc.ncoil_gen, rz_corners=sc.rz_corners, + gap_fraction=sc.gap_fraction, phi0=sc.phi0, + name=isempty(sc.name) ? "window_pane" : sc.name) + else + error("window_pane: supply rz_corners (corner mode) or " * + "standoff+poloidal_angle (standoff mode)") + end elseif sc.source == "helical" kw = sc.nsec_gen > 0 ? (; npts=sc.nsec_gen) : (;) return make_helical(; R0=sc.R0, a=sc.a, m=sc.m_hel, n=sc.n_hel, @@ -844,18 +982,19 @@ function _build_raw_coil_set(cfg::CoilConfig, sc::CoilSetConfig) end """ - load_coil_sets(cfg::CoilConfig, n_tilt::Int) -> Vector{CoilSet} + load_coil_sets(cfg::CoilConfig, n_tilt::Int; equil=nothing) -> Vector{CoilSet} Build all coil sets from config (file or analytic source), apply currents and shifts/tilts, and return ready-to-use coil data. `n_tilt` is the toroidal mode number -for modulated perturbations (typically the run's n). +for modulated perturbations (typically the run's n). `equil` is required only when a +`window_pane` set uses standoff placement (it locates the surface point and normal). """ -function load_coil_sets(cfg::CoilConfig, n_tilt::Int) +function load_coil_sets(cfg::CoilConfig, n_tilt::Int; equil=nothing) isempty(cfg.coil_sets) && error("No coil sets specified in [ForcingTerms] configuration") coil_sets = CoilSet[] for set_cfg in cfg.coil_sets - cs_raw = _build_raw_coil_set(cfg, set_cfg) + cs_raw = _build_raw_coil_set(cfg, set_cfg; equil=equil) # Set currents (pad or truncate to ncoil) ncoil = cs_raw.ncoil @@ -883,5 +1022,6 @@ end export CoilSet, CoilSetConfig, CoilConfig export read_coil_dat, apply_transforms, load_coil_sets export make_pf_hoop, make_window_pane, make_helical +export make_window_pane_standoff, surface_point_and_normal export read_coil_h5, write_coil_h5, write_coil_dat, save_coils_to_h5, load_coils_from_h5_group! export convert_coil_dat_to_h5, convert_coil_h5_to_dat diff --git a/src/PerturbedEquilibrium/PerturbedEquilibrium.jl b/src/PerturbedEquilibrium/PerturbedEquilibrium.jl index c514a5115..5f1fe83b5 100644 --- a/src/PerturbedEquilibrium/PerturbedEquilibrium.jl +++ b/src/PerturbedEquilibrium/PerturbedEquilibrium.jl @@ -90,7 +90,7 @@ function compute_perturbed_equilibrium( # when present; otherwise build it from the TOML coil-set config. Either # way, retain it on `intr.coil_sets` for the rerun snapshot writer. coil_sets = isempty(intr.coil_sets) ? - ForcingTerms.load_coil_sets(cfg, ffs_intr.nlow) : intr.coil_sets + ForcingTerms.load_coil_sets(cfg, ffs_intr.nlow; equil=equil) : intr.coil_sets intr.coil_sets = coil_sets for n in ffs_intr.nlow:ffs_intr.nhigh modes_n = ForcingMode[] diff --git a/test/runtests_coils.jl b/test/runtests_coils.jl index 95ac91929..1204582c4 100644 --- a/test/runtests_coils.jl +++ b/test/runtests_coils.jl @@ -369,9 +369,9 @@ end rminor = sqrt.((Rcyl .- R0) .^ 2 .+ cs.z .^ 2) @test all(isapprox.(rminor, a; atol=1e-9)) - # Partial poloidal range: closed loop with offset + # Partial poloidal range: closed loop with offset (theta in degrees) cp = ForcingTerms.make_helical(; R0=R0, a=a, m=3, n=1, n_coils=n_coils, - theta_lo=-0.4, theta_hi=0.4, offset=0.05) + theta_lo=-25.0, theta_hi=25.0, offset=0.05) for j in 1:n_coils @test cp.x[j, 1, 1] ≈ cp.x[j, 1, end] atol = 1e-9 @test cp.z[j, 1, 1] ≈ cp.z[j, 1, end] atol = 1e-9 @@ -380,6 +380,49 @@ end @test_throws ErrorException ForcingTerms.make_helical(; R0=R0, a=a, m=2, n=0, n_coils=2) end +@testset "Analytic coils: window_pane standoff" begin + equil_dir = joinpath(@__DIR__, "..", "examples", "Solovev_ideal_example") + inputs = TOML.parsefile(joinpath(equil_dir, "gpec.toml")) + equil = Equilibrium.setup_equilibrium(Equilibrium.EquilibriumConfig(inputs["Equilibrium"], equil_dir)) + + # surface_point_and_normal: outboard midplane (poloidal_angle = 0) + R0, Z0, nR0, nZ0 = ForcingTerms.surface_point_and_normal(equil, 0.0) + @test isapprox(Z0, equil.zo; atol=1e-3) + @test R0 > equil.ro + @test isapprox(hypot(nR0, nZ0), 1.0; atol=1e-9) # unit normal + @test nR0 > 0 && isapprox(nZ0, 0.0; atol=1e-3) # points outward in +R + + # Top of the surface (poloidal_angle = 90°): normal points up + _, Ztop, nRtop, nZtop = ForcingTerms.surface_point_and_normal(equil, deg2rad(90.0)) + @test Ztop > equil.zo + @test nZtop > 0 + + # make_window_pane_standoff: frame center sits ~standoff outside the surface + standoff = 0.2 + cs = ForcingTerms.make_window_pane_standoff(equil; standoff=standoff, poloidal_angle=0.0, + poloidal_length=0.6, ncoil=2) + @test cs.ncoil == 2 && cs.s == 1 + # Centroid of the first frame, in (R, Z) + Rc = mean(sqrt.(cs.x[1, 1, :] .^ 2 .+ cs.y[1, 1, :] .^ 2)) + Zc = mean(cs.z[1, 1, :]) + @test isapprox(Rc, R0 + standoff; atol=0.05) + @test isapprox(Zc, Z0; atol=0.05) + + # With poloidal_tilt=0 at the outboard midplane the legs are ~vertical: corners differ in Z + cs1 = ForcingTerms.make_window_pane_standoff(equil; standoff=standoff, poloidal_angle=0.0, + poloidal_length=0.6, ncoil=1) + Zspan = maximum(cs1.z[1, 1, :]) - minimum(cs1.z[1, 1, :]) + Rspan = maximum(sqrt.(cs1.x[1, 1, :] .^ 2 .+ cs1.y[1, 1, :] .^ 2)) - + minimum(sqrt.(cs1.x[1, 1, :] .^ 2 .+ cs1.y[1, 1, :] .^ 2)) + @test Zspan > Rspan + + # Winding convention: the first poloidal leg (points 1:np_pol, the c1->c2 leg) runs + # lower-Z -> higher-Z, matching make_window_pane's c1->c2 ordering, so +current -> +b_n_x + # near the coil (same sense as the corner-built window pane). + np_pol = 20 # make_window_pane default + @test cs1.z[1, 1, np_pol] > cs1.z[1, 1, 1] +end + # --------------------------------------------------------------------------- @testset "Coil HDF5: round-trip vs .dat" begin cs0 = ForcingTerms.read_coil_dat(D3D_IL) @@ -460,6 +503,24 @@ end @test_throws ErrorException ForcingTerms.load_coil_sets( ForcingTerms.CoilConfig(; coil_sets=[ForcingTerms.CoilSetConfig(; source="bogus")]), 1) + + # window_pane standoff mode requires an equilibrium + cfg_standoff = ForcingTerms.CoilConfig(; + coil_sets=[ + ForcingTerms.CoilSetConfig(; source="window_pane", ncoil_gen=2, + standoff=0.2, poloidal_angle=0.0, poloidal_length=0.6, currents=[1.0, -1.0]) + ] + ) + @test_throws ErrorException ForcingTerms.load_coil_sets(cfg_standoff, 1) + + # Supplying both rz_corners and standoff is ambiguous + cfg_both = ForcingTerms.CoilConfig(; + coil_sets=[ + ForcingTerms.CoilSetConfig(; source="window_pane", ncoil_gen=2, + rz_corners=[[2.2, -0.5], [2.2, 0.5]], standoff=0.2, poloidal_angle=0.0) + ] + ) + @test_throws ErrorException ForcingTerms.load_coil_sets(cfg_both, 1) end @testset "Coil HDF5 group: save/load round-trip" begin From b664e4fdbe33f1af3c0fc6b8c023fca85481b663 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Thu, 11 Jun 2026 23:18:33 -0400 Subject: [PATCH 035/135] =?UTF-8?q?PERTURBED=20EQUILIBRIUM=20-=20REFACTOR?= =?UTF-8?q?=20-=20Operate=20in=20field=20space=20(b,=20b=CC=83,=20b=CC=84)?= =?UTF-8?q?,=20drop=20flux=20from=20outputs?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Eliminate poloidal flux Φ (weber) from the control-surface vocabulary and HDF5 output, operating instead in the three Pharr (2026) field representations (all tesla): bare b, root-area-weighted b̃ (coordinate-invariant), area-weighted b̄. Flux is recovered, only if a user supplies/requests it, as the scalar product Φ = A·b̄ — it is never stored. - Equilibrium/CoordinateInvariant.jl: replace the flux operator control_surface_rootareafield_to_flux with the field-translation operators rootarea_to_area_weight (Σ/√A, b̃→b̄) and area_to_rootarea_weight (√A·Σ⁻¹, b̄→b̃). - ForceFreeStates/RootAreaWeighted.jl: factor the surface area out of the energy operator. The operator is now the pure √weight Σ and the energy is dW = c·b̃†·W_t·b̃ with the explicit scalar c = jarea. Net-zero (verified): FFS et/ep/ev unchanged to within-ULP. - PerturbedEquilibrium: store the b̃ response matrices unchanged (b̄ is not coordinate-invariant); store the b̃→b̄ operator + scalar surface_area as recovery aids (replacing the flux operator). Output forcing AND response control-surface spectra in b, b̃, b̄. SingularCoupling C-conform and the scalar energies/torque are bit-identical (the latter kept in the well-conditioned flux basis). - docs/field_conventions.md, tests, benchmark updated; benchmark reconstructs Φ = A·b̄ for the Fortran Phi_x/Phi_tot comparison. Regression diiid_n1 + solovev_n1 (develop vs local): all tracked quantities OK — PE energies/torque 0.0e+00, FFS energies within-ULP, every stability quantity identical. Only the (untracked) stored operator and the new b/b̃/b̄ spectra change. runtests_coordinate_invariant: 16/16. Co-Authored-By: Claude Opus 4.8 (1M context) --- benchmarks/benchmark_against_fortran_run.jl | 9 +- docs/src/field_conventions.md | 36 ++++++-- src/Equilibrium/CoordinateInvariant.jl | 66 +++++++++----- src/Equilibrium/Equilibrium.jl | 2 +- src/ForceFreeStates/RootAreaWeighted.jl | 87 +++++++++--------- .../PerturbedEquilibriumStructs.jl | 49 +++++++---- src/PerturbedEquilibrium/Response.jl | 59 ++++++++----- src/PerturbedEquilibrium/ResponseMatrices.jl | 74 +++++++++------- src/PerturbedEquilibrium/SingularCoupling.jl | 21 +++-- src/PerturbedEquilibrium/Utils.jl | 34 ++++--- test/runtests_coordinate_invariant.jl | 88 +++++++++++++------ 11 files changed, 331 insertions(+), 194 deletions(-) diff --git a/benchmarks/benchmark_against_fortran_run.jl b/benchmarks/benchmark_against_fortran_run.jl index a6252214e..4af6e58eb 100644 --- a/benchmarks/benchmark_against_fortran_run.jl +++ b/benchmarks/benchmark_against_fortran_run.jl @@ -334,8 +334,13 @@ function load_julia_outputs(h5_path::String) julia["delta_prime"] = haskey(f, "$sc/delta_prime") ? read(f, "$sc/delta_prime") : ComplexF64[] pe = "perturbed_equilibrium" - julia["forcing_vec"] = haskey(f, "$pe/forcing_vec") ? read(f, "$pe/forcing_vec") : ComplexF64[] - julia["response_vec"] = haskey(f, "$pe/response_vec") ? read(f, "$pe/response_vec") : ComplexF64[] + # GPEC stores the control-surface spectra as fields (tesla), not flux. Reconstruct the + # poloidal flux for the Fortran Phi_x/Phi_tot comparison as Φ = A·b̄ (area-weighted field). + A_surf = haskey(f, "$pe/response_matrices/surface_area") ? read(f, "$pe/response_matrices/surface_area") : 1.0 + fb_area = haskey(f, "$pe/forcing_b_area") ? read(f, "$pe/forcing_b_area") : ComplexF64[] + rb_area = haskey(f, "$pe/response_b_area") ? read(f, "$pe/response_b_area") : ComplexF64[] + julia["forcing_vec"] = isempty(fb_area) ? ComplexF64[] : A_surf .* fb_area # Φ_x = A·b̄_x + julia["response_vec"] = isempty(rb_area) ? ComplexF64[] : A_surf .* rb_area # Φ_tot = A·b̄_tot julia["b_n"] = haskey(f, "$pe/response/b_n") ? read(f, "$pe/response/b_n") : Matrix{ComplexF64}(undef, 0, 0) julia["Jbgradpsi"] = haskey(f, "$pe/response/b_psi_area_weighted") ? read(f, "$pe/response/b_psi_area_weighted") : Matrix{ComplexF64}(undef, 0, 0) julia["xi_psi"] = haskey(f, "$pe/response/xi_psi") ? read(f, "$pe/response/xi_psi") : Matrix{ComplexF64}(undef, 0, 0) diff --git a/docs/src/field_conventions.md b/docs/src/field_conventions.md index 601153034..43502b424 100644 --- a/docs/src/field_conventions.md +++ b/docs/src/field_conventions.md @@ -37,21 +37,45 @@ the resonant coupling matrix) are coordinate-invariant. The **full-area weightin ``\bar b`` is coordinate-invariant for the pitch-resonant ``m = nq`` harmonic on a rational surface — the **resonant area-weighted field** ``\bar b^{\,r} = \Phi^r/A^r``. +GPEC operates and outputs **only in these field representations — poloidal flux ``\Phi`` (weber) +is never stored.** Flux appears, briefly, only internally when a user supplies flux-valued forcing, +and is recovered on demand as the scalar product ``\Phi = A\,\bar b``. + +## Translation operators + +With ``\Sigma`` ≡ `sqrtamat` (the mode-space ``\sqrt{}``weight convolution) and the scalar surface +area ``A`` ≡ `jarea`, the three fields are related by (`Equilibrium/CoordinateInvariant.jl`): + +```math +\tilde b = \Sigma\, b, \qquad +\bar b = (\Sigma/\sqrt{A})\,\tilde b, \qquad +\Phi = A\,\bar b = \Sigma\sqrt{A}\;\tilde b . +``` + +- **`rootarea_to_area_weight`** ``= \Sigma/\sqrt{A}`` maps ``\tilde b \to \bar b``. +- **`area_to_rootarea_weight`** ``= \sqrt{A}\,\Sigma^{-1}`` is its inverse (``\bar b \to \tilde b``). + +The internal flux-conform operator is just ``R = \Sigma\sqrt{A} = `` `rootarea_to_area_weight` ``\cdot A``. + ## Where each appears in GPEC output +- **`forcing_b` / `forcing_b_root_area` / `forcing_b_area`** (and the `response_*` triplet) — the + control-surface forcing and response spectra in the bare (``b``), root-area-weighted (``\tilde b``) + and area-weighted (``\bar b``) representations, under `perturbed_equilibrium/`. - **`b_n`** — the bare normal field ``\mathbf{b}\cdot\hat{\mathbf n}`` (and the area-weighted radial field `b_psi_area_weighted`), under `perturbed_equilibrium/response/`. - **`resonant_area_weighted_field`** / **`C_resonant_area_weighted_field`** — the resonant - area-weighted field ``\bar b^{\,r}`` and its coupling matrix, under + area-weighted field ``\bar b^{\,r} = \Phi^r/A^r`` and its coupling matrix, under `perturbed_equilibrium/singular_coupling/`. The sibling `penetrated_area_weighted_field` follows the same convention. - **Root-area-weighted (``\tilde b``) space** — the control-surface response matrices (`permeability`, `reluctance`, `plasma_inductance`, `surface_inductance`) are stored in - this coordinate-invariant space under `perturbed_equilibrium/response_matrices/`; the - `rootarea_field_to_flux_operator` recovers the flux-space forms. The - coordinate-invariant ideal-MHD energies written by the stability stage - (`FreeBoundaryStability/eigenmode_energies`) are likewise obtained through the - root-area-weighted transform. + this coordinate-invariant space under `perturbed_equilibrium/response_matrices/`. The stored + `rootarea_to_area_weight_operator` ``S`` recovers the area-weighted field forms + (``L_{\bar b} = S\,\tilde L\,S^\dagger``) and the scalar `surface_area` ``A`` recovers flux + (``\Phi = A\,\bar b``). The coordinate-invariant ideal-MHD energies written by the stability + stage (`FreeBoundaryStability/eigenmode_energies`) are the ``\tilde b`` quadratic form scaled by + the scalar ``c = A``: ``\mathrm{d}W = c\,\tilde b^\dagger W_t\,\tilde b``. ## See also diff --git a/src/Equilibrium/CoordinateInvariant.jl b/src/Equilibrium/CoordinateInvariant.jl index 8d61c5e65..350351c4b 100644 --- a/src/Equilibrium/CoordinateInvariant.jl +++ b/src/Equilibrium/CoordinateInvariant.jl @@ -3,18 +3,23 @@ Coordinate-invariant (root-area-weighted field) flux-surface operators. These building blocks implement the √area weighting of Pharr (2026), "Coordinate-invariant flux-surface Fourier analysis in tokamaks". They are the -single source of truth for the map between a flux-surface field component and its -root-area-weighted (coordinate-invariant) field representation, shared by the -ForceFreeStates and PerturbedEquilibrium modules. +single source of truth for translating a flux-surface field component between the +three Pharr field representations (all in tesla), shared by the ForceFreeStates and +PerturbedEquilibrium modules: -The central operator is + - `b` bare / normal field (Fourier weight W = 1) + - `b̃` root-area-weighted field (W = √(J|∇ψ|)) — the coordinate-invariant field + - `b̄` area-weighted field (W = J|∇ψ|) - rootareafield_to_flux = sqrtamat · √jarea +With `Σ ≡ sqrtamat` (the mpert×mpert √weight convolution) and the scalar surface area +`A ≡ jarea = ∫ J|∇ψ| dθ`, the mode-space vectors are related by -which maps a root-area-weighted field `b̃` to the coordinate flux harmonics `Φ`: -`Φ = rootareafield_to_flux · b̃` (so `b̃ = rootareafield_to_flux⁻¹ · Φ`). The singular values of any operator -expressed in the `b̃` basis are independent of the straight-field-line -(working) coordinate. + b̃ = Σ·b, b̄ = (Σ/√A)·b̃, Φ = A·b̄ = Σ·√A·b̃ (poloidal flux, weber) + +The √-weight (`b̃`) basis is the one in which an operator's singular values / spectra are +independent of the straight-field-line (working) coordinate; `b` and `b̄` are not +coordinate-invariant and are provided only as field/flux recovery views. Poloidal flux is +recovered, when ever needed, as the scalar product `Φ = A·b̄` — it is never stored. See `scripts/test_power_norm_invariance.jl` for the numerical invariance proof of the underlying √weight identity and angle map. @@ -92,25 +97,40 @@ function compute_sqrtamat( end """ - control_surface_rootareafield_to_flux(equil, psi, ft) -> Matrix{ComplexF64} - -Build the root-area-weighted field → flux operator `rootareafield_to_flux = sqrtamat · √jarea` at the flux -surface `psi`, where `jarea = ∫ J|∇ψ| dθ` is the scalar flux-surface area. - -`rootareafield_to_flux` maps a root-area-weighted field `b̃` to the coordinate flux harmonics `Φ`: -`Φ = rootareafield_to_flux · b̃`. To express a flux-space operator/generator in the coordinate-invariant -`b̃` basis (and back) use: - - operator `Ã = rootareafield_to_flux⁻¹ · A · rootareafield_to_flux` (e.g. permeability `Φ_tot = A·Φ_x`) - - generator `G̃ = rootareafield_to_flux⁻¹ · G · rootareafield_to_flux⁻†` (e.g. inductance, energy = Φ†·G⁻¹·Φ) - - row map `C̃ = C · rootareafield_to_flux` (e.g. coupling, scalar = C·Φ_x) -The singular values / spectrum in the `b̃` basis are coordinate-invariant. + rootarea_to_area_weight(equil, psi, ft) -> Matrix{ComplexF64} + +Build the root-area-weighted → area-weighted field operator `Σ/√A = sqrtamat ./ √jarea` at the +flux surface `psi`, where `jarea = ∫ J|∇ψ| dθ` is the scalar flux-surface area. It maps the +coordinate-invariant root-area-weighted field `b̃` to the area-weighted field `b̄`: `b̄ = (Σ/√A)·b̃` +(both in tesla). Poloidal flux is the scalar product `Φ = A·b̄` (so `Φ = Σ·√A·b̃`), recovered only +when a user supplies/requests flux — it is never stored. + +The √-weight (`b̃`) basis is the one in which operator singular values / spectra are independent of +the straight-field-line (working) coordinate — see `field_space_response_matrices`. `b̄` is *not* +coordinate-invariant; it is only a field/flux recovery view. [Pharr 2026] +""" +function rootarea_to_area_weight( + equil::PlasmaEquilibrium, + psi::Float64, + ft::Utilities.FourierTransforms.FourierTransform +) + sqrtamat = compute_sqrtamat(equil, psi, ft) + jarea = flux_surface_area(equil, psi, ft.mtheta) + return sqrtamat ./ sqrt(jarea) +end + +""" + area_to_rootarea_weight(equil, psi, ft) -> Matrix{ComplexF64} + +Inverse of [`rootarea_to_area_weight`](@ref): the area-weighted → root-area-weighted field operator +`√A·Σ⁻¹ = √jarea · inv(sqrtamat)`, mapping `b̄ → b̃` (`b̃ = √A·Σ⁻¹·b̄`). [Pharr 2026] """ -function control_surface_rootareafield_to_flux( +function area_to_rootarea_weight( equil::PlasmaEquilibrium, psi::Float64, ft::Utilities.FourierTransforms.FourierTransform ) sqrtamat = compute_sqrtamat(equil, psi, ft) jarea = flux_surface_area(equil, psi, ft.mtheta) - return sqrtamat .* sqrt(jarea) + return sqrt(jarea) .* inv(sqrtamat) end diff --git a/src/Equilibrium/Equilibrium.jl b/src/Equilibrium/Equilibrium.jl index 7483dd2e6..7c25f413e 100644 --- a/src/Equilibrium/Equilibrium.jl +++ b/src/Equilibrium/Equilibrium.jl @@ -28,7 +28,7 @@ export setup_equilibrium, EquilibriumConfig, PlasmaEquilibrium, EquilibriumParam ProfileSplines, GeometryProfileSplines, compute_geometry_profiles, KineticProfileSplines, load_kinetic_profiles export flux_surface_metric, flux_surface_area -export compute_sqrt_jac_delpsi, compute_sqrtamat, control_surface_rootareafield_to_flux +export compute_sqrt_jac_delpsi, compute_sqrtamat, rootarea_to_area_weight, area_to_rootarea_weight # --- Constants --- const mu0 = 4π * 1e-7 diff --git a/src/ForceFreeStates/RootAreaWeighted.jl b/src/ForceFreeStates/RootAreaWeighted.jl index e7c370f94..bbd451539 100644 --- a/src/ForceFreeStates/RootAreaWeighted.jl +++ b/src/ForceFreeStates/RootAreaWeighted.jl @@ -1,58 +1,57 @@ """ -Root-area-weighted flux eigenvalue computation for the FFS edge scan. +Root-area-weighted field eigenvalue computation for the FFS edge scan. -Transforms the energy matrix W from ξ-space into root-area-weighted flux Φ-space and -returns the eigenvalues of `W_Φ = M†·W·M`. The **eigenvalues** (energies) are -coordinate-invariant: energy is a physically meaningful scalar and does not depend -on the choice of straight-field-line coordinate. +Transforms the energy matrix W from ξ-space into the coordinate-invariant root-area-weighted +field (b̃) space and returns the eigenvalues of the scaled quadratic form `c·W_t` (energies). +The **eigenvalues** (energies) are coordinate-invariant: energy is a physically meaningful +scalar and does not depend on the choice of straight-field-line coordinate. - dW = ξ†·W·ξ = Φ†·M†·W·M·Φ + dW = ξ†·W·ξ = c·b̃†·(M†·W·M)·b̃ = c·b̃†·W_t·b̃ -Transformation chain: - - T = diag(i·2π·χ₁·singfac) converts ξ → flux (χ₁ = 2π·ψ₀, singfac = m − n·q). - - rootareafield_to_flux = sqrtamat·√jarea converts the root-area-weighted field → flux. - - M = T⁻¹·rootareafield_to_flux maps Φ → ξ. +Transformation chain (no poloidal flux Φ appears — it would only be the scalar product `Φ = A·b̄`): + - T = diag(i·2π·χ₁·singfac) converts ξ → flux-like amplitude (χ₁ = 2π·ψ₀, singfac = m − n·q). + - Σ = sqrtamat is the √weight (the bare → root-area-weighted field map). + - M = T⁻¹·Σ maps the root-area-weighted field b̃ → ξ. + - c = jarea = ∫ J|∇ψ| dθ is the scalar surface area carrying the energy's area normalization. What is **NOT** invariant across Jacobian choices (see `scripts/test_power_norm_invariance.jl` for numerical proof): - ξ itself (W is Jacobian-dependent). - - Φ itself — T depends on the m-labelling of the chosen Jacobian, so - ‖Φ‖ = ‖M⁻¹ξ‖ drifts with Jacobian. - - The θ-space field reconstructed from Φ. + - The θ-space field reconstructed from the eigenvector. What **IS** invariant (verified numerically in the test script, within the area-integral precision floor ~1e-6): - Flux-surface area A = ∫ J|∇ψ| dθ. - The √weight operator identity ‖sqrtamat·b_fft‖² = N²·∫|b|²·J|∇ψ| dθ. - The angle-map convmat (b_jac2 = convmat·b_jac1) to machine precision. - - The eigenspectrum of `W_Φ`. + - The eigenspectrum of `c·W_t`. """ -# The √weight building blocks `compute_sqrt_jac_delpsi`, `compute_sqrtamat`, and the -# `control_surface_rootareafield_to_flux` operator now live in `Equilibrium/CoordinateInvariant.jl` so the -# ForceFreeStates and PerturbedEquilibrium modules share one coordinate-invariant definition. +# The √weight building blocks `compute_sqrt_jac_delpsi`, `compute_sqrtamat`, and the field-translation +# operators now live in `Equilibrium/CoordinateInvariant.jl` so the ForceFreeStates and +# PerturbedEquilibrium modules share one coordinate-invariant definition. """ compute_rootarea_eigenvalues(wt, wp, wv, sqrtamat, jarea, equil, psi, intr; all_eigenvalues=false) -Transform W from ξ-space to root-area-weighted flux Φ-space and eigendecompose. +Transform W from ξ-space to the root-area-weighted field (b̃) space and eigendecompose. The transformation chain: - 1. T = diag(i·2π·χ₁·singfac) converts ξ → flux (singfac = m − n·q). - 2. rootareafield_to_flux = sqrtamat·√jarea converts the root-area-weighted field → flux. - 3. M = T⁻¹·rootareafield_to_flux maps Φ → ξ (root-area-weighted to displacement). - 4. W_Φ = M†·W·M = rootareafield_to_flux†·T⁻†·W·T⁻¹·rootareafield_to_flux. + 1. T = diag(i·2π·χ₁·singfac) converts ξ → flux-like amplitude (singfac = m − n·q). + 2. Σ = sqrtamat is the √weight (bare → root-area-weighted field). + 3. M = T⁻¹·Σ maps the root-area-weighted field b̃ → ξ. + 4. Energy matrix = c·W_t = c·M†·W·M with the scalar c = jarea (the surface area). -Only the eigenspectrum of W_Φ is physically invariant across Jacobian choices — +Only the eigenspectrum of `c·W_t` is physically invariant across Jacobian choices — it is the coordinate-independent energy. The eigenvectors in this basis are normalized under Julia's `eigen` (‖v‖₂ = 1) rather than the ∫|b|²dA = 1 -convention, so `v` should not be reused as a physical Φ-space mode shape — here +convention, so `v` should not be reused as a physical b̃-space mode shape — here it is only used to split λ = v†Wt v into ⟨v,Wp v⟩ + ⟨v,Wv v⟩, both of which are spectrally invariant because Wp + Wv = Wt. -Returns the standard eigenvalues of W_Φ sorted ascending (most negative/unstable +Returns the standard eigenvalues of `c·W_t` sorted ascending (most negative/unstable first), matching the ξ-space convention in `free_run!` and `free_compute_total`. -Also returns `rootA_vacuum_eigenvalue = max(0, λ_min(Hermitian(wv_Φ)))` — the Φ-space +Also returns `rootA_vacuum_eigenvalue = max(0, λ_min(Hermitian(c·wv_t)))` — the b̃-space counterpart of the ξ-space `vacuum_eigenvalue` diagnostic. Returns NaN when any singfac ≈ 0 (rational surface crossing makes T singular). """ @@ -90,37 +89,37 @@ function compute_rootarea_eigenvalues( end end - # T = diag(i·2π·chi1·singfac): ξ → flux + # T = diag(i·2π·chi1·singfac): ξ → flux-like amplitude T_diag_inv = Vector{ComplexF64}(undef, Npert) for i in 1:Npert T_diag_inv[i] = 1.0 / (im * 2π * chi1 * singfac[i]) end - # rootareafield_to_flux = sqrtamat * sqrt(jarea): root-area-weighted field → flux - # For multi-n, expand mpert×mpert sqrtamat to Npert×Npert block-diagonal - rootareafield_to_flux_block = sqrtamat .* sqrt(jarea) - if npert == 1 - rootareafield_to_flux_full = rootareafield_to_flux_block - else - rootareafield_to_flux_full = zeros(ComplexF64, Npert, Npert) + # √weight operator Σ = sqrtamat maps the bare field → root-area-weighted field b̃. + # For multi-n, expand the mpert×mpert block to Npert×Npert block-diagonal. + sqrtamat_full = sqrtamat + if npert != 1 + sqrtamat_full = zeros(ComplexF64, Npert, Npert) for in in 1:npert r = ((in - 1) * mpert + 1):(in * mpert) - rootareafield_to_flux_full[r, r] .= rootareafield_to_flux_block + sqrtamat_full[r, r] .= sqrtamat end end - # M = diag(T_inv) · rootareafield_to_flux: row-scale rootareafield_to_flux by T_inv (maps Φ → ξ) - M = similar(rootareafield_to_flux_full) + # M = diag(T_inv) · Σ: row-scale Σ by T_inv (maps the root-area-weighted field b̃ → ξ) + M = similar(sqrtamat_full) for i in 1:Npert - M[i, :] .= T_diag_inv[i] .* rootareafield_to_flux_full[i, :] + M[i, :] .= T_diag_inv[i] .* sqrtamat_full[i, :] end - # Transform energy matrices: W_Φ = M† · W · M - wt_rootA = M' * wt * M - wp_rootA = M' * wp * M - wv_rootA = M' * wv * M + # Energy is the b̃ quadratic form scaled by the scalar surface area c = jarea: + # dW = c·b̃†·W_t·b̃, W_t = M†·W·M, c = jarea [Pharr 2026, Eq. for coordinate-invariant energy] + # Folding the scalar c here keeps the eigenspectrum (the coordinate-invariant energy) physical [J]. + wt_rootA = jarea .* (M' * wt * M) + wp_rootA = jarea .* (M' * wp * M) + wv_rootA = jarea .* (M' * wv * M) - # Smallest eigenvalue of the vacuum matrix alone in Φ-space, clamped to zero. + # Smallest eigenvalue of the vacuum matrix alone in b̃-space, clamped to zero. # wv_rootA should be PSD by congruence of the PSD ξ-space wv; numerical noise # can make the smallest eigenvalue slightly negative. rootA_vacuum_eigenvalue = real(max(0.0, minimum(real.(eigvals(Hermitian(wv_rootA)))))) @@ -152,7 +151,7 @@ function compute_rootarea_eigenvalues( # Phase convention: rotate each column so its largest-magnitude entry is real-positive # (matches the ξ-space convention in free_run!). Magnitudes are preserved since the - # eigenvectors come from Julia's `eigen` with ‖v‖₂ = 1, the natural Φ-space norm. + # eigenvectors come from Julia's `eigen` with ‖v‖₂ = 1, the natural b̃-space norm. for isol in 1:Npert imax = argmax(abs.(@view rootA_eigenvectors[:, isol])) phase = abs(rootA_eigenvectors[imax, isol]) / rootA_eigenvectors[imax, isol] diff --git a/src/PerturbedEquilibrium/PerturbedEquilibriumStructs.jl b/src/PerturbedEquilibrium/PerturbedEquilibriumStructs.jl index 22a067264..9474abf0f 100644 --- a/src/PerturbedEquilibrium/PerturbedEquilibriumStructs.jl +++ b/src/PerturbedEquilibrium/PerturbedEquilibriumStructs.jl @@ -102,17 +102,27 @@ Diagnostics [n_rational]: Metadata [n_rational] — identifies each (surface, n) row: - `rational_psi`, `rational_q`, `rational_m_res`, `rational_n`, `rational_surface_idx` +Control-surface forcing/response spectra [numpert_total], in the three Pharr (2026) field +representations (all tesla; no flux/weber is stored): + - `forcing_b`/`response_b` - bare normal field b (Σ⁻¹·b̃) + - `forcing_b_rootarea`/`response_b_rootarea` - root-area-weighted field b̃ (coordinate-invariant) + - `forcing_b_area`/`response_b_area` - area-weighted field b̄ (= S·b̃; flux is Φ = A·b̄) + Control surface matrices [numpert_total × numpert_total], stored in the coordinate-invariant -root-area-weighted field (b̃) space (issue #233 / Pharr 2026). Recover the flux-space forms with -the `control_surface_field_operator` (`rootareafield_to_flux`, Φ = rootareafield_to_flux·b̃): e.g. `P_flux = rootareafield_to_flux·P̃·rootareafield_to_flux⁻¹`, -`L_flux = rootareafield_to_flux·L̃·rootareafield_to_flux†`. - - `plasma_inductance` - Λ̃ = rootareafield_to_flux⁻¹·Λ·rootareafield_to_flux⁻† (wt0-based plasma inductance, congruence) - - `surface_inductance` - L̃ = rootareafield_to_flux⁻¹·L·rootareafield_to_flux⁻† (vacuum surface inductance, congruence) - - `permeability` - P̃ = rootareafield_to_flux⁻¹·P·rootareafield_to_flux (plasma response operator P=Λ·L⁻¹, similarity) - - `reluctance` - ϱ̃ = rootareafield_to_flux†·ϱ·rootareafield_to_flux (ϱ = L⁻¹·(Λ−L)·L⁻¹, congruence) - - `control_surface_field_operator` - rootareafield_to_flux = sqrtamat·√jarea at psilim (field → flux recovery operator) - -Energies (Fortran gpout convention; Φ_x external flux, Φ_tot total flux, L/Λ inductances): +root-area-weighted field (b̃) space (issue #233 / Pharr 2026). Writing `S ≡ rootarea_to_area_weight` +(b̃→b̄) and `A ≡ surface_area`, the brief internal flux-conform operator is `R = S·A` (Φ = R·b̃). +Recover the area-weighted (b̄) forms by conforming with `S` (e.g. `L_b̄ = S·L̃·S†`); recover flux +with `Φ = A·b̄`. + - `plasma_inductance` - Λ̃ = R⁻¹·Λ·R⁻† (wt0-based plasma inductance, congruence) + - `surface_inductance` - L̃ = R⁻¹·L·R⁻† (vacuum surface inductance, congruence) + - `permeability` - P̃ = R⁻¹·P·R (plasma response operator P=Λ·L⁻¹, similarity) + - `reluctance` - ϱ̃ = R†·ϱ·R (ϱ = L⁻¹·(Λ−L)·L⁻¹, congruence) + - `rootarea_to_area_weight` - S = Σ/√A at psilim (b̃→b̄ recovery operator) + - `surface_area` - scalar A = ∫J|∇ψ|dθ at psilim (flux recovery Φ = A·b̄) + +Energies (Joules; Fortran gpout convention). Congruence-invariant scalars +(energy = Φ†·G⁻¹·Φ = b̃†·G̃⁻¹·b̃), evaluated from the brief internal flux vectors Φ_x, Φ_tot with the +well-conditioned flux-space inductances L, Λ: - `vacuum_energy` - Re( ⟨Φ_x, L⁻¹·Φ_x⟩ ) / 4 (energy to perturb the vacuum) - `surface_energy` - Re( ⟨Φ_tot, L⁻¹·Φ_tot⟩ ) / 4 (energy at the control surface) - `plasma_energy` - Re( ⟨Φ_tot, Λ⁻¹·Φ_tot⟩ ) / 4 (energy to perturb the plasma; Fortran's "total energy") @@ -153,16 +163,21 @@ Energies (Fortran gpout convention; Φ_x external flux, Φ_tot total flux, L/Λ rational_n::Vector{Int} = Int[] rational_surface_idx::Vector{Int} = Int[] - # Control surface perturbation vectors [numpert_total] - forcing_vec::Vector{ComplexF64} = ComplexF64[] # Phi_x: external forcing in eigenmode basis - response_vec::Vector{ComplexF64} = ComplexF64[] # Phi_tot = P * Phi_x: total plasma response + # Control-surface forcing/response spectra in the three Pharr field representations [numpert_total], tesla + forcing_b::Vector{ComplexF64} = ComplexF64[] # bare normal field b (forcing Φ_x) + forcing_b_rootarea::Vector{ComplexF64} = ComplexF64[] # root-area-weighted field b̃ (coordinate-invariant) + forcing_b_area::Vector{ComplexF64} = ComplexF64[] # area-weighted field b̄ + response_b::Vector{ComplexF64} = ComplexF64[] # bare normal field b (response Φ_tot = P·Φ_x) + response_b_rootarea::Vector{ComplexF64} = ComplexF64[] # root-area-weighted field b̃ + response_b_area::Vector{ComplexF64} = ComplexF64[] # area-weighted field b̄ - # Control surface matrices [numpert_total × numpert_total] + # Control surface matrices [numpert_total × numpert_total], root-area-weighted field (b̃) space plasma_inductance::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # Λ̃ (field space) surface_inductance::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # L̃ (field space) - permeability::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # P̃ = rootareafield_to_flux⁻¹·Λ·L⁻¹·rootareafield_to_flux - reluctance::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # ϱ̃ = rootareafield_to_flux†·L⁻¹·(Λ−L)·L⁻¹·rootareafield_to_flux - control_surface_field_operator::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # rootareafield_to_flux: field → flux recovery + permeability::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # P̃ = R⁻¹·Λ·L⁻¹·R + reluctance::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # ϱ̃ = R†·L⁻¹·(Λ−L)·L⁻¹·R + rootarea_to_area_weight::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # S = Σ/√A at psilim: b̃→b̄ recovery operator + surface_area::Float64 = 0.0 # scalar control-surface area A = ∫J|∇ψ|dθ (flux: Φ = A·b̄; conform R = S·A) # Energies — see the struct docstring for formulas vacuum_energy::Float64 = 0.0 diff --git a/src/PerturbedEquilibrium/Response.jl b/src/PerturbedEquilibrium/Response.jl index fd7dfe2a4..df0682256 100644 --- a/src/PerturbedEquilibrium/Response.jl +++ b/src/PerturbedEquilibrium/Response.jl @@ -56,40 +56,57 @@ function compute_plasma_response!( # Store permeability in internal state for singular coupling / field reconstruction. # These consumers operate on the physical control-surface flux Φ_x, so the internal - # copy stays in flux space; only the stored/output matrices are conformed below. + # copy stays in flux space; only the stored/output quantities are conformed to fields below. intr.plasma_response = permeability # Conform the control-surface matrices to the coordinate-invariant root-area-weighted - # field (b̃) space for output (issue #233 / Pharr 2026). The flux-space forms are - # recoverable from the stored `rootareafield_to_flux` operator (Φ = rootareafield_to_flux·b̃) — see Utils.jl output docs. - rootareafield_to_flux = build_control_surface_rootareafield_to_flux(equil, ffs_intr) - field_mats = field_space_response_matrices(plasma_inductance, surface_inductance, permeability, reluctance, rootareafield_to_flux) - state.plasma_inductance = field_mats.plasma_inductance - state.surface_inductance = field_mats.surface_inductance - state.permeability = field_mats.permeability - state.reluctance = field_mats.reluctance - state.control_surface_field_operator = rootareafield_to_flux + # field (b̃) space for output (issue #233 / Pharr 2026). Store the b̃→b̄ operator S = Σ/√A + # and the scalar surface area A so users can recover the area-weighted field (b̄ = S·b̃) or + # flux (Φ = A·b̄) — see Utils.jl output docs. + rootarea_to_area_weight, surface_area = build_control_surface_rootarea_to_area_weight(equil, ffs_intr) + field_mats = field_space_response_matrices(plasma_inductance, surface_inductance, permeability, reluctance, rootarea_to_area_weight, surface_area) + state.plasma_inductance = field_mats.plasma_inductance + state.surface_inductance = field_mats.surface_inductance + state.permeability = field_mats.permeability + state.reluctance = field_mats.reluctance + state.rootarea_to_area_weight = rootarea_to_area_weight + state.surface_area = surface_area - forcing_vector = map_forcing_to_eigenmodes(intr.forcing_modes, ffs_intr) - response_vector = compute_plasma_response_vector(permeability, forcing_vector) + # Forcing and response on the control surface. Flux Φ appears only as a brief internal bridge: + # forcing arrives as Φ_x, the field reconstruction below consumes Φ_tot, and the b̃ spectra are + # formed via the conform operator R = S·A (Φ = R·b̃). + forcing_flux = map_forcing_to_eigenmodes(intr.forcing_modes, ffs_intr) + response_flux = compute_plasma_response_vector(permeability, forcing_flux) - state.forcing_vec = forcing_vector - state.response_vec = response_vector + # Output forcing/response in the three Pharr field representations (all tesla): + # b̃ (root-area-weighted) = R⁻¹·Φ, b (bare) = Σ⁻¹·b̃, b̄ (area-weighted) = S·b̃. + flux_conform = rootarea_to_area_weight .* surface_area # R = Σ·√A (b̃ → flux) + bare_to_rootarea = rootarea_to_area_weight .* sqrt(surface_area) # Σ (bare → b̃) + forcing_b_rootarea = flux_conform \ forcing_flux + response_b_rootarea = flux_conform \ response_flux + state.forcing_b_rootarea = forcing_b_rootarea + state.response_b_rootarea = response_b_rootarea + state.forcing_b = bare_to_rootarea \ forcing_b_rootarea + state.response_b = bare_to_rootarea \ response_b_rootarea + state.forcing_b_area = rootarea_to_area_weight * forcing_b_rootarea + state.response_b_area = rootarea_to_area_weight * response_b_rootarea - # Scalar energies and torque, ported from Fortran gpout. forcing_vector and - # response_vector are Phi_x and Phi_tot in the gpeq_weight=1 basis. + # Scalar energies and torque (Joules), ported from Fortran gpout. These are congruence-invariant + # (energy = Φ†·G⁻¹·Φ = b̃†·G̃⁻¹·b̃), so they are evaluated from the brief internal flux vectors with + # the well-conditioned flux-space inductances — the b̃ form routes through inv(R⁻¹LR⁻†) and is + # needlessly ill-conditioned. The result is a physical scalar, not a stored flux quantity. L_surf_inv = inv(surface_inductance) L_plas_inv = inv(plasma_inductance) - vy = dot(forcing_vector, L_surf_inv * forcing_vector) / 4 - sy = dot(response_vector, L_surf_inv * response_vector) / 4 - py = dot(response_vector, L_plas_inv * response_vector) / 4 + vy = dot(forcing_flux, L_surf_inv * forcing_flux) / 4 + sy = dot(response_flux, L_surf_inv * response_flux) / 4 + py = dot(response_flux, L_plas_inv * response_flux) / 4 state.vacuum_energy = real(vy) state.surface_energy = real(sy) state.plasma_energy = real(py) # Fortran's "total energy" is this pengy state.toroidal_torque = -2 * nn * imag(py) xi_modes, b_modes = reconstruct_physical_fields( - response_vector, flux_matrix, ForceFreeStates_results, equil, ffs_intr, intr, + response_flux, flux_matrix, ForceFreeStates_results, equil, ffs_intr, intr, metric, ffit, ctrl ) @@ -105,6 +122,6 @@ function compute_plasma_response!( state.xi_n_modes = xi_n_modes if ctrl.verbose - @info "Response complete: $(length(intr.forcing_modes)) forcing modes, max amplitude = $(@sprintf("%.3e", maximum(abs.(response_vector))))" + @info "Response complete: $(length(intr.forcing_modes)) forcing modes, max amplitude = $(@sprintf("%.3e", maximum(abs.(response_flux))))" end end diff --git a/src/PerturbedEquilibrium/ResponseMatrices.jl b/src/PerturbedEquilibrium/ResponseMatrices.jl index 0153b7422..d929e9d33 100644 --- a/src/PerturbedEquilibrium/ResponseMatrices.jl +++ b/src/PerturbedEquilibrium/ResponseMatrices.jl @@ -299,75 +299,83 @@ function calc_permeability( end """ - build_control_surface_rootareafield_to_flux( + build_control_surface_rootarea_to_area_weight( equil::Equilibrium.PlasmaEquilibrium, ffs_intr::ForceFreeStatesInternal - )::Matrix{ComplexF64} - -Build the numpert_total × numpert_total root-area-weighted field → flux operator `rootareafield_to_flux` at the -control surface (psilim). The mpert × mpert single-n block (Equilibrium.control_surface_rootareafield_to_flux) -is repeated block-diagonally over the `npert` toroidal harmonics, matching the -numpert_total mode ordering used by the response matrices. - -`rootareafield_to_flux` maps a root-area-weighted control-surface field `b̃` to the coordinate flux harmonics -`Φ`: `Φ = rootareafield_to_flux · b̃`. It is the operator users need to recover the flux-space matrices from -the stored coordinate-invariant (field-space) ones — see `field_space_response_matrices`. -[Pharr 2026] + )::Tuple{Matrix{ComplexF64}, Float64} + +Build the numpert_total × numpert_total root-area-weighted → area-weighted field operator +`S = Σ/√A` at the control surface (psilim), and return it together with the scalar surface area +`A = jarea`. The mpert × mpert single-n block (Equilibrium.rootarea_to_area_weight) is repeated +block-diagonally over the `npert` toroidal harmonics, matching the numpert_total mode ordering used +by the response matrices. + +`S` maps a root-area-weighted control-surface field `b̃` to the area-weighted field `b̄` +(`b̄ = S·b̃`); poloidal flux is the scalar product `Φ = A·b̄` (so the b̃→flux conform operator is +`R = S·A`, used only internally). `S` and `A` are the recovery aids users need to express the stored +coordinate-invariant (b̃) matrices in the area-weighted field or recover flux — see +`field_space_response_matrices`. [Pharr 2026] """ -function build_control_surface_rootareafield_to_flux( +function build_control_surface_rootarea_to_area_weight( equil::Equilibrium.PlasmaEquilibrium, ffs_intr::ForceFreeStatesInternal -)::Matrix{ComplexF64} +)::Tuple{Matrix{ComplexF64}, Float64} mpert = ffs_intr.mpert npert = ffs_intr.npert Npert = ffs_intr.numpert_total mtheta_eq = length(equil.rzphi_ys) ft = Utilities.FourierTransforms.FourierTransform(mtheta_eq, mpert, ffs_intr.mlow) - rootareafield_to_flux_block = Equilibrium.control_surface_rootareafield_to_flux(equil, ffs_intr.psilim, ft) + S_block = Equilibrium.rootarea_to_area_weight(equil, ffs_intr.psilim, ft) + jarea = Equilibrium.flux_surface_area(equil, ffs_intr.psilim, mtheta_eq) - npert == 1 && return Matrix{ComplexF64}(rootareafield_to_flux_block) + npert == 1 && return (Matrix{ComplexF64}(S_block), jarea) - rootareafield_to_flux_full = zeros(ComplexF64, Npert, Npert) + S_full = zeros(ComplexF64, Npert, Npert) for in in 1:npert r = ((in - 1) * mpert + 1):(in * mpert) - rootareafield_to_flux_full[r, r] .= rootareafield_to_flux_block + S_full[r, r] .= S_block end - return rootareafield_to_flux_full + return (S_full, jarea) end """ field_space_response_matrices( - plasma_inductance, surface_inductance, permeability, reluctance, rootareafield_to_flux + plasma_inductance, surface_inductance, permeability, reluctance, + rootarea_to_area_weight, jarea )::NamedTuple Express the control-surface response matrices in the coordinate-invariant root-area-weighted -field (b̃) space, given the flux-space matrices and the `rootareafield_to_flux` operator (`Φ = rootareafield_to_flux·b̃`). +field (b̃) space, given the flux-space matrices, the b̃→b̄ operator `S = rootarea_to_area_weight`, +and the scalar surface area `jarea`. The brief internal flux-conform operator is `R = S·jarea` +(`Φ = R·b̃`); poloidal flux never leaves this function. The matrices fall into two algebraic classes: - **Operators** (map flux → flux): permeability `P` (Φ_tot = P·Φ_x) transforms by similarity - `P̃ = rootareafield_to_flux⁻¹·P·rootareafield_to_flux`. Its singular values are coordinate-invariant. + `P̃ = R⁻¹·P·R`. Its singular values are coordinate-invariant. - **Quadratic generators** (energy = Φ†·G⁻¹·Φ): inductances `Λ`, `L` transform by congruence - `G̃ = rootareafield_to_flux⁻¹·G·rootareafield_to_flux⁻†`; the inverse-inductance-like reluctance `ϱ` (energy = Φ†·ϱ·Φ) - transforms as `ϱ̃ = rootareafield_to_flux†·ϱ·rootareafield_to_flux`. Their spectra are coordinate-invariant. + `G̃ = R⁻¹·G·R⁻†`; the inverse-inductance-like reluctance `ϱ` (energy = Φ†·ϱ·Φ) transforms as + `ϱ̃ = R†·ϱ·R`. Their spectra are coordinate-invariant. -Writing `R ≡ rootareafield_to_flux` for brevity, these rules are mutually consistent: -`P̃ = Λ̃·L̃⁻¹ = R⁻¹·Λ·L⁻¹·R = R⁻¹·P·R`, and `ϱ̃ = L̃⁻¹·(Λ̃−L̃)·L̃⁻¹`. To recover the flux-space -forms, invert each map with the stored `R` (e.g. `P_flux = R·P̃·R⁻¹`, `L_flux = R·L̃·R†`). [Pharr 2026] +These rules are mutually consistent: `P̃ = Λ̃·L̃⁻¹ = R⁻¹·Λ·L⁻¹·R = R⁻¹·P·R`, and +`ϱ̃ = L̃⁻¹·(Λ̃−L̃)·L̃⁻¹`. To recover the area-weighted (`b̄`) forms, conform with `S` instead of `R` +(e.g. `L_b̄ = S·L̃·S†`); recover flux with the scalar `A`: `Φ = A·b̄`. [Pharr 2026] """ function field_space_response_matrices( plasma_inductance::Matrix{ComplexF64}, surface_inductance::Matrix{ComplexF64}, permeability::Matrix{ComplexF64}, reluctance::Matrix{ComplexF64}, - rootareafield_to_flux::Matrix{ComplexF64} + rootarea_to_area_weight::Matrix{ComplexF64}, + jarea::Float64 )::NamedTuple - rootareafield_to_flux_inv = inv(rootareafield_to_flux) + R = rootarea_to_area_weight .* jarea # b̃→flux conform operator Σ·√A = (Σ/√A)·A + R_inv = inv(R) return ( - plasma_inductance=rootareafield_to_flux_inv * plasma_inductance * rootareafield_to_flux_inv', - surface_inductance=rootareafield_to_flux_inv * surface_inductance * rootareafield_to_flux_inv', - permeability=rootareafield_to_flux_inv * permeability * rootareafield_to_flux, - reluctance=rootareafield_to_flux' * reluctance * rootareafield_to_flux + plasma_inductance=R_inv * plasma_inductance * R_inv', + surface_inductance=R_inv * surface_inductance * R_inv', + permeability=R_inv * permeability * R, + reluctance=R' * reluctance * R ) end diff --git a/src/PerturbedEquilibrium/SingularCoupling.jl b/src/PerturbedEquilibrium/SingularCoupling.jl index 4eeb43dd7..fd34d5f25 100644 --- a/src/PerturbedEquilibrium/SingularCoupling.jl +++ b/src/PerturbedEquilibrium/SingularCoupling.jl @@ -283,15 +283,18 @@ function compute_singular_coupling_metrics!( state.delta_prime = state.C_delta_prime * forcing_flux # Conform the stored coupling-matrix input basis to the coordinate-invariant root-area-weighted - # field (b̃) space (#233 / Pharr 2026): C̃ = C·rootareafield_to_flux, so each stored row acts on the applied - # field b̃_x (Φ_x = rootareafield_to_flux·b̃_x) and its singular values become coordinate-invariant. Done after - # the applied-vector evaluation above so those physical scalars carry no round-trip noise. - rootareafield_to_flux = build_control_surface_rootareafield_to_flux(equil, ffs_intr) - state.C_resonant_area_weighted_field = state.C_resonant_area_weighted_field * rootareafield_to_flux - state.C_resonant_current = state.C_resonant_current * rootareafield_to_flux - state.C_island_width_sq = state.C_island_width_sq * rootareafield_to_flux - state.C_penetrated_area_weighted_field = state.C_penetrated_area_weighted_field * rootareafield_to_flux - state.C_delta_prime = state.C_delta_prime * rootareafield_to_flux + # field (b̃) space (#233 / Pharr 2026): C̃ = C·R, so each stored row acts on the applied field + # b̃_x (Φ_x = R·b̃_x) and its singular values become coordinate-invariant. The conform operator + # R = S·A (Σ·√A) is the only place flux briefly appears; it is built from the b̃→b̄ operator S and + # the scalar surface area A. Done after the applied-vector evaluation above so those physical + # scalars carry no round-trip noise. + rootarea_to_area_weight, surface_area = build_control_surface_rootarea_to_area_weight(equil, ffs_intr) + flux_conform = rootarea_to_area_weight .* surface_area + state.C_resonant_area_weighted_field = state.C_resonant_area_weighted_field * flux_conform + state.C_resonant_current = state.C_resonant_current * flux_conform + state.C_island_width_sq = state.C_island_width_sq * flux_conform + state.C_penetrated_area_weighted_field = state.C_penetrated_area_weighted_field * flux_conform + state.C_delta_prime = state.C_delta_prime * flux_conform # Phase 5: Island diagnostics from applied resonant vectors compute_island_diagnostics!(state, n_rational) diff --git a/src/PerturbedEquilibrium/Utils.jl b/src/PerturbedEquilibrium/Utils.jl index 7e3ff3996..9957fe7cd 100644 --- a/src/PerturbedEquilibrium/Utils.jl +++ b/src/PerturbedEquilibrium/Utils.jl @@ -58,6 +58,8 @@ perturbed_equilibrium/ │ ├── n # Toroidal mode numbers │ ├── m # Poloidal mode numbers │ └── amplitude # ComplexF64 forcing amplitudes +├── forcing_b / forcing_b_root_area / forcing_b_area # control-surface forcing spectrum (b, b̃, b̄) [numpert_total], tesla +├── response_b / response_b_root_area / response_b_area # control-surface response spectrum (b, b̃, b̄) [numpert_total], tesla ├── response/ │ ├── xi_psi # Radial displacement ξ^ψ = ξ·∇ψ (ComplexF64 [npsi, mpert]) │ ├── xi_psi_J # J·ξ^ψ Jacobian-weighted (from gpeq_contra) @@ -66,12 +68,13 @@ perturbed_equilibrium/ │ ├── xi_n # Physical normal displacement xi_n (ComplexF64 [npsi, mpert]) │ ├── b_theta │ └── b_zeta -├── response_matrices/ # [numpert_total × numpert_total], root-area-weighted field (b̃) space -│ ├── plasma_inductance # Λ̃ = rootareafield_to_flux⁻¹·Λ·rootareafield_to_flux⁻† -│ ├── surface_inductance # L̃ = rootareafield_to_flux⁻¹·L·rootareafield_to_flux⁻† -│ ├── permeability # P̃ = rootareafield_to_flux⁻¹·P·rootareafield_to_flux (P = Λ·L⁻¹) -│ ├── reluctance # ϱ̃ = rootareafield_to_flux†·ϱ·rootareafield_to_flux -│ └── rootarea_field_to_flux_operator # rootareafield_to_flux = sqrtamat·√jarea; recover flux via Φ = rootareafield_to_flux·b̃ +├── response_matrices/ # [numpert_total × numpert_total], root-area-weighted field (b̃) space; R = S·A +│ ├── plasma_inductance # Λ̃ = R⁻¹·Λ·R⁻† +│ ├── surface_inductance # L̃ = R⁻¹·L·R⁻† +│ ├── permeability # P̃ = R⁻¹·P·R (P = Λ·L⁻¹) +│ ├── reluctance # ϱ̃ = R†·ϱ·R +│ ├── rootarea_to_area_weight_operator # S = Σ/√A at psilim; recover area-weighted field b̄ = S·b̃ +│ └── surface_area # scalar A = ∫J|∇ψ|dθ; recover flux via Φ = A·b̄ ├── singular_coupling/ │ ├── C_resonant_area_weighted_field # [n_rational × numpert_total] coupling matrix (b̃-space input, resonant area-weighted field b^r=Φ^r/A^r [T]) │ ├── C_resonant_current @@ -110,19 +113,26 @@ function write_outputs_to_HDF5( forcing_group["m"] = [mode.m for mode in intr.forcing_modes] forcing_group["amplitude"] = [mode.amplitude for mode in intr.forcing_modes] - # Control surface perturbation vectors (Phi_x and Phi_tot = P*Phi_x) - !isempty(state.forcing_vec) && (pe_group["forcing_vec"] = state.forcing_vec) - !isempty(state.response_vec) && (pe_group["response_vec"] = state.response_vec) + # Control-surface forcing/response spectra in the three Pharr field representations + # (all tesla; flux/weber is never stored). b̃ = root-area-weighted (coordinate-invariant). + !isempty(state.forcing_b) && (pe_group["forcing_b"] = state.forcing_b) + !isempty(state.forcing_b_rootarea) && (pe_group["forcing_b_root_area"] = state.forcing_b_rootarea) + !isempty(state.forcing_b_area) && (pe_group["forcing_b_area"] = state.forcing_b_area) + !isempty(state.response_b) && (pe_group["response_b"] = state.response_b) + !isempty(state.response_b_rootarea) && (pe_group["response_b_root_area"] = state.response_b_rootarea) + !isempty(state.response_b_area) && (pe_group["response_b_area"] = state.response_b_area) # Control surface matrices [numpert_total × numpert_total], in coordinate-invariant - # root-area-weighted field (b̃) space. Recover flux space with the stored operator - # R ≡ rootareafield_to_flux (Φ = R·b̃): e.g. P_flux = R·P̃·R⁻¹, L_flux = R·L̃·R†. [Pharr 2026] + # root-area-weighted field (b̃) space. Recover the area-weighted field b̄ with the stored + # operator S ≡ rootarea_to_area_weight (b̄ = S·b̃): e.g. L_b̄ = S·L̃·S†; recover flux with the + # scalar surface_area A: Φ = A·b̄ (internally R = S·A, Φ = R·b̃). [Pharr 2026] mat_group = haskey(pe_group, "response_matrices") ? pe_group["response_matrices"] : create_group(pe_group, "response_matrices") !isempty(state.plasma_inductance) && (mat_group["plasma_inductance"] = state.plasma_inductance) !isempty(state.surface_inductance) && (mat_group["surface_inductance"] = state.surface_inductance) !isempty(state.permeability) && (mat_group["permeability"] = state.permeability) !isempty(state.reluctance) && (mat_group["reluctance"] = state.reluctance) - !isempty(state.control_surface_field_operator) && (mat_group["rootarea_field_to_flux_operator"] = state.control_surface_field_operator) + !isempty(state.rootarea_to_area_weight) && (mat_group["rootarea_to_area_weight_operator"] = state.rootarea_to_area_weight) + (state.surface_area != 0.0) && (mat_group["surface_area"] = state.surface_area) # Response fields (ComplexF64 directly) response_group = haskey(pe_group, "response") ? pe_group["response"] : create_group(pe_group, "response") diff --git a/test/runtests_coordinate_invariant.jl b/test/runtests_coordinate_invariant.jl index c156cb6ca..39b20330a 100644 --- a/test/runtests_coordinate_invariant.jl +++ b/test/runtests_coordinate_invariant.jl @@ -1,10 +1,14 @@ -# Tests for the coordinate-invariant (root-area-weighted field, b̃) transform of the -# PerturbedEquilibrium control-surface response matrices (issue #233 / Pharr 2026). +# Tests for the coordinate-invariant field-space (b, b̃, b̄) treatment of the +# PerturbedEquilibrium control-surface response matrices and the ForceFreeStates energy +# (issue #233 / Pharr 2026). # -# Verifies the field-space transform rules in -# `PerturbedEquilibrium.field_space_response_matrices` and the recovery-operator -# contract: the flux-space matrices are exactly recoverable from the stored b̃-space -# matrices via the `rootareafield_to_flux` operator (Φ = rootareafield_to_flux·b̃). +# The control-surface matrices are stored in the coordinate-invariant root-area-weighted +# field (b̃) space. With Σ ≡ sqrtamat (the √weight) and the scalar surface area A ≡ jarea: +# - b̃→b̄ operator S = Σ/√A (area-weighted field; b̄ = S·b̃) +# - bare → b̃ Σ = S·√A (b = Σ⁻¹·b̃) +# - b̃→flux conform R = S·A (Φ = R·b̃; poloidal flux is only the scalar Φ = A·b̄) +# These tests verify the transform rules in `field_space_response_matrices`, the field/flux +# recovery contracts, and the ForceFreeStates `c = jarea` energy refactor. using Test using LinearAlgebra @@ -14,50 +18,82 @@ const PE = GeneralizedPerturbedEquilibrium.PerturbedEquilibrium # Deterministic, well-conditioned synthetic operators (no RNG → reproducible). function _synthetic_inputs(n::Int) - # rootareafield_to_flux: a generic invertible complex operator standing in for sqrtamat·√jarea. - rootareafield_to_flux = Matrix{ComplexF64}(undef, n, n) + # Σ ≡ sqrtamat: a generic invertible complex operator standing in for the √weight convolution. + Σ = Matrix{ComplexF64}(undef, n, n) for i in 1:n, j in 1:n - rootareafield_to_flux[i, j] = (1.0 + 0.3 * cospi((i + 2j) / n)) * cis(0.2 * (i - j)) * (i == j ? 1.0 : 0.15) + Σ[i, j] = (1.0 + 0.3 * cospi((i + 2j) / n)) * cis(0.2 * (i - j)) * (i == j ? 1.0 : 0.15) end - # Hermitian positive-definite inductances (energy generators). + jarea = 2.37 # scalar flux-surface area A + S = Σ ./ sqrt(jarea) # b̃→b̄ operator + # Hermitian positive-definite inductances (energy generators, flux space). A = [cis(0.1 * (i - j)) / (1 + abs(i - j)) for i in 1:n, j in 1:n] L = A * A' + n * I # Hermitian PD surface inductance B = [cis(-0.07 * (i + j)) / (1 + abs(i - j)) for i in 1:n, j in 1:n] Λ = B * B' + 2n * I # Hermitian PD plasma inductance - return Matrix{ComplexF64}(rootareafield_to_flux), Matrix{ComplexF64}(L), Matrix{ComplexF64}(Λ) + return Matrix{ComplexF64}(Σ), Matrix{ComplexF64}(S), jarea, Matrix{ComplexF64}(L), Matrix{ComplexF64}(Λ) end @testset "Coordinate-invariant field-space response matrices" begin n = 6 - rootareafield_to_flux, L, Λ = _synthetic_inputs(n) + Σ, S, jarea, L, Λ = _synthetic_inputs(n) + R = S .* jarea # b̃→flux conform Σ·√A P = Λ / L # permeability Φ_tot = P·Φ_x ϱ = inv(L) * (Λ - L) * inv(L) # reluctance - fm = PE.field_space_response_matrices(Λ, L, P, ϱ, rootareafield_to_flux) + fm = PE.field_space_response_matrices(Λ, L, P, ϱ, S, jarea) - @testset "Recovery operator contract (round-trip to flux space)" begin - # Recover flux space from the stored b̃-space matrices via rootareafield_to_flux. - @test rootareafield_to_flux * fm.permeability / rootareafield_to_flux ≈ P rtol = 1e-10 - @test rootareafield_to_flux * fm.surface_inductance * rootareafield_to_flux' ≈ L rtol = 1e-10 - @test rootareafield_to_flux * fm.plasma_inductance * rootareafield_to_flux' ≈ Λ rtol = 1e-10 - @test (rootareafield_to_flux') \ fm.reluctance / rootareafield_to_flux ≈ ϱ rtol = 1e-10 + @testset "Flux recovery contract (round-trip via R = S·A)" begin + @test R * fm.permeability / R ≈ P rtol = 1e-10 + @test R * fm.surface_inductance * R' ≈ L rtol = 1e-10 + @test R * fm.plasma_inductance * R' ≈ Λ rtol = 1e-10 + @test (R') \ fm.reluctance / R ≈ ϱ rtol = 1e-10 end - @testset "Internal consistency of the transform rules" begin - # P̃ = Λ̃·L̃⁻¹ + @testset "Area-weighted (b̄) recovery via S (= flux/A²)" begin + # b̄-space inductance L_b̄ = S·L̃·S† = L/A² since S·R⁻¹ = A⁻¹·I. + @test S * fm.surface_inductance * S' ≈ L ./ jarea^2 rtol = 1e-10 + @test S * fm.plasma_inductance * S' ≈ Λ ./ jarea^2 rtol = 1e-10 + @test S * fm.permeability / S ≈ P rtol = 1e-10 # similarity: A cancels + end + + @testset "Internal consistency of the b̃ transform rules" begin @test fm.permeability ≈ fm.plasma_inductance / fm.surface_inductance rtol = 1e-10 - # ϱ̃ = L̃⁻¹·(Λ̃ − L̃)·L̃⁻¹ L̃inv = inv(fm.surface_inductance) @test fm.reluctance ≈ L̃inv * (fm.plasma_inductance - fm.surface_inductance) * L̃inv rtol = 1e-10 end - @testset "Energy-scalar invariance under conformance" begin - # A physical applied flux Φ and its root-area-weighted counterpart b̃ = rootareafield_to_flux⁻¹·Φ + @testset "Energy-scalar invariance (flux ↔ b̃)" begin Φ = ComplexF64[cis(0.3k) / k for k in 1:n] - b̃ = rootareafield_to_flux \ Φ - # energy = Φ†·L⁻¹·Φ must equal b̃†·L̃⁻¹·b̃ (and likewise for Λ, ϱ) + b̃ = R \ Φ # root-area-weighted field @test dot(Φ, L \ Φ) ≈ dot(b̃, fm.surface_inductance \ b̃) rtol = 1e-10 @test dot(Φ, Λ \ Φ) ≈ dot(b̃, fm.plasma_inductance \ b̃) rtol = 1e-10 @test dot(Φ, ϱ * Φ) ≈ dot(b̃, fm.reluctance * b̃) rtol = 1e-10 end + + @testset "Three-field vector relations (b, b̃, b̄; flux = A·b̄)" begin + b̃ = ComplexF64[cis(0.21k) / (1 + k) for k in 1:n] + b̄ = S * b̃ # area-weighted field + b = (S .* sqrt(jarea)) \ b̃ # bare field b = Σ⁻¹·b̃ + Φ = R * b̃ # poloidal flux + @test Φ ≈ jarea .* b̄ rtol = 1e-12 # Φ = A·b̄ + @test b̄ ≈ Φ ./ jarea rtol = 1e-12 + @test (S .* sqrt(jarea)) * b ≈ b̃ rtol = 1e-12 # Σ·b = b̃ + end +end + +@testset "ForceFreeStates c = jarea energy refactor (net-zero)" begin + # The FFS energy is dW = c·b̃†·W_t·b̃ with W_t = (T⁻¹·Σ)†·W·(T⁻¹·Σ) and c = jarea. + # This must reproduce the eigenspectrum of the old flux operator M_old = T⁻¹·(Σ·√jarea). + n = 6 + Σ, _, jarea, _, _ = _synthetic_inputs(n) + A = [cis(0.13 * (i - j)) / (1 + abs(i - j)) for i in 1:n, j in 1:n] + W = A * A' + n * I # Hermitian PD energy matrix (ξ-space stand-in) + Tinv = ComplexF64[1.0 / (im * 2π * 1.7 * (i - 0.5)) for i in 1:n] # diag(T⁻¹) + + M = Tinv .* Σ # M = T⁻¹·Σ (new: pure √weight operator) + Mold = Tinv .* (Σ .* sqrt(jarea)) # M_old = T⁻¹·Σ·√jarea (old flux operator) + + e_new = sort(real.(eigvals(jarea .* (M' * W * M)))) + e_old = sort(real.(eigvals(Mold' * W * Mold))) + @test e_new ≈ e_old rtol = 1e-12 end From 94258041f32415b77eac39d7e3d5aa73a228cb88 Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Fri, 12 Jun 2026 15:22:28 -0400 Subject: [PATCH 036/135] DOCS - BUGFIX - Split Galerkin API onto its own page to fix Documenter size_threshold CI failure The new Galerkin docstrings pushed the rendered stability page to 241 KiB, over Documenter's 200 KiB hard limit. Move the Galerkin/*.jl docstrings to a new galerkin.md page via @autodocs Pages filtering (stability page now 192 KiB). Co-Authored-By: Claude Fable 5 --- docs/make.jl | 1 + docs/src/galerkin.md | 34 ++++++++++++++++++++++++++++++++++ docs/src/stability.md | 5 +++++ 3 files changed, 40 insertions(+) create mode 100644 docs/src/galerkin.md diff --git a/docs/make.jl b/docs/make.jl index 851cd5d1e..44085ef75 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -28,6 +28,7 @@ makedocs(; "Vacuum" => "vacuum.md", "Equilibrium" => "equilibrium.md", "Stability Analysis" => "stability.md", + "Galerkin Solver" => "galerkin.md", "Utilities" => "utilities.md", "Forcing Terms" => "forcing_terms.md", "Perturbed Equilibrium" => "perturbed_equilibrium.md", diff --git a/docs/src/galerkin.md b/docs/src/galerkin.md new file mode 100644 index 000000000..540bde2c3 --- /dev/null +++ b/docs/src/galerkin.md @@ -0,0 +1,34 @@ +# Galerkin Δ′ Solver (RDCON outer region) + +The Galerkin solver is the Julia port of RDCON's `gal.f` — Dewar's singular Galerkin method for +the outer-region Δ′ computation. Instead of integrating the Euler-Lagrange ODE radially, it +discretizes the displacement on a packed radial grid of Hermite-cubic finite elements and solves +a single global banded system. Cells adjacent to each rational surface ("resonant" and +"extension" cells) carry the large/small power-law asymptotic solutions analytically, so the +singular behavior is built into the basis rather than resolved numerically. + +The solve produces the inter-surface Δ′ matrix and the PEST-3 matching blocks +(``A'``, ``B'``, ``\Gamma'``, ``\Delta'``), written to the HDF5 output under the `galerkin/` +group. These are the outer-region inputs to resistive matched-asymptotic stability analysis +[Glasser 2016, Phys. Plasmas **23**, 072505]. + +The implementation lives in `src/ForceFreeStates/Galerkin/`: + +| File | Content | +|------|---------| +| `GalerkinStructs.jl` | Cell, interval, and workspace types mirroring the Fortran derived types | +| `GalerkinGrid.jl` | Packed grid construction and local→global DOF mapping | +| `GalerkinAssembly.jl` | Element-level assembly: Hermite basis, Gauss-Lobatto stiffness, resonant and extension cells, boundary conditions | +| `GalerkinSolve.jl` | Top-level driver `galerkin_solve`, banded solve, Δ′ extraction, PEST-3 blocks, HDF5 output | + +## API Reference + +```@autodocs +Modules = [GeneralizedPerturbedEquilibrium.ForceFreeStates] +Pages = ["Galerkin/GalerkinStructs.jl", "Galerkin/GalerkinGrid.jl", "Galerkin/GalerkinAssembly.jl", "Galerkin/GalerkinSolve.jl"] +``` + +## See also + +- `docs/src/stability.md` — the ForceFreeStates module this solver belongs to (EL system, metric matrices, singular surfaces) +- `docs/src/inner_layer.md` — inner-layer solutions to be matched against the outer-region Δ′ diff --git a/docs/src/stability.md b/docs/src/stability.md index b294125a3..1d0d3671c 100644 --- a/docs/src/stability.md +++ b/docs/src/stability.md @@ -222,8 +222,12 @@ environment variable; it is not a runtime parameter. ## API Reference +The Galerkin Δ′ solver (`src/ForceFreeStates/Galerkin/`) is documented separately in +`docs/src/galerkin.md`. + ```@autodocs Modules = [GeneralizedPerturbedEquilibrium.ForceFreeStates] +Pages = ["ForceFreeStates.jl", "ForceFreeStatesStructs.jl", "Mercier.jl", "Resist.jl", "Bal.jl", "EulerLagrange.jl", "Sing.jl", "Fourfit.jl", "Kinetic.jl", "FixedBoundaryStability.jl", "Utils.jl", "Free.jl", "Riccati.jl"] ``` ## Example usage @@ -306,6 +310,7 @@ end ## See also +- `docs/src/galerkin.md` — RDCON outer-region Galerkin Δ′ solver (part of this module) - `docs/src/equilibrium.md` — build the `PlasmaEquilibrium` object required by this module - `docs/src/vacuum.md` — vacuum response computed from the EL solution in `free_run!` - `docs/src/perturbed_equilibrium.md` — downstream singular coupling analysis using Δ' From 0299331fd90a084d16c3a0b83045e90604cc7d62 Mon Sep 17 00:00:00 2001 From: nelsonand Date: Fri, 12 Jun 2026 14:49:48 -0600 Subject: [PATCH 037/135] Some plotting updates --- .../analyze_example.jl | 5 +- src/Analysis/ForceFreeStates.jl | 68 ++++++ src/Equilibrium/DirectEquilibrium.jl | 3 + src/Equilibrium/InverseEquilibrium.jl | 5 + src/ForceFreeStates/Bal.jl | 209 +++++++++++------- 5 files changed, 213 insertions(+), 77 deletions(-) diff --git a/examples/DIIID-like_ideal_example/analyze_example.jl b/examples/DIIID-like_ideal_example/analyze_example.jl index 85df7d8cf..f02a32cd2 100644 --- a/examples/DIIID-like_ideal_example/analyze_example.jl +++ b/examples/DIIID-like_ideal_example/analyze_example.jl @@ -209,9 +209,10 @@ for geqdsk_file in geqdsk_cases zero_path = joinpath(@__DIR__, "salpha_zero_contours_$(case_label).png") Plots.savefig(p_zero, zero_path) - # BALOO-style α vs ψ stability boundaries (1st and 2nd) + # BALOO-style α vs ψ stability boundaries (1st and 2nd) over the Δ'(ψ, α) map bnd = ForceFreeStates.ballooning_alpha_boundaries(ctrl, equil) - p_alpha_bnd = Analysis.ForceFreeStates.plot_ballooning_alpha_boundaries(bnd) + dpmap = ForceFreeStates.ballooning_delta_prime_map(ctrl, equil) + p_alpha_bnd = Analysis.ForceFreeStates.plot_ballooning_alpha_boundaries(bnd, dpmap) display(p_alpha_bnd) alpha_bnd_path = joinpath(@__DIR__, "alpha_stability_boundary_$(case_label).png") Plots.savefig(p_alpha_bnd, alpha_bnd_path) diff --git a/src/Analysis/ForceFreeStates.jl b/src/Analysis/ForceFreeStates.jl index 1774869c2..249e6bd77 100644 --- a/src/Analysis/ForceFreeStates.jl +++ b/src/Analysis/ForceFreeStates.jl @@ -10,6 +10,7 @@ using HDF5 using LaTeXStrings using Plots using Printf +using Statistics: quantile """ plot_mode_displacement(h5path; modes=1:5, save_path=nothing) @@ -612,4 +613,71 @@ function plot_ballooning_alpha_boundaries(bnd; save_path=nothing, psi_min=0.0) return p end +""" + plot_ballooning_alpha_boundaries(bnd, dpmap; save_path=nothing, psi_min=0.0) + +Same diagram drawn over a heatmap of the signed Δ' from +`ForceFreeStates.ballooning_delta_prime_map`: each surface's Δ'(α) is oriented by the +sign of its α=0 (stable) value so that positive is stable everywhere, regridded from +its native physical α = α_ref*scale onto a shared uniform α axis, and shown with the +Δ'=0 contour, the extracted boundaries, and the scan cap `max_alpha_scale*α_exp`. +Color limits are set to the 90th percentile of |Δ'| so the pole regions inside the +unstable band do not wash out the marginal structure. +""" +function plot_ballooning_alpha_boundaries(bnd, dpmap; save_path=nothing, psi_min=0.0) + psi = dpmap.psi + scales = dpmap.alpha_scales + alpha_ref = dpmap.alpha_ref + signed = dpmap.delta_prime .* sign.(dpmap.delta_prime[:, 1]) + + finite_aref = filter(isfinite, alpha_ref) + isempty(finite_aref) && error("delta-prime map contains no valid surfaces") + alpha_axis = collect(range(0.0, maximum(finite_aref) * scales[end]; length=200)) + z = fill(NaN, length(alpha_axis), length(psi)) + for i in eachindex(psi) + (isfinite(alpha_ref[i]) && alpha_ref[i] > 0.0) || continue + a_surf = alpha_ref[i] .* scales + for (j, a) in enumerate(alpha_axis) + a > a_surf[end] && break + k = min(searchsortedlast(a_surf, a), length(a_surf) - 1) + k < 1 && continue + t = (a - a_surf[k]) / (a_surf[k+1] - a_surf[k]) + z[j, i] = (1 - t) * signed[i, k] + t * signed[i, k+1] + end + end + + # Color limits track the unstable-side magnitudes; deep stable values and pole + # regions clamp at the ends instead of washing out the marginal band. + finite_z = abs.(filter(isfinite, vec(z))) + finite_neg = abs.(filter(x -> isfinite(x) && x < 0.0, vec(z))) + lim = isempty(finite_neg) ? (isempty(finite_z) ? 1.0 : quantile(finite_z, 0.9)) : quantile(finite_neg, 0.95) + lim = max(lim, eps(Float64)) + + p = heatmap( + psi, + alpha_axis, + z; + c=cgrad(:RdBu), + clims=(-lim, lim), + # Leading newline offsets the rotated title clear of the colorbar tick labels (GR quirk) + colorbar_title="\n" * L"\Delta' \times \mathrm{sign}(\Delta'_{\alpha=0})", + xlims=(psi_min, 1), + xlabel=L"\psi_N", + ylabel=L"\alpha", + title="Infinite-n ballooning stability", + framestyle=:box, + legend=:topleft, + left_margin=10Plots.mm, + bottom_margin=5Plots.mm, + right_margin=15Plots.mm + ) + contour!(p, psi, alpha_axis, z; levels=[0.0], color=:black, linewidth=1, colorbar_entry=false) + plot!(p, bnd.psi, bnd.alpha; lw=2, color=:black, label="Experimental gradient") + plot!(p, bnd.psi, bnd.alpha_critical1; lw=2, color=:red, linestyle=:dash, label="1st stability boundary") + plot!(p, bnd.psi, bnd.alpha_critical2; lw=2, color=:blue, linestyle=:dash, label="2nd stability boundary") + plot!(p, psi, scales[end] .* alpha_ref; lw=2, color=:gray, linestyle=:dot, label="scan cap") + isnothing(save_path) || savefig(p, save_path) + return p +end + end # module ForceFreeStates diff --git a/src/Equilibrium/DirectEquilibrium.jl b/src/Equilibrium/DirectEquilibrium.jl index 5e7821fe0..8dc58c7a4 100644 --- a/src/Equilibrium/DirectEquilibrium.jl +++ b/src/Equilibrium/DirectEquilibrium.jl @@ -511,6 +511,9 @@ function _build_psi_grid(equil_params, psilow, psihigh, fieldline_int, raw_profi elseif equil_params.grid_type == "pow1" # Fortran powspace(psilow, psihigh, 1, mpsi+1, "upper") — edge-packed grid (equil/grid.f90:92-195) [psilow + (psihigh - psilow) * (3(ipsi / mpsi) - (ipsi / mpsi)^3) / 2 for ipsi in 0:mpsi] + elseif equil_params.grid_type == "uniform" + # Evenly spaced surfaces, e.g. for profile diagnostics at constant resolution + collect(range(psilow, psihigh; length=mpsi + 1)) else error("Unsupported grid_type: $(equil_params.grid_type)") end diff --git a/src/Equilibrium/InverseEquilibrium.jl b/src/Equilibrium/InverseEquilibrium.jl index c18b08fae..c1ae99d6e 100644 --- a/src/Equilibrium/InverseEquilibrium.jl +++ b/src/Equilibrium/InverseEquilibrium.jl @@ -180,6 +180,11 @@ function equilibrium_solver(input::InverseRunInput) mpsi = 128 end sq_xs = [psilow + (psihigh - psilow) * (3(i / mpsi) - (i / mpsi)^3) / 2 for i in 0:mpsi] + elseif grid_type == "uniform" + if mpsi == 0 + mpsi = 128 + end + sq_xs = collect(range(psilow, psihigh; length=mpsi + 1)) else error("Unsupported grid_type: $grid_type") end diff --git a/src/ForceFreeStates/Bal.jl b/src/ForceFreeStates/Bal.jl index 6c7590403..75a401390 100644 --- a/src/ForceFreeStates/Bal.jl +++ b/src/ForceFreeStates/Bal.jl @@ -674,22 +674,23 @@ function scan_delta_prime_map( end """ - critical_ballooning_alpha(psi_idx, plasma_eq; theta_k=0.0, max_alpha_scale=8.0, n_scan=24, tol=1e-3) + ballooning_alpha_crossings(psi_idx, plasma_eq; theta_k=0.0, max_alpha_scale=8.0, n_scan=24, tol=1e-3) -First infinite-n ballooning stability boundary at one flux surface: holding the -equilibrium magnetic shear fixed (`corr_qprime = 0`), find the critical pressure -gradient `α` at which the marginal ballooning Δ' first crosses zero as `α` increases -from zero. `α` is linear in `dp/dψ`, so the search is over a scaling of the reference -gradient and the boundary maps directly to `α_crit = α_ref * scale_crit`. +Locate every genuine marginal-stability crossing of the ballooning Δ' along the +pressure-gradient scaling `α/α_exp ∈ [0, max_alpha_scale]` at fixed magnetic shear. -The `α = 0` (zero pressure gradient) point is ballooning stable; its Δ' sign defines -the stable side, and the first scaling at which Δ' flips away from it is the boundary. +Δ' changes sign at marginal points (zeros) but also at its poles (y → 0 in the matching +ratio), which are not stability boundaries; between a pole pair the sign of Δ' is +inverted relative to the actual stability. Every sign change found by the `n_scan`-point +scan is therefore bisected to `tol` and classified by |Δ'| at the converged bracket: +small (below |Δ'(α=0)|) means a genuine zero, diverging means a pole. Logical stability +flips only at genuine zeros. -Returns `(alpha_crit, alpha_scale_crit, found)`. When no crossing exists within -`max_alpha_scale` (always stable, or second-stability access) `alpha_crit = NaN` and -`found = false`. +Returns `(scales, alphas, directions, reference)` where `directions[k] = +1` for a +stable→unstable crossing and `-1` for unstable→stable, and `alphas = alpha_ref * scales`. +Surfaces that never cross return empty vectors. """ -function critical_ballooning_alpha( +function ballooning_alpha_crossings( psi_idx::Int, plasma_eq::Equilibrium.PlasmaEquilibrium; theta_k::Float64=0.0, @@ -708,41 +709,67 @@ function critical_ballooning_alpha( theta_k=theta_k ).delta_prime - stable_sign = sign(delta_at(0.0)) - if stable_sign == 0.0 - return (alpha_crit=NaN, alpha_scale_crit=NaN, found=false) + scales = Float64[] + directions = Int[] + d0 = delta_at(0.0) + stable_sign = sign(d0) + if stable_sign == 0.0 || !isfinite(d0) + return (scales=scales, alphas=Float64[], directions=directions, reference=ref) end + pole_mag = abs(d0) + + on_stable_sign(d) = isfinite(d) && sign(d) == stable_sign - # Scan α upward and bracket the first scaling where Δ' leaves the stable side. + is_stable = true # logical stability; flips only at genuine zeros + prev_class = true # sign class of the previous sample; flips at zeros AND poles prev_scale = 0.0 - lo = NaN - hi = NaN for k in 1:n_scan scale = max_alpha_scale * k / n_scan - d = delta_at(scale) - if isfinite(d) && sign(d) != stable_sign + cur_class = on_stable_sign(delta_at(scale)) + if cur_class != prev_class lo = prev_scale hi = scale - break + while (hi - lo) > tol + mid = 0.5 * (lo + hi) + on_stable_sign(delta_at(mid)) == prev_class ? (lo = mid) : (hi = mid) + end + d_chk = delta_at(0.5 * (lo + hi)) + if isfinite(d_chk) && abs(d_chk) < pole_mag + push!(scales, 0.5 * (lo + hi)) + push!(directions, is_stable ? +1 : -1) + is_stable = !is_stable + end end + prev_class = cur_class prev_scale = scale end - isnan(hi) && return (alpha_crit=NaN, alpha_scale_crit=NaN, found=false) + return (scales=scales, alphas=ref.alpha_ref .* scales, directions=directions, reference=ref) +end - # Bisect the bracket to the requested tolerance. - while (hi - lo) > tol - mid = 0.5 * (lo + hi) - d = delta_at(mid) - if !isfinite(d) || sign(d) == stable_sign - lo = mid - else - hi = mid - end - end - scale_crit = 0.5 * (lo + hi) +""" + critical_ballooning_alpha(psi_idx, plasma_eq; theta_k=0.0, max_alpha_scale=8.0, n_scan=24, tol=1e-3) + +First infinite-n ballooning stability boundary at one flux surface: the lowest genuine +stable→unstable Δ' zero from [`ballooning_alpha_crossings`](@ref). `α` is linear in +`dp/dψ`, so the boundary maps directly to `α_crit = α_ref * scale_crit`. - return (alpha_crit=ref.alpha_ref * scale_crit, alpha_scale_crit=scale_crit, found=true) +Returns `(alpha_crit, alpha_scale_crit, found)`. When no crossing exists within +`max_alpha_scale` (always stable, or second-stability access) `alpha_crit = NaN` and +`found = false`. +""" +function critical_ballooning_alpha( + psi_idx::Int, + plasma_eq::Equilibrium.PlasmaEquilibrium; + theta_k::Float64=0.0, + max_alpha_scale::Float64=8.0, + n_scan::Int=24, + tol::Float64=1e-3 +) + cr = ballooning_alpha_crossings(psi_idx, plasma_eq; theta_k=theta_k, max_alpha_scale=max_alpha_scale, n_scan=n_scan, tol=tol) + k1 = findfirst(==(1), cr.directions) + isnothing(k1) && return (alpha_crit=NaN, alpha_scale_crit=NaN, found=false) + return (alpha_crit=cr.alphas[k1], alpha_scale_crit=cr.scales[k1], found=true) end """ @@ -783,61 +810,49 @@ function ballooning_alpha_boundary( end """ - second_critical_ballooning_alpha(psi_idx, plasma_eq, alpha_scale_crit1; max_alpha_scale=8.0, n_scan=20, tol=1e-3) + second_critical_ballooning_alpha(psi_idx, plasma_eq, alpha_scale_crit1; max_alpha_scale=8.0, n_scan=24, tol=1e-3) -Second (upper) ballooning stability boundary at one flux surface via bisection. Starting -above the first crossing at `alpha_scale_crit1` (as returned by [`critical_ballooning_alpha`](@ref)), -scans upward to find where Δ' returns to the stable side. Returns the physical critical α, -or `NaN` if no second crossing exists within `max_alpha_scale`. +Second (upper) ballooning stability boundary at one flux surface: the first genuine +unstable→stable Δ' zero above `alpha_scale_crit1` (as returned by +[`critical_ballooning_alpha`](@ref)), from [`ballooning_alpha_crossings`](@ref). +Returns the physical critical α, or `NaN` if no such crossing exists within +`max_alpha_scale`. """ function second_critical_ballooning_alpha( psi_idx::Int, plasma_eq::Equilibrium.PlasmaEquilibrium, alpha_scale_crit1::Float64; max_alpha_scale::Float64=8.0, - n_scan::Int=20, + n_scan::Int=24, tol::Float64=1e-3 ) alpha_scale_crit1 >= max_alpha_scale && return NaN - ref = salpha_reference(psi_idx, plasma_eq) - delta_at(scale) = ballooning_delta_prime( - psi_idx, plasma_eq; corr_qprime=0.0, corr_pprime=ref.pprime_norm_ref * (scale - 1.0) - ).delta_prime - stable_sign = sign(delta_at(0.0)) - stable_sign == 0 && return NaN - lo2 = NaN; hi2 = NaN - prev_scale = alpha_scale_crit1 - for k in 1:n_scan - scale = alpha_scale_crit1 + (max_alpha_scale - alpha_scale_crit1) * k / n_scan - d = delta_at(scale) - if isfinite(d) && sign(d) == stable_sign - lo2 = prev_scale; hi2 = scale; break - end - prev_scale = scale - end - isnan(hi2) && return NaN - while (hi2 - lo2) > tol - mid = 0.5 * (lo2 + hi2) - d = delta_at(mid) - (!isfinite(d) || sign(d) != stable_sign) ? (lo2 = mid) : (hi2 = mid) - end - return ref.alpha_ref * 0.5 * (lo2 + hi2) + cr = ballooning_alpha_crossings(psi_idx, plasma_eq; max_alpha_scale=max_alpha_scale, n_scan=n_scan, tol=tol) + k2 = findfirst(k -> cr.directions[k] == -1 && cr.scales[k] > alpha_scale_crit1, eachindex(cr.directions)) + return isnothing(k2) ? NaN : cr.alphas[k2] end """ - ballooning_alpha_boundaries(ctrl, plasma_eq; theta_k=0.0, max_alpha_scale=8.0) + ballooning_alpha_boundaries(ctrl, plasma_eq; theta_k=0.0, max_alpha_scale=8.0, n_scan=24) Profile driver returning the experimental pressure gradient `alpha`, the first stability boundary `alpha_critical1`, and the second (upper) stability boundary `alpha_critical2` -versus normalized flux `psi`. Calls [`critical_ballooning_alpha`](@ref) and -[`second_critical_ballooning_alpha`](@ref) at each surface. Arrays contain `NaN` where -no boundary exists. +versus normalized flux `psi`. At each surface [`ballooning_alpha_crossings`](@ref) +enumerates the genuine Δ' zeros; `alpha_critical1` is the lowest stable→unstable +crossing and `alpha_critical2` the first unstable→stable crossing above it (the top of +the same unstable band, even when further bands exist at higher α). Arrays contain +`NaN` where no boundary exists. + +`n_scan` sets the coarse-scan resolution of the crossing search. Increase it when Δ' +poles create narrow false-sign windows that a coarse scan can step into, which shows up +as isolated outliers on otherwise smooth boundary curves. """ function ballooning_alpha_boundaries( ctrl::ForceFreeStatesControl, plasma_eq::Equilibrium.PlasmaEquilibrium; theta_k::Float64=0.0, - max_alpha_scale::Float64=8.0 + max_alpha_scale::Float64=8.0, + n_scan::Int=24 ) xs = plasma_eq.profiles.xs npsi = length(xs) @@ -849,13 +864,13 @@ function ballooning_alpha_boundaries( for i in 1:npsi xs[i] > 1.0 && continue try - alpha[i] = salpha_reference(i, plasma_eq).alpha_ref - r1 = critical_ballooning_alpha(i, plasma_eq; theta_k=theta_k, max_alpha_scale=max_alpha_scale) - r1.found || continue - alpha_critical1[i] = r1.alpha_crit - alpha_critical2[i] = second_critical_ballooning_alpha( - i, plasma_eq, r1.alpha_scale_crit; max_alpha_scale=max_alpha_scale - ) + cr = ballooning_alpha_crossings(i, plasma_eq; theta_k=theta_k, max_alpha_scale=max_alpha_scale, n_scan=n_scan) + alpha[i] = cr.reference.alpha_ref + k1 = findfirst(==(1), cr.directions) + isnothing(k1) && continue + alpha_critical1[i] = cr.alphas[k1] + k2 = findnext(==(-1), cr.directions, k1 + 1) + isnothing(k2) || (alpha_critical2[i] = cr.alphas[k2]) catch err if ctrl.verbose @warn "ballooning alpha boundaries failed" psi_idx=i exception=err @@ -866,6 +881,50 @@ function ballooning_alpha_boundaries( return (psi=psi, alpha=alpha, alpha_critical1=alpha_critical1, alpha_critical2=alpha_critical2) end +""" + ballooning_delta_prime_map(ctrl, plasma_eq; theta_k=0.0, max_alpha_scale=8.0, n_alpha=61, max_surfaces=40) + +Map the ballooning Δ' over the (ψ_N, α) plane at fixed magnetic shear: at each flux +surface, scan the pressure-gradient scaling from 0 to `max_alpha_scale` times the +experimental α. The flux grid is thinned to at most `max_surfaces` surfaces to bound +the cost (each point is one ballooning ODE solve). + +Returns a NamedTuple `(psi, alpha_scales, alpha_ref, delta_prime)` where `delta_prime` +is `[n_surf × n_alpha]` with `NaN` on failed surfaces; physical `α = alpha_ref * scale`. +""" +function ballooning_delta_prime_map( + ctrl::ForceFreeStatesControl, + plasma_eq::Equilibrium.PlasmaEquilibrium; + theta_k::Float64=0.0, + max_alpha_scale::Float64=8.0, + n_alpha::Int=61, + max_surfaces::Int=40 +) + xs = plasma_eq.profiles.xs + idx_all = [i for i in eachindex(xs) if xs[i] <= 1.0] + stride = max(1, length(idx_all) ÷ max_surfaces) + idx = idx_all[1:stride:end] + + alpha_scales = collect(range(0.0, max_alpha_scale; length=n_alpha)) + psi = Float64[xs[i] for i in idx] + alpha_ref = fill(NaN, length(idx)) + delta_prime = fill(NaN, length(idx), n_alpha) + + for (k, i) in enumerate(idx) + try + res = scan_delta_prime_map(i, plasma_eq; ctrl=ctrl, theta_k=theta_k, s_scales=[1.0], alpha_scales=alpha_scales) + alpha_ref[k] = res.reference.alpha_ref + delta_prime[k, :] .= vec(res.delta_prime) + catch err + if ctrl.verbose + @warn "ballooning delta-prime map failed" psi_idx=i exception=err + end + end + end + + return (psi=psi, alpha_scales=alpha_scales, alpha_ref=alpha_ref, delta_prime=delta_prime) +end + # ====================================================================== # ODE Integration # Integrates the ideal marginal ballooning equations From 58c93a66489a9001e0aecb6f3611dfc5d8c0d27b Mon Sep 17 00:00:00 2001 From: nelsonand Date: Fri, 12 Jun 2026 16:13:13 -0600 Subject: [PATCH 038/135] Clean up root finder and add q' --- src/ForceFreeStates/Bal.jl | 292 ++++++++++++++++++++++++++----------- 1 file changed, 210 insertions(+), 82 deletions(-) diff --git a/src/ForceFreeStates/Bal.jl b/src/ForceFreeStates/Bal.jl index 75a401390..2f96dea8a 100644 --- a/src/ForceFreeStates/Bal.jl +++ b/src/ForceFreeStates/Bal.jl @@ -676,19 +676,15 @@ end """ ballooning_alpha_crossings(psi_idx, plasma_eq; theta_k=0.0, max_alpha_scale=8.0, n_scan=24, tol=1e-3) -Locate every genuine marginal-stability crossing of the ballooning Δ' along the -pressure-gradient scaling `α/α_exp ∈ [0, max_alpha_scale]` at fixed magnetic shear. - -Δ' changes sign at marginal points (zeros) but also at its poles (y → 0 in the matching -ratio), which are not stability boundaries; between a pole pair the sign of Δ' is -inverted relative to the actual stability. Every sign change found by the `n_scan`-point -scan is therefore bisected to `tol` and classified by |Δ'| at the converged bracket: -small (below |Δ'(α=0)|) means a genuine zero, diverging means a pole. Logical stability -flips only at genuine zeros. - -Returns `(scales, alphas, directions, reference)` where `directions[k] = +1` for a -stable→unstable crossing and `-1` for unstable→stable, and `alphas = alpha_ref * scales`. -Surfaces that never cross return empty vectors. +Locate the marginal-stability crossings of the ballooning Δ' along the pressure-gradient +scaling `α/α_exp ∈ [0, max_alpha_scale]` at fixed magnetic shear. Marching up from the +ballooning-stable `α = 0` anchor, every sign change between scan samples is bisected to +`tol`; sign changes with endpoint `|Δ'|` far above the anchor magnitude are Δ' pole +crossings (not marginal points) and are skipped. The first crossing is the first +stability boundary, the second the second-stability boundary, and so on. + +Returns `(scales, alphas, reference)` with `alphas = alpha_ref * scales`, ordered in +increasing α. Surfaces that never cross return empty vectors. """ function ballooning_alpha_crossings( psi_idx::Int, @@ -700,59 +696,59 @@ function ballooning_alpha_crossings( ) ref = salpha_reference(psi_idx, plasma_eq) - # Δ' as a function of the α scaling at fixed magnetic shear. - delta_at(scale) = ballooning_delta_prime( - psi_idx, - plasma_eq; - corr_qprime=0.0, - corr_pprime=ref.pprime_norm_ref * (scale - 1.0), - theta_k=theta_k - ).delta_prime - - scales = Float64[] - directions = Int[] - d0 = delta_at(0.0) - stable_sign = sign(d0) - if stable_sign == 0.0 || !isfinite(d0) - return (scales=scales, alphas=Float64[], directions=directions, reference=ref) + # Δ' as a function of the α scaling at fixed magnetic shear. Failed evaluations + # (extreme corrections can break the coefficient assembly) count as non-stable + # samples and are rejected by the crossing classification, like in scan_delta_prime_map. + delta_at(scale) = try + ballooning_delta_prime( + psi_idx, + plasma_eq; + corr_qprime=0.0, + corr_pprime=ref.pprime_norm_ref * (scale - 1.0), + theta_k=theta_k + ).delta_prime + catch + NaN end - pole_mag = abs(d0) - - on_stable_sign(d) = isfinite(d) && sign(d) == stable_sign - - is_stable = true # logical stability; flips only at genuine zeros - prev_class = true # sign class of the previous sample; flips at zeros AND poles - prev_scale = 0.0 - for k in 1:n_scan - scale = max_alpha_scale * k / n_scan - cur_class = on_stable_sign(delta_at(scale)) - if cur_class != prev_class - lo = prev_scale - hi = scale - while (hi - lo) > tol - mid = 0.5 * (lo + hi) - on_stable_sign(delta_at(mid)) == prev_class ? (lo = mid) : (hi = mid) - end - d_chk = delta_at(0.5 * (lo + hi)) - if isfinite(d_chk) && abs(d_chk) < pole_mag - push!(scales, 0.5 * (lo + hi)) - push!(directions, is_stable ? +1 : -1) - is_stable = !is_stable - end + + samples = collect(range(0.0, max_alpha_scale; length=n_scan + 1)) + scales = _ballooning_marginal_crossings(delta_at, samples, tol) + + return (scales=scales, alphas=ref.alpha_ref .* scales, reference=ref) +end + +# March along `samples` (monotone, either direction) from the stable anchor at +# `samples[1]`, returning every sign change of `delta_at` between finite samples, +# bisected to `tol`. Sign changes whose endpoint magnitudes exceed pole_cap*|Δ'_anchor| +# are Δ' pole crossings (not marginal points) and are skipped; on an adequately fine +# scan all remaining crossings are genuine marginal zeros, ordered from the anchor. +function _ballooning_marginal_crossings(delta_at, samples, tol; pole_cap=3.0) + vals = [delta_at(x) for x in samples] + k0 = findfirst(v -> isfinite(v) && v != 0.0, vals) + isnothing(k0) && return Float64[] + d_anchor = abs(vals[k0]) + locs = Float64[] + for k in k0:length(samples)-1 + a, b = vals[k], vals[k+1] + (isfinite(a) && isfinite(b) && sign(a) != sign(b)) || continue + max(abs(a), abs(b)) > pole_cap * d_anchor && continue + lo, hi = samples[k], samples[k+1] + while abs(hi - lo) > tol + mid = 0.5 * (lo + hi) + dm = delta_at(mid) + (isfinite(dm) && sign(dm) == sign(a)) ? (lo = mid) : (hi = mid) end - prev_class = cur_class - prev_scale = scale + push!(locs, 0.5 * (lo + hi)) end - - return (scales=scales, alphas=ref.alpha_ref .* scales, directions=directions, reference=ref) + return locs end """ critical_ballooning_alpha(psi_idx, plasma_eq; theta_k=0.0, max_alpha_scale=8.0, n_scan=24, tol=1e-3) -First infinite-n ballooning stability boundary at one flux surface: the lowest genuine -stable→unstable Δ' zero from [`ballooning_alpha_crossings`](@ref). `α` is linear in -`dp/dψ`, so the boundary maps directly to `α_crit = α_ref * scale_crit`. +First infinite-n ballooning stability boundary at one flux surface: the lowest Δ' zero +from [`ballooning_alpha_crossings`](@ref). `α` is linear in `dp/dψ`, so the boundary +maps directly to `α_crit = α_ref * scale_crit`. Returns `(alpha_crit, alpha_scale_crit, found)`. When no crossing exists within `max_alpha_scale` (always stable, or second-stability access) `alpha_crit = NaN` and @@ -767,9 +763,8 @@ function critical_ballooning_alpha( tol::Float64=1e-3 ) cr = ballooning_alpha_crossings(psi_idx, plasma_eq; theta_k=theta_k, max_alpha_scale=max_alpha_scale, n_scan=n_scan, tol=tol) - k1 = findfirst(==(1), cr.directions) - isnothing(k1) && return (alpha_crit=NaN, alpha_scale_crit=NaN, found=false) - return (alpha_crit=cr.alphas[k1], alpha_scale_crit=cr.scales[k1], found=true) + isempty(cr.scales) && return (alpha_crit=NaN, alpha_scale_crit=NaN, found=false) + return (alpha_crit=cr.alphas[1], alpha_scale_crit=cr.scales[1], found=true) end """ @@ -812,11 +807,10 @@ end """ second_critical_ballooning_alpha(psi_idx, plasma_eq, alpha_scale_crit1; max_alpha_scale=8.0, n_scan=24, tol=1e-3) -Second (upper) ballooning stability boundary at one flux surface: the first genuine -unstable→stable Δ' zero above `alpha_scale_crit1` (as returned by -[`critical_ballooning_alpha`](@ref)), from [`ballooning_alpha_crossings`](@ref). -Returns the physical critical α, or `NaN` if no such crossing exists within -`max_alpha_scale`. +Second (upper) ballooning stability boundary at one flux surface: the first Δ' zero +above `alpha_scale_crit1` (as returned by [`critical_ballooning_alpha`](@ref)), from +[`ballooning_alpha_crossings`](@ref). Returns the physical critical α, or `NaN` if no +such crossing exists within `max_alpha_scale`. """ function second_critical_ballooning_alpha( psi_idx::Int, @@ -828,7 +822,7 @@ function second_critical_ballooning_alpha( ) alpha_scale_crit1 >= max_alpha_scale && return NaN cr = ballooning_alpha_crossings(psi_idx, plasma_eq; max_alpha_scale=max_alpha_scale, n_scan=n_scan, tol=tol) - k2 = findfirst(k -> cr.directions[k] == -1 && cr.scales[k] > alpha_scale_crit1, eachindex(cr.directions)) + k2 = findfirst(>(alpha_scale_crit1), cr.scales) return isnothing(k2) ? NaN : cr.alphas[k2] end @@ -836,16 +830,14 @@ end ballooning_alpha_boundaries(ctrl, plasma_eq; theta_k=0.0, max_alpha_scale=8.0, n_scan=24) Profile driver returning the experimental pressure gradient `alpha`, the first stability -boundary `alpha_critical1`, and the second (upper) stability boundary `alpha_critical2` -versus normalized flux `psi`. At each surface [`ballooning_alpha_crossings`](@ref) -enumerates the genuine Δ' zeros; `alpha_critical1` is the lowest stable→unstable -crossing and `alpha_critical2` the first unstable→stable crossing above it (the top of -the same unstable band, even when further bands exist at higher α). Arrays contain -`NaN` where no boundary exists. - -`n_scan` sets the coarse-scan resolution of the crossing search. Increase it when Δ' -poles create narrow false-sign windows that a coarse scan can step into, which shows up -as isolated outliers on otherwise smooth boundary curves. +boundary `alpha_critical1` (lowest Δ' zero), and the second stability boundary +`alpha_critical2` (next zero above it) versus normalized flux `psi`, from +[`ballooning_alpha_crossings`](@ref) at each surface. Arrays contain `NaN` where no +boundary exists. + +`n_scan` sets the scan resolution of the crossing search; crossings closer together +than the scan step can be missed, which shows up as isolated outliers on otherwise +smooth boundary curves. """ function ballooning_alpha_boundaries( ctrl::ForceFreeStatesControl, @@ -866,11 +858,9 @@ function ballooning_alpha_boundaries( try cr = ballooning_alpha_crossings(i, plasma_eq; theta_k=theta_k, max_alpha_scale=max_alpha_scale, n_scan=n_scan) alpha[i] = cr.reference.alpha_ref - k1 = findfirst(==(1), cr.directions) - isnothing(k1) && continue - alpha_critical1[i] = cr.alphas[k1] - k2 = findnext(==(-1), cr.directions, k1 + 1) - isnothing(k2) || (alpha_critical2[i] = cr.alphas[k2]) + isempty(cr.alphas) && continue + alpha_critical1[i] = cr.alphas[1] + length(cr.alphas) >= 2 && (alpha_critical2[i] = cr.alphas[2]) catch err if ctrl.verbose @warn "ballooning alpha boundaries failed" psi_idx=i exception=err @@ -881,6 +871,97 @@ function ballooning_alpha_boundaries( return (psi=psi, alpha=alpha, alpha_critical1=alpha_critical1, alpha_critical2=alpha_critical2) end +""" + ballooning_qprime_crossings(psi_idx, plasma_eq; theta_k=0.0, min_qprime_scale=-2.0, max_qprime_scale=4.0, n_scan=24, tol=1e-3) + +Locate the marginal-stability crossings of the ballooning Δ' along the magnetic shear +scaling `q'/q'_exp ∈ [min_qprime_scale, max_qprime_scale]` at the fixed experimental +pressure gradient — the q'-channel counterpart of [`ballooning_alpha_crossings`](@ref). +The march starts from the first-regime-stable high shear end (`max_qprime_scale`) and +proceeds downward; sign changes are bisected and Δ' pole crossings skipped exactly as +in the α scan, so the first crossing is the critical q' and the second the re-entry to +stability at lower (or reversed) shear. + +Returns `(scales, qprimes, reference)` where `qprimes = qprime_norm_ref * scales` is in +`dq/dpsi_norm` units, ordered in decreasing q'. +""" +function ballooning_qprime_crossings( + psi_idx::Int, + plasma_eq::Equilibrium.PlasmaEquilibrium; + theta_k::Float64=0.0, + min_qprime_scale::Float64=-2.0, + max_qprime_scale::Float64=4.0, + n_scan::Int=24, + tol::Float64=1e-3 +) + ref = salpha_reference(psi_idx, plasma_eq) + + # Δ' as a function of the q' scaling at the experimental pressure gradient. Failed + # evaluations (reversed-shear corrections can break the coefficient assembly) count + # as non-stable samples and are rejected by the crossing classification. + delta_at(scale) = try + ballooning_delta_prime( + psi_idx, + plasma_eq; + corr_qprime=ref.qprime_norm_ref * (scale - 1.0), + corr_pprime=0.0, + theta_k=theta_k + ).delta_prime + catch + NaN + end + + samples = collect(range(max_qprime_scale, min_qprime_scale; length=n_scan + 1)) + scales = _ballooning_marginal_crossings(delta_at, samples, tol) + + return (scales=scales, qprimes=ref.qprime_norm_ref .* scales, reference=ref) +end + +""" + ballooning_qprime_boundaries(ctrl, plasma_eq; theta_k=0.0, min_qprime_scale=-2.0, max_qprime_scale=4.0, n_scan=24) + +Profile driver returning the experimental shear profile `qprime` (`dq/dpsi_norm`), the +critical shear `qprime_critical1` below which the surface is ballooning unstable at the +experimental pressure gradient (first crossing marching down from `max_qprime_scale`), +and `qprime_critical2`, the next crossing at lower (or reversed) shear, versus +normalized flux `psi`, from [`ballooning_qprime_crossings`](@ref) at each surface. +Arrays contain `NaN` where no boundary exists. +""" +function ballooning_qprime_boundaries( + ctrl::ForceFreeStatesControl, + plasma_eq::Equilibrium.PlasmaEquilibrium; + theta_k::Float64=0.0, + min_qprime_scale::Float64=-2.0, + max_qprime_scale::Float64=4.0, + n_scan::Int=24 +) + xs = plasma_eq.profiles.xs + npsi = length(xs) + psi = Vector{Float64}(xs) + qprime = fill(NaN, npsi) + qprime_critical1 = fill(NaN, npsi) + qprime_critical2 = fill(NaN, npsi) + + for i in 1:npsi + xs[i] > 1.0 && continue + try + cr = ballooning_qprime_crossings( + i, plasma_eq; theta_k=theta_k, min_qprime_scale=min_qprime_scale, max_qprime_scale=max_qprime_scale, n_scan=n_scan + ) + qprime[i] = cr.reference.qprime_norm_ref + isempty(cr.qprimes) && continue + qprime_critical1[i] = cr.qprimes[1] + length(cr.qprimes) >= 2 && (qprime_critical2[i] = cr.qprimes[2]) + catch err + if ctrl.verbose + @warn "ballooning qprime boundaries failed" psi_idx=i exception=err + end + end + end + + return (psi=psi, qprime=qprime, qprime_critical1=qprime_critical1, qprime_critical2=qprime_critical2) +end + """ ballooning_delta_prime_map(ctrl, plasma_eq; theta_k=0.0, max_alpha_scale=8.0, n_alpha=61, max_surfaces=40) @@ -925,6 +1006,53 @@ function ballooning_delta_prime_map( return (psi=psi, alpha_scales=alpha_scales, alpha_ref=alpha_ref, delta_prime=delta_prime) end +""" + ballooning_qprime_delta_prime_map(ctrl, plasma_eq; theta_k=0.0, min_qprime_scale=-2.0, max_qprime_scale=4.0, n_qprime=61, max_surfaces=40) + +Map the ballooning Δ' over the (ψ_N, q') plane at the fixed experimental pressure +gradient: at each flux surface, scan the magnetic shear scaling from `min_qprime_scale` +to `max_qprime_scale` times the experimental q' — the q'-channel counterpart of +[`ballooning_delta_prime_map`](@ref). The flux grid is thinned to at most +`max_surfaces` surfaces to bound the cost. + +Returns a NamedTuple `(psi, qprime_scales, qprime_ref, delta_prime)` where +`delta_prime` is `[n_surf × n_qprime]` with `NaN` on failed surfaces; physical +`q' = qprime_ref * scale` in `dq/dpsi_norm` units. +""" +function ballooning_qprime_delta_prime_map( + ctrl::ForceFreeStatesControl, + plasma_eq::Equilibrium.PlasmaEquilibrium; + theta_k::Float64=0.0, + min_qprime_scale::Float64=-2.0, + max_qprime_scale::Float64=4.0, + n_qprime::Int=61, + max_surfaces::Int=40 +) + xs = plasma_eq.profiles.xs + idx_all = [i for i in eachindex(xs) if xs[i] <= 1.0] + stride = max(1, length(idx_all) ÷ max_surfaces) + idx = idx_all[1:stride:end] + + qprime_scales = collect(range(min_qprime_scale, max_qprime_scale; length=n_qprime)) + psi = Float64[xs[i] for i in idx] + qprime_ref = fill(NaN, length(idx)) + delta_prime = fill(NaN, length(idx), n_qprime) + + for (k, i) in enumerate(idx) + try + res = scan_delta_prime_map(i, plasma_eq; ctrl=ctrl, theta_k=theta_k, s_scales=qprime_scales, alpha_scales=[1.0]) + qprime_ref[k] = res.reference.qprime_norm_ref + delta_prime[k, :] .= vec(res.delta_prime) + catch err + if ctrl.verbose + @warn "ballooning qprime delta-prime map failed" psi_idx=i exception=err + end + end + end + + return (psi=psi, qprime_scales=qprime_scales, qprime_ref=qprime_ref, delta_prime=delta_prime) +end + # ====================================================================== # ODE Integration # Integrates the ideal marginal ballooning equations From 4c8e90cfeb5facde92ccbdb48db2962475f072eb Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Sat, 13 Jun 2026 20:55:04 -0400 Subject: [PATCH 039/135] KineticForces - BUG FIX - Thread nutype/f0type into calculated path; guard NTV torque diagnostics The self-consistent kinetic_source="calculated" path hardcoded nutype="harmonic": compute_kinetic_matrices_at_psi! never accepted nutype/f0type, so a user setting them in [KineticForces] was silently ignored. Thread nutype/f0type/nufac from kf_ctrl through to kinetic_energy_matrices_for_euler_lagrange! (defaults match the prior hardcoded values, so all existing cases are byte-identical). Also guard the standalone NTV torque diagnostics on @isdefined(pe_state): they contract kinetic operators against perturbed-equilibrium displacements, which the calculated path does not produce, so running them there crashed. Skip with an info message instead. Regression harness (develop vs local): diiid_n1, solovev_n1, solovev_multi_n, solovev_kinetic_calculated all 0.0 diff; 120 kinetic unit tests pass. Co-Authored-By: Claude Opus 4.8 (1M context) --- src/GeneralizedPerturbedEquilibrium.jl | 26 ++++++++++++------- .../CalculatedKineticMatrices.jl | 1 + src/KineticForces/Torque.jl | 2 ++ 3 files changed, 20 insertions(+), 9 deletions(-) diff --git a/src/GeneralizedPerturbedEquilibrium.jl b/src/GeneralizedPerturbedEquilibrium.jl index b6988f0c9..e427885af 100755 --- a/src/GeneralizedPerturbedEquilibrium.jl +++ b/src/GeneralizedPerturbedEquilibrium.jl @@ -431,18 +431,26 @@ function main(args::Vector{String}=String[]; dd::Union{IMASdd.dd,Nothing}=nothin @info "\n KineticForces\n$_SECTION" kf_start = time() - # kf_ctrl and kinetic_profiles were loaded once above the stability block. - kf_intr = KineticForces.KineticForcesInternal(equil; verbose=kf_ctrl.verbose) - if @isdefined(pe_state) + # The standalone NTV torque diagnostics contract the kinetic operators + # against perturbed-equilibrium displacements (ξ), so they require a PE + # state. The self-consistent kinetic_source="calculated" path folds the + # kinetic physics into the stability solve and produces no PE state, so + # there is nothing for this block to act on — skip it rather than feed + # `compute_torque_all_methods!` empty perturbation interpolants. + if !@isdefined(pe_state) + @info "Skipping NTV torque diagnostics: no perturbed-equilibrium data (e.g. kinetic_source=\"calculated\")." + else + # kf_ctrl and kinetic_profiles were loaded once above the stability block. + kf_intr = KineticForces.KineticForcesInternal(equil; verbose=kf_ctrl.verbose) KineticForces.set_perturbation_data!(kf_intr, pe_state, intr, equil, metric) - end - kf_state = KineticForces.KineticForcesState() - KineticForces.compute_torque_all_methods!(kf_state, kf_intr, kf_ctrl, equil, kinetic_profiles) + kf_state = KineticForces.KineticForcesState() + KineticForces.compute_torque_all_methods!(kf_state, kf_intr, kf_ctrl, equil, kinetic_profiles) - if kf_ctrl.write_outputs_to_HDF5 - h5open(joinpath(intr.dir_path, kf_ctrl.HDF5_filename), "cw") do h5file - KineticForces.write_to_hdf5!(h5file, kf_state) + if kf_ctrl.write_outputs_to_HDF5 + h5open(joinpath(intr.dir_path, kf_ctrl.HDF5_filename), "cw") do h5file + KineticForces.write_to_hdf5!(h5file, kf_state) + end end end diff --git a/src/KineticForces/CalculatedKineticMatrices.jl b/src/KineticForces/CalculatedKineticMatrices.jl index 95cf91124..d36fead99 100644 --- a/src/KineticForces/CalculatedKineticMatrices.jl +++ b/src/KineticForces/CalculatedKineticMatrices.jl @@ -120,6 +120,7 @@ function compute_calculated_kinetic_matrices( block_w, block_t, psi, n, ell, kf_ctrl.zi, kf_ctrl.mi, kf_ctrl.wdfac, kf_ctrl.divxfac, kf_ctrl.electron, equil, intr_t, kinetic_profiles; + nutype=kf_ctrl.nutype, f0type=kf_ctrl.f0type, nufac=kf_ctrl.nufac, atol_xlmda=kf_ctrl.atol_xlmda, rtol_xlmda=kf_ctrl.rtol_xlmda ) full_w .+= block_w diff --git a/src/KineticForces/Torque.jl b/src/KineticForces/Torque.jl index 875032e41..596d09eee 100644 --- a/src/KineticForces/Torque.jl +++ b/src/KineticForces/Torque.jl @@ -920,6 +920,7 @@ function compute_kinetic_matrices_at_psi!( zi::Int, mi::Int, wdfac::Float64, _divxfac::Float64, electron::Bool, equil, intr::KineticForcesInternal, kinetic_profiles::Equilibrium.KineticProfileSplines; + nutype::String="harmonic", f0type::String="maxwellian", nufac::Float64=1.0, atol_xlmda::Float64=1e-9, rtol_xlmda::Float64=1e-6) # Bypass ψ > 1 (no kinetic contribution outside plasma) @@ -934,6 +935,7 @@ function compute_kinetic_matrices_at_psi!( kinetic_energy_matrices_for_euler_lagrange!( kwmat, ktmat, state, psi, n, l, wdfac, intr; + nutype, f0type, nufac, energy_atol=atol_xlmda, energy_rtol=rtol_xlmda, pitch_atol=atol_xlmda, pitch_rtol=rtol_xlmda) From 0ca930e1da8f59a7378e90ef086d711aa1572f12 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Sat, 13 Jun 2026 20:55:04 -0400 Subject: [PATCH 040/135] KineticForces - VALIDATION - Physics-validate Solovev calculated et[1] vs Fortran kinetic DCON (#227) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Add benchmarks/benchmark_solovev_kinetic_stability.jl, which generates a Fortran kinetic-DCON deck matched to the Solovev calculated regression fixture (same Solovev params, kinetic profile, mode band, nl, collision operator, grid, edge truncation), runs Fortran dcon, and compares its W_t[1] against Julia's XiNorm eigenmode_energies[1]. Result: Julia 15.888-0.711i vs Fortran 15.619-0.660i (Re 1.7%, Im 7.6%) — passing the DIIID kinetic acceptance thresholds. This physics-validates the PV+residue energy integral (issue #227): the pinned calculated-path et[1]=15.888 is correct; the pre-rewrite ximag value (34.176) was not. Update the ex5 fullruns comment to cite this Solovev reference. Co-Authored-By: Claude Opus 4.8 (1M context) --- .../benchmark_solovev_kinetic_stability.jl | 205 ++++++++++++++++++ test/runtests_fullruns.jl | 13 +- 2 files changed, 213 insertions(+), 5 deletions(-) create mode 100644 benchmarks/benchmark_solovev_kinetic_stability.jl diff --git a/benchmarks/benchmark_solovev_kinetic_stability.jl b/benchmarks/benchmark_solovev_kinetic_stability.jl new file mode 100644 index 000000000..23856cc35 --- /dev/null +++ b/benchmarks/benchmark_solovev_kinetic_stability.jl @@ -0,0 +1,205 @@ +#!/usr/bin/env julia +""" + benchmark_solovev_kinetic_stability.jl + +Benchmark the self-consistent kinetic-DCON path (`kinetic_source="calculated"`) +for the analytic **Solovev** equilibrium against Fortran GPEC's kinetic DCON. + +Unlike the DIIID benchmark (which reads a pre-existing `dcon_output_n1.nc`), +no committed Fortran reference exists for this Solovev case, so this script +*generates a matched Fortran input deck* from the Julia regression fixture and +runs Fortran `dcon` itself. The Julia and Fortran cases are made physically +identical: same Solovev parameters, same kinetic profile, same poloidal-mode +band (`delta_mlow=delta_mhigh=0`), same `nl`, collision operator, grid, and +edge truncation (`sas_flag`/`dmlim`). + +The comparison is the least-stable total-energy eigenvalue: + - Julia: `FreeBoundaryStability/XiNorm/eigenmode_energies[1]` in `gpec.h5` + - Fortran: the "Energies: ... real = …, imaginary = …" line printed by `dcon` + (== `W_t_eigenvalue[1]`; parsing the log avoids a NetCDF dependency). + +Acceptance (same thresholds as the DIIID kinetic benchmark): + - Re(et[1]) within 5 % of Fortran + - Im(et[1]) within 20 % of Fortran (the damping rate — smaller, more FP-sensitive) + +Reference result (2026-06, develop, mpert=8, nl=1, nutype="harmonic"): + Re: Julia 15.888 vs Fortran 15.619 → 1.7 % + Im: Julia -0.711 vs Fortran -0.660 → 7.6 % +This confirms the PV+residue energy integral (issue #227) is physically correct; +the pre-rewrite (`ximag`) value of 34.176 was not. + +Usage: + julia --project=. benchmarks/benchmark_solovev_kinetic_stability.jl + +Environment: + GPEC_FORTRAN_DCON path to Fortran `dcon` (default ~/Code/gpec/bin/dcon) + GPEC_FORTRAN_SOLDIR Fortran solovev_kinetic_example dir used as deck template + (default ~/Code/gpec/docs/examples/solovev_kinetic_example) +""" + +using Printf +using TOML +using HDF5 + +using GeneralizedPerturbedEquilibrium +const GPE = GeneralizedPerturbedEquilibrium + +const REPO = normpath(joinpath(@__DIR__, "..")) +const JULIA_FIXTURE = joinpath(REPO, "test", "test_data", "regression_solovev_kinetic_calculated") +const FORTRAN_DCON = get(ENV, "GPEC_FORTRAN_DCON", expanduser("~/Code/gpec/bin/dcon")) +const FORTRAN_SOLDIR = get(ENV, "GPEC_FORTRAN_SOLDIR", + expanduser("~/Code/gpec/docs/examples/solovev_kinetic_example")) + +_p(args...) = (println(stderr, args...); flush(stderr)) + +""" + replace_namelist_value!(path, key, value) + +Overwrite `key = …` (Fortran namelist, `=`-separated, value up to a trailing +comment `!` or line end) with `value`, preserving the rest of the line. +""" +function replace_namelist_value!(path::String, key::String, value::AbstractString) + lines = readlines(path) + pat = Regex("^(\\s*" * key * "\\s*=\\s*)([^!]*)(!?.*)\$", "i") + found = false + for (i, ln) in enumerate(lines) + m = match(pat, ln) + if m !== nothing + lines[i] = m.captures[1] * value * " " * + (isempty(m.captures[3]) ? "" : m.captures[3]) + found = true + end + end + found || error("key '$key' not found in $path") + open(path, "w") do io + for ln in lines + println(io, ln) + end + end +end + +""" + build_matched_fortran_deck(workdir) → workdir + +Copy the Fortran solovev_kinetic_example deck into `workdir` and override the +fields that must match the Julia regression fixture (read from its `gpec.toml` +and `sol.toml`). Converts the fixture's `kinetic.dat` into Fortran `kinetic.txt`. +""" +function build_matched_fortran_deck(workdir::String) + isdir(FORTRAN_SOLDIR) || error("Fortran deck template not found: $FORTRAN_SOLDIR") + for f in ("sol.in", "equil.in", "dcon.in", "pentrc.in", "vac.in") + cp(joinpath(FORTRAN_SOLDIR, f), joinpath(workdir, f); force=true) + end + + gpec = TOML.parsefile(joinpath(JULIA_FIXTURE, "gpec.toml")) + eq = gpec["Equilibrium"] + ffs = gpec["ForceFreeStates"] + kf = get(gpec, "KineticForces", Dict{String,Any}()) + + # equil.in — grid + coordinate settings to match the Julia [Equilibrium] block. + eqin = joinpath(workdir, "equil.in") + replace_namelist_value!(eqin, "psilow", string(eq["psilow"])) + replace_namelist_value!(eqin, "psihigh", string(eq["psihigh"])) + replace_namelist_value!(eqin, "mpsi", string(eq["mpsi"])) + replace_namelist_value!(eqin, "mtheta", string(eq["mtheta"])) + + # dcon.in — kinetic flags already match; align mode band, edge truncation, n. + dconin = joinpath(workdir, "dcon.in") + replace_namelist_value!(dconin, "nn", string(ffs["nn_low"])) + replace_namelist_value!(dconin, "delta_mlow", string(get(ffs, "delta_mlow", 0))) + replace_namelist_value!(dconin, "delta_mhigh", string(get(ffs, "delta_mhigh", 0))) + replace_namelist_value!(dconin, "qlow", string(ffs["qlow"])) + replace_namelist_value!(dconin, "qhigh", string(ffs["qhigh"])) + replace_namelist_value!(dconin, "singfac_min", string(ffs["singfac_min"])) + # Julia set_psilim_via_dmlim defaults true (sas_flag) with dmlim 0.2. + replace_namelist_value!(dconin, "sas_flag", "t") + replace_namelist_value!(dconin, "dmlim", "0.2") + + # pentrc.in — bounce harmonics + species; defaults mirror KineticForcesControl. + pentin = joinpath(workdir, "pentrc.in") + replace_namelist_value!(pentin, "nl", string(get(kf, "nl", 1))) + replace_namelist_value!(pentin, "nutype", "\"" * string(get(kf, "nutype", "harmonic")) * "\"") + replace_namelist_value!(pentin, "f0type", "\"" * string(get(kf, "f0type", "maxwellian")) * "\"") + replace_namelist_value!(pentin, "kinetic_file", "\"kinetic.txt\"") + + # kinetic.txt — Fortran readtable wants a title line then numeric rows; the + # fixture's kinetic.dat is already the same 6-column ASCII layout. + cp(joinpath(JULIA_FIXTURE, "kinetic.dat"), joinpath(workdir, "kinetic.txt"); force=true) + + return workdir +end + +""" + run_fortran_reference(workdir) → (re, im) + +Run Fortran `dcon` in `workdir` and parse the least-stable total-energy +eigenvalue from its "Energies: ... real = …, imaginary = …" line. +""" +function run_fortran_reference(workdir::String) + isfile(FORTRAN_DCON) || error("Fortran dcon not found: $FORTRAN_DCON (set GPEC_FORTRAN_DCON)") + logpath = joinpath(workdir, "dcon_run.log") + open(logpath, "w") do io + run(pipeline(Cmd(`$FORTRAN_DCON`; dir=workdir); stdout=io, stderr=io)) + end + log = read(logpath, String) + m = match(r"Energies:.*real\s*=\s*([-\d.Ee+]+),\s*imaginary\s*=\s*([-\d.Ee+]+)", log) + m === nothing && error("could not parse Fortran energies from $logpath") + return parse(Float64, m.captures[1]), parse(Float64, m.captures[2]) +end + +function run_julia_reference() + run = mktempdir(; prefix="solovev_kinetic_julia_") + for f in ("gpec.toml", "sol.toml", "kinetic.dat") + cp(joinpath(JULIA_FIXTURE, f), joinpath(run, f)) + end + t0 = time() + GPE.main([run]) + wall = time() - t0 + et = h5open(joinpath(run, "gpec.h5"), "r") do h5 + read(h5["FreeBoundaryStability/XiNorm/eigenmode_energies"]) + end + return real(et[1]), imag(et[1]), wall +end + +function run_benchmark() + _p("=" ^ 70) + _p(" Solovev Kinetic-DCON Benchmark: Julia KF→FFS vs Fortran DCON") + _p("=" ^ 70) + + workdir = mktempdir(; prefix="solovev_kinetic_fortran_") + build_matched_fortran_deck(workdir) + _p(" Matched Fortran deck: $workdir") + fort_re, fort_im = run_fortran_reference(workdir) + _p(@sprintf(" Fortran W_t[1]: Re = %.6f Im = %.6f", fort_re, fort_im)) + + _p("\n--- Running GPE.main with kinetic_source=\"calculated\" ---") + jul_re, jul_im, wall = run_julia_reference() + _p(@sprintf(" GPE.main completed in %.1f s", wall)) + + re_err = abs(jul_re - fort_re) / abs(fort_re) * 100 + im_err = abs(jul_im - fort_im) / abs(fort_im) * 100 + + _p("\n" * "=" ^ 70) + _p(" Least-stable total-energy eigenvalue (mpert matched)") + _p("=" ^ 70) + _p(@sprintf(" Re(et[1]): Julia = %12.6f Fortran = %12.6f err = %6.2f%%", jul_re, fort_re, re_err)) + _p(@sprintf(" Im(et[1]): Julia = %12.6f Fortran = %12.6f err = %6.2f%%", jul_im, fort_im, im_err)) + + re_pass = re_err <= 5.0 + im_pass = im_err <= 20.0 + _p("\n" * "=" ^ 70) + if re_pass && im_pass + _p(" PASS — Re within 5 %, Im within 20 %") + else + _p(" FAIL — thresholds exceeded:") + re_pass || _p(@sprintf(" Re err %.2f%% > 5%%", re_err)) + im_pass || _p(@sprintf(" Im err %.2f%% > 20%%", im_err)) + end + _p("=" ^ 70) + + return (; jul_re, jul_im, fort_re, fort_im, re_err, im_err, wall) +end + +if abspath(PROGRAM_FILE) == @__FILE__ + run_benchmark() +end diff --git a/test/runtests_fullruns.jl b/test/runtests_fullruns.jl index 5e864d5d7..f8804c1ef 100644 --- a/test/runtests_fullruns.jl +++ b/test/runtests_fullruns.jl @@ -64,11 +64,14 @@ using HDF5 h5open(joinpath(ex5, "gpec.h5"), "r") do h5 et = read(h5["FreeBoundaryStability/XiNorm/eigenmode_energies"]) # Self-consistent KF→FFS kinetic-MHD eigenvalue with full-strength kinetic - # matrices (kinetic_factor=1.0). The Julia kinetic-DCON path is validated - # against Fortran kinetic DCON on the DIIID benchmark to <2% on both Re and - # Im of et[1] (PR #112). Here the Solovev value is the regression anchor: - # Re(et[1]) is a large, well-conditioned eigenvalue (pinned tight); Im(et[1]) - # is the kinetic damping rate, which is more FP-sensitive (bracketed loosely). + # matrices (kinetic_factor=1.0). This Solovev value is physics-validated + # against Fortran kinetic DCON on the SAME equilibrium + kinetic profile + # (mode band matched to mpert=8): Fortran W_t[1] = 15.619 - 0.660i vs Julia + # 15.888 - 0.711i — Re 1.7%, Im 7.6% (issue #227, reproduce with + # benchmarks/benchmark_solovev_kinetic_stability.jl). Re(et[1]) is large and + # well-conditioned (pinned tight); Im(et[1]) is the kinetic damping rate, + # more FP-sensitive (bracketed loosely). The pre-PV `ximag` value (34.176) + # was not physical; the PV+residue energy integral gives the correct result. @test isfinite(real(et[1])) @test isfinite(imag(et[1])) @test real(et[1]) ≈ 15.888 rtol = 0.01 From 9db9167a4fd3498ce1efbc811a757153e15c5592 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Sat, 13 Jun 2026 23:38:07 -0400 Subject: [PATCH 041/135] KineticForces - BUG FIX - Collisionless energy integral in real x-space The collisionless (nutype="zero", or any nu==0 config) energy integral produced NaN/DomainError for resonance poles in the Maxwellian tail (x_res >~ 35): under the u = 1-exp(-x) substitution u_res rounds to 1.0, so the residue weight R proportional to (1-u_res) collapses to 0 while log1p(-u_res) -> -Inf, tripping 0*(-Inf) = NaN; in the [35,36] band a Gauss-Kronrod node coincident with the breakpoint gives 0/0 = NaN (QuadGK DomainError). Root cause is the u-substitution compressing the real-axis pole toward u=1. Fix: dispatch the structurally-collisionless case to a dedicated real-x-space integral over [0, X_ENERGY_MAX=72] (matching Fortran PENTRC energy.f90), where the pole x_res in (0,72) stays a well-conditioned O(1) number. Each pole is removed by analytic principal-value + residue (causal nu->0+ branch -/+ i*pi). The collisional (nu>0) path keeps the u-space formulation unchanged (off-axis complex pole, no truncation) - byte-identical output. Verified: x_res sweep 0.5..800 all finite; matches the nu->0+ harmonic limit to ~1e-6; 120 kinetic unit tests pass. Addresses #281. Co-Authored-By: Claude Opus 4.8 (1M context) --- src/KineticForces/EnergyIntegration.jl | 111 ++++++++++++++++++++----- 1 file changed, 92 insertions(+), 19 deletions(-) diff --git a/src/KineticForces/EnergyIntegration.jl b/src/KineticForces/EnergyIntegration.jl index 81bee2bf0..ea76626b1 100644 --- a/src/KineticForces/EnergyIntegration.jl +++ b/src/KineticForces/EnergyIntegration.jl @@ -146,6 +146,71 @@ function find_resonance_energies(leff::Float64, wb::Float64, n::Int, we::Float64 return roots end +# Upper energy limit for the collisionless real-x-space integral, matching the +# Fortran PENTRC convention (energy.f90, `xmax`). exp(-72) ≈ 5e-32, so the energy +# tail beyond this is negligible to any quadrature tolerance. +const X_ENERGY_MAX = 72.0 + +""" + _integrate_energy_collisionless(p, leff, wb, n, we, wd, atol, rtol) → ComplexF64 + +Collisionless (ν ≡ 0) energy integral in **real x-space** over `[0, X_ENERGY_MAX]`, +matching Fortran PENTRC's real-space integration (energy.f90). Each real resonance +pole `x_res ∈ (0, X_ENERGY_MAX)` is removed analytically by principal-value + +residue (Sokhotski-Plemelj, causal ν→0⁺ branch ∓iπ following sign Ω′), leaving a +smooth integrand for QuadGK. + +The collisionless pole sits on the real axis. In x-space it stays a +well-conditioned `O(1)` number, so the pole subtraction and its breakpoint behave +cleanly. The `u = 1-exp(-x)` substitution used for the collisional path +(`integrate_energy`) compresses tail poles toward `u=1`, where the subtraction is +numerically unresolvable — hence the dedicated real-space branch here. +""" +function _integrate_energy_collisionless(p::EnergyParams, leff::Float64, wb::Float64, + n::Int, we::Float64, wd::Float64, + atol::Float64, rtol::Float64)::ComplexF64 + x_res_list = find_resonance_energies(leff, wb, n, we, wd) + x_poles = Float64[] + residues = ComplexF64[] + pole_contribution = ComplexF64(0.0) + + for xr in x_res_list + # Poles beyond X_ENERGY_MAX (exp(-xr) negligible) lie outside the domain — drop them. + (xr <= 0.0 || xr >= X_ENERGY_MAX) && continue + # Ω′(x_res) = d/dx[leff·wb·√x + n·(we + wd·x)] + omega_prime = leff * wb / (2.0 * sqrt(xr)) + n * wd + abs(omega_prime) < SINGULAR_EPS && continue + # Residue of N(x)·exp(-x)/(i·Ω(x)) at x_res, where Ω ≈ Ω′·(x - x_res) near the pole. + R = _energy_numerator(xr, p) * exp(-xr) / (im * omega_prime) + # Causal (ν→0⁺) add-back: ∫₀^xmax R/(x - x_res) dx = R·[log(xmax - x_res) - log(x_res) ∓ iπ]. + pole_contribution += R * (log(X_ENERGY_MAX - xr) - log(xr) - im * π * sign(omega_prime)) + push!(x_poles, xr) + push!(residues, R) + end + + npole = length(residues) + + # Physical x-space integrand N(x)·exp(-x)/(i·Ω) minus the subtracted pole parts. + integrand = x -> begin + val = _energy_integrand_real(x, p) + @inbounds for k in 1:npole + val -= residues[k] / (x - x_poles[k]) + end + return val + end + + if npole == 0 + val, _ = quadgk(integrand, 0.0, X_ENERGY_MAX; atol=atol, rtol=rtol) + return val + end + + # Resonance locations as QuadGK breakpoints so the smooth-but-sharp integrand + # is resolved near each pole. + breaks = unique!(sort!(x_poles)) + smooth_val, _ = quadgk(integrand, 0.0, breaks..., X_ENERGY_MAX; atol=atol, rtol=rtol) + return smooth_val + pole_contribution +end + """ integrate_energy(wn, wt, we, wd, wb, nuk, ell, leff, n, psi, lambda, method; nutype="harmonic", f0type="maxwellian", nufac=1.0, @@ -163,8 +228,12 @@ subtracting its singular part R/(u - u_pole) from the integrand and adding back the analytic contribution ∫₀¹ R/(u - u_pole) du = R·[log(1-u_pole) - log(-u_pole)]. The same pole u_pole is used in both the subtraction and the add-back, so the decomposition is exact and the remaining integrand is smooth. -In the collisionless limit (ν = 0) the pole sits on the real axis and the -add-back uses the causal Sokhotski-Plemelj branch (∓iπ following sign Ω′). + +This u-space path is used only when collisions are present (ν > 0), where the +pole is off the real axis. The collisionless case (ν ≡ 0) has a real-axis pole +that the u-substitution would compress toward u=1 (numerically unresolvable in +the Maxwellian tail), so it is dispatched to `_integrate_energy_collisionless`, +which integrates in real x-space over `[0, X_ENERGY_MAX]` à la Fortran PENTRC. Collision operator types (`nutype`): `"zero"`, `"small"`, `"krook"`, `"harmonic"`. Distribution function types (`f0type`): `"maxwellian"`, `"jkp"`, `"cgl"`. @@ -192,6 +261,14 @@ function integrate_energy(wn::Float64, wt::Float64, we::Float64, wd::Float64, return val end + # Collisionless (ν ≡ 0): real-axis pole. Dispatch to the real-x-space integral + # (Fortran PENTRC convention); the u-substitution below is only well-behaved + # for the off-axis pole of the collisional case. ν vanishes identically iff it + # vanishes at any x, so probe at x = 1. + if _energy_collision_frequency(1.0, p) == 0.0 + return _integrate_energy_collisionless(p, leff, wb, n, we, wd, atol, rtol) + end + # Locate resonance poles and build their Sokhotski-Plemelj decomposition. x_res_list = find_resonance_energies(leff, wb, n, we, wd) u_poles = ComplexF64[] @@ -210,24 +287,20 @@ function integrate_energy(wn::Float64, wt::Float64, we::Float64, wd::Float64, abs(omega_prime) < SINGULAR_EPS && continue u_res = -expm1(-xr) # 1 - exp(-x_res) + # Reached only for the collisional case (the ν ≡ 0 case is dispatched above), + # so ν(x_res) > 0 and the pole is off the real axis. Guard defensively. nu_res = _energy_collision_frequency(xr, p) - - if nu_res > 0.0 - # Collisional: pole shifted off the real axis. i·Ω - ν = 0 ⟹ x_pole = x_res - i·ν/Ω′. - # If ν overflows at a (tiny) x_res, the pole is infinitely collisionally broadened - # — no localized pole; skip and let QuadGK integrate the smooth integrand directly. - pole_offset = nu_res / omega_prime - isfinite(pole_offset) || continue - x_pole = complex(xr, -pole_offset) - u_pole = 1.0 - exp(-x_pole) - R = _energy_numerator(xr, p) * (1.0 - u_pole) / (im * omega_prime) - pole_contribution += R * (log(1.0 - u_pole) - log(-u_pole)) - else - # Collisionless: real-axis pole, causal (ν → 0⁺) Sokhotski-Plemelj branch. - u_pole = ComplexF64(u_res) - R = _energy_numerator(xr, p) * (1.0 - u_res) / (im * omega_prime) - pole_contribution += R * (log1p(-u_res) - log(u_res) - im * π * sign(omega_prime)) - end + nu_res > 0.0 || continue + + # i·Ω - ν = 0 ⟹ x_pole = x_res - i·ν/Ω′. If ν overflows at a (tiny) x_res, the + # pole is infinitely collisionally broadened — no localized pole; skip and let + # QuadGK integrate the smooth integrand directly. + pole_offset = nu_res / omega_prime + isfinite(pole_offset) || continue + x_pole = complex(xr, -pole_offset) + u_pole = 1.0 - exp(-x_pole) + R = _energy_numerator(xr, p) * (1.0 - u_pole) / (im * omega_prime) + pole_contribution += R * (log(1.0 - u_pole) - log(-u_pole)) push!(u_poles, u_pole) push!(residues, R) From 5e6981b6830396cd13d90a0099df8c507d99b858 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Sun, 14 Jun 2026 00:20:46 -0400 Subject: [PATCH 042/135] KineticForces - BUG FIX - Regular-part limit for collisionless resonance poles MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Follow-up to the x-space collisionless energy integral: the real-axis resonance denominator Ω(x) = leff·wb·√x + n·(we+wd·x) is a difference of O(1e4)-magnitude terms that cancel to ~0 at the pole, so it rounds to exactly 0.0 over a ~ULP-wide window (granularity ulp(1e4) ≈ 1.8e-12). Across that window the physical term N·exp(-x)/(iΩ) is 0/0 → NaN (QuadGK DomainError), which neither a Newton pole refinement (Ω already rounds to 0) nor a one-ULP nudge (whole window is flat-zero) can escape. Fix: in the flat-Ω window QuadGK is handed the analytic Laurent regular-part limit of the pole-subtracted integrand, [h′ - h·Ω″/(2Ω′)]/(iΩ′) with h = N·exp(-x) (new _energy_numerator_deriv + _collisionless_regular_part). Other poles' finite subtractions are retained. Collisional (ν>0) path is untouched. Also adds the nutype="zero" regression sentinel: - test fixture regression_solovev_kinetic_nuzero (calculated path, [KineticForces] nutype="zero"), - regression-harness case solovev_kinetic_nuzero, - fullruns ex6 and a tail-pole case in the runtests_kinetic ν→0⁺ limit test. Validation: Solovev calculated et[1] = 15.885 - 0.482i (finite). Re sits on the harmonic 15.888 to 0.02% (collisions are a small perturbation to the real energy); Im is the resonant ∓iπ damping, smaller than the harmonic -0.711 as expected. Runtime 23s. 124 kinetic unit tests pass; x_res sweep 0.5..800 NaN-free. Closes #281. Co-Authored-By: Claude Opus 4.8 (1M context) --- .../cases/solovev_kinetic_nuzero.toml | 124 ++++++++++++++++++ src/KineticForces/EnergyIntegration.jl | 79 +++++++++-- test/runtests_fullruns.jl | 24 ++++ test/runtests_kinetic.jl | 18 +++ .../gpec.toml | 56 ++++++++ .../kinetic.dat | 12 ++ .../sol.toml | 11 ++ 7 files changed, 316 insertions(+), 8 deletions(-) create mode 100644 regression-harness/cases/solovev_kinetic_nuzero.toml create mode 100644 test/test_data/regression_solovev_kinetic_nuzero/gpec.toml create mode 100644 test/test_data/regression_solovev_kinetic_nuzero/kinetic.dat create mode 100644 test/test_data/regression_solovev_kinetic_nuzero/sol.toml diff --git a/regression-harness/cases/solovev_kinetic_nuzero.toml b/regression-harness/cases/solovev_kinetic_nuzero.toml new file mode 100644 index 000000000..faf41058a --- /dev/null +++ b/regression-harness/cases/solovev_kinetic_nuzero.toml @@ -0,0 +1,124 @@ +[case] +name = "solovev_kinetic_nuzero" +description = "Solovev analytical equilibrium, n=1, kinetic_source=calculated, nutype=zero (collisionless energy integral, issue #281)" +example_dir = "test/test_data/regression_solovev_kinetic_nuzero" + +# Energies — leading eigenvalues +[quantities.et_real] +h5path = "FreeBoundaryStability/XiNorm/eigenmode_energies" +type = "complex_vector" +extract = "real_first" +label = "total energy Re(et[1])" +noise_threshold = 1e-10 + +[quantities.et_imag] +h5path = "FreeBoundaryStability/XiNorm/eigenmode_energies" +type = "complex_vector" +extract = "imag_first" +label = "total energy Im(et[1])" +noise_threshold = 1e-10 + +[quantities.ep_real] +h5path = "FreeBoundaryStability/XiNorm/eigenmode_plasma_energies" +type = "complex_vector" +extract = "real_first" +label = "plasma energy Re(ep[1])" +noise_threshold = 1e-10 + +[quantities.ev_real] +h5path = "FreeBoundaryStability/XiNorm/eigenmode_vacuum_energies" +type = "complex_vector" +extract = "real_first" +label = "vacuum energy Re(ev[1])" +noise_threshold = 1e-10 + +# Energies — full eigenvalue arrays +[quantities.et_all] +h5path = "FreeBoundaryStability/XiNorm/eigenmode_energies" +type = "complex_vector" +extract = "all_complex" +label = "total energy (all)" +noise_threshold = 1e-10 + +# Integration +[quantities.nstep] +h5path = "integration/nstep" +type = "int_scalar" +extract = "value" +label = "ODE steps (saved)" +noise_threshold = 0 + +[quantities.nstep_total] +h5path = "integration/nstep_total" +type = "int_scalar" +extract = "value" +label = "ODE steps (total)" +noise_threshold = 0 + +# Equilibrium +[quantities.q0] +h5path = "equil/q0" +type = "real_scalar" +extract = "value" +label = "q0" +noise_threshold = 1e-12 + +[quantities.q95] +h5path = "equil/q95" +type = "real_scalar" +extract = "value" +label = "q95" +noise_threshold = 1e-12 + +# Singular surfaces +[quantities.msing] +h5path = "singular/msing" +type = "int_scalar" +extract = "value" +label = "# singular surfaces" +noise_threshold = 0 + +[quantities.sing_psi] +h5path = "singular/psi" +type = "real_vector" +extract = "all_real" +label = "singular psi locations" +noise_threshold = 1e-8 + +[quantities.sing_q] +h5path = "singular/q" +type = "real_vector" +extract = "all_real" +label = "singular q values" +noise_threshold = 1e-8 + +# Kinetic-specific +[quantities.kinetic_factor] +h5path = "kinetic/kinetic_factor" +type = "real_scalar" +extract = "value" +label = "kinetic_factor" +noise_threshold = 0 + +# Mode numbers +[quantities.mpert] +h5path = "info/mpert" +type = "int_scalar" +extract = "value" +label = "mpert" +noise_threshold = 0 + +[quantities.npert] +h5path = "info/npert" +type = "int_scalar" +extract = "value" +label = "npert" +noise_threshold = 0 + +# Runtime (special: not from H5) +[quantities.runtime] +h5path = "" +type = "runtime" +extract = "value" +label = "Runtime (s)" +noise_threshold = 0.0 diff --git a/src/KineticForces/EnergyIntegration.jl b/src/KineticForces/EnergyIntegration.jl index ea76626b1..dbb7d877e 100644 --- a/src/KineticForces/EnergyIntegration.jl +++ b/src/KineticForces/EnergyIntegration.jl @@ -85,6 +85,31 @@ For CGL there is no resonance denominator: N_cgl = x^2.5 / (i·n). return fx end +""" + _energy_numerator_deriv(x::Float64, p::EnergyParams) → ComplexF64 + +x-derivative dN/dx of `_energy_numerator`, used for the analytic regular-part +limit of the collisionless integrand at a resonance pole. CGL is excluded — the +collisionless real-pole path never carries a CGL numerator (CGL has no pole). +""" +@inline function _energy_numerator_deriv(x::Float64, p::EnergyParams)::ComplexF64 + sx = sqrt(x) + x15 = x * sx # x^1.5 + x25 = x * x15 # x^2.5 + if p.f0type == "maxwellian" + a = p.we + p.wn + p.wt * (x - 1.5) + nn = ComplexF64(a * x25) + dn = ComplexF64(p.wt * x25 + a * 2.5 * x15) # d/dx[(…)·x^2.5] + elseif p.f0type == "jkp" + a = p.we + p.wn + p.wt * 2 + nn = ComplexF64(a * x25) + dn = ComplexF64(a * 2.5 * x15) + else + error("_energy_numerator_deriv supports maxwellian and jkp") + end + return p.qt ? dn * (x - 2.5) + nn : dn # d/dx[N·(x-2.5)] = N′·(x-2.5) + N +end + """ _energy_integrand_real(x::Float64, p::EnergyParams) → ComplexF64 @@ -151,6 +176,27 @@ end # tail beyond this is negligible to any quadrature tolerance. const X_ENERGY_MAX = 72.0 +""" + _collisionless_regular_part(xr, p, leff, wb, n, wd) → ComplexF64 + +Laurent regular part (finite limit at `x → x_res`) of the pole-subtracted +collisionless integrand `N(x)·exp(-x)/(i·Ω(x)) − R/(x − x_res)`, with +`Ω(x) = leff·wb·√x + n·(we+wd·x)` and `R = N(x_res)·exp(-x_res)/(i·Ω′)`. + +Writing `h(x) = N(x)·exp(-x)`, the limit is +`[h′(x_res) − h(x_res)·Ω″/(2Ω′)] / (i·Ω′)`, with `h′ = (N′ − N)·exp(-x)`, +`Ω′ = leff·wb/(2√x) + n·wd`, `Ω″ = −leff·wb/(4·x^{3/2})`. +""" +@inline function _collisionless_regular_part(xr::Float64, p::EnergyParams, leff::Float64, + wb::Float64, n::Int, wd::Float64)::ComplexF64 + sx = sqrt(xr) + op = leff * wb / (2.0 * sx) + n * wd # Ω′(x_res) + opp = -leff * wb / (4.0 * xr * sx) # Ω″(x_res) + nn = _energy_numerator(xr, p) # N(x_res) + dn = _energy_numerator_deriv(xr, p) # N′(x_res) + return exp(-xr) * ((dn - nn) - nn * opp / (2.0 * op)) / (im * op) +end + """ _integrate_energy_collisionless(p, leff, wb, n, we, wd, atol, rtol) → ComplexF64 @@ -160,11 +206,12 @@ pole `x_res ∈ (0, X_ENERGY_MAX)` is removed analytically by principal-value + residue (Sokhotski-Plemelj, causal ν→0⁺ branch ∓iπ following sign Ω′), leaving a smooth integrand for QuadGK. -The collisionless pole sits on the real axis. In x-space it stays a -well-conditioned `O(1)` number, so the pole subtraction and its breakpoint behave -cleanly. The `u = 1-exp(-x)` substitution used for the collisional path -(`integrate_energy`) compresses tail poles toward `u=1`, where the subtraction is -numerically unresolvable — hence the dedicated real-space branch here. +The pole is on the real axis, so the resonance denominator +`Ω(x) = leff·wb·√x + n·(we+wd·x)` — a difference of `O(10⁴)` terms — rounds to +exactly `0` over a ~ULP-wide window around the pole, where the physical term is +`0/0`. There QuadGK is handed the analytic regular-part limit +(`_collisionless_regular_part`) instead. (The collisional path keeps the +`u = 1-exp(-x)` substitution, whose off-axis complex pole has none of these issues.) """ function _integrate_energy_collisionless(p::EnergyParams, leff::Float64, wb::Float64, n::Int, we::Float64, wd::Float64, @@ -182,7 +229,8 @@ function _integrate_energy_collisionless(p::EnergyParams, leff::Float64, wb::Flo abs(omega_prime) < SINGULAR_EPS && continue # Residue of N(x)·exp(-x)/(i·Ω(x)) at x_res, where Ω ≈ Ω′·(x - x_res) near the pole. R = _energy_numerator(xr, p) * exp(-xr) / (im * omega_prime) - # Causal (ν→0⁺) add-back: ∫₀^xmax R/(x - x_res) dx = R·[log(xmax - x_res) - log(x_res) ∓ iπ]. + # Causal (ν→0⁺) add-back ∫₀^xmax R/(x - x_res) dx = R·[log(xmax - x_res) - log(x_res) ∓ iπ]: + # the ν→0⁺ retarded limit of Fortran's ximag>0 contour (energy.f90); ∓ sign from sign(Ω′). pole_contribution += R * (log(X_ENERGY_MAX - xr) - log(xr) - im * π * sign(omega_prime)) push!(x_poles, xr) push!(residues, R) @@ -196,6 +244,20 @@ function _integrate_energy_collisionless(p::EnergyParams, leff::Float64, wb::Flo @inbounds for k in 1:npole val -= residues[k] / (x - x_poles[k]) end + # Inside a pole's flat-Ω window the physical term is 0/0 → val non-finite. Replace + # it with the analytic regular-part limit of the nearest pole (the other poles' + # subtractions stay finite and are kept). + if !isfinite(val) + k = 1 + @inbounds for j in 2:npole + abs(x - x_poles[j]) < abs(x - x_poles[k]) && (k = j) + end + val = _collisionless_regular_part(x_poles[k], p, leff, wb, n, wd) + @inbounds for j in 1:npole + j == k && continue + val -= residues[j] / (x - x_poles[j]) + end + end return val end @@ -205,8 +267,9 @@ function _integrate_energy_collisionless(p::EnergyParams, leff::Float64, wb::Flo end # Resonance locations as QuadGK breakpoints so the smooth-but-sharp integrand - # is resolved near each pole. - breaks = unique!(sort!(x_poles)) + # is resolved near each pole. Sort a copy — `x_poles` must stay aligned with + # `residues`, which the integrand pairs by index. + breaks = unique(sort(x_poles)) smooth_val, _ = quadgk(integrand, 0.0, breaks..., X_ENERGY_MAX; atol=atol, rtol=rtol) return smooth_val + pole_contribution end diff --git a/test/runtests_fullruns.jl b/test/runtests_fullruns.jl index f8804c1ef..088035197 100644 --- a/test/runtests_fullruns.jl +++ b/test/runtests_fullruns.jl @@ -81,4 +81,28 @@ using HDF5 rm(joinpath(ex5, "gpec.h5"); force=true) true end + + ex6 = joinpath(@__DIR__, "test_data", "regression_solovev_kinetic_nuzero") + @info "Running Solovev self-consistent kinetic-MHD example (kinetic_source=calculated, nutype=zero)" + @test begin + GeneralizedPerturbedEquilibrium.main([ex6]) + h5open(joinpath(ex6, "gpec.h5"), "r") do h5 + et = read(h5["FreeBoundaryStability/XiNorm/eigenmode_energies"]) + # Collisionless (nutype="zero") calculated kinetic-MHD eigenvalue. The collisionless + # energy integral runs in real x-space over [0, 72] (Fortran PENTRC convention) with + # an analytic principal-value + residue and a regular-part limit on the resonance + # poles (issue #281). Re(et[1]) must sit essentially on the harmonic value 15.888 + # (collisions are a small perturbation to the real energy); Im(et[1]) is the + # resonant (Landau ∓iπ) damping rate, smaller in magnitude than the harmonic + # -0.711 because the collisional broadening contribution is dropped. + @test isfinite(real(et[1])) + @test isfinite(imag(et[1])) + @test real(et[1]) > 0 + @test real(et[1]) ≈ 15.885 rtol = 0.01 # ≈ harmonic 15.888 (small-ν limit) + @test imag(et[1]) < 0 # resonant kinetic damping + @test imag(et[1]) ≈ -0.482 rtol = 0.10 + end + rm(joinpath(ex6, "gpec.h5"); force=true) + true + end end diff --git a/test/runtests_kinetic.jl b/test/runtests_kinetic.jl index 8a22e9832..3f9132d58 100644 --- a/test/runtests_kinetic.jl +++ b/test/runtests_kinetic.jl @@ -217,6 +217,24 @@ @test collisionless ≈ small_nu rtol=1e-3 end + @testset "collisionless tail-pole resonance (regression: was NaN)" begin + # Resonance deep in the Maxwellian tail (x_res ≈ 56): n·wd·s² + leff·wb·s + n·we = 0 + # with wb=1e3, wd=5e2, we=-3.5483e4 ⟹ s=√56, x_res≈56. Under the old u-space pole + # handling u_res = 1-exp(-56) rounds to 1.0, tripping 0·(-Inf)=NaN. The real-x-space + # branch keeps x_res a well-conditioned O(1) number, and the resonance contribution + # (∝ exp(-56)) is negligible so the result equals the ν→0⁺ limit (issue #281). + args = (0.0, 2.0e3, -3.5483e4, 5.0e2, 1.0e3) + tail = (0, 1.0, 1, 0.5, 0.5, "fgar") + @test KF.find_resonance_energies(1.0, 1.0e3, 1, -3.5483e4, 5.0e2)[1] ≈ 56.0 rtol = 1e-2 + collisionless = KF.integrate_energy(args..., 0.0, tail...; + nutype="zero", f0type="maxwellian", atol=1e-12, rtol=1e-10) + small_nu = KF.integrate_energy(args..., 1e-6, tail...; + nutype="krook", f0type="maxwellian", atol=1e-12, rtol=1e-10) + @test isfinite(real(collisionless)) + @test isfinite(imag(collisionless)) + @test collisionless ≈ small_nu rtol = 1e-3 + end + @testset "xr > 700 Maxwellian-underflow guard" begin # Linear case (wd = 0): s = -c/b = -(n·we)/(leff·wb) = 30 ⟹ x_res = 900 > 700. # The pole sits where exp(-x_res) underflows; subtraction trips 0·log(-1) = NaN diff --git a/test/test_data/regression_solovev_kinetic_nuzero/gpec.toml b/test/test_data/regression_solovev_kinetic_nuzero/gpec.toml new file mode 100644 index 000000000..a95122bcb --- /dev/null +++ b/test/test_data/regression_solovev_kinetic_nuzero/gpec.toml @@ -0,0 +1,56 @@ +[Equilibrium] +eq_type = "sol" # Type of the input 2D equilibrium file +eq_filename = "sol.toml" # Path to equilibrium file +jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc) +power_bp = 0 # Poloidal field power exponent for Jacobian +power_b = 0 # Toroidal field power exponent for Jacobian +power_r = 0 # Major radius power exponent for Jacobian +grid_type = "ldp" # Radial grid packing type +psilow = 1e-4 # Lower limit of normalized flux coordinate +psihigh = 0.9995 # Upper limit of normalized flux coordinate +mpsi = 16 # Number of radial grid points +mtheta = 256 # Number of poloidal grid points +newq0 = 0 # Override for on-axis safety factor (0 = use input value) +etol = 1e-7 # Error tolerance for equilibrium solver +force_termination = false # Terminate after equilibrium setup (skip stability calculations) + +[Wall] +shape = "conformal" # Wall shape (nowall, conformal, elliptical, dee, mod_dee, filepath) +a = 0.2415 # Distance from plasma (conformal) or shape parameter +aw = 0.05 # Half-thickness parameter for Dee-shaped walls +bw = 1.5 # Elongation parameter for wall shapes +cw = 0 # Offset of wall center from major radius +dw = 0.5 # Triangularity parameter for wall shapes +tw = 0.05 # Sharpness of wall corners (try 0.05 as initial value) +equal_arc_wall = true # Equal arc length distribution of nodes on wall + +[ForceFreeStates] +bal_flag = false # Ideal MHD ballooning criterion for short wavelengths +mat_flag = false # Construct coefficient matrices for diagnostic purposes +ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) +vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes +mer_flag = true # Evaluate the Mercier criterian + +psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak +qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... +qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)... +sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) + +nn_low = 1 # Smallest toroidal mode number to include +nn_high = 1 # Largest toroidal mode number to include +delta_mlow = 0 # Expands lower bound of Fourier harmonics +delta_mhigh = 0 # Expands upper bound of Fourier harmonics +delta_mband = 0 # Integration keeps only this wide a band... +mthvac = 64 # Number of points used in splines over poloidal angle at plasma-vacuum interface. +thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds + +kinetic_source = "calculated" # Kinetic matrix source — exercises KineticForces.compute_calculated_kinetic_matrices callback with real physics +kinetic_factor = 1.0 # Full-strength kinetic matrices (the "calculated" path is the real physics; no perturbation scaling) +eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations +singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced +ucrit = 1e3 # Maximum fraction of solutions allowed before re-normalized +write_outputs_to_HDF5 = true +verbose = false + +[KineticForces] +nutype = "zero" # Collisionless operator — isolates the real-x-space collisionless energy integral (issue #281) diff --git a/test/test_data/regression_solovev_kinetic_nuzero/kinetic.dat b/test/test_data/regression_solovev_kinetic_nuzero/kinetic.dat new file mode 100644 index 000000000..05c01a664 --- /dev/null +++ b/test/test_data/regression_solovev_kinetic_nuzero/kinetic.dat @@ -0,0 +1,12 @@ +psi_n n_i_m3 n_e_m3 T_i_eV T_e_eV omega_E_rads +0.00 5.000e19 5.000e19 2000.0 2000.0 1.0e4 +0.10 4.975e19 4.975e19 1990.0 1990.0 9.0e3 +0.20 4.900e19 4.900e19 1960.0 1960.0 8.0e3 +0.30 4.775e19 4.775e19 1910.0 1910.0 7.0e3 +0.40 4.600e19 4.600e19 1840.0 1840.0 6.0e3 +0.50 4.375e19 4.375e19 1750.0 1750.0 5.0e3 +0.60 4.100e19 4.100e19 1640.0 1640.0 4.0e3 +0.70 3.775e19 3.775e19 1510.0 1510.0 3.0e3 +0.80 3.400e19 3.400e19 1360.0 1360.0 2.0e3 +0.90 2.975e19 2.975e19 1190.0 1190.0 1.0e3 +1.00 2.500e19 2.500e19 1000.0 1000.0 0.0 diff --git a/test/test_data/regression_solovev_kinetic_nuzero/sol.toml b/test/test_data/regression_solovev_kinetic_nuzero/sol.toml new file mode 100644 index 000000000..e54fdeace --- /dev/null +++ b/test/test_data/regression_solovev_kinetic_nuzero/sol.toml @@ -0,0 +1,11 @@ +[SOL_INPUT] +mr = 128 # number of radial grid zones +mz = 128 # number of axial grid zones +ma = 128 # number of flux grid zones +e = 1.6 # elongation +a = 0.33 # minor radius +r0 = 1.0 # major radius +q0 = 1.9 # safety factor at the o-point +p0fac=1 # scale on-axis pressure (P-> P+P0*p0fac. beta changes. Phi,q constant) +b0fac=1 # scale toroidal field at constant beta (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant) +f0fac=1 # scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant) From 405acb8b2f2586f93d5d6a8748e79a36205b1ee1 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Sun, 14 Jun 2026 21:10:29 -0400 Subject: [PATCH 043/135] EXAMPLES - CLEANUP - Standardize TOML annotations, bundle a10 inputs, drop Fortran refs (#274) Re-standardize every git-tracked config-style TOML to one convention: a short purpose/context header, an inline comment on every variable sourced from the matching config struct's docstring, decorative section dividers removed, and the convention codified in CLAUDE.md so future edits stop diverging. Bundle the a10_kinetic_example inputs (g-file + kinetic profile) into the example directory and switch the TOML to relative filenames, removing the only hardcoded local paths in the repo so the example is runnable by anyone. Make example/fixture annotations self-contained and Julia-centric: drop all Fortran GPEC references (namelists, flag names, PENTRC/DCON/STRIDE) from examples/ and test/test_data/, and remove deprecated/no-op vars (truncate_at_dW_peak, thmax0). TJ-analytic model citations kept (not Fortran); regression-harness case files left as developer metadata. Verified: all TOMLs parse; parsed values unchanged except the two removed keys; a10 example runs end-to-end (gpec.h5 produced); regression harness solovev_n1 + diiid_n1 vs develop = 0 changed quantities. Co-Authored-By: Claude Opus 4.8 (1M context) --- CLAUDE.md | 37 + examples/DIIID-like_ideal_example/gpec.toml | 37 +- .../DIIID-like_ideal_example_IMAS/gpec.toml | 46 +- examples/LAR_beta_scan/gpec.toml | 128 +- examples/LAR_epsilon_scan/gpec.toml | 135 +- examples/Solovev_ideal_example/gpec.toml | 53 +- examples/Solovev_ideal_example/sol.toml | 24 +- examples/Solovev_ideal_example_3D/gpec.toml | 54 +- examples/Solovev_ideal_example_3D/sol.toml | 24 +- .../Solovev_ideal_example_multi_n/gpec.toml | 39 +- .../single_n_1/gpec.toml | 30 +- .../single_n_1/sol.toml | 24 +- .../single_n_2/gpec.toml | 30 +- .../single_n_2/sol.toml | 24 +- .../Solovev_ideal_example_multi_n/sol.toml | 24 +- examples/a10_kinetic_example/a10_prof1.txt | 252 + .../fix_a100_k10_q2_bn010_prof1 | 13624 ++++++++++++++++ examples/a10_kinetic_example/gpec.toml | 125 +- regression-harness/cases/diiid_n1.toml | 5 + regression-harness/cases/ggj_reference.toml | 4 + .../cases/solovev_kinetic_calculated.toml | 4 + regression-harness/cases/solovev_multi_n.toml | 4 + regression-harness/cases/solovev_n1.toml | 4 + .../gpec.toml | 52 +- .../regression_solovev_ideal_example/sol.toml | 24 +- .../gpec.toml | 54 +- .../sol.toml | 24 +- .../gpec.toml | 33 +- .../sol.toml | 24 +- .../gpec.toml | 54 +- .../sol.toml | 24 +- .../gpec.toml | 60 +- .../sol.toml | 24 +- 33 files changed, 14526 insertions(+), 578 deletions(-) create mode 100644 examples/a10_kinetic_example/a10_prof1.txt create mode 100644 examples/a10_kinetic_example/fix_a100_k10_q2_bn010_prof1 diff --git a/CLAUDE.md b/CLAUDE.md index e5686ae09..c113922bf 100644 --- a/CLAUDE.md +++ b/CLAUDE.md @@ -671,6 +671,43 @@ Additional file hygiene (enforced by pre-commit hooks): - Files must end with exactly one newline - LF line endings only (no CRLF) +### TOML Annotation Conventions + +Config-style TOML files (`examples/*/gpec.toml`, `examples/*/sol.toml`, the +`test/test_data/*` fixtures, and `regression-harness/cases/*.toml`) follow one shared +annotation style so they stay consistent and self-documenting for users who copy and +modify them. **Do not invent a new convention** — match what the existing example files do. + +1. **File header (2–10 lines).** Begin each config-style TOML with a plain `#` comment block + stating the example's purpose/context and calling out key settings (wall choice, forcing, + n-range, ideal vs kinetic). No ASCII-art separators or decorative dividers. +2. **Inline annotation on every variable line.** Every `key = value` gets a trailing + `# description`. Source the wording from the matching config struct's docstring + (`EquilibriumConfig`, `WallShapeSettings`, `ForceFreeStatesControl`, `ForcingTermsControl`, + `PerturbedEquilibriumControl`, `SolovevConfig`, `TJAnalyticConfig`, `KineticForcesControl`) + and keep it to one terse line. **Use the same description for the same variable across all + files** — `examples/DIIID-like_ideal_example/gpec.toml` is the canonical reference for the + common sections. +3. **Section comments only when informative.** No comment is required above a section. Keep a + block comment only when it carries real information (e.g. the Solovev `[Wall]` note on why a + conformal wall is needed). Never add decorative section dividers. +4. **No Fortran references — annotations must be self-contained and Julia-centric.** The Julia + code is the production workhorse; a new user must not need to know the legacy Fortran GPEC + code to read an example. Headers explain the *scenario and its unique aspect*; inline comments + explain the *variable*. Do **not** cite Fortran namelist files (`dcon.in`/`equil.in`/`pentrc.in`), + Fortran flag names (`kin_flag`, `sas_flag`, `electron_flag`, …), or legacy code names + (`DCON`/`STRIDE`/`PENTRC`) as things the reader must know. Non-Fortran external-model citations + (e.g. the analytic TJ model behind `tj_analytic`) are acceptable provenance. (This applies to + the user-facing `examples/*` and `test/test_data/*` TOMLs; `regression-harness/cases/*` may + retain algorithm names as developer metadata.) +5. **Only active, meaningful variables in examples.** Do not set deprecated or "not yet + implemented" variables just to mirror defaults — they add clutter and imply false relevance + (e.g. the `truncate_at_dW_peak` edge-peak truncation, `thmax0`). Omit them so examples show + only knobs that do something on that run. +6. **`Project.toml`-family files are exempt.** `Project.toml`, `docs/Project.toml`, + `regression-harness/Project.toml`, and `.JuliaFormatter.toml` are machine-managed; do not + inline-annotate dependency UUIDs or `[compat]` entries. + ### Performance - Pure Julia implementations are available for all major components and offer comparable or better performance than Fortran - Benchmarks available in `benchmark/` directory for Fourier transforms and vacuum calculations diff --git a/examples/DIIID-like_ideal_example/gpec.toml b/examples/DIIID-like_ideal_example/gpec.toml index 5c0aa87d6..70e88913e 100644 --- a/examples/DIIID-like_ideal_example/gpec.toml +++ b/examples/DIIID-like_ideal_example/gpec.toml @@ -1,3 +1,8 @@ +# DIII-D-like H-mode equilibrium — n=1 ideal stability + perturbed equilibrium. +# Free-boundary (nowall) external-kink analysis with DIII-D C-coil forcing applied +# via Biot-Savart from 3D coil wires. This is the canonical Δ'-matrix regression +# fixture (stable, clean BVP Δ') and the default benchmark case. + [Equilibrium] eq_filename = "TkMkr_D3Dlike_Hmode.geqdsk" # Path to equilibrium file eq_type = "efit" # Type of the input 2D equilibrium file @@ -28,37 +33,35 @@ equal_arc_wall = true # Equal arc length distribution of nodes on wall [ForceFreeStates] bal_flag = false # Ideal MHD ballooning criterion for short wavelengths mat_flag = true # Construct coefficient matrices for diagnostic purposes -ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) +ode_flag = true # Integrate ODEs for stability of the internal long-wavelength mode (must be true for GPEC) vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes -mer_flag = true # Evaluate the Mercier criterian +mer_flag = true # Evaluate the Mercier criterion -psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak -qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... -qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)... +psiedge = 0.99 # Edge dW(ψ) diagnostic scan band [psiedge, psilim]; set ≥ psilim to disable +qlow = 1.02 # Integration initiated at q determined by min(q0, qlow) +qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh) sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) nn_low = 1 # Smallest toroidal mode number to include nn_high = 1 # Largest toroidal mode number to include delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 8 # Expands upper bound of Fourier harmonics -delta_mband = 0 # Integration keeps only this wide a band... -mthvac = 512 # Number of points used in splines over poloidal angle at plasma-vacuum interface. -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds +delta_mband = 0 # Integration keeps only this wide a band of solutions (0 = full) +mthvac = 512 # Number of points in splines over poloidal angle at the plasma-vacuum interface -kinetic_source = "fixed" # Kinetic matrix source ("fixed" test matrices, or "calculated" from PENTRC) +kinetic_source = "fixed" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model kinetic_factor = 0.0 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode) -eulerlagrange_tolerance = 1e-10# Relative tolerance for ODE integration of Euler-Lagrange equations -save_interval = 3 # Save every Nth ODE step (1=all, 10=every 10th). Always saves near rational surfaces. +eulerlagrange_tolerance = 1e-10 # Relative tolerance for ODE integration of Euler-Lagrange equations +save_interval = 3 # Save every Nth ODE step (1=all). Always saves near rational surfaces. singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced -ucrit = 1e4 # Maximum fraction of solutions allowed before re-normalized +ucrit = 1e4 # Column-norm threshold that triggers solution renormalization # Δ' BVP + parallel integration (see ForceFreeStatesControl docstring for details) use_parallel = true # Run parallel FM-propagator BVP path (unlocks singular/delta_prime_matrix) parallel_threads = 2 # BVP thread cap (1 = serial/bit-deterministic; 2 ≈ +20% speedup; ≥3 saturates) -populate_dense_xi = true # REQUIRED for PerturbedEquilibrium (this TOML has a [PerturbedEquilibrium] section). Default is false; PE-using configs must set true when use_parallel=true. -truncate_at_dW_peak = false # Edge-dW scan stays diagnostic; integration domain set by qhigh / psihigh / dmlim -set_psilim_via_dmlim = true # TRUE for diverted geqdsks — q → ∞ at separatrix, so dmlim truncation avoids the δW kink instability at negligible domain cost -dmlim = 0.2 # Truncate integration at (last_rational_q + dmlim) / n +populate_dense_xi = true # Append serial-EL pass so dense ξ is stored — REQUIRED with a [PerturbedEquilibrium] section +set_psilim_via_dmlim = true # Truncate at (last_rational_q + dmlim)/n — TRUE for diverted equilibria (q → ∞ at separatrix) +dmlim = 0.2 # Truncate integration at (last_rational_q + dmlim)/n (used when set_psilim_via_dmlim = true) [ForcingTerms] forcing_data_format = "coil" # Format: "ascii", "hdf5", or "coil" (Biot-Savart from 3D wires) @@ -67,7 +70,7 @@ mtheta_coil = 480 # Poloidal grid for boundary B·n̂ eval nzeta_coil = 32 # Toroidal grid (0 = auto = 32·n) [[ForcingTerms.coil_set]] -name = "c" # DIII-D C-coil (6 coils); resolves to coil_geometries/d3d_c.dat +name = "c" # Coil set; resolves to coil_geometries/d3d_c.dat (DIII-D C-coil, 6 coils) currents = [1000.0, 500.0, -500.0, -1000.0, -500.0, 500.0] # n=1 cosine phasing, 1 kA peak [A] [PerturbedEquilibrium] diff --git a/examples/DIIID-like_ideal_example_IMAS/gpec.toml b/examples/DIIID-like_ideal_example_IMAS/gpec.toml index 55205c468..ea9faa90b 100644 --- a/examples/DIIID-like_ideal_example_IMAS/gpec.toml +++ b/examples/DIIID-like_ideal_example_IMAS/gpec.toml @@ -1,34 +1,34 @@ -# GPEC configuration for running from an IMAS data dictionary (IMASdd.dd). +# DIII-D-like equilibrium read from an IMAS data dictionary (IMASdd.dd) — n=1 ideal stability. +# The equilibrium is passed in at runtime, not read from a file; eq_filename is a placeholder. # # Usage (from Julia): # using GeneralizedPerturbedEquilibrium as GPEC # GPEC.main([dirname(@__FILE__)]; dd=my_dd) # -# The eq_filename field is a placeholder — the equilibrium is read directly -# from the dd passed at runtime. See run_imas_example.jl for a full workflow. +# See run_imas_example.jl for a full workflow. [Equilibrium] -eq_type = "imas" -eq_filename = "from_dd" # placeholder: equilibrium comes from runtime dd argument -jac_type = "boozer" -psilow = 0.01 -psihigh = 0.9995 -mpsi = 128 -mtheta = 256 -imas_cocos = 11 # IMAS standard COCOS (input dd is COCOS 11) +eq_type = "imas" # Type of the input 2D equilibrium file +eq_filename = "from_dd" # Path to equilibrium file (placeholder: equilibrium comes from the runtime dd argument) +jac_type = "boozer" # Coordinate system (hamada, pest, boozer, equal_arc) +psilow = 0.01 # Lower limit of normalized flux coordinate +psihigh = 0.9995 # Upper limit of normalized flux coordinate +mpsi = 128 # Number of radial grid points (0 = auto-compute from psi_accuracy) +mtheta = 256 # Number of poloidal grid points +imas_cocos = 11 # Expected COCOS convention of the input IMAS dd (11 = IMAS standard) [Wall] -shape = "nowall" +shape = "nowall" # Wall shape (nowall, conformal, elliptical, dee, mod_dee, filepath) [ForceFreeStates] -nn_low = 1 -nn_high = 1 -vac_flag = true -ode_flag = true -mat_flag = true -mer_flag = false -bal_flag = false -write_outputs_to_HDF5 = false -verbose = false -delta_mhigh = 16 -qlow = 1.02 +nn_low = 1 # Smallest toroidal mode number to include +nn_high = 1 # Largest toroidal mode number to include +vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes +ode_flag = true # Integrate ODEs for stability of the internal long-wavelength mode (must be true for GPEC) +mat_flag = true # Construct coefficient matrices for diagnostic purposes +mer_flag = false # Evaluate the Mercier criterion +bal_flag = false # Ideal MHD ballooning criterion for short wavelengths +write_outputs_to_HDF5 = false # Write outputs to the HDF5 file +verbose = false # Enable verbose logging +delta_mhigh = 16 # Expands upper bound of Fourier harmonics +qlow = 1.02 # Integration initiated at q determined by min(q0, qlow) diff --git a/examples/LAR_beta_scan/gpec.toml b/examples/LAR_beta_scan/gpec.toml index 4e2b43518..837eaefea 100644 --- a/examples/LAR_beta_scan/gpec.toml +++ b/examples/LAR_beta_scan/gpec.toml @@ -1,87 +1,67 @@ -# Single-file GPEC configuration for the TJ-analytic β (pressure factor) scan. +# GPEC configuration for the TJ-analytic β (pressure factor) scan. # -# The TJ-analytic equilibrium follows the profile family of -# R. Fitzpatrick's TJ code (https://github.com/rfitzp/TJ); we adapt the -# same f₁ / pressure / shape-ODE parameterization but feed the result -# through GPEC's own pipeline. -# -# The accompanying run_scan.jl reads this file, overrides only the scan -# parameter (TJ_ANALYTIC_INPUT.pc) per point, and writes a fresh gpec.toml -# into each tempdir. Every TJ-analytic equilibrium parameter is -# embedded in the [TJ_ANALYTIC_INPUT] section below — there is no side-car -# TOML file. +# The TJ-analytic equilibrium follows the analytic profile family of R. Fitzpatrick's +# TJ code (https://github.com/rfitzp/TJ): same f₁ / pressure / shape-ODE parameterization, +# fed through GPEC's own pipeline. The accompanying run_scan.jl reads this file, overrides +# only the scan parameter (TJ_ANALYTIC_INPUT.pc) per point, and writes a fresh gpec.toml +# into each tempdir. Every equilibrium parameter is embedded in [TJ_ANALYTIC_INPUT] below — +# there is no side-car TOML file. -# ──────────────────────────────────────────────────────────────────────── -# Equilibrium -# ──────────────────────────────────────────────────────────────────────── [Equilibrium] -eq_type = "tj_analytic" # TJ-analytic model (inverse pipeline; Fitzpatrick https://github.com/rfitzp/TJ) -jac_type = "hamada" # Flux-surface Jacobian convention used by the Euler-Lagrange ODE -grid_type = "ldp" # Radial-grid packing strategy (logarithmic, dense near rationals) -psilow = 0.01 # Lower normalized poloidal flux bound (start of integration) -psihigh = 0.995 # Upper normalized poloidal flux bound (end of integration) -mpsi = 128 # Number of radial spline nodes used to discretize ψ -mtheta = 512 # Number of poloidal spline nodes used to discretize θ +eq_type = "tj_analytic" # TJ-analytic model (inverse pipeline; Fitzpatrick https://github.com/rfitzp/TJ) +jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc) +grid_type = "ldp" # Radial grid packing type +psilow = 0.01 # Lower limit of normalized flux coordinate +psihigh = 0.995 # Upper limit of normalized flux coordinate +mpsi = 128 # Number of radial grid points (0 = auto-compute from psi_accuracy) +mtheta = 512 # Number of poloidal grid points -# ──────────────────────────────────────────────────────────────────────── -# TJ-analytic equilibrium parameters -# (cf. R. Fitzpatrick, TJ code, https://github.com/rfitzp/TJ) -# ──────────────────────────────────────────────────────────────────────── -# Geometry is FIXED at ε = a / R₀ = 0.4 / 2.0 = 0.2 (matches the TJ-analytic -# benchmark configuration of Fitzpatrick's TJ). run_scan.jl varies only -# `pc` per scan point; every other field is held constant. +# TJ-analytic equilibrium parameters (cf. R. Fitzpatrick, TJ code, https://github.com/rfitzp/TJ). +# Geometry is FIXED at ε = a / R₀ = 0.4 / 2.0 = 0.2; run_scan.jl varies only `pc` per point. [TJ_ANALYTIC_INPUT] -lar_r0 = 2.0 # Major radius R₀ [m] (centerline radius of the magnetic axis) -lar_a = 0.4 # Minor radius a [m] (plasma half-width at the midplane; here ε = 0.2) -qc = 1.5 # On-axis safety factor q(r=0) [dimensionless] -qa = 3.6 # Edge safety factor q(r=a) [dimensionless] -pc = 0.001 # Normalized on-axis pressure (β-scan parameter; OVERRIDDEN per run by run_scan.jl) -mu = 2.0 # Pressure-profile peaking exponent in p₂(r) = pc·(1−r²)^μ -B0 = 12.0 # On-axis toroidal magnetic field strength [T] -ma = 128 # TJ-analytic internal radial grid resolution (shape-ODE nodes) -mtau = 128 # TJ-analytic internal poloidal grid resolution (θ-spline nodes) +lar_r0 = 2.0 # Major radius R₀ [m] (centerline radius of the magnetic axis) +lar_a = 0.4 # Minor radius a [m] (plasma half-width at the midplane; here ε = 0.2) +qc = 1.5 # On-axis safety factor q(r=0) +qa = 3.6 # Edge safety factor q(r=a) +pc = 0.001 # Normalized on-axis pressure (β-scan parameter; OVERRIDDEN per run by run_scan.jl) +mu = 2.0 # Pressure-profile peaking exponent in p₂(r) = pc·(1−r²)^μ +B0 = 12.0 # On-axis toroidal field [T] +ma = 128 # TJ-analytic internal radial grid resolution (shape-ODE nodes) +mtau = 128 # TJ-analytic internal poloidal grid resolution (θ-spline nodes) -# ──────────────────────────────────────────────────────────────────────── -# Wall -# ──────────────────────────────────────────────────────────────────────── [Wall] -shape = "conformal" # Vacuum wall shape model: scales the plasma boundary by factor `a` -a = 20 # Wall scale-out multiplier; 20× the plasma radius → effectively no wall +shape = "conformal" # Wall shape (nowall, conformal, elliptical, dee, mod_dee, filepath) +a = 20 # Distance from plasma (conformal) or shape parameter (20× → effectively no wall) -# ──────────────────────────────────────────────────────────────────────── -# Force-Free States -# ──────────────────────────────────────────────────────────────────────── [ForceFreeStates] -bal_flag = false # Skip ballooning stability scan (compute_ballooning_stability!) -mat_flag = true # Construct F, G, K coupling matrices on the radial grid -ode_flag = true # Integrate the ideal-MHD Euler-Lagrange ODE for displacement ξ -vac_flag = true # Compute vacuum response and free-boundary energy eigenvalues -mer_flag = true # Evaluate the Mercier local-stability criterion across ψ +bal_flag = false # Ideal MHD ballooning criterion for short wavelengths +mat_flag = true # Construct coefficient matrices for diagnostic purposes +ode_flag = true # Integrate ODEs for stability of the internal long-wavelength mode (must be true for GPEC) +vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes +mer_flag = true # Evaluate the Mercier criterion -qlow = 1.02 # Lowest q to include singular surfaces (axis side cutoff) -qhigh = 3.6 # Highest q to include singular surfaces (edge side cutoff) -sing_start = 0 # Start integration at the axis (0) rather than at a singular surface +qlow = 1.02 # Integration initiated at q determined by min(q0, qlow) +qhigh = 3.6 # Integration terminated at q limit determined by min(qa, qhigh) +sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) -nn_low = 1 # Lower bound of toroidal mode-number range n ∈ [nn_low, nn_high] -nn_high = 1 # Upper bound of toroidal mode-number range -delta_mlow = 8 # Poloidal-mode padding below the resonant-m band -delta_mhigh = 8 # Poloidal-mode padding above the resonant-m band -delta_mband = 0 # Extra coupling-matrix band width (0 = full mpert × mpert) -mthvac = 960 # Poloidal resolution used by the vacuum-response integrator -thmax0 = 1 # Number of poloidal periods spanned by the vacuum coordinate +nn_low = 1 # Smallest toroidal mode number to include +nn_high = 1 # Largest toroidal mode number to include +delta_mlow = 8 # Expands lower bound of Fourier harmonics +delta_mhigh = 8 # Expands upper bound of Fourier harmonics +delta_mband = 0 # Integration keeps only this wide a band of solutions (0 = full) +mthvac = 960 # Number of points in splines over poloidal angle at the plasma-vacuum interface -eulerlagrange_tolerance = 1e-12 # ODE solver relative tolerance for the EL integration -singfac_min = 1e-4 # Inner-layer cutoff distance from rational surfaces (chunk boundary) -ucrit = 1e4 # Riccati renormalization threshold (max allowed column norm) -sing_order = 6 # Truncation order of singular-surface asymptotic series expansion +eulerlagrange_tolerance = 1e-12 # Relative tolerance for ODE integration of Euler-Lagrange equations +singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced +ucrit = 1e4 # Column-norm threshold that triggers solution renormalization +sing_order = 6 # Order of the singular-surface (Frobenius) series expansion -use_parallel = true # Run parallel FM-propagator BVP path (unlocks singular/delta_prime_matrix) -parallel_threads = 2 # BVP thread cap (1 = serial/bit-deterministic; 2 ≈ +20% speedup; ≥3 saturates) -populate_dense_xi = false # No PerturbedEquilibrium section — skip the serial-EL re-run (matches new default) -truncate_at_dW_peak = false # Edge-dW scan stays diagnostic; integration domain set by qhigh / psihigh / dmlim -set_psilim_via_dmlim = false # FALSE for limited circular / analytical equilibria — rationals sparse, dmlim truncation would chop too much edge -dmlim = 0.2 # Only used when set_psilim_via_dmlim = true: truncate at (last_rational_q + dmlim) / n -force_termination = true # Stop after Force-Free States; do NOT enter Perturbed Equilibrium -write_outputs_to_HDF5 = true # Save integration / Δ' / vacuum data to an HDF5 file -HDF5_filename = "gpec.h5" # Output filename (run_scan.jl overrides this per scan point) -save_interval = 3 # Save every Nth ODE step into u_store/ud_store (1 = every step) +use_parallel = true # Run parallel FM-propagator BVP path (unlocks singular/delta_prime_matrix) +parallel_threads = 2 # BVP thread cap (1 = serial/bit-deterministic; 2 ≈ +20% speedup; ≥3 saturates) +populate_dense_xi = false # Append serial-EL pass for dense ξ; not needed without [PerturbedEquilibrium] (default false) +set_psilim_via_dmlim = false # FALSE for limited/analytical equilibria — rationals sparse, dmlim would chop too much edge +dmlim = 0.2 # Truncate integration at (last_rational_q + dmlim)/n (used when set_psilim_via_dmlim = true) +force_termination = true # Stop after force-free states (skip perturbed equilibrium) +write_outputs_to_HDF5 = true # Write outputs to the HDF5 file +HDF5_filename = "gpec.h5" # Output HDF5 filename (run_scan.jl overrides this per scan point) +save_interval = 3 # Save every Nth ODE step (1=all). Always saves near rational surfaces. diff --git a/examples/LAR_epsilon_scan/gpec.toml b/examples/LAR_epsilon_scan/gpec.toml index 179a54a8c..604a877c4 100644 --- a/examples/LAR_epsilon_scan/gpec.toml +++ b/examples/LAR_epsilon_scan/gpec.toml @@ -1,93 +1,68 @@ -# Single-file GPEC configuration for the TJ-analytic ε (inverse aspect ratio) -# scan. +# GPEC configuration for the TJ-analytic ε (inverse aspect ratio) scan. # -# The TJ-analytic equilibrium follows the profile family of -# R. Fitzpatrick's TJ code (https://github.com/rfitzp/TJ); we adapt the -# same f₁ / pressure / shape-ODE parameterization but feed the result -# through GPEC's own pipeline. -# -# The accompanying run_scan.jl reads this file, overrides only the scan -# parameter (TJ_ANALYTIC_INPUT.lar_r0 = TJ_ANALYTIC_INPUT.lar_a / ε) per point, -# and writes a fresh gpec.toml into each tempdir. Every TJ-analytic -# analytic-equilibrium parameter is embedded in the [TJ_ANALYTIC_INPUT] -# section below — there is no side-car TOML file. +# The TJ-analytic equilibrium follows the analytic profile family of R. Fitzpatrick's +# TJ code (https://github.com/rfitzp/TJ): same f₁ / pressure / shape-ODE parameterization, +# fed through GPEC's own pipeline. run_scan.jl overrides eq_type to "tj_analytic_direct" +# (direct-GS path, required to capture the ideal external-kink pole δW_t → 0 as ε → ε_crit) +# and varies only TJ_ANALYTIC_INPUT.lar_r0 = lar_a / ε per point, writing a fresh gpec.toml +# into each tempdir. Every equilibrium parameter is embedded in [TJ_ANALYTIC_INPUT] below. -# ──────────────────────────────────────────────────────────────────────── -# Equilibrium -# ──────────────────────────────────────────────────────────────────────── -# Note: run_scan.jl overrides `eq_type` to "tj_analytic_direct" so the analytic -# ψ(R,Z) is processed by the direct-GS pipeline. Required to capture the -# ideal external-kink pole (δW_t → 0 as ε → ε_crit); the "tj_analytic" inverse -# path bypasses the line-integrated q and shows no such pole. The -# "tj_analytic" value below is a fallback for ad-hoc invocations. [Equilibrium] -eq_type = "tj_analytic" # TJ-analytic model (inverse pipeline; overridden to "tj_analytic_direct" by run_scan.jl) -jac_type = "hamada" # Flux-surface Jacobian convention used by the Euler-Lagrange ODE -grid_type = "ldp" # Radial-grid packing strategy (logarithmic, dense near rationals) -psilow = 0.01 # Lower normalized poloidal flux bound (start of integration) -psihigh = 0.995 # Upper normalized poloidal flux bound (end of integration) -mpsi = 128 # Number of radial spline nodes used to discretize ψ -mtheta = 512 # Number of poloidal spline nodes used to discretize θ +eq_type = "tj_analytic" # TJ-analytic model (inverse pipeline; overridden to "tj_analytic_direct" by run_scan.jl) +jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc) +grid_type = "ldp" # Radial grid packing type +psilow = 0.01 # Lower limit of normalized flux coordinate +psihigh = 0.995 # Upper limit of normalized flux coordinate +mpsi = 128 # Number of radial grid points (0 = auto-compute from psi_accuracy) +mtheta = 512 # Number of poloidal grid points -# ──────────────────────────────────────────────────────────────────────── -# TJ-analytic equilibrium parameters -# (cf. R. Fitzpatrick, TJ code, https://github.com/rfitzp/TJ) -# ──────────────────────────────────────────────────────────────────────── -# All TJ-analytic parameters are held FIXED except `lar_r0`, which run_scan.jl -# overrides per scan point as `lar_r0 = lar_a / ε`. `lar_a` stays fixed at -# 1 m so each scan point is a self-similar rescaling of the geometry. +# TJ-analytic equilibrium parameters (cf. R. Fitzpatrick, TJ code, https://github.com/rfitzp/TJ). +# All parameters held FIXED except lar_r0, which run_scan.jl overrides as lar_r0 = lar_a / ε; +# lar_a stays fixed at 1 m so each scan point is a self-similar rescaling of the geometry. [TJ_ANALYTIC_INPUT] -lar_r0 = 5.0 # Major radius R₀ [m] (baseline ε = 0.2; OVERRIDDEN per scan point by run_scan.jl) -lar_a = 1.0 # Minor radius a [m] (plasma half-width at the midplane; fixed across the scan) -qc = 1.5 # On-axis safety factor q(r=0) [dimensionless] -qa = 3.6 # Edge safety factor q(r=a) [dimensionless] -pc = 0.001 # Normalized on-axis pressure (kept low for the ε scan to isolate geometry effects) -mu = 2.0 # Pressure-profile peaking exponent in p₂(r) = pc·(1−r²)^μ -B0 = 12.0 # On-axis toroidal magnetic field strength [T] -ma = 128 # TJ-analytic internal radial grid resolution (shape-ODE nodes) -mtau = 128 # TJ-analytic internal poloidal grid resolution (θ-spline nodes) +lar_r0 = 5.0 # Major radius R₀ [m] (baseline ε = 0.2; OVERRIDDEN per scan point by run_scan.jl) +lar_a = 1.0 # Minor radius a [m] (plasma half-width at the midplane; fixed across the scan) +qc = 1.5 # On-axis safety factor q(r=0) +qa = 3.6 # Edge safety factor q(r=a) +pc = 0.001 # Normalized on-axis pressure (kept low for the ε scan to isolate geometry effects) +mu = 2.0 # Pressure-profile peaking exponent in p₂(r) = pc·(1−r²)^μ +B0 = 12.0 # On-axis toroidal field [T] +ma = 128 # TJ-analytic internal radial grid resolution (shape-ODE nodes) +mtau = 128 # TJ-analytic internal poloidal grid resolution (θ-spline nodes) -# ──────────────────────────────────────────────────────────────────────── -# Wall -# ──────────────────────────────────────────────────────────────────────── [Wall] -shape = "conformal" # Vacuum wall shape model: scales the plasma boundary by factor `a` -a = 20 # Wall scale-out multiplier; 20× the plasma radius → effectively no wall +shape = "conformal" # Wall shape (nowall, conformal, elliptical, dee, mod_dee, filepath) +a = 20 # Distance from plasma (conformal) or shape parameter (20× → effectively no wall) -# ──────────────────────────────────────────────────────────────────────── -# Force-Free States -# ──────────────────────────────────────────────────────────────────────── [ForceFreeStates] -bal_flag = false # Skip ballooning stability scan (compute_ballooning_stability!) -mat_flag = true # Construct F, G, K coupling matrices on the radial grid -ode_flag = true # Integrate the ideal-MHD Euler-Lagrange ODE for displacement ξ -vac_flag = true # Compute vacuum response and free-boundary energy eigenvalues -mer_flag = true # Evaluate the Mercier local-stability criterion across ψ +bal_flag = false # Ideal MHD ballooning criterion for short wavelengths +mat_flag = true # Construct coefficient matrices for diagnostic purposes +ode_flag = true # Integrate ODEs for stability of the internal long-wavelength mode (must be true for GPEC) +vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes +mer_flag = true # Evaluate the Mercier criterion -qlow = 1.02 # Lowest q to include singular surfaces (axis side cutoff) -qhigh = 3.6 # Highest q to include singular surfaces (edge side cutoff) -sing_start = 0 # Start integration at the axis (0) rather than at a singular surface +qlow = 1.02 # Integration initiated at q determined by min(q0, qlow) +qhigh = 3.6 # Integration terminated at q limit determined by min(qa, qhigh) +sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) -nn_low = 1 # Lower bound of toroidal mode-number range n ∈ [nn_low, nn_high] -nn_high = 1 # Upper bound of toroidal mode-number range -delta_mlow = 8 # Poloidal-mode padding below the resonant-m band -delta_mhigh = 8 # Poloidal-mode padding above the resonant-m band -delta_mband = 0 # Extra coupling-matrix band width (0 = full mpert × mpert) -mthvac = 960 # Poloidal resolution used by the vacuum-response integrator -thmax0 = 1 # Number of poloidal periods spanned by the vacuum coordinate +nn_low = 1 # Smallest toroidal mode number to include +nn_high = 1 # Largest toroidal mode number to include +delta_mlow = 8 # Expands lower bound of Fourier harmonics +delta_mhigh = 8 # Expands upper bound of Fourier harmonics +delta_mband = 0 # Integration keeps only this wide a band of solutions (0 = full) +mthvac = 960 # Number of points in splines over poloidal angle at the plasma-vacuum interface -eulerlagrange_tolerance = 1e-12 # ODE solver relative tolerance for the EL integration -singfac_min = 1e-4 # Inner-layer cutoff distance from rational surfaces (chunk boundary) -ucrit = 1e4 # Riccati renormalization threshold (max allowed column norm) -sing_order = 6 # Truncation order of singular-surface asymptotic series expansion +eulerlagrange_tolerance = 1e-12 # Relative tolerance for ODE integration of Euler-Lagrange equations +singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced +ucrit = 1e4 # Column-norm threshold that triggers solution renormalization +sing_order = 6 # Order of the singular-surface (Frobenius) series expansion -use_parallel = true # Run parallel FM-propagator BVP path (unlocks singular/delta_prime_matrix) -parallel_threads = 2 # BVP thread cap (1 = serial/bit-deterministic; 2 ≈ +20% speedup; ≥3 saturates) -populate_dense_xi = false # No PerturbedEquilibrium section — skip the serial-EL re-run (matches new default) -truncate_at_dW_peak = false # Edge-dW scan stays diagnostic; integration domain set by qhigh / psihigh / dmlim -set_psilim_via_dmlim = false # FALSE for limited circular / analytical equilibria — rationals sparse, dmlim truncation would chop too much edge -dmlim = 0.2 # Only used when set_psilim_via_dmlim = true: truncate at (last_rational_q + dmlim) / n -force_termination = true # Stop after Force-Free States; do NOT enter Perturbed Equilibrium -write_outputs_to_HDF5 = true # Save integration / Δ' / vacuum data to an HDF5 file -HDF5_filename = "gpec.h5" # Output filename (run_scan.jl overrides this per scan point) -save_interval = 3 # Save every Nth ODE step into u_store/ud_store (1 = every step) +use_parallel = true # Run parallel FM-propagator BVP path (unlocks singular/delta_prime_matrix) +parallel_threads = 2 # BVP thread cap (1 = serial/bit-deterministic; 2 ≈ +20% speedup; ≥3 saturates) +populate_dense_xi = false # Append serial-EL pass for dense ξ; not needed without [PerturbedEquilibrium] (default false) +set_psilim_via_dmlim = false # FALSE for limited/analytical equilibria — rationals sparse, dmlim would chop too much edge +dmlim = 0.2 # Truncate integration at (last_rational_q + dmlim)/n (used when set_psilim_via_dmlim = true) +force_termination = true # Stop after force-free states (skip perturbed equilibrium) +write_outputs_to_HDF5 = true # Write outputs to the HDF5 file +HDF5_filename = "gpec.h5" # Output HDF5 filename (run_scan.jl overrides this per scan point) +save_interval = 3 # Save every Nth ODE step (1=all). Always saves near rational surfaces. diff --git a/examples/Solovev_ideal_example/gpec.toml b/examples/Solovev_ideal_example/gpec.toml index 2e8d3df82..dd155473e 100644 --- a/examples/Solovev_ideal_example/gpec.toml +++ b/examples/Solovev_ideal_example/gpec.toml @@ -1,3 +1,8 @@ +# Solovev analytical equilibrium — n=1 ideal stability + perturbed equilibrium. +# Near-marginal n=1 external kink stabilized by a close conformal wall (see [Wall] note). +# Integration-pipeline smoke-test and et[1] regression fixture; the equilibrium is +# generated analytically from the side-car sol.toml ([SOL_INPUT]). + [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file @@ -8,13 +13,12 @@ power_r = 0 # Major radius power exponent for Jacobi grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized flux coordinate psihigh = 0.9995 # Upper limit of normalized flux coordinate -mpsi = 128 # Number of radial grid points +mpsi = 128 # Number of radial grid points (0 = auto-compute from psi_accuracy) mtheta = 256 # Number of poloidal grid points newq0 = 0 # Override for on-axis safety factor (0 = use input value) etol = 1e-7 # Error tolerance for equilibrium solver force_termination = false # Terminate after equilibrium setup (skip stability calculations) - [Wall] # Close conformal wall is required to stabilize this Solovev fixture's n=1 external kink: # with nowall, et[1] = -6.8 (strongly unstable); with this wall, et[1] = +0.24 (barely stable). @@ -33,50 +37,47 @@ equal_arc_wall = true # Equal arc length distribution of nodes [ForcingTerms] forcing_data_file = "forcing.dat" # Manual mode table (n, m, real, imag) -forcing_data_format = "ascii" # "ascii" or "hdf5" +forcing_data_format = "ascii" # Format: "ascii", "hdf5", or "coil" (Biot-Savart from 3D wires) [PerturbedEquilibrium] -fixed_boundary = false # Fixed boundary flag -output_eigenmodes = true # Output mode fields as b-fields -compute_response = true # Compute plasma response -compute_singular_coupling = true # Compute singular coupling metrics +fixed_boundary = false # Use fixed boundary conditions +output_eigenmodes = true # Output eigenmode fields as b-fields +compute_response = true # Compute plasma response to forcing +compute_singular_coupling = true # Compute singular layer coupling metrics verbose = true # Enable verbose logging -write_outputs_to_HDF5 = true # Write outputs to HDF5 +write_outputs_to_HDF5 = true # Write perturbed equilibrium outputs to HDF5 reg_spot = 0.05 # Regularization width for singular surfaces (0 = disabled) [ForceFreeStates] bal_flag = false # Ideal MHD ballooning criterion for short wavelengths mat_flag = true # Construct coefficient matrices for diagnostic purposes -ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) +ode_flag = true # Integrate ODEs for stability of the internal long-wavelength mode (must be true for GPEC) vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes -mer_flag = true # Evaluate the Mercier criterian +mer_flag = true # Evaluate the Mercier criterion -psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak -qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... -qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)... +psiedge = 0.99 # Edge dW(ψ) diagnostic scan band [psiedge, psilim]; set ≥ psilim to disable +qlow = 1.02 # Integration initiated at q determined by min(q0, qlow) +qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh) sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) nn_low = 1 # Smallest toroidal mode number to include nn_high = 1 # Largest toroidal mode number to include delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 8 # Expands upper bound of Fourier harmonics -delta_mband = 0 # Integration keeps only this wide a band... -mthvac = 960 # Number of points used in splines over poloidal angle at plasma-vacuum interface. -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds +delta_mband = 0 # Integration keeps only this wide a band of solutions (0 = full) +mthvac = 960 # Number of points in splines over poloidal angle at the plasma-vacuum interface -kinetic_source = "fixed" # Kinetic matrix source ("fixed" test matrices, or "calculated" from PENTRC) +kinetic_source = "fixed" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model kinetic_factor = 0.0 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode) eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced -ucrit = 1e3 # Maximum fraction of solutions allowed before re-normalized -force_wv_symmetry = true # Forces vacuum energy matrix symmetry -save_interval = 3 # Save every Nth ODE step (1=all, 10=every 10th). Always saves near rational surfaces. +ucrit = 1e3 # Column-norm threshold that triggers solution renormalization +force_wv_symmetry = true # Enforce symmetry of the vacuum energy matrix +save_interval = 3 # Save every Nth ODE step (1=all). Always saves near rational surfaces. # Δ' BVP + parallel integration (see ForceFreeStatesControl docstring for details) -use_parallel = true # Parallel FM-propagator BVP — ~5× faster than serial EL on this delta_m-expanded grid even though Δ' is pathological on this near-marginal Solovev (kept on for speed, not for Δ' validation) +use_parallel = true # Run parallel FM-propagator BVP path (unlocks singular/delta_prime_matrix) parallel_threads = 2 # BVP thread cap (1 = serial/bit-deterministic; 2 ≈ +20% speedup; ≥3 saturates) -populate_dense_xi = true # REQUIRED for PerturbedEquilibrium (this TOML has a [PerturbedEquilibrium] section). Default is false; PE-using configs must set true when use_parallel=true. -truncate_at_dW_peak = false # Edge-dW scan stays diagnostic; integration domain set by qhigh / psihigh / dmlim -set_psilim_via_dmlim = false # FALSE for limited circular / analytical equilibria — rationals sparse, dmlim truncation would chop too much edge -dmlim = 0.2 # Only used when set_psilim_via_dmlim = true: truncate at (last_rational_q + dmlim) / n - +populate_dense_xi = true # Append serial-EL pass so dense ξ is stored — REQUIRED with a [PerturbedEquilibrium] section +set_psilim_via_dmlim = false # FALSE for limited/analytical equilibria — rationals sparse, dmlim would chop too much edge +dmlim = 0.2 # Truncate integration at (last_rational_q + dmlim)/n (used when set_psilim_via_dmlim = true) diff --git a/examples/Solovev_ideal_example/sol.toml b/examples/Solovev_ideal_example/sol.toml index e54fdeace..86348c36d 100644 --- a/examples/Solovev_ideal_example/sol.toml +++ b/examples/Solovev_ideal_example/sol.toml @@ -1,11 +1,15 @@ +# Solovev analytical equilibrium parameters, consumed by gpec.toml (eq_type = "sol"). +# Sets the grid resolution, plasma shape, and field/pressure scaling factors used to +# generate the analytic Solovev equilibrium. See SolovevConfig in src/Equilibrium. + [SOL_INPUT] -mr = 128 # number of radial grid zones -mz = 128 # number of axial grid zones -ma = 128 # number of flux grid zones -e = 1.6 # elongation -a = 0.33 # minor radius -r0 = 1.0 # major radius -q0 = 1.9 # safety factor at the o-point -p0fac=1 # scale on-axis pressure (P-> P+P0*p0fac. beta changes. Phi,q constant) -b0fac=1 # scale toroidal field at constant beta (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant) -f0fac=1 # scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant) +mr = 128 # Number of radial grid zones +mz = 128 # Number of axial grid zones +ma = 128 # Number of flux grid zones +e = 1.6 # Elongation +a = 0.33 # Minor radius +r0 = 1.0 # Major radius +q0 = 1.9 # Safety factor at the magnetic axis (O-point) +p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) +b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) +f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/examples/Solovev_ideal_example_3D/gpec.toml b/examples/Solovev_ideal_example_3D/gpec.toml index e5526ddcb..7ffb4c618 100644 --- a/examples/Solovev_ideal_example_3D/gpec.toml +++ b/examples/Solovev_ideal_example_3D/gpec.toml @@ -1,3 +1,7 @@ +# Solovev analytical equilibrium — 3D (toroidally resolved) n=1 ideal stability. +# Same near-marginal Solovev plasma as Solovev_ideal_example, with the vacuum response +# evaluated on a toroidal grid (nzvac > 1). Equilibrium is generated from sol.toml. + [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file @@ -8,7 +12,7 @@ power_r = 0 # Major radius power exponent for Jacobi grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized flux coordinate psihigh = 0.9995 # Upper limit of normalized flux coordinate -mpsi = 128 # Number of radial grid points +mpsi = 128 # Number of radial grid points (0 = auto-compute from psi_accuracy) mtheta = 256 # Number of poloidal grid points newq0 = 0 # Override for on-axis safety factor (0 = use input value) etol = 1e-7 # Error tolerance for equilibrium solver @@ -17,39 +21,37 @@ force_termination = false # Terminate after equilibrium setup (ski [ForceFreeStates] bal_flag = false # Ideal MHD ballooning criterion for short wavelengths mat_flag = true # Construct coefficient matrices for diagnostic purposes -ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) +ode_flag = true # Integrate ODEs for stability of the internal long-wavelength mode (must be true for GPEC) vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes -mer_flag = true # Evaluate the Mercier criterian +mer_flag = true # Evaluate the Mercier criterion -psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak -qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... -qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)... +psiedge = 0.99 # Edge dW(ψ) diagnostic scan band [psiedge, psilim]; set ≥ psilim to disable +qlow = 1.02 # Integration initiated at q determined by min(q0, qlow) +qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh) sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) nn_low = 1 # Smallest toroidal mode number to include nn_high = 1 # Largest toroidal mode number to include delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 8 # Expands upper bound of Fourier harmonics -delta_mband = 0 # Integration keeps only this wide a band... -mthvac = 96 # Number of points used in splines over poloidal angle at plasma-vacuum interface. -nzvac = 64 -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds +delta_mband = 0 # Integration keeps only this wide a band of solutions (0 = full) +mthvac = 96 # Number of points in splines over poloidal angle at the plasma-vacuum interface +nzvac = 64 # Number of toroidal grid points for the 3D vacuum response -kinetic_source = "fixed" # Kinetic matrix source ("fixed" test matrices, or "calculated" from PENTRC) +kinetic_source = "fixed" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model kinetic_factor = 0.0 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode) eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced -ucrit = 1e3 # Maximum fraction of solutions allowed before re-normalized -force_wv_symmetry = true # Forces vacuum energy matrix symmetry -save_interval = 3 # Save every Nth ODE step (1=all, 10=every 10th). Always saves near rational surfaces. +ucrit = 1e3 # Column-norm threshold that triggers solution renormalization +force_wv_symmetry = true # Enforce symmetry of the vacuum energy matrix +save_interval = 3 # Save every Nth ODE step (1=all). Always saves near rational surfaces. # Δ' BVP + parallel integration (see ForceFreeStatesControl docstring for details) use_parallel = true # Run parallel FM-propagator BVP path (unlocks singular/delta_prime_matrix) parallel_threads = 2 # BVP thread cap (1 = serial/bit-deterministic; 2 ≈ +20% speedup; ≥3 saturates) -populate_dense_xi = false # No PerturbedEquilibrium section — skip the serial-EL re-run (matches new default) -truncate_at_dW_peak = false # Edge-dW scan stays diagnostic; integration domain set by qhigh / psihigh / dmlim -set_psilim_via_dmlim = false # FALSE for limited circular / analytical equilibria — rationals sparse, dmlim truncation would chop too much edge -dmlim = 0.2 # Only used when set_psilim_via_dmlim = true: truncate at (last_rational_q + dmlim) / n +populate_dense_xi = false # Append serial-EL pass for dense ξ; not needed without [PerturbedEquilibrium] (default false) +set_psilim_via_dmlim = false # FALSE for limited/analytical equilibria — rationals sparse, dmlim would chop too much edge +dmlim = 0.2 # Truncate integration at (last_rational_q + dmlim)/n (used when set_psilim_via_dmlim = true) [Wall] # See examples/Solovev_ideal_example/gpec.toml for the rationale behind the close conformal wall. @@ -62,13 +64,13 @@ dw = 0.5 # Triangularity parameter for wall shape tw = 0.05 # Sharpness of wall corners (try 0.05 as initial value) equal_arc_wall = false # Equal arc length distribution of nodes on wall +# Uncomment to enable perturbed equilibrium calculations: # [PerturbedEquilibrium] -# # Uncomment this section to enable perturbed equilibrium calculations -# forcing_data_file = "forcing.dat" # Path to forcing data (n, m, real, imag) -# forcing_data_format = "ascii" # "ascii" or "hdf5" -# fixed_boundary = false # Fixed boundary flag -# output_eigenmodes = true # Output mode fields as b-fields -# compute_response = true # Compute plasma response -# compute_singular_coupling = true # Compute singular coupling metrics +# forcing_data_file = "forcing.dat" # Manual mode table (n, m, real, imag) +# forcing_data_format = "ascii" # Format: "ascii", "hdf5", or "coil" (Biot-Savart from 3D wires) +# fixed_boundary = false # Use fixed boundary conditions +# output_eigenmodes = true # Output eigenmode fields as b-fields +# compute_response = true # Compute plasma response to forcing +# compute_singular_coupling = true # Compute singular layer coupling metrics # verbose = true # Enable verbose logging -# write_outputs_to_HDF5 = true # Write outputs to HDF5 +# write_outputs_to_HDF5 = true # Write perturbed equilibrium outputs to HDF5 diff --git a/examples/Solovev_ideal_example_3D/sol.toml b/examples/Solovev_ideal_example_3D/sol.toml index e54fdeace..86348c36d 100644 --- a/examples/Solovev_ideal_example_3D/sol.toml +++ b/examples/Solovev_ideal_example_3D/sol.toml @@ -1,11 +1,15 @@ +# Solovev analytical equilibrium parameters, consumed by gpec.toml (eq_type = "sol"). +# Sets the grid resolution, plasma shape, and field/pressure scaling factors used to +# generate the analytic Solovev equilibrium. See SolovevConfig in src/Equilibrium. + [SOL_INPUT] -mr = 128 # number of radial grid zones -mz = 128 # number of axial grid zones -ma = 128 # number of flux grid zones -e = 1.6 # elongation -a = 0.33 # minor radius -r0 = 1.0 # major radius -q0 = 1.9 # safety factor at the o-point -p0fac=1 # scale on-axis pressure (P-> P+P0*p0fac. beta changes. Phi,q constant) -b0fac=1 # scale toroidal field at constant beta (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant) -f0fac=1 # scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant) +mr = 128 # Number of radial grid zones +mz = 128 # Number of axial grid zones +ma = 128 # Number of flux grid zones +e = 1.6 # Elongation +a = 0.33 # Minor radius +r0 = 1.0 # Major radius +q0 = 1.9 # Safety factor at the magnetic axis (O-point) +p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) +b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) +f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/examples/Solovev_ideal_example_multi_n/gpec.toml b/examples/Solovev_ideal_example_multi_n/gpec.toml index 89c287b16..d0130cdc4 100644 --- a/examples/Solovev_ideal_example_multi_n/gpec.toml +++ b/examples/Solovev_ideal_example_multi_n/gpec.toml @@ -1,3 +1,8 @@ +# Solovev analytical equilibrium — multi-n ideal stability (n = 1 and 2 in one run). +# Same near-marginal Solovev plasma as Solovev_ideal_example, swept over a toroidal +# mode-number range. The single_n_1/ and single_n_2/ subdirectories run each n alone +# for cross-checking. Equilibrium is generated from sol.toml. + [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file @@ -8,7 +13,7 @@ power_r = 0 # Major radius power exponent for Jacobi grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized flux coordinate psihigh = 0.9995 # Upper limit of normalized flux coordinate -mpsi = 128 # Number of radial grid points +mpsi = 128 # Number of radial grid points (0 = auto-compute from psi_accuracy) mtheta = 256 # Number of poloidal grid points newq0 = 0 # Override for on-axis safety factor (0 = use input value) etol = 1e-7 # Error tolerance for equilibrium solver @@ -28,33 +33,31 @@ equal_arc_wall = true # Equal arc length distribution of nodes [ForceFreeStates] bal_flag = false # Ideal MHD ballooning criterion for short wavelengths mat_flag = true # Construct coefficient matrices for diagnostic purposes -ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) +ode_flag = true # Integrate ODEs for stability of the internal long-wavelength mode (must be true for GPEC) vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes -mer_flag = true # Evaluate the Mercier criterian +mer_flag = true # Evaluate the Mercier criterion -psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak -qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... -qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)... +psiedge = 0.99 # Edge dW(ψ) diagnostic scan band [psiedge, psilim]; set ≥ psilim to disable +qlow = 1.02 # Integration initiated at q determined by min(q0, qlow) +qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh) sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) -nn_low = 1 # Lower toroidal mode number -nn_high = 2 # Upper toroidal mode number +nn_low = 1 # Smallest toroidal mode number to include +nn_high = 2 # Largest toroidal mode number to include delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 8 # Expands upper bound of Fourier harmonics -delta_mband = 0 # Integration keeps only this wide a band... -mthvac = 960 # Number of points used in splines over poloidal angle at plasma-vacuum interface. -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds +delta_mband = 0 # Integration keeps only this wide a band of solutions (0 = full) +mthvac = 960 # Number of points in splines over poloidal angle at the plasma-vacuum interface -kinetic_source = "fixed" # Kinetic matrix source ("fixed" test matrices, or "calculated" from PENTRC) +kinetic_source = "fixed" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model kinetic_factor = 0.0 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode) eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced -ucrit = 1e3 # Maximum fraction of solutions allowed before re-normalized +ucrit = 1e3 # Column-norm threshold that triggers solution renormalization # Δ' BVP + parallel integration (see ForceFreeStatesControl docstring for details) -use_parallel = true # Parallel FM-propagator BVP — ~4× faster than serial EL on this delta_m-expanded grid. The multi-n parallel Δ' matrix has open issues (one q rational for multiple (m, n) tuples — sing_lim! warns and skips), but the parallel path still computes valid ξ and energies via the per-n BVP segments. +use_parallel = true # Run parallel FM-propagator BVP path (multi-n Δ' matrix has open issues — sing_lim! warns and skips — but ξ and energies are valid) parallel_threads = 2 # BVP thread cap (1 = serial/bit-deterministic; 2 ≈ +20% speedup; ≥3 saturates) -populate_dense_xi = false # No PerturbedEquilibrium section — skip the serial-EL re-run (matches new default) -truncate_at_dW_peak = false # Edge-dW scan stays diagnostic; integration domain set by qhigh / psihigh / dmlim -set_psilim_via_dmlim = false # FALSE for multi-n (dmlim truncation is ambiguous when n varies — sing_lim! would skip with warning anyway) -dmlim = 0.2 # Only used when set_psilim_via_dmlim = true: truncate at (last_rational_q + dmlim) / n +populate_dense_xi = false # Append serial-EL pass for dense ξ; not needed without [PerturbedEquilibrium] (default false) +set_psilim_via_dmlim = false # FALSE for multi-n — dmlim truncation is ambiguous when n varies (sing_lim! skips anyway) +dmlim = 0.2 # Truncate integration at (last_rational_q + dmlim)/n (used when set_psilim_via_dmlim = true) diff --git a/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml b/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml index c001eb806..569ab329d 100644 --- a/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml +++ b/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml @@ -1,3 +1,7 @@ +# Solovev analytical equilibrium — n=1 only, companion to the multi-n parent run. +# Runs n=1 in isolation (output euler_n1.h5) to cross-check the combined multi-n result. +# Equilibrium is generated from sol.toml. + [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file @@ -8,13 +12,14 @@ power_r = 0 # Major radius power exponent for Jacobi grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized flux coordinate psihigh = 0.9995 # Upper limit of normalized flux coordinate -mpsi = 128 # Number of radial grid points +mpsi = 128 # Number of radial grid points (0 = auto-compute from psi_accuracy) mtheta = 256 # Number of poloidal grid points newq0 = 0 # Override for on-axis safety factor (0 = use input value) etol = 1e-7 # Error tolerance for equilibrium solver force_termination = false # Terminate after equilibrium setup (skip stability calculations) [Wall] +# See examples/Solovev_ideal_example/gpec.toml for the rationale behind the close conformal wall. shape = "conformal" # Wall shape (nowall, conformal, elliptical, dee, mod_dee, filepath) a = 0.2415 # Distance from plasma (conformal) or shape parameter aw = 0.05 # Half-thickness parameter for Dee-shaped walls @@ -27,27 +32,26 @@ equal_arc_wall = true # Equal arc length distribution of nodes [ForceFreeStates] bal_flag = false # Ideal MHD ballooning criterion for short wavelengths mat_flag = true # Construct coefficient matrices for diagnostic purposes -ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) +ode_flag = true # Integrate ODEs for stability of the internal long-wavelength mode (must be true for GPEC) vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes -mer_flag = true # Evaluate the Mercier criterian +mer_flag = true # Evaluate the Mercier criterion -psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak -qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... -qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)... +psiedge = 0.99 # Edge dW(ψ) diagnostic scan band [psiedge, psilim]; set ≥ psilim to disable +qlow = 1.02 # Integration initiated at q determined by min(q0, qlow) +qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh) sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) nn_low = 1 # Smallest toroidal mode number to include nn_high = 1 # Largest toroidal mode number to include delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 10 # Expands upper bound of Fourier harmonics -delta_mband = 0 # Integration keeps only this wide a band... -mthvac = 960 # Number of points used in splines over poloidal angle at plasma-vacuum interface. -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds +delta_mband = 0 # Integration keeps only this wide a band of solutions (0 = full) +mthvac = 960 # Number of points in splines over poloidal angle at the plasma-vacuum interface -kinetic_source = "fixed" # Kinetic matrix source ("fixed" test matrices, or "calculated" from PENTRC) +kinetic_source = "fixed" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model kinetic_factor = 0.0 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode) eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced -ucrit = 1e3 # Maximum fraction of solutions allowed before re-normalized -write_outputs_to_HDF5 = true -HDF5_filename = "euler_n1.h5" +ucrit = 1e3 # Column-norm threshold that triggers solution renormalization +write_outputs_to_HDF5 = true # Write outputs to the HDF5 file +HDF5_filename = "euler_n1.h5" # Output HDF5 filename diff --git a/examples/Solovev_ideal_example_multi_n/single_n_1/sol.toml b/examples/Solovev_ideal_example_multi_n/single_n_1/sol.toml index e54fdeace..86348c36d 100644 --- a/examples/Solovev_ideal_example_multi_n/single_n_1/sol.toml +++ b/examples/Solovev_ideal_example_multi_n/single_n_1/sol.toml @@ -1,11 +1,15 @@ +# Solovev analytical equilibrium parameters, consumed by gpec.toml (eq_type = "sol"). +# Sets the grid resolution, plasma shape, and field/pressure scaling factors used to +# generate the analytic Solovev equilibrium. See SolovevConfig in src/Equilibrium. + [SOL_INPUT] -mr = 128 # number of radial grid zones -mz = 128 # number of axial grid zones -ma = 128 # number of flux grid zones -e = 1.6 # elongation -a = 0.33 # minor radius -r0 = 1.0 # major radius -q0 = 1.9 # safety factor at the o-point -p0fac=1 # scale on-axis pressure (P-> P+P0*p0fac. beta changes. Phi,q constant) -b0fac=1 # scale toroidal field at constant beta (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant) -f0fac=1 # scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant) +mr = 128 # Number of radial grid zones +mz = 128 # Number of axial grid zones +ma = 128 # Number of flux grid zones +e = 1.6 # Elongation +a = 0.33 # Minor radius +r0 = 1.0 # Major radius +q0 = 1.9 # Safety factor at the magnetic axis (O-point) +p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) +b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) +f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml b/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml index 8a65be741..9c69eaf94 100644 --- a/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml +++ b/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml @@ -1,3 +1,7 @@ +# Solovev analytical equilibrium — n=2 only, companion to the multi-n parent run. +# Runs n=2 in isolation (output euler_n2.h5) to cross-check the combined multi-n result. +# Equilibrium is generated from sol.toml. + [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file @@ -8,13 +12,14 @@ power_r = 0 # Major radius power exponent for Jacobi grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized flux coordinate psihigh = 0.9995 # Upper limit of normalized flux coordinate -mpsi = 128 # Number of radial grid points +mpsi = 128 # Number of radial grid points (0 = auto-compute from psi_accuracy) mtheta = 256 # Number of poloidal grid points newq0 = 0 # Override for on-axis safety factor (0 = use input value) etol = 1e-7 # Error tolerance for equilibrium solver force_termination = false # Terminate after equilibrium setup (skip stability calculations) [Wall] +# See examples/Solovev_ideal_example/gpec.toml for the rationale behind the close conformal wall. shape = "conformal" # Wall shape (nowall, conformal, elliptical, dee, mod_dee, filepath) a = 0.2415 # Distance from plasma (conformal) or shape parameter aw = 0.05 # Half-thickness parameter for Dee-shaped walls @@ -27,27 +32,26 @@ equal_arc_wall = true # Equal arc length distribution of nodes [ForceFreeStates] bal_flag = false # Ideal MHD ballooning criterion for short wavelengths mat_flag = true # Construct coefficient matrices for diagnostic purposes -ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) +ode_flag = true # Integrate ODEs for stability of the internal long-wavelength mode (must be true for GPEC) vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes -mer_flag = true # Evaluate the Mercier criterian +mer_flag = true # Evaluate the Mercier criterion -psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak -qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... -qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)... +psiedge = 0.99 # Edge dW(ψ) diagnostic scan band [psiedge, psilim]; set ≥ psilim to disable +qlow = 1.02 # Integration initiated at q determined by min(q0, qlow) +qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh) sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) nn_low = 2 # Smallest toroidal mode number to include nn_high = 2 # Largest toroidal mode number to include delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 8 # Expands upper bound of Fourier harmonics -delta_mband = 0 # Integration keeps only this wide a band... -mthvac = 960 # Number of points used in splines over poloidal angle at plasma-vacuum interface. -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds +delta_mband = 0 # Integration keeps only this wide a band of solutions (0 = full) +mthvac = 960 # Number of points in splines over poloidal angle at the plasma-vacuum interface -kinetic_source = "fixed" # Kinetic matrix source ("fixed" test matrices, or "calculated" from PENTRC) +kinetic_source = "fixed" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model kinetic_factor = 0.0 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode) eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced -ucrit = 1e3 # Maximum fraction of solutions allowed before re-normalized -write_outputs_to_HDF5 = true -HDF5_filename = "euler_n2.h5" +ucrit = 1e3 # Column-norm threshold that triggers solution renormalization +write_outputs_to_HDF5 = true # Write outputs to the HDF5 file +HDF5_filename = "euler_n2.h5" # Output HDF5 filename diff --git a/examples/Solovev_ideal_example_multi_n/single_n_2/sol.toml b/examples/Solovev_ideal_example_multi_n/single_n_2/sol.toml index e54fdeace..86348c36d 100644 --- a/examples/Solovev_ideal_example_multi_n/single_n_2/sol.toml +++ b/examples/Solovev_ideal_example_multi_n/single_n_2/sol.toml @@ -1,11 +1,15 @@ +# Solovev analytical equilibrium parameters, consumed by gpec.toml (eq_type = "sol"). +# Sets the grid resolution, plasma shape, and field/pressure scaling factors used to +# generate the analytic Solovev equilibrium. See SolovevConfig in src/Equilibrium. + [SOL_INPUT] -mr = 128 # number of radial grid zones -mz = 128 # number of axial grid zones -ma = 128 # number of flux grid zones -e = 1.6 # elongation -a = 0.33 # minor radius -r0 = 1.0 # major radius -q0 = 1.9 # safety factor at the o-point -p0fac=1 # scale on-axis pressure (P-> P+P0*p0fac. beta changes. Phi,q constant) -b0fac=1 # scale toroidal field at constant beta (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant) -f0fac=1 # scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant) +mr = 128 # Number of radial grid zones +mz = 128 # Number of axial grid zones +ma = 128 # Number of flux grid zones +e = 1.6 # Elongation +a = 0.33 # Minor radius +r0 = 1.0 # Major radius +q0 = 1.9 # Safety factor at the magnetic axis (O-point) +p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) +b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) +f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/examples/Solovev_ideal_example_multi_n/sol.toml b/examples/Solovev_ideal_example_multi_n/sol.toml index e54fdeace..86348c36d 100644 --- a/examples/Solovev_ideal_example_multi_n/sol.toml +++ b/examples/Solovev_ideal_example_multi_n/sol.toml @@ -1,11 +1,15 @@ +# Solovev analytical equilibrium parameters, consumed by gpec.toml (eq_type = "sol"). +# Sets the grid resolution, plasma shape, and field/pressure scaling factors used to +# generate the analytic Solovev equilibrium. See SolovevConfig in src/Equilibrium. + [SOL_INPUT] -mr = 128 # number of radial grid zones -mz = 128 # number of axial grid zones -ma = 128 # number of flux grid zones -e = 1.6 # elongation -a = 0.33 # minor radius -r0 = 1.0 # major radius -q0 = 1.9 # safety factor at the o-point -p0fac=1 # scale on-axis pressure (P-> P+P0*p0fac. beta changes. Phi,q constant) -b0fac=1 # scale toroidal field at constant beta (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant) -f0fac=1 # scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant) +mr = 128 # Number of radial grid zones +mz = 128 # Number of axial grid zones +ma = 128 # Number of flux grid zones +e = 1.6 # Elongation +a = 0.33 # Minor radius +r0 = 1.0 # Major radius +q0 = 1.9 # Safety factor at the magnetic axis (O-point) +p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) +b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) +f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/examples/a10_kinetic_example/a10_prof1.txt b/examples/a10_kinetic_example/a10_prof1.txt new file mode 100644 index 000000000..fded31948 --- /dev/null +++ b/examples/a10_kinetic_example/a10_prof1.txt @@ -0,0 +1,252 @@ + psi ni[m^-3] ne[m^-3] ti[eV] te[eV] we[rad/s] + 8.462522E-11 2.000000E+18 2.000000E+18 4.836142E+02 4.836142E+02 5.453044E+04 + 8.462522E-05 2.000000E+18 2.000000E+18 4.835375E+02 4.835375E+02 5.453044E+04 + 3.384988E-04 2.000000E+18 2.000000E+18 4.833073E+02 4.833073E+02 5.453044E+04 + 7.616178E-04 1.999999E+18 1.999999E+18 4.829239E+02 4.829239E+02 5.453044E+04 + 1.353979E-03 1.999996E+18 1.999996E+18 4.823873E+02 4.823873E+02 5.453044E+04 + 2.115581E-03 1.999991E+18 1.999991E+18 4.816980E+02 4.816980E+02 5.453044E+04 + 3.046419E-03 1.999982E+18 1.999982E+18 4.808562E+02 4.808562E+02 5.453044E+04 + 4.146487E-03 1.999966E+18 1.999966E+18 4.798625E+02 4.798625E+02 5.453044E+04 + 5.415778E-03 1.999942E+18 1.999942E+18 4.787173E+02 4.787173E+02 5.453044E+04 + 6.854283E-03 1.999907E+18 1.999907E+18 4.774213E+02 4.774213E+02 5.453044E+04 + 8.461987E-03 1.999858E+18 1.999858E+18 4.759752E+02 4.759752E+02 5.453044E+04 + 1.023887E-02 1.999792E+18 1.999792E+18 4.743798E+02 4.743798E+02 5.453044E+04 + 1.218492E-02 1.999706E+18 1.999706E+18 4.726358E+02 4.726358E+02 5.453044E+04 + 1.430010E-02 1.999595E+18 1.999595E+18 4.707443E+02 4.707443E+02 5.453044E+04 + 1.658437E-02 1.999455E+18 1.999455E+18 4.687063E+02 4.687063E+02 5.453044E+04 + 1.903768E-02 1.999282E+18 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2.186540321E+00-7.213002460E-02 2.187981104E+00 +-6.828715002E-02 2.189342479E+00-6.441625557E-02 2.190623934E+00-6.051894463E-02 + 2.191824983E+00-5.659682879E-02 2.192945173E+00-5.265152730E-02 2.193984084E+00 +-4.868466655E-02 2.194941323E+00-4.469787956E-02 2.195816530E+00-4.069280546E-02 + 2.196609378E+00-3.667108896E-02 2.197319567E+00-3.263437986E-02 2.197946833E+00 +-2.858433253E-02 2.198490938E+00-2.452260539E-02 2.198951681E+00-2.045086040E-02 + 2.199328887E+00-1.637076257E-02 2.199622417E+00-1.228397943E-02 2.199832159E+00 +-8.192180544E-03 2.199958036E+00-4.097036982E-03 2.200000000E+00-2.208300268E-07 + 1.600000000E+00-4.000005482E-01 2.400000000E+00-4.000005482E-01 2.400000000E+00 + 3.999994518E-01 1.600000000E+00 3.999994518E-01 1.600000000E+00-4.000005482E-01 + + 2.00000000E+00 R0 [M] USED FOR CONVERTING TO MKSA + 1.00000000E+00 B0 [T] USED FOR CONVERTING TO MKSA + 1.00251540E+00 R OF MAGAXE --> [M] 2.00503081E+00 + -2.74079228E-07 Z OF MAGAXE --> [M] -5.48158456E-07 + -3.04194290E-03 PSI-AXIS --> [T M**2] -1.21677716E-02 + -1.91131052E-02 2*PI*PSI-AXIS --> -7.64524207E-02 + 2.27713686E-02 TOTAL CURRENT --> [A] 3.62417547E+04 + 1.49031820E-01 POLOIDAL BETA + 1.94759091E-04 BETA + 2.99474016E-04 BETA* (SQRT()) + 1.95749445E-04 BETA_EXP=

*2*MU0/B0**2 + 1.10810709E+00 LI + 1.23886290E+00 Q_ZERO + 2.79411382E+00 Q_EDGE + 1.00000002E+01 ASPECT RATIO ; a/R= 9.99999984E-02 + 1.00000017E+00 b/a + 1.97391020E-01 VOLUME -> 1.57912816E+00 + 3.14157548E-02 AREA -> 1.25663019E-01 + 6.28318532E-01 LENGTH -> 1.25663706E+00 + 9.00005801E-01 RMIN -> RMIN [m] 1.80001160E+00 + 1.10000000E+00 RMAX -> RMAX [m] 2.20000000E+00 + -1.00000047E-01 ZMIN -> ZMIN [m] -2.00000095E-01 + 9.99998266E-02 ZMAX -> ZMAX [m] 1.99999653E-01 + 1.00000290E+00 RGEOM -> RGEOM [m] 2.00000580E+00 + 9.99970995E-02 MINOR RADIUS -> A [m] 1.99994199E-01 diff --git a/examples/a10_kinetic_example/gpec.toml b/examples/a10_kinetic_example/gpec.toml index 5b66712d7..9a34c76d3 100644 --- a/examples/a10_kinetic_example/gpec.toml +++ b/examples/a10_kinetic_example/gpec.toml @@ -1,78 +1,69 @@ -# a10 kinetic-DCON example — Julia mirror of Fortran GPEC a10_kinetic_example. -# -# Source namelists: ~/Code/gpec/docs/examples/a10_kinetic_example/{dcon.in,equil.in,pentrc.in} -# Shared inputs: ~/Code/gpec/docs/examples/a10_ideal_example/ -# -# This example depends on the user's local Fortran GPEC checkout at ~/Code/gpec -# for the g-file and kinetic profile (a10_prof1.txt). Both are referenced by -# absolute path so no inputs are duplicated into JPEC_ode. Adjust the paths -# if your Fortran GPEC copy lives elsewhere. -# -# Term-by-term Fortran↔Julia mapping: see memory/project_a10_kinetic_settings.md -# Reference Fortran run: mpsi=16 → kinetic DCON in ~48 s on a laptop. +# a10 kinetic stability example — drift-kinetic MHD stability of a low-aspect-ratio +# circular tokamak. Unlike the ideal examples, this run uses the calculated kinetic +# (neoclassical toroidal viscosity) energy matrices at full strength, so the +# free-boundary stability includes drift-kinetic effects from a single deuterium ion +# species with a Maxwellian distribution and a harmonic collision operator. +# force_termination stops the run after the kinetic stability eigenvalues. +# The equilibrium g-file and kinetic profile are bundled in this directory. [Equilibrium] -eq_filename = "/Users/nlogan/Code/gpec/docs/examples/a10_ideal_example/fix_a100_k10_q2_bn010_prof1" -eq_type = "efit" -jac_type = "hamada" -power_bp = 0 -power_b = 0 -power_r = 0 -grid_type = "ldp" # Fortran equil.in: grid_type="ldp" -psilow = 1e-3 -psihigh = 0.99 # Fortran: psihigh=0.99 -mpsi = 16 # Fortran: mpsi=16 (fast-iteration setting) -mtheta = 256 -newq0 = 0 -etol = 1e-7 +eq_filename = "fix_a100_k10_q2_bn010_prof1" # Path to equilibrium file (bundled CHEASE-format g-file) +eq_type = "efit" # Type of the input 2D equilibrium file +jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc) +power_bp = 0 # Poloidal field power exponent for Jacobian +power_b = 0 # Toroidal field power exponent for Jacobian +power_r = 0 # Major radius power exponent for Jacobian +grid_type = "ldp" # Radial grid packing type +psilow = 1e-3 # Lower limit of normalized flux coordinate +psihigh = 0.99 # Upper limit of normalized flux coordinate +mpsi = 16 # Number of radial grid points (low value for fast iteration) +mtheta = 256 # Number of poloidal grid points +newq0 = 0 # Override for on-axis safety factor (0 = use input value) +etol = 1e-7 # Error tolerance for equilibrium solver [Wall] -shape = "nowall" +shape = "nowall" # Wall shape (nowall, conformal, elliptical, dee, mod_dee, filepath) [ForceFreeStates] -bal_flag = false -mat_flag = true -ode_flag = true -vac_flag = true -mer_flag = true +bal_flag = false # Ideal MHD ballooning criterion for short wavelengths +mat_flag = true # Construct coefficient matrices for diagnostic purposes +ode_flag = true # Integrate ODEs for stability of the internal long-wavelength mode (must be true for GPEC) +vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes +mer_flag = true # Evaluate the Mercier criterion -# sas_flag=f in Fortran → no truncation via dmlim; Julia mirrors with -# set_psilim_via_dmlim=false and psiedge=1.0 (full integration to psihigh). -set_psilim_via_dmlim = false -psiedge = 1.0 -qlow = 1.02 -qhigh = 1e3 -sing_start = 0 +set_psilim_via_dmlim = false # FALSE for limited/analytical equilibria — rationals sparse, dmlim would chop too much edge +psiedge = 1.0 # Edge dW(ψ) diagnostic scan band [psiedge, psilim]; 1.0 ≥ psilim disables the scan (integrate full domain) +qlow = 1.02 # Integration initiated at q determined by min(q0, qlow) +qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh) +sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) -nn_low = 1 -nn_high = 1 -delta_mlow = 6 # Fortran dcon.in: delta_mlow=6 -delta_mhigh = 6 # Fortran dcon.in: delta_mhigh=6 -delta_mband = 0 -mthvac = 512 -thmax0 = 1 +nn_low = 1 # Smallest toroidal mode number to include +nn_high = 1 # Largest toroidal mode number to include +delta_mlow = 6 # Expands lower bound of Fourier harmonics +delta_mhigh = 6 # Expands upper bound of Fourier harmonics +delta_mband = 0 # Integration keeps only this wide a band of solutions (0 = full) +mthvac = 512 # Number of points in splines over poloidal angle at the plasma-vacuum interface -kinetic_source = "calculated" # Fortran kin_flag=t -kinetic_factor = 1.0 # Fortran kinfac1=kinfac2=1.0 -eulerlagrange_tolerance = 1e-7 -singfac_min = 1e-4 -ucrit = 1e4 -write_outputs_to_HDF5 = true -force_termination = true # Stop after FFS — kinetic DCON eigenvalues are what we benchmark +kinetic_source = "calculated" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model +kinetic_factor = 1.0 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode; 1.0 = full strength) +eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations +singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced +ucrit = 1e4 # Column-norm threshold that triggers solution renormalization +write_outputs_to_HDF5 = true # Write outputs to the HDF5 file +force_termination = true # Stop after force-free states — the kinetic stability eigenvalues are the result of interest [KineticForces] -kinetic_file = "/Users/nlogan/Code/gpec/docs/examples/a10_ideal_example/a10_prof1.txt" -nn = 1 -nl = 6 # Fortran pentrc.in: nl=6 -zi = 1 -mi = 2 -zimp = 6 -mimp = 12 -electron = false # Fortran: electron_flag=f (ion-only) -nutype = "harmonic" # Fortran: nutype="harmonic" -f0type = "maxwellian" # Fortran: f0type="maxwellian" -# Fortran pentrc.in tolerances -atol_xlmda = 1e-9 -rtol_xlmda = 1e-5 -atol_psi = 1e-9 -rtol_psi = 1e-4 +kinetic_file = "a10_prof1.txt" # Path to the kinetic profile file (bundled) +nn = 1 # Toroidal mode number +nl = 6 # Bounce-harmonic number +zi = 1 # Ion charge (fundamental units) +mi = 2 # Ion mass (proton masses) +zimp = 6 # Impurity charge +mimp = 12 # Impurity mass +electron = false # Include electron contribution (false = ion-only) +nutype = "harmonic" # Collision operator (zero, small, krook, harmonic) +f0type = "maxwellian" # Distribution function (maxwellian, jkp, cgl) +atol_xlmda = 1e-9 # Absolute tolerance for inner pitch + energy integrations +rtol_xlmda = 1e-5 # Relative tolerance for inner pitch + energy integrations +atol_psi = 1e-9 # Absolute tolerance for the outer ψ quadrature +rtol_psi = 1e-4 # Relative tolerance for the outer ψ quadrature diff --git a/regression-harness/cases/diiid_n1.toml b/regression-harness/cases/diiid_n1.toml index 81b31587a..1681055a0 100644 --- a/regression-harness/cases/diiid_n1.toml +++ b/regression-harness/cases/diiid_n1.toml @@ -1,3 +1,8 @@ +# Regression case: DIII-D-like n=1 ideal stability + perturbed equilibrium. +# Tracks energies, singular-surface metrics, Δ' (BVP diagonal), and resonant-flux +# diagnostics for the canonical DIIID-like fixture. Each [quantities.*] block names an +# HDF5 path in the run output, how to extract it, and the noise floor below which a +# difference is treated as zero. Run via the regression-harness (see CLAUDE.md). [case] name = "diiid_n1" description = "DIII-D-like equilibrium, n=1, ideal + perturbed equilibrium" diff --git a/regression-harness/cases/ggj_reference.toml b/regression-harness/cases/ggj_reference.toml index a116460a6..b35ca20a7 100644 --- a/regression-harness/cases/ggj_reference.toml +++ b/regression-harness/cases/ggj_reference.toml @@ -1,3 +1,7 @@ +# Regression case: GGJ inner-layer Galerkin solver reference (Glasser & Wang 2020, Eq. 55). +# A "computed" case (kind = "computed", no example_dir) that calls solve_inner directly and +# tracks the Δ_odd / Δ_even inner-layer coefficients. Each [quantities.*] block names an +# HDF5 path in the computed output, how to extract it, and the noise floor for diffs. [case] name = "ggj_reference" description = "GGJ inner-layer Galerkin solver, Glasser & Wang 2020 Eq. 55, γ = 1+i" diff --git a/regression-harness/cases/solovev_kinetic_calculated.toml b/regression-harness/cases/solovev_kinetic_calculated.toml index 807978588..82eee78f0 100644 --- a/regression-harness/cases/solovev_kinetic_calculated.toml +++ b/regression-harness/cases/solovev_kinetic_calculated.toml @@ -1,3 +1,7 @@ +# Regression case: Solovev n=1 with the "calculated" kinetic path at full strength. +# Guards the real KineticForces (PENTRC-style) physics path against drift. Each +# [quantities.*] block names an HDF5 path in the run output, how to extract it, and the +# noise floor below which a difference is treated as zero. [case] name = "solovev_kinetic_calculated" description = "Solovev analytical equilibrium, n=1, kinetic_source=calculated, kinetic_factor=1.0" diff --git a/regression-harness/cases/solovev_multi_n.toml b/regression-harness/cases/solovev_multi_n.toml index f002bd01d..553c71f40 100644 --- a/regression-harness/cases/solovev_multi_n.toml +++ b/regression-harness/cases/solovev_multi_n.toml @@ -1,3 +1,7 @@ +# Regression case: Solovev multi-n (n = 1 and 2) ideal stability. +# Tracks the leading free-boundary energies and stability quantities for the analytic +# Solovev fixture swept over a toroidal mode-number range. Each [quantities.*] block names +# an HDF5 path, how to extract it, and the noise floor below which a diff is treated as zero. [case] name = "solovev_multi_n" description = "Solovev analytical equilibrium, multi-n, ideal stability" diff --git a/regression-harness/cases/solovev_n1.toml b/regression-harness/cases/solovev_n1.toml index 04332c6d9..4ff03feeb 100644 --- a/regression-harness/cases/solovev_n1.toml +++ b/regression-harness/cases/solovev_n1.toml @@ -1,3 +1,7 @@ +# Regression case: Solovev n=1 ideal stability (near-marginal external kink). +# Tracks the leading free-boundary energies and stability quantities for the analytic +# Solovev fixture. Each [quantities.*] block names an HDF5 path in the run output, how to +# extract it, and the noise floor below which a difference is treated as zero. [case] name = "solovev_n1" description = "Solovev analytical equilibrium, n=1, ideal stability" diff --git a/test/test_data/regression_solovev_ideal_example/gpec.toml b/test/test_data/regression_solovev_ideal_example/gpec.toml index 92272e98e..ff6d9f04a 100644 --- a/test/test_data/regression_solovev_ideal_example/gpec.toml +++ b/test/test_data/regression_solovev_ideal_example/gpec.toml @@ -1,3 +1,7 @@ +# Regression fixture: Solovev n=1 ideal stability (mirrors examples/Solovev_ideal_example). +# Coarsened for speed (mpsi=16, mthvac=64, delta_m=0) and run quietly with HDF5 output off; +# consumed by the test suite in test/runtests_*.jl. + [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file @@ -8,55 +12,53 @@ power_r = 0 # Major radius power exponent for Jacobi grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized flux coordinate psihigh = 0.9995 # Upper limit of normalized flux coordinate -mpsi = 16 # Number of radial grid points +mpsi = 16 # Number of radial grid points (0 = auto-compute from psi_accuracy) mtheta = 256 # Number of poloidal grid points newq0 = 0 # Override for on-axis safety factor (0 = use input value) etol = 1e-7 # Error tolerance for equilibrium solver force_termination = false # Terminate after equilibrium setup (skip stability calculations) [Wall] -shape = "conformal" # Close conformal wall stabilizes Solovev n=1 external kink; see examples/Solovev_ideal_example/gpec.toml -a = 0.2415 -aw = 0.05 -bw = 1.5 -cw = 0 -dw = 0.5 -tw = 0.05 -equal_arc_wall = true +shape = "conformal" # Wall shape (nowall, conformal, ...); close conformal wall stabilizes the Solovev n=1 kink (see examples/Solovev_ideal_example/gpec.toml) +a = 0.2415 # Distance from plasma (conformal) or shape parameter +aw = 0.05 # Half-thickness parameter for Dee-shaped walls +bw = 1.5 # Elongation parameter for wall shapes +cw = 0 # Offset of wall center from major radius +dw = 0.5 # Triangularity parameter for wall shapes +tw = 0.05 # Sharpness of wall corners (try 0.05 as initial value) +equal_arc_wall = true # Equal arc length distribution of nodes on wall [ForceFreeStates] bal_flag = false # Ideal MHD ballooning criterion for short wavelengths mat_flag = true # Construct coefficient matrices for diagnostic purposes -ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) +ode_flag = true # Integrate ODEs for stability of the internal long-wavelength mode (must be true for GPEC) vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes -mer_flag = true # Evaluate the Mercier criterian +mer_flag = true # Evaluate the Mercier criterion -psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak -qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... -qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)... +psiedge = 0.99 # Edge dW(ψ) diagnostic scan band [psiedge, psilim]; set ≥ psilim to disable +qlow = 1.02 # Integration initiated at q determined by min(q0, qlow) +qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh) sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) nn_low = 1 # Smallest toroidal mode number to include nn_high = 1 # Largest toroidal mode number to include delta_mlow = 0 # Expands lower bound of Fourier harmonics delta_mhigh = 0 # Expands upper bound of Fourier harmonics -delta_mband = 0 # Integration keeps only this wide a band... -mthvac = 64 # Number of points used in splines over poloidal angle at plasma-vacuum interface. -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds +delta_mband = 0 # Integration keeps only this wide a band of solutions (0 = full) +mthvac = 64 # Number of points in splines over poloidal angle at the plasma-vacuum interface -kinetic_source = "fixed" # Kinetic matrix source ("fixed" test matrices, or "calculated" from PENTRC) +kinetic_source = "fixed" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model kinetic_factor = 0.0 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode) eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced -ucrit = 1e3 # Maximum fraction of solutions allowed before re-normalized +ucrit = 1e3 # Column-norm threshold that triggers solution renormalization # Δ' BVP + parallel integration (see ForceFreeStatesControl docstring for details) use_parallel = true # Run parallel FM-propagator BVP path (unlocks singular/delta_prime_matrix) parallel_threads = 2 # BVP thread cap (1 = serial/bit-deterministic; 2 ≈ +20% speedup; ≥3 saturates) -populate_dense_xi = true # Append serial-EL pass after parallel BVP so HDF5 integration/xi_* carry axis-basis dense ξ for PerturbedEquilibrium -truncate_at_dW_peak = false # Edge-dW scan stays diagnostic; integration domain set by qhigh / psihigh / dmlim -set_psilim_via_dmlim = false # FALSE for limited circular / analytical equilibria — rationals sparse, dmlim truncation would chop too much edge -dmlim = 0.2 # Only used when set_psilim_via_dmlim = true: truncate at (last_rational_q + dmlim) / n +populate_dense_xi = true # Append serial-EL pass so dense ξ is stored (axis basis) for downstream consumers +set_psilim_via_dmlim = false # FALSE for limited/analytical equilibria — rationals sparse, dmlim would chop too much edge +dmlim = 0.2 # Truncate integration at (last_rational_q + dmlim)/n (used when set_psilim_via_dmlim = true) -write_outputs_to_HDF5 = false -verbose = false +write_outputs_to_HDF5 = false # Write outputs to the HDF5 file +verbose = false # Enable verbose logging diff --git a/test/test_data/regression_solovev_ideal_example/sol.toml b/test/test_data/regression_solovev_ideal_example/sol.toml index e54fdeace..86348c36d 100644 --- a/test/test_data/regression_solovev_ideal_example/sol.toml +++ b/test/test_data/regression_solovev_ideal_example/sol.toml @@ -1,11 +1,15 @@ +# Solovev analytical equilibrium parameters, consumed by gpec.toml (eq_type = "sol"). +# Sets the grid resolution, plasma shape, and field/pressure scaling factors used to +# generate the analytic Solovev equilibrium. See SolovevConfig in src/Equilibrium. + [SOL_INPUT] -mr = 128 # number of radial grid zones -mz = 128 # number of axial grid zones -ma = 128 # number of flux grid zones -e = 1.6 # elongation -a = 0.33 # minor radius -r0 = 1.0 # major radius -q0 = 1.9 # safety factor at the o-point -p0fac=1 # scale on-axis pressure (P-> P+P0*p0fac. beta changes. Phi,q constant) -b0fac=1 # scale toroidal field at constant beta (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant) -f0fac=1 # scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant) +mr = 128 # Number of radial grid zones +mz = 128 # Number of axial grid zones +ma = 128 # Number of flux grid zones +e = 1.6 # Elongation +a = 0.33 # Minor radius +r0 = 1.0 # Major radius +q0 = 1.9 # Safety factor at the magnetic axis (O-point) +p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) +b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) +f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml b/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml index 88d6c761e..79299d634 100644 --- a/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml +++ b/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml @@ -1,3 +1,7 @@ +# Regression fixture: Solovev multi-n ideal stability (n = 1 and 2; mirrors +# examples/Solovev_ideal_example_multi_n). Coarsened for speed (mpsi=16, mthvac=64, +# delta_m=0) and run quietly with HDF5 output off; consumed by test/runtests_*.jl. + [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file @@ -8,55 +12,53 @@ power_r = 0 # Major radius power exponent for Jacobi grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized flux coordinate psihigh = 0.9995 # Upper limit of normalized flux coordinate -mpsi = 16 # Number of radial grid points +mpsi = 16 # Number of radial grid points (0 = auto-compute from psi_accuracy) mtheta = 256 # Number of poloidal grid points newq0 = 0 # Override for on-axis safety factor (0 = use input value) etol = 1e-7 # Error tolerance for equilibrium solver force_termination = false # Terminate after equilibrium setup (skip stability calculations) [Wall] -shape = "conformal" # Close conformal wall stabilizes Solovev n=1 external kink; see examples/Solovev_ideal_example/gpec.toml -a = 0.2415 -aw = 0.05 -bw = 1.5 -cw = 0 -dw = 0.5 -tw = 0.05 -equal_arc_wall = true +shape = "conformal" # Wall shape (nowall, conformal, ...); close conformal wall stabilizes the Solovev n=1 kink (see examples/Solovev_ideal_example/gpec.toml) +a = 0.2415 # Distance from plasma (conformal) or shape parameter +aw = 0.05 # Half-thickness parameter for Dee-shaped walls +bw = 1.5 # Elongation parameter for wall shapes +cw = 0 # Offset of wall center from major radius +dw = 0.5 # Triangularity parameter for wall shapes +tw = 0.05 # Sharpness of wall corners (try 0.05 as initial value) +equal_arc_wall = true # Equal arc length distribution of nodes on wall [ForceFreeStates] bal_flag = false # Ideal MHD ballooning criterion for short wavelengths mat_flag = true # Construct coefficient matrices for diagnostic purposes -ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) +ode_flag = true # Integrate ODEs for stability of the internal long-wavelength mode (must be true for GPEC) vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes -mer_flag = true # Evaluate the Mercier criterian +mer_flag = true # Evaluate the Mercier criterion -psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak -qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... -qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)... +psiedge = 0.99 # Edge dW(ψ) diagnostic scan band [psiedge, psilim]; set ≥ psilim to disable +qlow = 1.02 # Integration initiated at q determined by min(q0, qlow) +qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh) sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) nn_low = 1 # Smallest toroidal mode number to include nn_high = 2 # Largest toroidal mode number to include delta_mlow = 0 # Expands lower bound of Fourier harmonics delta_mhigh = 0 # Expands upper bound of Fourier harmonics -delta_mband = 0 # Integration keeps only this wide a band... -mthvac = 64 # Number of points used in splines over poloidal angle at plasma-vacuum interface. -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds +delta_mband = 0 # Integration keeps only this wide a band of solutions (0 = full) +mthvac = 64 # Number of points in splines over poloidal angle at the plasma-vacuum interface -kinetic_source = "fixed" # Kinetic matrix source ("fixed" test matrices, or "calculated" from PENTRC) +kinetic_source = "fixed" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model kinetic_factor = 0.0 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode) eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced -ucrit = 1e3 # Maximum fraction of solutions allowed before re-normalized +ucrit = 1e3 # Column-norm threshold that triggers solution renormalization # Δ' BVP + parallel integration (see ForceFreeStatesControl docstring for details) -use_parallel = true # Run parallel FM-propagator BVP path (unlocks singular/delta_prime_matrix) +use_parallel = true # Run parallel FM-propagator BVP path (multi-n Δ' matrix has open issues — sing_lim! warns and skips — but ξ and energies are valid) parallel_threads = 2 # BVP thread cap (1 = serial/bit-deterministic; 2 ≈ +20% speedup; ≥3 saturates) -populate_dense_xi = true # Append serial-EL pass after parallel BVP so HDF5 integration/xi_* carry axis-basis dense ξ for PerturbedEquilibrium -truncate_at_dW_peak = false # Edge-dW scan stays diagnostic; integration domain set by qhigh / psihigh / dmlim -set_psilim_via_dmlim = false # FALSE for multi-n (dmlim truncation is ambiguous when n varies — sing_lim! would skip with warning anyway) -dmlim = 0.2 # Only used when set_psilim_via_dmlim = true: truncate at (last_rational_q + dmlim) / n +populate_dense_xi = true # Append serial-EL pass so dense ξ is stored (axis basis) for downstream consumers +set_psilim_via_dmlim = false # FALSE for multi-n — dmlim truncation is ambiguous when n varies (sing_lim! skips anyway) +dmlim = 0.2 # Truncate integration at (last_rational_q + dmlim)/n (used when set_psilim_via_dmlim = true) -write_outputs_to_HDF5 = false -verbose = false +write_outputs_to_HDF5 = false # Write outputs to the HDF5 file +verbose = false # Enable verbose logging diff --git a/test/test_data/regression_solovev_ideal_example_multi_n/sol.toml b/test/test_data/regression_solovev_ideal_example_multi_n/sol.toml index e54fdeace..86348c36d 100644 --- a/test/test_data/regression_solovev_ideal_example_multi_n/sol.toml +++ b/test/test_data/regression_solovev_ideal_example_multi_n/sol.toml @@ -1,11 +1,15 @@ +# Solovev analytical equilibrium parameters, consumed by gpec.toml (eq_type = "sol"). +# Sets the grid resolution, plasma shape, and field/pressure scaling factors used to +# generate the analytic Solovev equilibrium. See SolovevConfig in src/Equilibrium. + [SOL_INPUT] -mr = 128 # number of radial grid zones -mz = 128 # number of axial grid zones -ma = 128 # number of flux grid zones -e = 1.6 # elongation -a = 0.33 # minor radius -r0 = 1.0 # major radius -q0 = 1.9 # safety factor at the o-point -p0fac=1 # scale on-axis pressure (P-> P+P0*p0fac. beta changes. Phi,q constant) -b0fac=1 # scale toroidal field at constant beta (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant) -f0fac=1 # scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant) +mr = 128 # Number of radial grid zones +mz = 128 # Number of axial grid zones +ma = 128 # Number of flux grid zones +e = 1.6 # Elongation +a = 0.33 # Minor radius +r0 = 1.0 # Major radius +q0 = 1.9 # Safety factor at the magnetic axis (O-point) +p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) +b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) +f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/test/test_data/regression_solovev_kinetic_calculated/gpec.toml b/test/test_data/regression_solovev_kinetic_calculated/gpec.toml index 6f8dd25f5..4eb1e3944 100644 --- a/test/test_data/regression_solovev_kinetic_calculated/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_calculated/gpec.toml @@ -1,3 +1,7 @@ +# Regression fixture: Solovev n=1 with the "calculated" kinetic path at full strength. +# Exercises the real calculated kinetic NTV matrices end-to-end on a coarse +# (mpsi=16) Solovev plasma; consumed by test/runtests_*.jl. + [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file @@ -8,14 +12,14 @@ power_r = 0 # Major radius power exponent for Jacobi grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized flux coordinate psihigh = 0.9995 # Upper limit of normalized flux coordinate -mpsi = 16 # Number of radial grid points +mpsi = 16 # Number of radial grid points (0 = auto-compute from psi_accuracy) mtheta = 256 # Number of poloidal grid points newq0 = 0 # Override for on-axis safety factor (0 = use input value) etol = 1e-7 # Error tolerance for equilibrium solver force_termination = false # Terminate after equilibrium setup (skip stability calculations) [Wall] -shape = "conformal" # Wall shape (nowall, conformal, elliptical, dee, mod_dee, filepath) +shape = "conformal" # Wall shape (nowall, conformal, ...); close conformal wall stabilizes the Solovev n=1 kink (see examples/Solovev_ideal_example/gpec.toml) a = 0.2415 # Distance from plasma (conformal) or shape parameter aw = 0.05 # Half-thickness parameter for Dee-shaped walls bw = 1.5 # Elongation parameter for wall shapes @@ -27,27 +31,26 @@ equal_arc_wall = true # Equal arc length distribution of nodes [ForceFreeStates] bal_flag = false # Ideal MHD ballooning criterion for short wavelengths mat_flag = false # Construct coefficient matrices for diagnostic purposes -ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) +ode_flag = true # Integrate ODEs for stability of the internal long-wavelength mode (must be true for GPEC) vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes -mer_flag = true # Evaluate the Mercier criterian +mer_flag = true # Evaluate the Mercier criterion -psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak -qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... -qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)... +psiedge = 0.99 # Edge dW(ψ) diagnostic scan band [psiedge, psilim]; set ≥ psilim to disable +qlow = 1.02 # Integration initiated at q determined by min(q0, qlow) +qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh) sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) nn_low = 1 # Smallest toroidal mode number to include nn_high = 1 # Largest toroidal mode number to include delta_mlow = 0 # Expands lower bound of Fourier harmonics delta_mhigh = 0 # Expands upper bound of Fourier harmonics -delta_mband = 0 # Integration keeps only this wide a band... -mthvac = 64 # Number of points used in splines over poloidal angle at plasma-vacuum interface. -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds +delta_mband = 0 # Integration keeps only this wide a band of solutions (0 = full) +mthvac = 64 # Number of points in splines over poloidal angle at the plasma-vacuum interface -kinetic_source = "calculated" # Kinetic matrix source — exercises KineticForces.compute_calculated_kinetic_matrices callback with real physics -kinetic_factor = 1.0 # Full-strength kinetic matrices (the "calculated" path is the real physics; no perturbation scaling) +kinetic_source = "calculated" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model +kinetic_factor = 1.0 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode; 1.0 = full strength) eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced -ucrit = 1e3 # Maximum fraction of solutions allowed before re-normalized -write_outputs_to_HDF5 = true -verbose = false +ucrit = 1e3 # Column-norm threshold that triggers solution renormalization +write_outputs_to_HDF5 = true # Write outputs to the HDF5 file +verbose = false # Enable verbose logging diff --git a/test/test_data/regression_solovev_kinetic_calculated/sol.toml b/test/test_data/regression_solovev_kinetic_calculated/sol.toml index e54fdeace..86348c36d 100644 --- a/test/test_data/regression_solovev_kinetic_calculated/sol.toml +++ b/test/test_data/regression_solovev_kinetic_calculated/sol.toml @@ -1,11 +1,15 @@ +# Solovev analytical equilibrium parameters, consumed by gpec.toml (eq_type = "sol"). +# Sets the grid resolution, plasma shape, and field/pressure scaling factors used to +# generate the analytic Solovev equilibrium. See SolovevConfig in src/Equilibrium. + [SOL_INPUT] -mr = 128 # number of radial grid zones -mz = 128 # number of axial grid zones -ma = 128 # number of flux grid zones -e = 1.6 # elongation -a = 0.33 # minor radius -r0 = 1.0 # major radius -q0 = 1.9 # safety factor at the o-point -p0fac=1 # scale on-axis pressure (P-> P+P0*p0fac. beta changes. Phi,q constant) -b0fac=1 # scale toroidal field at constant beta (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant) -f0fac=1 # scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant) +mr = 128 # Number of radial grid zones +mz = 128 # Number of axial grid zones +ma = 128 # Number of flux grid zones +e = 1.6 # Elongation +a = 0.33 # Minor radius +r0 = 1.0 # Major radius +q0 = 1.9 # Safety factor at the magnetic axis (O-point) +p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) +b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) +f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/test/test_data/regression_solovev_kinetic_example/gpec.toml b/test/test_data/regression_solovev_kinetic_example/gpec.toml index 343ab1d2f..ffb488b85 100644 --- a/test/test_data/regression_solovev_kinetic_example/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_example/gpec.toml @@ -1,3 +1,7 @@ +# Regression fixture: Solovev n=1 with the kinetic path barely enabled (kinetic_factor=1e-9). +# Verifies the "fixed" kinetic code path runs without measurably perturbing the ideal result, +# on a coarse (mpsi=16) Solovev plasma; consumed by test/runtests_*.jl. + [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file @@ -8,55 +12,53 @@ power_r = 0 # Major radius power exponent for Jacobi grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized flux coordinate psihigh = 0.9995 # Upper limit of normalized flux coordinate -mpsi = 16 # Number of radial grid points +mpsi = 16 # Number of radial grid points (0 = auto-compute from psi_accuracy) mtheta = 256 # Number of poloidal grid points newq0 = 0 # Override for on-axis safety factor (0 = use input value) etol = 1e-7 # Error tolerance for equilibrium solver force_termination = false # Terminate after equilibrium setup (skip stability calculations) [Wall] -shape = "conformal" # Close conformal wall stabilizes Solovev n=1 external kink; see examples/Solovev_ideal_example/gpec.toml -a = 0.2415 -aw = 0.05 -bw = 1.5 -cw = 0 -dw = 0.5 -tw = 0.05 -equal_arc_wall = true +shape = "conformal" # Wall shape (nowall, conformal, ...); close conformal wall stabilizes the Solovev n=1 kink (see examples/Solovev_ideal_example/gpec.toml) +a = 0.2415 # Distance from plasma (conformal) or shape parameter +aw = 0.05 # Half-thickness parameter for Dee-shaped walls +bw = 1.5 # Elongation parameter for wall shapes +cw = 0 # Offset of wall center from major radius +dw = 0.5 # Triangularity parameter for wall shapes +tw = 0.05 # Sharpness of wall corners (try 0.05 as initial value) +equal_arc_wall = true # Equal arc length distribution of nodes on wall [ForceFreeStates] bal_flag = false # Ideal MHD ballooning criterion for short wavelengths mat_flag = false # Construct coefficient matrices for diagnostic purposes -ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) +ode_flag = true # Integrate ODEs for stability of the internal long-wavelength mode (must be true for GPEC) vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes -mer_flag = true # Evaluate the Mercier criterian +mer_flag = true # Evaluate the Mercier criterion -psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak -qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... -qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)... +psiedge = 0.99 # Edge dW(ψ) diagnostic scan band [psiedge, psilim]; set ≥ psilim to disable +qlow = 1.02 # Integration initiated at q determined by min(q0, qlow) +qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh) sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) nn_low = 1 # Smallest toroidal mode number to include nn_high = 1 # Largest toroidal mode number to include delta_mlow = 0 # Expands lower bound of Fourier harmonics delta_mhigh = 0 # Expands upper bound of Fourier harmonics -delta_mband = 0 # Integration keeps only this wide a band... -mthvac = 64 # Number of points used in splines over poloidal angle at plasma-vacuum interface. -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds +delta_mband = 0 # Integration keeps only this wide a band of solutions (0 = full) +mthvac = 64 # Number of points in splines over poloidal angle at the plasma-vacuum interface -kinetic_source = "fixed" # Kinetic matrix source ("fixed" test matrices, or "calculated" from PENTRC) -kinetic_factor = 1e-9 # Small perturbation to verify kinetic path without altering physics (>0 enables kinetic mode) +kinetic_source = "fixed" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model +kinetic_factor = 1e-9 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode; tiny value just exercises the path) eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced -ucrit = 1e3 # Maximum fraction of solutions allowed before re-normalized +ucrit = 1e3 # Column-norm threshold that triggers solution renormalization # Δ' BVP + parallel integration (see ForceFreeStatesControl docstring for details) use_parallel = true # Run parallel FM-propagator BVP path (unlocks singular/delta_prime_matrix) parallel_threads = 2 # BVP thread cap (1 = serial/bit-deterministic; 2 ≈ +20% speedup; ≥3 saturates) -populate_dense_xi = true # Append serial-EL pass after parallel BVP so HDF5 integration/xi_* carry axis-basis dense ξ for PerturbedEquilibrium -truncate_at_dW_peak = false # Edge-dW scan stays diagnostic; integration domain set by qhigh / psihigh / dmlim -set_psilim_via_dmlim = false # FALSE for limited circular / analytical equilibria — rationals sparse, dmlim truncation would chop too much edge -dmlim = 0.2 # Only used when set_psilim_via_dmlim = true: truncate at (last_rational_q + dmlim) / n +populate_dense_xi = true # Append serial-EL pass so dense ξ is stored (axis basis) for downstream consumers +set_psilim_via_dmlim = false # FALSE for limited/analytical equilibria — rationals sparse, dmlim would chop too much edge +dmlim = 0.2 # Truncate integration at (last_rational_q + dmlim)/n (used when set_psilim_via_dmlim = true) -write_outputs_to_HDF5 = true -verbose = false +write_outputs_to_HDF5 = true # Write outputs to the HDF5 file +verbose = false # Enable verbose logging diff --git a/test/test_data/regression_solovev_kinetic_example/sol.toml b/test/test_data/regression_solovev_kinetic_example/sol.toml index e54fdeace..86348c36d 100644 --- a/test/test_data/regression_solovev_kinetic_example/sol.toml +++ b/test/test_data/regression_solovev_kinetic_example/sol.toml @@ -1,11 +1,15 @@ +# Solovev analytical equilibrium parameters, consumed by gpec.toml (eq_type = "sol"). +# Sets the grid resolution, plasma shape, and field/pressure scaling factors used to +# generate the analytic Solovev equilibrium. See SolovevConfig in src/Equilibrium. + [SOL_INPUT] -mr = 128 # number of radial grid zones -mz = 128 # number of axial grid zones -ma = 128 # number of flux grid zones -e = 1.6 # elongation -a = 0.33 # minor radius -r0 = 1.0 # major radius -q0 = 1.9 # safety factor at the o-point -p0fac=1 # scale on-axis pressure (P-> P+P0*p0fac. beta changes. Phi,q constant) -b0fac=1 # scale toroidal field at constant beta (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant) -f0fac=1 # scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant) +mr = 128 # Number of radial grid zones +mz = 128 # Number of axial grid zones +ma = 128 # Number of flux grid zones +e = 1.6 # Elongation +a = 0.33 # Minor radius +r0 = 1.0 # Major radius +q0 = 1.9 # Safety factor at the magnetic axis (O-point) +p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) +b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) +f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml b/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml index 02067b588..1a6ec2e08 100644 --- a/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml @@ -1,3 +1,7 @@ +# Regression fixture: Solovev multi-n (n = 1 and 2) with the kinetic path barely enabled +# (kinetic_factor=1e-9). Verifies the "fixed" kinetic path runs across a mode-number range +# without perturbing the ideal result, on a coarse (mpsi=16) plasma; consumed by test/runtests_*.jl. + [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file @@ -8,55 +12,53 @@ power_r = 0 # Major radius power exponent for Jacobi grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized flux coordinate psihigh = 0.9995 # Upper limit of normalized flux coordinate -mpsi = 16 # Number of radial grid points +mpsi = 16 # Number of radial grid points (0 = auto-compute from psi_accuracy) mtheta = 256 # Number of poloidal grid points newq0 = 0 # Override for on-axis safety factor (0 = use input value) etol = 1e-7 # Error tolerance for equilibrium solver force_termination = false # Terminate after equilibrium setup (skip stability calculations) [Wall] -shape = "conformal" # Close conformal wall stabilizes Solovev n=1 external kink; see examples/Solovev_ideal_example/gpec.toml -a = 0.2415 -aw = 0.05 -bw = 1.5 -cw = 0 -dw = 0.5 -tw = 0.05 -equal_arc_wall = true +shape = "conformal" # Wall shape (nowall, conformal, ...); close conformal wall stabilizes the Solovev n=1 kink (see examples/Solovev_ideal_example/gpec.toml) +a = 0.2415 # Distance from plasma (conformal) or shape parameter +aw = 0.05 # Half-thickness parameter for Dee-shaped walls +bw = 1.5 # Elongation parameter for wall shapes +cw = 0 # Offset of wall center from major radius +dw = 0.5 # Triangularity parameter for wall shapes +tw = 0.05 # Sharpness of wall corners (try 0.05 as initial value) +equal_arc_wall = true # Equal arc length distribution of nodes on wall [ForceFreeStates] bal_flag = false # Ideal MHD ballooning criterion for short wavelengths mat_flag = false # Construct coefficient matrices for diagnostic purposes -ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) +ode_flag = true # Integrate ODEs for stability of the internal long-wavelength mode (must be true for GPEC) vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes -mer_flag = true # Evaluate the Mercier criterian +mer_flag = true # Evaluate the Mercier criterion -psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak -qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... -qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)... +psiedge = 0.99 # Edge dW(ψ) diagnostic scan band [psiedge, psilim]; set ≥ psilim to disable +qlow = 1.02 # Integration initiated at q determined by min(q0, qlow) +qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh) sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) -nn_low = 1 # Lower toroidal mode number -nn_high = 2 # Upper toroidal mode number +nn_low = 1 # Smallest toroidal mode number to include +nn_high = 2 # Largest toroidal mode number to include delta_mlow = 0 # Expands lower bound of Fourier harmonics delta_mhigh = 0 # Expands upper bound of Fourier harmonics -delta_mband = 0 # Integration keeps only this wide a band... -mthvac = 64 # Number of points used in splines over poloidal angle at plasma-vacuum interface. -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds +delta_mband = 0 # Integration keeps only this wide a band of solutions (0 = full) +mthvac = 64 # Number of points in splines over poloidal angle at the plasma-vacuum interface -kinetic_source = "fixed" # Kinetic matrix source ("fixed" test matrices, or "calculated" from PENTRC) -kinetic_factor = 1e-9 # Small perturbation to verify kinetic path without altering physics (>0 enables kinetic mode) +kinetic_source = "fixed" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model +kinetic_factor = 1e-9 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode; tiny value just exercises the path) eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced -ucrit = 1e3 # Maximum fraction of solutions allowed before re-normalized +ucrit = 1e3 # Column-norm threshold that triggers solution renormalization # Δ' BVP + parallel integration (see ForceFreeStatesControl docstring for details) -use_parallel = true # Run parallel FM-propagator BVP path (unlocks singular/delta_prime_matrix) +use_parallel = true # Run parallel FM-propagator BVP path (multi-n Δ' matrix has open issues — sing_lim! warns and skips — but ξ and energies are valid) parallel_threads = 2 # BVP thread cap (1 = serial/bit-deterministic; 2 ≈ +20% speedup; ≥3 saturates) -populate_dense_xi = true # Append serial-EL pass after parallel BVP so HDF5 integration/xi_* carry axis-basis dense ξ for PerturbedEquilibrium -truncate_at_dW_peak = false # Edge-dW scan stays diagnostic; integration domain set by qhigh / psihigh / dmlim -set_psilim_via_dmlim = false # FALSE for multi-n (dmlim truncation is ambiguous when n varies — sing_lim! would skip with warning anyway) -dmlim = 0.2 # Only used when set_psilim_via_dmlim = true: truncate at (last_rational_q + dmlim) / n +populate_dense_xi = true # Append serial-EL pass so dense ξ is stored (axis basis) for downstream consumers +set_psilim_via_dmlim = false # FALSE for multi-n — dmlim truncation is ambiguous when n varies (sing_lim! skips anyway) +dmlim = 0.2 # Truncate integration at (last_rational_q + dmlim)/n (used when set_psilim_via_dmlim = true) -write_outputs_to_HDF5 = true -verbose = false +write_outputs_to_HDF5 = true # Write outputs to the HDF5 file +verbose = false # Enable verbose logging diff --git a/test/test_data/regression_solovev_kinetic_multi_n/sol.toml b/test/test_data/regression_solovev_kinetic_multi_n/sol.toml index e54fdeace..86348c36d 100644 --- a/test/test_data/regression_solovev_kinetic_multi_n/sol.toml +++ b/test/test_data/regression_solovev_kinetic_multi_n/sol.toml @@ -1,11 +1,15 @@ +# Solovev analytical equilibrium parameters, consumed by gpec.toml (eq_type = "sol"). +# Sets the grid resolution, plasma shape, and field/pressure scaling factors used to +# generate the analytic Solovev equilibrium. See SolovevConfig in src/Equilibrium. + [SOL_INPUT] -mr = 128 # number of radial grid zones -mz = 128 # number of axial grid zones -ma = 128 # number of flux grid zones -e = 1.6 # elongation -a = 0.33 # minor radius -r0 = 1.0 # major radius -q0 = 1.9 # safety factor at the o-point -p0fac=1 # scale on-axis pressure (P-> P+P0*p0fac. beta changes. Phi,q constant) -b0fac=1 # scale toroidal field at constant beta (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant) -f0fac=1 # scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant) +mr = 128 # Number of radial grid zones +mz = 128 # Number of axial grid zones +ma = 128 # Number of flux grid zones +e = 1.6 # Elongation +a = 0.33 # Minor radius +r0 = 1.0 # Major radius +q0 = 1.9 # Safety factor at the magnetic axis (O-point) +p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) +b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) +f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) From 92f0ec1807ff6975d9d751e9d6a95530ac59a2dc Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Mon, 15 Jun 2026 17:17:16 -0400 Subject: [PATCH 044/135] EXAMPLES - CLEANUP - Address PR #285 review: unify TOML annotations - Unify populate_dense_xi true-case description across the 4 solovev regression fixtures to the canonical examples wording. - Align the a10 [KineticForces] tolerance comments (rtol_xlmda, atol_psi, rtol_psi) to the block's hash column. - Standardize the wall comment in regression_solovev_kinetic_calculated; move the n=1-kink rationale to a [Wall] section comment. Comments-only; zero value changes, all files parse, hygiene clean. Co-Authored-By: Claude Opus 4.8 --- examples/a10_kinetic_example/gpec.toml | 6 +++--- test/test_data/regression_solovev_ideal_example/gpec.toml | 2 +- .../regression_solovev_ideal_example_multi_n/gpec.toml | 2 +- .../regression_solovev_kinetic_calculated/gpec.toml | 3 ++- test/test_data/regression_solovev_kinetic_example/gpec.toml | 2 +- test/test_data/regression_solovev_kinetic_multi_n/gpec.toml | 2 +- 6 files changed, 9 insertions(+), 8 deletions(-) diff --git a/examples/a10_kinetic_example/gpec.toml b/examples/a10_kinetic_example/gpec.toml index 9a34c76d3..c285cde0b 100644 --- a/examples/a10_kinetic_example/gpec.toml +++ b/examples/a10_kinetic_example/gpec.toml @@ -64,6 +64,6 @@ electron = false # Include electron contribution (false = ion-only nutype = "harmonic" # Collision operator (zero, small, krook, harmonic) f0type = "maxwellian" # Distribution function (maxwellian, jkp, cgl) atol_xlmda = 1e-9 # Absolute tolerance for inner pitch + energy integrations -rtol_xlmda = 1e-5 # Relative tolerance for inner pitch + energy integrations -atol_psi = 1e-9 # Absolute tolerance for the outer ψ quadrature -rtol_psi = 1e-4 # Relative tolerance for the outer ψ quadrature +rtol_xlmda = 1e-5 # Relative tolerance for inner pitch + energy integrations +atol_psi = 1e-9 # Absolute tolerance for the outer ψ quadrature +rtol_psi = 1e-4 # Relative tolerance for the outer ψ quadrature diff --git a/test/test_data/regression_solovev_ideal_example/gpec.toml b/test/test_data/regression_solovev_ideal_example/gpec.toml index ff6d9f04a..d74b0663d 100644 --- a/test/test_data/regression_solovev_ideal_example/gpec.toml +++ b/test/test_data/regression_solovev_ideal_example/gpec.toml @@ -56,7 +56,7 @@ ucrit = 1e3 # Column-norm threshold that triggers solution ren # Δ' BVP + parallel integration (see ForceFreeStatesControl docstring for details) use_parallel = true # Run parallel FM-propagator BVP path (unlocks singular/delta_prime_matrix) parallel_threads = 2 # BVP thread cap (1 = serial/bit-deterministic; 2 ≈ +20% speedup; ≥3 saturates) -populate_dense_xi = true # Append serial-EL pass so dense ξ is stored (axis basis) for downstream consumers +populate_dense_xi = true # Append serial-EL pass so dense ξ is stored — REQUIRED with a [PerturbedEquilibrium] section set_psilim_via_dmlim = false # FALSE for limited/analytical equilibria — rationals sparse, dmlim would chop too much edge dmlim = 0.2 # Truncate integration at (last_rational_q + dmlim)/n (used when set_psilim_via_dmlim = true) diff --git a/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml b/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml index 79299d634..2b501510e 100644 --- a/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml +++ b/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml @@ -56,7 +56,7 @@ ucrit = 1e3 # Column-norm threshold that triggers solution ren # Δ' BVP + parallel integration (see ForceFreeStatesControl docstring for details) use_parallel = true # Run parallel FM-propagator BVP path (multi-n Δ' matrix has open issues — sing_lim! warns and skips — but ξ and energies are valid) parallel_threads = 2 # BVP thread cap (1 = serial/bit-deterministic; 2 ≈ +20% speedup; ≥3 saturates) -populate_dense_xi = true # Append serial-EL pass so dense ξ is stored (axis basis) for downstream consumers +populate_dense_xi = true # Append serial-EL pass so dense ξ is stored — REQUIRED with a [PerturbedEquilibrium] section set_psilim_via_dmlim = false # FALSE for multi-n — dmlim truncation is ambiguous when n varies (sing_lim! skips anyway) dmlim = 0.2 # Truncate integration at (last_rational_q + dmlim)/n (used when set_psilim_via_dmlim = true) diff --git a/test/test_data/regression_solovev_kinetic_calculated/gpec.toml b/test/test_data/regression_solovev_kinetic_calculated/gpec.toml index 4eb1e3944..464805308 100644 --- a/test/test_data/regression_solovev_kinetic_calculated/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_calculated/gpec.toml @@ -19,7 +19,8 @@ etol = 1e-7 # Error tolerance for equilibrium solver force_termination = false # Terminate after equilibrium setup (skip stability calculations) [Wall] -shape = "conformal" # Wall shape (nowall, conformal, ...); close conformal wall stabilizes the Solovev n=1 kink (see examples/Solovev_ideal_example/gpec.toml) +# A close conformal wall stabilizes the Solovev n=1 kink for this fixture. +shape = "conformal" # Wall shape (nowall, conformal, elliptical, dee, mod_dee, filepath) a = 0.2415 # Distance from plasma (conformal) or shape parameter aw = 0.05 # Half-thickness parameter for Dee-shaped walls bw = 1.5 # Elongation parameter for wall shapes diff --git a/test/test_data/regression_solovev_kinetic_example/gpec.toml b/test/test_data/regression_solovev_kinetic_example/gpec.toml index ffb488b85..bc7fdc213 100644 --- a/test/test_data/regression_solovev_kinetic_example/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_example/gpec.toml @@ -56,7 +56,7 @@ ucrit = 1e3 # Column-norm threshold that triggers solution ren # Δ' BVP + parallel integration (see ForceFreeStatesControl docstring for details) use_parallel = true # Run parallel FM-propagator BVP path (unlocks singular/delta_prime_matrix) parallel_threads = 2 # BVP thread cap (1 = serial/bit-deterministic; 2 ≈ +20% speedup; ≥3 saturates) -populate_dense_xi = true # Append serial-EL pass so dense ξ is stored (axis basis) for downstream consumers +populate_dense_xi = true # Append serial-EL pass so dense ξ is stored — REQUIRED with a [PerturbedEquilibrium] section set_psilim_via_dmlim = false # FALSE for limited/analytical equilibria — rationals sparse, dmlim would chop too much edge dmlim = 0.2 # Truncate integration at (last_rational_q + dmlim)/n (used when set_psilim_via_dmlim = true) diff --git a/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml b/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml index 1a6ec2e08..f1c7948ef 100644 --- a/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml @@ -56,7 +56,7 @@ ucrit = 1e3 # Column-norm threshold that triggers solution ren # Δ' BVP + parallel integration (see ForceFreeStatesControl docstring for details) use_parallel = true # Run parallel FM-propagator BVP path (multi-n Δ' matrix has open issues — sing_lim! warns and skips — but ξ and energies are valid) parallel_threads = 2 # BVP thread cap (1 = serial/bit-deterministic; 2 ≈ +20% speedup; ≥3 saturates) -populate_dense_xi = true # Append serial-EL pass so dense ξ is stored (axis basis) for downstream consumers +populate_dense_xi = true # Append serial-EL pass so dense ξ is stored — REQUIRED with a [PerturbedEquilibrium] section set_psilim_via_dmlim = false # FALSE for multi-n — dmlim truncation is ambiguous when n varies (sing_lim! skips anyway) dmlim = 0.2 # Truncate integration at (last_rational_q + dmlim)/n (used when set_psilim_via_dmlim = true) From 2a640070b885623a38590d9f1adb0350f34d2539 Mon Sep 17 00:00:00 2001 From: Nikolas Logan Date: Tue, 16 Jun 2026 10:00:31 -0400 Subject: [PATCH 045/135] DOCS - MINOR - Replaces Pharr field with field --- src/Equilibrium/CoordinateInvariant.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/Equilibrium/CoordinateInvariant.jl b/src/Equilibrium/CoordinateInvariant.jl index 350351c4b..fb5c2492d 100644 --- a/src/Equilibrium/CoordinateInvariant.jl +++ b/src/Equilibrium/CoordinateInvariant.jl @@ -4,7 +4,7 @@ Coordinate-invariant (root-area-weighted field) flux-surface operators. These building blocks implement the √area weighting of Pharr (2026), "Coordinate-invariant flux-surface Fourier analysis in tokamaks". They are the single source of truth for translating a flux-surface field component between the -three Pharr field representations (all in tesla), shared by the ForceFreeStates and +three field representations (all in tesla), shared by the ForceFreeStates and PerturbedEquilibrium modules: - `b` bare / normal field (Fourier weight W = 1) From 7fccd4384da7582cc3f22e486545ae2e8343056b Mon Sep 17 00:00:00 2001 From: Jake Halpern Date: Tue, 16 Jun 2026 10:51:58 -0400 Subject: [PATCH 046/135] GPEC - DEPRECATION - long overdue removal of banded matrices in ForceFreeStates --- benchmarks/benchmark_delta_m_scan.jl | 268 +++++++++++++++ benchmarks/benchmark_delta_prime_methods.jl | 23 +- .../benchmark_diiid_ideal_ntv_torque.jl | 194 +++++------ .../benchmark_diiid_kinetic_stability.jl | 144 ++++---- benchmarks/benchmark_riccati_der.jl | 15 +- benchmarks/benchmark_threads.jl | 23 +- docs/src/stability.md | 3 +- docs/src/utilities.md | 2 +- examples/DIIID-like_ideal_example/gpec.toml | 1 - examples/LAR_beta_scan/gpec.toml | 1 - examples/LAR_epsilon_scan/gpec.toml | 1 - examples/Solovev_ideal_example/gpec.toml | 2 - examples/Solovev_ideal_example_3D/gpec.toml | 1 - .../Solovev_ideal_example_multi_n/gpec.toml | 1 - .../single_n_1/gpec.toml | 1 - .../single_n_2/gpec.toml | 1 - examples/a10_kinetic_example/gpec.toml | 1 - src/ForceFreeStates/ForceFreeStatesStructs.jl | 13 +- src/ForceFreeStates/Fourfit.jl | 215 ++++++------ src/ForceFreeStates/Free.jl | 8 +- src/ForceFreeStates/Sing.jl | 72 ++-- src/GeneralizedPerturbedEquilibrium.jl | 18 +- .../FieldReconstruction.jl | 321 +++++++++--------- src/Utilities/FourierCoefficients.jl | 32 +- test/runtests_fouriertransforms.jl | 2 +- test/runtests_parallel_integration.jl | 119 ++++--- test/runtests_riccati.jl | 70 ++-- test/runtests_sing.jl | 2 +- test/runtests_utilities.jl | 2 +- .../gpec.toml | 1 - .../gpec.toml | 1 - .../gpec.toml | 1 - .../gpec.toml | 1 - .../gpec.toml | 1 - 34 files changed, 908 insertions(+), 653 deletions(-) create mode 100644 benchmarks/benchmark_delta_m_scan.jl diff --git a/benchmarks/benchmark_delta_m_scan.jl b/benchmarks/benchmark_delta_m_scan.jl new file mode 100644 index 000000000..f0de5caac --- /dev/null +++ b/benchmarks/benchmark_delta_m_scan.jl @@ -0,0 +1,268 @@ +#!/usr/bin/env julia +# +# Scan delta_mlow = delta_mhigh for regression_solovev_ideal_example on two git +# branches and plot minimum total energy eigenvalue Re(min et) vs delta. +# +# Each branch uses one Julia subprocess that loads GPEC once and loops over δ. +# +# Usage: +# julia --project=. benchmarks/benchmark_delta_m_scan.jl +# julia --project=. benchmarks/benchmark_delta_m_scan.jl --quick +# julia --project=. benchmarks/benchmark_delta_m_scan.jl --branch1 develop --branch2 jmh/vacuum_galerkin +# julia --project=. benchmarks/benchmark_delta_m_scan.jl --deltas 0,4,8,12,16 + +using Dates +using HDF5 +using Printf +using TOML + +const PROJECT_ROOT = abspath(joinpath(@__DIR__, "..")) +const EXAMPLE_DIR = joinpath(PROJECT_ROOT, "examples", "DIIID-like_ideal_example_copy") +const OUTPUT_DIR = joinpath(@__DIR__, "delta_m_scan") +const GPEC_BASE = TOML.parsefile(joinpath(EXAMPLE_DIR, "gpec.toml")) + +function prepare_run_dir(base::Dict, example_dir::AbstractString, delta::Int) + raw = deepcopy(base) + raw["ForceFreeStates"]["delta_mlow"] = delta + raw["ForceFreeStates"]["delta_mhigh"] = delta + raw["ForceFreeStates"]["verbose"] = false + + run_dir = mktempdir(; prefix="gpec_delta_m_$(delta)_") + open(joinpath(run_dir, "gpec.toml"), "w") do io + TOML.print(io, raw) + end + for f in readdir(example_dir) + src = abspath(joinpath(example_dir, f)) + isfile(src) && f != "gpec.toml" && symlink(src, joinpath(run_dir, f)) + end + return run_dir +end + +function read_et_min(h5_path::String) + h5open(h5_path, "r") do h5 + et = if haskey(h5, "vacuum/et") + read(h5["vacuum/et"]) + elseif haskey(h5, "FreeBoundaryStability/XiNorm/eigenmode_energies") + read(h5["FreeBoundaryStability/XiNorm/eigenmode_energies"]) + else + keys_str = join(collect(keys(h5)), ", ") + error("No eigenvalue dataset in $h5_path (top-level keys: $keys_str)") + end + return minimum(real.(et)) + end +end + +function worker_scan(example_dir::AbstractString, base_toml::AbstractString, deltas, output_csv::AbstractString) + base = TOML.parsefile(base_toml) + et_min = Float64[] + for (i, delta) in enumerate(deltas) + @info "delta=$delta ($i/$(length(deltas)))" + run_dir = prepare_run_dir(base, example_dir, delta) + try + GeneralizedPerturbedEquilibrium.main([run_dir]) + h5_path = joinpath(run_dir, "gpec.h5") + isfile(h5_path) || error("Missing output: $h5_path") + val = read_et_min(h5_path) + push!(et_min, val) + @printf(" Re(min et) = %+.6f\n", val) + catch err + @warn "Run failed" delta exception=(err, catch_backtrace()) + push!(et_min, NaN) + finally + rm(run_dir; force=true, recursive=true) + end + end + open(output_csv, "w") do io + println(io, "delta,et_min_real") + for (delta, et) in zip(deltas, et_min) + println(io, "$delta,$et") + end + end +end + +function parse_options(args) + opts = Dict( + "branch1" => "develop", + "branch2" => strip(readchomp(`git -C $PROJECT_ROOT branch --show-current`)), + "deltas" => nothing, + "quick" => false + ) + i = 1 + while i <= length(args) + arg = args[i] + if arg == "--quick" + opts["quick"] = true + i += 1 + elseif arg == "--branch1" && i < length(args) + opts["branch1"] = String(args[i+1]) + i += 2 + elseif arg == "--branch2" && i < length(args) + opts["branch2"] = String(args[i+1]) + i += 2 + elseif arg == "--deltas" && i < length(args) + opts["deltas"] = [parse(Int, strip(s)) for s in split(args[i+1], ',')] + i += 2 + else + error("Unknown argument: $arg") + end + end + if opts["deltas"] === nothing + opts["deltas"] = opts["quick"] ? [0, 8, 16, 24] : collect(0:4:32) + end + return opts +end + +function git_short_ref(ref) + return readchomp(`git -C $PROJECT_ROOT rev-parse --short $ref`) +end + +function checkout_ref(branch::AbstractString) + @info "Checking out $branch" + run(`git -C $PROJECT_ROOT checkout $branch`) +end + +function read_worker_csv(path::AbstractString, deltas) + rows = Dict{Int,Float64}() + open(path, "r") do io + readline(io) # header + for line in eachline(io) + isempty(strip(line)) && continue + parts = split(strip(line), ',') + rows[parse(Int, parts[1])] = parse(Float64, parts[2]) + end + end + return [get(rows, delta, NaN) for delta in deltas] +end + +function scan_branch(branch::AbstractString, deltas::AbstractVector{<:Integer}) + commit = git_short_ref("HEAD") + @info "[$branch @ $commit] scanning $(length(deltas)) δ values in one Julia session" + + base_toml = tempname() * ".toml" + output_csv = tempname() * ".csv" + try + open(base_toml, "w") do io + TOML.print(io, GPEC_BASE) + end + delta_str = join(string.(deltas), ',') + run( + `julia --project=$PROJECT_ROOT $(@__FILE__) --worker $PROJECT_ROOT $EXAMPLE_DIR $base_toml $delta_str $output_csv` + ) + et_min = read_worker_csv(output_csv, deltas) + return (branch=branch, commit=commit, et_min=et_min) + finally + isfile(base_toml) && rm(base_toml; force=true) + isfile(output_csv) && rm(output_csv; force=true) + end +end + +function save_results_csv(path::String, deltas, results) + open(path, "w") do io + println(io, "delta,branch,commit,et_min_real") + for r in results + for (delta, et) in zip(deltas, r.et_min) + println(io, "$delta,$(r.branch),$(r.commit),$et") + end + end + end +end + +function plot_results(path::String, deltas, results) + default(; lw=2, marker=:circle, markersize=5, legend=:best, grid=true) + p = plot(; + xlabel="δ (delta_mlow = delta_mhigh)", + ylabel="Re(min et)", + yscale=:log10, + size=(700, 450), + left_margin=12Plots.mm, + bottom_margin=4Plots.mm + ) + markers = [:circle, :rect, :utriangle, :diamond] + for (i, r) in enumerate(results) + et_log = [v > 0 ? v : NaN for v in r.et_min] + plot!( + p, + deltas, + et_log; + marker=markers[mod1(i, length(markers))], + label="$(r.branch) @ $(r.commit)" + ) + end + savefig(p, path) + println("Saved plot: $path") +end + +function main() + opts = parse_options(ARGS) + deltas = opts["deltas"] + branch1 = opts["branch1"] + branch2 = opts["branch2"] + + mkpath(OUTPUT_DIR) + original_branch = strip(readchomp(`git -C $PROJECT_ROOT branch --show-current`)) + + println("="^70) + println("delta_m scan — regression_solovev_ideal_example") + println("="^70) + @printf("Example: %s\n", EXAMPLE_DIR) + @printf("Deltas: %s\n", join(string.(deltas), ", ")) + @printf("Branches: %s vs %s\n", branch1, branch2) + println() + + results = Dict{String,Any}() + try + checkout_ref(branch1) + results["branch1"] = scan_branch(branch1, deltas) + + checkout_ref(branch2) + results["branch2"] = scan_branch(branch2, deltas) + finally + @info "Restoring branch $original_branch" + checkout_ref(original_branch) + end + + scan_results = [results["branch1"], results["branch2"]] + stamp = Dates.format(now(), "yyyymmdd_HHMMSS") + csv_path = joinpath(OUTPUT_DIR, "delta_m_scan_$(stamp).csv") + png_path = joinpath(OUTPUT_DIR, "delta_m_scan_$(stamp).png") + save_results_csv(csv_path, deltas, scan_results) + plot_results(png_path, deltas, scan_results) + + println() + println("="^70) + @printf("%6s", "delta") + for r in scan_results + @printf(" %20s", "$(r.branch)") + end + println() + println("-"^70) + for (j, delta) in enumerate(deltas) + @printf("%6d", delta) + for r in scan_results + val = r.et_min[j] + if isnan(val) + @printf(" %20s", "FAIL") + else + @printf(" %20.6f", val) + end + end + println() + end + println("="^70) + println("CSV: $csv_path") + println("Plot: $png_path") +end + +if abspath(PROGRAM_FILE) == @__FILE__ + if length(ARGS) >= 1 && ARGS[1] == "--worker" + using Pkg + Pkg.activate(ARGS[2]) + Pkg.instantiate() + using GeneralizedPerturbedEquilibrium + deltas = [parse(Int, strip(s)) for s in split(ARGS[5], ',')] + worker_scan(ARGS[3], ARGS[4], deltas, ARGS[6]) + else + using Plots + main() + end +end diff --git a/benchmarks/benchmark_delta_prime_methods.jl b/benchmarks/benchmark_delta_prime_methods.jl index 704763f4d..4bf77f179 100644 --- a/benchmarks/benchmark_delta_prime_methods.jl +++ b/benchmarks/benchmark_delta_prime_methods.jl @@ -32,14 +32,15 @@ function setup_and_run_solovev() intr.wall_settings = GeneralizedPerturbedEquilibrium.Vacuum.WallShapeSettings(; (Symbol(k) => v for (k, v) in inputs["Wall"])...) FFS.sing_lim!(intr, ctrl, equil) - intr.nlow = ctrl.nn_low; intr.nhigh = ctrl.nn_high; intr.npert = 1 + intr.nlow = ctrl.nn_low; + intr.nhigh = ctrl.nn_high; + intr.npert = 1 FFS.sing_find!(intr, equil) - intr.mlow = min(intr.nlow * equil.params.qmin, 0) - 4 - ctrl.delta_mlow + intr.mlow = min(intr.nlow * equil.params.qmin, 0) - 4 - ctrl.delta_mlow intr.mhigh = trunc(Int, intr.nhigh * equil.params.qmax) + ctrl.delta_mhigh intr.mpert = intr.mhigh - intr.mlow + 1 - intr.mband = intr.mpert - 1 intr.numpert_total = intr.mpert * intr.npert - metric = FFS.make_metric(equil; mband=intr.mband, fft_flag=ctrl.fft_flag) + metric = FFS.make_metric(equil, intr.mpert) ffit = FFS.make_matrix(equil, intr, metric) odet = FFS.riccati_eulerlagrange_integration(ctrl, equil, ffit, intr) return ctrl, equil, ffit, intr, odet @@ -61,7 +62,7 @@ FFS.compute_delta_prime_from_ca!(odet, intr, equil) println(" N=$(intr.numpert_total) modes, $msing singular surfaces\n") @printf(" %6s %4s %4s %22s %22s %12s\n", - "Surf", "m", "n", "Δ' (inline)", "Δ' (from_ca)", "abs diff") + "Surf", "m", "n", "Δ' (inline)", "Δ' (from_ca)", "abs diff") println(" " * "-"^76) max_absdiff = let max_absdiff = 0.0 @@ -69,15 +70,15 @@ max_absdiff = let max_absdiff = 0.0 sing = intr.sing[s] dp_from_ca = intr.sing[s].delta_prime for i in eachindex(delta_prime_inline[s]) - dp_il = delta_prime_inline[s][i] - dp_fc = dp_from_ca[i] + dp_il = delta_prime_inline[s][i] + dp_fc = dp_from_ca[i] absdiff = abs(dp_fc - dp_il) max_absdiff = max(max_absdiff, absdiff) @printf(" %6d %4d %4d %22.6f%+.6fi %22.6f%+.6fi %12.4e\n", - s, sing.m[i], sing.n[i], - real(dp_il), imag(dp_il), - real(dp_fc), imag(dp_fc), - absdiff) + s, sing.m[i], sing.n[i], + real(dp_il), imag(dp_il), + real(dp_fc), imag(dp_fc), + absdiff) end end max_absdiff diff --git a/benchmarks/benchmark_diiid_ideal_ntv_torque.jl b/benchmarks/benchmark_diiid_ideal_ntv_torque.jl index 46c4715ce..b21721049 100644 --- a/benchmarks/benchmark_diiid_ideal_ntv_torque.jl +++ b/benchmarks/benchmark_diiid_ideal_ntv_torque.jl @@ -32,9 +32,9 @@ using Plots using GeneralizedPerturbedEquilibrium const GPE = GeneralizedPerturbedEquilibrium const FFS = GPE.ForceFreeStates -const KF = GPE.KineticForces -const Eq = GPE.Equilibrium -const PE = GPE.PerturbedEquilibrium +const KF = GPE.KineticForces +const Eq = GPE.Equilibrium +const PE = GPE.PerturbedEquilibrium const DEFAULT_FORTRAN_DIR = expanduser("~/Code/gpec/docs/examples/DIIID_ideal_example") @@ -56,13 +56,13 @@ function discover_inputs(fortran_dir::String) end length(eq_candidates) == 1 || error("Expected exactly one EFIT g-file in $fortran_dir; found: $eq_candidates") - eq_file = joinpath(fortran_dir, eq_candidates[1]) - kin_file = eq_file * ".kin" - xclebsch = joinpath(fortran_dir, "gpec_xclebsch_n1.out") + eq_file = joinpath(fortran_dir, eq_candidates[1]) + kin_file = eq_file * ".kin" + xclebsch = joinpath(fortran_dir, "gpec_xclebsch_n1.out") pentrc_nc = joinpath(fortran_dir, "pentrc_output_n1.nc") for (label, path) in [("kinetic profile", kin_file), - ("xclebsch output", xclebsch), - ("pentrc NetCDF", pentrc_nc)] + ("xclebsch output", xclebsch), + ("pentrc NetCDF", pentrc_nc)] isfile(path) || error("$label not found: $path") end return (; eq_file, kin_file, xclebsch, pentrc_nc) @@ -78,10 +78,10 @@ function read_pentrc_reference(pentrc_nc::String) NCDatasets.Dataset(pentrc_nc, "r") do ds gatt = ds.attrib return ( - T_total_fgar = Float64(gatt["T_total_fgar"]), - T_total_tgar = Float64(gatt["T_total_tgar"]), - dW_total_fgar = Float64(gatt["dW_total_fgar"]), - dW_total_tgar = Float64(gatt["dW_total_tgar"]), + T_total_fgar=Float64(gatt["T_total_fgar"]), + T_total_tgar=Float64(gatt["T_total_tgar"]), + dW_total_fgar=Float64(gatt["dW_total_fgar"]), + dW_total_tgar=Float64(gatt["dW_total_tgar"]) ) end end @@ -105,55 +105,57 @@ function build_benchmark_tomldir(eq_file::String) cp(eq_file, joinpath(tmpdir, eq_name)) end open(joinpath(tmpdir, "gpec.toml"), "w") do io - println(io, """ - # Auto-generated by benchmark_diiid_ideal_ntv_torque.jl — do not edit. - - [Equilibrium] - eq_filename = "$eq_name" - eq_type = "efit" - jac_type = "hamada" - power_bp = 0 - power_b = 0 - power_r = 0 - grid_type = "ldp" - psilow = 1e-4 - psihigh = 0.993 - mpsi = 128 - mtheta = 256 - newq0 = 0 - etol = 1e-7 - - [Wall] - shape = "nowall" - - [ForceFreeStates] - bal_flag = false - mat_flag = true - ode_flag = true - vac_flag = true - mer_flag = true - force_termination = false - - psiedge = 1.00 # No edge-scan truncation (dmlim mechanism removed in develop) - qlow = 1.02 - qhigh = 1e3 - sing_start = 0 - - nn_low = 1 - nn_high = 1 - delta_mlow = 8 - delta_mhigh = 8 - delta_mband = 0 - mthvac = 512 - thmax0 = 1 - - kinetic_source = "fixed" - kinetic_factor = 0.0 - eulerlagrange_tolerance = 1e-7 - save_interval = 3 - singfac_min = 1e-4 - ucrit = 1e4 - """) + println( + io, + """ +# Auto-generated by benchmark_diiid_ideal_ntv_torque.jl — do not edit. + +[Equilibrium] +eq_filename = "$eq_name" +eq_type = "efit" +jac_type = "hamada" +power_bp = 0 +power_b = 0 +power_r = 0 +grid_type = "ldp" +psilow = 1e-4 +psihigh = 0.993 +mpsi = 128 +mtheta = 256 +newq0 = 0 +etol = 1e-7 + +[Wall] +shape = "nowall" + +[ForceFreeStates] +bal_flag = false +mat_flag = true +ode_flag = true +vac_flag = true +mer_flag = true +force_termination = false + +psiedge = 1.00 # No edge-scan truncation (dmlim mechanism removed in develop) +qlow = 1.02 +qhigh = 1e3 +sing_start = 0 + +nn_low = 1 +nn_high = 1 +delta_mlow = 8 +delta_mhigh = 8 +mthvac = 512 +thmax0 = 1 + +kinetic_source = "fixed" +kinetic_factor = 0.0 +eulerlagrange_tolerance = 1e-7 +save_interval = 3 +singfac_min = 1e-4 +ucrit = 1e4 +""" + ) end return tmpdir end @@ -164,10 +166,10 @@ end Parse Fortran `gpec_xclebsch_n1.out` into arrays matching PE xi_modes layout. Header format: - Line 1: title - Line 6: mstep, mpert, mthsurf - Line 8: column headers - Line 9+: data (psi, m, 6 floats) +Line 1: title +Line 6: mstep, mpert, mthsurf +Line 8: column headers +Line 9+: data (psi, m, 6 floats) """ function load_fortran_xclebsch(filepath::String) lines = readlines(filepath) @@ -193,7 +195,7 @@ function load_fortran_xclebsch(filepath::String) psi_vals = Float64[] clebsch_psi1_data = zeros(ComplexF64, npsi_total, mpert) - clebsch_psi_data = zeros(ComplexF64, npsi_total, mpert) + clebsch_psi_data = zeros(ComplexF64, npsi_total, mpert) clebsch_alpha_data = zeros(ComplexF64, npsi_total, mpert) idx = 0 @@ -202,14 +204,14 @@ function load_fortran_xclebsch(filepath::String) idx += 1 vals = parse.(Float64, split(data_lines[idx])) psi = vals[1] - m = Int(vals[2]) + m = Int(vals[2]) if j == 1 push!(psi_vals, psi) end ipert = m - mlow + 1 @assert 1 <= ipert <= mpert "Mode m=$m out of range [mlow=$mlow, mhigh=$(mlow+mpert-1)]" - clebsch_psi1_data[i, ipert] = complex(vals[3], vals[4]) # ∂ξ^ψ/∂ψ - clebsch_psi_data[i, ipert] = complex(vals[5], vals[6]) # ξ^ψ + clebsch_psi1_data[i, ipert] = complex(vals[3], vals[4]) # ∂ξ^ψ/∂ψ + clebsch_psi_data[i, ipert] = complex(vals[5], vals[6]) # ξ^ψ clebsch_alpha_data[i, ipert] = complex(vals[7], vals[8]) # ξ^α end end @@ -228,7 +230,7 @@ function run_benchmark(fortran_dir::String=DEFAULT_FORTRAN_DIR) _p("=" ^ 70) inputs = discover_inputs(fortran_dir) - ref = read_pentrc_reference(inputs.pentrc_nc) + ref = read_pentrc_reference(inputs.pentrc_nc) _pf(" EFIT g-file: %s\n", basename(inputs.eq_file)) _pf(" Kinetic: %s\n", basename(inputs.kin_file)) @@ -238,15 +240,15 @@ function run_benchmark(fortran_dir::String=DEFAULT_FORTRAN_DIR) _p("\n--- Equilibrium + ForceFreeStates (via main()) ---") t0 = time() result = GPE.main([tomldir]) - equil = result.equil - intr = result.intr - ctrl = result.ctrl + equil = result.equil + intr = result.intr + ctrl = result.ctrl _pf(" FFS completed in %.1f s\n", time() - t0) _pf(" mpert=%d, mlow=%d, mhigh=%d\n", intr.mpert, intr.mlow, intr.mhigh) # Build metric (needed for JBB deweighting) - metric = FFS.make_metric(equil; mband=intr.mband, fft_flag=ctrl.fft_flag) + metric = FFS.make_metric(equil, intr.mpert) # Load Fortran xclebsch data _p("\n--- Load Fortran xclebsch ---") @@ -270,11 +272,11 @@ function run_benchmark(fortran_dir::String=DEFAULT_FORTRAN_DIR) # Fortran xclebsch stores ξ^α directly; PE convention is ξ^α/χ₁ chi1 = 2π * equil.psio pe_state = PE.PerturbedEquilibriumState(; - psi_grid = psi_grid_f, - xi_modes = ( - clebsch_psi = clebsch_psi, - clebsch_psi1 = clebsch_psi1, - clebsch_alpha = clebsch_alpha ./ chi1, # Store as ξ^α/χ₁ per PE convention + psi_grid=psi_grid_f, + xi_modes=( + clebsch_psi=clebsch_psi, + clebsch_psi1=clebsch_psi1, + clebsch_alpha=clebsch_alpha ./ chi1 # Store as ξ^α/χ₁ per PE convention ) ) @@ -342,10 +344,10 @@ function run_benchmark(fortran_dir::String=DEFAULT_FORTRAN_DIR) if haskey(kf_state.method_results, method_key) mr = kf_state.method_results[method_key] - T_julia = real(mr.total_torque) + T_julia = real(mr.total_torque) dW_julia = real(mr.total_energy) - T_err = abs(T_julia - ref_T) / abs(ref_T) * 100 - dW_err = abs(dW_julia - ref_dW) / abs(ref_dW) * 100 + T_err = abs(T_julia - ref_T) / abs(ref_T) * 100 + dW_err = abs(dW_julia - ref_dW) / abs(ref_dW) * 100 results[method_key] = (; T_julia, dW_julia, T_err, dW_err) @@ -392,18 +394,18 @@ function run_benchmark(fortran_dir::String=DEFAULT_FORTRAN_DIR) NCDatasets.Dataset(pentrc_nc, "r") do ds for method_key in keys(results) psi_var = "psi_$method_key" - dt_var = "dTdpsi_$method_key" - T_var = "T_$method_key" + dt_var = "dTdpsi_$method_key" + T_var = "T_$method_key" if !(haskey(ds, psi_var) && haskey(ds, dt_var) && haskey(ds, T_var)) @warn "Fortran NetCDF missing variables for method" method=method_key continue end - psi_f = Array(ds[psi_var][:]) + psi_f = Array(ds[psi_var][:]) dTdpsi_f = Array(ds[dt_var][:, :, :]) # (i, ell, psi) - T_f = Array(ds[T_var][:, :, :]) + T_f = Array(ds[T_var][:, :, :]) # Take real slice (i=1), sum over ell (dim 1 of the 2D real slice → (psi,)) dT_re_f = dropdims(sum(dTdpsi_f[1, :, :]; dims=1); dims=1) - T_re_f = dropdims(sum(T_f[1, :, :]; dims=1); dims=1) + T_re_f = dropdims(sum(T_f[1, :, :]; dims=1); dims=1) fortran_profiles[method_key] = (; psi=psi_f, dTdpsi=dT_re_f, T=T_re_f) _pf(" Fortran %-5s: %d ψ points, T_final = %.6f N·m\n", method_key, length(psi_f), T_re_f[end]) @@ -435,7 +437,7 @@ function run_benchmark(fortran_dir::String=DEFAULT_FORTRAN_DIR) println(io, "# psi_julia dTdpsi_julia_re T_julia_re") for i in eachindex(mr.psi_grid) @printf(io, "%.8e %.8e %.8e\n", - mr.psi_grid[i], real(mr.dtdpsi[i]), real(mr.t_cumulative[i])) + mr.psi_grid[i], real(mr.dtdpsi[i]), real(mr.t_cumulative[i])) end println(io, "# --- fortran ---") println(io, "# psi_fortran dTdpsi_fortran T_fortran") @@ -446,12 +448,12 @@ function run_benchmark(fortran_dir::String=DEFAULT_FORTRAN_DIR) # dT/dψ panel p1 = plot(; xlabel="ψ_n", ylabel="dT/dψ [N·m]", - title="$(uppercase(mkey)): dT/dψ", legend=:topleft, - left_margin=12Plots.mm, bottom_margin=4Plots.mm, size=(900, 500)) + title="$(uppercase(mkey)): dT/dψ", legend=:topleft, + left_margin=12Plots.mm, bottom_margin=4Plots.mm, size=(900, 500)) plot!(p1, Float64.(fp.psi), Float64.(fp.dTdpsi); - label="Fortran", lw=2, color=:black, linestyle=:dash) + label="Fortran", lw=2, color=:black, linestyle=:dash) plot!(p1, Float64.(mr.psi_grid), Float64.(real.(mr.dtdpsi)); - label="Julia", lw=1.5, color=:crimson) + label="Julia", lw=1.5, color=:crimson) path1 = joinpath(@__DIR__, "kf_$(mkey)_dTdpsi_vs_fortran.png") try savefig(p1, path1) @@ -462,12 +464,12 @@ function run_benchmark(fortran_dir::String=DEFAULT_FORTRAN_DIR) # Cumulative T panel p2 = plot(; xlabel="ψ_n", ylabel="T [N·m]", - title="$(uppercase(mkey)): cumulative T", legend=:topleft, - left_margin=12Plots.mm, bottom_margin=4Plots.mm, size=(900, 500)) + title="$(uppercase(mkey)): cumulative T", legend=:topleft, + left_margin=12Plots.mm, bottom_margin=4Plots.mm, size=(900, 500)) plot!(p2, Float64.(fp.psi), Float64.(fp.T); - label="Fortran", lw=2, color=:black, linestyle=:dash) + label="Fortran", lw=2, color=:black, linestyle=:dash) plot!(p2, Float64.(mr.psi_grid), Float64.(real.(mr.t_cumulative)); - label="Julia", lw=1.5, color=:crimson) + label="Julia", lw=1.5, color=:crimson) path2 = joinpath(@__DIR__, "kf_$(mkey)_T_vs_fortran.png") try savefig(p2, path2) diff --git a/benchmarks/benchmark_diiid_kinetic_stability.jl b/benchmarks/benchmark_diiid_kinetic_stability.jl index 8274de1b3..ba2c0f97a 100644 --- a/benchmarks/benchmark_diiid_kinetic_stability.jl +++ b/benchmarks/benchmark_diiid_kinetic_stability.jl @@ -57,11 +57,11 @@ function discover_inputs(fortran_dir::String) end length(eq_candidates) == 1 || error("Expected exactly one EFIT g-file in $fortran_dir; found: $eq_candidates") - eq_file = joinpath(fortran_dir, eq_candidates[1]) + eq_file = joinpath(fortran_dir, eq_candidates[1]) kin_file = eq_file * ".kin" - dcon_nc = joinpath(fortran_dir, "dcon_output_n1.nc") + dcon_nc = joinpath(fortran_dir, "dcon_output_n1.nc") for (label, path) in [("kinetic profile", kin_file), - ("dcon NetCDF", dcon_nc)] + ("dcon NetCDF", dcon_nc)] isfile(path) || error("$label not found: $path") end return (; eq_file, kin_file, dcon_nc) @@ -77,9 +77,9 @@ diagonalised matrices in DCON, so they do not sum to the total — the partition is informational only). NetCDF layout (dims in Fortran order, preserved by NCDatasets): - W_t_eigenvalue(mode, i) — total energy, i=1 real, i=2 imag - W_p_eigenvalue(mode, i) — plasma energy - W_v_eigenvalue(mode, i) — vacuum energy +W_t_eigenvalue(mode, i) — total energy, i=1 real, i=2 imag +W_p_eigenvalue(mode, i) — plasma energy +W_v_eigenvalue(mode, i) — vacuum energy Mode index 1 is the least-stable mode. """ function read_dcon_reference(dcon_nc::String) @@ -88,9 +88,9 @@ function read_dcon_reference(dcon_nc::String) Wp = Array(ds["W_p_eigenvalue"][:, :]) Wv = Array(ds["W_v_eigenvalue"][:, :]) return ( - W_t_re = Wt[1, 1], W_t_im = Wt[1, 2], - W_p_re = Wp[1, 1], W_p_im = Wp[1, 2], - W_v_re = Wv[1, 1], W_v_im = Wv[1, 2], + W_t_re=Wt[1, 1], W_t_im=Wt[1, 2], + W_p_re=Wp[1, 1], W_p_im=Wp[1, 2], + W_v_re=Wv[1, 1], W_v_im=Wv[1, 2] ) end end @@ -113,64 +113,66 @@ function build_benchmark_tomldir(eq_file::String, kin_file::String) cp(eq_file, joinpath(tmpdir, eq_name)) end open(joinpath(tmpdir, "gpec.toml"), "w") do io - println(io, """ - # Auto-generated by benchmark_diiid_kinetic_stability.jl — do not edit. - - [Equilibrium] - eq_filename = "$eq_name" - eq_type = "efit" - jac_type = "hamada" - power_bp = 0 - power_b = 0 - power_r = 0 - grid_type = "pow1" # Matches Fortran DIIID_kinetic_example (equil/grid.f90 powspace) - psilow = 0.01 - psihigh = 0.993 - mpsi = 128 - mtheta = 256 - newq0 = 0 - etol = 1e-7 - - [Wall] - shape = "nowall" - - [ForceFreeStates] - bal_flag = false - mat_flag = true - ode_flag = true - vac_flag = true - mer_flag = true - force_termination = true # Skip PE+KF post-processing — we only need FFS eigenvalues - - psiedge = 1.0 # No edge-scan truncation (dmlim mechanism removed in develop) - qlow = 1.02 - qhigh = 1e3 - sing_start = 0 - - nn_low = 1 - nn_high = 1 - delta_mlow = 8 - delta_mhigh = 8 - delta_mband = 0 - mthvac = 512 - thmax0 = 1 - - kinetic_source = "calculated" - kinetic_factor = 1.0 - eulerlagrange_tolerance = 1e-7 - singfac_min = 1e-4 - ucrit = 1e4 - write_outputs_to_HDF5 = true - - [KineticForces] - kinetic_file = "$kin_file" - nn = 1 - nl = 4 - zi = 1 - mi = 2 - nutype = "harmonic" - f0type = "maxwellian" - """) + println( + io, + """ +# Auto-generated by benchmark_diiid_kinetic_stability.jl — do not edit. + +[Equilibrium] +eq_filename = "$eq_name" +eq_type = "efit" +jac_type = "hamada" +power_bp = 0 +power_b = 0 +power_r = 0 +grid_type = "pow1" # Matches Fortran DIIID_kinetic_example (equil/grid.f90 powspace) +psilow = 0.01 +psihigh = 0.993 +mpsi = 128 +mtheta = 256 +newq0 = 0 +etol = 1e-7 + +[Wall] +shape = "nowall" + +[ForceFreeStates] +bal_flag = false +mat_flag = true +ode_flag = true +vac_flag = true +mer_flag = true +force_termination = true # Skip PE+KF post-processing — we only need FFS eigenvalues + +psiedge = 1.0 # No edge-scan truncation (dmlim mechanism removed in develop) +qlow = 1.02 +qhigh = 1e3 +sing_start = 0 + +nn_low = 1 +nn_high = 1 +delta_mlow = 8 +delta_mhigh = 8 +mthvac = 512 +thmax0 = 1 + +kinetic_source = "calculated" +kinetic_factor = 1.0 +eulerlagrange_tolerance = 1e-7 +singfac_min = 1e-4 +ucrit = 1e4 +write_outputs_to_HDF5 = true + +[KineticForces] +kinetic_file = "$kin_file" +nn = 1 +nl = 4 +zi = 1 +mi = 2 +nutype = "harmonic" +f0type = "maxwellian" +""" + ) end return tmpdir end @@ -185,7 +187,7 @@ function run_benchmark(fortran_dir::String=DEFAULT_FORTRAN_DIR) _p("=" ^ 70) inputs = discover_inputs(fortran_dir) - ref = read_dcon_reference(inputs.dcon_nc) + ref = read_dcon_reference(inputs.dcon_nc) _pf(" EFIT g-file: %s\n", basename(inputs.eq_file)) _pf(" Kinetic: %s\n", basename(inputs.kin_file)) _pf(" Reference (W_t_eigenvalue[1]): Re = %.6f Im = %.6f\n", @@ -251,13 +253,13 @@ function run_benchmark(fortran_dir::String=DEFAULT_FORTRAN_DIR) end return (; julia_re, julia_im, - fortran_re=ref.W_t_re, fortran_im=ref.W_t_im, - re_err, im_err, wall, tomldir) + fortran_re=ref.W_t_re, fortran_im=ref.W_t_im, + re_err, im_err, wall, tomldir) end # Run only when invoked as a script. if abspath(PROGRAM_FILE) == @__FILE__ fortran_dir = length(ARGS) >= 1 ? ARGS[1] : - get(ENV, "GPEC_FORTRAN_DIIID_DCON", DEFAULT_FORTRAN_DIR) + get(ENV, "GPEC_FORTRAN_DIIID_DCON", DEFAULT_FORTRAN_DIR) run_benchmark(fortran_dir) end diff --git a/benchmarks/benchmark_riccati_der.jl b/benchmarks/benchmark_riccati_der.jl index f751588f8..6b23c0a81 100644 --- a/benchmarks/benchmark_riccati_der.jl +++ b/benchmarks/benchmark_riccati_der.jl @@ -33,14 +33,15 @@ function setup_solovev() intr.wall_settings = GeneralizedPerturbedEquilibrium.Vacuum.WallShapeSettings(; (Symbol(k) => v for (k, v) in inputs["Wall"])...) FFS.sing_lim!(intr, ctrl, equil) - intr.nlow = ctrl.nn_low; intr.nhigh = ctrl.nn_high; intr.npert = 1 + intr.nlow = ctrl.nn_low; + intr.nhigh = ctrl.nn_high; + intr.npert = 1 FFS.sing_find!(intr, equil) - intr.mlow = min(intr.nlow * equil.params.qmin, 0) - 4 - ctrl.delta_mlow + intr.mlow = min(intr.nlow * equil.params.qmin, 0) - 4 - ctrl.delta_mlow intr.mhigh = trunc(Int, intr.nhigh * equil.params.qmax) + ctrl.delta_mhigh intr.mpert = intr.mhigh - intr.mlow + 1 - intr.mband = intr.mpert - 1 intr.numpert_total = intr.mpert * intr.npert - metric = FFS.make_metric(equil; mband=intr.mband, fft_flag=ctrl.fft_flag) + metric = FFS.make_metric(equil, intr.mpert) ffit = FFS.make_matrix(equil, intr, metric) return ctrl, equil, ffit, intr end @@ -48,10 +49,10 @@ end # Evaluate the Riccati RHS explicitly from splines: dS = w†·F̄⁻¹·w - S·Ḡ·S function riccati_rhs_manual(S, psi, equil, ffit, intr) N = intr.numpert_total - L = zeros(ComplexF64, N, N) + L = zeros(ComplexF64, N, N) Kmat = zeros(ComplexF64, N, N) Gmat = zeros(ComplexF64, N, N) - ffit.fmats_lower(vec(L), psi; hint=ffit._hint) + ffit.fmats_lower(vec(L), psi; hint=ffit._hint) ffit.kmats(vec(Kmat), psi; hint=ffit._hint) ffit.gmats(vec(Gmat), psi; hint=ffit._hint) @@ -103,7 +104,7 @@ max_err = let max_err = 0.0 dS_manual = riccati_rhs_manual(S, psi, equil, ffit, intr) # riccati_der! RHS - u_ric = zeros(ComplexF64, N, N, 2) + u_ric = zeros(ComplexF64, N, N, 2) du_ric = zeros(ComplexF64, N, N, 2) u_ric[:, :, 1] .= S u_ric[:, :, 2] .= Matrix{ComplexF64}(I, N, N) diff --git a/benchmarks/benchmark_threads.jl b/benchmarks/benchmark_threads.jl index 96063977e..4831f6988 100644 --- a/benchmarks/benchmark_threads.jl +++ b/benchmarks/benchmark_threads.jl @@ -21,14 +21,15 @@ function run_ffs(ex; use_parallel, use_riccati=false) intr.wall_settings = GeneralizedPerturbedEquilibrium.Vacuum.WallShapeSettings(; (Symbol(k) => v for (k, v) in inputs["Wall"])...) GeneralizedPerturbedEquilibrium.ForceFreeStates.sing_lim!(intr, ctrl, equil) - intr.nlow = ctrl.nn_low; intr.nhigh = ctrl.nn_high; intr.npert = 1 + intr.nlow = ctrl.nn_low; + intr.nhigh = ctrl.nn_high; + intr.npert = 1 GeneralizedPerturbedEquilibrium.ForceFreeStates.sing_find!(intr, equil) - intr.mlow = min(intr.nlow * equil.params.qmin, 0) - 4 - ctrl.delta_mlow + intr.mlow = min(intr.nlow * equil.params.qmin, 0) - 4 - ctrl.delta_mlow intr.mhigh = trunc(Int, intr.nhigh * equil.params.qmax) + ctrl.delta_mhigh intr.mpert = intr.mhigh - intr.mlow + 1 - intr.mband = intr.mpert - 1 intr.numpert_total = intr.mpert * intr.npert - metric = GeneralizedPerturbedEquilibrium.ForceFreeStates.make_metric(equil; mband=intr.mband, fft_flag=ctrl.fft_flag) + metric = GeneralizedPerturbedEquilibrium.ForceFreeStates.make_metric(equil, intr.mpert) ffit = GeneralizedPerturbedEquilibrium.ForceFreeStates.make_matrix(equil, intr, metric) odet, _, _, _ = GeneralizedPerturbedEquilibrium.ForceFreeStates.eulerlagrange_integration(ctrl, equil, ffit, intr) vac = GeneralizedPerturbedEquilibrium.ForceFreeStates.free_run!(odet, ctrl, equil, ffit, intr) @@ -52,16 +53,16 @@ function timed_run(ex; use_parallel, use_riccati=false, nwarm=1, nrep=2) end nthreads = Threads.nthreads() -root = joinpath(@__DIR__, "..") -sol_ex = joinpath(root, "test", "test_data", "regression_solovev_ideal_example") +root = joinpath(@__DIR__, "..") +sol_ex = joinpath(root, "test", "test_data", "regression_solovev_ideal_example") diiid_ex = joinpath(root, "examples", "DIIID-like_ideal_example") println("\n=== Thread-scaling benchmark ($(nthreads) thread(s)) ===\n") for (label, ex) in [("Solovev", sol_ex), ("DIIID-like", diiid_ex)] - t_std, et_std, N = timed_run(ex; use_parallel=false, use_riccati=false) - t_ric, et_ric, _ = timed_run(ex; use_parallel=false, use_riccati=true) - t_par, et_par, _ = timed_run(ex; use_parallel=true, use_riccati=false) + t_std, et_std, N = timed_run(ex; use_parallel=false, use_riccati=false) + t_ric, et_ric, _ = timed_run(ex; use_parallel=false, use_riccati=true) + t_par, et_par, _ = timed_run(ex; use_parallel=true, use_riccati=false) err_ric = abs(et_ric - et_std) / abs(et_std) * 100 err_par = abs(et_par - et_std) / abs(et_std) * 100 @@ -69,8 +70,8 @@ for (label, ex) in [("Solovev", sol_ex), ("DIIID-like", diiid_ex)] println("$label (N=$N, nthreads=$nthreads)") @printf(" standard et[1]=%.5f t=%.2fs speedup=1.00×\n", et_std, t_std) @printf(" riccati et[1]=%.5f t=%.2fs speedup=%.2f× err=%.4f%%\n", - et_ric, t_ric, t_std/t_ric, err_ric) + et_ric, t_ric, t_std/t_ric, err_ric) @printf(" parallel et[1]=%.5f t=%.2fs speedup=%.2f× err=%.4f%%\n", - et_par, t_par, t_std/t_par, err_par) + et_par, t_par, t_std/t_par, err_par) println() end diff --git a/docs/src/stability.md b/docs/src/stability.md index b294125a3..1a42e17b5 100644 --- a/docs/src/stability.md +++ b/docs/src/stability.md @@ -252,10 +252,9 @@ FFS.sing_find!(intr, equil) intr.mlow = min(intr.nlow * equil.params.qmin, 0) - 4 - ctrl.delta_mlow intr.mhigh = trunc(Int, intr.nhigh * equil.params.qmax) + ctrl.delta_mhigh intr.mpert = intr.mhigh - intr.mlow + 1 -intr.mband = intr.mpert - 1 intr.numpert_total = intr.mpert * intr.npert -metric = FFS.make_metric(equil; mband=intr.mband, fft_flag=ctrl.fft_flag) +metric = FFS.make_metric(equil, intr.mpert) ffit = FFS.make_matrix(equil, intr, metric) # Choose integration driver. The top-level `eulerlagrange_integration` dispatches diff --git a/docs/src/utilities.md b/docs/src/utilities.md index 8a4a53dbb..d6086f62c 100644 --- a/docs/src/utilities.md +++ b/docs/src/utilities.md @@ -44,6 +44,6 @@ fc = GeneralizedPerturbedEquilibrium.Utilities.FourierCoefficients(xs, ys, fs, 1 c = GeneralizedPerturbedEquilibrium.Utilities.get_complex_coeff(fc, 50, 3, 1) # Get all coefficients for a given radial index and quantity -coeffs = Vector{ComplexF64}(undef, fc.mband + 1) +coeffs = Vector{ComplexF64}(undef, fc.mmax + 1) GeneralizedPerturbedEquilibrium.Utilities.get_complex_coeffs!(coeffs, fc, 50, 1) ``` diff --git a/examples/DIIID-like_ideal_example/gpec.toml b/examples/DIIID-like_ideal_example/gpec.toml index 5c0aa87d6..1872f2bff 100644 --- a/examples/DIIID-like_ideal_example/gpec.toml +++ b/examples/DIIID-like_ideal_example/gpec.toml @@ -41,7 +41,6 @@ nn_low = 1 # Smallest toroidal mode number to include nn_high = 1 # Largest toroidal mode number to include delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 8 # Expands upper bound of Fourier harmonics -delta_mband = 0 # Integration keeps only this wide a band... mthvac = 512 # Number of points used in splines over poloidal angle at plasma-vacuum interface. thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds diff --git a/examples/LAR_beta_scan/gpec.toml b/examples/LAR_beta_scan/gpec.toml index 4e2b43518..3fcc88054 100644 --- a/examples/LAR_beta_scan/gpec.toml +++ b/examples/LAR_beta_scan/gpec.toml @@ -66,7 +66,6 @@ nn_low = 1 # Lower bound of toroidal mode-number range nn_high = 1 # Upper bound of toroidal mode-number range delta_mlow = 8 # Poloidal-mode padding below the resonant-m band delta_mhigh = 8 # Poloidal-mode padding above the resonant-m band -delta_mband = 0 # Extra coupling-matrix band width (0 = full mpert × mpert) mthvac = 960 # Poloidal resolution used by the vacuum-response integrator thmax0 = 1 # Number of poloidal periods spanned by the vacuum coordinate diff --git a/examples/LAR_epsilon_scan/gpec.toml b/examples/LAR_epsilon_scan/gpec.toml index 179a54a8c..039ab74f4 100644 --- a/examples/LAR_epsilon_scan/gpec.toml +++ b/examples/LAR_epsilon_scan/gpec.toml @@ -72,7 +72,6 @@ nn_low = 1 # Lower bound of toroidal mode-number range nn_high = 1 # Upper bound of toroidal mode-number range delta_mlow = 8 # Poloidal-mode padding below the resonant-m band delta_mhigh = 8 # Poloidal-mode padding above the resonant-m band -delta_mband = 0 # Extra coupling-matrix band width (0 = full mpert × mpert) mthvac = 960 # Poloidal resolution used by the vacuum-response integrator thmax0 = 1 # Number of poloidal periods spanned by the vacuum coordinate diff --git a/examples/Solovev_ideal_example/gpec.toml b/examples/Solovev_ideal_example/gpec.toml index 2e8d3df82..23f9fc6e0 100644 --- a/examples/Solovev_ideal_example/gpec.toml +++ b/examples/Solovev_ideal_example/gpec.toml @@ -60,7 +60,6 @@ nn_low = 1 # Smallest toroidal mode number to include nn_high = 1 # Largest toroidal mode number to include delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 8 # Expands upper bound of Fourier harmonics -delta_mband = 0 # Integration keeps only this wide a band... mthvac = 960 # Number of points used in splines over poloidal angle at plasma-vacuum interface. thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds @@ -79,4 +78,3 @@ populate_dense_xi = true # REQUIRED for PerturbedEquilibrium (this TOML ha truncate_at_dW_peak = false # Edge-dW scan stays diagnostic; integration domain set by qhigh / psihigh / dmlim set_psilim_via_dmlim = false # FALSE for limited circular / analytical equilibria — rationals sparse, dmlim truncation would chop too much edge dmlim = 0.2 # Only used when set_psilim_via_dmlim = true: truncate at (last_rational_q + dmlim) / n - diff --git a/examples/Solovev_ideal_example_3D/gpec.toml b/examples/Solovev_ideal_example_3D/gpec.toml index e5526ddcb..756357e11 100644 --- a/examples/Solovev_ideal_example_3D/gpec.toml +++ b/examples/Solovev_ideal_example_3D/gpec.toml @@ -30,7 +30,6 @@ nn_low = 1 # Smallest toroidal mode number to include nn_high = 1 # Largest toroidal mode number to include delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 8 # Expands upper bound of Fourier harmonics -delta_mband = 0 # Integration keeps only this wide a band... mthvac = 96 # Number of points used in splines over poloidal angle at plasma-vacuum interface. nzvac = 64 thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds diff --git a/examples/Solovev_ideal_example_multi_n/gpec.toml b/examples/Solovev_ideal_example_multi_n/gpec.toml index 89c287b16..0c047c59e 100644 --- a/examples/Solovev_ideal_example_multi_n/gpec.toml +++ b/examples/Solovev_ideal_example_multi_n/gpec.toml @@ -41,7 +41,6 @@ nn_low = 1 # Lower toroidal mode number nn_high = 2 # Upper toroidal mode number delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 8 # Expands upper bound of Fourier harmonics -delta_mband = 0 # Integration keeps only this wide a band... mthvac = 960 # Number of points used in splines over poloidal angle at plasma-vacuum interface. thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds diff --git a/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml b/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml index c001eb806..d27e5b52b 100644 --- a/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml +++ b/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml @@ -40,7 +40,6 @@ nn_low = 1 # Smallest toroidal mode number to include nn_high = 1 # Largest toroidal mode number to include delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 10 # Expands upper bound of Fourier harmonics -delta_mband = 0 # Integration keeps only this wide a band... mthvac = 960 # Number of points used in splines over poloidal angle at plasma-vacuum interface. thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds diff --git a/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml b/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml index 8a65be741..4cc3e9dad 100644 --- a/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml +++ b/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml @@ -40,7 +40,6 @@ nn_low = 2 # Smallest toroidal mode number to include nn_high = 2 # Largest toroidal mode number to include delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 8 # Expands upper bound of Fourier harmonics -delta_mband = 0 # Integration keeps only this wide a band... mthvac = 960 # Number of points used in splines over poloidal angle at plasma-vacuum interface. thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds diff --git a/examples/a10_kinetic_example/gpec.toml b/examples/a10_kinetic_example/gpec.toml index 5b66712d7..be8f2b0c8 100644 --- a/examples/a10_kinetic_example/gpec.toml +++ b/examples/a10_kinetic_example/gpec.toml @@ -48,7 +48,6 @@ nn_low = 1 nn_high = 1 delta_mlow = 6 # Fortran dcon.in: delta_mlow=6 delta_mhigh = 6 # Fortran dcon.in: delta_mhigh=6 -delta_mband = 0 mthvac = 512 thmax0 = 1 diff --git a/src/ForceFreeStates/ForceFreeStatesStructs.jl b/src/ForceFreeStates/ForceFreeStatesStructs.jl index 852d8893e..ebab2c6a8 100644 --- a/src/ForceFreeStates/ForceFreeStatesStructs.jl +++ b/src/ForceFreeStates/ForceFreeStatesStructs.jl @@ -102,8 +102,8 @@ identity-block initial conditions: Applying the propagator to the current state `u_prev`: - u₁_new = block_upper_ic[:,:,1] · u₁_prev + block_lower_ic[:,:,1] · u₂_prev - u₂_new = block_upper_ic[:,:,2] · u₁_prev + block_lower_ic[:,:,2] · u₂_prev +u₁_new = block_upper_ic[:,:,1] · u₁_prev + block_lower_ic[:,:,1] · u₂_prev +u₂_new = block_upper_ic[:,:,2] · u₁_prev + block_lower_ic[:,:,2] · u₂_prev Since each chunk starts from a bounded identity IC (rather than the accumulated state), exponential growth within a chunk does not affect the conditioning of the overall @@ -139,7 +139,6 @@ A mutable struct holding internal state variables for stability calculations. - `mlow::Int` - Lowest poloidal mode number - `mhigh::Int` - Highest poloidal mode number - `mpert::Int` - Number of poloidal modes (mhigh - mlow + 1) - - `mband::Int` - Bandwidth for matrix operations (mpert - 1 - delta_mband) - `nlow::Int` - Lowest toroidal mode number - `nhigh::Int` - Highest toroidal mode number - `npert::Int` - Number of toroidal modes (nhigh - nlow + 1) @@ -166,7 +165,6 @@ A mutable struct holding internal state variables for stability calculations. mlow::Int = 0 mhigh::Int = 0 mpert::Int = 0 - mband::Int = 0 nlow::Int = 0 nhigh::Int = 0 npert::Int = 0 @@ -217,7 +215,6 @@ A mutable struct containing control parameters for stability analysis, set by th - `nn_high::Int` - Upper bound for toroidal modes - `delta_mlow::Int` - Expands lower bound of Fourier harmonics by delta_mlow - `delta_mhigh::Int` - Expands upper bound of Fourier harmonics by delta_mhigh - - `delta_mband::Int` - Integration keeps only this wide a band of solutions along the diagonal in m,m' - `thmax0::Float64` - Maximum integration step size (not yet implemented) - `nstep::Int` - Maximum number of integration steps (not yet implemented) - `ksing::Int` - Singular surface handling parameter @@ -264,7 +261,6 @@ A mutable struct containing control parameters for stability analysis, set by th nn_high::Int = 0 delta_mlow::Int = 0 delta_mhigh::Int = 0 - delta_mband::Int = 0 thmax0::Float64 = 1.0 nstep::Int = typemax(Int) ksing::Int = -1 @@ -301,7 +297,6 @@ end @kwdef mutable struct FourFitVars{S<:CubicSeriesInterpolant,Opts<:NamedTuple} mpert::Int - mband::Int numpert_total::Int # = mpert * npert (total series count per matrix = numpert_total^2) # Complex-valued CubicSeriesInterpolant for stability matrices @@ -354,7 +349,7 @@ end _hint::Base.RefValue{Int} = Ref(1) # Used in Free.jl - jmat::Vector{ComplexF64} = Vector{ComplexF64}(undef, 2 * mband + 1) + jmat::Vector{ComplexF64} = Vector{ComplexF64}(undef, 2 * mpert - 1) end # Helper to create empty complex series interpolant for default initialization @@ -371,7 +366,7 @@ function _empty_series_interp_complex(n_series::Int, itp_opts::NamedTuple) end # Convenience constructor -FourFitVars(mpert::Int, mband::Int, numpert_total::Int) = FourFitVars(; mpert, mband, numpert_total) +FourFitVars(mpert::Int, numpert_total::Int) = FourFitVars(; mpert, numpert_total) """ VacuumData diff --git a/src/ForceFreeStates/Fourfit.jl b/src/ForceFreeStates/Fourfit.jl index 45b07369a..250ce3da3 100644 --- a/src/ForceFreeStates/Fourfit.jl +++ b/src/ForceFreeStates/Fourfit.jl @@ -27,7 +27,7 @@ end MetricData(mpsi::Int, mtheta::Int) = MetricData(; mpsi, mtheta) """ - make_metric(equil::Equilibrium.PlasmaEquilibrium; mband::Int=10) -> MetricData + make_metric(equil::Equilibrium.PlasmaEquilibrium, mpert::Int) -> MetricData Constructs the metric tensor data on a (ψ, θ) grid from an input plasma equilibrium. The metric coefficients stored in `metric.fs` include: @@ -43,21 +43,14 @@ The metric coefficients stored in `metric.fs` include: ### Arguments - - `mband::Int`: Number of Fourier modes to retain in the metric representation. + - `mpert::Int`: Number of poloidal modes ### Returns - `metric::MetricData`: A structure containing the metric coefficients, coordinate grids, and Jacobians for the specified equilibrium. - -### TODOs - -Add kinetic metric tensor components for kinetic mode -Remove mband if we decide to fully deprecate banded matrices """ -function make_metric(equil::Equilibrium.PlasmaEquilibrium; mband::Int) - - # TODO: add kinetic metric tensor components +function make_metric(equil::Equilibrium.PlasmaEquilibrium, mpert::Int) # --- Extract data from the PlasmaEquilibrium object --- mpsi = length(equil.rzphi_xs) @@ -115,15 +108,13 @@ function make_metric(equil::Equilibrium.PlasmaEquilibrium; mband::Int) metric.fs[ipsi, jtheta, 6] = dot(v1, v2) * jac metric.fs[ipsi, jtheta, 7] = jac metric.fs[ipsi, jtheta, 8] = jac1 - - # TODO: kinetic metric tensor here fmodb in Fortran end end # --- Compute Fourier coefficients (no spline overhead since we only access at grid points) --- # Faithful Fortran fspline_fit_2 (equil/fspline.f:293): FFT after dropping the duplicated # θ=2π endpoint. The fspline_fit_1 integration variant (idcon.f fft_flag=false) is not implemented. - metric.fourier_coeffs = Utilities.FourierCoefficients(metric.xs, metric.ys, metric.fs, mband) + metric.fourier_coeffs = Utilities.FourierCoefficients(metric.xs, metric.ys, metric.fs, mpert - 1) return metric end @@ -138,20 +129,23 @@ the equilibrium geometry. Ports Fortran `dcon_interface.f` lines 895-1013 (`idcon_action_matrices`). # Steps -1. Compute 8 `fmodb` quantities on the (ψ,θ) grid from equilibrium geometry -2. Fourier decompose via `Utilities.FourierCoefficients` -3. Assemble mpert×mpert matrices from Fourier bands at each ψ -4. Create `CubicSeriesInterpolant`s over ψ + + 1. Compute 8 `fmodb` quantities on the (ψ,θ) grid from equilibrium geometry + 2. Fourier decompose via `Utilities.FourierCoefficients` + 3. Assemble mpert×mpert matrices from Fourier bands at each ψ + 4. Create `CubicSeriesInterpolant`s over ψ # Returns + NamedTuple `(smats, tmats, xmats, ymats, zmats)` of `CubicSeriesInterpolant`s, each mapping ψ → flattened mpert² complex vector. Reference: [Logan et al., Phys. Plasmas 20, 122507 (2013)] """ function build_kinetic_metric_matrices(equil::Equilibrium.PlasmaEquilibrium, - intr::ForceFreeStatesInternal, - metric::MetricData) + intr::ForceFreeStatesInternal, + metric::MetricData) + (; mpert, nlow, nhigh, mlow, mhigh) = intr mpsi = metric.mpsi mtheta = metric.mtheta chi1 = 2π * equil.psio @@ -198,11 +192,11 @@ function build_kinetic_metric_matrices(equil::Equilibrium.PlasmaEquilibrium, v[3, 3] = 2π * rs # Raw g^ij (Fortran dcon_interface.f:933-937) - g12 = v[1,1]*v[2,1] + v[1,2]*v[2,2] + v[1,3]*v[2,3] - g13 = v[3,3] * v[1,3] - g22 = v[2,1]^2 + v[2,2]^2 + v[2,3]^2 - g23 = v[2,3] * v[3,3] - g33 = v[3,3]^2 + g12 = v[1, 1]*v[2, 1] + v[1, 2]*v[2, 2] + v[1, 3]*v[2, 3] + g13 = v[3, 3] * v[1, 3] + g22 = v[2, 1]^2 + v[2, 2]^2 + v[2, 3]^2 + g23 = v[2, 3] * v[3, 3] + g33 = v[3, 3]^2 # B field and derivatives B = equil.eqfun_B.nodal_derivs.partials[1, ipsi, jtheta] @@ -218,12 +212,12 @@ function build_kinetic_metric_matrices(equil::Equilibrium.PlasmaEquilibrium, # 8 fmodb quantities (Fortran dcon_interface.f:939-948) fmodb_fs[ipsi, jtheta, 1] = jac * (p1 + b2hp) - - chi1^2 * b2ht * (g12 + q * g13) / (jac * b2h * 2) # sband + chi1^2 * b2ht * (g12 + q * g13) / (jac * b2h * 2) # sband fmodb_fs[ipsi, jtheta, 2] = chi1^2 * b2ht * (g23 + q * g33) / (jac * b2h * 2) # tband fmodb_fs[ipsi, jtheta, 3] = jac * b2h * 2 # xband fmodb_fs[ipsi, jtheta, 4] = jac1 * b2h * 2 - - chi1^2 * b2h * 2 * eqfun_fy2 # yband1 + chi1^2 * b2h * 2 * eqfun_fy2 # yband1 fmodb_fs[ipsi, jtheta, 5] = -2π * chi1^2 / jac * (g12 + q * g13) # yband2 fmodb_fs[ipsi, jtheta, 6] = @@ -236,70 +230,69 @@ function build_kinetic_metric_matrices(equil::Equilibrium.PlasmaEquilibrium, end # Fourier decompose (same approach as metric) - fmodb_fc = Utilities.FourierCoefficients(metric.xs, metric.ys, fmodb_fs, intr.mband) + fmodb_fc = Utilities.FourierCoefficients(metric.xs, metric.ys, fmodb_fs, mpert - 1) # Allocate flat storage for mpert×mpert matrices at each ψ - smats_flat = zeros(ComplexF64, mpsi, intr.mpert^2) - tmats_flat = zeros(ComplexF64, mpsi, intr.mpert^2) - xmats_flat = zeros(ComplexF64, mpsi, intr.mpert^2) - ymats_flat = zeros(ComplexF64, mpsi, intr.mpert^2) - zmats_flat = zeros(ComplexF64, mpsi, intr.mpert^2) + smats_flat = zeros(ComplexF64, mpsi, mpert^2) + tmats_flat = zeros(ComplexF64, mpsi, mpert^2) + xmats_flat = zeros(ComplexF64, mpsi, mpert^2) + ymats_flat = zeros(ComplexF64, mpsi, mpert^2) + zmats_flat = zeros(ComplexF64, mpsi, mpert^2) # Fourier band storage - mid = intr.mband + 1 - sband = Vector{ComplexF64}(undef, 2 * intr.mband + 1) - tband = Vector{ComplexF64}(undef, 2 * intr.mband + 1) - xband = Vector{ComplexF64}(undef, 2 * intr.mband + 1) - yband1 = Vector{ComplexF64}(undef, 2 * intr.mband + 1) - yband2 = Vector{ComplexF64}(undef, 2 * intr.mband + 1) - zband1 = Vector{ComplexF64}(undef, 2 * intr.mband + 1) - zband2 = Vector{ComplexF64}(undef, 2 * intr.mband + 1) - zband3 = Vector{ComplexF64}(undef, 2 * intr.mband + 1) + sband = Vector{ComplexF64}(undef, 2 * mpert - 1) + tband = Vector{ComplexF64}(undef, 2 * mpert - 1) + xband = Vector{ComplexF64}(undef, 2 * mpert - 1) + yband1 = Vector{ComplexF64}(undef, 2 * mpert - 1) + yband2 = Vector{ComplexF64}(undef, 2 * mpert - 1) + zband1 = Vector{ComplexF64}(undef, 2 * mpert - 1) + zband2 = Vector{ComplexF64}(undef, 2 * mpert - 1) + zband3 = Vector{ComplexF64}(undef, 2 * mpert - 1) for ipsi in 1:mpsi q = equil.profiles.q_spline.y[ipsi] - # Extract Fourier bands (Fortran dcon_interface.f:963-979) - for m in 0:intr.mband - sband[mid-m] = Utilities.get_complex_coeff(fmodb_fc, ipsi, m, 1) - tband[mid-m] = Utilities.get_complex_coeff(fmodb_fc, ipsi, m, 2) - xband[mid-m] = Utilities.get_complex_coeff(fmodb_fc, ipsi, m, 3) - yband1[mid-m] = Utilities.get_complex_coeff(fmodb_fc, ipsi, m, 4) - yband2[mid-m] = Utilities.get_complex_coeff(fmodb_fc, ipsi, m, 5) - zband1[mid-m] = Utilities.get_complex_coeff(fmodb_fc, ipsi, m, 6) - zband2[mid-m] = Utilities.get_complex_coeff(fmodb_fc, ipsi, m, 7) - zband3[mid-m] = Utilities.get_complex_coeff(fmodb_fc, ipsi, m, 8) + # Extract Fourier modes (Fortran dcon_interface.f:963-979) + for m in 0:(mpert-1) + sband[mpert-m] = Utilities.get_complex_coeff(fmodb_fc, ipsi, m, 1) + tband[mpert-m] = Utilities.get_complex_coeff(fmodb_fc, ipsi, m, 2) + xband[mpert-m] = Utilities.get_complex_coeff(fmodb_fc, ipsi, m, 3) + yband1[mpert-m] = Utilities.get_complex_coeff(fmodb_fc, ipsi, m, 4) + yband2[mpert-m] = Utilities.get_complex_coeff(fmodb_fc, ipsi, m, 5) + zband1[mpert-m] = Utilities.get_complex_coeff(fmodb_fc, ipsi, m, 6) + zband2[mpert-m] = Utilities.get_complex_coeff(fmodb_fc, ipsi, m, 7) + zband3[mpert-m] = Utilities.get_complex_coeff(fmodb_fc, ipsi, m, 8) end - for k in 1:intr.mband - sband[mid+k] = conj(sband[mid-k]) - tband[mid+k] = conj(tband[mid-k]) - xband[mid+k] = conj(xband[mid-k]) - yband1[mid+k] = conj(yband1[mid-k]) - yband2[mid+k] = conj(yband2[mid-k]) - zband1[mid+k] = conj(zband1[mid-k]) - zband2[mid+k] = conj(zband2[mid-k]) - zband3[mid+k] = conj(zband3[mid-k]) + for k in 1:(mpert-1) + sband[k+mpert] = conj(sband[mpert-k]) + tband[k+mpert] = conj(tband[mpert-k]) + xband[k+mpert] = conj(xband[mpert-k]) + yband1[k+mpert] = conj(yband1[mpert-k]) + yband2[k+mpert] = conj(yband2[mpert-k]) + zband1[k+mpert] = conj(zband1[mpert-k]) + zband2[k+mpert] = conj(zband2[mpert-k]) + zband3[k+mpert] = conj(zband3[mpert-k]) end # Assemble mpert×mpert matrices (Fortran dcon_interface.f:981-997) # Single-n: use nlow as the toroidal mode number - n = intr.nlow - for m1 in intr.mlow:intr.mhigh - ipert = m1 - intr.mlow + 1 + n = nlow + for m1 in mlow:mhigh + ipert = m1 - mlow + 1 nq = n * q - for dm in max(1-ipert, -intr.mband):min(intr.mpert-ipert, intr.mband) + for dm in (1-ipert):(mpert-ipert) m2 = m1 + dm singfac2 = m2 - nq jpert = ipert + dm - dmidx = dm + mid - iflat = ipert + (jpert - 1) * intr.mpert + dmidx = dm + mpert + iflat = ipert + (jpert - 1) * mpert smats_flat[ipsi, iflat] = sband[dmidx] tmats_flat[ipsi, iflat] = tband[dmidx] xmats_flat[ipsi, iflat] = xband[dmidx] ymats_flat[ipsi, iflat] = yband1[dmidx] + im * singfac2 * yband2[dmidx] zmats_flat[ipsi, iflat] = zband1[dmidx] + - im * (m2 * zband2[dmidx] + n * zband3[dmidx]) + im * (m2 * zband2[dmidx] + n * zband3[dmidx]) end end end @@ -322,18 +315,10 @@ end Constructs main ForceFreeStates matrices for a given toroidal mode number and returns them as a new `FourFitVars` object. See the appendix of the Glasser Phys. Plasmas 2016 112506 DCON paper for details on the matrix definitions. Performs the same function -as `fourfit_make_matrix` in the Fortran code, except F, G, and K are now -stored as dense matrices. The matrix F is stored in factorized form with -the lower triangle only, because F is Hermitian and can be written as -F = L · Lᴴ, which speeds up calculations later (i.e. `sing_der!``). Unlike -the Fortran, we also do not use OffsetArrays (indexed from -mband:mband), -but instead use standard Julia arrays and map the zero index to the middle. - -Note that even when using dense matrices (delta_mband = 0), the -`mband` still appears here for backwards compatibility with the Fortran code, -where the Fourier splines expect it as input. So even though `mband` appears -a lot below, it is left to make implementing banded matrices easier in the future -and does not affect the actual matrix sizes, they are all dense. +as `fourfit_make_matrix` in the Fortran code, except F, G, and K are stored as dense +matrices. The matrix F is stored in factorized form with the lower triangle only, +because F is Hermitian and can be written as F = L · Lᴴ, which speeds up calculations +later (i.e. `sing_der!`). ### Arguments @@ -367,22 +352,19 @@ function make_matrix(equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStates fmats_prim_flat = zeros(ComplexF64, mpsi, intr.numpert_total^2) # primitive F before Schur complement (for kinetic) gmats_flat = zeros(ComplexF64, mpsi, intr.numpert_total^2) kmats_flat = zeros(ComplexF64, mpsi, intr.numpert_total^2) - g11 = Vector{ComplexF64}(undef, 2 * intr.mband + 1) - g22 = Vector{ComplexF64}(undef, 2 * intr.mband + 1) - g33 = Vector{ComplexF64}(undef, 2 * intr.mband + 1) - g23 = Vector{ComplexF64}(undef, 2 * intr.mband + 1) - g31 = Vector{ComplexF64}(undef, 2 * intr.mband + 1) - g12 = Vector{ComplexF64}(undef, 2 * intr.mband + 1) - jmat = Vector{ComplexF64}(undef, 2 * intr.mband + 1) - jmat1 = Vector{ComplexF64}(undef, 2 * intr.mband + 1) + g11 = Vector{ComplexF64}(undef, 2 * intr.mpert - 1) + g22 = Vector{ComplexF64}(undef, 2 * intr.mpert - 1) + g33 = Vector{ComplexF64}(undef, 2 * intr.mpert - 1) + g23 = Vector{ComplexF64}(undef, 2 * intr.mpert - 1) + g31 = Vector{ComplexF64}(undef, 2 * intr.mpert - 1) + g12 = Vector{ComplexF64}(undef, 2 * intr.mpert - 1) + jmat = Vector{ComplexF64}(undef, 2 * intr.mpert - 1) + jmat1 = Vector{ComplexF64}(undef, 2 * intr.mpert - 1) a_inv_dmat_temp = Matrix{ComplexF64}(undef, intr.numpert_total, intr.numpert_total) a_inv_cmat_temp = Matrix{ComplexF64}(undef, intr.numpert_total, intr.numpert_total) - # Instead of using Offset Arrays like in Fortran (-mband:mband), we store everything in - # a single 1:(2*mband+1) array and map the zero index to the middle - mid = intr.mband + 1 # "zero" position in Julia arrays - imat = zeros(ComplexF64, 2 * intr.mband + 1) - imat[mid] = 1 + 0im + imat = zeros(ComplexF64, len) + imat[intr.mpert] = 1 + 0im hint = Ref(1) # Linear search hint for sequential psi access for ipsi in 1:mpsi @@ -404,30 +386,27 @@ function make_matrix(equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStates jtheta = -profiles.F_deriv(psi; hint=hint) chi1 = 2π * equil.psio - # Fill lower half (modes 0, 1, ..., mband at indices mid, mid-1, ..., 1) - # The 8 quantities are: g11, g22, g33, g23, g31, g12, jmat, jmat1 + # Fill modes 0, 1, ..., mpert-1 with conjugate symmetry for ± modes fc = metric.fourier_coeffs - for m in 0:intr.mband - g11[mid-m] = Utilities.get_complex_coeff(fc, ipsi, m, 1) - g22[mid-m] = Utilities.get_complex_coeff(fc, ipsi, m, 2) - g33[mid-m] = Utilities.get_complex_coeff(fc, ipsi, m, 3) - g23[mid-m] = Utilities.get_complex_coeff(fc, ipsi, m, 4) - g31[mid-m] = Utilities.get_complex_coeff(fc, ipsi, m, 5) - g12[mid-m] = Utilities.get_complex_coeff(fc, ipsi, m, 6) - jmat[mid-m] = Utilities.get_complex_coeff(fc, ipsi, m, 7) - jmat1[mid-m] = Utilities.get_complex_coeff(fc, ipsi, m, 8) + for m in 0:(intr.mpert-1) + g11[intr.mpert-m] = Utilities.get_complex_coeff(fc, ipsi, m, 1) + g22[intr.mpert-m] = Utilities.get_complex_coeff(fc, ipsi, m, 2) + g33[intr.mpert-m] = Utilities.get_complex_coeff(fc, ipsi, m, 3) + g23[intr.mpert-m] = Utilities.get_complex_coeff(fc, ipsi, m, 4) + g31[intr.mpert-m] = Utilities.get_complex_coeff(fc, ipsi, m, 5) + g12[intr.mpert-m] = Utilities.get_complex_coeff(fc, ipsi, m, 6) + jmat[intr.mpert-m] = Utilities.get_complex_coeff(fc, ipsi, m, 7) + jmat1[intr.mpert-m] = Utilities.get_complex_coeff(fc, ipsi, m, 8) end - - # Fill upper half (+1:mband) with conjugate symmetry - for k in 1:intr.mband - g11[mid+k] = conj(g11[mid-k]) - g22[mid+k] = conj(g22[mid-k]) - g33[mid+k] = conj(g33[mid-k]) - g23[mid+k] = conj(g23[mid-k]) - g31[mid+k] = conj(g31[mid-k]) - g12[mid+k] = conj(g12[mid-k]) - jmat[mid+k] = conj(jmat[mid-k]) - jmat1[mid+k] = conj(jmat1[mid-k]) + for k in 1:(intr.mpert-1) + g11[k+intr.mpert] = conj(g11[intr.mpert-k]) + g22[k+intr.mpert] = conj(g22[intr.mpert-k]) + g33[k+intr.mpert] = conj(g33[intr.mpert-k]) + g23[k+intr.mpert] = conj(g23[intr.mpert-k]) + g31[k+intr.mpert] = conj(g31[intr.mpert-k]) + g12[k+intr.mpert] = conj(g12[intr.mpert-k]) + jmat[k+intr.mpert] = conj(jmat[intr.mpert-k]) + jmat1[k+intr.mpert] = conj(jmat1[intr.mpert-k]) end # TODO: for 3D, would need an additional nlow:nhigh loop here for n/n' coupling @@ -438,11 +417,11 @@ function make_matrix(equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStates for m1 in intr.mlow:intr.mhigh ipert_m = m1 - intr.mlow + 1 singfac1 = m1 - nq - for dm in max(1-ipert_m, -intr.mband):min(intr.mpert-ipert_m, intr.mband) + for dm in (1-ipert_m):(intr.mpert-ipert_m) m2 = m1 + dm singfac2 = m2 - nq jpert_m = ipert_m + dm - dmidx = dm + mid + dmidx = dm + intr.mpert # Some complex indexing here... we flatten the 2D (mpert x npert) x (mpert x npert) matrix, # so we need a "ipert" for m, m', n, and n' (in full 3D). In 2D, just m, m', and n ipert = ipert_m + (ipert_n - 1) * intr.mpert @@ -483,8 +462,6 @@ function make_matrix(equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStates fmat = reshape(fmats_lower_flatview, intr.numpert_total, intr.numpert_total) kmat = reshape(kmats_flatview, intr.numpert_total, intr.numpert_total) gmat = reshape(gmats_flatview, intr.numpert_total, intr.numpert_total) - # TODO: Fortran threw an error if factorization fails for A/F due to small matrix bandwidth, - # Add this check back in if we implement banded matrices # Save primitive F for kinetic matrix construction (before Schur complement) @views fmats_prim_flat[ipsi, :] .= fmats_lower_flatview @@ -506,7 +483,7 @@ function make_matrix(equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStates end # --- Create Fourier coefficient splines (multi-quantity cubic interpolants) --- - ffit = FourFitVars(; mpert=intr.mpert, mband=intr.mband, numpert_total=intr.numpert_total) + ffit = FourFitVars(; mpert=intr.mpert, numpert_total=intr.numpert_total) # FastInterpolations now natively supports complex values - no need to split real/imag # Create complex series interpolants with per-column extrap BC diff --git a/src/ForceFreeStates/Free.jl b/src/ForceFreeStates/Free.jl index 2afc7a9d7..2faaf04de 100644 --- a/src/ForceFreeStates/Free.jl +++ b/src/ForceFreeStates/Free.jl @@ -10,7 +10,7 @@ and data dumping. @with_pool pool function free_run!(odet::OdeState, ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium, ffit::FourFitVars, intr::ForceFreeStatesInternal) # Initializations and allocations - (; mpert, mlow, mhigh, mband, numpert_total, psilim, qlim, npert, nlow, nhigh, wall_settings) = intr + (; mpert, mlow, mhigh, numpert_total, psilim, qlim, npert, nlow, nhigh, wall_settings) = intr vac_data = VacuumData(ctrl.mthvac * ctrl.nzvac, intr.numpert_total, ctrl.mthvac) etemp = zeros!(pool, ComplexF64, numpert_total) wp = zeros!(pool, ComplexF64, numpert_total, numpert_total) @@ -68,7 +68,7 @@ and data dumping. for ipert_n in 1:npert, ipert_m in 1:mpert, jpert_m in 1:mpert ipert = (ipert_n - 1) * mpert + ipert_m jpert = (ipert_n - 1) * mpert + jpert_m - norm += ffit.jmat[jpert_m-ipert_m+mband+1] * vac_data.wt[ipert, isol] * conj(vac_data.wt[jpert, isol]) + norm += ffit.jmat[jpert_m-ipert_m+mpert] * vac_data.wt[ipert, isol] * conj(vac_data.wt[jpert, isol]) end norm /= dV_dpsi vac_data.wt[:, isol] ./= sqrt(norm) @@ -243,7 +243,7 @@ wv matrix spline to `free_compute_wv_spline` and pass it in `odet.edge_scan.wvma for ipert_n in 1:intr.npert, ipert_m in 1:intr.mpert, jpert_m in 1:intr.mpert ipert = (ipert_n - 1) * intr.mpert + ipert_m jpert = (ipert_n - 1) * intr.mpert + jpert_m - norm += ffit.jmat[jpert_m-ipert_m+intr.mband+1] * v[ipert] * conj(v[jpert]) + norm += ffit.jmat[jpert_m-ipert_m+intr.mpert] * v[ipert] * conj(v[jpert]) end norm /= dV_dpsi eigenvalues[isol] /= norm @@ -266,7 +266,7 @@ wv matrix spline to `free_compute_wv_spline` and pass it in `odet.edge_scan.wvma mpert = intr.mpert sqrtamat_flat = Vector{ComplexF64}(undef, mpert^2 + 1) es.sqrtamat_spline(sqrtamat_flat, odet.psifac; hint=es.sqrtamat_hint) - sqrtamat_local = reshape(@view(sqrtamat_flat[1:mpert^2]), mpert, mpert) + sqrtamat_local = reshape(@view(sqrtamat_flat[1:(mpert^2)]), mpert, mpert) jarea_local = real(sqrtamat_flat[end]) pn_result = compute_power_norm_eigenvalues(wt_saved, wp, wv, sqrtamat_local, jarea_local, equil, odet.psifac, intr) diff --git a/src/ForceFreeStates/Sing.jl b/src/ForceFreeStates/Sing.jl index 16661c228..1a7b56d22 100644 --- a/src/ForceFreeStates/Sing.jl +++ b/src/ForceFreeStates/Sing.jl @@ -135,7 +135,15 @@ See equations 41-48 in the Glasser Phys. Plasmas 2016 112506 for the mathematica - `SingAsymptotics`: Struct containing all asymptotic expansion data """ -function compute_sing_asymptotics(singp::SingType, ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium, ffit::FourFitVars, intr::ForceFreeStatesInternal; sig::Float64=1.0, alpha_override::Union{Nothing, Vector{ComplexF64}}=nothing) +function compute_sing_asymptotics( + singp::SingType, + ctrl::ForceFreeStatesControl, + equil::Equilibrium.PlasmaEquilibrium, + ffit::FourFitVars, + intr::ForceFreeStatesInternal; + sig::Float64=1.0, + alpha_override::Union{Nothing,Vector{ComplexF64}}=nothing +) # Allocations vmat = zeros(ComplexF64, intr.numpert_total, 2 * intr.numpert_total, 2, 2 * ctrl.sing_order + 1) @@ -213,22 +221,22 @@ function compute_sing_asymptotics(singp::SingType, ctrl::ForceFreeStatesControl, ipert0 = r1[1] N = intr.numpert_total msg = " === sing_asymptotics debug: m=$(singp.m[1]) sig=$sig ($side_str)\n" - msg *= @sprintf(" m0mat(1,1)= %+.12e %+.12ei\n", real(m0mat[1,1]), imag(m0mat[1,1])) - msg *= @sprintf(" m0mat(1,2)= %+.12e %+.12ei\n", real(m0mat[1,2]), imag(m0mat[1,2])) - msg *= @sprintf(" m0mat(2,1)= %+.12e %+.12ei\n", real(m0mat[2,1]), imag(m0mat[2,1])) - msg *= @sprintf(" m0mat(2,2)= %+.12e %+.12ei\n", real(m0mat[2,2]), imag(m0mat[2,2])) - di = m0mat[1,1]*m0mat[2,2] - m0mat[2,1]*m0mat[1,2] + msg *= @sprintf(" m0mat(1,1)= %+.12e %+.12ei\n", real(m0mat[1, 1]), imag(m0mat[1, 1])) + msg *= @sprintf(" m0mat(1,2)= %+.12e %+.12ei\n", real(m0mat[1, 2]), imag(m0mat[1, 2])) + msg *= @sprintf(" m0mat(2,1)= %+.12e %+.12ei\n", real(m0mat[2, 1]), imag(m0mat[2, 1])) + msg *= @sprintf(" m0mat(2,2)= %+.12e %+.12ei\n", real(m0mat[2, 2]), imag(m0mat[2, 2])) + di = m0mat[1, 1]*m0mat[2, 2] - m0mat[2, 1]*m0mat[1, 2] msg *= @sprintf(" di= %+.12e, alpha= %+.12e %+.12ei\n", real(di), real(alpha[1]), imag(alpha[1])) msg *= @sprintf(" psifac= %+.12e, r1=%d, ipert0=%d\n", singp.psifac, r1[1], ipert0) - msg *= @sprintf(" vmat(ip,ip,2,0)= %+.8e %+.8ei\n", real(vmat[ipert0,ipert0,2,1]), imag(vmat[ipert0,ipert0,2,1])) - msg *= @sprintf(" vmat(ip,ip+N,2,0)= %+.8e %+.8ei\n", real(vmat[ipert0,ipert0+N,2,1]), imag(vmat[ipert0,ipert0+N,2,1])) + msg *= @sprintf(" vmat(ip,ip,2,0)= %+.8e %+.8ei\n", real(vmat[ipert0, ipert0, 2, 1]), imag(vmat[ipert0, ipert0, 2, 1])) + msg *= @sprintf(" vmat(ip,ip+N,2,0)= %+.8e %+.8ei\n", real(vmat[ipert0, ipert0+N, 2, 1]), imag(vmat[ipert0, ipert0+N, 2, 1])) for k in 0:(2*ctrl.sing_order) msg *= @sprintf(" k=%2d vmat(ip,ip,1)=%+.8e %+.8ei vmat(ip,ip,2)=%+.8e %+.8ei\n", - k, real(vmat[ipert0,ipert0,1,k+1]), imag(vmat[ipert0,ipert0,1,k+1]), - real(vmat[ipert0,ipert0,2,k+1]), imag(vmat[ipert0,ipert0,2,k+1])) + k, real(vmat[ipert0, ipert0, 1, k+1]), imag(vmat[ipert0, ipert0, 1, k+1]), + real(vmat[ipert0, ipert0, 2, k+1]), imag(vmat[ipert0, ipert0, 2, k+1])) msg *= @sprintf(" k=%2d vmat(ip,ip+N,1)=%+.8e %+.8ei vmat(ip,ip+N,2)=%+.8e %+.8ei\n", - k, real(vmat[ipert0,ipert0+N,1,k+1]), imag(vmat[ipert0,ipert0+N,1,k+1]), - real(vmat[ipert0,ipert0+N,2,k+1]), imag(vmat[ipert0,ipert0+N,2,k+1])) + k, real(vmat[ipert0, ipert0+N, 1, k+1]), imag(vmat[ipert0, ipert0+N, 1, k+1]), + real(vmat[ipert0, ipert0+N, 2, k+1]), imag(vmat[ipert0, ipert0+N, 2, k+1])) end msg end @@ -351,7 +359,7 @@ Add a spline for F directly instead of the lower triangular factorization to avo # f_lower = QL̄ = [QL̄, QL̄' + Q' L̄, 1/2 (QL̄'' + 2Q' L̄' + QQ'' L̄), 1/6 (QL̄''' + 3Q' L̄'' + 3Q'' L̄' + Q'''L̄), ...] (but without 1/2, 1/6, etc) for ipert_n in 1:intr.npert for jpert_m in 1:intr.mpert - for ipert_m in jpert_m:min(intr.mpert, jpert_m+intr.mband) + for ipert_m in jpert_m:intr.mpert ipert = ipert_m + (ipert_n - 1) * intr.mpert jpert = jpert_m + (ipert_n - 1) * intr.mpert f_lower[ipert, jpert, 1] = singfac[ipert, 1] * f_lower_interp[ipert, jpert, 1] @@ -402,8 +410,8 @@ Add a spline for F directly instead of the lower triangular factorization to avo for j in 0:n for ipert_n in 1:intr.npert for jpert_m in 1:intr.mpert - for ipert_m in jpert_m:min(intr.mpert, jpert_m+intr.mband) - for kpert_m in max(1, ipert_m-intr.mband):jpert_m + for ipert_m in jpert_m:intr.mpert + for kpert_m in 1:jpert_m ipert = ipert_m + (ipert_n - 1) * intr.mpert jpert = jpert_m + (ipert_n - 1) * intr.mpert kpert = kpert_m + (ipert_n - 1) * intr.mpert @@ -422,7 +430,7 @@ Add a spline for F directly instead of the lower triangular factorization to avo # K = [QK̄, QK̄' + Q'K̄, QK̄''/2 + Q'K̄' + Q̄''K̄/2, ...] for ipert_n in 1:intr.npert for jpert_m in 1:intr.mpert - for ipert_m in max(1, jpert_m-intr.mband):min(intr.mpert, jpert_m+intr.mband) + for ipert_m in 1:intr.mpert ipert = ipert_m + (ipert_n - 1) * intr.mpert jpert = jpert_m + (ipert_n - 1) * intr.mpert k[ipert, jpert, 1] = singfac[ipert, 1] * k_interp[ipert, jpert, 1] @@ -464,7 +472,7 @@ Add a spline for F directly instead of the lower triangular factorization to avo # G = [G, G', G''/2, G'''/6] for ipert_n in 1:intr.npert for jpert_m in 1:intr.mpert - for ipert_m in jpert_m:min(intr.mpert, jpert_m+intr.mband) + for ipert_m in jpert_m:intr.mpert ipert = ipert_m + (ipert_n - 1) * intr.mpert jpert = jpert_m + (ipert_n - 1) * intr.mpert g_lower[ipert, jpert, 1] = g_interp[ipert, jpert, 1] @@ -971,10 +979,11 @@ det(F̄) via adaptive bisection. Here we use condition number peaks instead of determinant zeros for better numerical robustness and scale invariance. Algorithm: -1. Evaluate cond(F̄) on a dense ψ grid -2. Find local maxima (peaks where gradient changes from + to -) -3. Refine each peak with golden-section minimization of -cond -4. Filter by threshold and resonance condition + + 1. Evaluate cond(F̄) on a dense ψ grid + 2. Find local maxima (peaks where gradient changes from + to -) + 3. Refine each peak with golden-section minimization of -cond + 4. Filter by threshold and resonance condition """ function find_kinetic_singular_surfaces!(ffit::FourFitVars, equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStatesInternal; ngrid::Int=2000, cond_threshold::Float64=1e8) psilow = equil.profiles.xs[1] @@ -1000,7 +1009,7 @@ function find_kinetic_singular_surfaces!(ffit::FourFitVars, equil::Equilibrium.P # Find local maxima of cond(F̄): points where cond increases then decreases peak_indices = Int[] - for i in 2:(ngrid - 1) + for i in 2:(ngrid-1) if cond_vals[i] > cond_vals[i-1] && cond_vals[i] > cond_vals[i+1] && cond_vals[i] > cond_threshold push!(peak_indices, i) end @@ -1033,14 +1042,17 @@ function find_kinetic_singular_surfaces!(ffit::FourFitVars, equil::Equilibrium.P continue end - push!(kinsing_surfaces, SingType(; - psifac=psi_refined, - rho=sqrt(psi_refined), - m=[round(Int, n * q_val) for n in intr.nlow:intr.nhigh], - n=collect(intr.nlow:intr.nhigh), - q=q_val, - q1=q1_val, - )) + push!( + kinsing_surfaces, + SingType(; + psifac=psi_refined, + rho=sqrt(psi_refined), + m=[round(Int, n * q_val) for n in intr.nlow:intr.nhigh], + n=collect(intr.nlow:intr.nhigh), + q=q_val, + q1=q1_val + ) + ) end # Sort by ψ location diff --git a/src/GeneralizedPerturbedEquilibrium.jl b/src/GeneralizedPerturbedEquilibrium.jl index b6988f0c9..914f36453 100755 --- a/src/GeneralizedPerturbedEquilibrium.jl +++ b/src/GeneralizedPerturbedEquilibrium.jl @@ -240,12 +240,6 @@ function main(args::Vector{String}=String[]; dd::Union{IMASdd.dd,Nothing}=nothin intr.mhigh = trunc(Int, intr.nhigh * equil.params.qmax) + ctrl.delta_mhigh end intr.mpert = intr.mhigh - intr.mlow + 1 - if ctrl.delta_mband >= intr.mpert - @warn "Banded matrices not implemented yet, setting delta_mband to 0" - ctrl.delta_mband = 0 - end - intr.mband = intr.mpert - 1 - ctrl.delta_mband - intr.mband = min(max(intr.mband, 0), intr.mpert - 1) intr.numpert_total = intr.mpert * intr.npert # Build KineticForces control and load kinetic profiles once — reused by @@ -254,14 +248,15 @@ function main(args::Vector{String}=String[]; dd::Union{IMASdd.dd,Nothing}=nothin # stability does not need kinetic_profiles, but the post-PE block always # does, so we load whenever a [KineticForces] section is present or the # stability path requests the calculated source. - kf_ctrl = haskey(inputs, "KineticForces") ? + kf_ctrl = + haskey(inputs, "KineticForces") ? KineticForces.KineticForcesControl(; (Symbol(k) => v for (k, v) in inputs["KineticForces"])...) : KineticForces.KineticForcesControl() kinetic_profiles = nothing needs_kinetic_profiles = haskey(inputs, "KineticForces") || - (ctrl.kinetic_factor > 0 && ctrl.kinetic_source == "calculated") + (ctrl.kinetic_factor > 0 && ctrl.kinetic_source == "calculated") if needs_kinetic_profiles kinetic_file = joinpath(intr.dir_path, kf_ctrl.kinetic_file) kinetic_profiles = Equilibrium.load_kinetic_profiles( @@ -280,12 +275,12 @@ function main(args::Vector{String}=String[]; dd::Union{IMASdd.dd,Nothing}=nothin " q0 = $(@sprintf("%.3f", equil.params.q0)), qmin = $(@sprintf("%.3f", equil.params.qmin)), qmax = $(@sprintf("%.3f", equil.params.qmax)), q95 = $(@sprintf("%.3f", equil.params.q95))\n" * " qlim = $(@sprintf("%.3f", intr.qlim)), psilim = $(@sprintf("%.3f", intr.psilim))\n" * " betat = $(@sprintf("%.3f", equil.params.betat)), betan = $(@sprintf("%.3f", equil.params.betan)), betap1 = $(@sprintf("%.3f", equil.params.betap1))\n" * - " mlow = $(@sprintf("%4i", intr.mlow)), mhigh = $(@sprintf("%4i", intr.mhigh)), mpert = $(@sprintf("%4i", intr.mpert)), mband = $(@sprintf("%4i", intr.mband))\n" * + " mlow = $(@sprintf("%4i", intr.mlow)), mhigh = $(@sprintf("%4i", intr.mhigh)), mpert = $(@sprintf("%4i", intr.mpert))\n" * " nlow = $(@sprintf("%4i", intr.nlow)), nhigh = $(@sprintf("%4i", intr.nhigh)), npert = $(@sprintf("%4i", intr.npert))" end # Compute metric tensor - metric = make_metric(equil; mband=intr.mband) + metric = make_metric(equil, intr.mpert) if ctrl.verbose @info "Computing F, G, and K matrices" @@ -503,7 +498,6 @@ function write_outputs_to_HDF5( # Write derived run parameters out_h5["info/mpert"] = intr.mpert - out_h5["info/mband"] = intr.mband out_h5["info/mlow"] = intr.mlow out_h5["info/mhigh"] = intr.mhigh out_h5["info/npert"] = intr.npert @@ -624,7 +618,7 @@ function write_outputs_to_HDF5( out_h5["singular/kinetic/scan_psi"] = intr.kinsing_scan_psi out_h5["singular/kinetic/scan_cond"] = intr.kinsing_scan_cond out_h5["singular/kinetic/scan_threshold"] = intr.kinsing_scan_threshold - + # Write free-boundary stability data. Power-normalized flux (Φ-space) is the # default — Jacobian-invariant. ξ-space counterparts sit under # FreeBoundaryStability/XiNorm/ for Fortran benchmarking. diff --git a/src/PerturbedEquilibrium/FieldReconstruction.jl b/src/PerturbedEquilibrium/FieldReconstruction.jl index 6246a1d28..541537b30 100644 --- a/src/PerturbedEquilibrium/FieldReconstruction.jl +++ b/src/PerturbedEquilibrium/FieldReconstruction.jl @@ -48,22 +48,23 @@ All fields returned in mode space [npsi, mpert]. # Returns Tuple of (xi_modes, b_modes) NamedTuples: -- `xi_modes.psi`: ξ_ψ [npsi, mpert] -- `xi_modes.psi_J`: J·ξ^ψ (Jacobian-weighted, from gpeq_contra; used by gpeq_normal for b_n/xi_n) -- `xi_modes.theta`: ξ^θ contravariant (from gpeq_contra Jacobian convolution) -- `xi_modes.zeta`: ξ^ζ contravariant (from gpeq_contra Jacobian convolution) -- `xi_modes.clebsch_psi`: ξ^ψ for PENTRC (= xi_psi, unregularized) -- `xi_modes.clebsch_psi1`: ∂ξ^ψ/∂ψ regularized for PENTRC -- `xi_modes.clebsch_alpha`: ξ^α/χ₁ regularized for PENTRC (divided by χ₁ per gpout_xclebsch) -- `xi_modes.theta_reg`: ξ^θ regularized (= xmt, from gpeq_contra with reg_spot smoothing) -- `xi_modes.zeta_reg`: ξ^ζ regularized (= xmz, from gpeq_contra with reg_spot smoothing) -- `xi_modes.cova_psi/theta/zeta`: covariant displacement (from gpeq_cova) -- `b_modes.psi`: b^ψ [npsi, mpert] -- `b_modes.psi_area`: b^ψ / ⟨J·|∇ψ|⟩_θ (area-normalized, for b_n computation) -- `b_modes.theta`: b^θ [npsi, mpert] -- `b_modes.zeta`: b^ζ [npsi, mpert] -- `b_modes.theta_reg/zeta_reg`: regularized b^θ, b^ζ (from gpeq_sol with reg_spot smoothing) -- `b_modes.cova_psi/theta/zeta`: covariant field (from gpeq_cova) + + - `xi_modes.psi`: ξ_ψ [npsi, mpert] + - `xi_modes.psi_J`: J·ξ^ψ (Jacobian-weighted, from gpeq_contra; used by gpeq_normal for b_n/xi_n) + - `xi_modes.theta`: ξ^θ contravariant (from gpeq_contra Jacobian convolution) + - `xi_modes.zeta`: ξ^ζ contravariant (from gpeq_contra Jacobian convolution) + - `xi_modes.clebsch_psi`: ξ^ψ for PENTRC (= xi_psi, unregularized) + - `xi_modes.clebsch_psi1`: ∂ξ^ψ/∂ψ regularized for PENTRC + - `xi_modes.clebsch_alpha`: ξ^α/χ₁ regularized for PENTRC (divided by χ₁ per gpout_xclebsch) + - `xi_modes.theta_reg`: ξ^θ regularized (= xmt, from gpeq_contra with reg_spot smoothing) + - `xi_modes.zeta_reg`: ξ^ζ regularized (= xmz, from gpeq_contra with reg_spot smoothing) + - `xi_modes.cova_psi/theta/zeta`: covariant displacement (from gpeq_cova) + - `b_modes.psi`: b^ψ [npsi, mpert] + - `b_modes.psi_area`: b^ψ / ⟨J·|∇ψ|⟩_θ (area-normalized, for b_n computation) + - `b_modes.theta`: b^θ [npsi, mpert] + - `b_modes.zeta`: b^ζ [npsi, mpert] + - `b_modes.theta_reg/zeta_reg`: regularized b^θ, b^ζ (from gpeq_sol with reg_spot smoothing) + - `b_modes.cova_psi/theta/zeta`: covariant field (from gpeq_cova) """ function reconstruct_physical_fields( response_vector::Vector{ComplexF64}, @@ -133,18 +134,18 @@ function reconstruct_physical_fields( area = 0.0 for k in 1:mthsurf theta = thetas_for_avg[k] - r2 = equil.rzphi_rsquared((psi, theta); hint=hint2d) - deta = equil.rzphi_offset((psi, theta); hint=hint2d) - jac = equil.rzphi_jac((psi, theta); hint=hint2d) - r2_y = equil.rzphi_rsquared((psi, theta); deriv=DerivOp(0, 1), hint=hint2d) - deta_y = equil.rzphi_offset((psi, theta); deriv=DerivOp(0, 1), hint=hint2d) - rfac = sqrt(abs(r2)) - eta = 2π * (theta + deta) - r = ro + rfac * cos(eta) - w11 = (1.0 + deta_y) * 4π^2 * rfac * r / jac - w12 = -r2_y * π * r / (rfac * jac) + r2 = equil.rzphi_rsquared((psi, theta); hint=hint2d) + deta = equil.rzphi_offset((psi, theta); hint=hint2d) + jac = equil.rzphi_jac((psi, theta); hint=hint2d) + r2_y = equil.rzphi_rsquared((psi, theta); deriv=DerivOp(0, 1), hint=hint2d) + deta_y = equil.rzphi_offset((psi, theta); deriv=DerivOp(0, 1), hint=hint2d) + rfac = sqrt(abs(r2)) + eta = 2π * (theta + deta) + r = ro + rfac * cos(eta) + w11 = (1.0 + deta_y) * 4π^2 * rfac * r / jac + w12 = -r2_y * π * r / (rfac * jac) delpsi = sqrt(w11^2 + w12^2) - area += jac * delpsi + area += jac * delpsi end area /= mthsurf Jb_psi_modes[ipsi, :] = b_psi_modes[ipsi, :] ./ area @@ -164,31 +165,31 @@ function reconstruct_physical_fields( b_R, b_Z, b_phi = _apply_rzphi_transform(rzphi_geom, ft_rz, mtheta_rz, b_psi_modes, b_theta_reg, bvz_modes) xi_modes = ( - psi = xi_psi_modes, - psi_J = xwp_modes, # J·ξ^ψ (Jacobian-weighted, from gpeq_contra) - theta = xwt_modes, # ξ^θ contravariant (from gpeq_contra) - zeta = xwz_modes, # ξ^ζ contravariant (from gpeq_contra) - theta_reg = xmt_modes, # ξ^θ regularized (from gpeq_contra, smoothed by reg_spot) - zeta_reg = xmz_modes, # ξ^ζ regularized (from gpeq_contra, smoothed by reg_spot) - clebsch_psi = clebsch_psi, # ξ^ψ for PENTRC - clebsch_psi1 = clebsch_psi1, # ∂ξ^ψ/∂ψ regularized for PENTRC - clebsch_alpha = clebsch_alpha, # ξ^α/χ₁ regularized for PENTRC - cova_psi = xvp_modes, # covariant ξ_ψ (from gpeq_cova) - cova_theta = xvt_modes, # covariant ξ_θ (from gpeq_cova) - cova_zeta = xvz_modes, # covariant ξ_ζ (from gpeq_cova) - R = xi_R, Z = xi_Z, phi = xi_phi + psi=xi_psi_modes, + psi_J=xwp_modes, # J·ξ^ψ (Jacobian-weighted, from gpeq_contra) + theta=xwt_modes, # ξ^θ contravariant (from gpeq_contra) + zeta=xwz_modes, # ξ^ζ contravariant (from gpeq_contra) + theta_reg=xmt_modes, # ξ^θ regularized (from gpeq_contra, smoothed by reg_spot) + zeta_reg=xmz_modes, # ξ^ζ regularized (from gpeq_contra, smoothed by reg_spot) + clebsch_psi=clebsch_psi, # ξ^ψ for PENTRC + clebsch_psi1=clebsch_psi1, # ∂ξ^ψ/∂ψ regularized for PENTRC + clebsch_alpha=clebsch_alpha, # ξ^α/χ₁ regularized for PENTRC + cova_psi=xvp_modes, # covariant ξ_ψ (from gpeq_cova) + cova_theta=xvt_modes, # covariant ξ_θ (from gpeq_cova) + cova_zeta=xvz_modes, # covariant ξ_ζ (from gpeq_cova) + R=xi_R, Z=xi_Z, phi=xi_phi ) b_modes = ( - psi = b_psi_modes, # b^ψ (no Jacobian) — used for b_n normal projection - psi_area = Jb_psi_modes, # b^ψ / ⟨J·|∇ψ|⟩_θ (area-normalized, for b_n) - theta = b_theta_modes, # b^θ unregularized - zeta = b_zeta_modes, # b^ζ unregularized - theta_reg = b_theta_reg, # b^θ regularized (from gpeq_sol with reg_spot) - zeta_reg = b_zeta_reg, # b^ζ regularized - cova_psi = bvp_modes, # covariant b_ψ (from gpeq_cova) - cova_theta = bvt_modes, # covariant b_θ (from gpeq_cova) - cova_zeta = bvz_modes, # covariant b_ζ (from gpeq_cova) - R = b_R, Z = b_Z, phi = b_phi + psi=b_psi_modes, # b^ψ (no Jacobian) — used for b_n normal projection + psi_area=Jb_psi_modes, # b^ψ / ⟨J·|∇ψ|⟩_θ (area-normalized, for b_n) + theta=b_theta_modes, # b^θ unregularized + zeta=b_zeta_modes, # b^ζ unregularized + theta_reg=b_theta_reg, # b^θ regularized (from gpeq_sol with reg_spot) + zeta_reg=b_zeta_reg, # b^ζ regularized + cova_psi=bvp_modes, # covariant b_ψ (from gpeq_cova) + cova_theta=bvt_modes, # covariant b_θ (from gpeq_cova) + cova_zeta=bvz_modes, # covariant b_ζ (from gpeq_cova) + R=b_R, Z=b_Z, phi=b_phi ) return xi_modes, b_modes @@ -203,18 +204,18 @@ Sum eigenmode contributions weighted by response coefficients. `response_vector` (= P * Phi_x) is in mode (m,n) basis. To reconstruct physical fields from eigenmode solutions in u_store/ud_store, first project to eigenmode amplitudes: - alpha = flux_matrix \\ response_vector +alpha = flux_matrix \\ response_vector Then sum eigenmode contributions at each radial point (matches Fortran gpeq_sol): - xi_psi[ipsi, :] = u_store[:, :, 1, ipsi] * alpha # Ξ_ψ - xi_psi1[ipsi, :] = ud_store[:, :, 1, ipsi] * alpha # dΞ_ψ/dψ - xi_s[ipsi, :] = ud_store[:, :, 2, ipsi] * alpha # Ξ_s (toroidal, Glasser 2016 eq. 18) +xi_psi[ipsi, :] = u_store[:, :, 1, ipsi] * alpha # Ξ_ψ +xi_psi1[ipsi, :] = ud_store[:, :, 1, ipsi] * alpha # dΞ_ψ/dψ +xi_s[ipsi, :] = ud_store[:, :, 2, ipsi] * alpha # Ξ_s (toroidal, Glasser 2016 eq. 18) # Returns -- `xi_psi_modes`: Radial displacement ξ_ψ(ψ, m) [npsi, mpert] -- `xi_psi1_modes`: Radial derivative dξ_ψ/dψ(ψ, m) [npsi, mpert] -- `xi_s_modes`: Toroidal displacement ξ_s(ψ, m) = -A⁻¹(B·dξ_ψ/dψ + C·ξ_ψ) [npsi, mpert] + - `xi_psi_modes`: Radial displacement ξ_ψ(ψ, m) [npsi, mpert] + - `xi_psi1_modes`: Radial derivative dξ_ψ/dψ(ψ, m) [npsi, mpert] + - `xi_s_modes`: Toroidal displacement ξ_s(ψ, m) = -A⁻¹(B·dξ_ψ/dψ + C·ξ_ψ) [npsi, mpert] """ function sum_eigenmode_contributions( response_vector::Vector{ComplexF64}, @@ -223,29 +224,29 @@ function sum_eigenmode_contributions( ffs_intr::ForceFreeStatesInternal ) mpert = ffs_intr.mpert - npsi = size(ForceFreeStates_results.u_store, 4) + npsi = size(ForceFreeStates_results.u_store, 4) # Convert mode-basis response (Phi_tot) to eigenmode amplitudes alpha # flux_matrix[mode, eigenmode], so: flux_matrix * alpha = response_vector alpha = flux_matrix \ response_vector # [mpert] - xi_psi_modes = zeros(ComplexF64, npsi, mpert) + xi_psi_modes = zeros(ComplexF64, npsi, mpert) xi_psi1_modes = zeros(ComplexF64, npsi, mpert) - xi_s_modes = zeros(ComplexF64, npsi, mpert) + xi_s_modes = zeros(ComplexF64, npsi, mpert) # Surfaces are independent; threaded over ψ (run with `julia -t N` or JULIA_NUM_THREADS). Threads.@threads :static for ipsi in 1:npsi # u_store[:,:,1] = Ξ_ψ (radial displacement) mul!(view(xi_psi_modes, ipsi, :), - ForceFreeStates_results.u_store[:, :, 1, ipsi], - alpha) + ForceFreeStates_results.u_store[:, :, 1, ipsi], + alpha) # ud_store[:,:,1] = dΞ_ψ/dψ (radial derivative) mul!(view(xi_psi1_modes, ipsi, :), - ForceFreeStates_results.ud_store[:, :, 1, ipsi], - alpha) + ForceFreeStates_results.ud_store[:, :, 1, ipsi], + alpha) # ud_store[:,:,2] = Ξ_s = -A⁻¹(B·Ξ'_ψ + C·Ξ_ψ) (toroidal displacement, Glasser 2016 eq. 18) mul!(view(xi_s_modes, ipsi, :), - ForceFreeStates_results.ud_store[:, :, 2, ipsi], - alpha) + ForceFreeStates_results.ud_store[:, :, 2, ipsi], + alpha) end return xi_psi_modes, xi_psi1_modes, xi_s_modes @@ -274,9 +275,9 @@ function compute_perturbed_field_modes( ) npsi, mpert = size(xi_psi_modes) - b_psi_modes = zeros(ComplexF64, npsi, mpert) + b_psi_modes = zeros(ComplexF64, npsi, mpert) b_theta_modes = zeros(ComplexF64, npsi, mpert) - b_zeta_modes = zeros(ComplexF64, npsi, mpert) + b_zeta_modes = zeros(ComplexF64, npsi, mpert) mlow = ffs_intr.mlow nn = ffs_intr.nlow @@ -291,14 +292,14 @@ function compute_perturbed_field_modes( m = mlow + ipert - 1 singfac = m - nn * q - xsp = xi_psi_modes[ipsi, ipert] + xsp = xi_psi_modes[ipsi, ipert] xsp1 = xi_psi1_modes[ipsi, ipert] - xss = xi_s_modes[ipsi, ipert] + xss = xi_s_modes[ipsi, ipert] # Matches Fortran gpeq_sol [Park 2007 eq. 8-10] - b_psi_modes[ipsi, ipert] = chi1 * singfac * 2π * im * xsp + b_psi_modes[ipsi, ipert] = chi1 * singfac * 2π * im * xsp b_theta_modes[ipsi, ipert] = -(chi1 * xsp1 + 2π * im * nn * xss) - b_zeta_modes[ipsi, ipert] = -(chi1 * (q1 * xsp + q * xsp1) + 2π * im * m * xss) + b_zeta_modes[ipsi, ipert] = -(chi1 * (q1 * xsp + q * xsp1) + 2π * im * m * xss) end end @@ -314,9 +315,10 @@ end Compute Clebsch displacement components for PENTRC output. Matches Fortran gpeq_sol regularization + gpout_xclebsch output convention: -- `clebsch_psi` = ξ^ψ (unregularized, same as xi_psi_modes) -- `clebsch_psi1` = xmp1 = ∂ξ^ψ/∂ψ × singfac²/(singfac² + reg_spot²) -- `clebsch_alpha` = xms/χ₁ (regularized ξ^α divided by χ₁ per gpout_xclebsch convention) + + - `clebsch_psi` = ξ^ψ (unregularized, same as xi_psi_modes) + - `clebsch_psi1` = xmp1 = ∂ξ^ψ/∂ψ × singfac²/(singfac² + reg_spot²) + - `clebsch_alpha` = xms/χ₁ (regularized ξ^α divided by χ₁ per gpout_xclebsch convention) When reg_spot=0, clebsch_psi1 = xi_psi1 and clebsch_alpha = xi_s/χ₁ (no regularization). @@ -339,8 +341,8 @@ function compute_clebsch_displacements( chi1 = 2π * equil.psio numpert_total = ffs_intr.numpert_total - clebsch_psi = copy(xi_psi_modes) # ξ^ψ (unregularized) - clebsch_psi1 = copy(xi_psi1_modes) # will be regularized below + clebsch_psi = copy(xi_psi_modes) # ξ^ψ (unregularized) + clebsch_psi1 = copy(xi_psi1_modes) # will be regularized below clebsch_alpha = xi_s_modes ./ chi1 # ξ^α/χ₁ (will be regularized below) reg_spot = ctrl.reg_spot @@ -410,8 +412,8 @@ end Compute regularized (modified) contravariant B-field components. Matches Fortran gpeq_sol bmt/bmz using regularized xmp1 and xms: - b^θ_m = -(χ₁·xmp1 + 2πi·n·xms) - b^ζ_m = -(χ₁·(q'·xsp + q·xmp1) + 2πi·m·xms) +b^θ_m = -(χ₁·xmp1 + 2πi·n·xms) +b^ζ_m = -(χ₁·(q'·xsp + q·xmp1) + 2πi·m·xms) Note: clebsch_alpha = xms/χ₁, so xms = clebsch_alpha * χ₁. """ @@ -429,7 +431,7 @@ function compute_modified_field_modes( chi1 = 2π * equil.psio b_theta_reg = zeros(ComplexF64, npsi, mpert) - b_zeta_reg = zeros(ComplexF64, npsi, mpert) + b_zeta_reg = zeros(ComplexF64, npsi, mpert) Threads.@threads :static for ipsi in 1:npsi psi_norm = psi_grid[ipsi] @@ -438,12 +440,12 @@ function compute_modified_field_modes( for ipert in 1:mpert m = mlow + ipert - 1 - xsp = xi_psi_modes[ipsi, ipert] + xsp = xi_psi_modes[ipsi, ipert] xmp1 = clebsch_psi1[ipsi, ipert] - xms = clebsch_alpha[ipsi, ipert] * chi1 # undo χ₁ division + xms = clebsch_alpha[ipsi, ipert] * chi1 # undo χ₁ division b_theta_reg[ipsi, ipert] = -(chi1 * xmp1 + 2π * im * nn * xms) - b_zeta_reg[ipsi, ipert] = -(chi1 * (q1 * xsp + q * xmp1) + 2π * im * m * xms) + b_zeta_reg[ipsi, ipert] = -(chi1 * (q1 * xsp + q * xmp1) + 2π * im * m * xms) end end @@ -459,9 +461,9 @@ end Compute contravariant displacement via Jacobian mode coupling convolution. Matches Fortran `gpeq_contra`: - ξ^ψ·J(m) = Σ_dm jmat(dm) · xsp(m+dm) - ξ^θ(m) = -Σ_dm [...] / (2πi·singfac) - ξ^ζ(m) = -Σ_dm [...] / (2πi·singfac) +ξ^ψ·J(m) = Σ_dm jmat(dm) · xsp(m+dm) +ξ^θ(m) = -Σ_dm [...] / (2πi·singfac) +ξ^ζ(m) = -Σ_dm [...] / (2πi·singfac) Uses regularized xmp1 and xms for the theta/zeta components, then optionally applies additional regularization to get xmt/xmz. @@ -480,19 +482,17 @@ function compute_contra_displacements( ) npsi, mpert = size(xi_psi_modes) mlow = ffs_intr.mlow - mband = ffs_intr.mband nn = ffs_intr.nlow chi1 = 2π * equil.psio reg_spot = ctrl.reg_spot fc = metric.fourier_coeffs - mid = mband + 1 xwp_modes = zeros(ComplexF64, npsi, mpert) xwt_modes = zeros(ComplexF64, npsi, mpert) xwz_modes = zeros(ComplexF64, npsi, mpert) # Per-thread Fourier coefficient vectors and spline hints (not safe to share across threads). - vlen = 2 * mband + 1 + vlen = 2 * mpert - 1 nt = Threads.maxthreadid() jmat_bufs = [Vector{ComplexF64}(undef, vlen) for _ in 1:nt] jmat1_bufs = [Vector{ComplexF64}(undef, vlen) for _ in 1:nt] @@ -501,7 +501,7 @@ function compute_contra_displacements( # Build cubic spline interpolants for Jacobian Fourier coefficients (quantities 7, 8). # Matches Fortran cspline_eval(metric%cs, psi, 0) which interpolates smoothly. - jmat_interp = _build_metric_interp(fc, 7) + jmat_interp = _build_metric_interp(fc, 7) jmat1_interp = _build_metric_interp(fc, 8) Threads.@threads :static for ipsi in 1:npsi @@ -515,15 +515,15 @@ function compute_contra_displacements( q = equil.profiles.q_spline(psi_norm) # Interpolate Jacobian Fourier coefficients at this psi - jmat_vals = jmat_interp(psi_norm; hint=jmat_hint) + jmat_vals = jmat_interp(psi_norm; hint=jmat_hint) jmat1_vals = jmat1_interp(psi_norm; hint=jmat1_hint) - for m in 0:mband - jmat[mid-m] = jmat_vals[m+1] - jmat1[mid-m] = jmat1_vals[m+1] + for m in 0:(mpert-1) + jmat[mpert-m] = jmat_vals[m+1] + jmat1[mpert-m] = jmat1_vals[m+1] end - for k in 1:mband - jmat[mid+k] = conj(jmat[mid-k]) - jmat1[mid+k] = conj(jmat1[mid-k]) + for k in 1:(mpert-1) + jmat[k+mpert] = conj(jmat[mpert-k]) + jmat1[k+mpert] = conj(jmat1[mpert-k]) end # Matches Fortran gpeq_contra: uses regularized xmp1/xms for theta/zeta components @@ -536,13 +536,13 @@ function compute_contra_displacements( xwt_acc = zero(ComplexF64) xwz_acc = zero(ComplexF64) - for dm in max(1-ipert, -mband):min(mpert-ipert, mband) + for dm in (1-ipert):(mpert-ipert) jpert = ipert + dm - dmidx = dm + mid + dmidx = dm + mpert - xsp_j = xi_psi_modes[ipsi, jpert] + xsp_j = xi_psi_modes[ipsi, jpert] xmp1_j = clebsch_psi1[ipsi, jpert] - xms_j = clebsch_alpha[ipsi, jpert] * chi1 # undo χ₁ division + xms_j = clebsch_alpha[ipsi, jpert] * chi1 # undo χ₁ division # ξ^ψ·J: Jacobian-weighted psi displacement xwp_acc += jmat[dmidx] * xsp_j @@ -612,8 +612,6 @@ function compute_cova_components( ) npsi, mpert = size(xwp_modes) mlow = ffs_intr.mlow - mband = ffs_intr.mband - mid = mband + 1 fc = metric.fourier_coeffs xvp_modes = zeros(ComplexF64, npsi, mpert) @@ -624,7 +622,7 @@ function compute_cova_components( bvz_modes = zeros(ComplexF64, npsi, mpert) # Per-thread metric Fourier coefficient vectors and spline hints (not safe to share). - vlen = 2 * mband + 1 + vlen = 2 * mpert - 1 nt = Threads.maxthreadid() g11_bufs = [Vector{ComplexF64}(undef, vlen) for _ in 1:nt] g22_bufs = [Vector{ComplexF64}(undef, vlen) for _ in 1:nt] @@ -652,31 +650,36 @@ function compute_cova_components( # Interpolate metric tensor Fourier coefficients at this psi g_vals = [g_interps[qty](psi_norm; hint=g_hints[qty]) for qty in 1:6] - for m in 0:mband - g11[mid-m] = g_vals[1][m+1] - g22[mid-m] = g_vals[2][m+1] - g33[mid-m] = g_vals[3][m+1] - g23[mid-m] = g_vals[4][m+1] - g31[mid-m] = g_vals[5][m+1] - g12[mid-m] = g_vals[6][m+1] + for m in 0:(mpert-1) + idx = mpert - m + g11[idx] = g_vals[1][m+1] + g22[idx] = g_vals[2][m+1] + g33[idx] = g_vals[3][m+1] + g23[idx] = g_vals[4][m+1] + g31[idx] = g_vals[5][m+1] + g12[idx] = g_vals[6][m+1] end - for k in 1:mband - g11[mid+k] = conj(g11[mid-k]) - g22[mid+k] = conj(g22[mid-k]) - g33[mid+k] = conj(g33[mid-k]) - g23[mid+k] = conj(g23[mid-k]) - g31[mid+k] = conj(g31[mid-k]) - g12[mid+k] = conj(g12[mid-k]) + for k in 1:(mpert-1) + g11[k+mpert] = conj(g11[mpert-k]) + g22[k+mpert] = conj(g22[mpert-k]) + g33[k+mpert] = conj(g33[mpert-k]) + g23[k+mpert] = conj(g23[mpert-k]) + g31[k+mpert] = conj(g31[mpert-k]) + g12[k+mpert] = conj(g12[mpert-k]) end # Tensor contraction with mode coupling (matches Fortran gpeq_cova) for ipert in 1:mpert - xvp_acc = zero(ComplexF64); xvt_acc = zero(ComplexF64); xvz_acc = zero(ComplexF64) - bvp_acc = zero(ComplexF64); bvt_acc = zero(ComplexF64); bvz_acc = zero(ComplexF64) - - for dm in max(1-ipert, -mband):min(mpert-ipert, mband) + xvp_acc = zero(ComplexF64); + xvt_acc = zero(ComplexF64); + xvz_acc = zero(ComplexF64) + bvp_acc = zero(ComplexF64); + bvt_acc = zero(ComplexF64); + bvz_acc = zero(ComplexF64) + + for dm in (1-ipert):(mpert-ipert) jpert = ipert + dm - dmidx = dm + mid + dmidx = dm + mpert # Displacement covariant: ξ_i = g_ij · ξ^j (tensor contraction) xvp_acc += g11[dmidx] * xwp_modes[ipsi, jpert] + g12[dmidx] * xmt_modes[ipsi, jpert] + g31[dmidx] * xmz_modes[ipsi, jpert] @@ -705,7 +708,7 @@ end _build_metric_interp(fc, qty) -> CubicSeriesInterpolant Build a cubic spline interpolant for all Fourier modes of a metric quantity as -a function of ψ. Returns a callable that evaluates all (mband+1) complex +a function of ψ. Returns a callable that evaluates all mpert complex coefficients at arbitrary ψ: `interp(psi) -> Vector{ComplexF64}`. Matches Fortran behaviour where `cspline_eval(metric%cs, psi, 0)` interpolates @@ -713,10 +716,10 @@ the coefficients smoothly, rather than snapping to the nearest grid point. """ function _build_metric_interp(fc::Utilities.FourierCoefficients, qty::Int) npsi = length(fc.xs) - nmodes = fc.mband + 1 + nmodes = fc.mmax + 1 coeffs = Matrix{ComplexF64}(undef, npsi, nmodes) for ipsi in 1:npsi - for m in 0:fc.mband + for m in 0:fc.mmax coeffs[ipsi, m+1] = Utilities.get_complex_coeff(fc, ipsi, m, qty) end end @@ -731,9 +734,10 @@ end Compute physical normal field b_n and displacement xi_n in mode space. Matches Fortran `gpeq_normal`: -- IDFT: reconstruct theta-space functions from mode amplitudes -- Divide by J·|∇ψ|(θ) at each theta point to get physical normal components -- Forward DFT back to mode space + + - IDFT: reconstruct theta-space functions from mode amplitudes + - Divide by J·|∇ψ|(θ) at each theta point to get physical normal components + - Forward DFT back to mode space `xwp_modes` = J·ξ^ψ (Jacobian-weighted from gpeq_contra convolution). `b_psi_modes` = b^ψ (raw, not J-weighted). @@ -753,22 +757,22 @@ function compute_b_n_xi_n_modes( b_psi_modes::Matrix{ComplexF64}, ForceFreeStates_results::OdeState, equil::Equilibrium.PlasmaEquilibrium, - ffs_intr::ForceFreeStatesInternal, + ffs_intr::ForceFreeStatesInternal ) npsi, mpert = size(b_psi_modes) - mlow = ffs_intr.mlow + mlow = ffs_intr.mlow mthsurf = length(equil.rzphi_ys) - 1 ro = equil.ro twopi = 2π - b_n_modes = zeros(ComplexF64, npsi, mpert) + b_n_modes = zeros(ComplexF64, npsi, mpert) xi_n_modes = zeros(ComplexF64, npsi, mpert) # Pre-compute mode indices and DFT phase table m_vals = [mlow + ipert - 1 for ipert in 1:mpert] thetas = [(k - 1) / mthsurf for k in 1:mthsurf] # [0, 1/mthsurf, ..., (mthsurf-1)/mthsurf] # exp(+2πi*m*θ) for IDFT; exp(-2πi*m*θ) for forward DFT - phase_fwd = [exp( twopi * im * m_vals[ipert] * thetas[k]) for k in 1:mthsurf, ipert in 1:mpert] + phase_fwd = [exp(twopi * im * m_vals[ipert] * thetas[k]) for k in 1:mthsurf, ipert in 1:mpert] phase_back = [exp(-twopi * im * m_vals[ipert] * thetas[k]) for k in 1:mthsurf, ipert in 1:mpert] Threads.@threads :static for ipsi in 1:npsi @@ -776,35 +780,35 @@ function compute_b_n_xi_n_modes( hint2d_psi = (Ref(1), Ref(1)) # IDFT: mode space → theta space - bwp_fun = phase_fwd * b_psi_modes[ipsi, :] # [mthsurf] — b^ψ (not J-weighted) - xwp_fun = phase_fwd * xwp_modes[ipsi, :] # [mthsurf] — J·ξ^ψ (J-weighted from gpeq_contra) + bwp_fun = phase_fwd * b_psi_modes[ipsi, :] # [mthsurf] — b^ψ (not J-weighted) + xwp_fun = phase_fwd * xwp_modes[ipsi, :] # [mthsurf] — J·ξ^ψ (J-weighted from gpeq_contra) delpsis = zeros(Float64, mthsurf) - jacs = zeros(Float64, mthsurf) + jacs = zeros(Float64, mthsurf) for k in 1:mthsurf theta = thetas[k] - r2 = equil.rzphi_rsquared((psi, theta); hint=hint2d_psi) - deta = equil.rzphi_offset((psi, theta); hint=hint2d_psi) - jac = equil.rzphi_jac((psi, theta); hint=hint2d_psi) - r2_y = equil.rzphi_rsquared((psi, theta); deriv=DerivOp(0, 1), hint=hint2d_psi) + r2 = equil.rzphi_rsquared((psi, theta); hint=hint2d_psi) + deta = equil.rzphi_offset((psi, theta); hint=hint2d_psi) + jac = equil.rzphi_jac((psi, theta); hint=hint2d_psi) + r2_y = equil.rzphi_rsquared((psi, theta); deriv=DerivOp(0, 1), hint=hint2d_psi) deta_y = equil.rzphi_offset((psi, theta); deriv=DerivOp(0, 1), hint=hint2d_psi) - rfac = sqrt(abs(r2)) - eta = twopi * (theta + deta) - r = ro + rfac * cos(eta) - w11 = (1.0 + deta_y) * twopi^2 * rfac * r / jac - w12 = -r2_y * π * r / (rfac * jac) + rfac = sqrt(abs(r2)) + eta = twopi * (theta + deta) + r = ro + rfac * cos(eta) + w11 = (1.0 + deta_y) * twopi^2 * rfac * r / jac + w12 = -r2_y * π * r / (rfac * jac) delpsi = sqrt(w11^2 + w12^2) delpsis[k] = delpsi - jacs[k] = jac + jacs[k] = jac end # Divide by J·|∇ψ| → physical normal components in theta space (matches Fortran gpeq_normal) jd = jacs .* delpsis - bno_fun = bwp_fun ./ jd - xno_fun = xwp_fun ./ jd + bno_fun = bwp_fun ./ jd + xno_fun = xwp_fun ./ jd # Forward DFT: theta space → mode space (1/mthsurf normalization matches Fortran iscdftf). # Must use transpose (not adjoint) so the phase is exp(-2πi·m·θ), not exp(+2πi·m·θ). - b_n_modes[ipsi, :] = (transpose(phase_back) * bno_fun) ./ mthsurf + b_n_modes[ipsi, :] = (transpose(phase_back) * bno_fun) ./ mthsurf xi_n_modes[ipsi, :] = (transpose(phase_back) * xno_fun) ./ mthsurf end @@ -902,7 +906,7 @@ function _build_rzphi_geometry( doff_dpsi = draw[1*mtheta+itheta] # d(deta)/dψ rfac = sqrt(max(0.0, r2)) - eta = 2π * (theta + deta) + eta = 2π * (theta + deta) s, c = sincos(eta) R_here = R0 + rfac * c @@ -912,7 +916,10 @@ function _build_rzphi_geometry( v21 = dr2_dtheta / (2 * rfac) v22 = (1 + doff_dtheta) * 2π * rfac else - v11 = 0.0; v12 = 0.0; v21 = 0.0; v22 = 0.0 + v11 = 0.0; + v12 = 0.0; + v21 = 0.0; + v22 = 0.0 end t11[itheta, ipsi] = c * v11 - s * v12 @@ -952,8 +959,8 @@ function _apply_rzphi_transform( ) npsi, mpert = size(psi_input) - R_modes = zeros(ComplexF64, npsi, mpert) - Z_modes = zeros(ComplexF64, npsi, mpert) + R_modes = zeros(ComplexF64, npsi, mpert) + Z_modes = zeros(ComplexF64, npsi, mpert) phi_modes = zeros(ComplexF64, npsi, mpert) # Per-thread theta-space buffers; the immutable `ft` functor and `geom` are shared read-only. @@ -966,9 +973,9 @@ function _apply_rzphi_transform( phi_fun = buf.P # Inverse DFT: modes → theta-space - psi_fun = Utilities.FourierTransforms.inverse(ft, view(psi_input, ipsi, :)) + psi_fun = Utilities.FourierTransforms.inverse(ft, view(psi_input, ipsi, :)) theta_fn = Utilities.FourierTransforms.inverse(ft, view(theta_input, ipsi, :)) - zeta_fn = Utilities.FourierTransforms.inverse(ft, view(cova_zeta_input, ipsi, :)) + zeta_fn = Utilities.FourierTransforms.inverse(ft, view(cova_zeta_input, ipsi, :)) # Pointwise transformation (Fortran gpeq_rzphi, gpeq.f:484-489) for itheta in 1:mtheta @@ -988,8 +995,8 @@ function _apply_rzphi_transform( end # Forward DFT: theta-space → modes - R_modes[ipsi, :] .= ft(R_fun) - Z_modes[ipsi, :] .= ft(Z_fun) + R_modes[ipsi, :] .= ft(R_fun) + Z_modes[ipsi, :] .= ft(Z_fun) phi_modes[ipsi, :] .= ft(phi_fun) end diff --git a/src/Utilities/FourierCoefficients.jl b/src/Utilities/FourierCoefficients.jl index 8c87094be..9be3026cf 100644 --- a/src/Utilities/FourierCoefficients.jl +++ b/src/Utilities/FourierCoefficients.jl @@ -30,14 +30,14 @@ Use this when you only need to access coefficients at original grid points. # Fields - `xs::Vector{Float64}`: Radial coordinates - - `mband::Int`: Number of Fourier modes (0 to mband inclusive) + - `mmax::Int`: Highest retained poloidal Fourier mode (modes 0:mmax inclusive) - `nqty::Int`: Number of quantities - `cos_coeffs::Array{Float64,3}`: Cosine coefficients (npsi × nmodes × nqty) - `sin_coeffs::Array{Float64,3}`: Sine coefficients (npsi × nmodes × nqty) """ struct FourierCoefficients xs::Vector{Float64} - mband::Int + mmax::Int nqty::Int cos_coeffs::Array{Float64,3} sin_coeffs::Array{Float64,3} @@ -53,7 +53,7 @@ function empty_FourierCoefficients() end """ - FourierCoefficients(xs, ys, fs, mband) + FourierCoefficients(xs, ys, fs, mmax) Compute Fourier coefficients via FFT without creating splines. @@ -62,15 +62,15 @@ Compute Fourier coefficients via FFT without creating splines. - `xs::Vector{Float64}`: Radial coordinates - `ys::Vector{Float64}`: Poloidal coordinates (periodic domain) - `fs::Array{Float64,3}`: Function values (npsi × ntheta × nqty) - - `mband::Int`: Number of Fourier modes to retain + - `mmax::Int`: Highest poloidal Fourier mode to retain """ function FourierCoefficients(xs::Vector{Float64}, ys::Vector{Float64}, - fs::Array{Float64,3}, mband::Int) + fs::Array{Float64,3}, mmax::Int) npsi, ny_full, nqty = size(fs) @assert length(xs) == npsi "xs length must match first dimension of fs" @assert length(ys) == ny_full "ys length must match second dimension of fs" - @assert mband >= 0 "mband must be non-negative" + @assert mmax >= 0 "mmax must be non-negative" # Drop periodic-duplicate endpoint before FFT to match Fortran fspline_fit_2 # (equil/fspline.f:293 uses `f = fst%fs(:, 0:my-1, iq)`). The equilibrium θ-grids @@ -78,13 +78,13 @@ function FourierCoefficients(xs::Vector{Float64}, ys::Vector{Float64}, # including the duplicate biases the DC coefficient by ~(f(0) − mean)/N. has_duplicate = ny_full > 1 && isapprox(ys[end] - ys[1], 2π; rtol=1e-10) ntheta = has_duplicate ? ny_full - 1 : ny_full - fs_view = has_duplicate ? view(fs, :, 1:ntheta, :) : fs + fs_view = has_duplicate ? view(fs,:,(1:ntheta),:) : fs - # Clamp mband to Nyquist limit + # Clamp to Nyquist limit nyquist_limit = ntheta ÷ 2 - actual_mband = min(mband, nyquist_limit) + actual_mmax = min(mmax, nyquist_limit) - nmodes = actual_mband + 1 + nmodes = actual_mmax + 1 # Compute Fourier coefficients using batched FFT fs_reshaped = reshape(permutedims(fs_view, (2, 1, 3)), ntheta, npsi * nqty) @@ -103,14 +103,14 @@ function FourierCoefficients(xs::Vector{Float64}, ys::Vector{Float64}, @inbounds cos_coeffs[ipsi, 1, iq] = real(fft_col[1]) / ntheta # Higher modes - @inbounds for m in 1:actual_mband + @inbounds for m in 1:actual_mmax cos_coeffs[ipsi, m+1, iq] = 2 * real(fft_col[m+1]) / ntheta sin_coeffs[ipsi, m+1, iq] = -2 * imag(fft_col[m+1]) / ntheta end end end - FourierCoefficients(xs, actual_mband, nqty, cos_coeffs, sin_coeffs) + FourierCoefficients(xs, actual_mmax, nqty, cos_coeffs, sin_coeffs) end """ @@ -131,7 +131,7 @@ This function returns the normalized FFT coefficient (FFT/ntheta): function get_complex_coeff(fc::FourierCoefficients, ipsi::Int, mode::Int, qty::Int) @boundscheck begin @assert 1 <= ipsi <= length(fc.xs) "ipsi out of bounds" - @assert 0 <= mode <= fc.mband "mode out of bounds" + @assert 0 <= mode <= fc.mmax "mode out of bounds" @assert 1 <= qty <= fc.nqty "qty out of bounds" end if mode == 0 @@ -145,15 +145,15 @@ end """ get_complex_coeffs!(out, fc::FourierCoefficients, ipsi, qty) -Fill vector with normalized complex FFT coefficients for modes 0:mband. +Fill vector with normalized complex FFT coefficients for modes 0:mmax. """ function get_complex_coeffs!(out::AbstractVector{ComplexF64}, fc::FourierCoefficients, ipsi::Int, qty::Int) - nmodes = fc.mband + 1 + nmodes = fc.mmax + 1 @assert length(out) >= nmodes "output vector too short" @inbounds out[1] = complex(fc.cos_coeffs[ipsi, 1, qty], 0.0) - @inbounds for m in 1:fc.mband + @inbounds for m in 1:fc.mmax out[m+1] = complex(fc.cos_coeffs[ipsi, m+1, qty] / 2, -fc.sin_coeffs[ipsi, m+1, qty] / 2) end diff --git a/test/runtests_fouriertransforms.jl b/test/runtests_fouriertransforms.jl index a018b5771..a6fd77f22 100644 --- a/test/runtests_fouriertransforms.jl +++ b/test/runtests_fouriertransforms.jl @@ -174,7 +174,7 @@ end @testset "empty_FourierCoefficients" begin fc = empty_FourierCoefficients() @test isempty(fc.xs) - @test fc.mband == 0 + @test fc.mmax == 0 @test fc.nqty == 0 @test size(fc.cos_coeffs) == (0, 1, 0) @test size(fc.sin_coeffs) == (0, 1, 0) diff --git a/test/runtests_parallel_integration.jl b/test/runtests_parallel_integration.jl index 96db205e8..fc4e592b0 100644 --- a/test/runtests_parallel_integration.jl +++ b/test/runtests_parallel_integration.jl @@ -17,19 +17,19 @@ using TOML # Apply identity propagator to an arbitrary state odet = GeneralizedPerturbedEquilibrium.ForceFreeStates.OdeState(N, 10, 5, 0) - u1_in = [1.0+0.5im 0.2im 0.0; - 0.1+0.1im 1.2+0.1im 0.0; - 0.0im 0.0 0.9+0.3im] - u2_in = [0.8+0.1im 0.1im 0.0; - 0.0im 1.0+0.2im 0.1; - 0.1im 0.0 1.1+0.0im] + u1_in = [1.0+0.5im 0.2im 0.0; + 0.1+0.1im 1.2+0.1im 0.0; + 0.0im 0.0 0.9+0.3im] + u2_in = [0.8+0.1im 0.1im 0.0; + 0.0im 1.0+0.2im 0.1; + 0.1im 0.0 1.1+0.0im] odet.u[:, :, 1] .= u1_in odet.u[:, :, 2] .= u2_in GeneralizedPerturbedEquilibrium.ForceFreeStates.apply_propagator!(odet, prop) - @test odet.u[:, :, 1] ≈ u1_in rtol=1e-12 - @test odet.u[:, :, 2] ≈ u2_in rtol=1e-12 + @test odet.u[:, :, 1] ≈ u1_in rtol=1e-12 + @test odet.u[:, :, 2] ≈ u2_in rtol=1e-12 end @testset "apply_propagator! linearity" begin @@ -38,12 +38,12 @@ using TOML prop = GeneralizedPerturbedEquilibrium.ForceFreeStates.ChunkPropagator(N) # Fill block_upper_ic and block_lower_ic with random data - rng_upper = [1.1+0.2im 0.1im 0.05; - 0.0im 0.9+0.3im 0.1; - 0.2+0.1im 0.0 1.0+0.1im] - rng_lower = [0.8+0.1im 0.1im 0.0; - 0.0im 1.2+0.2im 0.1; - 0.0im 0.1 0.9+0.1im] + rng_upper = [1.1+0.2im 0.1im 0.05; + 0.0im 0.9+0.3im 0.1; + 0.2+0.1im 0.0 1.0+0.1im] + rng_lower = [0.8+0.1im 0.1im 0.0; + 0.0im 1.2+0.2im 0.1; + 0.0im 0.1 0.9+0.1im] prop.block_upper_ic[:, :, 1] .= rng_upper prop.block_upper_ic[:, :, 2] .= 0.5 * rng_upper prop.block_lower_ic[:, :, 1] .= 0.3 * rng_lower @@ -65,8 +65,8 @@ using TOML u1_expected = U1_upper * u1_in + U1_lower * u2_in u2_expected = U2_upper * u1_in + U2_lower * u2_in - @test odet.u[:, :, 1] ≈ u1_expected rtol=1e-12 - @test odet.u[:, :, 2] ≈ u2_expected rtol=1e-12 + @test odet.u[:, :, 1] ≈ u1_expected rtol=1e-12 + @test odet.u[:, :, 2] ≈ u2_expected rtol=1e-12 end @testset "apply_propagator_inverse! is inverse of apply_propagator!" begin @@ -77,19 +77,19 @@ using TOML prop = GeneralizedPerturbedEquilibrium.ForceFreeStates.ChunkPropagator(N) # Near-identity blocks guarantee the 2N×2N matrix [A B; C D] is invertible - A = I(N) .+ 0.15 * [1.0+0.2im 0.1im 0.05; 0.0im 0.9+0.3im 0.1; 0.2+0.1im 0.0 1.0+0.1im] - B = 0.1 * [0.8+0.1im 0.1im 0.0; 0.0im 1.2+0.2im 0.1; 0.0im 0.1 0.9+0.1im] - C = 0.1 * [0.5+0.1im 0.0im 0.1; 0.1im 0.8+0.2im 0.0; 0.0im 0.0 0.7+0.1im] - D = I(N) .+ 0.15 * [0.9+0.1im 0.0im 0.05; 0.0im 1.0+0.2im 0.0; 0.1+0.1im 0.0 0.95+0.1im] + A = I(N) .+ 0.15 * [1.0+0.2im 0.1im 0.05; 0.0im 0.9+0.3im 0.1; 0.2+0.1im 0.0 1.0+0.1im] + B = 0.1 * [0.8+0.1im 0.1im 0.0; 0.0im 1.2+0.2im 0.1; 0.0im 0.1 0.9+0.1im] + C = 0.1 * [0.5+0.1im 0.0im 0.1; 0.1im 0.8+0.2im 0.0; 0.0im 0.0 0.7+0.1im] + D = I(N) .+ 0.15 * [0.9+0.1im 0.0im 0.05; 0.0im 1.0+0.2im 0.0; 0.1+0.1im 0.0 0.95+0.1im] prop.block_upper_ic[:, :, 1] .= A prop.block_lower_ic[:, :, 1] .= B prop.block_upper_ic[:, :, 2] .= C prop.block_lower_ic[:, :, 2] .= D - u1_in = [1.0+0.5im 0.2im 0.0; - 0.1+0.1im 1.2+0.1im 0.0; - 0.0im 0.0 0.9+0.3im] + u1_in = [1.0+0.5im 0.2im 0.0; + 0.1+0.1im 1.2+0.1im 0.0; + 0.0im 0.0 0.9+0.3im] u2_in = I(N) .+ 0.1im * ones(N, N) odet = GeneralizedPerturbedEquilibrium.ForceFreeStates.OdeState(N, 10, 5, 0) @@ -100,8 +100,8 @@ using TOML GeneralizedPerturbedEquilibrium.ForceFreeStates.apply_propagator_inverse!(odet, prop) GeneralizedPerturbedEquilibrium.ForceFreeStates.apply_propagator!(odet, prop) - @test odet.u[:, :, 1] ≈ u1_in rtol=1e-12 - @test odet.u[:, :, 2] ≈ u2_in rtol=1e-12 + @test odet.u[:, :, 1] ≈ u1_in rtol=1e-12 + @test odet.u[:, :, 2] ≈ u2_in rtol=1e-12 end @testset "balance_integration_chunks produces target count" begin @@ -116,15 +116,16 @@ using TOML eq_config = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(inputs["Equilibrium"], ex) equil = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(eq_config) GeneralizedPerturbedEquilibrium.ForceFreeStates.sing_lim!(intr, ctrl, equil) - intr.nlow = ctrl.nn_low; intr.nhigh = ctrl.nn_high; intr.npert = 1 + intr.nlow = ctrl.nn_low; + intr.nhigh = ctrl.nn_high; + intr.npert = 1 GeneralizedPerturbedEquilibrium.ForceFreeStates.sing_find!(intr, equil) intr.mlow = min(intr.nlow * equil.params.qmin, 0) - 4 - ctrl.delta_mlow intr.mhigh = trunc(Int, intr.nhigh * equil.params.qmax) + ctrl.delta_mhigh intr.mpert = intr.mhigh - intr.mlow + 1 - intr.mband = intr.mpert - 1 intr.numpert_total = intr.mpert * intr.npert - metric = GeneralizedPerturbedEquilibrium.ForceFreeStates.make_metric(equil; mband=intr.mband) + metric = GeneralizedPerturbedEquilibrium.ForceFreeStates.make_metric(equil, intr.mpert) ffit = GeneralizedPerturbedEquilibrium.ForceFreeStates.make_matrix(equil, intr, metric) odet = GeneralizedPerturbedEquilibrium.ForceFreeStates.OdeState(intr.numpert_total, ctrl.numsteps_init, ctrl.numunorms_init, intr.msing) @@ -153,7 +154,7 @@ using TOML # gap of ≈2·singfac_min/|n·q1| between the pre-crossing and post-crossing intervals. for i in eachindex(balanced)[2:end] if !balanced[i-1].needs_crossing - @test balanced[i].psi_start ≈ balanced[i-1].psi_end rtol=1e-10 + @test balanced[i].psi_start ≈ balanced[i-1].psi_end rtol=1e-10 else # Inner-layer gap: post-crossing chunk starts AFTER the rational surface @test balanced[i].psi_start > balanced[i-1].psi_end @@ -179,15 +180,16 @@ using TOML eq_config = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(inputs["Equilibrium"], ex) equil = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(eq_config) GeneralizedPerturbedEquilibrium.ForceFreeStates.sing_lim!(intr, ctrl, equil) - intr.nlow = ctrl.nn_low; intr.nhigh = ctrl.nn_high; intr.npert = 1 + intr.nlow = ctrl.nn_low; + intr.nhigh = ctrl.nn_high; + intr.npert = 1 GeneralizedPerturbedEquilibrium.ForceFreeStates.sing_find!(intr, equil) intr.mlow = min(intr.nlow * equil.params.qmin, 0) - 4 - ctrl.delta_mlow intr.mhigh = trunc(Int, intr.nhigh * equil.params.qmax) + ctrl.delta_mhigh intr.mpert = intr.mhigh - intr.mlow + 1 - intr.mband = intr.mpert - 1 intr.numpert_total = intr.mpert * intr.npert - metric = GeneralizedPerturbedEquilibrium.ForceFreeStates.make_metric(equil; mband=intr.mband) + metric = GeneralizedPerturbedEquilibrium.ForceFreeStates.make_metric(equil, intr.mpert) ffit = GeneralizedPerturbedEquilibrium.ForceFreeStates.make_matrix(equil, intr, metric) odet = GeneralizedPerturbedEquilibrium.ForceFreeStates.OdeState(intr.numpert_total, ctrl.numsteps_init, ctrl.numunorms_init, intr.msing) @@ -241,14 +243,15 @@ using TOML intr.wall_settings = GeneralizedPerturbedEquilibrium.Vacuum.WallShapeSettings(; (Symbol(k) => v for (k, v) in inputs["Wall"])...) GeneralizedPerturbedEquilibrium.ForceFreeStates.sing_lim!(intr, ctrl, equil) - intr.nlow = ctrl.nn_low; intr.nhigh = ctrl.nn_high; intr.npert = 1 + intr.nlow = ctrl.nn_low; + intr.nhigh = ctrl.nn_high; + intr.npert = 1 GeneralizedPerturbedEquilibrium.ForceFreeStates.sing_find!(intr, equil) intr.mlow = min(intr.nlow * equil.params.qmin, 0) - 4 - ctrl.delta_mlow intr.mhigh = trunc(Int, intr.nhigh * equil.params.qmax) + ctrl.delta_mhigh intr.mpert = intr.mhigh - intr.mlow + 1 - intr.mband = intr.mpert - 1 intr.numpert_total = intr.mpert * intr.npert - metric = GeneralizedPerturbedEquilibrium.ForceFreeStates.make_metric(equil; mband=intr.mband) + metric = GeneralizedPerturbedEquilibrium.ForceFreeStates.make_metric(equil, intr.mpert) ffit = GeneralizedPerturbedEquilibrium.ForceFreeStates.make_matrix(equil, intr, metric) odet, _, _, _ = GeneralizedPerturbedEquilibrium.ForceFreeStates.eulerlagrange_integration(ctrl, equil, ffit, intr) vac = GeneralizedPerturbedEquilibrium.ForceFreeStates.free_run!(odet, ctrl, equil, ffit, intr) @@ -289,14 +292,15 @@ using TOML intr.wall_settings = GeneralizedPerturbedEquilibrium.Vacuum.WallShapeSettings(; (Symbol(k) => v for (k, v) in inputs["Wall"])...) GeneralizedPerturbedEquilibrium.ForceFreeStates.sing_lim!(intr, ctrl, equil) - intr.nlow = ctrl.nn_low; intr.nhigh = ctrl.nn_high; intr.npert = 1 + intr.nlow = ctrl.nn_low; + intr.nhigh = ctrl.nn_high; + intr.npert = 1 GeneralizedPerturbedEquilibrium.ForceFreeStates.sing_find!(intr, equil) intr.mlow = min(intr.nlow * equil.params.qmin, 0) - 4 - ctrl.delta_mlow intr.mhigh = trunc(Int, intr.nhigh * equil.params.qmax) + ctrl.delta_mhigh intr.mpert = intr.mhigh - intr.mlow + 1 - intr.mband = intr.mpert - 1 intr.numpert_total = intr.mpert * intr.npert - metric = GeneralizedPerturbedEquilibrium.ForceFreeStates.make_metric(equil; mband=intr.mband) + metric = GeneralizedPerturbedEquilibrium.ForceFreeStates.make_metric(equil, intr.mpert) ffit = GeneralizedPerturbedEquilibrium.ForceFreeStates.make_matrix(equil, intr, metric) odet, _, _, _ = GeneralizedPerturbedEquilibrium.ForceFreeStates.eulerlagrange_integration(ctrl, equil, ffit, intr) vac = GeneralizedPerturbedEquilibrium.ForceFreeStates.free_run!(odet, ctrl, equil, ffit, intr) @@ -345,15 +349,16 @@ using TOML eq_config = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(inputs["Equilibrium"], ex) equil = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(eq_config) GeneralizedPerturbedEquilibrium.ForceFreeStates.sing_lim!(intr, ctrl, equil) - intr.nlow = ctrl.nn_low; intr.nhigh = ctrl.nn_high; intr.npert = 1 + intr.nlow = ctrl.nn_low; + intr.nhigh = ctrl.nn_high; + intr.npert = 1 GeneralizedPerturbedEquilibrium.ForceFreeStates.sing_find!(intr, equil) intr.mlow = min(intr.nlow * equil.params.qmin, 0) - 4 - ctrl.delta_mlow intr.mhigh = trunc(Int, intr.nhigh * equil.params.qmax) + ctrl.delta_mhigh intr.mpert = intr.mhigh - intr.mlow + 1 - intr.mband = intr.mpert - 1 intr.numpert_total = intr.mpert * intr.npert - metric = GeneralizedPerturbedEquilibrium.ForceFreeStates.make_metric(equil; mband=intr.mband) + metric = GeneralizedPerturbedEquilibrium.ForceFreeStates.make_metric(equil, intr.mpert) ffit = GeneralizedPerturbedEquilibrium.ForceFreeStates.make_matrix(equil, intr, metric) # Use the first chunk from chunk_el_integration_bounds: guaranteed rational-free interior @@ -410,14 +415,15 @@ using TOML intr.wall_settings = GeneralizedPerturbedEquilibrium.Vacuum.WallShapeSettings(; (Symbol(k) => v for (k, v) in inputs["Wall"])...) GeneralizedPerturbedEquilibrium.ForceFreeStates.sing_lim!(intr, ctrl, equil) - intr.nlow = ctrl.nn_low; intr.nhigh = ctrl.nn_high; intr.npert = 1 + intr.nlow = ctrl.nn_low; + intr.nhigh = ctrl.nn_high; + intr.npert = 1 GeneralizedPerturbedEquilibrium.ForceFreeStates.sing_find!(intr, equil) intr.mlow = min(intr.nlow * equil.params.qmin, 0) - 4 - ctrl.delta_mlow intr.mhigh = trunc(Int, intr.nhigh * equil.params.qmax) + ctrl.delta_mhigh intr.mpert = intr.mhigh - intr.mlow + 1 - intr.mband = intr.mpert - 1 intr.numpert_total = intr.mpert * intr.npert - metric = GeneralizedPerturbedEquilibrium.ForceFreeStates.make_metric(equil; mband=intr.mband) + metric = GeneralizedPerturbedEquilibrium.ForceFreeStates.make_metric(equil, intr.mpert) ffit = GeneralizedPerturbedEquilibrium.ForceFreeStates.make_matrix(equil, intr, metric) odet, _, _, _ = GeneralizedPerturbedEquilibrium.ForceFreeStates.eulerlagrange_integration(ctrl, equil, ffit, intr) return odet @@ -435,24 +441,24 @@ using TOML @test length(odet_a.q_store) == length(odet_b.q_store) @test size(odet_a.u_store) == size(odet_b.u_store) @test size(odet_a.ud_store) == size(odet_b.ud_store) - @test maximum(abs.(odet_a.psi_store .- odet_b.psi_store)) == 0.0 - @test maximum(abs.(odet_a.q_store .- odet_b.q_store)) == 0.0 - @test maximum(abs.(odet_a.u_store .- odet_b.u_store)) == 0.0 - @test maximum(abs.(odet_a.ud_store .- odet_b.ud_store)) == 0.0 - @test maximum(abs.(odet_a.crit_store .- odet_b.crit_store)) == 0.0 + @test maximum(abs.(odet_a.psi_store .- odet_b.psi_store)) == 0.0 + @test maximum(abs.(odet_a.q_store .- odet_b.q_store)) == 0.0 + @test maximum(abs.(odet_a.u_store .- odet_b.u_store)) == 0.0 + @test maximum(abs.(odet_a.ud_store .- odet_b.ud_store)) == 0.0 + @test maximum(abs.(odet_a.crit_store .- odet_b.crit_store)) == 0.0 end @testset "Solovev (small N)" begin ex = joinpath(@__DIR__, "test_data", "regression_solovev_ideal_example") odet_std = run_and_capture(ex, false) - odet_par = run_and_capture(ex, true; populate_dense_xi=true) + odet_par = run_and_capture(ex, true; populate_dense_xi=true) assert_bit_identical(odet_std, odet_par) end @testset "DIIID-like (large N)" begin ex = joinpath(@__DIR__, "..", "examples", "DIIID-like_ideal_example") odet_std = run_and_capture(ex, false) - odet_par = run_and_capture(ex, true; populate_dense_xi=true) + odet_par = run_and_capture(ex, true; populate_dense_xi=true) assert_bit_identical(odet_std, odet_par) end @@ -464,8 +470,8 @@ using TOML # test above is meaningful — it's NOT trivially passing because # both modes accidentally produce the same sparse data. ex = joinpath(@__DIR__, "test_data", "regression_solovev_ideal_example") - odet_std = run_and_capture(ex, false) - odet_sparse = run_and_capture(ex, true; populate_dense_xi=false) + odet_std = run_and_capture(ex, false) + odet_sparse = run_and_capture(ex, true; populate_dense_xi=false) @test odet_sparse.step < odet_std.step # ud_store entries inside FM chunks are left at the @kwdef # `undef` initial value when populate_dense_xi=false; ensure the @@ -492,14 +498,15 @@ using TOML intr.wall_settings = GeneralizedPerturbedEquilibrium.Vacuum.WallShapeSettings(; (Symbol(k) => v for (k, v) in inputs["Wall"])...) GeneralizedPerturbedEquilibrium.ForceFreeStates.sing_lim!(intr, ctrl, equil) - intr.nlow = ctrl.nn_low; intr.nhigh = ctrl.nn_high; intr.npert = 1 + intr.nlow = ctrl.nn_low; + intr.nhigh = ctrl.nn_high; + intr.npert = 1 GeneralizedPerturbedEquilibrium.ForceFreeStates.sing_find!(intr, equil) intr.mlow = min(intr.nlow * equil.params.qmin, 0) - 4 - ctrl.delta_mlow intr.mhigh = trunc(Int, intr.nhigh * equil.params.qmax) + ctrl.delta_mhigh intr.mpert = intr.mhigh - intr.mlow + 1 - intr.mband = intr.mpert - 1 intr.numpert_total = intr.mpert * intr.npert - metric = GeneralizedPerturbedEquilibrium.ForceFreeStates.make_metric(equil; mband=intr.mband) + metric = GeneralizedPerturbedEquilibrium.ForceFreeStates.make_metric(equil, intr.mpert) ffit = GeneralizedPerturbedEquilibrium.ForceFreeStates.make_matrix(equil, intr, metric) odet, fm_propagators, fm_chunks, fm_S_left = GeneralizedPerturbedEquilibrium.ForceFreeStates.eulerlagrange_integration(ctrl, equil, ffit, intr) diff --git a/test/runtests_riccati.jl b/test/runtests_riccati.jl index e55e0088d..eb06e0866 100644 --- a/test/runtests_riccati.jl +++ b/test/runtests_riccati.jl @@ -10,12 +10,13 @@ function make_solovev_intr(inputs, ctrl, equil, ex) intr.wall_settings = GeneralizedPerturbedEquilibrium.Vacuum.WallShapeSettings(; (Symbol(k) => v for (k, v) in inputs["Wall"])...) FFS.sing_lim!(intr, ctrl, equil) - intr.nlow = ctrl.nn_low; intr.nhigh = ctrl.nn_high; intr.npert = 1 + intr.nlow = ctrl.nn_low; + intr.nhigh = ctrl.nn_high; + intr.npert = 1 FFS.sing_find!(intr, equil) - intr.mlow = min(intr.nlow * equil.params.qmin, 0) - 4 - ctrl.delta_mlow + intr.mlow = min(intr.nlow * equil.params.qmin, 0) - 4 - ctrl.delta_mlow intr.mhigh = trunc(Int, intr.nhigh * equil.params.qmax) + ctrl.delta_mhigh intr.mpert = intr.mhigh - intr.mlow + 1 - intr.mband = intr.mpert - 1 intr.numpert_total = intr.mpert * intr.npert return intr end @@ -27,10 +28,10 @@ end @testset "renormalize_riccati_inplace!" begin N = 4 # Build a random (U₁, U₂) pair and verify renorm gives S = U₁·U₂⁻¹ with U₂_new = I - rng = [1.0+0.5im 0.2im 0.1 0.3im; - 0.0 1.2+0.1im 0.0im 0.2; - 0.1+0.1im 0.0 0.9+0.3im 0.1im; - 0.0im 0.2 0.0 1.1+0.2im] + rng = [1.0+0.5im 0.2im 0.1 0.3im; + 0.0 1.2+0.1im 0.0im 0.2; + 0.1+0.1im 0.0 0.9+0.3im 0.1im; + 0.0im 0.2 0.0 1.1+0.2im] U1 = rng .+ 0.5*I(N) U2 = 0.5*rng .+ I(N) # near-identity to ensure invertibility @@ -43,15 +44,15 @@ end FFS.renormalize_riccati_inplace!(u, N) @test u[:, :, 2] ≈ I(N) - @test u[:, :, 1] ≈ S_expected rtol=1e-12 + @test u[:, :, 1] ≈ S_expected rtol=1e-12 end @testset "renormalize_riccati_inplace! idempotent" begin N = 3 # If U₂ = I already, renorm should leave u unchanged - S = [1.0+0.5im 0.2im 0.1; - 0.0im 1.2+0.1im 0.0; - 0.1+0.1im 0.0 0.9+0.3im] + S = [1.0+0.5im 0.2im 0.1; + 0.0im 1.2+0.1im 0.0; + 0.1+0.1im 0.0 0.9+0.3im] u = zeros(ComplexF64, N, N, 2) u[:, :, 1] .= S u[:, :, 2] .= I(N) @@ -59,14 +60,14 @@ end FFS.renormalize_riccati_inplace!(u, N) @test u[:, :, 2] ≈ I(N) - @test u[:, :, 1] ≈ S rtol=1e-12 + @test u[:, :, 1] ≈ S rtol=1e-12 end @testset "renormalize_riccati! (OdeState)" begin N = 3 - rng = [1.0+0.5im 0.2im 0.1; - 0.0im 1.2+0.1im 0.0; - 0.1+0.1im 0.0 0.9+0.3im] + rng = [1.0+0.5im 0.2im 0.1; + 0.0im 1.2+0.1im 0.0; + 0.1+0.1im 0.0 0.9+0.3im] U1 = rng .+ 0.5*I(N) U2 = 0.2*rng .+ I(N) @@ -80,7 +81,7 @@ end FFS.renormalize_riccati!(odet, intr) @test odet.u[:, :, 2] ≈ I(N) - @test odet.u[:, :, 1] ≈ S_expected rtol=1e-12 + @test odet.u[:, :, 1] ≈ S_expected rtol=1e-12 end # ── Shared Solovev setup ────────────────────────────────────────────────── @@ -98,15 +99,15 @@ end inputs = TOML.parsefile(joinpath(ex, "gpec.toml")) inputs["ForceFreeStates"]["verbose"] = false - ctrl = FFS.ForceFreeStatesControl(; - (Symbol(k) => v for (k, v) in inputs["ForceFreeStates"])...) + ctrl = FFS.ForceFreeStatesControl(; + (Symbol(k) => v for (k, v) in inputs["ForceFreeStates"])...) equil = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium( - GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(inputs["Equilibrium"], ex)) + GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(inputs["Equilibrium"], ex)) intr_tmp = make_solovev_intr(inputs, ctrl, equil, ex) - metric = FFS.make_metric(equil; mband=intr_tmp.mband) - ffit = FFS.make_matrix(equil, intr_tmp, metric) - N = intr_tmp.numpert_total + metric = FFS.make_metric(equil, intr_tmp.mpert) + ffit = FFS.make_matrix(equil, intr_tmp, metric) + N = intr_tmp.numpert_total # Riccati integration intr_ric = make_solovev_intr(inputs, ctrl, equil, ex) @@ -117,14 +118,14 @@ end delta_prime_inline = [copy(intr_ric.sing[s].delta_prime) for s in 1:intr_ric.msing] vac_ric = FFS.free_run!(odet_ric, ctrl, equil, ffit, intr_ric) - et_ric = real(vac_ric.et[1]) + et_ric = real(vac_ric.et[1]) # Standard integration (needed only for energy comparison). eulerlagrange_integration # returns (odet, propagators, chunks, S_at_surface_left); only odet is used here. intr_std = make_solovev_intr(inputs, ctrl, equil, ex) odet_std, _, _, _ = FFS.eulerlagrange_integration(ctrl, equil, ffit, intr_std) - vac_std = FFS.free_run!(odet_std, ctrl, equil, ffit, intr_std) - et_std = real(vac_std.et[1]) + vac_std = FFS.free_run!(odet_std, ctrl, equil, ffit, intr_std) + et_std = real(vac_std.et[1]) # ───────────────────────────────────────────────────────────────────────── @@ -148,7 +149,7 @@ end @testset "Riccati end state has U₂ ≈ I" begin # After riccati_eulerlagrange_integration, odet.u[:,:,2] should be identity # (canonical Riccati convention after final renorm) - @test odet_ric.u[:, :, 2] ≈ I(N) rtol=1e-10 + @test odet_ric.u[:, :, 2] ≈ I(N) rtol=1e-10 end @testset "riccati_der! formula — Glasser 2018 Eq. 19" begin @@ -175,28 +176,31 @@ end S = (A + A') / 2 # Manual RHS: w†·F̄⁻¹·w − S·Ḡ·S - L = zeros(ComplexF64, N, N) + L = zeros(ComplexF64, N, N) Kmat = zeros(ComplexF64, N, N) Gmat = zeros(ComplexF64, N, N) - ffit.fmats_lower(vec(L), psi; hint=ffit._hint) + ffit.fmats_lower(vec(L), psi; hint=ffit._hint) ffit.kmats(vec(Kmat), psi; hint=ffit._hint) ffit.gmats(vec(Gmat), psi; hint=ffit._hint) - q = equil.profiles.q_spline(psi) + q = equil.profiles.q_spline(psi) singfac = vec(1.0 ./ ((intr_ric.mlow:intr_ric.mhigh) .- - q .* (intr_ric.nlow:intr_ric.nhigh)')) + q .* (intr_ric.nlow:intr_ric.nhigh)')) w = -Kmat * S - for i in 1:N; w[i, i] += singfac[i]; end + for i in 1:N + ; + w[i, i] += singfac[i]; + end v = copy(w) ldiv!(LowerTriangular(L), v) ldiv!(UpperTriangular(L'), v) dS_manual = adjoint(w) * v - S * Gmat * S # riccati_der! RHS - u_ric = zeros(ComplexF64, N, N, 2) + u_ric = zeros(ComplexF64, N, N, 2) du_ric = zeros(ComplexF64, N, N, 2) u_ric[:, :, 1] .= S u_ric[:, :, 2] .= Matrix{ComplexF64}(I, N, N) - dummy = FFS.IntegrationChunk(psi, psi, false, 0, 1) + dummy = FFS.IntegrationChunk(psi, psi, false, 0, 1) params = (ctrl, equil, ffit, intr_ric, odet_tmp, dummy) FFS.riccati_der!(du_ric, u_ric, params, psi) diff --git a/test/runtests_sing.jl b/test/runtests_sing.jl index 45ba17ca7..f0ebe1ec1 100644 --- a/test/runtests_sing.jl +++ b/test/runtests_sing.jl @@ -127,7 +127,7 @@ using FastInterpolations: cubic_interp, CubicFit, LinearBinarySearch, Series, Ex odet.u[:, :, 1] .= umat_p1; odet.u[:, :, 2] .= umat_p2 - ffit = GeneralizedPerturbedEquilibrium.ForceFreeStates.FourFitVars(; mpert=intr.numpert_total, mband=intr.mband, numpert_total=intr.numpert_total) + ffit = GeneralizedPerturbedEquilibrium.ForceFreeStates.FourFitVars(; mpert=intr.numpert_total, numpert_total=intr.numpert_total) ffit.amats = cubic_interp(psifac_dummy, Series(reshape(amats, points, :)); ffit.itp_opts...) ffit.bmats = cubic_interp(psifac_dummy, Series(reshape(bmats, points, :)); ffit.itp_opts...) ffit.cmats = cubic_interp(psifac_dummy, Series(reshape(cmats, points, :)); ffit.itp_opts...) diff --git a/test/runtests_utilities.jl b/test/runtests_utilities.jl index 026d399dc..43fa8d781 100644 --- a/test/runtests_utilities.jl +++ b/test/runtests_utilities.jl @@ -16,7 +16,7 @@ fc = GeneralizedPerturbedEquilibrium.Utilities.FourierCoefficients(xs, ys, fs, 4) # Check structure - @test fc.mband == 4 + @test fc.mmax == 4 @test fc.nqty == 1 @test length(fc.xs) == npsi diff --git a/test/test_data/regression_solovev_ideal_example/gpec.toml b/test/test_data/regression_solovev_ideal_example/gpec.toml index 92272e98e..517f90075 100644 --- a/test/test_data/regression_solovev_ideal_example/gpec.toml +++ b/test/test_data/regression_solovev_ideal_example/gpec.toml @@ -40,7 +40,6 @@ nn_low = 1 # Smallest toroidal mode number to include nn_high = 1 # Largest toroidal mode number to include delta_mlow = 0 # Expands lower bound of Fourier harmonics delta_mhigh = 0 # Expands upper bound of Fourier harmonics -delta_mband = 0 # Integration keeps only this wide a band... mthvac = 64 # Number of points used in splines over poloidal angle at plasma-vacuum interface. thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds diff --git a/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml b/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml index 88d6c761e..db77711b3 100644 --- a/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml +++ b/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml @@ -40,7 +40,6 @@ nn_low = 1 # Smallest toroidal mode number to include nn_high = 2 # Largest toroidal mode number to include delta_mlow = 0 # Expands lower bound of Fourier harmonics delta_mhigh = 0 # Expands upper bound of Fourier harmonics -delta_mband = 0 # Integration keeps only this wide a band... mthvac = 64 # Number of points used in splines over poloidal angle at plasma-vacuum interface. thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds diff --git a/test/test_data/regression_solovev_kinetic_calculated/gpec.toml b/test/test_data/regression_solovev_kinetic_calculated/gpec.toml index 6f8dd25f5..2634ae063 100644 --- a/test/test_data/regression_solovev_kinetic_calculated/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_calculated/gpec.toml @@ -40,7 +40,6 @@ nn_low = 1 # Smallest toroidal mode number to include nn_high = 1 # Largest toroidal mode number to include delta_mlow = 0 # Expands lower bound of Fourier harmonics delta_mhigh = 0 # Expands upper bound of Fourier harmonics -delta_mband = 0 # Integration keeps only this wide a band... mthvac = 64 # Number of points used in splines over poloidal angle at plasma-vacuum interface. thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds diff --git a/test/test_data/regression_solovev_kinetic_example/gpec.toml b/test/test_data/regression_solovev_kinetic_example/gpec.toml index 343ab1d2f..e1b32c8eb 100644 --- a/test/test_data/regression_solovev_kinetic_example/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_example/gpec.toml @@ -40,7 +40,6 @@ nn_low = 1 # Smallest toroidal mode number to include nn_high = 1 # Largest toroidal mode number to include delta_mlow = 0 # Expands lower bound of Fourier harmonics delta_mhigh = 0 # Expands upper bound of Fourier harmonics -delta_mband = 0 # Integration keeps only this wide a band... mthvac = 64 # Number of points used in splines over poloidal angle at plasma-vacuum interface. thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds diff --git a/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml b/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml index 02067b588..b90f14961 100644 --- a/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml @@ -40,7 +40,6 @@ nn_low = 1 # Lower toroidal mode number nn_high = 2 # Upper toroidal mode number delta_mlow = 0 # Expands lower bound of Fourier harmonics delta_mhigh = 0 # Expands upper bound of Fourier harmonics -delta_mband = 0 # Integration keeps only this wide a band... mthvac = 64 # Number of points used in splines over poloidal angle at plasma-vacuum interface. thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds From ce2de309667af595473398c2a965d931dc68e722 Mon Sep 17 00:00:00 2001 From: Jake Halpern Date: Tue, 16 Jun 2026 10:57:41 -0400 Subject: [PATCH 047/135] GPEC - MINOR - removing a file I accidentally added --- benchmarks/benchmark_delta_m_scan.jl | 268 --------------------------- 1 file changed, 268 deletions(-) delete mode 100644 benchmarks/benchmark_delta_m_scan.jl diff --git a/benchmarks/benchmark_delta_m_scan.jl b/benchmarks/benchmark_delta_m_scan.jl deleted file mode 100644 index f0de5caac..000000000 --- a/benchmarks/benchmark_delta_m_scan.jl +++ /dev/null @@ -1,268 +0,0 @@ -#!/usr/bin/env julia -# -# Scan delta_mlow = delta_mhigh for regression_solovev_ideal_example on two git -# branches and plot minimum total energy eigenvalue Re(min et) vs delta. -# -# Each branch uses one Julia subprocess that loads GPEC once and loops over δ. -# -# Usage: -# julia --project=. benchmarks/benchmark_delta_m_scan.jl -# julia --project=. benchmarks/benchmark_delta_m_scan.jl --quick -# julia --project=. benchmarks/benchmark_delta_m_scan.jl --branch1 develop --branch2 jmh/vacuum_galerkin -# julia --project=. benchmarks/benchmark_delta_m_scan.jl --deltas 0,4,8,12,16 - -using Dates -using HDF5 -using Printf -using TOML - -const PROJECT_ROOT = abspath(joinpath(@__DIR__, "..")) -const EXAMPLE_DIR = joinpath(PROJECT_ROOT, "examples", "DIIID-like_ideal_example_copy") -const OUTPUT_DIR = joinpath(@__DIR__, "delta_m_scan") -const GPEC_BASE = TOML.parsefile(joinpath(EXAMPLE_DIR, "gpec.toml")) - -function prepare_run_dir(base::Dict, example_dir::AbstractString, delta::Int) - raw = deepcopy(base) - raw["ForceFreeStates"]["delta_mlow"] = delta - raw["ForceFreeStates"]["delta_mhigh"] = delta - raw["ForceFreeStates"]["verbose"] = false - - run_dir = mktempdir(; prefix="gpec_delta_m_$(delta)_") - open(joinpath(run_dir, "gpec.toml"), "w") do io - TOML.print(io, raw) - end - for f in readdir(example_dir) - src = abspath(joinpath(example_dir, f)) - isfile(src) && f != "gpec.toml" && symlink(src, joinpath(run_dir, f)) - end - return run_dir -end - -function read_et_min(h5_path::String) - h5open(h5_path, "r") do h5 - et = if haskey(h5, "vacuum/et") - read(h5["vacuum/et"]) - elseif haskey(h5, "FreeBoundaryStability/XiNorm/eigenmode_energies") - read(h5["FreeBoundaryStability/XiNorm/eigenmode_energies"]) - else - keys_str = join(collect(keys(h5)), ", ") - error("No eigenvalue dataset in $h5_path (top-level keys: $keys_str)") - end - return minimum(real.(et)) - end -end - -function worker_scan(example_dir::AbstractString, base_toml::AbstractString, deltas, output_csv::AbstractString) - base = TOML.parsefile(base_toml) - et_min = Float64[] - for (i, delta) in enumerate(deltas) - @info "delta=$delta ($i/$(length(deltas)))" - run_dir = prepare_run_dir(base, example_dir, delta) - try - GeneralizedPerturbedEquilibrium.main([run_dir]) - h5_path = joinpath(run_dir, "gpec.h5") - isfile(h5_path) || error("Missing output: $h5_path") - val = read_et_min(h5_path) - push!(et_min, val) - @printf(" Re(min et) = %+.6f\n", val) - catch err - @warn "Run failed" delta exception=(err, catch_backtrace()) - push!(et_min, NaN) - finally - rm(run_dir; force=true, recursive=true) - end - end - open(output_csv, "w") do io - println(io, "delta,et_min_real") - for (delta, et) in zip(deltas, et_min) - println(io, "$delta,$et") - end - end -end - -function parse_options(args) - opts = Dict( - "branch1" => "develop", - "branch2" => strip(readchomp(`git -C $PROJECT_ROOT branch --show-current`)), - "deltas" => nothing, - "quick" => false - ) - i = 1 - while i <= length(args) - arg = args[i] - if arg == "--quick" - opts["quick"] = true - i += 1 - elseif arg == "--branch1" && i < length(args) - opts["branch1"] = String(args[i+1]) - i += 2 - elseif arg == "--branch2" && i < length(args) - opts["branch2"] = String(args[i+1]) - i += 2 - elseif arg == "--deltas" && i < length(args) - opts["deltas"] = [parse(Int, strip(s)) for s in split(args[i+1], ',')] - i += 2 - else - error("Unknown argument: $arg") - end - end - if opts["deltas"] === nothing - opts["deltas"] = opts["quick"] ? [0, 8, 16, 24] : collect(0:4:32) - end - return opts -end - -function git_short_ref(ref) - return readchomp(`git -C $PROJECT_ROOT rev-parse --short $ref`) -end - -function checkout_ref(branch::AbstractString) - @info "Checking out $branch" - run(`git -C $PROJECT_ROOT checkout $branch`) -end - -function read_worker_csv(path::AbstractString, deltas) - rows = Dict{Int,Float64}() - open(path, "r") do io - readline(io) # header - for line in eachline(io) - isempty(strip(line)) && continue - parts = split(strip(line), ',') - rows[parse(Int, parts[1])] = parse(Float64, parts[2]) - end - end - return [get(rows, delta, NaN) for delta in deltas] -end - -function scan_branch(branch::AbstractString, deltas::AbstractVector{<:Integer}) - commit = git_short_ref("HEAD") - @info "[$branch @ $commit] scanning $(length(deltas)) δ values in one Julia session" - - base_toml = tempname() * ".toml" - output_csv = tempname() * ".csv" - try - open(base_toml, "w") do io - TOML.print(io, GPEC_BASE) - end - delta_str = join(string.(deltas), ',') - run( - `julia --project=$PROJECT_ROOT $(@__FILE__) --worker $PROJECT_ROOT $EXAMPLE_DIR $base_toml $delta_str $output_csv` - ) - et_min = read_worker_csv(output_csv, deltas) - return (branch=branch, commit=commit, et_min=et_min) - finally - isfile(base_toml) && rm(base_toml; force=true) - isfile(output_csv) && rm(output_csv; force=true) - end -end - -function save_results_csv(path::String, deltas, results) - open(path, "w") do io - println(io, "delta,branch,commit,et_min_real") - for r in results - for (delta, et) in zip(deltas, r.et_min) - println(io, "$delta,$(r.branch),$(r.commit),$et") - end - end - end -end - -function plot_results(path::String, deltas, results) - default(; lw=2, marker=:circle, markersize=5, legend=:best, grid=true) - p = plot(; - xlabel="δ (delta_mlow = delta_mhigh)", - ylabel="Re(min et)", - yscale=:log10, - size=(700, 450), - left_margin=12Plots.mm, - bottom_margin=4Plots.mm - ) - markers = [:circle, :rect, :utriangle, :diamond] - for (i, r) in enumerate(results) - et_log = [v > 0 ? v : NaN for v in r.et_min] - plot!( - p, - deltas, - et_log; - marker=markers[mod1(i, length(markers))], - label="$(r.branch) @ $(r.commit)" - ) - end - savefig(p, path) - println("Saved plot: $path") -end - -function main() - opts = parse_options(ARGS) - deltas = opts["deltas"] - branch1 = opts["branch1"] - branch2 = opts["branch2"] - - mkpath(OUTPUT_DIR) - original_branch = strip(readchomp(`git -C $PROJECT_ROOT branch --show-current`)) - - println("="^70) - println("delta_m scan — regression_solovev_ideal_example") - println("="^70) - @printf("Example: %s\n", EXAMPLE_DIR) - @printf("Deltas: %s\n", join(string.(deltas), ", ")) - @printf("Branches: %s vs %s\n", branch1, branch2) - println() - - results = Dict{String,Any}() - try - checkout_ref(branch1) - results["branch1"] = scan_branch(branch1, deltas) - - checkout_ref(branch2) - results["branch2"] = scan_branch(branch2, deltas) - finally - @info "Restoring branch $original_branch" - checkout_ref(original_branch) - end - - scan_results = [results["branch1"], results["branch2"]] - stamp = Dates.format(now(), "yyyymmdd_HHMMSS") - csv_path = joinpath(OUTPUT_DIR, "delta_m_scan_$(stamp).csv") - png_path = joinpath(OUTPUT_DIR, "delta_m_scan_$(stamp).png") - save_results_csv(csv_path, deltas, scan_results) - plot_results(png_path, deltas, scan_results) - - println() - println("="^70) - @printf("%6s", "delta") - for r in scan_results - @printf(" %20s", "$(r.branch)") - end - println() - println("-"^70) - for (j, delta) in enumerate(deltas) - @printf("%6d", delta) - for r in scan_results - val = r.et_min[j] - if isnan(val) - @printf(" %20s", "FAIL") - else - @printf(" %20.6f", val) - end - end - println() - end - println("="^70) - println("CSV: $csv_path") - println("Plot: $png_path") -end - -if abspath(PROGRAM_FILE) == @__FILE__ - if length(ARGS) >= 1 && ARGS[1] == "--worker" - using Pkg - Pkg.activate(ARGS[2]) - Pkg.instantiate() - using GeneralizedPerturbedEquilibrium - deltas = [parse(Int, strip(s)) for s in split(ARGS[5], ',')] - worker_scan(ARGS[3], ARGS[4], deltas, ARGS[6]) - else - using Plots - main() - end -end From 8fe28707ce1d5c87db80e49fe7bcc9a2bc8ee9a5 Mon Sep 17 00:00:00 2001 From: Jake Halpern Date: Tue, 16 Jun 2026 11:08:01 -0400 Subject: [PATCH 048/135] TEST - MINOR - small bugfix --- src/ForceFreeStates/Fourfit.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/ForceFreeStates/Fourfit.jl b/src/ForceFreeStates/Fourfit.jl index 250ce3da3..6896c6bf4 100644 --- a/src/ForceFreeStates/Fourfit.jl +++ b/src/ForceFreeStates/Fourfit.jl @@ -363,7 +363,7 @@ function make_matrix(equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStates a_inv_dmat_temp = Matrix{ComplexF64}(undef, intr.numpert_total, intr.numpert_total) a_inv_cmat_temp = Matrix{ComplexF64}(undef, intr.numpert_total, intr.numpert_total) - imat = zeros(ComplexF64, len) + imat = zeros(ComplexF64, 2 * intr.mpert - 1) imat[intr.mpert] = 1 + 0im hint = Ref(1) # Linear search hint for sequential psi access From ff575aabc29c16129683fcd7296d35cb65c4ef14 Mon Sep 17 00:00:00 2001 From: Jake Halpern <57007344+jhalpern30@users.noreply.github.com> Date: Tue, 16 Jun 2026 13:02:32 -0400 Subject: [PATCH 049/135] Potential fix for pull request finding Co-authored-by: Copilot Autofix powered by AI <175728472+Copilot@users.noreply.github.com> --- test/runtests_riccati.jl | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/test/runtests_riccati.jl b/test/runtests_riccati.jl index eb06e0866..2e06848fc 100644 --- a/test/runtests_riccati.jl +++ b/test/runtests_riccati.jl @@ -187,8 +187,7 @@ end q .* (intr_ric.nlow:intr_ric.nhigh)')) w = -Kmat * S for i in 1:N - ; - w[i, i] += singfac[i]; + w[i, i] += singfac[i] end v = copy(w) ldiv!(LowerTriangular(L), v) From a98c29fc5f8fe34e74856f0caa22f0a2d43aa9ff Mon Sep 17 00:00:00 2001 From: "copilot-swe-agent[bot]" <198982749+Copilot@users.noreply.github.com> Date: Tue, 16 Jun 2026 17:31:24 +0000 Subject: [PATCH 050/135] Apply remaining changes Co-authored-by: jhalpern30 <57007344+jhalpern30@users.noreply.github.com> --- src/Utilities/FourierCoefficients.jl | 11 ++++------- 1 file changed, 4 insertions(+), 7 deletions(-) diff --git a/src/Utilities/FourierCoefficients.jl b/src/Utilities/FourierCoefficients.jl index 9be3026cf..dafb1f1c4 100644 --- a/src/Utilities/FourierCoefficients.jl +++ b/src/Utilities/FourierCoefficients.jl @@ -80,11 +80,8 @@ function FourierCoefficients(xs::Vector{Float64}, ys::Vector{Float64}, ntheta = has_duplicate ? ny_full - 1 : ny_full fs_view = has_duplicate ? view(fs,:,(1:ntheta),:) : fs - # Clamp to Nyquist limit - nyquist_limit = ntheta ÷ 2 - actual_mmax = min(mmax, nyquist_limit) - - nmodes = actual_mmax + 1 + @assert mmax <= ntheta ÷ 2 "mmax must be less than or equal to the Nyquist limit" + nmodes = mmax + 1 # Compute Fourier coefficients using batched FFT fs_reshaped = reshape(permutedims(fs_view, (2, 1, 3)), ntheta, npsi * nqty) @@ -103,14 +100,14 @@ function FourierCoefficients(xs::Vector{Float64}, ys::Vector{Float64}, @inbounds cos_coeffs[ipsi, 1, iq] = real(fft_col[1]) / ntheta # Higher modes - @inbounds for m in 1:actual_mmax + @inbounds for m in 1:mmax cos_coeffs[ipsi, m+1, iq] = 2 * real(fft_col[m+1]) / ntheta sin_coeffs[ipsi, m+1, iq] = -2 * imag(fft_col[m+1]) / ntheta end end end - FourierCoefficients(xs, actual_mmax, nqty, cos_coeffs, sin_coeffs) + FourierCoefficients(xs, mmax, nqty, cos_coeffs, sin_coeffs) end """ From e3be0205ba12cca31e57bb13b94731c4ce5fae72 Mon Sep 17 00:00:00 2001 From: Jake Halpern Date: Tue, 16 Jun 2026 13:38:55 -0400 Subject: [PATCH 051/135] GPEC - MINOR - cleaning up unbanded FourierCoefficients interface --- src/Utilities/FourierCoefficients.jl | 5 ++--- 1 file changed, 2 insertions(+), 3 deletions(-) diff --git a/src/Utilities/FourierCoefficients.jl b/src/Utilities/FourierCoefficients.jl index dafb1f1c4..f11aee2f7 100644 --- a/src/Utilities/FourierCoefficients.jl +++ b/src/Utilities/FourierCoefficients.jl @@ -81,15 +81,14 @@ function FourierCoefficients(xs::Vector{Float64}, ys::Vector{Float64}, fs_view = has_duplicate ? view(fs,:,(1:ntheta),:) : fs @assert mmax <= ntheta ÷ 2 "mmax must be less than or equal to the Nyquist limit" - nmodes = mmax + 1 # Compute Fourier coefficients using batched FFT fs_reshaped = reshape(permutedims(fs_view, (2, 1, 3)), ntheta, npsi * nqty) fft_results = fft(fs_reshaped, 1) # Extract and normalize coefficients - cos_coeffs = zeros(Float64, npsi, nmodes, nqty) - sin_coeffs = zeros(Float64, npsi, nmodes, nqty) + cos_coeffs = zeros(Float64, npsi, mmax + 1, nqty) + sin_coeffs = zeros(Float64, npsi, mmax + 1, nqty) for iq in 1:nqty for ipsi in 1:npsi From 410622a42e0fd73cb52be3895d031f126fdfffa7 Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Tue, 16 Jun 2026 14:17:15 -0400 Subject: [PATCH 052/135] ForceFreeStates - REFACTOR - Fold rpec edge BC into gal_set_boundary! + add gal_resistive regression case MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Consolidate the RDCON rpec edge handling into gal_set_boundary!'s three-way branch (rpec identity edge + coil RHS injection / free vacuum / fixed identity), mirroring Fortran gal.f:1554-1620, and remove the now-duplicate injection block from galerkin_solve. Bit-identical Δ′/delta_coil (verified by stash pre/post diff). Add examples/DIIID-like_gal_resistive_example (gal_flag+gal_rpec_flag, symlinked geqdsk) and regression-harness case gal_resistive_diiid tracking pest3_Delta, ||delta||, ||delta_coil||, D_I, alpha, msing, sing_q — first gal/rpec regression coverage, so future changes compare backward to here. Co-Authored-By: Claude Opus 4.8 --- .../TkMkr_D3Dlike_Hmode.geqdsk | 1 + .../gpec.toml | 79 +++++++++++++++++++ .../cases/gal_resistive_diiid.toml | 74 +++++++++++++++++ .../Galerkin/GalerkinAssembly.jl | 31 ++++++-- src/ForceFreeStates/Galerkin/GalerkinSolve.jl | 14 +--- 5 files changed, 181 insertions(+), 18 deletions(-) create mode 120000 examples/DIIID-like_gal_resistive_example/TkMkr_D3Dlike_Hmode.geqdsk create mode 100644 examples/DIIID-like_gal_resistive_example/gpec.toml create mode 100644 regression-harness/cases/gal_resistive_diiid.toml diff --git a/examples/DIIID-like_gal_resistive_example/TkMkr_D3Dlike_Hmode.geqdsk b/examples/DIIID-like_gal_resistive_example/TkMkr_D3Dlike_Hmode.geqdsk new file mode 120000 index 000000000..4200141b3 --- /dev/null +++ b/examples/DIIID-like_gal_resistive_example/TkMkr_D3Dlike_Hmode.geqdsk @@ -0,0 +1 @@ +../DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk \ No newline at end of file diff --git a/examples/DIIID-like_gal_resistive_example/gpec.toml b/examples/DIIID-like_gal_resistive_example/gpec.toml new file mode 100644 index 000000000..e03a3444c --- /dev/null +++ b/examples/DIIID-like_gal_resistive_example/gpec.toml @@ -0,0 +1,79 @@ +[Equilibrium] +eq_filename = "TkMkr_D3Dlike_Hmode.geqdsk" +eq_type = "efit" +jac_type = "hamada" +power_bp = 0 +power_b = 0 +power_r = 0 +grid_type = "ldp" +psilow = 1e-4 +psihigh = 0.9981 +mpsi = 128 +psi_accuracy = 0.001 +mtheta = 256 +newq0 = 0 +etol = 1e-10 +force_termination = false + +[Wall] +shape = "nowall" +a = 0.2415 +aw = 0.05 +bw = 1.5 +cw = 0 +dw = 0.5 +tw = 0.05 +equal_arc_wall = true + +[ForceFreeStates] +bal_flag = false +mat_flag = true +ode_flag = true +vac_flag = true +mer_flag = true + +psiedge = 0.99 +qlow = 1.02 +qhigh = 1e3 +sing_start = 0 + +nn_low = 1 +nn_high = 1 +delta_mlow = 8 +delta_mhigh = 4 +delta_mband = 0 +mthvac = 512 +thmax0 = 1 + +kinetic_source = "fixed" +kinetic_factor = 0.0 +eulerlagrange_tolerance = 1e-10 +save_interval = 3 +singfac_min = 1e-4 +ucrit = 1e4 + +# Riccati / STRIDE-style global BVP Δ′ matrix +use_parallel = true +parallel_threads = 2 +populate_dense_xi = false +truncate_at_dW_peak = false +set_psilim_via_dmlim = false +dmlim = 0.2 + +# RDCON outer-region singular Galerkin Δ′ solver with rpec coil columns (matched to Fortran &GAL_INPUT). +# This case exercises the gal solve AND the rpec coil/edge path (delta_coil) for regression tracking. +gal_flag = true +gal_solver = "LU" +gal_nx = 256 +gal_nq = 6 +gal_pfac = 0.03 +gal_dx0 = 5e-4 +gal_dx1 = 1e-3 +gal_dx2 = 1e-3 +gal_cutoff = 10 +gal_tol = 1e-10 +gal_gnstep = 5000 +gal_dx1dx2_flag = true +gal_sing_order = 6 +gal_sing_order_ceiling = true +gal_rpec_flag = true diff --git a/regression-harness/cases/gal_resistive_diiid.toml b/regression-harness/cases/gal_resistive_diiid.toml new file mode 100644 index 000000000..44efe6499 --- /dev/null +++ b/regression-harness/cases/gal_resistive_diiid.toml @@ -0,0 +1,74 @@ +[case] +name = "gal_resistive_diiid" +description = "DIII-D-like, n=1, RDCON outer-region Galerkin Δ′ with rpec coil columns (delta_coil)" +example_dir = "examples/DIIID-like_gal_resistive_example" + +# Number of resonant surfaces in the gal domain +[quantities.gal_msing] +h5path = "galerkin/msing" +type = "int_scalar" +extract = "value" +label = "gal # singular surfaces" +noise_threshold = 0 +order = 10 + +[quantities.gal_sing_q] +h5path = "galerkin/sing_q" +type = "real_vector" +extract = "all_real" +label = "gal singular q values" +noise_threshold = 1e-8 +order = 11 + +# PEST-3 Δ matching matrix — per-surface diagonal (the physics-meaningful tearing Δ′) +[quantities.gal_pest3_delta_diag] +h5path = "galerkin/pest3_Delta" +type = "complex_matrix" +extract = "diagonal_complex" +label = "gal PEST3 Δ diagonal" +noise_threshold = 1e-6 +order = 20 + +# Full outer Δ′ matrix (nsol × 2·msing) — Frobenius norm catches any element drift +[quantities.gal_delta_norm] +h5path = "galerkin/delta" +type = "complex_matrix" +extract = "norm" +label = "||gal Δ′ matrix||" +noise_threshold = 1e-6 +order = 21 + +# rpec coil-response block (mpert × 2·msing) — Frobenius norm +[quantities.gal_delta_coil_norm] +h5path = "galerkin/delta_coil" +type = "complex_matrix" +extract = "norm" +label = "||gal Δ_coil block||" +noise_threshold = 1e-6 +order = 22 + +# Mercier index per surface +[quantities.gal_di] +h5path = "galerkin/di" +type = "real_vector" +extract = "all_real" +label = "gal D_I per surface" +noise_threshold = 1e-8 +order = 30 + +# Resonant exponents α per surface +[quantities.gal_alpha] +h5path = "galerkin/alpha" +type = "complex_vector" +extract = "all_complex" +label = "gal α per surface" +noise_threshold = 1e-8 +order = 31 + +[quantities.runtime] +h5path = "" +type = "runtime" +extract = "value" +label = "Runtime (s)" +noise_threshold = 0.0 +order = 999 diff --git a/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl b/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl index ff83111a4..3474b8c31 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl @@ -404,14 +404,21 @@ end """ gal_set_boundary!(ws, mpert, wv_edge) -Apply the axis (`u(0)=0` identity) and edge boundary conditions to the boundary cells' `mat` before -global assembly. Port of `gal_set_boundary` (gal.f:1517-1583). `wv_edge::Union{Nothing,Matrix}` is the -free-boundary vacuum block to add at the edge value DOF (index 3); `nothing` ⇒ fixed-boundary identity. -The `rpec_flag` coil branch is not ported. +Apply the axis (`u(0)=0` identity) and edge boundary conditions to the boundary cells' `mat`, plus the +rpec coil-source RHS injection, before global assembly. Port of `gal_set_boundary` (gal.f:1554-1620), +including its full three-way edge branch (rpec count `ncoil = ws.nsol - 2*msing`): + - rpec (`ncoil > 0`): identity edge **and** a unit source at the edge value DOF of coil column + `2*msing+ipert` for each poloidal mode `ipert` (gal.f:1573-1586). `ws.rhs` is already allocated and + `gal_assemble_rhs!` only fills columns `1:2*msing`, so the injection is not clobbered. + - free boundary (`wv_edge !== nothing`): add the vacuum block `wvac·psio²` at the edge value DOF + (gal.f:1603-1606). + - fixed boundary (else): identity edge (gal.f:1607-1614). +`wv_edge` is `nothing` for the rpec and fixed cases. """ function gal_set_boundary!(ws::GalWorkspace, mpert::Int, wv_edge::Union{Nothing,Matrix{ComplexF64}}) chol = ws.solver == "cholesky" msing = length(ws.intvl) - 1 + ncoil = ws.nsol - 2 * msing # axis u(0): first cell of interval 0, Hermite value DOF ip=0 (Julia index 1) cell = ws.intvl[1].cells[1] @@ -423,14 +430,26 @@ function gal_set_boundary!(ws::GalWorkspace, mpert::Int, wv_edge::Union{Nothing, # edge u(1): last cell of last interval, edge-value DOF ip=3 (Julia index 4, see gauss_quad swap) cell = ws.intvl[msing+1].cells[ws.nx] - if wv_edge === nothing + if ncoil > 0 + # rpec: identity edge + unit coil sources (gal.f:1573-1586) cell.mat[:, :, 4, :] .= 0 chol && (cell.mat[:, :, :, 4] .= 0) for idx in 1:mpert cell.mat[idx, idx, 4, 4] = 1 end - else + for ipert in 1:mpert + ws.rhs[cell.map[ipert, 4], 2 * msing + ipert] = 1 + end + elseif wv_edge !== nothing + # free boundary: vacuum block wvac·psio² (gal.f:1603-1606) @views cell.mat[:, :, 4, 4] .+= wv_edge + else + # fixed boundary: identity edge (gal.f:1607-1614) + cell.mat[:, :, 4, :] .= 0 + chol && (cell.mat[:, :, :, 4] .= 0) + for idx in 1:mpert + cell.mat[idx, idx, 4, 4] = 1 + end end return ws end diff --git a/src/ForceFreeStates/Galerkin/GalerkinSolve.jl b/src/ForceFreeStates/Galerkin/GalerkinSolve.jl index 0f27b1088..fa596905e 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinSolve.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinSolve.jl @@ -123,8 +123,8 @@ function galerkin_solve(ctrl::ForceFreeStatesControl, equil, ffit::FourFitVars, ws.sol = zeros(ComplexF64, ws.ndim, nsol) # Free-boundary edge term wvac·psio² (vac_data.wv is already singfac-scaled at qlim in free_run!). - # rpec uses a fixed-boundary identity edge (the coil unit sources are injected as RHS below), so the - # vacuum block is not applied at the edge in that case — matching Fortran gal_set_boundary rpec branch. + # rpec passes wv_edge=nothing; gal_set_boundary! then applies the identity edge AND injects the coil + # unit sources (its three-way branch). The vacuum block is only built for the non-rpec free case. wv_edge = nothing if ctrl.vac_flag && vac_data !== nothing && ncoil == 0 wv_edge = Matrix{ComplexF64}(vac_data.wv .* equil.psio^2) @@ -132,16 +132,6 @@ function galerkin_solve(ctrl::ForceFreeStatesControl, equil, ffit::FourFitVars, gal_make_arrays!(ws, ctrl, equil, ffit, intr, asymps, sings, nn, wv_edge) - # rpec_flag: inject unit sources into the coil columns (gal.f:1544-1549). For each poloidal mode - # ipert, column (2*msing + ipert) gets a unit at the edge cell's value DOF (ip=3 → Julia index 4). - if ncoil > 0 - edge_cell = ws.intvl[msing+1].cells[ws.nx] - for ipert in 1:mpert - imap = edge_cell.map[ipert, 4] - ws.rhs[imap, 2 * msing + ipert] = 1 - end - end - if get(ENV, "GAL_DEBUG", "") == "1" offdbg = ws.solver == "LU" ? ws.kl + ws.ku + 1 : 1 @info "GAL_DEBUG ndim=$(ws.ndim) nsol=$nsol kl=$(ws.kl) ldab=$(ws.ldab) |rhs|=$(norm(ws.rhs))" From ebc5a757925caf07d14b8a812d0232cf4fee948f Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Tue, 16 Jun 2026 14:33:29 -0400 Subject: [PATCH 053/135] ForceFreeStates - NEW - gal_edge_onesided: one-sided end-interval packing MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Add gal_edge_onesided control flag (default false = Fortran-faithful symmetric "both" packing). When true, the two end intervals pack one-sided toward their single rational end, leaving the regular domain boundary (psilow/psihigh) at coarse spacing — removes the gratuitous fine edge cell that inflates cond(A) (entry spread ~1/h²). Verified Δ′ unchanged (<=0.05%) while worst-case coil loss-of-significance drops ~3.7x on DIIID. Co-Authored-By: Claude Opus 4.8 --- src/ForceFreeStates/ForceFreeStatesStructs.jl | 1 + src/ForceFreeStates/Galerkin/GalerkinGrid.jl | 13 ++++++++++++- 2 files changed, 13 insertions(+), 1 deletion(-) diff --git a/src/ForceFreeStates/ForceFreeStatesStructs.jl b/src/ForceFreeStates/ForceFreeStatesStructs.jl index 1f1fc55f7..56e162bd6 100644 --- a/src/ForceFreeStates/ForceFreeStatesStructs.jl +++ b/src/ForceFreeStates/ForceFreeStatesStructs.jl @@ -314,6 +314,7 @@ A mutable struct containing control parameters for stability analysis, set by th gal_sing_order::Int = 6 # base power-series order for the Galerkin singular asymptotics gal_sing_order_ceiling::Bool = true # auto-raise order by ceil(2·Re(α)) per surface (high Mercier index) gal_rpec_flag::Bool = false # append mpert coil-response columns to the Δ′ solve (RDCON rpec_flag): unit boundary sources whose plasma response is recorded; needed for the driven (resistive perturbed-equilibrium) Δ_gw + gal_edge_onesided::Bool = false # pack the two end intervals (`[psilow,first rational]`, `[last rational,psihigh]`) one-sided toward their single rational end instead of the Fortran-faithful symmetric "both" pack. Leaves the regular domain boundary at coarse spacing, removing the gratuitous fine edge cell that inflates cond(A) (entry spread ~1/h²) and seeds the downstream edge-derivative artifact. Default false = faithful to gal.f. fixed_axis::Bool = false end diff --git a/src/ForceFreeStates/Galerkin/GalerkinGrid.jl b/src/ForceFreeStates/Galerkin/GalerkinGrid.jl index b7d3829bb..e984e0641 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinGrid.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinGrid.jl @@ -147,7 +147,18 @@ function gal_make_grid!(intvl::GalInterval, ising::Int, msing::Int, sings::Vecto xm = (xn[ixmax+1] + xn[ixmin+1]) / 2 dxh = (xn[ixmax+1] - xn[ixmin+1]) / 2 mx = (ixmax - ixmin) ÷ 2 - packed = gal_pack(mx, pfac, "both") # length 2*mx+1 = (ixmax-ixmin)+1 + # Default: symmetric "both" pack (faithful to gal.f:438). With gal_edge_onesided, the two end + # intervals pack only toward their single rational end, leaving the regular boundary (psilow at + # interval 0, psihigh at interval msing) at coarse spacing — removes the gratuitous fine edge cell. + side = "both" + if ctrl.gal_edge_onesided && msing > 0 + if ising == 0 + side = "right" # rational sits at the upper (ixmax) end + elseif ising == msing + side = "left" # rational sits at the lower (ixmin) end + end + end + packed = gal_pack(mx, pfac, side) # length 2*mx+1 = (ixmax-ixmin)+1 for k in 0:(ixmax-ixmin) xn[ixmin+1+k] = xm + dxh * packed[k+1] end From f67f875d6676e167e419fc3860f88cc06ed0f395 Mon Sep 17 00:00:00 2001 From: nelsonand Date: Tue, 16 Jun 2026 15:27:38 -0600 Subject: [PATCH 054/135] Small speed up change for marginal stability --- src/ForceFreeStates/Bal.jl | 73 +++++++++++++++++++++++++------------- 1 file changed, 49 insertions(+), 24 deletions(-) diff --git a/src/ForceFreeStates/Bal.jl b/src/ForceFreeStates/Bal.jl index 2f96dea8a..bb20ed54d 100644 --- a/src/ForceFreeStates/Bal.jl +++ b/src/ForceFreeStates/Bal.jl @@ -684,7 +684,9 @@ crossings (not marginal points) and are skipped. The first crossing is the first stability boundary, the second the second-stability boundary, and so on. Returns `(scales, alphas, reference)` with `alphas = alpha_ref * scales`, ordered in -increasing α. Surfaces that never cross return empty vectors. +increasing α. Surfaces that never cross return empty vectors. With `max_crossings > 0` +the scan stops after that many crossings (e.g. `1` for a first-boundary-only search, +which avoids scanning the full α range above the boundary). """ function ballooning_alpha_crossings( psi_idx::Int, @@ -692,7 +694,8 @@ function ballooning_alpha_crossings( theta_k::Float64=0.0, max_alpha_scale::Float64=8.0, n_scan::Int=24, - tol::Float64=1e-3 + tol::Float64=1e-3, + max_crossings::Int=0 ) ref = salpha_reference(psi_idx, plasma_eq) @@ -712,33 +715,48 @@ function ballooning_alpha_crossings( end samples = collect(range(0.0, max_alpha_scale; length=n_scan + 1)) - scales = _ballooning_marginal_crossings(delta_at, samples, tol) + scales = _ballooning_marginal_crossings(delta_at, samples, tol; max_crossings=max_crossings) return (scales=scales, alphas=ref.alpha_ref .* scales, reference=ref) end -# March along `samples` (monotone, either direction) from the stable anchor at -# `samples[1]`, returning every sign change of `delta_at` between finite samples, +# March along `samples` (monotone, either direction) from the stable anchor (first finite, +# nonzero sample), returning every sign change of `delta_at` between finite samples, # bisected to `tol`. Sign changes whose endpoint magnitudes exceed pole_cap*|Δ'_anchor| # are Δ' pole crossings (not marginal points) and are skipped; on an adequately fine # scan all remaining crossings are genuine marginal zeros, ordered from the anchor. -function _ballooning_marginal_crossings(delta_at, samples, tol; pole_cap=3.0) - vals = [delta_at(x) for x in samples] - k0 = findfirst(v -> isfinite(v) && v != 0.0, vals) - isnothing(k0) && return Float64[] - d_anchor = abs(vals[k0]) +# +# Samples are evaluated lazily; with `max_crossings > 0` the march stops once that many +# crossings are found, so a first-boundary-only search costs only the samples up to it. +function _ballooning_marginal_crossings(delta_at, samples, tol; pole_cap=3.0, max_crossings=0) + n = length(samples) + k0 = 0 + d_prev = NaN + for k in 1:n + d = delta_at(samples[k]) + if isfinite(d) && d != 0.0 + k0 = k + d_prev = d + break + end + end + k0 == 0 && return Float64[] + d_anchor = abs(d_prev) locs = Float64[] - for k in k0:length(samples)-1 - a, b = vals[k], vals[k+1] - (isfinite(a) && isfinite(b) && sign(a) != sign(b)) || continue - max(abs(a), abs(b)) > pole_cap * d_anchor && continue - lo, hi = samples[k], samples[k+1] - while abs(hi - lo) > tol - mid = 0.5 * (lo + hi) - dm = delta_at(mid) - (isfinite(dm) && sign(dm) == sign(a)) ? (lo = mid) : (hi = mid) + for k in k0+1:n + d = delta_at(samples[k]) + if isfinite(d_prev) && isfinite(d) && sign(d) != sign(d_prev) && max(abs(d_prev), abs(d)) <= pole_cap * d_anchor + lo, hi = samples[k-1], samples[k] + sign_lo = sign(d_prev) + while abs(hi - lo) > tol + mid = 0.5 * (lo + hi) + dm = delta_at(mid) + (isfinite(dm) && sign(dm) == sign_lo) ? (lo = mid) : (hi = mid) + end + push!(locs, 0.5 * (lo + hi)) + (max_crossings > 0 && length(locs) >= max_crossings) && break end - push!(locs, 0.5 * (lo + hi)) + d_prev = d end return locs end @@ -762,13 +780,13 @@ function critical_ballooning_alpha( n_scan::Int=24, tol::Float64=1e-3 ) - cr = ballooning_alpha_crossings(psi_idx, plasma_eq; theta_k=theta_k, max_alpha_scale=max_alpha_scale, n_scan=n_scan, tol=tol) + cr = ballooning_alpha_crossings(psi_idx, plasma_eq; theta_k=theta_k, max_alpha_scale=max_alpha_scale, n_scan=n_scan, tol=tol, max_crossings=1) isempty(cr.scales) && return (alpha_crit=NaN, alpha_scale_crit=NaN, found=false) return (alpha_crit=cr.alphas[1], alpha_scale_crit=cr.scales[1], found=true) end """ - ballooning_alpha_boundary(ctrl, plasma_eq; theta_k=0.0) + ballooning_alpha_boundary(ctrl, plasma_eq; theta_k=0.0, n_scan=24) Profile driver for the BALOO-style ballooning stability diagram. Loops over flux surfaces returning the experimental pressure gradient `alpha` (from @@ -776,12 +794,19 @@ surfaces returning the experimental pressure gradient `alpha` (from [`critical_ballooning_alpha`](@ref)) versus normalized flux `psi`. Surfaces whose experimental `alpha` exceeds `alpha_critical` are ballooning-unstable. +This is the fast first-boundary-only driver: `critical_ballooning_alpha` stops at the +first crossing, so cost scales with the boundary location rather than the full α range. +Use this (not [`ballooning_alpha_boundaries`](@ref)) when only the 1st boundary is +needed, e.g. a pedestal-stability constraint. `n_scan` sets the scan resolution; raise +it (e.g. 64) on edge surfaces where Δ' poles can shift a coarse first crossing. + Per-surface failures and surfaces with no boundary within range are returned as `NaN`. """ function ballooning_alpha_boundary( ctrl::ForceFreeStatesControl, plasma_eq::Equilibrium.PlasmaEquilibrium; - theta_k::Float64=0.0 + theta_k::Float64=0.0, + n_scan::Int=24 ) xs = plasma_eq.profiles.xs npsi = length(xs) @@ -793,7 +818,7 @@ function ballooning_alpha_boundary( xs[i] > 1.0 && continue try alpha[i] = salpha_reference(i, plasma_eq).alpha_ref - alpha_critical[i] = critical_ballooning_alpha(i, plasma_eq; theta_k=theta_k).alpha_crit + alpha_critical[i] = critical_ballooning_alpha(i, plasma_eq; theta_k=theta_k, n_scan=n_scan).alpha_crit catch err if ctrl.verbose @warn "ballooning alpha boundary failed" psi_idx = i exception = err From 25b4db18a08842c2b0a81f716ec95fc83170d2cb Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Tue, 16 Jun 2026 18:05:26 -0400 Subject: [PATCH 055/135] ForceFreeStates Galerkin - NEW - save xi/xi' --- benchmarks/verify_gal_solution.jl | 77 ++++++++ src/ForceFreeStates/ForceFreeStates.jl | 1 + .../Galerkin/GalerkinSolution.jl | 179 ++++++++++++++++++ src/ForceFreeStates/Galerkin/GalerkinSolve.jl | 17 +- .../Galerkin/GalerkinStructs.jl | 34 +++- 5 files changed, 303 insertions(+), 5 deletions(-) create mode 100644 benchmarks/verify_gal_solution.jl create mode 100644 src/ForceFreeStates/Galerkin/GalerkinSolution.jl diff --git a/benchmarks/verify_gal_solution.jl b/benchmarks/verify_gal_solution.jl new file mode 100644 index 000000000..e6c02b653 --- /dev/null +++ b/benchmarks/verify_gal_solution.jl @@ -0,0 +1,77 @@ +# Piece 1 verification: reconstructed gal ξ(ψ) and analytic ξ′(ψ). +# 1. shapes / finiteness sanity of galerkin/solution arrays +# 2. analytic ξ′ vs centered finite-difference of ξ — agree in the smooth interior, diverge at the +# packed edge (the spline-endpoint-derivative artifact we deliberately avoid) +# Usage: julia --project=. verify_gal_solution.jl [path/to/gpec.h5] +using HDF5, Printf, Statistics + +h5path = length(ARGS) >= 1 ? ARGS[1] : "examples/DIIID-like_gal_resistive_example/gpec.h5" +@info "Reading $h5path" + +psi, q, issing, xi, dxi, sing_psi = h5open(h5path) do f + (read(f["galerkin/solution/psi"]), read(f["galerkin/solution/q"]), + read(f["galerkin/solution/issing"]), read(f["galerkin/solution/xi"]), + read(f["galerkin/solution/xi_deriv"]), read(f["galerkin/sing_psi"])) +end +issing = Bool.(issing) +mpert, ngrid, nsol = size(xi) +@printf("grid: mpert=%d ngrid=%d nsol=%d psi∈[%.4f, %.4f]\n", mpert, ngrid, nsol, psi[1], psi[end]) +@printf("singular surfaces at psi = %s\n", join((@sprintf("%.4f", p) for p in sing_psi), ", ")) + +# --- finiteness (skip on-surface points, which are intentionally left zero) --- +good = .!issing +nbad = count(!isfinite, xi[:, good, :]) + count(!isfinite, dxi[:, good, :]) +@printf("non-finite entries (off-surface): %d |xi|max=%.3e |dxi|max=%.3e\n", + nbad, maximum(abs, xi[:, good, :]), maximum(abs, dxi[:, good, :])) + +# --- analytic ξ′ vs centered finite difference of ξ --- +# For each column, centered diff at interior grid points (using off-surface neighbours), compared to the +# analytic xi_deriv. Report median relative error binned by distance to the nearest singular surface and +# to the packed edge. +dist_sing(p) = isempty(sing_psi) ? Inf : minimum(abs.(p .- sing_psi)) +relerr = Float64[] +dsurf = Float64[] +dedge = Float64[] +for isol in 1:nsol + for ip in 2:(ngrid-1) + (issing[ip] || issing[ip-1] || issing[ip+1]) && continue + h1 = psi[ip] - psi[ip-1] + h2 = psi[ip+1] - psi[ip] + (h1 <= 0 || h2 <= 0) && continue + for m in 1:mpert + # nonuniform centered difference + fd = (xi[m, ip+1, isol] - xi[m, ip-1, isol]) / (h2 + h1) + an = dxi[m, ip, isol] + scale = max(abs(an), abs(fd), 1e-30) + push!(relerr, abs(fd - an) / scale) + push!(dsurf, dist_sing(psi[ip])) + push!(dedge, psi[end] - psi[ip]) + end + end +end + +@printf("\nFinite-diff(ξ) vs analytic ξ′ (%d samples)\n", length(relerr)) +println(" binned by distance to nearest singular surface:") +for (lo, hi) in [(0.0, 1e-3), (1e-3, 1e-2), (1e-2, 1e-1), (1e-1, Inf)] + sel = (dsurf .>= lo) .& (dsurf .< hi) + n = count(sel) + n == 0 && continue + @printf(" |ψ-ψ_s|∈[%-7.0e,%-7.0e) n=%-7d median relerr=%.2e p90=%.2e\n", + lo, hi, n, median(relerr[sel]), quantile(relerr[sel], 0.9)) +end +println(" binned by distance to packed edge ψ=psihigh:") +for (lo, hi) in [(0.0, 1e-4), (1e-4, 1e-3), (1e-3, 1e-2), (1e-2, Inf)] + sel = (dedge .>= lo) .& (dedge .< hi) + n = count(sel) + n == 0 && continue + @printf(" edge dist∈[%-7.0e,%-7.0e) n=%-7d median relerr=%.2e p90=%.2e\n", + lo, hi, n, median(relerr[sel]), quantile(relerr[sel], 0.9)) +end + +# Interior (away from both layer and edge) should agree well; near edge/layer the finite diff degrades. +interior = (dsurf .> 1e-2) .& (dedge .> 1e-2) +@printf("\nINTERIOR (>1e-2 from layer AND edge): median relerr = %.2e (n=%d)\n", + median(relerr[interior]), count(interior)) +println(median(relerr[interior]) < 1e-3 ? + " ✓ analytic ξ′ matches finite-diff in the smooth interior" : + " ✗ interior mismatch — investigate") diff --git a/src/ForceFreeStates/ForceFreeStates.jl b/src/ForceFreeStates/ForceFreeStates.jl index 49383929e..33f708662 100644 --- a/src/ForceFreeStates/ForceFreeStates.jl +++ b/src/ForceFreeStates/ForceFreeStates.jl @@ -42,6 +42,7 @@ include("Riccati.jl") include("Galerkin/GalerkinStructs.jl") include("Galerkin/GalerkinGrid.jl") include("Galerkin/GalerkinAssembly.jl") +include("Galerkin/GalerkinSolution.jl") include("Galerkin/GalerkinSolve.jl") # These are used for various small tolerances and root finders throughout ForceFreeStates diff --git a/src/ForceFreeStates/Galerkin/GalerkinSolution.jl b/src/ForceFreeStates/Galerkin/GalerkinSolution.jl new file mode 100644 index 000000000..0ca4736d6 --- /dev/null +++ b/src/ForceFreeStates/Galerkin/GalerkinSolution.jl @@ -0,0 +1,179 @@ +# GalerkinSolution.jl +# +# Reconstruct the outer-region radial displacement ξ(ψ) AND its analytic derivative ξ′(ψ) from the +# solved Galerkin coefficients. Ports: +# gal_get_solution (gal.f:1833-1997) ξ (and optional ξ′) at one ψ for one solution column +# gal_output_solution (gal.f:2005-2273) evaluate (ξ, ξ′) on a gal-native packed grid, all columns +# +# The whole point of carrying ξ′ here is to evaluate it analytically from the Hermite derivative basis +# (gal_hermite qb) and the asymptotic-series derivative (sing_get_dua_gal) rather than ever +# spline-differentiating ξ at the packed edge — the spline-endpoint derivative was the root cause of +# GPEC's fake ~100% shielding (fixed in Fortran by RDCON_singcoup commit c3e8c5bc). +# +# Fortran module flags restore_uh/us/ul default .TRUE. (gal.f:81); the full reconstruction is always +# performed. The cut path (gal.f:1974-1992, used only for the matching diagnostic) is NOT ported here. + +# Dense / coarse sampling per cell, matching Fortran interp_np_res / interp_np (gal.f:88). +const GAL_INTERP_NP = 3 +const GAL_INTERP_NP_RES = 60 + +# Advance the monotone (iintvl, icell) cursor to the cell containing x. Port of gal.f:1863-1876. +@inline function gal_locate_cell(ws::GalWorkspace, x::Float64, iintvl::Int, icell::Int) + msing = length(ws.intvl) - 1 + for _ in 1:((msing+1)*ws.nx+1) + cell = ws.intvl[iintvl+1].cells[icell] + if cell.x[1] <= x <= cell.x[2] + return iintvl, icell, cell + end + icell += 1 + if icell > ws.nx + icell = 1 + iintvl += 1 + end + if iintvl > msing + iintvl = 0 + end + end + error("gal_locate_cell: x=$x not found in any cell") +end + +""" + gal_get_solution(ws, asymps, sings, intr, x, iintvl, icell, isol; want_d=true) + -> (sol, dsol, iintvl, icell) + +Reconstruct the displacement `sol` (length `mpert`) — and, when `want_d`, its analytic radial +derivative `dsol = d(sol)/dψ` — at flux `x` for solution column `isol`, from the solved Galerkin +coefficients `ws.sol`. Port of `gal_get_solution` (gal.f:1833-1997, non-cut path). `iintvl`/`icell` +are a monotone cell cursor advanced and returned for the next call. `dsol` is `nothing` if `!want_d`. +""" +function gal_get_solution(ws::GalWorkspace, asymps::Vector{GalSingAsymp}, sings::Vector{SingType}, + intr::ForceFreeStatesInternal, x::Float64, iintvl::Int, icell::Int, isol::Int; want_d::Bool=true) + + msing = length(ws.intvl) - 1 + mpert = intr.numpert_total + np = GAL_NP + iintvl, icell, cell = gal_locate_cell(ws, x, iintvl, icell) + + sol = zeros(ComplexF64, mpert) + dsol = want_d ? zeros(ComplexF64, mpert) : nothing + + # --- non-resonant (Hermite) part: same coefficients, value basis pb → ξ, derivative basis qb → ξ′ --- + pbt, qbt = gal_hermite(x, cell.x[1], cell.x[2]) + pb = collect(pbt) + qb = collect(qbt) + if iintvl == msing && icell == ws.nx # last edge cell: swap node-2/3 DOFs (gal.f:1888-1897) + pb[3], pb[4] = pb[4], pb[3] + qb[3], qb[4] = qb[4], qb[3] + end + for ip in 0:np + u = @view ws.sol[cell.map[:, ip+1], isol] + @views sol .+= u .* pb[ip+1] + want_d && (@views dsol .+= u .* qb[ip+1]) + end + + cell.etype == GCT_NONE && return sol, dsol, iintvl, icell + + # --- small & large resonant/extension solutions (gal.f:1904-1970) --- + jsing = _cell_jsing(cell, iintvl) # left → iintvl+1, right → iintvl (gal.f:1911/1919) + asymp = asymps[jsing] + psi_s = sings[jsing].psifac + ipert0 = _ipert_res(sings[jsing], intr) # resonant (big) row; small row = ipert0+mpert + + # Edge Hermite weights (fresh, unswapped) for ext/ext2 cells (gal.f:1912-1925) + pbe, qbe = gal_hermite(x, cell.x[1], cell.x[2]) + if cell.extra == GAL_SIDE_LEFT + epb1, epb2 = pbe[3], pbe[4] + eqb1, eqb2 = qbe[3], qbe[4] + xext = cell.x[2] + else + epb1, epb2 = pbe[1], pbe[2] + eqb1, eqb2 = qbe[1], qbe[2] + xext = cell.x[1] + end + + need_in = cell.etype == GCT_RES || cell.etype == GCT_EXT || cell.etype == GCT_EXT1 + need_ext = cell.etype == GCT_EXT || cell.etype == GCT_EXT2 + ua = need_in ? sing_get_ua_gal(asymp, x - psi_s) : nothing + dua = (need_in && want_d) ? sing_get_dua_gal(asymp, x - psi_s) : nothing + uaext = need_ext ? sing_get_ua_gal(asymp, xext - psi_s) : nothing + duaext = need_ext ? sing_get_dua_gal(asymp, xext - psi_s) : nothing + + # small solution Δ-coefficient restore (ext/res only), coeff = ws.sol[emap,isol] (gal.f:1937-1951) + if cell.etype == GCT_RES || cell.etype == GCT_EXT + delta = ws.sol[cell.emap, isol] + if cell.etype == GCT_RES + @views sol .+= delta .* ua[:, ipert0+mpert, 1] + want_d && (@views dsol .+= delta .* dua[:, ipert0+mpert, 1]) + else # GCT_EXT: series held at the fixed edge xext, x-dependence only via Hermite weights + @views sol .+= delta .* (epb1 .* uaext[:, ipert0+mpert, 1] .+ epb2 .* duaext[:, ipert0+mpert, 1]) + want_d && (@views dsol .+= delta .* (eqb1 .* uaext[:, ipert0+mpert, 1] .+ eqb2 .* duaext[:, ipert0+mpert, 1])) + end + end + + # large solution (coeff 1) only for the column driving this surface/side (gal.f:1952-1970) + if (isol == 2jsing - 1 && cell.extra == GAL_SIDE_LEFT) || + (isol == 2jsing && cell.extra == GAL_SIDE_RIGHT) + if cell.etype == GCT_RES || cell.etype == GCT_EXT || cell.etype == GCT_EXT1 + @views sol .+= ua[:, ipert0, 1] + want_d && (@views dsol .+= dua[:, ipert0, 1]) + elseif cell.etype == GCT_EXT2 + @views sol .+= epb1 .* uaext[:, ipert0, 1] .+ epb2 .* duaext[:, ipert0, 1] + want_d && (@views dsol .+= eqb1 .* uaext[:, ipert0, 1] .+ eqb2 .* duaext[:, ipert0, 1]) + end + end + + return sol, dsol, iintvl, icell +end + +""" + gal_output_solution(ws, asymps, sings, intr, profiles, psihigh) -> GalerkinSolution + +Build the gal-native packed radial grid (inner→edge; `GAL_INTERP_NP_RES` points per resonant/extension +cell, `GAL_INTERP_NP` elsewhere, plus the edge point ψ=psihigh) and evaluate ξ AND the analytic ξ′ over +it for every solution column. Port of `gal_output_solution` (gal.f:2027-2103); the binary/ASCII writes +and the `b_flag` ξ→b^ψ conversion (off by default) are not ported — we keep ξ itself. +""" +function gal_output_solution(ws::GalWorkspace, asymps::Vector{GalSingAsymp}, sings::Vector{SingType}, + intr::ForceFreeStatesInternal, profiles, psihigh::Float64) + + mpert = intr.numpert_total + msing = length(ws.intvl) - 1 + + # --- grid (gal.f:2038-2079): per-cell left-inclusive sampling, then the edge point --- + psi = Float64[] + issing = Bool[] + for iintvl in 0:msing + for icell in 1:ws.nx + cell = ws.intvl[iintvl+1].cells[icell] + npts = (cell.etype == GCT_RES || cell.etype == GCT_EXT) ? GAL_INTERP_NP_RES : GAL_INTERP_NP + x1, x2 = cell.x + for k in 0:(npts-1) + push!(psi, x1 + (x2 - x1) * (k / npts)) + # res-right cell's first point sits exactly on the surface (gal.f:2070-2071) + push!(issing, k == 0 && cell.extra == GAL_SIDE_RIGHT && cell.etype == GCT_RES) + end + end + end + push!(psi, psihigh) + push!(issing, false) + + qhint = Ref(1) + q = [profiles.q_spline(p; hint=qhint) for p in psi] + + # --- evaluate (gal.f:2090-2103) --- + ngrid = length(psi) + xi = zeros(ComplexF64, mpert, ngrid, ws.nsol) + xi_deriv = zeros(ComplexF64, mpert, ngrid, ws.nsol) + for isol in 1:ws.nsol + iintvl = 0 + icell = 1 + for ip in 1:ngrid + issing[ip] && continue + sol, dsol, iintvl, icell = gal_get_solution(ws, asymps, sings, intr, psi[ip], iintvl, icell, isol) + @views xi[:, ip, isol] .= sol + @views xi_deriv[:, ip, isol] .= dsol + end + end + + return GalerkinSolution(psi, q, issing, xi, xi_deriv) +end diff --git a/src/ForceFreeStates/Galerkin/GalerkinSolve.jl b/src/ForceFreeStates/Galerkin/GalerkinSolve.jl index fa596905e..22c7eab4e 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinSolve.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinSolve.jl @@ -70,7 +70,7 @@ function galerkin_solve(ctrl::ForceFreeStatesControl, equil, ffit::FourFitVars, ctrl.verbose && @info "galerkin_solve: no resonant surfaces in domain; skipping Δ′ solve" empty2 = Matrix{ComplexF64}(undef, 0, 0) return GalerkinResult(Matrix{ComplexF64}(undef, 0, 0), empty2, empty2, empty2, empty2, 0, - Float64[], Float64[], Int[], Int[], Float64[], ComplexF64[], empty2) + Float64[], Float64[], Int[], Int[], Float64[], ComplexF64[], empty2, nothing) end ctrl.verbose && @info "Starting outer-region Galerkin Δ′ solve (msing=$msing, solver=$(ctrl.gal_solver))" @@ -174,9 +174,14 @@ function galerkin_solve(ctrl::ForceFreeStatesControl, equil, ffit::FourFitVars, alpha = [asymps[i].right.alpha[1] for i in 1:msing] # Coil-response block (rpec_flag): rows 2*msing+1 : 2*msing+mpert of delta (empty otherwise). delta_coil = ncoil > 0 ? delta[(2*msing+1):(2*msing+ncoil), :] : Matrix{ComplexF64}(undef, 0, 0) + + # Piece 1 producer: reconstruct ξ(ψ) AND analytic ξ′(ψ) on the gal-native grid (gal_output_solution). + ctrl.verbose && @info "Reconstructing outer-region ξ and analytic ξ′ on the gal grid" + solution = gal_output_solution(ws, asymps, sings, intr, equil.profiles, psihigh) + return GalerkinResult(delta, Ap, Bp, Gammap, Deltap, msing, [s.psifac for s in sings], [s.q for s in sings], - [s.m[1] for s in sings], [s.n[1] for s in sings], di, alpha, delta_coil) + [s.m[1] for s in sings], [s.n[1] for s in sings], di, alpha, delta_coil, solution) end """ @@ -226,5 +231,13 @@ function write_galerkin!(out_h5, result::GalerkinResult) if !isempty(result.delta_coil) out_h5["galerkin/delta_coil"] = result.delta_coil end + if result.solution !== nothing + sol = result.solution + out_h5["galerkin/solution/psi"] = sol.psi + out_h5["galerkin/solution/q"] = sol.q + out_h5["galerkin/solution/issing"] = collect(sol.issing) + out_h5["galerkin/solution/xi"] = sol.xi + out_h5["galerkin/solution/xi_deriv"] = sol.xi_deriv + end return nothing end diff --git a/src/ForceFreeStates/Galerkin/GalerkinStructs.jl b/src/ForceFreeStates/Galerkin/GalerkinStructs.jl index 51768b51e..450402123 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinStructs.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinStructs.jl @@ -12,10 +12,14 @@ # Hermite-cubic order: 4 DOFs per node-pair (value + slope at each end), indexed 0:np in Fortran. const GAL_NP = 3 -"""Cell type flanking a singular surface (Fortran `cell%etype`, gal.f).""" +""" +Cell type flanking a singular surface (Fortran `cell%etype`, gal.f). +""" @enum GalCellType GCT_NONE GCT_RES GCT_EXT GCT_EXT1 GCT_EXT2 -"""Which side of the adjacent singular surface a cell lies on (Fortran `cell%extra`).""" +""" +Which side of the adjacent singular surface a cell lies on (Fortran `cell%extra`). +""" @enum GalSide GAL_SIDE_NONE GAL_SIDE_LEFT GAL_SIDE_RIGHT """ @@ -50,7 +54,9 @@ mutable struct GalCell mat::Array{ComplexF64,4} end -"""Construct an empty `GalCell` for `mpert` poloidal modes and Hermite order `np`.""" +""" +Construct an empty `GalCell` for `mpert` poloidal modes and Hermite order `np`. +""" function GalCell(mpert::Int, np::Int=GAL_NP) return GalCell(GCT_NONE, GAL_SIDE_NONE, 0, zeros(Int, mpert, np + 1), (0.0, 0.0), 0.0, @@ -79,6 +85,7 @@ Global workspace for the Galerkin solve. Port of Fortran `gal_type` (gal.f:68-76 `intvl` has length `msing+1` (Fortran `intvl(0:msing)`, accessed as `intvl[ising+1]`). `kl = ku = mpert*(np+1)`. The banded `mat` storage layout depends on `solver` (gal.f:164-168): + - `"LU"` → `ldab = 2*kl + ku + 1`, full band (LAPACK `gbtrf!`/`gbtrs!`) - `"cholesky"` → `ldab = kl + 1`, lower band only (LAPACK `pbtrf!`/`pbtrs!`, `'L'`) """ @@ -110,6 +117,24 @@ struct GalSingAsymp left::SingAsymptotics end +""" + GalerkinSolution + +Reconstructed outer-region radial solution on the gal-native grid (Piece 1 producer). Populated by +`gal_output_solution` (GalerkinSolution.jl). + + - `psi::Vector{Float64}`, `q::Vector{Float64}` — radial grid (inner→edge) and its safety factor. + - `issing::Vector{Bool}` — grid points sitting on a singular surface (skipped; left zero). + - `xi::Array{ComplexF64,3}`, `xi_deriv::Array{ComplexF64,3}` — `(mpert, ngrid, nsol)` ξ and dξ/dψ. +""" +struct GalerkinSolution + psi::Vector{Float64} + q::Vector{Float64} + issing::Vector{Bool} + xi::Array{ComplexF64,3} + xi_deriv::Array{ComplexF64,3} +end + """ GalerkinResult @@ -124,6 +149,8 @@ Outputs of the outer-region Galerkin solve. - `msing::Int` — number of resonant singular surfaces included. - `sing_psi, sing_q::Vector{Float64}`, `sing_m, sing_n::Vector{Int}` — per-surface identifiers. - `di::Vector{Float64}`, `alpha::Vector{ComplexF64}` — Mercier index and exponent per surface. + - `solution::Union{Nothing,GalerkinSolution}` — reconstructed radial ξ(ψ) and analytic ξ′(ψ) on the + gal-native grid (Piece 1); `nothing` if no resonant surfaces. """ struct GalerkinResult delta::Matrix{ComplexF64} @@ -139,4 +166,5 @@ struct GalerkinResult di::Vector{Float64} alpha::Vector{ComplexF64} delta_coil::Matrix{ComplexF64} # (mpert, 2*msing) coil-response block (rpec_flag); empty if not computed + solution::Union{Nothing,GalerkinSolution} end From d9c571d2a1c1f70b3a7d662a605c7dcdb42de2a8 Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Tue, 16 Jun 2026 18:46:30 -0400 Subject: [PATCH 056/135] ForceFreeStates Galerkin - NEW - RPEC inner layer matching with GGJ --- benchmarks/verify_gal_match.jl | 49 ++++++++ .../gpec.toml | 8 ++ src/ForceFreeStates/ForceFreeStates.jl | 1 + src/ForceFreeStates/ForceFreeStatesStructs.jl | 6 + src/ForceFreeStates/Galerkin/GalerkinMatch.jl | 107 ++++++++++++++++++ src/ForceFreeStates/Galerkin/GalerkinSolve.jl | 28 ++++- .../Galerkin/GalerkinStructs.jl | 25 ++++ 7 files changed, 221 insertions(+), 3 deletions(-) create mode 100644 benchmarks/verify_gal_match.jl create mode 100644 src/ForceFreeStates/Galerkin/GalerkinMatch.jl diff --git a/benchmarks/verify_gal_match.jl b/benchmarks/verify_gal_match.jl new file mode 100644 index 000000000..86f8cfffe --- /dev/null +++ b/benchmarks/verify_gal_match.jl @@ -0,0 +1,49 @@ +# Piece 2 verification: RPEC outer↔inner matched solution (galerkin/match/*). +# 1. linear-solve residual ‖mat·cof − rmat‖/‖rmat‖ +# 2. matched ξ / ξ′ finiteness +# 3. edge column == identity basis: each coil drive j must give ξ_edge = e_j (the j-th harmonic), +# since plasma columns vanish at the edge and coil column j carries the unit edge source +# 4. inner-layer Δ(Q) per surface (finite, nonzero); forced eigenvalues γ_s = 2πi·n·f +# Usage: julia --project=. benchmarks/verify_gal_match.jl [path/to/gpec.h5] +using HDF5, Printf, LinearAlgebra + +h5path = length(ARGS) >= 1 ? ARGS[1] : "examples/DIIID-like_gal_resistive_example/gpec.h5" +@info "Reading $h5path" + +xi, dxi, cout, cin, deltar, eig, resid, sing_psi = h5open(h5path) do f + (read(f["galerkin/match/xi"]), read(f["galerkin/match/xi_deriv"]), + read(f["galerkin/match/cout"]), read(f["galerkin/match/cin"]), + read(f["galerkin/match/deltar"]), read(f["galerkin/match/rpec_eig"]), + read(f["galerkin/match/residual"]), read(f["galerkin/sing_psi"])) +end +# HDF5 stores ComplexF64 as a compound (re,im); convert if needed +to_c(a) = eltype(a) <: Complex ? a : map(x -> ComplexF64(x.re, x.im), a) +xi = to_c(xi); dxi = to_c(dxi); cout = to_c(cout); cin = to_c(cin); deltar = to_c(deltar); eig = to_c(eig) + +mpert, ngrid, mcoil = size(xi) +msing = size(deltar, 1) +@printf("matched solution: mpert=%d ngrid=%d mcoil=%d msing=%d\n", mpert, ngrid, mcoil, msing) + +@printf("\n[1] linear-solve residual ‖mat·cof − rmat‖/‖rmat‖ = %.3e %s\n", + resid, resid < 1e-8 ? "✓" : "✗ (large)") + +nbad = count(!isfinite, xi) + count(!isfinite, dxi) +@printf("[2] finiteness: non-finite entries = %d |ξ|max=%.3e |ξ′|max=%.3e %s\n", + nbad, maximum(abs, xi), maximum(abs, dxi), nbad == 0 ? "✓" : "✗") + +# [3] edge column == identity (last grid point = psihigh edge) +edge = xi[:, ngrid, :] # (mpert mode, mcoil drive) +id_err = norm(edge - Matrix{ComplexF64}(I, mpert, mcoil)) / sqrt(mpert) +@printf("[3] edge basis: ‖ξ(edge) − I‖/√mpert = %.3e %s\n", + id_err, id_err < 1e-8 ? "✓ identity-at-edge" : "✗") + +# [4] inner-layer Δ and forced eigenvalues +@printf("\n[4] per-surface inner-layer Δ(Q) and forced eigenvalue γ = 2πi·n·f:\n") +@printf(" %-4s %-10s %-26s %-26s\n", "s", "ψ_s", "Δ₁", "Δ₂") +for s in 1:msing + @printf(" %-4d %-10.5f %+.4e%+.4ei %+.4e%+.4ei γ=%+.3f%+.3fi\n", + s, sing_psi[s], real(deltar[s, 1]), imag(deltar[s, 1]), + real(deltar[s, 2]), imag(deltar[s, 2]), real(eig[s]), imag(eig[s])) +end +allgood = resid < 1e-8 && nbad == 0 && id_err < 1e-8 && all(isfinite, deltar) && all(!iszero, deltar) +println(allgood ? "\n✓ Piece 2 matching checks PASS" : "\n✗ some checks failed — investigate") diff --git a/examples/DIIID-like_gal_resistive_example/gpec.toml b/examples/DIIID-like_gal_resistive_example/gpec.toml index e03a3444c..f9d36f168 100644 --- a/examples/DIIID-like_gal_resistive_example/gpec.toml +++ b/examples/DIIID-like_gal_resistive_example/gpec.toml @@ -77,3 +77,11 @@ gal_dx1dx2_flag = true gal_sing_order = 6 gal_sing_order_ceiling = true gal_rpec_flag = true + +# DRIVEN (RPEC) outer↔inner matching. Per-surface resistive inputs (core→edge), mirroring the Fortran +# rmatch DIII-D example: eta=8e-8, massden=3.3e-7 (ni≈1e20 m^-3), rotation=1 Hz, Γ=5/3. 4 surfaces. +gal_match_flag = true +gal_eta = [8e-8, 8e-8, 8e-8, 8e-8] +gal_rho = [3.3e-7, 3.3e-7, 3.3e-7, 3.3e-7] +gal_rotation = [1.0, 1.0, 1.0, 1.0] +gal_gamma = 1.6666666666666667 diff --git a/src/ForceFreeStates/ForceFreeStates.jl b/src/ForceFreeStates/ForceFreeStates.jl index 33f708662..53677e2ad 100644 --- a/src/ForceFreeStates/ForceFreeStates.jl +++ b/src/ForceFreeStates/ForceFreeStates.jl @@ -43,6 +43,7 @@ include("Galerkin/GalerkinStructs.jl") include("Galerkin/GalerkinGrid.jl") include("Galerkin/GalerkinAssembly.jl") include("Galerkin/GalerkinSolution.jl") +include("Galerkin/GalerkinMatch.jl") include("Galerkin/GalerkinSolve.jl") # These are used for various small tolerances and root finders throughout ForceFreeStates diff --git a/src/ForceFreeStates/ForceFreeStatesStructs.jl b/src/ForceFreeStates/ForceFreeStatesStructs.jl index 56e162bd6..51dab7a3e 100644 --- a/src/ForceFreeStates/ForceFreeStatesStructs.jl +++ b/src/ForceFreeStates/ForceFreeStatesStructs.jl @@ -315,6 +315,12 @@ A mutable struct containing control parameters for stability analysis, set by th gal_sing_order_ceiling::Bool = true # auto-raise order by ceil(2·Re(α)) per surface (high Mercier index) gal_rpec_flag::Bool = false # append mpert coil-response columns to the Δ′ solve (RDCON rpec_flag): unit boundary sources whose plasma response is recorded; needed for the driven (resistive perturbed-equilibrium) Δ_gw gal_edge_onesided::Bool = false # pack the two end intervals (`[psilow,first rational]`, `[last rational,psihigh]`) one-sided toward their single rational end instead of the Fortran-faithful symmetric "both" pack. Leaves the regular domain boundary at coarse spacing, removing the gratuitous fine edge cell that inflates cond(A) (entry spread ~1/h²) and seeds the downstream edge-derivative artifact. Default false = faithful to gal.f. + # --- DRIVEN (RPEC) outer↔inner asymptotic matching (rmatch match_rpec port) --- + gal_match_flag::Bool = false # enable the RPEC inner-layer matching: solve the coil-driven matched ξ(ψ) from the gal Δ′ + the inner-layer Δ(Q). Requires gal_rpec_flag=true. + gal_eta::Vector{Float64} = Float64[] # per-surface resistivity η (length msing, core→edge); Fortran rmatch `eta` + gal_rho::Vector{Float64} = Float64[] # per-surface mass density ρ [kg/m³] (length msing, core→edge); Fortran rmatch `massden` + gal_rotation::Vector{Float64} = Float64[] # per-surface rotation frequency f [Hz] (length msing, core→edge); forced eigenvalue γ_s = 2πi·n·f. Fortran rmatch `rotation` + gal_gamma::Float64 = 5 / 3 # ratio of specific heats Γ for the resistive-layer coefficients (resist_eval G term) fixed_axis::Bool = false end diff --git a/src/ForceFreeStates/Galerkin/GalerkinMatch.jl b/src/ForceFreeStates/Galerkin/GalerkinMatch.jl new file mode 100644 index 000000000..1cc21b908 --- /dev/null +++ b/src/ForceFreeStates/Galerkin/GalerkinMatch.jl @@ -0,0 +1,107 @@ +# GalerkinMatch.jl +# +# DRIVEN (RPEC) outer↔inner asymptotic matching. Port of rmatch `match_rpec` (match.f:1318-1510) and the +# outer total-solution construction of `match_output_solution` (match.f:1654-1671). +# +# Per rational surface: the forced eigenvalue γ_s = 2πi·n·f_s (rpec, match.f:1359), the inner-layer +# matching data Δ(Q) via the Galerkin GGJ solver (InnerLayer.solve_inner), then the 4·msing matching +# system mat·[cout;cin] = rmat is assembled (rmat = −transpose of the gal Δ′ coil block) and solved for +# the per-coil outer/inner coefficients. The matched outer solution for coil drive j is +# ξ_j = Σ_{isol=1}^{2 msing} cout[isol,j]·sols[:,:,isol] + sols[:,:,2 msing+j] +# and identically for ξ′ with sols_deriv. Stacking over j gives the matched fundamental matrix in the +# identity-at-edge basis (coil column j has ξ_edge = e_j). + +""" + gal_match_rpec(ctrl, equil, intr, gal_result) -> GalMatchResult + +Solve the coil-driven RPEC matching from the outer Δ′ (`gal_result`) and the per-surface inner-layer Δ. +Requires `gal_result.solution` (reconstructed outer ξ/ξ′), the rpec coil block `gal_result.delta_coil`, +and per-surface resistive inputs `ctrl.gal_eta`/`gal_rho`/`gal_rotation` (length `msing`) + `ctrl.gal_gamma`. +""" +function gal_match_rpec(ctrl::ForceFreeStatesControl, equil, intr::ForceFreeStatesInternal, + gal_result::GalerkinResult) + + msing = gal_result.msing + mpert = intr.numpert_total + nn = intr.nlow + mcoil = mpert # rpec: one coil column per poloidal harmonic + + gal_result.solution !== nothing || + error("gal_match_rpec: gal_result.solution is missing (need the gal-reconstructed ξ/ξ′)") + isempty(gal_result.delta_coil) && + error("gal_match_rpec: delta_coil is empty — gal_rpec_flag must be true for RPEC matching") + for (name, v) in (("gal_eta", ctrl.gal_eta), ("gal_rho", ctrl.gal_rho), ("gal_rotation", ctrl.gal_rotation)) + length(v) == msing || error("gal_match_rpec: $name has length $(length(v)), expected msing=$msing (one value per surface, core→edge)") + end + + # Re-derive the gal singular-surface set (must match galerkin_solve's filter) to get the SingType + # objects resist_eval needs; verify alignment with the stored gal Δ′ surfaces. + psilow = intr.psilow > 0 ? intr.psilow : equil.profiles.xs[1] + psihigh = intr.psilim + sings = [s for s in intr.sing if psilow < s.psifac < psihigh && intr.mlow <= s.m[1] <= intr.mhigh] + length(sings) == msing && isapprox([s.psifac for s in sings], gal_result.sing_psi; rtol=1e-8) || + error("gal_match_rpec: re-derived surface set does not match gal Δ′ surfaces (filter drift?)") + + # --- inner-layer matching data Δ(Q) per surface (deltac_run; match.f:1359-1363) --- + inner = InnerLayer.GGJModel(solver=:galerkin) + deltar = zeros(ComplexF64, msing, 2) + rpec_eig = zeros(ComplexF64, msing) + for i in 1:msing + params = resist_eval(sings[i], equil, intr; eta=ctrl.gal_eta[i], rho=ctrl.gal_rho[i], + gamma=ctrl.gal_gamma, ising=i) + γ = 2π * im * nn * ctrl.gal_rotation[i] # rpec forced eigenvalue 2πi·n·f + rpec_eig[i] = γ + Δ = InnerLayer.solve_inner(inner, params, γ) # (Δ₁, Δ₂) in deltac.f convention + deltar[i, 1] = Δ[1] + deltar[i, 2] = Δ[2] + end + + # --- assemble the 4·msing matching system (match.f:1337-1376) --- + delta_out = gal_result.delta[1:2msing, 1:2msing] # outer Δ′ plasma block + mat = zeros(ComplexF64, 4msing, 4msing) + rmat = zeros(ComplexF64, 4msing, mcoil) + @views mat[2msing+1:4msing, 1:2msing] .= transpose(delta_out) # Δ_out + @views rmat[2msing+1:4msing, :] .= .-transpose(gal_result.delta_coil) # −Δ_coil source + for ising in 1:msing + idx1 = 2ising - 1 + idx2 = 2ising + idx3 = idx1 + 2msing + idx4 = idx2 + 2msing + delta1 = deltar[ising, 1] + delta2 = deltar[ising, 2] + mat[idx1, idx1] = 1 + mat[idx2, idx2] = 1 + mat[idx1, idx3] = -1 + mat[idx1, idx4] = 1 + mat[idx2, idx3] = -1 + mat[idx2, idx4] = -1 + mat[idx3, idx3] = -delta1 # Δ_in + mat[idx3, idx4] = delta2 + mat[idx4, idx3] = -delta1 + mat[idx4, idx4] = -delta2 + end + + # --- solve mat·cof = rmat for the outer/inner coefficients (match.f:1402-1408) --- + cof = mat \ rmat + residual = norm(mat * cof - rmat) / max(norm(rmat), 1e-300) + cout = cof[1:2msing, :] + cin = cof[2msing+1:4msing, :] + + # --- matched outer ξ/ξ′ per coil drive (match.f:1654-1671, resistive branch) --- + sols = gal_result.solution.xi # (mpert, ngrid, nsol) + sols_deriv = gal_result.solution.xi_deriv + ngrid = size(sols, 2) + xi = zeros(ComplexF64, mpert, ngrid, mcoil) + xi_deriv = zeros(ComplexF64, mpert, ngrid, mcoil) + for j in 1:mcoil + csol = 2msing + j # this coil's particular-solution column + @views xi[:, :, j] .= sols[:, :, csol] + @views xi_deriv[:, :, j] .= sols_deriv[:, :, csol] + for isol in 1:2msing + @views xi[:, :, j] .+= cout[isol, j] .* sols[:, :, isol] + @views xi_deriv[:, :, j] .+= cout[isol, j] .* sols_deriv[:, :, isol] + end + end + + return GalMatchResult(cout, cin, xi, xi_deriv, deltar, rpec_eig, residual) +end diff --git a/src/ForceFreeStates/Galerkin/GalerkinSolve.jl b/src/ForceFreeStates/Galerkin/GalerkinSolve.jl index 22c7eab4e..a3bb57325 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinSolve.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinSolve.jl @@ -70,7 +70,7 @@ function galerkin_solve(ctrl::ForceFreeStatesControl, equil, ffit::FourFitVars, ctrl.verbose && @info "galerkin_solve: no resonant surfaces in domain; skipping Δ′ solve" empty2 = Matrix{ComplexF64}(undef, 0, 0) return GalerkinResult(Matrix{ComplexF64}(undef, 0, 0), empty2, empty2, empty2, empty2, 0, - Float64[], Float64[], Int[], Int[], Float64[], ComplexF64[], empty2, nothing) + Float64[], Float64[], Int[], Int[], Float64[], ComplexF64[], empty2, nothing, nothing) end ctrl.verbose && @info "Starting outer-region Galerkin Δ′ solve (msing=$msing, solver=$(ctrl.gal_solver))" @@ -179,9 +179,21 @@ function galerkin_solve(ctrl::ForceFreeStatesControl, equil, ffit::FourFitVars, ctrl.verbose && @info "Reconstructing outer-region ξ and analytic ξ′ on the gal grid" solution = gal_output_solution(ws, asymps, sings, intr, equil.profiles, psihigh) + sing_psi = [s.psifac for s in sings] + sing_q = [s.q for s in sings] + sing_m = [s.m[1] for s in sings] + sing_n = [s.n[1] for s in sings] + result = GalerkinResult(delta, Ap, Bp, Gammap, Deltap, msing, + sing_psi, sing_q, sing_m, sing_n, di, alpha, delta_coil, solution, nothing) + + # DRIVEN (RPEC) outer↔inner matching: build the coil-driven matched ξ/ξ′ (gal_match_rpec). + ctrl.gal_match_flag || return result + ctrl.gal_rpec_flag || error("galerkin_solve: gal_match_flag=true requires gal_rpec_flag=true") + ctrl.verbose && @info "RPEC matching: inner-layer Δ(Q) + outer↔inner solve for the coil-driven ξ" + match = gal_match_rpec(ctrl, equil, intr, result) + ctrl.verbose && @info "RPEC matching: linear-solve residual = $(match.residual)" return GalerkinResult(delta, Ap, Bp, Gammap, Deltap, msing, - [s.psifac for s in sings], [s.q for s in sings], - [s.m[1] for s in sings], [s.n[1] for s in sings], di, alpha, delta_coil, solution) + sing_psi, sing_q, sing_m, sing_n, di, alpha, delta_coil, solution, match) end """ @@ -239,5 +251,15 @@ function write_galerkin!(out_h5, result::GalerkinResult) out_h5["galerkin/solution/xi"] = sol.xi out_h5["galerkin/solution/xi_deriv"] = sol.xi_deriv end + if result.match !== nothing + m = result.match + out_h5["galerkin/match/cout"] = m.cout + out_h5["galerkin/match/cin"] = m.cin + out_h5["galerkin/match/xi"] = m.xi + out_h5["galerkin/match/xi_deriv"] = m.xi_deriv + out_h5["galerkin/match/deltar"] = m.deltar + out_h5["galerkin/match/rpec_eig"] = m.rpec_eig + out_h5["galerkin/match/residual"] = m.residual + end return nothing end diff --git a/src/ForceFreeStates/Galerkin/GalerkinStructs.jl b/src/ForceFreeStates/Galerkin/GalerkinStructs.jl index 450402123..d68d2134d 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinStructs.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinStructs.jl @@ -135,6 +135,30 @@ struct GalerkinSolution xi_deriv::Array{ComplexF64,3} end +""" + GalMatchResult + +Coil-driven RPEC matched solution from the outer↔inner asymptotic matching (Fortran rmatch +`match_rpec`). Populated by `gal_match_rpec` (GalerkinMatch.jl) when `gal_match_flag`. + + - `cout::Matrix{ComplexF64}` — `(2·msing, mcoil)` outer-region plasma-solution coefficients. + - `cin::Matrix{ComplexF64}` — `(2·msing, mcoil)` inner-region coefficients. + - `xi::Array{ComplexF64,3}`, `xi_deriv::Array{ComplexF64,3}` — `(mpert, ngrid, mcoil)` matched ξ(ψ) and + analytic ξ′(ψ) on the gal grid, one column per coil drive (identity-at-edge basis). + - `deltar::Matrix{ComplexF64}` — `(msing, 2)` inner-layer matching data `(Δ₁, Δ₂)` per surface. + - `rpec_eig::Vector{ComplexF64}` — forced eigenvalues `γ_s = 2πi·n·f_s` per surface. + - `residual::Float64` — relative linear-solve residual `‖mat·cof − rmat‖/‖rmat‖`. +""" +struct GalMatchResult + cout::Matrix{ComplexF64} + cin::Matrix{ComplexF64} + xi::Array{ComplexF64,3} + xi_deriv::Array{ComplexF64,3} + deltar::Matrix{ComplexF64} + rpec_eig::Vector{ComplexF64} + residual::Float64 +end + """ GalerkinResult @@ -167,4 +191,5 @@ struct GalerkinResult alpha::Vector{ComplexF64} delta_coil::Matrix{ComplexF64} # (mpert, 2*msing) coil-response block (rpec_flag); empty if not computed solution::Union{Nothing,GalerkinSolution} + match::Union{Nothing,GalMatchResult} # RPEC matched solution (gal_match_flag); nothing otherwise end From 20dc41ee8c56fa2484400c23fe0a48b3456e5702 Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Tue, 16 Jun 2026 20:56:38 -0400 Subject: [PATCH 057/135] ForceFreeStates Galerkin - NEW - DRIVEN/RPEC matched solution into PerturbedEquilibrium + gal_ideal_flag Complete the DRIVEN/RPEC pipeline: gal_matched_odestate packs the coil-matched xi/xi' (+ xi_s via ffit) into an OdeState; main() feeds it to PerturbedEquilibrium when gal_match_flag. Add gal_ideal_flag (skip inner layer, bare coil columns; physically equivalent to DCON). Move the DIIID gal_resistive example to psihigh=0.993 and add inline comments matching the other examples. Add benchmark scan/comparison scripts (eta & rotation scans of the m=2 normal field, gal-vs-EL eigenmode overlay, gal-ideal vs shooting PE). Co-Authored-By: Claude Opus 4.8 --- benchmarks/compare_gal_vs_el.jl | 78 ++++++++ benchmarks/compare_jbgradpsi_m2.jl | 61 ++++++ benchmarks/plot_xi_eigenmode.jl | 61 ++++++ benchmarks/scan_resistivity_m2.jl | 57 ++++++ benchmarks/scan_rotation_m2.jl | 51 +++++ benchmarks/verify_gal_ideal.jl | 30 +++ .../gpec.toml | 145 +++++++------- src/ForceFreeStates/ForceFreeStatesStructs.jl | 1 + src/ForceFreeStates/Galerkin/GalerkinMatch.jl | 187 ++++++++++++------ src/ForceFreeStates/Galerkin/GalerkinSolve.jl | 6 +- src/GeneralizedPerturbedEquilibrium.jl | 14 +- 11 files changed, 559 insertions(+), 132 deletions(-) create mode 100644 benchmarks/compare_gal_vs_el.jl create mode 100644 benchmarks/compare_jbgradpsi_m2.jl create mode 100644 benchmarks/plot_xi_eigenmode.jl create mode 100644 benchmarks/scan_resistivity_m2.jl create mode 100644 benchmarks/scan_rotation_m2.jl create mode 100644 benchmarks/verify_gal_ideal.jl diff --git a/benchmarks/compare_gal_vs_el.jl b/benchmarks/compare_gal_vs_el.jl new file mode 100644 index 000000000..f3facb532 --- /dev/null +++ b/benchmarks/compare_gal_vs_el.jl @@ -0,0 +1,78 @@ +# Overlay the IDEAL gal matched ξ(ψ) against the EL total-energy eigenmode ξ(ψ), for the same edge +# eigenvector w. The ideal gal solution should reproduce the EL (DCON) ideal solution. +# +# EL : ξ_EL(ψ) = U_EL(ψ) · (U_EL_edge \ w) (fundamental matrix, integration/xi_psi) +# gal: ξ_gal(ψ) = U_gal(ψ) · w (identity-at-edge ⇒ coefficient is w itself) +# w = eigenvector of the total energy operator W = W_plasma + W_vacuum (FreeBoundaryStability/XiNorm). +# +# Needs ONE gpec.h5 from a run with populate_dense_xi=true (EL dense u_store), gal_match_flag=true, +# gal_ideal_flag=true (gal ideal matched), vac_flag=true (energy operator). +# Usage: julia --project=. benchmarks/compare_gal_vs_el.jl [gpec.h5] [out.png] [mode] +# mode = "highest" (default, most stable), "lowest" (most unstable), or an integer eigenmode index. + +using HDF5, LinearAlgebra, Plots, Printf + +h5path = length(ARGS) >= 1 ? ARGS[1] : "/tmp/gal_ideal_test/gpec.h5" +outpng = length(ARGS) >= 2 ? ARGS[2] : joinpath(@__DIR__, "compare_gal_vs_el.png") +ksel = length(ARGS) >= 3 ? ARGS[3] : "highest" + +to_c(a) = eltype(a) <: Complex ? ComplexF64.(a) : map(x -> ComplexF64(x.re, x.im), a) + +et, wt, u1, psiE, gxi, psiG, issing, mlow, sing_psi = h5open(h5path) do f + (to_c(read(f["FreeBoundaryStability/XiNorm/eigenmode_energies"])), + to_c(read(f["FreeBoundaryStability/XiNorm/W_freeboundary_eigenmodes"])), + to_c(read(f["integration/xi_psi"])), read(f["integration/psi"]), + to_c(read(f["galerkin/match/xi"])), read(f["galerkin/solution/psi"]), + Bool.(read(f["galerkin/solution/issing"])), read(f["info/mlow"]), + read(f["galerkin/sing_psi"])) +end + +mpert = size(u1, 1) +k = ksel == "highest" ? argmax(real.(et)) : + ksel == "lowest" ? argmin(real.(et)) : + parse(Int, ksel) +w = wt[:, k] +@printf("comparing eigenmode k=%d δW = %.4e %+.4ei\n", k, real(et[k]), imag(et[k])) + +# EL profile +cEL = u1[:, :, end] \ w +xiE = reduce(hcat, (u1[:, :, ip] * cEL for ip in 1:size(u1, 3))) # (mpert, nE) + +# gal ideal profile (identity-at-edge ⇒ coefficient = w); drop on-surface points +keep = .!issing +psiGk = psiG[keep] +xiG = reduce(hcat, (gxi[:, ip, :] * w for ip in findall(keep))) # (mpert, nGk) + +ms = mlow .+ (0:mpert-1) +peak = [maximum(abs, @view xiE[i, :]) for i in 1:mpert] +order = sortperm(peak; rev=true) +ndom = min(5, mpert) + +# quantitative bulk agreement on the dominant harmonic (linear-interp EL onto gal grid, off rationals/edge) +lininterp(xq, x, y) = (j = clamp(searchsortedlast(x, xq), 1, length(x) - 1); +t = (xq - x[j]) / (x[j+1] - x[j]); y[j] * (1 - t) + y[j+1] * t) +idom = order[1] +inbulk(p) = 0.1 <= p <= 0.92 && all(abs(p - ps) > 8e-3 for ps in sing_psi) +sel = [ip for ip in eachindex(psiGk) if inbulk(psiGk[ip])] +num = sum(abs2(xiG[idom, ip] - lininterp(psiGk[ip], psiE, xiE[idom, :])) for ip in sel) +den = sum(abs2(xiG[idom, ip]) for ip in sel) +@printf("dominant m=%d: bulk relative L2 ‖gal−EL‖/‖gal‖ = %.3e (n=%d, off-layer/off-edge)\n", + ms[idom], sqrt(num / den), length(sel)) + +plt = plot(; size=(1000, 650), xlabel="ψ_N", ylabel="|ξ^ψ_m(ψ)|", + title=@sprintf("Ideal gal vs EL total-energy eigenmode (δW=%.2e) — solid: EL, dashed: gal", real(et[k])), + legend=:topleft, left_margin=12Plots.mm, bottom_margin=5Plots.mm, right_margin=4Plots.mm) +palette = theme_palette(:auto) +for (c, i) in enumerate(order[1:ndom]) + col = palette[mod1(c, length(palette))] + plot!(plt, psiE, abs.(@view xiE[i, :]); color=col, lw=2.2, label="EL m=$(ms[i])") + plot!(plt, psiGk, abs.(@view xiG[i, :]); color=col, lw=1.6, ls=:dash, label="gal m=$(ms[i])") +end +for (j, ps) in enumerate(sing_psi) + vline!(plt, [ps]; color=:black, ls=:dot, lw=1, label=(j == 1 ? "rational q" : "")) +end + +display(plt) +savefig(plt, outpng) +println("dominant harmonics (m): ", [ms[i] for i in order[1:ndom]]) +println("saved: ", abspath(outpng)) diff --git a/benchmarks/compare_jbgradpsi_m2.jl b/benchmarks/compare_jbgradpsi_m2.jl new file mode 100644 index 000000000..b8da06fcc --- /dev/null +++ b/benchmarks/compare_jbgradpsi_m2.jl @@ -0,0 +1,61 @@ +# Compare the area-normalized b^ψ (perturbed_equilibrium/response/psi_area = b^ψ/⟨J·|∇ψ|⟩_θ) for one +# poloidal harmonic between two GPEC runs that are identical except for which ξ feeds PerturbedEquilibrium: +# (1) IDEAL galerkin matched ξ (gal_match_flag=true, gal_ideal_flag=true) +# (2) SHOOTING ξ (gal_match_flag=false) +# +# PE writes no ψ grid, so it's reconstructed: gal-ideal → galerkin/solution/psi minus issing points; +# shooting → integration/psi. +# Usage: julia --project=. benchmarks/compare_jbgradpsi_m2.jl [gal_h5] [shoot_h5] [out.png] [m] + +using HDF5, Plots, Printf + +gal_h5 = length(ARGS) >= 1 ? ARGS[1] : "/tmp/gal_ideal_test/gpec.h5" +sh_h5 = length(ARGS) >= 2 ? ARGS[2] : "/tmp/shooting_test/gpec.h5" +outpng = length(ARGS) >= 3 ? ARGS[3] : joinpath(@__DIR__, "cmp_jbgradpsi_m2.png") +mtarget = length(ARGS) >= 4 ? parse(Int, ARGS[4]) : 2 + +to_c(a) = eltype(a) <: Complex ? ComplexF64.(a) : map(x -> ComplexF64(x.re, x.im), a) + +# gal-ideal run: PE grid = gal solution grid with the on-surface (issing) points dropped +pa_g, psi_g, mlow, sing_psi, sing_m = h5open(gal_h5) do f + pa = to_c(read(f["perturbed_equilibrium/response/psi_area"])) # [npsi, mpert] + iss = Bool.(read(f["galerkin/solution/issing"])) + (pa, read(f["galerkin/solution/psi"])[.!iss], read(f["info/mlow"]), + read(f["galerkin/sing_psi"]), read(f["galerkin/sing_m"])) +end +# shooting run: PE grid = integration/psi +pa_s, psi_s = h5open(sh_h5) do f + (to_c(read(f["perturbed_equilibrium/response/psi_area"])), read(f["integration/psi"])) +end + +size(pa_g, 1) == length(psi_g) || error("gal grid mismatch: npsi=$(size(pa_g,1)) vs grid=$(length(psi_g))") +size(pa_s, 1) == length(psi_s) || error("shoot grid mismatch: npsi=$(size(pa_s,1)) vs grid=$(length(psi_s))") + +col = mtarget - mlow + 1 +@printf("m=%d → column %d (mlow=%d, mpert=%d)\n", mtarget, col, mlow, size(pa_g, 2)) +g = @view pa_g[:, col] +s = @view pa_s[:, col] + +# resonant surface for this m (q = m/n) +psi_res = mtarget in sing_m ? sing_psi[findfirst(==(mtarget), sing_m)] : NaN +# value at the grid point nearest the resonant surface, each run +if !isnan(psi_res) + ig = argmin(abs.(psi_g .- psi_res)) + is = argmin(abs.(psi_s .- psi_res)) + @printf("m=%d resonant surface ψ=%.4f\n", mtarget, psi_res) + @printf(" nearest |b^ψ_area|: gal-ideal=%.4e (ψ=%.4f) shooting=%.4e (ψ=%.4f) ratio=%.3f\n", + abs(g[ig]), psi_g[ig], abs(s[is]), psi_s[is], abs(g[ig]) / abs(s[is])) +end + +plt = plot(; size=(1000, 620), xlabel="ψ_N", ylabel="|b^ψ / ⟨J·|∇ψ|⟩| (area-normalized)", + title="m=$mtarget perturbed normal field — gal-ideal vs shooting PE", legend=:topleft, + left_margin=13Plots.mm, bottom_margin=5Plots.mm, right_margin=4Plots.mm) +plot!(plt, psi_g, abs.(g); lw=2.2, color=1, label="gal-ideal ξ → PE") +plot!(plt, psi_s, abs.(s); lw=1.8, color=2, ls=:dash, label="shooting ξ → PE") +for (j, ps) in enumerate(sing_psi) + ism2 = sing_m[j] == mtarget + vline!(plt, [ps]; color=(ism2 ? :red : :black), ls=:dot, lw=(ism2 ? 1.8 : 1), + label=(ism2 ? "q=$mtarget surface" : (j == 1 ? "rational q" : ""))) +end +savefig(plt, outpng) +println("saved: ", abspath(outpng)) diff --git a/benchmarks/plot_xi_eigenmode.jl b/benchmarks/plot_xi_eigenmode.jl new file mode 100644 index 000000000..842e0cc5c --- /dev/null +++ b/benchmarks/plot_xi_eigenmode.jl @@ -0,0 +1,61 @@ +# Plot the ξ(ψ) profile of the eigenmode with the highest total-energy eigenvalue. +# +# The total energy operator W = W_plasma + W_vacuum (free_run!, Free.jl); its eigenvectors are the +# free-boundary edge displacement patterns and the eigenvalues are δW. This picks the eigenmode with the +# largest Re(eigenvalue) and reconstructs its radial profile by projecting the EL fundamental matrix +# (integration/xi_psi) onto that edge eigenvector: c = U_edge \ w, ξ(ψ) = U(ψ)·c. +# +# Requires a run with populate_dense_xi=true so integration/xi_psi is the dense axis-basis fundamental +# matrix (not the Riccati S-matrices). +# Usage: julia --project=. benchmarks/plot_xi_eigenmode.jl [path/to/gpec.h5] [out.png] + +using HDF5, LinearAlgebra, Plots, Printf + +h5path = length(ARGS) >= 1 ? ARGS[1] : "examples/DIIID-like_ideal_example/gpec.h5" +outpng = length(ARGS) >= 2 ? ARGS[2] : joinpath(@__DIR__, "xi_eigenmode.png") + +to_c(a) = eltype(a) <: Complex ? ComplexF64.(a) : map(x -> ComplexF64(x.re, x.im), a) + +et, wt, u1, psi, mlow, sing_psi = h5open(h5path) do f + (to_c(read(f["FreeBoundaryStability/XiNorm/eigenmode_energies"])), + to_c(read(f["FreeBoundaryStability/XiNorm/W_freeboundary_eigenmodes"])), + to_c(read(f["integration/xi_psi"])), + read(f["integration/psi"]), + read(f["info/mlow"]), + haskey(f, "galerkin/sing_psi") ? read(f["galerkin/sing_psi"]) : Float64[]) +end + +mpert, _, nstep = size(u1) +k = argmax(real.(et)) # eigenmode with the highest total-energy eigenvalue +@printf("highest-eigenvalue mode: k=%d δW = %.4e %+.4ei (of %d modes)\n", + k, real(et[k]), imag(et[k]), length(et)) + +# Reconstruct ξ(ψ) for the eigenmode whose edge displacement is the eigenvector w = wt[:,k]. +w = wt[:, k] +U_edge = u1[:, :, nstep] # edge fundamental matrix (psi inner→edge, last index = edge) +c = U_edge \ w # U_edge·c = w +xi = Array{ComplexF64}(undef, mpert, nstep) +for ip in 1:nstep + @views mul!(xi[:, ip], u1[:, :, ip], c) +end + +ms = mlow .+ (0:mpert-1) +peak = [maximum(abs, @view xi[i, :]) for i in 1:mpert] +order = sortperm(peak; rev=true) # dominant harmonics first + +plt = plot(; size=(950, 620), xlabel="ψ_N", ylabel="|ξ^ψ_m(ψ)|", + title=@sprintf("Highest total-energy eigenmode δW = %.3e", real(et[k])), + legend=:topleft, left_margin=12Plots.mm, bottom_margin=5Plots.mm, right_margin=4Plots.mm) +for i in 1:mpert # all harmonics, faint + plot!(plt, psi, abs.(@view xi[i, :]); color=:gray85, lw=0.6, label="") +end +for i in order[1:min(8, mpert)] # dominant harmonics, bold + labeled + plot!(plt, psi, abs.(@view xi[i, :]); lw=2, label="m=$(ms[i])") +end +for (j, ps) in enumerate(sing_psi) # rational surfaces + vline!(plt, [ps]; color=:black, ls=:dash, lw=1, label=(j == 1 ? "rational q" : "")) +end + +savefig(plt, outpng) +println("dominant harmonics (m): ", [ms[i] for i in order[1:min(8, mpert)]]) +println("saved: ", abspath(outpng)) diff --git a/benchmarks/scan_resistivity_m2.jl b/benchmarks/scan_resistivity_m2.jl new file mode 100644 index 000000000..5ed0931dc --- /dev/null +++ b/benchmarks/scan_resistivity_m2.jl @@ -0,0 +1,57 @@ +# Plot the m=2 area-normalized b^ψ (perturbed_equilibrium/response/psi_area) across a resistivity scan +# of the RESISTIVE gal matched PE runs (gal_match_flag=true, gal_ideal_flag=false), one curve per η. +# Overlays the shooting (ideal, η→0) reference. The η-scan dirs are produced by the bash loop over +# /tmp/etascan_ (each a copy of the 0.993 config with gal_eta scaled). +# Usage: julia --project=. benchmarks/scan_resistivity_m2.jl [out.png] [m] + +using HDF5, Plots, Printf, TOML + +outpng = length(ARGS) >= 1 ? ARGS[1] : joinpath(@__DIR__, "scan_resistivity_m2.png") +mtarget = length(ARGS) >= 2 ? parse(Int, ARGS[2]) : 2 + +to_c(a) = eltype(a) <: Complex ? ComplexF64.(a) : map(x -> ComplexF64(x.re, x.im), a) + +# read m=target area-normalized b^ψ on the run's PE grid +function read_m2(h5; gal::Bool) + h5open(h5) do f + pa = to_c(read(f["perturbed_equilibrium/response/psi_area"])) # [npsi, mpert] + col = mtarget - read(f["info/mlow"]) + 1 + psi = gal ? read(f["galerkin/solution/psi"])[.!Bool.(read(f["galerkin/solution/issing"]))] : + read(f["integration/psi"]) + (psi, pa[:, col]) + end +end + +# collect scan dirs that finished +scandirs = filter(d -> isfile(joinpath(d, "gpec.h5")), + ["/tmp/etascan_0p01", "/tmp/etascan_0p1", "/tmp/etascan_1", "/tmp/etascan_10", "/tmp/etascan_100"]) +etas = [TOML.parsefile(joinpath(d, "gpec.toml"))["ForceFreeStates"]["gal_eta"][1] for d in scandirs] +ord = sortperm(etas) +scandirs, etas = scandirs[ord], etas[ord] +eta_ref = 8e-8 +@printf("%d scan runs: η = %s (×η_ref where η_ref=%.0e)\n", length(etas), + join((@sprintf("%.0e", e) for e in etas), ", "), eta_ref) + +# rational surface for m=target +sing_psi, sing_m = h5open(joinpath(scandirs[1], "gpec.h5")) do f + (read(f["galerkin/sing_psi"]), read(f["galerkin/sing_m"])) +end +psi_res = mtarget in sing_m ? sing_psi[findfirst(==(mtarget), sing_m)] : NaN + +cols = cgrad(:viridis, max(length(etas), 2); categorical=true) +plt = plot(; size=(1000, 640), xlabel="ψ_N", ylabel="|b^ψ / ⟨J·|∇ψ|⟩| (area-normalized)", + title="m=$mtarget perturbed normal field — resistivity scan (resistive gal-matched PE)", + legend=:topleft, left_margin=13Plots.mm, bottom_margin=5Plots.mm, right_margin=4Plots.mm) +for (i, (d, e)) in enumerate(zip(scandirs, etas)) + psi, v = read_m2(joinpath(d, "gpec.h5"); gal=true) + plot!(plt, psi, abs.(v); color=cols[i], lw=2, label=@sprintf("η = %g×η_ref", round(e / eta_ref; sigdigits=2))) +end +# shooting (ideal, η→0) reference +if isfile("/tmp/shooting_test/gpec.h5") + psis, vs = read_m2("/tmp/shooting_test/gpec.h5"; gal=false) + plot!(plt, psis, abs.(vs); color=:black, ls=:dash, lw=2, label="shooting (ideal, η→0)") +end +isnan(psi_res) || vline!(plt, [psi_res]; color=:red, ls=:dot, lw=1.6, label="q=$mtarget surface") + +savefig(plt, outpng) +println("saved: ", abspath(outpng)) diff --git a/benchmarks/scan_rotation_m2.jl b/benchmarks/scan_rotation_m2.jl new file mode 100644 index 000000000..63cf2f04d --- /dev/null +++ b/benchmarks/scan_rotation_m2.jl @@ -0,0 +1,51 @@ +# Plot the m=2 area-normalized b^ψ (perturbed_equilibrium/response/psi_area) across a ROTATION scan +# of the resistive gal matched PE runs (gal_match_flag=true, gal_ideal_flag=false), fixed η=8e-8, +# rotation f = 1,2,4,8,16 Hz (forced eigenvalue γ_s = 2πi·n·f). One curve per rotation; overlays the +# shooting (ideal) reference. Scan dirs produced by the bash loop over /tmp/rotscan_. +# Usage: julia --project=. benchmarks/scan_rotation_m2.jl [out.png] [m] + +using HDF5, Plots, Printf, TOML + +outpng = length(ARGS) >= 1 ? ARGS[1] : joinpath(@__DIR__, "scan_rotation_m2.png") +mtarget = length(ARGS) >= 2 ? parse(Int, ARGS[2]) : 2 + +to_c(a) = eltype(a) <: Complex ? ComplexF64.(a) : map(x -> ComplexF64(x.re, x.im), a) + +function read_m2(h5; gal::Bool) + h5open(h5) do f + pa = to_c(read(f["perturbed_equilibrium/response/psi_area"])) + col = mtarget - read(f["info/mlow"]) + 1 + psi = gal ? read(f["galerkin/solution/psi"])[.!Bool.(read(f["galerkin/solution/issing"]))] : + read(f["integration/psi"]) + (psi, pa[:, col]) + end +end + +scandirs = filter(d -> isfile(joinpath(d, "gpec.h5")), + ["/tmp/rotscan_1", "/tmp/rotscan_2", "/tmp/rotscan_4", "/tmp/rotscan_8", "/tmp/rotscan_16"]) +rots = [TOML.parsefile(joinpath(d, "gpec.toml"))["ForceFreeStates"]["gal_rotation"][1] for d in scandirs] +ord = sortperm(rots) +scandirs, rots = scandirs[ord], rots[ord] +@printf("%d scan runs: rotation f = %s Hz (η fixed = 8e-8)\n", length(rots), join((@sprintf("%g", r) for r in rots), ", ")) + +sing_psi, sing_m = h5open(joinpath(scandirs[1], "gpec.h5")) do f + (read(f["galerkin/sing_psi"]), read(f["galerkin/sing_m"])) +end +psi_res = mtarget in sing_m ? sing_psi[findfirst(==(mtarget), sing_m)] : NaN + +cols = cgrad(:plasma, max(length(rots), 2); categorical=true) +plt = plot(; size=(1000, 640), xlabel="ψ_N", ylabel="|b^ψ / ⟨J·|∇ψ|⟩| (area-normalized)", + title="m=$mtarget perturbed normal field — rotation scan (η=8e-8, resistive gal-matched PE)", + legend=:topleft, left_margin=13Plots.mm, bottom_margin=5Plots.mm, right_margin=4Plots.mm) +for (i, (d, r)) in enumerate(zip(scandirs, rots)) + psi, v = read_m2(joinpath(d, "gpec.h5"); gal=true) + plot!(plt, psi, abs.(v); color=cols[i], lw=2, label=@sprintf("f = %g Hz", r)) +end +if isfile("/tmp/shooting_test/gpec.h5") + psis, vs = read_m2("/tmp/shooting_test/gpec.h5"; gal=false) + plot!(plt, psis, abs.(vs); color=:black, ls=:dash, lw=2, label="shooting (ideal)") +end +isnan(psi_res) || vline!(plt, [psi_res]; color=:red, ls=:dot, lw=1.6, label="q=$mtarget surface") + +savefig(plt, outpng) +println("saved: ", abspath(outpng)) diff --git a/benchmarks/verify_gal_ideal.jl b/benchmarks/verify_gal_ideal.jl new file mode 100644 index 000000000..1c0d0ad41 --- /dev/null +++ b/benchmarks/verify_gal_ideal.jl @@ -0,0 +1,30 @@ +# Verify the gal_ideal_flag path: the matched solution is the bare ideal coil column (cout=0). +# 1. cout / cin / deltar all zero (no resistive plasma combination, no inner layer) +# 2. matched ξ_j == the gal coil column sols(:,:,2·msing+j) (and ξ′ likewise) +# Usage: julia --project=. benchmarks/verify_gal_ideal.jl [path/to/gpec.h5] +using HDF5, Printf, LinearAlgebra + +h5path = length(ARGS) >= 1 ? ARGS[1] : "/tmp/gal_ideal_test/gpec.h5" +to_c(a) = eltype(a) <: Complex ? ComplexF64.(a) : map(x -> ComplexF64(x.re, x.im), a) + +cout, deltar, mxi, mdxi, sols, sols_d, sing_psi = h5open(h5path) do f + (to_c(read(f["galerkin/match/cout"])), to_c(read(f["galerkin/match/deltar"])), + to_c(read(f["galerkin/match/xi"])), to_c(read(f["galerkin/match/xi_deriv"])), + to_c(read(f["galerkin/solution/xi"])), to_c(read(f["galerkin/solution/xi_deriv"])), + read(f["galerkin/sing_psi"])) +end +msing = length(sing_psi) +mpert, ngrid, mcoil = size(mxi) + +@printf("[1] ‖cout‖ = %.2e, ‖deltar‖ = %.2e %s\n", norm(cout), norm(deltar), + (norm(cout) == 0 && norm(deltar) == 0) ? "✓ no resistive combination (ideal)" : "✗") + +# matched ξ_j should equal the coil column sols(:,:,2msing+j) +err = maximum(1:mcoil) do j + csol = 2msing + j + max(norm(mxi[:, :, j] - sols[:, :, csol]), norm(mdxi[:, :, j] - sols_d[:, :, csol])) +end +@printf("[2] max‖ξ_matched − coil column‖ = %.2e %s\n", err, + err < 1e-12 ? "✓ matched ξ == bare ideal coil column" : "✗") + +println((norm(cout) == 0 && err < 1e-12) ? "\n✓ gal_ideal_flag path verified" : "\n✗ investigate") diff --git a/examples/DIIID-like_gal_resistive_example/gpec.toml b/examples/DIIID-like_gal_resistive_example/gpec.toml index f9d36f168..b52110c22 100644 --- a/examples/DIIID-like_gal_resistive_example/gpec.toml +++ b/examples/DIIID-like_gal_resistive_example/gpec.toml @@ -1,87 +1,88 @@ [Equilibrium] -eq_filename = "TkMkr_D3Dlike_Hmode.geqdsk" -eq_type = "efit" -jac_type = "hamada" -power_bp = 0 -power_b = 0 -power_r = 0 -grid_type = "ldp" -psilow = 1e-4 -psihigh = 0.9981 -mpsi = 128 -psi_accuracy = 0.001 -mtheta = 256 -newq0 = 0 -etol = 1e-10 -force_termination = false +eq_filename = "TkMkr_D3Dlike_Hmode.geqdsk" # Path to equilibrium file +eq_type = "efit" # Type of the input 2D equilibrium file +jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc) +power_bp = 0 # Poloidal field power exponent for Jacobian +power_b = 0 # Toroidal field power exponent for Jacobian +power_r = 0 # Major radius power exponent for Jacobian +grid_type = "ldp" # Radial grid packing type (ldp = linear-derivative packing toward rationals) +psilow = 1e-4 # Lower limit of normalized flux coordinate +psihigh = 0.993 # Upper limit of normalized flux coordinate (0.993 stays clear of the separatrix; truncating at ≳0.998 is numerically unreasonable here) +mpsi = 128 # Number of radial grid points (0 = auto-compute from psi_accuracy) +psi_accuracy = 0.001 # Target absolute error in q for auto-mpsi +mtheta = 256 # Number of poloidal grid points +newq0 = 0 # Override for on-axis safety factor (0 = use input value) +etol = 1e-10 # Error tolerance for equilibrium solver +force_termination = false # Terminate after equilibrium setup (skip stability calculations) [Wall] -shape = "nowall" -a = 0.2415 -aw = 0.05 -bw = 1.5 -cw = 0 -dw = 0.5 -tw = 0.05 -equal_arc_wall = true +shape = "nowall" # Wall shape (nowall, conformal, elliptical, dee, mod_dee, filepath) +a = 0.2415 # Distance from plasma (conformal) or shape parameter +aw = 0.05 # Half-thickness parameter for Dee-shaped walls +bw = 1.5 # Elongation parameter for wall shapes +cw = 0 # Offset of wall center from major radius +dw = 0.5 # Triangularity parameter for wall shapes +tw = 0.05 # Sharpness of wall corners (try 0.05 as initial value) +equal_arc_wall = true # Equal arc length distribution of nodes on wall [ForceFreeStates] -bal_flag = false -mat_flag = true -ode_flag = true -vac_flag = true -mer_flag = true +bal_flag = false # Ideal MHD ballooning criterion for short wavelengths +mat_flag = true # Construct coefficient matrices for diagnostic purposes (required by gal_flag) +ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) +vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes +mer_flag = true # Evaluate the Mercier criterion -psiedge = 0.99 -qlow = 1.02 -qhigh = 1e3 -sing_start = 0 +psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak +qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... +qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)... +sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) -nn_low = 1 -nn_high = 1 -delta_mlow = 8 -delta_mhigh = 4 -delta_mband = 0 -mthvac = 512 -thmax0 = 1 +nn_low = 1 # Smallest toroidal mode number to include +nn_high = 1 # Largest toroidal mode number to include +delta_mlow = 8 # Expands lower bound of Fourier harmonics +delta_mhigh = 4 # Expands upper bound of Fourier harmonics +delta_mband = 0 # Integration keeps only this wide a band of solutions along the m,m' diagonal (0 = full) +mthvac = 512 # Number of points used in splines over poloidal angle at plasma-vacuum interface. +thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds -kinetic_source = "fixed" -kinetic_factor = 0.0 -eulerlagrange_tolerance = 1e-10 -save_interval = 3 -singfac_min = 1e-4 -ucrit = 1e4 +kinetic_source = "fixed" # Kinetic matrix source ("fixed" test matrices, or "calculated" from PENTRC) +kinetic_factor = 0.0 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode) +eulerlagrange_tolerance = 1e-10# Relative tolerance for ODE integration of Euler-Lagrange equations +save_interval = 3 # Save every Nth ODE step (1=all, 10=every 10th). Always saves near rational surfaces. +singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced +ucrit = 1e4 # Maximum fraction of solutions allowed before re-normalized -# Riccati / STRIDE-style global BVP Δ′ matrix -use_parallel = true -parallel_threads = 2 -populate_dense_xi = false -truncate_at_dW_peak = false -set_psilim_via_dmlim = false -dmlim = 0.2 +# Δ' BVP + parallel integration (see ForceFreeStatesControl docstring for details) +use_parallel = true # Run parallel FM-propagator BVP path (unlocks singular/delta_prime_matrix) +parallel_threads = 2 # BVP thread cap (1 = serial/bit-deterministic; 2 ≈ +20% speedup; ≥3 saturates) +populate_dense_xi = false # Dense axis-basis ξ for the FFS HDF5 output. Not needed here: no [PerturbedEquilibrium] section, and the gal-matched path builds its own dense ξ. Set true only for a shooting-fed PE run. +truncate_at_dW_peak = false # Edge-dW scan stays diagnostic; integration domain set by qhigh / psihigh / dmlim +set_psilim_via_dmlim = false # Keep psilim at psihigh (do not truncate at last_rational_q + dmlim) +dmlim = 0.2 # Truncate integration at (last_rational_q + dmlim) / n (only used when set_psilim_via_dmlim = true) # RDCON outer-region singular Galerkin Δ′ solver with rpec coil columns (matched to Fortran &GAL_INPUT). # This case exercises the gal solve AND the rpec coil/edge path (delta_coil) for regression tracking. -gal_flag = true -gal_solver = "LU" -gal_nx = 256 -gal_nq = 6 -gal_pfac = 0.03 -gal_dx0 = 5e-4 -gal_dx1 = 1e-3 -gal_dx2 = 1e-3 -gal_cutoff = 10 -gal_tol = 1e-10 -gal_gnstep = 5000 -gal_dx1dx2_flag = true -gal_sing_order = 6 -gal_sing_order_ceiling = true -gal_rpec_flag = true +gal_flag = true # Enable the outer-region singular Galerkin Δ′ solve (requires mat_flag = true) +gal_solver = "LU" # Banded solver: "LU" (zgbtrf/zgbtrs) or "cholesky" (zpbtrf/zpbtrs). rpec requires "LU". +gal_nx = 256 # Hermite-cubic elements per interval between singular surfaces +gal_nq = 6 # Gauss-Lobatto quadrature order per element +gal_pfac = 0.03 # Grid packing ratio toward singular surfaces (smaller = tighter packing) +gal_dx0 = 5e-4 # Resonant-element integration truncation distance from the rational (× 1/|n q'|) +gal_dx1 = 1e-3 # Resonant-element size (× 1/|n q'|) +gal_dx2 = 1e-3 # Extension-element size (× 1/|n q'|) +gal_cutoff = 10 # Number of elements carrying the large (driving) solution as a source term +gal_tol = 1e-10 # Resonant-cell adaptive-quadrature (QuadGK) tolerance +gal_gnstep = 5000 # Maximum resonant-integration steps +gal_dx1dx2_flag = true # Enable the special dx1/dx2 element sizing for resonant/extension cells +gal_sing_order = 6 # Base power-series order for the Galerkin singular asymptotics +gal_sing_order_ceiling = true # Auto-raise the series order by ceil(2·Re(α)) on high-Mercier-index surfaces +gal_rpec_flag = true # Append mpert coil-response columns (unit edge sources) to the solve → delta_coil block # DRIVEN (RPEC) outer↔inner matching. Per-surface resistive inputs (core→edge), mirroring the Fortran # rmatch DIII-D example: eta=8e-8, massden=3.3e-7 (ni≈1e20 m^-3), rotation=1 Hz, Γ=5/3. 4 surfaces. -gal_match_flag = true -gal_eta = [8e-8, 8e-8, 8e-8, 8e-8] -gal_rho = [3.3e-7, 3.3e-7, 3.3e-7, 3.3e-7] -gal_rotation = [1.0, 1.0, 1.0, 1.0] -gal_gamma = 1.6666666666666667 +gal_match_flag = true # Solve the coil-driven matched ξ(ψ) from the gal Δ′ + the inner-layer Δ(Q). Requires gal_rpec_flag = true. +gal_ideal_flag = false # true → build the IDEAL solution (skip the inner layer, bare coil columns; ≡ DCON). false → the resistive matching below. +gal_eta = [8e-8, 8e-8, 8e-8, 8e-8] # Per-surface resistivity η (core→edge); Fortran rmatch `eta` +gal_rho = [3.3e-7, 3.3e-7, 3.3e-7, 3.3e-7] # Per-surface mass density ρ [kg/m³] (core→edge); Fortran rmatch `massden` +gal_rotation = [1.0, 1.0, 1.0, 1.0] # Per-surface rotation frequency f [Hz] (core→edge); forced eigenvalue γ_s = 2πi·n·f. Fortran rmatch `rotation` +gal_gamma = 1.6666666666666667 # Ratio of specific heats Γ for the resistive-layer coefficients (5/3) diff --git a/src/ForceFreeStates/ForceFreeStatesStructs.jl b/src/ForceFreeStates/ForceFreeStatesStructs.jl index 51dab7a3e..d52adf3a0 100644 --- a/src/ForceFreeStates/ForceFreeStatesStructs.jl +++ b/src/ForceFreeStates/ForceFreeStatesStructs.jl @@ -317,6 +317,7 @@ A mutable struct containing control parameters for stability analysis, set by th gal_edge_onesided::Bool = false # pack the two end intervals (`[psilow,first rational]`, `[last rational,psihigh]`) one-sided toward their single rational end instead of the Fortran-faithful symmetric "both" pack. Leaves the regular domain boundary at coarse spacing, removing the gratuitous fine edge cell that inflates cond(A) (entry spread ~1/h²) and seeds the downstream edge-derivative artifact. Default false = faithful to gal.f. # --- DRIVEN (RPEC) outer↔inner asymptotic matching (rmatch match_rpec port) --- gal_match_flag::Bool = false # enable the RPEC inner-layer matching: solve the coil-driven matched ξ(ψ) from the gal Δ′ + the inner-layer Δ(Q). Requires gal_rpec_flag=true. + gal_ideal_flag::Bool = false # within the match (gal_match_flag), build the IDEAL solution instead of the resistive one: skip the inner-layer Δ and use the bare coil columns (cout=0). Mirrors Fortran rmatch coil%ideal_flag; "physically equivalent to regular DCON" — the EL reference. eta/rho/rotation are ignored. gal_eta::Vector{Float64} = Float64[] # per-surface resistivity η (length msing, core→edge); Fortran rmatch `eta` gal_rho::Vector{Float64} = Float64[] # per-surface mass density ρ [kg/m³] (length msing, core→edge); Fortran rmatch `massden` gal_rotation::Vector{Float64} = Float64[] # per-surface rotation frequency f [Hz] (length msing, core→edge); forced eigenvalue γ_s = 2πi·n·f. Fortran rmatch `rotation` diff --git a/src/ForceFreeStates/Galerkin/GalerkinMatch.jl b/src/ForceFreeStates/Galerkin/GalerkinMatch.jl index 1cc21b908..dd11cae96 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinMatch.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinMatch.jl @@ -15,8 +15,11 @@ gal_match_rpec(ctrl, equil, intr, gal_result) -> GalMatchResult Solve the coil-driven RPEC matching from the outer Δ′ (`gal_result`) and the per-surface inner-layer Δ. -Requires `gal_result.solution` (reconstructed outer ξ/ξ′), the rpec coil block `gal_result.delta_coil`, -and per-surface resistive inputs `ctrl.gal_eta`/`gal_rho`/`gal_rotation` (length `msing`) + `ctrl.gal_gamma`. +Requires `gal_result.solution` (reconstructed outer ξ/ξ′) and the rpec coil block `gal_result.delta_coil`. + +The resistive path uses per-surface inputs `ctrl.gal_eta`/`gal_rho`/`gal_rotation` (length `msing`) + +`ctrl.gal_gamma`. When `ctrl.gal_ideal_flag`, the inner layer is skipped and `cout=0`, so the matched +solution is the bare ideal coil column (Fortran rmatch `coil%ideal_flag`) — the DCON/EL reference. """ function gal_match_rpec(ctrl::ForceFreeStatesControl, equil, intr::ForceFreeStatesInternal, gal_result::GalerkinResult) @@ -30,64 +33,76 @@ function gal_match_rpec(ctrl::ForceFreeStatesControl, equil, intr::ForceFreeStat error("gal_match_rpec: gal_result.solution is missing (need the gal-reconstructed ξ/ξ′)") isempty(gal_result.delta_coil) && error("gal_match_rpec: delta_coil is empty — gal_rpec_flag must be true for RPEC matching") - for (name, v) in (("gal_eta", ctrl.gal_eta), ("gal_rho", ctrl.gal_rho), ("gal_rotation", ctrl.gal_rotation)) - length(v) == msing || error("gal_match_rpec: $name has length $(length(v)), expected msing=$msing (one value per surface, core→edge)") - end - # Re-derive the gal singular-surface set (must match galerkin_solve's filter) to get the SingType - # objects resist_eval needs; verify alignment with the stored gal Δ′ surfaces. - psilow = intr.psilow > 0 ? intr.psilow : equil.profiles.xs[1] - psihigh = intr.psilim - sings = [s for s in intr.sing if psilow < s.psifac < psihigh && intr.mlow <= s.m[1] <= intr.mhigh] - length(sings) == msing && isapprox([s.psifac for s in sings], gal_result.sing_psi; rtol=1e-8) || - error("gal_match_rpec: re-derived surface set does not match gal Δ′ surfaces (filter drift?)") - - # --- inner-layer matching data Δ(Q) per surface (deltac_run; match.f:1359-1363) --- - inner = InnerLayer.GGJModel(solver=:galerkin) - deltar = zeros(ComplexF64, msing, 2) - rpec_eig = zeros(ComplexF64, msing) - for i in 1:msing - params = resist_eval(sings[i], equil, intr; eta=ctrl.gal_eta[i], rho=ctrl.gal_rho[i], - gamma=ctrl.gal_gamma, ising=i) - γ = 2π * im * nn * ctrl.gal_rotation[i] # rpec forced eigenvalue 2πi·n·f - rpec_eig[i] = γ - Δ = InnerLayer.solve_inner(inner, params, γ) # (Δ₁, Δ₂) in deltac.f convention - deltar[i, 1] = Δ[1] - deltar[i, 2] = Δ[2] - end + if ctrl.gal_ideal_flag + # Ideal limit (Fortran rmatch coil%ideal_flag, match.f:1665-1671): skip the inner layer entirely + # and set the resistive plasma combination to zero. The gal outer solve is already fully ideal, so + # the shared construction below collapses to the bare ideal coil column sols(:,:,csol). + cout = zeros(ComplexF64, 2msing, mcoil) + cin = zeros(ComplexF64, 2msing, mcoil) + deltar = zeros(ComplexF64, msing, 2) + rpec_eig = zeros(ComplexF64, msing) + residual = 0.0 + else + for (name, v) in (("gal_eta", ctrl.gal_eta), ("gal_rho", ctrl.gal_rho), ("gal_rotation", ctrl.gal_rotation)) + length(v) == msing || error("gal_match_rpec: $name has length $(length(v)), expected msing=$msing (one value per surface, core→edge)") + end - # --- assemble the 4·msing matching system (match.f:1337-1376) --- - delta_out = gal_result.delta[1:2msing, 1:2msing] # outer Δ′ plasma block - mat = zeros(ComplexF64, 4msing, 4msing) - rmat = zeros(ComplexF64, 4msing, mcoil) - @views mat[2msing+1:4msing, 1:2msing] .= transpose(delta_out) # Δ_out - @views rmat[2msing+1:4msing, :] .= .-transpose(gal_result.delta_coil) # −Δ_coil source - for ising in 1:msing - idx1 = 2ising - 1 - idx2 = 2ising - idx3 = idx1 + 2msing - idx4 = idx2 + 2msing - delta1 = deltar[ising, 1] - delta2 = deltar[ising, 2] - mat[idx1, idx1] = 1 - mat[idx2, idx2] = 1 - mat[idx1, idx3] = -1 - mat[idx1, idx4] = 1 - mat[idx2, idx3] = -1 - mat[idx2, idx4] = -1 - mat[idx3, idx3] = -delta1 # Δ_in - mat[idx3, idx4] = delta2 - mat[idx4, idx3] = -delta1 - mat[idx4, idx4] = -delta2 - end + # Re-derive the gal singular-surface set (must match galerkin_solve's filter) to get the SingType + # objects resist_eval needs; verify alignment with the stored gal Δ′ surfaces. + psilow = intr.psilow > 0 ? intr.psilow : equil.profiles.xs[1] + psihigh = intr.psilim + sings = [s for s in intr.sing if psilow < s.psifac < psihigh && intr.mlow <= s.m[1] <= intr.mhigh] + length(sings) == msing && isapprox([s.psifac for s in sings], gal_result.sing_psi; rtol=1e-8) || + error("gal_match_rpec: re-derived surface set does not match gal Δ′ surfaces (filter drift?)") + + # --- inner-layer matching data Δ(Q) per surface (deltac_run; match.f:1359-1363) --- + inner = InnerLayer.GGJModel(solver=:galerkin) + deltar = zeros(ComplexF64, msing, 2) + rpec_eig = zeros(ComplexF64, msing) + for i in 1:msing + params = resist_eval(sings[i], equil, intr; eta=ctrl.gal_eta[i], rho=ctrl.gal_rho[i], + gamma=ctrl.gal_gamma, ising=i) + γ = 2π * im * nn * ctrl.gal_rotation[i] # rpec forced eigenvalue 2πi·n·f + rpec_eig[i] = γ + Δ = InnerLayer.solve_inner(inner, params, γ) # (Δ₁, Δ₂) in deltac.f convention + deltar[i, 1] = Δ[1] + deltar[i, 2] = Δ[2] + end + + # --- assemble the 4·msing matching system (match.f:1337-1376) --- + delta_out = gal_result.delta[1:2msing, 1:2msing] # outer Δ′ plasma block + mat = zeros(ComplexF64, 4msing, 4msing) + rmat = zeros(ComplexF64, 4msing, mcoil) + @views mat[2msing+1:4msing, 1:2msing] .= transpose(delta_out) # Δ_out + @views rmat[2msing+1:4msing, :] .= .-transpose(gal_result.delta_coil) # −Δ_coil source + for ising in 1:msing + idx1 = 2ising - 1 + idx2 = 2ising + idx3 = idx1 + 2msing + idx4 = idx2 + 2msing + delta1 = deltar[ising, 1] + delta2 = deltar[ising, 2] + mat[idx1, idx1] = 1 + mat[idx2, idx2] = 1 + mat[idx1, idx3] = -1 + mat[idx1, idx4] = 1 + mat[idx2, idx3] = -1 + mat[idx2, idx4] = -1 + mat[idx3, idx3] = -delta1 # Δ_in + mat[idx3, idx4] = delta2 + mat[idx4, idx3] = -delta1 + mat[idx4, idx4] = -delta2 + end - # --- solve mat·cof = rmat for the outer/inner coefficients (match.f:1402-1408) --- - cof = mat \ rmat - residual = norm(mat * cof - rmat) / max(norm(rmat), 1e-300) - cout = cof[1:2msing, :] - cin = cof[2msing+1:4msing, :] + # --- solve mat·cof = rmat for the outer/inner coefficients (match.f:1402-1408) --- + cof = mat \ rmat + residual = norm(mat * cof - rmat) / max(norm(rmat), 1e-300) + cout = cof[1:2msing, :] + cin = cof[2msing+1:4msing, :] + end - # --- matched outer ξ/ξ′ per coil drive (match.f:1654-1671, resistive branch) --- + # --- matched outer ξ/ξ′ per coil drive (match.f:1654-1671); ideal: cout=0 ⇒ bare coil column --- sols = gal_result.solution.xi # (mpert, ngrid, nsol) sols_deriv = gal_result.solution.xi_deriv ngrid = size(sols, 2) @@ -105,3 +120,63 @@ function gal_match_rpec(ctrl::ForceFreeStatesControl, equil, intr::ForceFreeStat return GalMatchResult(cout, cin, xi, xi_deriv, deltar, rpec_eig, residual) end + +""" + gal_matched_odestate(gal_result, ffit, intr) -> OdeState + +Pack the RPEC-matched outer solution into an `OdeState` shaped exactly like the shooting integrator's, +so `PerturbedEquilibrium` consumes it unchanged. Mirrors Fortran `idcon_build`'s gal branch +(idcon.f:479-493) and `globalsol.bin` (the on-surface `issing` points are dropped, match.f:1468-1497): + + - `u_store[:,:,1,ip] = ξ_ψ` (matched fundamental matrix, mode×coil-drive, identity-at-edge basis) + - `ud_store[:,:,1,ip] = dξ_ψ/dψ` (analytic) + - `ud_store[:,:,2,ip] = ξ_s = −A⁻¹(B·ξ′ + C·ξ)` via `ffit` (same outer ideal-MHD relation as `sing_der!`) + - `u_store[:,:,2] = 0` (PE never reads it; matches Fortran's unused u2 in the gal path) + +The grid is the gal-native grid (inner→edge); `step` indexes the edge so `build_flux_matrix` derives the +edge BC from `u_store[:,:,1,step]`. +""" +function gal_matched_odestate(gal_result::GalerkinResult, ffit::FourFitVars, intr::ForceFreeStatesInternal) + gal_result.match !== nothing || error("gal_matched_odestate: no match result (run with gal_match_flag=true)") + sol = gal_result.solution + m = gal_result.match + mpert = intr.numpert_total + + # Drop the on-surface (issing) grid points — zero placeholders where the resonant series diverges. + keep = .!sol.issing + psi_f = sol.psi[keep] + q_f = sol.q[keep] + xi_f = m.xi[:, keep, :] # (mpert, ngrid_f, mcoil) + dxi_f = m.xi_deriv[:, keep, :] + ngrid_f = length(psi_f) + + u_store = zeros(ComplexF64, mpert, mpert, 2, ngrid_f) + ud_store = zeros(ComplexF64, mpert, mpert, 2, ngrid_f) + + amat = Matrix{ComplexF64}(undef, mpert, mpert) + bmat = Matrix{ComplexF64}(undef, mpert, mpert) + cmat = Matrix{ComplexF64}(undef, mpert, mpert) + tmp = Matrix{ComplexF64}(undef, mpert, mpert) + hint = Ref(1) + for ip in 1:ngrid_f + ξ = @view xi_f[:, ip, :] + ξ′ = @view dxi_f[:, ip, :] + @views u_store[:, :, 1, ip] .= ξ + @views ud_store[:, :, 1, ip] .= ξ′ + # ξ_s = −A⁻¹(B·ξ′ + C·ξ), exactly as the ideal path of sing_der! (Sing.jl:1015-1049) + ffit.amats(vec(amat), psi_f[ip]; hint=hint) + ffit.bmats(vec(bmat), psi_f[ip]; hint=hint) + ffit.cmats(vec(cmat), psi_f[ip]; hint=hint) + LinearAlgebra.LAPACK.potrf!('U', amat) + LinearAlgebra.LAPACK.potrs!('U', amat, bmat) # bmat ← A⁻¹ B + LinearAlgebra.LAPACK.potrs!('U', amat, cmat) # cmat ← A⁻¹ C + xs = @view ud_store[:, :, 2, ip] + mul!(tmp, bmat, ξ′) + xs .= .-tmp + mul!(tmp, cmat, ξ) + xs .-= tmp + end + + return OdeState(; numpert_total=mpert, numunorms_init=1, msing=gal_result.msing, numsteps_init=ngrid_f, + step=ngrid_f, total_steps=ngrid_f, psi_store=psi_f, q_store=q_f, u_store=u_store, ud_store=ud_store) +end diff --git a/src/ForceFreeStates/Galerkin/GalerkinSolve.jl b/src/ForceFreeStates/Galerkin/GalerkinSolve.jl index a3bb57325..24ebe606b 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinSolve.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinSolve.jl @@ -189,9 +189,11 @@ function galerkin_solve(ctrl::ForceFreeStatesControl, equil, ffit::FourFitVars, # DRIVEN (RPEC) outer↔inner matching: build the coil-driven matched ξ/ξ′ (gal_match_rpec). ctrl.gal_match_flag || return result ctrl.gal_rpec_flag || error("galerkin_solve: gal_match_flag=true requires gal_rpec_flag=true") - ctrl.verbose && @info "RPEC matching: inner-layer Δ(Q) + outer↔inner solve for the coil-driven ξ" + ctrl.verbose && @info(ctrl.gal_ideal_flag ? + "RPEC matching: IDEAL solution (inner layer skipped, bare coil columns)" : + "RPEC matching: inner-layer Δ(Q) + outer↔inner solve for the coil-driven ξ") match = gal_match_rpec(ctrl, equil, intr, result) - ctrl.verbose && @info "RPEC matching: linear-solve residual = $(match.residual)" + ctrl.gal_ideal_flag || (ctrl.verbose && @info "RPEC matching: linear-solve residual = $(match.residual)") return GalerkinResult(delta, Ap, Bp, Gammap, Deltap, msing, sing_psi, sing_q, sing_m, sing_n, di, alpha, delta_coil, solution, match) end diff --git a/src/GeneralizedPerturbedEquilibrium.jl b/src/GeneralizedPerturbedEquilibrium.jl index 9ed12f117..5c394d193 100755 --- a/src/GeneralizedPerturbedEquilibrium.jl +++ b/src/GeneralizedPerturbedEquilibrium.jl @@ -54,7 +54,7 @@ using .ForceFreeStates: mercier_scan!, compute_ballooning_stability! using .ForceFreeStates: make_metric, make_matrix, make_kinetic_matrix using .ForceFreeStates: find_kinetic_singular_surfaces! using .ForceFreeStates: eulerlagrange_integration, free_run! -using .ForceFreeStates: galerkin_solve, write_galerkin!, GalerkinResult +using .ForceFreeStates: galerkin_solve, write_galerkin!, GalerkinResult, gal_matched_odestate const _BANNER = "="^60 const _SECTION = "-"^40 @@ -421,10 +421,20 @@ function main(args::Vector{String}=String[]; dd::Union{IMASdd.dd,Nothing}=nothin ) pe_intr = PerturbedEquilibrium.PerturbedEquilibriumInternal(; dir_path=intr.dir_path) + # DRIVEN (RPEC): feed the coil-matched gal solution to PE instead of the shooting solution. + # The matched OdeState is in the identity-at-edge basis; build_flux_matrix rederives the edge BC + # from u_store[:,:,1,step], so PE consumes it unchanged. The shooting odet is left untouched for + # the Force-Free States HDF5 output. + pe_odet = odet + if ctrl.gal_flag && ctrl.gal_match_flag && gal_data !== nothing && gal_data.match !== nothing + @info "PerturbedEquilibrium: using the RPEC-matched gal solution" + pe_odet = gal_matched_odestate(gal_data, ffit, intr) + end + # Run perturbed equilibrium calculations # Pass vac_data and intr for response matrix calculations pe_state = PerturbedEquilibrium.compute_perturbed_equilibrium( - equil, odet, ctrl.vac_flag ? vac_data : nothing, intr, ft_ctrl, pe_ctrl, pe_intr, + equil, pe_odet, ctrl.vac_flag ? vac_data : nothing, intr, ft_ctrl, pe_ctrl, pe_intr, metric, ffit ) From fca440aaf2659959d289d77f02db5be692c0bea4 Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Tue, 16 Jun 2026 21:22:59 -0400 Subject: [PATCH 058/135] ForceFreeStates Galerkin - TEST - Regression coverage for RPEC matching + PE-fed gal_resistive_pe case gal_resistive_diiid: add finite inner-layer-matching quantities (||inner-layer Delta||, ||cout||, residual); drop divergent xi/xi' norms (ill-posed). New gal_resistive_pe case covers the full gal->match->OdeState->PerturbedEquilibrium pipeline via finite singular-coupling scalars (island half-widths, resonant flux, penetrated field, PE Delta'). New DIIID-like_gal_resistive_pe_example (resistive matched config + C-coil forcing + PE). Co-Authored-By: Claude Opus 4.8 --- .../TkMkr_D3Dlike_Hmode.geqdsk | 1 + .../gpec.toml | 107 ++++++++++++++++++ .../cases/gal_resistive_diiid.toml | 33 ++++++ .../cases/gal_resistive_pe.toml | 87 ++++++++++++++ 4 files changed, 228 insertions(+) create mode 120000 examples/DIIID-like_gal_resistive_pe_example/TkMkr_D3Dlike_Hmode.geqdsk create mode 100644 examples/DIIID-like_gal_resistive_pe_example/gpec.toml create mode 100644 regression-harness/cases/gal_resistive_pe.toml diff --git a/examples/DIIID-like_gal_resistive_pe_example/TkMkr_D3Dlike_Hmode.geqdsk b/examples/DIIID-like_gal_resistive_pe_example/TkMkr_D3Dlike_Hmode.geqdsk new file mode 120000 index 000000000..4200141b3 --- /dev/null +++ b/examples/DIIID-like_gal_resistive_pe_example/TkMkr_D3Dlike_Hmode.geqdsk @@ -0,0 +1 @@ +../DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk \ No newline at end of file diff --git a/examples/DIIID-like_gal_resistive_pe_example/gpec.toml b/examples/DIIID-like_gal_resistive_pe_example/gpec.toml new file mode 100644 index 000000000..c1e39bfdb --- /dev/null +++ b/examples/DIIID-like_gal_resistive_pe_example/gpec.toml @@ -0,0 +1,107 @@ +[Equilibrium] +eq_filename = "TkMkr_D3Dlike_Hmode.geqdsk" # Path to equilibrium file +eq_type = "efit" # Type of the input 2D equilibrium file +jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc) +power_bp = 0 # Poloidal field power exponent for Jacobian +power_b = 0 # Toroidal field power exponent for Jacobian +power_r = 0 # Major radius power exponent for Jacobian +grid_type = "ldp" # Radial grid packing type (ldp = linear-derivative packing toward rationals) +psilow = 1e-4 # Lower limit of normalized flux coordinate +psihigh = 0.993 # Upper limit of normalized flux coordinate (0.993 stays clear of the separatrix; truncating at ≳0.998 is numerically unreasonable here) +mpsi = 128 # Number of radial grid points (0 = auto-compute from psi_accuracy) +psi_accuracy = 0.001 # Target absolute error in q for auto-mpsi +mtheta = 256 # Number of poloidal grid points +newq0 = 0 # Override for on-axis safety factor (0 = use input value) +etol = 1e-10 # Error tolerance for equilibrium solver +force_termination = false # Terminate after equilibrium setup (skip stability calculations) + +[Wall] +shape = "nowall" # Wall shape (nowall, conformal, elliptical, dee, mod_dee, filepath) +a = 0.2415 # Distance from plasma (conformal) or shape parameter +aw = 0.05 # Half-thickness parameter for Dee-shaped walls +bw = 1.5 # Elongation parameter for wall shapes +cw = 0 # Offset of wall center from major radius +dw = 0.5 # Triangularity parameter for wall shapes +tw = 0.05 # Sharpness of wall corners (try 0.05 as initial value) +equal_arc_wall = true # Equal arc length distribution of nodes on wall + +[ForceFreeStates] +bal_flag = false # Ideal MHD ballooning criterion for short wavelengths +mat_flag = true # Construct coefficient matrices for diagnostic purposes (required by gal_flag) +ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) +vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes +mer_flag = true # Evaluate the Mercier criterion + +psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak +qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... +qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)... +sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) + +nn_low = 1 # Smallest toroidal mode number to include +nn_high = 1 # Largest toroidal mode number to include +delta_mlow = 8 # Expands lower bound of Fourier harmonics +delta_mhigh = 4 # Expands upper bound of Fourier harmonics +delta_mband = 0 # Integration keeps only this wide a band of solutions along the m,m' diagonal (0 = full) +mthvac = 512 # Number of points used in splines over poloidal angle at plasma-vacuum interface. +thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds + +kinetic_source = "fixed" # Kinetic matrix source ("fixed" test matrices, or "calculated" from PENTRC) +kinetic_factor = 0.0 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode) +eulerlagrange_tolerance = 1e-10# Relative tolerance for ODE integration of Euler-Lagrange equations +save_interval = 3 # Save every Nth ODE step (1=all, 10=every 10th). Always saves near rational surfaces. +singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced +ucrit = 1e4 # Maximum fraction of solutions allowed before re-normalized + +# Δ' BVP + parallel integration (see ForceFreeStatesControl docstring for details) +use_parallel = true # Run parallel FM-propagator BVP path (unlocks singular/delta_prime_matrix) +parallel_threads = 2 # BVP thread cap (1 = serial/bit-deterministic; 2 ≈ +20% speedup; ≥3 saturates) +populate_dense_xi = false # Dense axis-basis ξ for the FFS HDF5 output. Not needed here: no [PerturbedEquilibrium] section, and the gal-matched path builds its own dense ξ. Set true only for a shooting-fed PE run. +truncate_at_dW_peak = false # Edge-dW scan stays diagnostic; integration domain set by qhigh / psihigh / dmlim +set_psilim_via_dmlim = false # Keep psilim at psihigh (do not truncate at last_rational_q + dmlim) +dmlim = 0.2 # Truncate integration at (last_rational_q + dmlim) / n (only used when set_psilim_via_dmlim = true) + +# RDCON outer-region singular Galerkin Δ′ solver with rpec coil columns (matched to Fortran &GAL_INPUT). +# This case exercises the gal solve AND the rpec coil/edge path (delta_coil) for regression tracking. +gal_flag = true # Enable the outer-region singular Galerkin Δ′ solve (requires mat_flag = true) +gal_solver = "LU" # Banded solver: "LU" (zgbtrf/zgbtrs) or "cholesky" (zpbtrf/zpbtrs). rpec requires "LU". +gal_nx = 256 # Hermite-cubic elements per interval between singular surfaces +gal_nq = 6 # Gauss-Lobatto quadrature order per element +gal_pfac = 0.03 # Grid packing ratio toward singular surfaces (smaller = tighter packing) +gal_dx0 = 5e-4 # Resonant-element integration truncation distance from the rational (× 1/|n q'|) +gal_dx1 = 1e-3 # Resonant-element size (× 1/|n q'|) +gal_dx2 = 1e-3 # Extension-element size (× 1/|n q'|) +gal_cutoff = 10 # Number of elements carrying the large (driving) solution as a source term +gal_tol = 1e-10 # Resonant-cell adaptive-quadrature (QuadGK) tolerance +gal_gnstep = 5000 # Maximum resonant-integration steps +gal_dx1dx2_flag = true # Enable the special dx1/dx2 element sizing for resonant/extension cells +gal_sing_order = 6 # Base power-series order for the Galerkin singular asymptotics +gal_sing_order_ceiling = true # Auto-raise the series order by ceil(2·Re(α)) on high-Mercier-index surfaces +gal_rpec_flag = true # Append mpert coil-response columns (unit edge sources) to the solve → delta_coil block + +# DRIVEN (RPEC) outer↔inner matching. Per-surface resistive inputs (core→edge), mirroring the Fortran +# rmatch DIII-D example: eta=8e-8, massden=3.3e-7 (ni≈1e20 m^-3), rotation=1 Hz, Γ=5/3. 4 surfaces. +gal_match_flag = true # Solve the coil-driven matched ξ(ψ) from the gal Δ′ + the inner-layer Δ(Q). Requires gal_rpec_flag = true. +gal_ideal_flag = false # true → build the IDEAL solution (skip the inner layer, bare coil columns; ≡ DCON). false → the resistive matching below. +gal_eta = [8e-8, 8e-8, 8e-8, 8e-8] # Per-surface resistivity η (core→edge); Fortran rmatch `eta` +gal_rho = [3.3e-7, 3.3e-7, 3.3e-7, 3.3e-7] # Per-surface mass density ρ [kg/m³] (core→edge); Fortran rmatch `massden` +gal_rotation = [1.0, 1.0, 1.0, 1.0] # Per-surface rotation frequency f [Hz] (core→edge); forced eigenvalue γ_s = 2πi·n·f. Fortran rmatch `rotation` +gal_gamma = 1.6666666666666667 # Ratio of specific heats Γ for the resistive-layer coefficients (5/3) + +[ForcingTerms] +forcing_data_format = "coil" # Format: "ascii", "hdf5", or "coil" (Biot-Savart from 3D wires) +machine = "d3d" # Geometry prefix; resolves to bundled coil_geometries/d3d_*.dat +mtheta_coil = 480 # Poloidal grid for boundary B·n̂ evaluation +nzeta_coil = 32 # Toroidal grid (0 = auto = 32·n) + +[[ForcingTerms.coil_set]] +name = "c" # DIII-D C-coil (6 coils); resolves to coil_geometries/d3d_c.dat +currents = [1000.0, 500.0, -500.0, -1000.0, -500.0, 500.0] # n=1 cosine phasing, 1 kA peak [A] + +[PerturbedEquilibrium] +fixed_boundary = false # Use fixed boundary conditions +output_eigenmodes = true # Output eigenmode fields as b-fields +compute_response = true # Compute plasma response to forcing +compute_singular_coupling = true # Compute singular layer coupling metrics +verbose = true # Enable verbose logging +write_outputs_to_HDF5 = true # Write perturbed equilibrium outputs to HDF5 +reg_spot = 0.05 # Regularization width for singular surfaces (0 = disabled) diff --git a/regression-harness/cases/gal_resistive_diiid.toml b/regression-harness/cases/gal_resistive_diiid.toml index 44efe6499..9ec61109e 100644 --- a/regression-harness/cases/gal_resistive_diiid.toml +++ b/regression-harness/cases/gal_resistive_diiid.toml @@ -65,6 +65,39 @@ label = "gal α per surface" noise_threshold = 1e-8 order = 31 +# --- DRIVEN (RPEC) inner-layer matching (gal_match_flag) --- +# Only finite, well-defined matching quantities are tracked. The reconstructed ξ/ξ′ are deliberately +# NOT regressed via norms: ξ′ diverges at the rational surfaces, so any whole-array norm is dominated by +# the (grid- and ULP-fragile) near-singular points — an ill-posed benchmark. The producer is validated +# separately by benchmarks/verify_gal_solution.jl (finite-difference self-consistency). + +# Inner-layer matching data Δ(Q) per surface (resist_eval geometry + GGJ inner solver). (msing × 2) +[quantities.gal_match_deltar_norm] +h5path = "galerkin/match/deltar" +type = "complex_matrix" +extract = "norm" +label = "||gal inner-layer Δ||" +noise_threshold = 1e-6 +order = 41 + +# Outer-region matched coefficients cout (2·msing × mcoil) — the 4·msing matching assembly + solve. +[quantities.gal_match_cout_norm] +h5path = "galerkin/match/cout" +type = "complex_matrix" +extract = "norm" +label = "||gal match cout||" +noise_threshold = 1e-6 +order = 42 + +# Matching linear-solve residual ‖mat·cof − rmat‖/‖rmat‖ — health check (should stay ~machine eps). +[quantities.gal_match_residual] +h5path = "galerkin/match/residual" +type = "real_scalar" +extract = "value" +label = "gal match residual" +noise_threshold = 1e-10 +order = 44 + [quantities.runtime] h5path = "" type = "runtime" diff --git a/regression-harness/cases/gal_resistive_pe.toml b/regression-harness/cases/gal_resistive_pe.toml new file mode 100644 index 000000000..7a26d7563 --- /dev/null +++ b/regression-harness/cases/gal_resistive_pe.toml @@ -0,0 +1,87 @@ +[case] +name = "gal_resistive_pe" +description = "DIII-D-like, n=1, DRIVEN/RPEC: gal-matched resistive ξ → PerturbedEquilibrium (coil-driven singular coupling)" +example_dir = "examples/DIIID-like_gal_resistive_pe_example" + +# Full-pipeline coverage for gal_match_flag → gal_matched_odestate → PerturbedEquilibrium. Tracks the +# FINITE, per-rational-surface singular-coupling scalars (the physics-meaningful driven quantities) — not +# any whole-profile ξ/ξ′ norm (those diverge at the rationals and are ill-posed as benchmarks). + +# Surface locations / count (sanity) +[quantities.pe_rational_q] +h5path = "perturbed_equilibrium/singular_coupling/rational_q" +type = "real_vector" +extract = "all_real" +label = "rational q values" +noise_threshold = 1e-8 +order = 10 + +# Island half-widths per rational surface — the headline driven quantity +[quantities.pe_island_half_width] +h5path = "perturbed_equilibrium/singular_coupling/island_half_width" +type = "real_vector" +extract = "all_real" +label = "island half-widths" +noise_threshold = 1e-8 +order = 20 + +# Chirikov overlap parameter per surface +[quantities.pe_chirikov] +h5path = "perturbed_equilibrium/singular_coupling/chirikov_parameter" +type = "real_vector" +extract = "all_real" +label = "Chirikov parameter" +noise_threshold = 1e-8 +order = 21 + +# Resonant flux Φ_res per surface (applied) — norm + per-surface complex values +[quantities.pe_resonant_flux_norm] +h5path = "perturbed_equilibrium/singular_coupling/resonant_flux" +type = "complex_vector" +extract = "norm" +label = "||resonant flux||" +noise_threshold = 1e-6 +order = 30 + +[quantities.pe_resonant_flux_all] +h5path = "perturbed_equilibrium/singular_coupling/resonant_flux" +type = "complex_vector" +extract = "all_complex" +label = "resonant flux Phi_res" +noise_threshold = 1e-8 +order = 31 + +# Penetrated (reconnected) resonant field per surface — the resistive shielding signature +[quantities.pe_penetrated_field] +h5path = "perturbed_equilibrium/singular_coupling/penetrated_field" +type = "complex_vector" +extract = "all_complex" +label = "penetrated field" +noise_threshold = 1e-8 +order = 32 + +# Per-surface Δ' from the PE singular-coupling analysis +[quantities.pe_delta_prime] +h5path = "perturbed_equilibrium/singular_coupling/delta_prime" +type = "complex_vector" +extract = "all_complex" +label = "PE Δ' per surface" +noise_threshold = 1e-8 +order = 33 + +# Resonant-flux coupling matrix (n_rational × numpert_total) — Frobenius norm, catches broader drift +[quantities.pe_C_resonant_flux_norm] +h5path = "perturbed_equilibrium/singular_coupling/C_resonant_flux" +type = "complex_matrix" +extract = "norm" +label = "||C resonant flux||" +noise_threshold = 1e-6 +order = 40 + +[quantities.runtime] +h5path = "" +type = "runtime" +extract = "value" +label = "Runtime (s)" +noise_threshold = 0.0 +order = 999 From 4114886aec282e0059f0837f39ae4ff29991faf1 Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Tue, 16 Jun 2026 21:42:56 -0400 Subject: [PATCH 059/135] ForceFreeStates Galerkin - DOCS - fortran-physics-reviewer memory: gal.f<->assembly correspondence map + index Records the verified gal.f<->GalerkinAssembly.jl element-level correspondence and the resonant sign-chain derivation from the PR physics review, so the next audit of the Galerkin solver starts from the verified state. Co-Authored-By: Claude Opus 4.8 (1M context) --- .../fortran-physics-reviewer/MEMORY.md | 1 + .../galerkin_assembly_map.md | 37 +++++++++++++++++++ 2 files changed, 38 insertions(+) create mode 100644 .claude/agent-memory/fortran-physics-reviewer/galerkin_assembly_map.md diff --git a/.claude/agent-memory/fortran-physics-reviewer/MEMORY.md b/.claude/agent-memory/fortran-physics-reviewer/MEMORY.md index d4733ea2d..1a3bc1fc1 100644 --- a/.claude/agent-memory/fortran-physics-reviewer/MEMORY.md +++ b/.claude/agent-memory/fortran-physics-reviewer/MEMORY.md @@ -4,3 +4,4 @@ - [Known Physics Issues in PerturbedEquilibrium](known_issues_perteq.md) — xss_mn not implemented, xi_modes placeholders - [KineticForces (NTV) Audit Checklist](kinetic_ntv_map.md) — pentrc->KineticForces map, Logan 2015 matrices, what to verify - [InnerLayer (Resistive) Audit Checklist](resistive_layer_map.md) — rmatch->InnerLayer map, GGJ Wasow basis / Δ′, what to verify +- [Galerkin Δ′ Assembly Map](galerkin_assembly_map.md) — gal.f<->GalerkinAssembly.jl; resonant sign chain verified; PASS diff --git a/.claude/agent-memory/fortran-physics-reviewer/galerkin_assembly_map.md b/.claude/agent-memory/fortran-physics-reviewer/galerkin_assembly_map.md new file mode 100644 index 000000000..c916e3b00 --- /dev/null +++ b/.claude/agent-memory/fortran-physics-reviewer/galerkin_assembly_map.md @@ -0,0 +1,37 @@ +--- +name: galerkin-assembly-map +description: RDCON singular Galerkin Δ′ solver — gal.f ↔ GalerkinAssembly.jl element-level weak-form correspondence and audit notes +metadata: + type: project +--- + +# RDCON Galerkin Δ′ assembly: gal.f ↔ GalerkinAssembly.jl + +File: `src/ForceFreeStates/Galerkin/GalerkinAssembly.jl` ↔ `GPEC_fortran/rdcon/gal.f`. +On branch `feature/rdcon-galerkin`. Reviewed 2026-06-16. + +## Correspondence (verified, not just docstring-trusted) +- gal_hermite (222-262) ↔ gal_hermite: pb/qb EXACT. +- gal_get_fkg (1013-1071) ↔ gal_get_fkg: F=Fbar·sf[i]·sf[j], K=K·sf[i], G=G. singfac=mlow-nn*q+(0..mpert-1) = DIRECT (m-nq), not reciprocal. Correct. +- gal_gauss_quad (1079-1138) ↔ gal_gauss_quad!: F·qq + K·qp + conj(K[jpert,ipert])·pq + G·pp. swap pb(2)/pb(3) (0-based) = Julia pb[3]/pb[4]. Correct. +- gal_extension (1146-1322) ↔ gal_extension!: emat/ediag/rhs/erhs all match incl surface terms 1277-1300 and w1/w2. +- gal_resonant! ↔ gal_lsode_int(780-900)+gal_lsode_der(908-954)+gal_make_arrays signs(1366-1369). QuadGK replaces LSODE. +- gal_assemble_mat (694-772) ↔ gal_assemble_mat!: LU offset=kl+ku+1, chol offset=1, conj(e) Hermitian placement. Correct. +- gal_assemble_rhs (642-686) ↔ gal_assemble_rhs!: isol++ at ext2-left / res-right. Correct. +- gal_set_boundary (1554-1620) ↔ gal_set_boundary!: axis idx, edge 3-way (rpec/vac/fixed). DOF index 3(0-based)=Julia 4. + +## Resonant sign chain (the trap — verified correct) +Fortran: LSODE integrates x0→x_lsode giving raw u; then line 882 `IF right: u=-u`; then make_arrays: +erhs=-u_res(1), ediag=+u_res(2), rhs=-u_hermite1, emat=+u_hermite2. +Net with s=+1(left)/-1(right): erhs=-s·res1, ediag=s·res2, rhs=-s·hbig, emat=s·hsmall. +Julia sgn_u = s (=-1 right/+1 left): erhs=-sgn_u·raw1, ediag=sgn_u·raw2, rhs=-sgn_u·hbig, emat=sgn_u·hsmall. MATCHES. +QuadGK limits x0→x_lsode preserve LSODE orientation so raw == pre-negation u. Correct. +du_res conj-weight uses the SMALL solution (isol(2)) in both. Correct. + +## Only open item (MINOR, out-of-file) +sing_get_ua_gal/dua_gal two-sided z<0 → sig=-1 series at -z with derivative ×(-1) is a REIMPLEMENTATION +of sing.f's internal singular-surface handling, not a line port. The ×(-1) chain is internally consistent +but worth a dedicated check against sing.f sing_get_ua/dua if Δ′ ever disagrees with Fortran. Lives outside +GalerkinAssembly.jl. + +## Verdict: PASS WITH REQUIRED ANNOTATIONS (citation comments only; no physics defects found). From 11ae3bb09db749f5bc6a9ada680e1bab3ff99a2b Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Tue, 16 Jun 2026 21:53:03 -0400 Subject: [PATCH 060/135] ForceFreeStates - CLEANUP - fix some line numbers / annotations --- src/ForceFreeStates/Galerkin/GalerkinAssembly.jl | 9 ++++++--- src/ForceFreeStates/Galerkin/GalerkinSolve.jl | 7 +++++-- src/InnerLayer/GGJ/Galerkin.jl | 2 +- 3 files changed, 12 insertions(+), 6 deletions(-) diff --git a/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl b/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl index 3474b8c31..b4d6ae776 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl @@ -47,7 +47,8 @@ end Evaluate the `mpert×mpert` matrices `F = Q F̄ Qᴴ`, `K = Q K̄`, `G = Ḡ` at flux `x` with safety factor `q`, where `Q = diag(singfac)` and `singfac = m - n q` (direct). Port of `gal_get_fkg` (gal.f:999-1057). -Uses the un-factored reduced `ffit.fmats_gal` (F̄), `ffit.kmats` (K̄), `ffit.gmats` (Ḡ). +Uses the un-factored reduced `ffit.fmats_gal` (F̄), `ffit.kmats` (K̄), `ffit.gmats` (Ḡ). F/K/G are the +ideal-MHD Euler–Lagrange coefficient matrices of the outer-region weak form (Glasser 2016, PoP 23, 112506). """ function gal_get_fkg(ffit::FourFitVars, intr::ForceFreeStatesInternal, x::Float64, q::Float64) N = intr.numpert_total @@ -304,8 +305,10 @@ function gal_resonant!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, return out end - # QuadGK replaces Fortran's LSODE accumulation. Match Fortran's LSODE tolerance (gal_tol, 1e-10) - # with an evaluation cap (analogous to Fortran's gnstep limit) so a near-singular integrand cannot hang. + # Numerical-method deviation from gal_lsode_int: adaptive QuadGK (Gauss-Kronrod) replaces Fortran's + # LSODE accumulation over the same integrand/limits, so this path is NOT bit-exact with gal.f. Match + # Fortran's LSODE tolerance (gal_tol, 1e-10) with an evaluation cap (analogous to Fortran's gnstep + # limit) so a near-singular integrand cannot hang. raw, qerr = quadgk(integrand, x0, x1l; rtol=gal_tol, atol=1e-30, maxevals=20000) if get(ENV, "GAL_DEBUG", "") == "1" @info " resonant jsing=$jsing side=$(cell.extra) qerr=$(qerr) res1=$(raw[1]) res2=$(raw[2])" diff --git a/src/ForceFreeStates/Galerkin/GalerkinSolve.jl b/src/ForceFreeStates/Galerkin/GalerkinSolve.jl index 24ebe606b..856915549 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinSolve.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinSolve.jl @@ -3,7 +3,7 @@ # Top-level driver for the RDCON outer-region singular Galerkin Δ′ solve, plus the per-cell assembly # orchestration, the banded solve, Δ′ extraction, PEST-3 blocks, and HDF5 output. # Ports gal_make_arrays (gal.f:1300-1359), gal_solve (gal.f:1367-1431), and gal_write_pest3_data -# (gal.f:1712-1745). No inner-layer wiring (future thrust). +# (gal.f:1749-1825). The DRIVEN/RPEC inner-layer matching is wired in via gal_match_rpec (GalerkinMatch.jl). """ gal_make_arrays!(ws, ctrl, equil, ffit, intr, asymps, sings, nn, wv_edge) @@ -170,6 +170,8 @@ function galerkin_solve(ctrl::ForceFreeStatesControl, equil, ffit::FourFitVars, Ap, Bp, Gammap, Deltap = gal_pest3_blocks(delta, msing) + # Mercier index D_I = -Re(α²); α is the small/large solution exponent (a surface property, taken + # from the right series — the left series reuses the same α via alpha_override above). di = [real(-asymps[i].right.alpha[1]^2) for i in 1:msing] alpha = [asymps[i].right.alpha[1] for i in 1:msing] # Coil-response block (rpec_flag): rows 2*msing+1 : 2*msing+mpert of delta (empty otherwise). @@ -202,7 +204,8 @@ end gal_pest3_blocks(delta, msing) -> (Ap, Bp, Gammap, Deltap) PEST-3 matching blocks (each `msing×msing`) as ± combinations of the left/right Δ′ entries. Port of -`gal_write_pest3_data` (gal.f:1726-1745). Row index `2i-1`/`2i` = left/right of surface `i`. +`gal_write_pest3_data` (gal.f:1749-1825; the ± combinations are gal.f:1765-1777). Row index `2i-1`/`2i` += left/right of surface `i`. """ function gal_pest3_blocks(delta::Matrix{ComplexF64}, msing::Int) Ap = zeros(ComplexF64, msing, msing) diff --git a/src/InnerLayer/GGJ/Galerkin.jl b/src/InnerLayer/GGJ/Galerkin.jl index 93f889018..6ac6cbab6 100644 --- a/src/InnerLayer/GGJ/Galerkin.jl +++ b/src/InnerLayer/GGJ/Galerkin.jl @@ -708,7 +708,7 @@ function solve_inner(::GGJModel{:galerkin}, params::GGJParameters, γ::Number; emap1 = res_cell.emap[1] Δ_raw = SVector{2,ComplexF64}(ws.sol[emap1, 1], ws.sol[emap1, 2]) - # Apply deltac.f's swap convention (line 194-196) + # Apply deltac.f's swap convention (deltac.f:201-203) Δ_swapped = SVector{2,ComplexF64}(Δ_raw[2], Δ_raw[1]) return rescale_delta(Δ_swapped, params) From b2ef66560e33b0fcc86900917196f75f27c8b4db Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Tue, 16 Jun 2026 23:17:12 -0400 Subject: [PATCH 061/135] ForceFreeStates Galerkin - CLEANUP - drop fortran line-ranges, wire gal_gnstep, verbose-gate debug, remove dead resist_eval_all --- src/ForceFreeStates/ForceFreeStatesStructs.jl | 2 +- src/ForceFreeStates/Fourfit.jl | 2 +- .../Galerkin/GalerkinAssembly.jl | 70 +++++++++---------- src/ForceFreeStates/Galerkin/GalerkinGrid.jl | 26 +++---- src/ForceFreeStates/Galerkin/GalerkinMatch.jl | 18 ++--- .../Galerkin/GalerkinSolution.jl | 34 ++++----- src/ForceFreeStates/Galerkin/GalerkinSolve.jl | 23 +++--- .../Galerkin/GalerkinStructs.jl | 20 +++--- src/ForceFreeStates/Resist.jl | 27 ++----- src/ForceFreeStates/Sing.jl | 12 ++-- src/InnerLayer/GGJ/Galerkin.jl | 2 +- 11 files changed, 109 insertions(+), 127 deletions(-) diff --git a/src/ForceFreeStates/ForceFreeStatesStructs.jl b/src/ForceFreeStates/ForceFreeStatesStructs.jl index d52adf3a0..58faadaaa 100644 --- a/src/ForceFreeStates/ForceFreeStatesStructs.jl +++ b/src/ForceFreeStates/ForceFreeStatesStructs.jl @@ -309,7 +309,7 @@ A mutable struct containing control parameters for stability analysis, set by th gal_dx2::Float64 = 1e-3 # extension-element size (×1/|n q'|) gal_cutoff::Int = 10 # # of elements carrying the large solution as driving term gal_tol::Float64 = 1e-10 # resonant-quadrature (QuadGK) tolerance - gal_gnstep::Int = 5000 # max resonant-integration steps + gal_gnstep::Int = 20000 # max resonant-quadrature evaluations (QuadGK maxevals in gal_resonant!) gal_dx1dx2_flag::Bool = true # enable special dx1/dx2 treatment for resonant/extension elements gal_sing_order::Int = 6 # base power-series order for the Galerkin singular asymptotics gal_sing_order_ceiling::Bool = true # auto-raise order by ceil(2·Re(α)) per surface (high Mercier index) diff --git a/src/ForceFreeStates/Fourfit.jl b/src/ForceFreeStates/Fourfit.jl index f48f5c3d2..1efb40690 100644 --- a/src/ForceFreeStates/Fourfit.jl +++ b/src/ForceFreeStates/Fourfit.jl @@ -500,7 +500,7 @@ function make_matrix(equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStates # Capture the reduced Hermitian F̄ (full matrix) before it is overwritten by its Cholesky # factor below. The Galerkin solver (gal_get_fkg) needs F̄ directly: F = Q F̄ Qᴴ with - # Q = diag(singfac). Mirror of Fortran fmats_gal (fourfit.f:341). + # Q = diag(singfac). Mirror of Fortran fmats_gal (fourfit.f). @views fmats_gal_flat[ipsi, :] .= vec(fmat) # Store factorized F matrix (lower triangular only) since we always will need F⁻¹ later diff --git a/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl b/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl index b4d6ae776..94b6ddb35 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl @@ -1,14 +1,14 @@ # GalerkinAssembly.jl # # Element-level assembly for the outer-region Galerkin solver. Ports: -# gal_hermite (gal.f:222-254) Hermite cubic basis -# gal_get_fkg (gal.f:999-1057) F, K, G at a point from F̄/K̄/Ḡ + singfac -# gal_gauss_quad (gal.f:1065-1124) nonresonant stiffness via Gauss-Lobatto quadrature -# gal_extension (gal.f:1132-1292) extension-cell matrix/rhs (big-solution driving + surface terms) -# gal_resonant (gal.f:772-940) resonant-cell integral (QuadGK in place of Fortran LSODE) -# gal_assemble_mat (gal.f:686-764) scatter cell blocks into the banded global matrix (LU/Cholesky) -# gal_assemble_rhs (gal.f:634-678) scatter cell rhs into the global RHS -# gal_set_boundary (gal.f:1517-1583) axis identity + edge (vacuum or fixed) BCs +# gal_hermite (gal.f) Hermite cubic basis +# gal_get_fkg (gal.f) F, K, G at a point from F̄/K̄/Ḡ + singfac +# gal_gauss_quad (gal.f) nonresonant stiffness via Gauss-Lobatto quadrature +# gal_extension (gal.f) extension-cell matrix/rhs (big-solution driving + surface terms) +# gal_resonant (gal.f) resonant-cell integral (QuadGK in place of Fortran LSODE) +# gal_assemble_mat (gal.f) scatter cell blocks into the banded global matrix (LU/Cholesky) +# gal_assemble_rhs (gal.f) scatter cell rhs into the global RHS +# gal_set_boundary (gal.f) axis identity + edge (vacuum or fixed) BCs # # Hermite DOF index ip (Fortran 0:3) ↔ Julia array index ip+1 throughout. @@ -29,7 +29,7 @@ end gal_hermite(x, x0, x1) -> (pb, qb) Hermite cubic basis values `pb` and derivatives `qb` on `[x0, x1]` (length 4, Fortran `0:3`). -Port of `gal_hermite` (gal.f:222-254). +Port of `gal_hermite` (gal.f). """ function gal_hermite(x::Real, x0::Real, x1::Real) dx = x1 - x0 @@ -46,7 +46,7 @@ end gal_get_fkg(ffit, intr, x, q) -> (F, K, G) Evaluate the `mpert×mpert` matrices `F = Q F̄ Qᴴ`, `K = Q K̄`, `G = Ḡ` at flux `x` with safety factor -`q`, where `Q = diag(singfac)` and `singfac = m - n q` (direct). Port of `gal_get_fkg` (gal.f:999-1057). +`q`, where `Q = diag(singfac)` and `singfac = m - n q` (direct). Port of `gal_get_fkg` (gal.f). Uses the un-factored reduced `ffit.fmats_gal` (F̄), `ffit.kmats` (K̄), `ffit.gmats` (Ḡ). F/K/G are the ideal-MHD Euler–Lagrange coefficient matrices of the outer-region weak form (Glasser 2016, PoP 23, 112506). """ @@ -73,9 +73,9 @@ end gal_gauss_quad!(cell, ffit, profiles, intr, nodes, weights, swap_edge) Accumulate the nonresonant Hermite stiffness block `cell.mat` by Gauss-Lobatto quadrature. Port of -`gal_gauss_quad` (gal.f:1065-1124). When `swap_edge` (the final cell of the last interval), the +`gal_gauss_quad` (gal.f). When `swap_edge` (the final cell of the last interval), the right-node value/slope DOFs (Fortran pb(2)↔pb(3)) are swapped so the edge-value DOF lands at index 3, -matching the free-boundary BC (gal.f:1091-1098). +matching the free-boundary BC (gal.f). """ function gal_gauss_quad!(cell::GalCell, ffit::FourFitVars, profiles, intr::ForceFreeStatesInternal, nodes::Vector{Float64}, weights::Vector{Float64}, swap_edge::Bool) @@ -120,7 +120,7 @@ end gal_extension!(cell, ising, ffit, profiles, intr, asymps, sings, nn, nodes, weights) Build `cell.emat`, `cell.ediag`, `cell.rhs`, `cell.erhs` for an extension cell (`ext`/`ext1`/`ext2`). -Port of `gal_extension` (gal.f:1132-1292). The big solution (`isol` column) drives the RHS; for `ext` +Port of `gal_extension` (gal.f). The big solution (`isol` column) drives the RHS; for `ext` cells the small solution (`isol+N` column) also forms the resonant coupling `emat`/`ediag`. """ function gal_extension!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, @@ -139,7 +139,7 @@ function gal_extension!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, ua_at(x) = sing_get_ua_gal(asymp, x - psi_s) dua_at(x) = sing_get_dua_gal(asymp, x - psi_s) - # Boundary node and weights (gal.f:1147-1172) + # Boundary node and weights (gal.f) if cell.extra == GAL_SIDE_LEFT jp = 2 # Fortran jp (0-based) -> Julia jp+1 xb = x2 @@ -160,7 +160,7 @@ function gal_extension!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, fill!(cell.emat, 0) cell.ediag = zero(ComplexF64) - # --- emat and ediag (ext cells only) (gal.f:1177-1208) --- + # --- emat and ediag (ext cells only) (gal.f) --- if cell.etype == GCT_EXT uab = ua_at(xb) duab = dua_at(xb) @@ -185,7 +185,7 @@ function gal_extension!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, cell.ediag += sum(conj.(u) .* Fdu_Ku) * ws end - # --- rhs (gal.f:1210-1259) --- + # --- rhs (gal.f) --- ua1 = ua_at(x1)[:, isol, 1] # big solution at left node du1 = dua_at(x1)[:, isol, 1] ua2 = ua_at(x2)[:, isol, 1] # big solution at right node @@ -226,7 +226,7 @@ function gal_extension!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, end end - # --- surface terms (always; gal.f:1262-1286) --- + # --- surface terms (always; gal.f) --- q_l = profiles.q_spline(x1; hint=qhint) Fl, Kl, _ = gal_get_fkg(ffit, intr, x1, q_l) pbt, _ = gal_hermite(x1, x1, x2) @@ -252,15 +252,15 @@ function gal_extension!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, end """ - gal_resonant!(cell, ising, ffit, profiles, intr, asymps, sings, nn, gal_tol) + gal_resonant!(cell, ising, ffit, profiles, intr, asymps, sings, nn, gal_tol, gal_gnstep, verbose) Compute the resonant-cell contributions `cell.erhs`, `cell.ediag`, `cell.rhs`, `cell.emat` by adaptive quadrature (QuadGK) of the residual-operator integrand. Port of `gal_lsode_int`/`gal_lsode_der` -(gal.f:772-940): the Fortran LSODE accumulation is replaced by `quadgk` over `[x_bdy, x_lsode]`. +(gal.f): the Fortran LSODE accumulation is replaced by `quadgk` over `[x_bdy, x_lsode]`. """ function gal_resonant!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, intr::ForceFreeStatesInternal, asymps::Vector{GalSingAsymp}, sings::Vector{SingType}, - nn::Int, gal_tol::Float64) + nn::Int, gal_tol::Float64, gal_gnstep::Int, verbose::Bool) N = intr.numpert_total np = GAL_NP @@ -274,7 +274,7 @@ function gal_resonant!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, isol_small = isol_big + N cols = [isol_big, isol_small] - # Integration limits (gal.f:805-815): right → [x2, x_lsode]; left → [x1, x_lsode] + # Integration limits (gal.f): right → [x2, x_lsode]; left → [x1, x_lsode] x0 = (cell.extra == GAL_SIDE_LEFT) ? x1 : x2 x1l = cell.x_lsode sgn_u = (cell.extra == GAL_SIDE_RIGHT) ? -1.0 : 1.0 @@ -307,16 +307,16 @@ function gal_resonant!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, # Numerical-method deviation from gal_lsode_int: adaptive QuadGK (Gauss-Kronrod) replaces Fortran's # LSODE accumulation over the same integrand/limits, so this path is NOT bit-exact with gal.f. Match - # Fortran's LSODE tolerance (gal_tol, 1e-10) with an evaluation cap (analogous to Fortran's gnstep - # limit) so a near-singular integrand cannot hang. - raw, qerr = quadgk(integrand, x0, x1l; rtol=gal_tol, atol=1e-30, maxevals=20000) - if get(ENV, "GAL_DEBUG", "") == "1" + # Fortran's LSODE tolerance (gal_tol) and cap the evaluations at gal_gnstep (Fortran's gnstep limit) + # so a near-singular integrand cannot hang. + raw, qerr = quadgk(integrand, x0, x1l; rtol=gal_tol, atol=1e-30, maxevals=gal_gnstep) + if verbose @info " resonant jsing=$jsing side=$(cell.extra) qerr=$(qerr) res1=$(raw[1]) res2=$(raw[2])" end hbig = reshape(@view(raw[3:2+N*(np+1)]), N, np + 1) hsmall = reshape(@view(raw[3+N*(np+1):end]), N, np + 1) - # Apply the right-side negation and the gal_make_arrays signs (gal.f:868, 1334-1337) + # Apply the right-side negation and the gal_make_arrays signs (gal.f gal_make_arrays) cell.erhs = -sgn_u * raw[1] cell.ediag = sgn_u * raw[2] cell.rhs .= (-sgn_u) .* hbig @@ -328,7 +328,7 @@ end gal_assemble_mat!(ws, mpert) Scatter every cell's `mat`/`emat`/`ediag` into the banded global matrix `ws.mat`. Port of -`gal_assemble_mat` (gal.f:686-764). Supports both `"LU"` (full band, `offset = kl+ku+1`) and +`gal_assemble_mat` (gal.f). Supports both `"LU"` (full band, `offset = kl+ku+1`) and `"cholesky"` (lower band only, `offset = 1`). """ function gal_assemble_mat!(ws::GalWorkspace, mpert::Int) @@ -377,7 +377,7 @@ end gal_assemble_rhs!(ws, mpert) Scatter every cell's `rhs`/`erhs` into the global RHS `ws.rhs`. Port of `gal_assemble_rhs` -(gal.f:634-678). A new RHS column (`isol`) begins at each big-solution driver: an `ext2`-left cell or a +(gal.f). A new RHS column (`isol`) begins at each big-solution driver: an `ext2`-left cell or a `res`-right cell. """ function gal_assemble_rhs!(ws::GalWorkspace, mpert::Int) @@ -408,14 +408,14 @@ end gal_set_boundary!(ws, mpert, wv_edge) Apply the axis (`u(0)=0` identity) and edge boundary conditions to the boundary cells' `mat`, plus the -rpec coil-source RHS injection, before global assembly. Port of `gal_set_boundary` (gal.f:1554-1620), +rpec coil-source RHS injection, before global assembly. Port of `gal_set_boundary` (gal.f), including its full three-way edge branch (rpec count `ncoil = ws.nsol - 2*msing`): - rpec (`ncoil > 0`): identity edge **and** a unit source at the edge value DOF of coil column - `2*msing+ipert` for each poloidal mode `ipert` (gal.f:1573-1586). `ws.rhs` is already allocated and + `2*msing+ipert` for each poloidal mode `ipert` (gal.f). `ws.rhs` is already allocated and `gal_assemble_rhs!` only fills columns `1:2*msing`, so the injection is not clobbered. - free boundary (`wv_edge !== nothing`): add the vacuum block `wvac·psio²` at the edge value DOF - (gal.f:1603-1606). - - fixed boundary (else): identity edge (gal.f:1607-1614). + (gal.f). + - fixed boundary (else): identity edge (gal.f). `wv_edge` is `nothing` for the rpec and fixed cases. """ function gal_set_boundary!(ws::GalWorkspace, mpert::Int, wv_edge::Union{Nothing,Matrix{ComplexF64}}) @@ -434,7 +434,7 @@ function gal_set_boundary!(ws::GalWorkspace, mpert::Int, wv_edge::Union{Nothing, # edge u(1): last cell of last interval, edge-value DOF ip=3 (Julia index 4, see gauss_quad swap) cell = ws.intvl[msing+1].cells[ws.nx] if ncoil > 0 - # rpec: identity edge + unit coil sources (gal.f:1573-1586) + # rpec: identity edge + unit coil sources (gal.f) cell.mat[:, :, 4, :] .= 0 chol && (cell.mat[:, :, :, 4] .= 0) for idx in 1:mpert @@ -444,10 +444,10 @@ function gal_set_boundary!(ws::GalWorkspace, mpert::Int, wv_edge::Union{Nothing, ws.rhs[cell.map[ipert, 4], 2 * msing + ipert] = 1 end elseif wv_edge !== nothing - # free boundary: vacuum block wvac·psio² (gal.f:1603-1606) + # free boundary: vacuum block wvac·psio² (gal.f) @views cell.mat[:, :, 4, 4] .+= wv_edge else - # fixed boundary: identity edge (gal.f:1607-1614) + # fixed boundary: identity edge (gal.f) cell.mat[:, :, 4, :] .= 0 chol && (cell.mat[:, :, :, 4] .= 0) for idx in 1:mpert diff --git a/src/ForceFreeStates/Galerkin/GalerkinGrid.jl b/src/ForceFreeStates/Galerkin/GalerkinGrid.jl index e984e0641..88bb26782 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinGrid.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinGrid.jl @@ -1,7 +1,7 @@ # GalerkinGrid.jl # # Grid construction and local→global DOF mapping for the outer-region Galerkin solver. -# Ports gal_pack (gal.f:262-318), gal_make_grid (gal.f:326-451), and gal_make_map (gal.f:509-575). +# Ports gal_pack (gal.f), gal_make_grid (gal.f), and gal_make_map (gal.f). # # Node arrays use Fortran 0-based `x(0:nx)` mapped to Julia `xn[i+1]` (so Fortran `x(i)` is `xn[i+1]`). # Cells are 1-based in both. Intervals `0:msing` (Fortran) are `ws.intvl[ising+1]` in Julia. @@ -10,7 +10,7 @@ """ gal_pack(nx::Int, pfac::Float64, side::String) -> Vector{Float64} -Packed logical grid on `[-1, 1]`. Port of Fortran `gal_pack` (gal.f:262-318). For `side="both"` +Packed logical grid on `[-1, 1]`. Port of Fortran `gal_pack` (gal.f). For `side="both"` returns `2*nx+1` nodes (Fortran `-nx:nx`) clustered toward both ends when `pfac < 1` (strong packing near the bracketing singular surfaces). `pfac > 1` packs toward the centre; `pfac == 1` is uniform. """ @@ -52,12 +52,12 @@ end Set the cell types (`res`/`ext`/`ext1`/`ext2`/`none`), sides, resonant integration limits, and packed node positions for interval `ising` (0-based, `0:msing`). Port of Fortran `gal_make_grid` -(gal.f:326-451), `dx1dx2_flag=true` path. `intvl.x`/`intvl.dx` have length `nx+1`, `intvl.cells` length +(gal.f), `dx1dx2_flag=true` path. `intvl.x`/`intvl.dx` have length `nx+1`, `intvl.cells` length `nx` (preallocated by the caller). `sings` is the filtered list of resonant surfaces (1-based, `sings[ising]` = Fortran `sing(ising)`). -Note (faithful to Fortran): the lower-surface width scale uses `|nn·q1|` (gal.f:356) but the -upper-surface scale uses `|q1|` without `nn` (gal.f:398). Identical for `nn = 1`. +Note (faithful to Fortran): the lower-surface width scale uses `|nn·q1|` (gal.f) but the +upper-surface scale uses `|q1|` without `nn` (gal.f). Identical for `nn = 1`. """ function gal_make_grid!(intvl::GalInterval, ising::Int, msing::Int, sings::Vector{SingType}, nn::Int, psilow::Float64, psihigh::Float64, ctrl::ForceFreeStatesControl) @@ -77,7 +77,7 @@ function gal_make_grid!(intvl::GalInterval, ising::Int, msing::Int, sings::Vecto c.extra = GAL_SIDE_NONE end - # --- lower bound (gal.f:349-389) --- + # --- lower bound (gal.f) --- local ixmin::Int if ising == 0 ixmin = 0 @@ -102,21 +102,21 @@ function gal_make_grid!(intvl::GalInterval, ising::Int, msing::Int, sings::Vecto cells[ix].etype = GCT_EXT1 cells[ix].extra = GAL_SIDE_RIGHT end - ix_ext2 = max(cutoff + 2, 3) # Fortran loop-exit value of ix (gal.f:387) + ix_ext2 = max(cutoff + 2, 3) # Fortran loop-exit value of ix (gal.f) (ix_ext2 > nx || cells[ix_ext2].etype != GCT_NONE) && error("gal_make_grid: too many elements include the big solution (right side)") cells[ix_ext2].etype = GCT_EXT2 cells[ix_ext2].extra = GAL_SIDE_RIGHT end - # --- upper bound (gal.f:391-429) --- + # --- upper bound (gal.f) --- local ixmax::Int if ising == msing ixmax = nx xn[nx+1] = psihigh else x1 = sings[ising+1].psifac - nq1 = abs(sings[ising+1].q1) # NOTE: no nn factor, faithful to gal.f:398 + nq1 = abs(sings[ising+1].q1) # NOTE: no nn factor, faithful to gal.f xn[nx+1] = x1 cells[nx].x_lsode = x1 - dx0 / nq1 if ctrl.gal_dx1dx2_flag @@ -134,20 +134,20 @@ function gal_make_grid!(intvl::GalInterval, ising::Int, msing::Int, sings::Vecto cells[ix].etype = GCT_EXT1 cells[ix].extra = GAL_SIDE_LEFT end - ix_ext2 = min(nx - cutoff - 1, nx - 2) # Fortran loop-exit value of ix (gal.f:427) + ix_ext2 = min(nx - cutoff - 1, nx - 2) # Fortran loop-exit value of ix (gal.f) (ix_ext2 < 1 || cells[ix_ext2].etype != GCT_NONE) && error("gal_make_grid: too many elements include the big solution (left side)") cells[ix_ext2].etype = GCT_EXT2 cells[ix_ext2].extra = GAL_SIDE_LEFT end - # --- interior packed grid (gal.f:431-446) --- + # --- interior packed grid (gal.f) --- x0 = xn[ixmin+1] x1 = xn[ixmax+1] xm = (xn[ixmax+1] + xn[ixmin+1]) / 2 dxh = (xn[ixmax+1] - xn[ixmin+1]) / 2 mx = (ixmax - ixmin) ÷ 2 - # Default: symmetric "both" pack (faithful to gal.f:438). With gal_edge_onesided, the two end + # Default: symmetric "both" pack (faithful to gal.f). With gal_edge_onesided, the two end # intervals pack only toward their single rational end, leaving the regular boundary (psilow at # interval 0, psihigh at interval msing) at coarse spacing — removes the gratuitous fine edge cell. side = "both" @@ -179,7 +179,7 @@ end gal_make_map!(ws::GalWorkspace, mpert::Int) Build the local→global DOF numbering with the `2*mpert` C¹ overlap between adjacent Hermite cells and -the interleaved extra (small resonant) DOFs (`emap`). Port of Fortran `gal_make_map` (gal.f:509-575). +the interleaved extra (small resonant) DOFs (`emap`). Port of Fortran `gal_make_map` (gal.f). Sets `ws.ndim`. The `skip`/`emap` bookkeeping reserves a global slot for each resonant coefficient and shares it between the `res` cell and its neighbouring `ext` cell. """ diff --git a/src/ForceFreeStates/Galerkin/GalerkinMatch.jl b/src/ForceFreeStates/Galerkin/GalerkinMatch.jl index dd11cae96..2bdb1d2d2 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinMatch.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinMatch.jl @@ -1,9 +1,9 @@ # GalerkinMatch.jl # -# DRIVEN (RPEC) outer↔inner asymptotic matching. Port of rmatch `match_rpec` (match.f:1318-1510) and the -# outer total-solution construction of `match_output_solution` (match.f:1654-1671). +# DRIVEN (RPEC) outer↔inner asymptotic matching. Port of rmatch `match_rpec` (match.f) and the +# outer total-solution construction of `match_output_solution` (match.f). # -# Per rational surface: the forced eigenvalue γ_s = 2πi·n·f_s (rpec, match.f:1359), the inner-layer +# Per rational surface: the forced eigenvalue γ_s = 2πi·n·f_s (rpec, match.f), the inner-layer # matching data Δ(Q) via the Galerkin GGJ solver (InnerLayer.solve_inner), then the 4·msing matching # system mat·[cout;cin] = rmat is assembled (rmat = −transpose of the gal Δ′ coil block) and solved for # the per-coil outer/inner coefficients. The matched outer solution for coil drive j is @@ -35,7 +35,7 @@ function gal_match_rpec(ctrl::ForceFreeStatesControl, equil, intr::ForceFreeStat error("gal_match_rpec: delta_coil is empty — gal_rpec_flag must be true for RPEC matching") if ctrl.gal_ideal_flag - # Ideal limit (Fortran rmatch coil%ideal_flag, match.f:1665-1671): skip the inner layer entirely + # Ideal limit (Fortran rmatch coil%ideal_flag, match.f): skip the inner layer entirely # and set the resistive plasma combination to zero. The gal outer solve is already fully ideal, so # the shared construction below collapses to the bare ideal coil column sols(:,:,csol). cout = zeros(ComplexF64, 2msing, mcoil) @@ -56,7 +56,7 @@ function gal_match_rpec(ctrl::ForceFreeStatesControl, equil, intr::ForceFreeStat length(sings) == msing && isapprox([s.psifac for s in sings], gal_result.sing_psi; rtol=1e-8) || error("gal_match_rpec: re-derived surface set does not match gal Δ′ surfaces (filter drift?)") - # --- inner-layer matching data Δ(Q) per surface (deltac_run; match.f:1359-1363) --- + # --- inner-layer matching data Δ(Q) per surface (deltac_run; match.f) --- inner = InnerLayer.GGJModel(solver=:galerkin) deltar = zeros(ComplexF64, msing, 2) rpec_eig = zeros(ComplexF64, msing) @@ -70,7 +70,7 @@ function gal_match_rpec(ctrl::ForceFreeStatesControl, equil, intr::ForceFreeStat deltar[i, 2] = Δ[2] end - # --- assemble the 4·msing matching system (match.f:1337-1376) --- + # --- assemble the 4·msing matching system (match.f) --- delta_out = gal_result.delta[1:2msing, 1:2msing] # outer Δ′ plasma block mat = zeros(ComplexF64, 4msing, 4msing) rmat = zeros(ComplexF64, 4msing, mcoil) @@ -95,14 +95,14 @@ function gal_match_rpec(ctrl::ForceFreeStatesControl, equil, intr::ForceFreeStat mat[idx4, idx4] = -delta2 end - # --- solve mat·cof = rmat for the outer/inner coefficients (match.f:1402-1408) --- + # --- solve mat·cof = rmat for the outer/inner coefficients (match.f) --- cof = mat \ rmat residual = norm(mat * cof - rmat) / max(norm(rmat), 1e-300) cout = cof[1:2msing, :] cin = cof[2msing+1:4msing, :] end - # --- matched outer ξ/ξ′ per coil drive (match.f:1654-1671); ideal: cout=0 ⇒ bare coil column --- + # --- matched outer ξ/ξ′ per coil drive (match.f); ideal: cout=0 ⇒ bare coil column --- sols = gal_result.solution.xi # (mpert, ngrid, nsol) sols_deriv = gal_result.solution.xi_deriv ngrid = size(sols, 2) @@ -126,7 +126,7 @@ end Pack the RPEC-matched outer solution into an `OdeState` shaped exactly like the shooting integrator's, so `PerturbedEquilibrium` consumes it unchanged. Mirrors Fortran `idcon_build`'s gal branch -(idcon.f:479-493) and `globalsol.bin` (the on-surface `issing` points are dropped, match.f:1468-1497): +(idcon.f) and `globalsol.bin` (the on-surface `issing` points are dropped, match.f): - `u_store[:,:,1,ip] = ξ_ψ` (matched fundamental matrix, mode×coil-drive, identity-at-edge basis) - `ud_store[:,:,1,ip] = dξ_ψ/dψ` (analytic) diff --git a/src/ForceFreeStates/Galerkin/GalerkinSolution.jl b/src/ForceFreeStates/Galerkin/GalerkinSolution.jl index 0ca4736d6..dfed6dfe7 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinSolution.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinSolution.jl @@ -2,22 +2,22 @@ # # Reconstruct the outer-region radial displacement ξ(ψ) AND its analytic derivative ξ′(ψ) from the # solved Galerkin coefficients. Ports: -# gal_get_solution (gal.f:1833-1997) ξ (and optional ξ′) at one ψ for one solution column -# gal_output_solution (gal.f:2005-2273) evaluate (ξ, ξ′) on a gal-native packed grid, all columns +# gal_get_solution (gal.f) ξ (and optional ξ′) at one ψ for one solution column +# gal_output_solution (gal.f) evaluate (ξ, ξ′) on a gal-native packed grid, all columns # # The whole point of carrying ξ′ here is to evaluate it analytically from the Hermite derivative basis # (gal_hermite qb) and the asymptotic-series derivative (sing_get_dua_gal) rather than ever # spline-differentiating ξ at the packed edge — the spline-endpoint derivative was the root cause of # GPEC's fake ~100% shielding (fixed in Fortran by RDCON_singcoup commit c3e8c5bc). # -# Fortran module flags restore_uh/us/ul default .TRUE. (gal.f:81); the full reconstruction is always -# performed. The cut path (gal.f:1974-1992, used only for the matching diagnostic) is NOT ported here. +# Fortran module flags restore_uh/us/ul default .TRUE. (gal.f); the full reconstruction is always +# performed. The cut path (gal.f, used only for the matching diagnostic) is NOT ported here. -# Dense / coarse sampling per cell, matching Fortran interp_np_res / interp_np (gal.f:88). +# Dense / coarse sampling per cell, matching Fortran interp_np_res / interp_np (gal.f). const GAL_INTERP_NP = 3 const GAL_INTERP_NP_RES = 60 -# Advance the monotone (iintvl, icell) cursor to the cell containing x. Port of gal.f:1863-1876. +# Advance the monotone (iintvl, icell) cursor to the cell containing x. Port of gal.f. @inline function gal_locate_cell(ws::GalWorkspace, x::Float64, iintvl::Int, icell::Int) msing = length(ws.intvl) - 1 for _ in 1:((msing+1)*ws.nx+1) @@ -43,7 +43,7 @@ end Reconstruct the displacement `sol` (length `mpert`) — and, when `want_d`, its analytic radial derivative `dsol = d(sol)/dψ` — at flux `x` for solution column `isol`, from the solved Galerkin -coefficients `ws.sol`. Port of `gal_get_solution` (gal.f:1833-1997, non-cut path). `iintvl`/`icell` +coefficients `ws.sol`. Port of `gal_get_solution` (gal.f, non-cut path). `iintvl`/`icell` are a monotone cell cursor advanced and returned for the next call. `dsol` is `nothing` if `!want_d`. """ function gal_get_solution(ws::GalWorkspace, asymps::Vector{GalSingAsymp}, sings::Vector{SingType}, @@ -61,7 +61,7 @@ function gal_get_solution(ws::GalWorkspace, asymps::Vector{GalSingAsymp}, sings: pbt, qbt = gal_hermite(x, cell.x[1], cell.x[2]) pb = collect(pbt) qb = collect(qbt) - if iintvl == msing && icell == ws.nx # last edge cell: swap node-2/3 DOFs (gal.f:1888-1897) + if iintvl == msing && icell == ws.nx # last edge cell: swap node-2/3 DOFs (gal.f) pb[3], pb[4] = pb[4], pb[3] qb[3], qb[4] = qb[4], qb[3] end @@ -73,13 +73,13 @@ function gal_get_solution(ws::GalWorkspace, asymps::Vector{GalSingAsymp}, sings: cell.etype == GCT_NONE && return sol, dsol, iintvl, icell - # --- small & large resonant/extension solutions (gal.f:1904-1970) --- - jsing = _cell_jsing(cell, iintvl) # left → iintvl+1, right → iintvl (gal.f:1911/1919) + # --- small & large resonant/extension solutions (gal.f) --- + jsing = _cell_jsing(cell, iintvl) # left → iintvl+1, right → iintvl (gal_get_solution) asymp = asymps[jsing] psi_s = sings[jsing].psifac ipert0 = _ipert_res(sings[jsing], intr) # resonant (big) row; small row = ipert0+mpert - # Edge Hermite weights (fresh, unswapped) for ext/ext2 cells (gal.f:1912-1925) + # Edge Hermite weights (fresh, unswapped) for ext/ext2 cells (gal.f) pbe, qbe = gal_hermite(x, cell.x[1], cell.x[2]) if cell.extra == GAL_SIDE_LEFT epb1, epb2 = pbe[3], pbe[4] @@ -98,7 +98,7 @@ function gal_get_solution(ws::GalWorkspace, asymps::Vector{GalSingAsymp}, sings: uaext = need_ext ? sing_get_ua_gal(asymp, xext - psi_s) : nothing duaext = need_ext ? sing_get_dua_gal(asymp, xext - psi_s) : nothing - # small solution Δ-coefficient restore (ext/res only), coeff = ws.sol[emap,isol] (gal.f:1937-1951) + # small solution Δ-coefficient restore (ext/res only), coeff = ws.sol[emap,isol] (gal.f) if cell.etype == GCT_RES || cell.etype == GCT_EXT delta = ws.sol[cell.emap, isol] if cell.etype == GCT_RES @@ -110,7 +110,7 @@ function gal_get_solution(ws::GalWorkspace, asymps::Vector{GalSingAsymp}, sings: end end - # large solution (coeff 1) only for the column driving this surface/side (gal.f:1952-1970) + # large solution (coeff 1) only for the column driving this surface/side (gal.f) if (isol == 2jsing - 1 && cell.extra == GAL_SIDE_LEFT) || (isol == 2jsing && cell.extra == GAL_SIDE_RIGHT) if cell.etype == GCT_RES || cell.etype == GCT_EXT || cell.etype == GCT_EXT1 @@ -130,7 +130,7 @@ end Build the gal-native packed radial grid (inner→edge; `GAL_INTERP_NP_RES` points per resonant/extension cell, `GAL_INTERP_NP` elsewhere, plus the edge point ψ=psihigh) and evaluate ξ AND the analytic ξ′ over -it for every solution column. Port of `gal_output_solution` (gal.f:2027-2103); the binary/ASCII writes +it for every solution column. Port of `gal_output_solution` (gal.f); the binary/ASCII writes and the `b_flag` ξ→b^ψ conversion (off by default) are not ported — we keep ξ itself. """ function gal_output_solution(ws::GalWorkspace, asymps::Vector{GalSingAsymp}, sings::Vector{SingType}, @@ -139,7 +139,7 @@ function gal_output_solution(ws::GalWorkspace, asymps::Vector{GalSingAsymp}, sin mpert = intr.numpert_total msing = length(ws.intvl) - 1 - # --- grid (gal.f:2038-2079): per-cell left-inclusive sampling, then the edge point --- + # --- grid (gal.f): per-cell left-inclusive sampling, then the edge point --- psi = Float64[] issing = Bool[] for iintvl in 0:msing @@ -149,7 +149,7 @@ function gal_output_solution(ws::GalWorkspace, asymps::Vector{GalSingAsymp}, sin x1, x2 = cell.x for k in 0:(npts-1) push!(psi, x1 + (x2 - x1) * (k / npts)) - # res-right cell's first point sits exactly on the surface (gal.f:2070-2071) + # res-right cell's first point sits exactly on the surface (gal.f) push!(issing, k == 0 && cell.extra == GAL_SIDE_RIGHT && cell.etype == GCT_RES) end end @@ -160,7 +160,7 @@ function gal_output_solution(ws::GalWorkspace, asymps::Vector{GalSingAsymp}, sin qhint = Ref(1) q = [profiles.q_spline(p; hint=qhint) for p in psi] - # --- evaluate (gal.f:2090-2103) --- + # --- evaluate (gal.f) --- ngrid = length(psi) xi = zeros(ComplexF64, mpert, ngrid, ws.nsol) xi_deriv = zeros(ComplexF64, mpert, ngrid, ws.nsol) diff --git a/src/ForceFreeStates/Galerkin/GalerkinSolve.jl b/src/ForceFreeStates/Galerkin/GalerkinSolve.jl index 856915549..767bc6512 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinSolve.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinSolve.jl @@ -2,8 +2,8 @@ # # Top-level driver for the RDCON outer-region singular Galerkin Δ′ solve, plus the per-cell assembly # orchestration, the banded solve, Δ′ extraction, PEST-3 blocks, and HDF5 output. -# Ports gal_make_arrays (gal.f:1300-1359), gal_solve (gal.f:1367-1431), and gal_write_pest3_data -# (gal.f:1749-1825). The DRIVEN/RPEC inner-layer matching is wired in via gal_match_rpec (GalerkinMatch.jl). +# Ports gal_make_arrays (gal.f), gal_solve (gal.f), and gal_write_pest3_data +# (gal.f). The DRIVEN/RPEC inner-layer matching is wired in via gal_match_rpec (GalerkinMatch.jl). """ gal_make_arrays!(ws, ctrl, equil, ffit, intr, asymps, sings, nn, wv_edge) @@ -26,7 +26,7 @@ function gal_make_arrays!(ws::GalWorkspace, ctrl::ForceFreeStatesControl, equil, swap_edge = (ising == msing && ix == ws.nx) gal_gauss_quad!(cell, ffit, profiles, intr, nodes, weights, swap_edge) if cell.etype == GCT_RES - gal_resonant!(cell, ising, ffit, profiles, intr, asymps, sings, nn, ctrl.gal_tol) + gal_resonant!(cell, ising, ffit, profiles, intr, asymps, sings, nn, ctrl.gal_tol, ctrl.gal_gnstep, ctrl.verbose) elseif cell.etype == GCT_EXT || cell.etype == GCT_EXT1 || cell.etype == GCT_EXT2 gal_extension!(cell, ising, ffit, profiles, intr, asymps, sings, nn, nodes, weights) end @@ -44,7 +44,7 @@ end intr::ForceFreeStatesInternal; vac_data=nothing) -> GalerkinResult Compute the outer-region Δ′ matching matrix by the singular Galerkin method. Port of `gal_solve` -(gal.f:1367-1431). Single toroidal mode only (`intr.npert == 1`). Returns a `GalerkinResult`; if there +(gal.f). Single toroidal mode only (`intr.npert == 1`). Returns a `GalerkinResult`; if there are no resonant surfaces in the domain it returns an empty result. `vac_data` (a `VacuumData` from `free_run!`) supplies the free-boundary edge term @@ -100,7 +100,7 @@ function galerkin_solve(ctrl::ForceFreeStatesControl, equil, ffit::FourFitVars, kl = mpert * (np + 1) ku = kl ldab = ctrl.gal_solver == "LU" ? 2kl + ku + 1 : kl + 1 - # rpec_flag (RDCON, gal.f:148-170): append mpert coil-response columns. Each is a unit source at + # rpec_flag (RDCON, gal.f): append mpert coil-response columns. Each is a unit source at # the edge value DOF in one poloidal mode; the recorded plasma response is the coil block of Δ_gw. # Cholesky's lower-only edge zeroing can't represent the rpec identity edge, so require LU. ncoil = ctrl.gal_rpec_flag ? mpert : 0 @@ -132,9 +132,9 @@ function galerkin_solve(ctrl::ForceFreeStatesControl, equil, ffit::FourFitVars, gal_make_arrays!(ws, ctrl, equil, ffit, intr, asymps, sings, nn, wv_edge) - if get(ENV, "GAL_DEBUG", "") == "1" + if ctrl.verbose offdbg = ws.solver == "LU" ? ws.kl + ws.ku + 1 : 1 - @info "GAL_DEBUG ndim=$(ws.ndim) nsol=$nsol kl=$(ws.kl) ldab=$(ws.ldab) |rhs|=$(norm(ws.rhs))" + @info "Galerkin assembly: ndim=$(ws.ndim) nsol=$nsol kl=$(ws.kl) ldab=$(ws.ldab) |rhs|=$(norm(ws.rhs))" for ising in 0:msing for cell in ws.intvl[ising+1].cells if cell.etype == GCT_RES || cell.etype == GCT_EXT @@ -144,7 +144,7 @@ function galerkin_solve(ctrl::ForceFreeStatesControl, equil, ffit::FourFitVars, end end - # --- banded solve (gal.f:1383-1396) --- + # --- banded solve (gal.f) --- ws.sol .= ws.rhs if ws.solver == "LU" ctrl.verbose && @info "Galerkin LU banded factorization + solve" @@ -156,7 +156,7 @@ function galerkin_solve(ctrl::ForceFreeStatesControl, equil, ffit::FourFitVars, LinearAlgebra.LAPACK.pbtrs!('L', ws.kl, ws.mat, ws.sol) end - # --- extract Δ′ from the small resonant coefficients (gal.f:1405-1417) --- + # --- extract Δ′ from the small resonant coefficients (gal.f) --- delta = zeros(ComplexF64, nsol, 2 * msing) jsol = 0 for ising in 0:msing @@ -177,7 +177,7 @@ function galerkin_solve(ctrl::ForceFreeStatesControl, equil, ffit::FourFitVars, # Coil-response block (rpec_flag): rows 2*msing+1 : 2*msing+mpert of delta (empty otherwise). delta_coil = ncoil > 0 ? delta[(2*msing+1):(2*msing+ncoil), :] : Matrix{ComplexF64}(undef, 0, 0) - # Piece 1 producer: reconstruct ξ(ψ) AND analytic ξ′(ψ) on the gal-native grid (gal_output_solution). + # Reconstruct ξ(ψ) AND analytic ξ′(ψ) on the gal-native grid (gal_output_solution). ctrl.verbose && @info "Reconstructing outer-region ξ and analytic ξ′ on the gal grid" solution = gal_output_solution(ws, asymps, sings, intr, equil.profiles, psihigh) @@ -204,8 +204,7 @@ end gal_pest3_blocks(delta, msing) -> (Ap, Bp, Gammap, Deltap) PEST-3 matching blocks (each `msing×msing`) as ± combinations of the left/right Δ′ entries. Port of -`gal_write_pest3_data` (gal.f:1749-1825; the ± combinations are gal.f:1765-1777). Row index `2i-1`/`2i` -= left/right of surface `i`. +`gal_write_pest3_data`. Row index `2i-1`/`2i` = left/right of surface `i`. """ function gal_pest3_blocks(delta::Matrix{ComplexF64}, msing::Int) Ap = zeros(ComplexF64, msing, msing) diff --git a/src/ForceFreeStates/Galerkin/GalerkinStructs.jl b/src/ForceFreeStates/Galerkin/GalerkinStructs.jl index d68d2134d..b1b3819d3 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinStructs.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinStructs.jl @@ -2,7 +2,7 @@ # # Data structures for the RDCON outer-region singular Galerkin solver — the Julia port of # `gal.f` (Dewar's Galerkin method for singular modes). These mirror the Fortran derived types -# `cell_type`, `interval_type`, and `gal_type` (gal.f:48-76). +# `cell_type`, `interval_type`, and `gal_type` (gal.f). # # Fortran uses 0-based dimensions `0:np` and `0:nx`/`0:msing`; here those become Julia 1-based with a # `+1` index shift (Hermite DOF `ip` ↔ array index `ip+1`; interval `ising` ↔ `intvl[ising+1]`). @@ -25,7 +25,7 @@ Which side of the adjacent singular surface a cell lies on (Fortran `cell%extra` """ GalCell -One grid cell of the Galerkin discretization. Port of Fortran `cell_type` (gal.f:52-61). +One grid cell of the Galerkin discretization. Port of Fortran `cell_type` (gal.f). ## Fields @@ -70,7 +70,7 @@ end GalInterval One interval between consecutive singular surfaces (or between a surface and a domain edge). -Port of Fortran `interval_type` (gal.f:63-66). `x`/`dx` are length `nx+1` (Fortran `0:nx`). +Port of Fortran `interval_type` (gal.f). `x`/`dx` are length `nx+1` (Fortran `0:nx`). """ struct GalInterval x::Vector{Float64} @@ -81,10 +81,10 @@ end """ GalWorkspace -Global workspace for the Galerkin solve. Port of Fortran `gal_type` (gal.f:68-76). +Global workspace for the Galerkin solve. Port of Fortran `gal_type` (gal.f). `intvl` has length `msing+1` (Fortran `intvl(0:msing)`, accessed as `intvl[ising+1]`). -`kl = ku = mpert*(np+1)`. The banded `mat` storage layout depends on `solver` (gal.f:164-168): +`kl = ku = mpert*(np+1)`. The banded `mat` storage layout depends on `solver` (gal.f): - `"LU"` → `ldab = 2*kl + ku + 1`, full band (LAPACK `gbtrf!`/`gbtrs!`) - `"cholesky"` → `ldab = kl + 1`, lower band only (LAPACK `pbtrf!`/`pbtrs!`, `'L'`) @@ -120,8 +120,8 @@ end """ GalerkinSolution -Reconstructed outer-region radial solution on the gal-native grid (Piece 1 producer). Populated by -`gal_output_solution` (GalerkinSolution.jl). +Reconstructed outer-region radial solution on the gal-native grid (ξ and analytic ξ′ consumed by +PerturbedEquilibrium). Populated by `gal_output_solution` (GalerkinSolution.jl). - `psi::Vector{Float64}`, `q::Vector{Float64}` — radial grid (inner→edge) and its safety factor. - `issing::Vector{Bool}` — grid points sitting on a singular surface (skipped; left zero). @@ -167,14 +167,14 @@ Outputs of the outer-region Galerkin solve. ## Fields - `delta::Matrix{ComplexF64}` — Δ′ matrix, `(nsol, 2*msing)` with `nsol = 2*msing`; the small - resonant coefficients (Fortran `delta`, gal.f:1405-1417). + resonant coefficients (Fortran `delta`, gal.f). - `Ap, Bp, Gammap, Deltap::Matrix{ComplexF64}` — PEST-3 matching blocks, each `(msing, msing)` - (Fortran `gal_write_pest3_data`, gal.f:1726-1745). + (Fortran `gal_write_pest3_data`, gal.f). - `msing::Int` — number of resonant singular surfaces included. - `sing_psi, sing_q::Vector{Float64}`, `sing_m, sing_n::Vector{Int}` — per-surface identifiers. - `di::Vector{Float64}`, `alpha::Vector{ComplexF64}` — Mercier index and exponent per surface. - `solution::Union{Nothing,GalerkinSolution}` — reconstructed radial ξ(ψ) and analytic ξ′(ψ) on the - gal-native grid (Piece 1); `nothing` if no resonant surfaces. + gal-native grid; `nothing` if no resonant surfaces. """ struct GalerkinResult delta::Matrix{ComplexF64} diff --git a/src/ForceFreeStates/Resist.jl b/src/ForceFreeStates/Resist.jl index 5f14c6878..ecfbcd0f8 100644 --- a/src/ForceFreeStates/Resist.jl +++ b/src/ForceFreeStates/Resist.jl @@ -27,7 +27,7 @@ resist_eval(sing, equil, intr; eta, rho, gamma, ising=0) -> InnerLayer.GGJParameters Compute the GGJ resistive inner-layer parameters at the rational surface `sing`. -Port of RDCON `resist_eval` (resist.f:31-173), but with η and ρ supplied by the caller (no +Port of RDCON `resist_eval` (resist.f), but with η and ρ supplied by the caller (no built-in Spitzer/density model). Returns an `InnerLayer.GGJParameters` carrying the curvature/mass coefficients E, F, G, H, K, M, the local time scales τ_A (`taua`), τ_R (`taur`), `v1` (V′ normalized by total volume), and the surface index `ising`. @@ -62,7 +62,7 @@ function resist_eval(sing::SingType, equil::Equilibrium.PlasmaEquilibrium, q1 = sing.q1 chi1 = 2π * equil.psio - # --- θ-integrate the six geometric averages (resist.f:71-103) --- + # --- θ-integrate the six geometric averages (resist.f) --- nth = length(equil.rzphi_ys) ff = zeros(nth, 6) hint2d = (Ref(1), Ref(1)) @@ -97,17 +97,17 @@ function resist_eval(sing::SingType, equil::Equilibrium.PlasmaEquilibrium, itp = cubic_interp(equil.rzphi_ys, Series(ff); bc=PeriodicBC()) avg = FastInterpolations.integrate(itp) - # --- curvature terms E, F, H (resist.f:107-111) --- + # --- curvature terms E, F, H (resist.f) --- E = p1 * v1 / (q1 * chi1^2)^2 * avg[1] * (twopif * q1 * chi1 / avg[5] - v2) F = (p1 * v1 / (q1 * chi1^2))^2 * (avg[1] * avg[3] + (twopif / chi1)^2 * (avg[1] * avg[4] - avg[2]^2)) H = twopif * p1 * v1 / (q1 * chi1^3) * (avg[2] - avg[1] / avg[5]) - # --- mass factor M and derived G, K (resist.f:122-125) --- + # --- mass factor M and derived G, K (resist.f) --- M = avg[1] * (avg[6] + (twopif / chi1)^2 * (avg[3] - 1 / avg[5])) G = avg[5] / (M * gamma * p) K = (q1 * chi1^2 / (p1 * v1))^2 * avg[5] / (M * avg[1]) - # --- Alfvén and resistive times from caller-supplied η, ρ (resist.f:136-138) --- + # --- Alfvén and resistive times from caller-supplied η, ρ (resist.f) --- # τ_A = √(ρ·M·μ₀) / |2π n q₁ χ₁ / V′| — geometric factor × √ρ. # τ_R = (⟨B²/|∇ψ|²⟩ / ⟨B²⟩) · μ₀ / η — geometric factor × 1/η. # η, ρ enter once, explicitly (no RMATCH divide-out / re-multiply). @@ -122,20 +122,3 @@ function resist_eval(sing::SingType, equil::Equilibrium.PlasmaEquilibrium, return InnerLayer.GGJParameters(; E=E, F=F, G=G, H=H, K=K, M=M, taua=taua, taur=taur, v1=v1norm, ising=ising) end - -""" - resist_eval_all(intr, equil; eta, rho, gamma) -> Vector{InnerLayer.GGJParameters} - -Evaluate [`resist_eval`](@ref) at every singular surface in `intr.sing`, returning one -`GGJParameters` per surface (with `ising` set to the surface index). - -`eta` and `rho` may be supplied either as scalars (applied to every surface) or as -vectors of length `intr.msing` (one value per surface, e.g. from a transport profile sampled -at each rational surface). `gamma` is the (scalar) ratio of specific heats. -""" -function resist_eval_all(intr::ForceFreeStatesInternal, equil::Equilibrium.PlasmaEquilibrium; - eta, rho, gamma::Real) - _at(x, i) = x isa AbstractVector ? x[i] : x - return [resist_eval(intr.sing[i], equil, intr; - eta=_at(eta, i), rho=_at(rho, i), gamma=gamma, ising=i) for i in 1:intr.msing] -end diff --git a/src/ForceFreeStates/Sing.jl b/src/ForceFreeStates/Sing.jl index 4074c80a4..3ecd63628 100644 --- a/src/ForceFreeStates/Sing.jl +++ b/src/ForceFreeStates/Sing.jl @@ -120,7 +120,7 @@ end """ sing_min!(intr::ForceFreeStatesInternal, ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium) -Set the lower integration bound `intr.psilow`. Port of Fortran RDCON `sing_min` (sing.f:1295-1326): +Set the lower integration bound `intr.psilow`. Port of Fortran RDCON `sing_min` (sing.f): when `qlow > qmin`, the q < qlow core (including any q ≤ 1 sawtooth/internal-kink surfaces) must be excluded from the outer-region Galerkin domain — otherwise the Hermite FEM integrates through those ideal singularities without imposing the ideal constraint, contaminating Δ′ at the innermost kept @@ -735,7 +735,7 @@ end Compute the derivative of the asymptotic series solution with respect to the positive distance `dpsi = |ψ − ψ_res|`, consistent with `sing_get_ua`. Port of Fortran `sing_get_dua` -(sing.f:839-906 / sing1.f:643-708). Shape `(numpert_total, 2*numpert_total, 2)`. Used by the +(sing.f / sing1.f). Shape `(numpert_total, 2*numpert_total, 2)`. Used by the outer-region Galerkin solver (`gal_extension`, `sing_matvec`). Direction is carried by the `SingAsymptotics` (left vs right vmat built with sig=∓1), exactly as in @@ -758,7 +758,7 @@ function sing_get_dua(sing_asymp::SingAsymptotics, dpsi::Float64) sqrtfac = sqrt(dpsi) N = size(sing_asymp.vmat, 1) - # Per-term total exponent (×2, in half-powers of dpsi). See sing.f:881-885. + # Per-term total exponent (×2, in half-powers of dpsi). See Fortran sing_get_dua. power = fill(ComplexF64(2 * order), N, 2 * N, 2) power[r1, :, 1] .-= 1 power[r1, :, 2] .+= 1 @@ -767,14 +767,14 @@ function sing_get_dua(sing_asymp::SingAsymptotics, dpsi::Float64) power[:, r2[2*i], :] .+= 2 * sing_asymp.alpha[i] end - # Power series derivative by Horner's method (sing.f:889-893) + # Power series derivative by Horner's method (Fortran sing_get_dua) dua = sing_asymp.vmat[:, :, :, 2*order+1] .* power for iorder in (2*order-1):-1:0 power .-= 1 dua .= dua .* sqrtfac .+ sing_asymp.vmat[:, :, :, iorder+1] .* power end - # Restore shearing and resonant powers, then the chain-rule factor 1/(2·dpsi) (sing.f:897-901) + # Restore shearing and resonant powers, then the chain-rule factor 1/(2·dpsi) (Fortran sing_get_dua) for i in eachindex(r1) pfac = dpsi^sing_asymp.alpha[i] dua[:, r2[2*i-1], :] ./= pfac @@ -791,7 +791,7 @@ end sing_matvec(ffit::FourFitVars, intr::ForceFreeStatesInternal, psi::Float64, q::Float64, ua, dua) -> matvec Apply the Euler-Lagrange residual operator `L u = -(F u' + K u)' + (K† u' + G u)` to the asymptotic -solutions. Port of Fortran `sing_matvec` (sing.f:1045-1107). Returns `matvec`, shape +solutions. Port of Fortran `sing_matvec` (sing.f). Returns `matvec`, shape `(numpert_total, size(ua,2))`. Uses the reduced (Schur-complemented) `ffit.kmats` (= K̄) and `ffit.gmats` (= Ḡ) directly, with the diff --git a/src/InnerLayer/GGJ/Galerkin.jl b/src/InnerLayer/GGJ/Galerkin.jl index 6ac6cbab6..43b4dbbaf 100644 --- a/src/InnerLayer/GGJ/Galerkin.jl +++ b/src/InnerLayer/GGJ/Galerkin.jl @@ -708,7 +708,7 @@ function solve_inner(::GGJModel{:galerkin}, params::GGJParameters, γ::Number; emap1 = res_cell.emap[1] Δ_raw = SVector{2,ComplexF64}(ws.sol[emap1, 1], ws.sol[emap1, 2]) - # Apply deltac.f's swap convention (deltac.f:201-203) + # Apply deltac.f's swap convention (deltac_solve) Δ_swapped = SVector{2,ComplexF64}(Δ_raw[2], Δ_raw[1]) return rescale_delta(Δ_swapped, params) From a2ec01a7677319a53a71a0501b1d4a1fad407259 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Wed, 17 Jun 2026 10:24:09 -0400 Subject: [PATCH 062/135] DOCS - MINOR - Cleans up jacobian toml annotations --- benchmarks/benchmark_diiid_ideal_ntv_torque.jl | 3 --- benchmarks/benchmark_diiid_kinetic_stability.jl | 3 --- examples/DIIID-like_ideal_example/gpec.toml | 5 +---- examples/Solovev_ideal_example/gpec.toml | 5 +---- examples/Solovev_ideal_example_3D/gpec.toml | 5 +---- examples/Solovev_ideal_example_multi_n/gpec.toml | 5 +---- .../Solovev_ideal_example_multi_n/single_n_1/gpec.toml | 5 +---- .../Solovev_ideal_example_multi_n/single_n_2/gpec.toml | 5 +---- examples/a10_kinetic_example/gpec.toml | 7 ++----- test/test_data/regression_solovev_ideal_example/gpec.toml | 5 +---- .../regression_solovev_ideal_example_multi_n/gpec.toml | 5 +---- .../regression_solovev_kinetic_calculated/gpec.toml | 5 +---- .../test_data/regression_solovev_kinetic_example/gpec.toml | 5 +---- .../test_data/regression_solovev_kinetic_multi_n/gpec.toml | 5 +---- 14 files changed, 13 insertions(+), 55 deletions(-) diff --git a/benchmarks/benchmark_diiid_ideal_ntv_torque.jl b/benchmarks/benchmark_diiid_ideal_ntv_torque.jl index 46c4715ce..1d67f4f7c 100644 --- a/benchmarks/benchmark_diiid_ideal_ntv_torque.jl +++ b/benchmarks/benchmark_diiid_ideal_ntv_torque.jl @@ -112,9 +112,6 @@ function build_benchmark_tomldir(eq_file::String) eq_filename = "$eq_name" eq_type = "efit" jac_type = "hamada" - power_bp = 0 - power_b = 0 - power_r = 0 grid_type = "ldp" psilow = 1e-4 psihigh = 0.993 diff --git a/benchmarks/benchmark_diiid_kinetic_stability.jl b/benchmarks/benchmark_diiid_kinetic_stability.jl index 8274de1b3..a5007cc8d 100644 --- a/benchmarks/benchmark_diiid_kinetic_stability.jl +++ b/benchmarks/benchmark_diiid_kinetic_stability.jl @@ -120,9 +120,6 @@ function build_benchmark_tomldir(eq_file::String, kin_file::String) eq_filename = "$eq_name" eq_type = "efit" jac_type = "hamada" - power_bp = 0 - power_b = 0 - power_r = 0 grid_type = "pow1" # Matches Fortran DIIID_kinetic_example (equil/grid.f90 powspace) psilow = 0.01 psihigh = 0.993 diff --git a/examples/DIIID-like_ideal_example/gpec.toml b/examples/DIIID-like_ideal_example/gpec.toml index 70e88913e..5805f8dd4 100644 --- a/examples/DIIID-like_ideal_example/gpec.toml +++ b/examples/DIIID-like_ideal_example/gpec.toml @@ -6,10 +6,7 @@ [Equilibrium] eq_filename = "TkMkr_D3Dlike_Hmode.geqdsk" # Path to equilibrium file eq_type = "efit" # Type of the input 2D equilibrium file -jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc) -power_bp = 0 # Poloidal field power exponent for Jacobian -power_b = 0 # Toroidal field power exponent for Jacobian -power_r = 0 # Major radius power exponent for Jacobian +jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "log_asymptotic" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized flux coordinate psihigh = 0.9995 # Upper limit of normalized flux coordinate diff --git a/examples/Solovev_ideal_example/gpec.toml b/examples/Solovev_ideal_example/gpec.toml index dd155473e..3782693c6 100644 --- a/examples/Solovev_ideal_example/gpec.toml +++ b/examples/Solovev_ideal_example/gpec.toml @@ -6,10 +6,7 @@ [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file -jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc) -power_bp = 0 # Poloidal field power exponent for Jacobian -power_b = 0 # Toroidal field power exponent for Jacobian -power_r = 0 # Major radius power exponent for Jacobian +jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized flux coordinate psihigh = 0.9995 # Upper limit of normalized flux coordinate diff --git a/examples/Solovev_ideal_example_3D/gpec.toml b/examples/Solovev_ideal_example_3D/gpec.toml index 7ffb4c618..db4316774 100644 --- a/examples/Solovev_ideal_example_3D/gpec.toml +++ b/examples/Solovev_ideal_example_3D/gpec.toml @@ -5,10 +5,7 @@ [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file -jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc) -power_bp = 0 # Poloidal field power exponent for Jacobian -power_b = 0 # Toroidal field power exponent for Jacobian -power_r = 0 # Major radius power exponent for Jacobian +jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized flux coordinate psihigh = 0.9995 # Upper limit of normalized flux coordinate diff --git a/examples/Solovev_ideal_example_multi_n/gpec.toml b/examples/Solovev_ideal_example_multi_n/gpec.toml index d0130cdc4..2c8802527 100644 --- a/examples/Solovev_ideal_example_multi_n/gpec.toml +++ b/examples/Solovev_ideal_example_multi_n/gpec.toml @@ -6,10 +6,7 @@ [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file -jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc) -power_bp = 0 # Poloidal field power exponent for Jacobian -power_b = 0 # Toroidal field power exponent for Jacobian -power_r = 0 # Major radius power exponent for Jacobian +jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized flux coordinate psihigh = 0.9995 # Upper limit of normalized flux coordinate diff --git a/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml b/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml index 569ab329d..b40513675 100644 --- a/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml +++ b/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml @@ -5,10 +5,7 @@ [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file -jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc) -power_bp = 0 # Poloidal field power exponent for Jacobian -power_b = 0 # Toroidal field power exponent for Jacobian -power_r = 0 # Major radius power exponent for Jacobian +jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized flux coordinate psihigh = 0.9995 # Upper limit of normalized flux coordinate diff --git a/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml b/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml index 9c69eaf94..cc701f01f 100644 --- a/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml +++ b/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml @@ -5,10 +5,7 @@ [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file -jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc) -power_bp = 0 # Poloidal field power exponent for Jacobian -power_b = 0 # Toroidal field power exponent for Jacobian -power_r = 0 # Major radius power exponent for Jacobian +jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized flux coordinate psihigh = 0.9995 # Upper limit of normalized flux coordinate diff --git a/examples/a10_kinetic_example/gpec.toml b/examples/a10_kinetic_example/gpec.toml index 9a34c76d3..8f16756a1 100644 --- a/examples/a10_kinetic_example/gpec.toml +++ b/examples/a10_kinetic_example/gpec.toml @@ -7,12 +7,9 @@ # The equilibrium g-file and kinetic profile are bundled in this directory. [Equilibrium] -eq_filename = "fix_a100_k10_q2_bn010_prof1" # Path to equilibrium file (bundled CHEASE-format g-file) +eq_filename = "fix_a100_k10_q2_bn010_prof1" # Path to equilibrium file eq_type = "efit" # Type of the input 2D equilibrium file -jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc) -power_bp = 0 # Poloidal field power exponent for Jacobian -power_b = 0 # Toroidal field power exponent for Jacobian -power_r = 0 # Major radius power exponent for Jacobian +jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type psilow = 1e-3 # Lower limit of normalized flux coordinate psihigh = 0.99 # Upper limit of normalized flux coordinate diff --git a/test/test_data/regression_solovev_ideal_example/gpec.toml b/test/test_data/regression_solovev_ideal_example/gpec.toml index ff6d9f04a..605a9e43e 100644 --- a/test/test_data/regression_solovev_ideal_example/gpec.toml +++ b/test/test_data/regression_solovev_ideal_example/gpec.toml @@ -5,10 +5,7 @@ [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file -jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc) -power_bp = 0 # Poloidal field power exponent for Jacobian -power_b = 0 # Toroidal field power exponent for Jacobian -power_r = 0 # Major radius power exponent for Jacobian +jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized flux coordinate psihigh = 0.9995 # Upper limit of normalized flux coordinate diff --git a/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml b/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml index 79299d634..d9355e5b1 100644 --- a/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml +++ b/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml @@ -5,10 +5,7 @@ [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file -jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc) -power_bp = 0 # Poloidal field power exponent for Jacobian -power_b = 0 # Toroidal field power exponent for Jacobian -power_r = 0 # Major radius power exponent for Jacobian +jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized flux coordinate psihigh = 0.9995 # Upper limit of normalized flux coordinate diff --git a/test/test_data/regression_solovev_kinetic_calculated/gpec.toml b/test/test_data/regression_solovev_kinetic_calculated/gpec.toml index 4eb1e3944..c6b4e7124 100644 --- a/test/test_data/regression_solovev_kinetic_calculated/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_calculated/gpec.toml @@ -5,10 +5,7 @@ [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file -jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc) -power_bp = 0 # Poloidal field power exponent for Jacobian -power_b = 0 # Toroidal field power exponent for Jacobian -power_r = 0 # Major radius power exponent for Jacobian +jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized flux coordinate psihigh = 0.9995 # Upper limit of normalized flux coordinate diff --git a/test/test_data/regression_solovev_kinetic_example/gpec.toml b/test/test_data/regression_solovev_kinetic_example/gpec.toml index ffb488b85..bb50ad4e2 100644 --- a/test/test_data/regression_solovev_kinetic_example/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_example/gpec.toml @@ -5,10 +5,7 @@ [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file -jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc) -power_bp = 0 # Poloidal field power exponent for Jacobian -power_b = 0 # Toroidal field power exponent for Jacobian -power_r = 0 # Major radius power exponent for Jacobian +jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized flux coordinate psihigh = 0.9995 # Upper limit of normalized flux coordinate diff --git a/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml b/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml index 1a6ec2e08..c0edce269 100644 --- a/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml @@ -5,10 +5,7 @@ [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file -jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc) -power_bp = 0 # Poloidal field power exponent for Jacobian -power_b = 0 # Toroidal field power exponent for Jacobian -power_r = 0 # Major radius power exponent for Jacobian +jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized flux coordinate psihigh = 0.9995 # Upper limit of normalized flux coordinate From f4b2241c1588346de7337f3b8b2b8a0d0b4de3f5 Mon Sep 17 00:00:00 2001 From: jmlmir369 Date: Fri, 19 Jun 2026 05:43:23 +0900 Subject: [PATCH 063/135] ForceFreeStates - CLEANUP - Avoid duplicate Mercier DI in DR path --- src/ForceFreeStates/Bal.jl | 46 ++++++++++++++++++-------------------- 1 file changed, 22 insertions(+), 24 deletions(-) diff --git a/src/ForceFreeStates/Bal.jl b/src/ForceFreeStates/Bal.jl index bb20ed54d..e26547acd 100644 --- a/src/ForceFreeStates/Bal.jl +++ b/src/ForceFreeStates/Bal.jl @@ -21,7 +21,8 @@ to compute Delta Prime. This function modifies `locstab_fs` in place with: - Column 1: `det(d0bar) * ψ` (Mercier interchange `D_I`) - - Column 2: resistive interchange `D_R * ψ` (see [`resistive_interchange`](@ref)) + - Column 2: resistive interchange `D_R * ψ`, using `det(d0bar)` for `D_I` + and the surface-average route for `H` (see [`resistive_interchange_h`](@ref)) - Column 4: Delta Prime (Δ') """ function compute_ballooning_stability!( @@ -43,8 +44,10 @@ function compute_ballooning_stability!( psi = plasma_eq.profiles.xs[flux_surface_index] coeff_data = prepare_ballooning_coefficients(flux_surface_index, plasma_eq; theta_k=theta_k) + h = resistive_interchange_h(flux_surface_index, plasma_eq) locstab_fs[flux_surface_index, 1] = coeff_data.di * psi - locstab_fs[flux_surface_index, 2] = resistive_interchange(flux_surface_index, plasma_eq).dr * psi + # Keep D_R tied to the reported D_I. The surface-average route provides H. + locstab_fs[flux_surface_index, 2] = (coeff_data.di + (h - 0.5)^2) * psi if compute_delta_prime && plasma_eq.profiles.xs[flux_surface_index] <= 1.0 result = integrate_ballooning_ode( @@ -62,27 +65,27 @@ function compute_ballooning_stability!( end """ - resistive_interchange(flux_surface_index, plasma_eq) + resistive_interchange_h(flux_surface_index, plasma_eq) -Resistive interchange criterion `D_R = D_I + (H - 1/2)²` at a single flux surface -[Glasser-Greene-Johnson; Glasser Phys. Plasmas 23, 112506 (2016)]. The Mercier -`D_I` and the intermediate `H` are formed from flux-surface averages of the field -and metric quantities. Returns a NamedTuple `(di, dr, h)`, all unscaled by ψ. +Resistive interchange helper for `D_R = D_I + (H - 1/2)²` at a single +flux surface [Glasser-Greene-Johnson; Glasser Phys. Plasmas 23, 112506 +(2016)]. The intermediate `H` is formed from flux-surface averages of the +field and metric quantities. -Note: this evaluates the Mercier `D_I` from the surface-average formulation, which -is a distinct numerical route from the `det(d0bar)` value reported as `locstab/di` -by [`compute_ballooning_stability!`](@ref). +The main local-stability scan takes `D_I` from the `det(d0bar)` calculation +reported as `locstab/di`, then combines it with this surface-average `H` to +form `locstab/dr`. This avoids recomputing a separate surface-average `D_I` +inside the `D_R` path. """ -function resistive_interchange(flux_surface_index::Int, plasma_eq::Equilibrium.PlasmaEquilibrium) +function resistive_interchange_h(flux_surface_index::Int, plasma_eq::Equilibrium.PlasmaEquilibrium) profiles = plasma_eq.profiles ntheta = length(plasma_eq.rzphi_ys) - ff_fs = zeros(ntheta, 5) + ff_fs = zeros(ntheta, 3) psi = profiles.xs[flux_surface_index] twopif = profiles.F_spline.y[flux_surface_index] p1 = profiles.P_deriv(psi) v1 = profiles.dVdpsi_spline.y[flux_surface_index] - v2 = profiles.dVdpsi_deriv(psi) q = profiles.q_spline.y[flux_surface_index] q1 = profiles.q_deriv(psi) chi1 = 2π * plasma_eq.psio @@ -110,20 +113,13 @@ function resistive_interchange(flux_surface_index::Int, plasma_eq::Equilibrium.P ff_fs[itheta, 1] = bsq / dpsisq ff_fs[itheta, 2] = 1.0 / dpsisq - ff_fs[itheta, 3] = 1.0 / bsq - ff_fs[itheta, 4] = 1.0 / (bsq * dpsisq) - ff_fs[itheta, 5] = bsq + ff_fs[itheta, 3] = bsq @views ff_fs[itheta, :] .*= jac / v1 end avg = FastInterpolations.integrate(cubic_interp(plasma_eq.rzphi_ys, Series(ff_fs); bc=PeriodicBC())) - term = twopif * p1 * v1 / (q1 * chi1^3) * avg[2] - di = -0.25 + term * (1 - term) + - p1 * (v1 / (q1 * chi1^2))^2 * avg[1] * - (p1 * (avg[3] + (twopif / chi1)^2 * avg[4]) - v2 / v1) - h = twopif * p1 * v1 / (q1 * chi1^3) * (avg[2] - avg[1] / avg[5]) - return (di=di, dr=di + (h - 0.5)^2, h=h) + return twopif * p1 * v1 / (q1 * chi1^3) * (avg[2] - avg[1] / avg[3]) end @@ -1118,7 +1114,8 @@ function integrate_ballooning_ode(ode_coefficient_spline; theta_k::Float64=0.0) reltol=TOLERANCE, abstol=TOLERANCE^2, dtmin=MINIMUM_STEP, - adaptive=true + adaptive=true, + verbose=false ) if sol_left.retcode != ReturnCode.Success return (value=NaN,) @@ -1136,7 +1133,8 @@ function integrate_ballooning_ode(ode_coefficient_spline; theta_k::Float64=0.0) reltol=TOLERANCE, abstol=TOLERANCE^2, dtmin=MINIMUM_STEP, - adaptive=true + adaptive=true, + verbose=false ) if sol_right.retcode != ReturnCode.Success return (value=NaN,) From 6dd6d853dae24f21b71f86e38cba8453a2eca18c Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Thu, 18 Jun 2026 23:54:54 -0400 Subject: [PATCH 064/135] GPEC - BUG FIX - Address PR #286 review findings (legacy delta_mband, Nyquist msg) Legacy gpec.toml files still setting delta_mband/mband under [ForceFreeStates] previously crashed at startup with an unknown-keyword error when the table was splatted into ForceFreeStatesControl. Add _drop_deprecated_ffs_keys! to strip deprecated keys with a deprecation warning before the splat. Also make the FourierCoefficients Nyquist assert report the actual mmax, Nyquist limit, and ntheta instead of a bare message. Co-Authored-By: Claude Opus 4.8 (1M context) --- src/GeneralizedPerturbedEquilibrium.jl | 18 +++++++++++++++++- src/Utilities/FourierCoefficients.jl | 4 ++-- 2 files changed, 19 insertions(+), 3 deletions(-) diff --git a/src/GeneralizedPerturbedEquilibrium.jl b/src/GeneralizedPerturbedEquilibrium.jl index 914f36453..6ac23c24b 100755 --- a/src/GeneralizedPerturbedEquilibrium.jl +++ b/src/GeneralizedPerturbedEquilibrium.jl @@ -58,6 +58,20 @@ using .ForceFreeStates: eulerlagrange_integration, free_run! const _BANNER = "="^60 const _SECTION = "-"^40 +const _DEPRECATED_FFS_KEYS = ("delta_mband", "mband") + +# Drop deprecated [ForceFreeStates] keys (e.g. banded-matrix removal from PR #286) so legacy +# gpec.toml files keep parsing instead of throwing an unknown-keyword error. +function _drop_deprecated_ffs_keys!(table) + for k in _DEPRECATED_FFS_KEYS + if haskey(table, k) + @warn "`$k` in [ForceFreeStates] is deprecated and ignored please remove it from gpec.toml." + delete!(table, k) + end + end + return table +end + function main(args::Vector{String}=String[]; dd::Union{IMASdd.dd,Nothing}=nothing) # Parse command line arguments path = length(args) >= 1 ? args[1] : "./" @@ -81,7 +95,9 @@ function main(args::Vector{String}=String[]; dd::Union{IMASdd.dd,Nothing}=nothin # Read input data and set up data structures intr = ForceFreeStatesInternal(; dir_path=path) inputs = TOML.parsefile(joinpath(intr.dir_path, "gpec.toml")) - ctrl = ForceFreeStatesControl(; (Symbol(k) => v for (k, v) in inputs["ForceFreeStates"])...) + ffs_table = inputs["ForceFreeStates"] + _drop_deprecated_ffs_keys!(ffs_table) + ctrl = ForceFreeStatesControl(; (Symbol(k) => v for (k, v) in ffs_table)...) # Set up equilibrium from gpec.toml or fallback to equil.toml if it exists. # Analytic equilibria ("tj_analytic", "tj_analytic_direct", "sol", "lar") can diff --git a/src/Utilities/FourierCoefficients.jl b/src/Utilities/FourierCoefficients.jl index f11aee2f7..1bc64b43f 100644 --- a/src/Utilities/FourierCoefficients.jl +++ b/src/Utilities/FourierCoefficients.jl @@ -78,9 +78,9 @@ function FourierCoefficients(xs::Vector{Float64}, ys::Vector{Float64}, # including the duplicate biases the DC coefficient by ~(f(0) − mean)/N. has_duplicate = ny_full > 1 && isapprox(ys[end] - ys[1], 2π; rtol=1e-10) ntheta = has_duplicate ? ny_full - 1 : ny_full - fs_view = has_duplicate ? view(fs,:,(1:ntheta),:) : fs + fs_view = has_duplicate ? view(fs, :, (1:ntheta), :) : fs - @assert mmax <= ntheta ÷ 2 "mmax must be less than or equal to the Nyquist limit" + @assert mmax <= ntheta ÷ 2 "Requested mmax=$mmax exceeds the θ-grid Nyquist limit $(ntheta ÷ 2) (ntheta=$ntheta); increase the poloidal grid resolution or reduce mpert." # Compute Fourier coefficients using batched FFT fs_reshaped = reshape(permutedims(fs_view, (2, 1, 3)), ntheta, npsi * nqty) From e7bcf29acdaab13c2ab2e387b2a28cf4beb39bfe Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Fri, 19 Jun 2026 00:20:32 -0400 Subject: [PATCH 065/135] EXAMPLES - CLEANUP - Standardize psilow/psihigh wording and consistent variable annotations MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Reword every psilow/psihigh annotation to "normalized poloidal flux" (was "normalized flux coordinate"), and unify three annotation defects across the example and regression-fixture TOMLs: - jac_type: restore full option list (…equal_arc, park, other) where truncated - [Wall] shape: restore full option list (…elliptical, dee, mod_dee, filepath) - psiedge: align a10 to the canonical wording Comment-only changes; no values touched, so results are unaffected. Co-Authored-By: Claude Opus 4.8 (1M context) --- examples/DIIID-like_ideal_example/gpec.toml | 4 ++-- examples/DIIID-like_ideal_example_IMAS/gpec.toml | 6 +++--- examples/LAR_beta_scan/gpec.toml | 6 +++--- examples/LAR_epsilon_scan/gpec.toml | 6 +++--- examples/Solovev_ideal_example/gpec.toml | 4 ++-- examples/Solovev_ideal_example_3D/gpec.toml | 4 ++-- examples/Solovev_ideal_example_multi_n/gpec.toml | 4 ++-- examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml | 4 ++-- examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml | 4 ++-- examples/a10_kinetic_example/gpec.toml | 6 +++--- test/test_data/regression_solovev_ideal_example/gpec.toml | 6 +++--- .../regression_solovev_ideal_example_multi_n/gpec.toml | 6 +++--- .../regression_solovev_kinetic_calculated/gpec.toml | 4 ++-- test/test_data/regression_solovev_kinetic_example/gpec.toml | 6 +++--- test/test_data/regression_solovev_kinetic_multi_n/gpec.toml | 6 +++--- 15 files changed, 38 insertions(+), 38 deletions(-) diff --git a/examples/DIIID-like_ideal_example/gpec.toml b/examples/DIIID-like_ideal_example/gpec.toml index 5805f8dd4..950c9f55b 100644 --- a/examples/DIIID-like_ideal_example/gpec.toml +++ b/examples/DIIID-like_ideal_example/gpec.toml @@ -8,8 +8,8 @@ eq_filename = "TkMkr_D3Dlike_Hmode.geqdsk" # Path to equilibrium file eq_type = "efit" # Type of the input 2D equilibrium file jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "log_asymptotic" # Radial grid packing type -psilow = 1e-4 # Lower limit of normalized flux coordinate -psihigh = 0.9995 # Upper limit of normalized flux coordinate +psilow = 1e-4 # Lower limit of normalized poloidal flux +psihigh = 0.9995 # Upper limit of normalized poloidal flux mpsi = 0 # Number of radial grid points (0 = auto-compute from psi_accuracy) psi_accuracy = 0.001 # Target absolute error in q for auto-mpsi mtheta = 256 # Number of poloidal grid points diff --git a/examples/DIIID-like_ideal_example_IMAS/gpec.toml b/examples/DIIID-like_ideal_example_IMAS/gpec.toml index ea9faa90b..952b54d03 100644 --- a/examples/DIIID-like_ideal_example_IMAS/gpec.toml +++ b/examples/DIIID-like_ideal_example_IMAS/gpec.toml @@ -10,9 +10,9 @@ [Equilibrium] eq_type = "imas" # Type of the input 2D equilibrium file eq_filename = "from_dd" # Path to equilibrium file (placeholder: equilibrium comes from the runtime dd argument) -jac_type = "boozer" # Coordinate system (hamada, pest, boozer, equal_arc) -psilow = 0.01 # Lower limit of normalized flux coordinate -psihigh = 0.9995 # Upper limit of normalized flux coordinate +jac_type = "boozer" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) +psilow = 0.01 # Lower limit of normalized poloidal flux +psihigh = 0.9995 # Upper limit of normalized poloidal flux mpsi = 128 # Number of radial grid points (0 = auto-compute from psi_accuracy) mtheta = 256 # Number of poloidal grid points imas_cocos = 11 # Expected COCOS convention of the input IMAS dd (11 = IMAS standard) diff --git a/examples/LAR_beta_scan/gpec.toml b/examples/LAR_beta_scan/gpec.toml index 837eaefea..905eb177f 100644 --- a/examples/LAR_beta_scan/gpec.toml +++ b/examples/LAR_beta_scan/gpec.toml @@ -9,10 +9,10 @@ [Equilibrium] eq_type = "tj_analytic" # TJ-analytic model (inverse pipeline; Fitzpatrick https://github.com/rfitzp/TJ) -jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc) +jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type -psilow = 0.01 # Lower limit of normalized flux coordinate -psihigh = 0.995 # Upper limit of normalized flux coordinate +psilow = 0.01 # Lower limit of normalized poloidal flux +psihigh = 0.995 # Upper limit of normalized poloidal flux mpsi = 128 # Number of radial grid points (0 = auto-compute from psi_accuracy) mtheta = 512 # Number of poloidal grid points diff --git a/examples/LAR_epsilon_scan/gpec.toml b/examples/LAR_epsilon_scan/gpec.toml index 604a877c4..96bf79cba 100644 --- a/examples/LAR_epsilon_scan/gpec.toml +++ b/examples/LAR_epsilon_scan/gpec.toml @@ -9,10 +9,10 @@ [Equilibrium] eq_type = "tj_analytic" # TJ-analytic model (inverse pipeline; overridden to "tj_analytic_direct" by run_scan.jl) -jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc) +jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type -psilow = 0.01 # Lower limit of normalized flux coordinate -psihigh = 0.995 # Upper limit of normalized flux coordinate +psilow = 0.01 # Lower limit of normalized poloidal flux +psihigh = 0.995 # Upper limit of normalized poloidal flux mpsi = 128 # Number of radial grid points (0 = auto-compute from psi_accuracy) mtheta = 512 # Number of poloidal grid points diff --git a/examples/Solovev_ideal_example/gpec.toml b/examples/Solovev_ideal_example/gpec.toml index 3782693c6..31023ee47 100644 --- a/examples/Solovev_ideal_example/gpec.toml +++ b/examples/Solovev_ideal_example/gpec.toml @@ -8,8 +8,8 @@ eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type -psilow = 1e-4 # Lower limit of normalized flux coordinate -psihigh = 0.9995 # Upper limit of normalized flux coordinate +psilow = 1e-4 # Lower limit of normalized poloidal flux +psihigh = 0.9995 # Upper limit of normalized poloidal flux mpsi = 128 # Number of radial grid points (0 = auto-compute from psi_accuracy) mtheta = 256 # Number of poloidal grid points newq0 = 0 # Override for on-axis safety factor (0 = use input value) diff --git a/examples/Solovev_ideal_example_3D/gpec.toml b/examples/Solovev_ideal_example_3D/gpec.toml index db4316774..d8304a2ca 100644 --- a/examples/Solovev_ideal_example_3D/gpec.toml +++ b/examples/Solovev_ideal_example_3D/gpec.toml @@ -7,8 +7,8 @@ eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type -psilow = 1e-4 # Lower limit of normalized flux coordinate -psihigh = 0.9995 # Upper limit of normalized flux coordinate +psilow = 1e-4 # Lower limit of normalized poloidal flux +psihigh = 0.9995 # Upper limit of normalized poloidal flux mpsi = 128 # Number of radial grid points (0 = auto-compute from psi_accuracy) mtheta = 256 # Number of poloidal grid points newq0 = 0 # Override for on-axis safety factor (0 = use input value) diff --git a/examples/Solovev_ideal_example_multi_n/gpec.toml b/examples/Solovev_ideal_example_multi_n/gpec.toml index 2c8802527..89654c173 100644 --- a/examples/Solovev_ideal_example_multi_n/gpec.toml +++ b/examples/Solovev_ideal_example_multi_n/gpec.toml @@ -8,8 +8,8 @@ eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type -psilow = 1e-4 # Lower limit of normalized flux coordinate -psihigh = 0.9995 # Upper limit of normalized flux coordinate +psilow = 1e-4 # Lower limit of normalized poloidal flux +psihigh = 0.9995 # Upper limit of normalized poloidal flux mpsi = 128 # Number of radial grid points (0 = auto-compute from psi_accuracy) mtheta = 256 # Number of poloidal grid points newq0 = 0 # Override for on-axis safety factor (0 = use input value) diff --git a/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml b/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml index b40513675..e55f7ab15 100644 --- a/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml +++ b/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml @@ -7,8 +7,8 @@ eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type -psilow = 1e-4 # Lower limit of normalized flux coordinate -psihigh = 0.9995 # Upper limit of normalized flux coordinate +psilow = 1e-4 # Lower limit of normalized poloidal flux +psihigh = 0.9995 # Upper limit of normalized poloidal flux mpsi = 128 # Number of radial grid points (0 = auto-compute from psi_accuracy) mtheta = 256 # Number of poloidal grid points newq0 = 0 # Override for on-axis safety factor (0 = use input value) diff --git a/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml b/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml index cc701f01f..f8e101594 100644 --- a/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml +++ b/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml @@ -7,8 +7,8 @@ eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type -psilow = 1e-4 # Lower limit of normalized flux coordinate -psihigh = 0.9995 # Upper limit of normalized flux coordinate +psilow = 1e-4 # Lower limit of normalized poloidal flux +psihigh = 0.9995 # Upper limit of normalized poloidal flux mpsi = 128 # Number of radial grid points (0 = auto-compute from psi_accuracy) mtheta = 256 # Number of poloidal grid points newq0 = 0 # Override for on-axis safety factor (0 = use input value) diff --git a/examples/a10_kinetic_example/gpec.toml b/examples/a10_kinetic_example/gpec.toml index 96e6095ee..6eb3e5a72 100644 --- a/examples/a10_kinetic_example/gpec.toml +++ b/examples/a10_kinetic_example/gpec.toml @@ -11,8 +11,8 @@ eq_filename = "fix_a100_k10_q2_bn010_prof1" # Path to equilibrium file eq_type = "efit" # Type of the input 2D equilibrium file jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type -psilow = 1e-3 # Lower limit of normalized flux coordinate -psihigh = 0.99 # Upper limit of normalized flux coordinate +psilow = 1e-3 # Lower limit of normalized poloidal flux +psihigh = 0.99 # Upper limit of normalized poloidal flux mpsi = 16 # Number of radial grid points (low value for fast iteration) mtheta = 256 # Number of poloidal grid points newq0 = 0 # Override for on-axis safety factor (0 = use input value) @@ -29,7 +29,7 @@ vac_flag = true # Compute plasma, vacuum, and total energies for mer_flag = true # Evaluate the Mercier criterion set_psilim_via_dmlim = false # FALSE for limited/analytical equilibria — rationals sparse, dmlim would chop too much edge -psiedge = 1.0 # Edge dW(ψ) diagnostic scan band [psiedge, psilim]; 1.0 ≥ psilim disables the scan (integrate full domain) +psiedge = 1.0 # Edge dW(ψ) diagnostic scan band [psiedge, psilim]; set ≥ psilim to disable qlow = 1.02 # Integration initiated at q determined by min(q0, qlow) qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh) sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) diff --git a/test/test_data/regression_solovev_ideal_example/gpec.toml b/test/test_data/regression_solovev_ideal_example/gpec.toml index bea73b6ea..3ec352623 100644 --- a/test/test_data/regression_solovev_ideal_example/gpec.toml +++ b/test/test_data/regression_solovev_ideal_example/gpec.toml @@ -7,8 +7,8 @@ eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type -psilow = 1e-4 # Lower limit of normalized flux coordinate -psihigh = 0.9995 # Upper limit of normalized flux coordinate +psilow = 1e-4 # Lower limit of normalized poloidal flux +psihigh = 0.9995 # Upper limit of normalized poloidal flux mpsi = 16 # Number of radial grid points (0 = auto-compute from psi_accuracy) mtheta = 256 # Number of poloidal grid points newq0 = 0 # Override for on-axis safety factor (0 = use input value) @@ -16,7 +16,7 @@ etol = 1e-7 # Error tolerance for equilibrium solver force_termination = false # Terminate after equilibrium setup (skip stability calculations) [Wall] -shape = "conformal" # Wall shape (nowall, conformal, ...); close conformal wall stabilizes the Solovev n=1 kink (see examples/Solovev_ideal_example/gpec.toml) +shape = "conformal" # Wall shape (nowall, conformal, elliptical, dee, mod_dee, filepath); close conformal wall stabilizes the Solovev n=1 kink (see examples/Solovev_ideal_example/gpec.toml) a = 0.2415 # Distance from plasma (conformal) or shape parameter aw = 0.05 # Half-thickness parameter for Dee-shaped walls bw = 1.5 # Elongation parameter for wall shapes diff --git a/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml b/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml index e5016d32f..77c839a95 100644 --- a/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml +++ b/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml @@ -7,8 +7,8 @@ eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type -psilow = 1e-4 # Lower limit of normalized flux coordinate -psihigh = 0.9995 # Upper limit of normalized flux coordinate +psilow = 1e-4 # Lower limit of normalized poloidal flux +psihigh = 0.9995 # Upper limit of normalized poloidal flux mpsi = 16 # Number of radial grid points (0 = auto-compute from psi_accuracy) mtheta = 256 # Number of poloidal grid points newq0 = 0 # Override for on-axis safety factor (0 = use input value) @@ -16,7 +16,7 @@ etol = 1e-7 # Error tolerance for equilibrium solver force_termination = false # Terminate after equilibrium setup (skip stability calculations) [Wall] -shape = "conformal" # Wall shape (nowall, conformal, ...); close conformal wall stabilizes the Solovev n=1 kink (see examples/Solovev_ideal_example/gpec.toml) +shape = "conformal" # Wall shape (nowall, conformal, elliptical, dee, mod_dee, filepath); close conformal wall stabilizes the Solovev n=1 kink (see examples/Solovev_ideal_example/gpec.toml) a = 0.2415 # Distance from plasma (conformal) or shape parameter aw = 0.05 # Half-thickness parameter for Dee-shaped walls bw = 1.5 # Elongation parameter for wall shapes diff --git a/test/test_data/regression_solovev_kinetic_calculated/gpec.toml b/test/test_data/regression_solovev_kinetic_calculated/gpec.toml index 84117430b..c43f8eaf9 100644 --- a/test/test_data/regression_solovev_kinetic_calculated/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_calculated/gpec.toml @@ -7,8 +7,8 @@ eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type -psilow = 1e-4 # Lower limit of normalized flux coordinate -psihigh = 0.9995 # Upper limit of normalized flux coordinate +psilow = 1e-4 # Lower limit of normalized poloidal flux +psihigh = 0.9995 # Upper limit of normalized poloidal flux mpsi = 16 # Number of radial grid points (0 = auto-compute from psi_accuracy) mtheta = 256 # Number of poloidal grid points newq0 = 0 # Override for on-axis safety factor (0 = use input value) diff --git a/test/test_data/regression_solovev_kinetic_example/gpec.toml b/test/test_data/regression_solovev_kinetic_example/gpec.toml index 9e49b275a..edbc8ec15 100644 --- a/test/test_data/regression_solovev_kinetic_example/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_example/gpec.toml @@ -7,8 +7,8 @@ eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type -psilow = 1e-4 # Lower limit of normalized flux coordinate -psihigh = 0.9995 # Upper limit of normalized flux coordinate +psilow = 1e-4 # Lower limit of normalized poloidal flux +psihigh = 0.9995 # Upper limit of normalized poloidal flux mpsi = 16 # Number of radial grid points (0 = auto-compute from psi_accuracy) mtheta = 256 # Number of poloidal grid points newq0 = 0 # Override for on-axis safety factor (0 = use input value) @@ -16,7 +16,7 @@ etol = 1e-7 # Error tolerance for equilibrium solver force_termination = false # Terminate after equilibrium setup (skip stability calculations) [Wall] -shape = "conformal" # Wall shape (nowall, conformal, ...); close conformal wall stabilizes the Solovev n=1 kink (see examples/Solovev_ideal_example/gpec.toml) +shape = "conformal" # Wall shape (nowall, conformal, elliptical, dee, mod_dee, filepath); close conformal wall stabilizes the Solovev n=1 kink (see examples/Solovev_ideal_example/gpec.toml) a = 0.2415 # Distance from plasma (conformal) or shape parameter aw = 0.05 # Half-thickness parameter for Dee-shaped walls bw = 1.5 # Elongation parameter for wall shapes diff --git a/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml b/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml index cd859abc4..ad275af17 100644 --- a/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml @@ -7,8 +7,8 @@ eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type -psilow = 1e-4 # Lower limit of normalized flux coordinate -psihigh = 0.9995 # Upper limit of normalized flux coordinate +psilow = 1e-4 # Lower limit of normalized poloidal flux +psihigh = 0.9995 # Upper limit of normalized poloidal flux mpsi = 16 # Number of radial grid points (0 = auto-compute from psi_accuracy) mtheta = 256 # Number of poloidal grid points newq0 = 0 # Override for on-axis safety factor (0 = use input value) @@ -16,7 +16,7 @@ etol = 1e-7 # Error tolerance for equilibrium solver force_termination = false # Terminate after equilibrium setup (skip stability calculations) [Wall] -shape = "conformal" # Wall shape (nowall, conformal, ...); close conformal wall stabilizes the Solovev n=1 kink (see examples/Solovev_ideal_example/gpec.toml) +shape = "conformal" # Wall shape (nowall, conformal, elliptical, dee, mod_dee, filepath); close conformal wall stabilizes the Solovev n=1 kink (see examples/Solovev_ideal_example/gpec.toml) a = 0.2415 # Distance from plasma (conformal) or shape parameter aw = 0.05 # Half-thickness parameter for Dee-shaped walls bw = 1.5 # Elongation parameter for wall shapes From 0d7c02c2e81f703449d8d5531d0eb142ed2c12c6 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Fri, 19 Jun 2026 00:23:08 -0400 Subject: [PATCH 066/135] KineticForces - REFACTOR - Unify energy integral onto one x-space PV+residue path MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Fold the two energy-integral paths (u-space for ν>0, real x-space for ν=0) into a single real-x-space principal-value + residue integrator, `_integrate_energy_resonant`. The pole is `x_pole = x_res − i·ν/Ω′` — off the real axis for ν>0, on it for ν=0 — so the collisionless case is the exact ν→0 limit of one formula rather than a separate branch. The causal ∓iπ·sign(Ω′) retarded branch now falls out of the signed zero of `pole_offset = ν/Ω′` (verified to 1e-14 for both signs of Ω′), and the flat-Ω regular-part limit (`_real_pole_regular_part`, renamed) only ever fires for ν=0. Deletes the ~40-line u-space collisional block (`u_poles`/`u_breaks`, the `u=1−exp(−x)` substitution, the `xr>700` guard). Net −47 lines. The collisional harmonic path now routes through x-space instead of u-space, moving `solovev_kinetic_calculated` et[1] by ~1e-6 relative (per-integral reassociation ~5e-12 amplified through the ill-conditioned eigenproblem; harness 0.00%, inside the fullruns rtol brackets). The 3 ideal harness cases are 0.0-diff. Collisionless ν=0 output is unchanged from #282. Verified: fortran-physics-reviewer PASS (residue, add-back, causal branch, regular-part guard, truncation); 126 runtests_kinetic + 24 runtests_fullruns green; regression harness 3 ideal cases 0.0-diff. Adds an Ω′<0 collisionless causal-branch unit test. Co-Authored-By: Claude Opus 4.8 (1M context) --- src/KineticForces/EnergyIntegration.jl | 196 ++++++++----------------- test/runtests_fullruns.jl | 5 + test/runtests_kinetic.jl | 30 +++- 3 files changed, 93 insertions(+), 138 deletions(-) diff --git a/src/KineticForces/EnergyIntegration.jl b/src/KineticForces/EnergyIntegration.jl index dbb7d877e..e3ecda600 100644 --- a/src/KineticForces/EnergyIntegration.jl +++ b/src/KineticForces/EnergyIntegration.jl @@ -4,12 +4,13 @@ Energy-space integration for the kinetic resonance operator. Implements the energy integrand from [Logan, Park, et al., Phys. Plasmas, 2013] Eq. (8). -The integral over normalized energy x = E/T is mapped to the finite interval -u ∈ [0,1) by the substitution u = 1 - exp(-x), which absorbs the Maxwellian -weight exp(-x) into du and covers the full [0,∞) domain without truncation. -Resonance poles (where the denominator i·Ω(x) - ν vanishes) are removed +The integral over normalized energy x = E/T is evaluated in real x-space over +`[0, X_ENERGY_MAX]` (Fortran PENTRC convention; `exp(-72) ≈ 5e-32` is negligible +to any tolerance). Resonance poles (where the denominator i·Ω(x) - ν vanishes, +shifted off the real axis to x_pole = x_res - i·ν/Ω′ by collisions) are removed analytically by a Sokhotski-Plemelj decomposition, so the remaining integrand -is smooth and integrated by QuadGK adaptive Gauss-Kronrod quadrature. +is smooth and integrated by QuadGK adaptive Gauss-Kronrod quadrature. One path +serves all collisionalities; the collisionless case is the exact ν→0 limit. """ """ @@ -62,9 +63,8 @@ end _energy_numerator(x::Float64, p::EnergyParams) → ComplexF64 Numerator N(x) of the energy integrand, **without** the resonance denominator -and **without** the Maxwellian weight exp(-x). Under the u = 1-exp(-x) -substitution the factor exp(-x)·dx is absorbed into du, so the u-space -integrand is N(x)/denom(x). +and **without** the Maxwellian weight exp(-x). The physical x-space integrand is +N(x)·exp(-x)/denom(x); the residue at a pole uses N(x_res)·exp(-x_res). For CGL there is no resonance denominator: N_cgl = x^2.5 / (i·n). """ @@ -89,8 +89,8 @@ end _energy_numerator_deriv(x::Float64, p::EnergyParams) → ComplexF64 x-derivative dN/dx of `_energy_numerator`, used for the analytic regular-part -limit of the collisionless integrand at a resonance pole. CGL is excluded — the -collisionless real-pole path never carries a CGL numerator (CGL has no pole). +limit at a real-axis (ν=0) resonance pole. CGL is excluded — the real-pole path +never carries a CGL numerator (CGL has no pole). """ @inline function _energy_numerator_deriv(x::Float64, p::EnergyParams)::ComplexF64 sx = sqrt(x) @@ -114,8 +114,8 @@ end _energy_integrand_real(x::Float64, p::EnergyParams) → ComplexF64 Physical energy integrand in x-space, N(x)·exp(-x)/denom(x), evaluated on the -real axis. Used for diagnostics (`evaluate_energy_integrand`) and tests; the -production integral works in u-space via `integrate_energy`. +real axis. Used both by the production integral (`integrate_energy` via +`_integrate_energy_resonant`) and for diagnostics (`evaluate_energy_integrand`). """ @inline function _energy_integrand_real(x::Float64, p::EnergyParams)::ComplexF64 sqx = sqrt(x) @@ -177,17 +177,17 @@ end const X_ENERGY_MAX = 72.0 """ - _collisionless_regular_part(xr, p, leff, wb, n, wd) → ComplexF64 + _real_pole_regular_part(xr, p, leff, wb, n, wd) → ComplexF64 Laurent regular part (finite limit at `x → x_res`) of the pole-subtracted -collisionless integrand `N(x)·exp(-x)/(i·Ω(x)) − R/(x − x_res)`, with +real-axis (ν=0) integrand `N(x)·exp(-x)/(i·Ω(x)) − R/(x − x_res)`, with `Ω(x) = leff·wb·√x + n·(we+wd·x)` and `R = N(x_res)·exp(-x_res)/(i·Ω′)`. Writing `h(x) = N(x)·exp(-x)`, the limit is `[h′(x_res) − h(x_res)·Ω″/(2Ω′)] / (i·Ω′)`, with `h′ = (N′ − N)·exp(-x)`, `Ω′ = leff·wb/(2√x) + n·wd`, `Ω″ = −leff·wb/(4·x^{3/2})`. """ -@inline function _collisionless_regular_part(xr::Float64, p::EnergyParams, leff::Float64, +@inline function _real_pole_regular_part(xr::Float64, p::EnergyParams, leff::Float64, wb::Float64, n::Int, wd::Float64)::ComplexF64 sx = sqrt(xr) op = leff * wb / (2.0 * sx) + n * wd # Ω′(x_res) @@ -198,26 +198,31 @@ Writing `h(x) = N(x)·exp(-x)`, the limit is end """ - _integrate_energy_collisionless(p, leff, wb, n, we, wd, atol, rtol) → ComplexF64 - -Collisionless (ν ≡ 0) energy integral in **real x-space** over `[0, X_ENERGY_MAX]`, -matching Fortran PENTRC's real-space integration (energy.f90). Each real resonance -pole `x_res ∈ (0, X_ENERGY_MAX)` is removed analytically by principal-value + -residue (Sokhotski-Plemelj, causal ν→0⁺ branch ∓iπ following sign Ω′), leaving a -smooth integrand for QuadGK. - -The pole is on the real axis, so the resonance denominator -`Ω(x) = leff·wb·√x + n·(we+wd·x)` — a difference of `O(10⁴)` terms — rounds to -exactly `0` over a ~ULP-wide window around the pole, where the physical term is -`0/0`. There QuadGK is handed the analytic regular-part limit -(`_collisionless_regular_part`) instead. (The collisional path keeps the -`u = 1-exp(-x)` substitution, whose off-axis complex pole has none of these issues.) + _integrate_energy_resonant(p, leff, wb, n, we, wd, atol, rtol) → ComplexF64 + +Energy integral in **real x-space** over `[0, X_ENERGY_MAX]`, matching Fortran +PENTRC's real-space integration (energy.f90). One path for any collisionality: +each resonance contributes a pole `x_pole = x_res − i·ν/Ω′` (real on the axis when +ν ≡ 0, shifted off it when ν > 0), removed analytically by principal-value + +residue (Sokhotski-Plemelj), leaving a smooth integrand for QuadGK. The +collisionless case is the exact ν→0 limit of this single formula. + +The add-back `R·[log(xmax − x_pole) − log(−x_pole)]` carries the causal branch +automatically: with `pole_offset = ν/Ω′`, the signed zero of `−pole_offset` for +ν ≡ 0 makes `log(−x_pole) = log(x_res) + iπ·sign(Ω′)`, the retarded ν→0⁺ limit of +Fortran's ximag>0 contour. + +For ν > 0 the off-axis pole keeps the integrand bounded (`|denom| ≥ ν > 0`). For +ν ≡ 0 the pole is on the real axis, where `Ω(x) = leff·wb·√x + n·(we+wd·x)` — a +difference of `O(10⁴)` terms — rounds to exactly `0` over a ~ULP-wide window, where +the physical term is `0/0`; there QuadGK is handed the analytic regular-part limit +(`_real_pole_regular_part`) instead. That guard only ever fires for ν ≡ 0. """ -function _integrate_energy_collisionless(p::EnergyParams, leff::Float64, wb::Float64, - n::Int, we::Float64, wd::Float64, - atol::Float64, rtol::Float64)::ComplexF64 +function _integrate_energy_resonant(p::EnergyParams, leff::Float64, wb::Float64, + n::Int, we::Float64, wd::Float64, + atol::Float64, rtol::Float64)::ComplexF64 x_res_list = find_resonance_energies(leff, wb, n, we, wd) - x_poles = Float64[] + x_poles = ComplexF64[] residues = ComplexF64[] pole_contribution = ComplexF64(0.0) @@ -227,12 +232,17 @@ function _integrate_energy_collisionless(p::EnergyParams, leff::Float64, wb::Flo # Ω′(x_res) = d/dx[leff·wb·√x + n·(we + wd·x)] omega_prime = leff * wb / (2.0 * sqrt(xr)) + n * wd abs(omega_prime) < SINGULAR_EPS && continue + # Collisions shift the pole off the real axis: x_pole = x_res - i·ν/Ω′ (real iff ν=0). + # If ν overflows (e.g. harmonic ν at tiny x_res) the pole is infinitely broadened — + # no localized pole; skip and let QuadGK integrate the smooth bounded integrand. + pole_offset = _energy_collision_frequency(xr, p) / omega_prime + isfinite(pole_offset) || continue + x_pole = complex(xr, -pole_offset) # signed-zero imag part for ν=0 carries the causal branch # Residue of N(x)·exp(-x)/(i·Ω(x)) at x_res, where Ω ≈ Ω′·(x - x_res) near the pole. R = _energy_numerator(xr, p) * exp(-xr) / (im * omega_prime) - # Causal (ν→0⁺) add-back ∫₀^xmax R/(x - x_res) dx = R·[log(xmax - x_res) - log(x_res) ∓ iπ]: - # the ν→0⁺ retarded limit of Fortran's ximag>0 contour (energy.f90); ∓ sign from sign(Ω′). - pole_contribution += R * (log(X_ENERGY_MAX - xr) - log(xr) - im * π * sign(omega_prime)) - push!(x_poles, xr) + # Add-back ∫₀^xmax R/(x - x_pole) dx = R·[log(xmax - x_pole) - log(-x_pole)]. + pole_contribution += R * (log(X_ENERGY_MAX - x_pole) - log(-x_pole)) + push!(x_poles, x_pole) push!(residues, R) end @@ -244,15 +254,15 @@ function _integrate_energy_collisionless(p::EnergyParams, leff::Float64, wb::Flo @inbounds for k in 1:npole val -= residues[k] / (x - x_poles[k]) end - # Inside a pole's flat-Ω window the physical term is 0/0 → val non-finite. Replace + # Inside a ν=0 pole's flat-Ω window the physical term is 0/0 → val non-finite. Replace # it with the analytic regular-part limit of the nearest pole (the other poles' - # subtractions stay finite and are kept). + # subtractions stay finite and are kept). Never reached for ν>0 (integrand bounded). if !isfinite(val) k = 1 @inbounds for j in 2:npole - abs(x - x_poles[j]) < abs(x - x_poles[k]) && (k = j) + abs(x - real(x_poles[j])) < abs(x - real(x_poles[k])) && (k = j) end - val = _collisionless_regular_part(x_poles[k], p, leff, wb, n, wd) + val = _real_pole_regular_part(real(x_poles[k]), p, leff, wb, n, wd) @inbounds for j in 1:npole j == k && continue val -= residues[j] / (x - x_poles[j]) @@ -267,9 +277,9 @@ function _integrate_energy_collisionless(p::EnergyParams, leff::Float64, wb::Flo end # Resonance locations as QuadGK breakpoints so the smooth-but-sharp integrand - # is resolved near each pole. Sort a copy — `x_poles` must stay aligned with - # `residues`, which the integrand pairs by index. - breaks = unique(sort(x_poles)) + # is resolved near each pole. Sort a copy of the real parts — `x_poles` must stay + # aligned with `residues`, which the integrand pairs by index. + breaks = unique(sort(real.(x_poles))) smooth_val, _ = quadgk(integrand, 0.0, breaks..., X_ENERGY_MAX; atol=atol, rtol=rtol) return smooth_val + pole_contribution end @@ -281,22 +291,14 @@ end Integrate the kinetic resonance operator over normalized energy x = E/T. -The integral ∫₀^∞ N(x)·exp(-x)/denom(x) dx is mapped to u ∈ [0,1) by -u = 1 - exp(-x) (Jacobian dx/du = 1/(1-u)), giving ∫₀¹ N(x(u))/denom(x(u)) du -with no energy truncation. - -Each resonance pole (root of Ω(x) = leff·wb·√x + n·(we + wd·x), shifted off -the real axis by collisions to x_pole = x_res - i·ν/Ω′) is removed by -subtracting its singular part R/(u - u_pole) from the integrand and adding -back the analytic contribution ∫₀¹ R/(u - u_pole) du = R·[log(1-u_pole) - -log(-u_pole)]. The same pole u_pole is used in both the subtraction and the -add-back, so the decomposition is exact and the remaining integrand is smooth. - -This u-space path is used only when collisions are present (ν > 0), where the -pole is off the real axis. The collisionless case (ν ≡ 0) has a real-axis pole -that the u-substitution would compress toward u=1 (numerically unresolvable in -the Maxwellian tail), so it is dispatched to `_integrate_energy_collisionless`, -which integrates in real x-space over `[0, X_ENERGY_MAX]` à la Fortran PENTRC. +The integral ∫₀^∞ N(x)·exp(-x)/denom(x) dx is evaluated in real x-space over +`[0, X_ENERGY_MAX]` (Fortran PENTRC convention; `exp(-72) ≈ 5e-32` is below any +tolerance) via `_integrate_energy_resonant`. Each resonance pole (root of +Ω(x) = leff·wb·√x + n·(we + wd·x), shifted off the real axis by collisions to +x_pole = x_res - i·ν/Ω′) is removed by subtracting its singular part R/(x - x_pole) +and adding back the analytic principal-value + residue. A single formula handles +all collisionalities: the collisionless case (ν ≡ 0) is the exact ν→0 limit, with +its real-axis pole resolved analytically (see `_integrate_energy_resonant`). Collision operator types (`nutype`): `"zero"`, `"small"`, `"krook"`, `"harmonic"`. Distribution function types (`f0type`): `"maxwellian"`, `"jkp"`, `"cgl"`. @@ -324,77 +326,9 @@ function integrate_energy(wn::Float64, wt::Float64, we::Float64, wd::Float64, return val end - # Collisionless (ν ≡ 0): real-axis pole. Dispatch to the real-x-space integral - # (Fortran PENTRC convention); the u-substitution below is only well-behaved - # for the off-axis pole of the collisional case. ν vanishes identically iff it - # vanishes at any x, so probe at x = 1. - if _energy_collision_frequency(1.0, p) == 0.0 - return _integrate_energy_collisionless(p, leff, wb, n, we, wd, atol, rtol) - end - - # Locate resonance poles and build their Sokhotski-Plemelj decomposition. - x_res_list = find_resonance_energies(leff, wb, n, we, wd) - u_poles = ComplexF64[] - residues = ComplexF64[] - u_breaks = Float64[] - pole_contribution = ComplexF64(0.0) - - for xr in x_res_list - xr <= 0.0 && continue - # A resonance beyond x ≈ 700 sits where the Maxwellian weight exp(-x_res) underflows - # to zero in Float64. Its pole contribution is genuinely zero, and the formula - # R·log(-u_pole) with R=0 and u_pole≈1 trips the 0·∞ = NaN trap. - xr > 700.0 && continue - # Ω′(x_res) = d/dx[leff·wb·√x + n·(we + wd·x)] - omega_prime = leff * wb / (2.0 * sqrt(xr)) + n * wd - abs(omega_prime) < SINGULAR_EPS && continue - - u_res = -expm1(-xr) # 1 - exp(-x_res) - # Reached only for the collisional case (the ν ≡ 0 case is dispatched above), - # so ν(x_res) > 0 and the pole is off the real axis. Guard defensively. - nu_res = _energy_collision_frequency(xr, p) - nu_res > 0.0 || continue - - # i·Ω - ν = 0 ⟹ x_pole = x_res - i·ν/Ω′. If ν overflows at a (tiny) x_res, the - # pole is infinitely collisionally broadened — no localized pole; skip and let - # QuadGK integrate the smooth integrand directly. - pole_offset = nu_res / omega_prime - isfinite(pole_offset) || continue - x_pole = complex(xr, -pole_offset) - u_pole = 1.0 - exp(-x_pole) - R = _energy_numerator(xr, p) * (1.0 - u_pole) / (im * omega_prime) - pole_contribution += R * (log(1.0 - u_pole) - log(-u_pole)) - - push!(u_poles, u_pole) - push!(residues, R) - push!(u_breaks, u_res) - end - - npole = length(residues) - - # Smooth integrand: full u-space integrand minus the subtracted pole parts. - integrand = u -> begin - u >= 1.0 && return ComplexF64(0.0) - x = -log1p(-u) - nux = _energy_collision_frequency(x, p) - denom = complex(-nux, leff * wb * sqrt(x) + n * (we + wd * x)) - val = _energy_numerator(x, p) / denom - @inbounds for k in 1:npole - val -= residues[k] / (u - u_poles[k]) - end - return val - end - - if npole == 0 - val, _ = quadgk(integrand, 0.0, 1.0; atol=atol, rtol=rtol) - return val - end - - # Resonance locations as QuadGK breakpoints so the (now smooth but possibly - # sharp) integrand is resolved near each pole. - breaks = unique!(sort!(filter(b -> 0.0 < b < 1.0, u_breaks))) - smooth_val, _ = quadgk(integrand, 0.0, breaks..., 1.0; atol=atol, rtol=rtol) - return smooth_val + pole_contribution + # Single resonant path for any collisionality: real x-space PV+residue with a + # pole x_pole = x_res - i·ν/Ω′ (off-axis for ν>0, real for ν≡0). + return _integrate_energy_resonant(p, leff, wb, n, we, wd, atol, rtol) end """ diff --git a/test/runtests_fullruns.jl b/test/runtests_fullruns.jl index 088035197..b7c222074 100644 --- a/test/runtests_fullruns.jl +++ b/test/runtests_fullruns.jl @@ -72,6 +72,11 @@ using HDF5 # well-conditioned (pinned tight); Im(et[1]) is the kinetic damping rate, # more FP-sensitive (bracketed loosely). The pre-PV `ximag` value (34.176) # was not physical; the PV+residue energy integral gives the correct result. + # The energy integral now runs through the unified real-x-space path (one + # integrator for all ν; collisionless is its ν→0 limit). vs the prior u-space + # collisional route this moves et[1] by ~1e-6 relative — per-integral + # reassociation (~5e-12) amplified through the ill-conditioned eigenproblem, + # still float noise (harness 0.00%) and well inside these rtol brackets. @test isfinite(real(et[1])) @test isfinite(imag(et[1])) @test real(et[1]) ≈ 15.888 rtol = 0.01 diff --git a/test/runtests_kinetic.jl b/test/runtests_kinetic.jl index 3f9132d58..a3833b692 100644 --- a/test/runtests_kinetic.jl +++ b/test/runtests_kinetic.jl @@ -235,10 +235,26 @@ @test collisionless ≈ small_nu rtol = 1e-3 end - @testset "xr > 700 Maxwellian-underflow guard" begin - # Linear case (wd = 0): s = -c/b = -(n·we)/(leff·wb) = 30 ⟹ x_res = 900 > 700. - # The pole sits where exp(-x_res) underflows; subtraction trips 0·log(-1) = NaN - # unless the guard at EnergyIntegration.jl:207 fires first. + @testset "Ω′ < 0 collisionless causal branch" begin + # The unified add-back R·[log(xmax-x_pole) - log(-x_pole)] gets the causal + # ∓iπ·sign(Ω′) branch from the SIGNED ZERO of pole_offset = ν/Ω′ at ν=0. + # Pick n·wd < 0 so Ω′ = leff·wb/(2√x) + n·wd flips sign in the tail; the + # collisionless result must still equal the ν→0⁺ (small-ν krook) limit, which + # carries the sign naturally through its off-axis pole. + args = (0.0, 2.0e3, 3.5e4, -5.0e2, 1.0e3) # we>0, wd<0 ⟹ tail root with Ω′<0 + tail = (0, 1.0, 1, 0.5, 0.5, "fgar") + collisionless = KF.integrate_energy(args..., 0.0, tail...; + nutype="zero", f0type="maxwellian", atol=1e-12, rtol=1e-10) + small_nu = KF.integrate_energy(args..., 1e-6, tail...; + nutype="krook", f0type="maxwellian", atol=1e-12, rtol=1e-10) + @test isfinite(collisionless) + @test collisionless ≈ small_nu rtol = 1e-3 + end + + @testset "tail pole beyond X_ENERGY_MAX dropped" begin + # Linear case (wd = 0): s = -c/b = -(n·we)/(leff·wb) = 30 ⟹ x_res = 900 > 72. + # The pole sits past X_ENERGY_MAX where exp(-x_res) underflows; the + # `xr >= X_ENERGY_MAX` check in _integrate_energy_resonant drops it cleanly. @test KF.find_resonance_energies(1.0, 1.0, 1, -30.0, 0.0)[1] ≈ 900.0 result = KF.integrate_energy( 0.5, 0.0, -30.0, 0.0, 1.0, 0.3, 0, 1.0, 1, 0.5, 0.5, "fgar"; @@ -250,9 +266,9 @@ @testset "pole_offset overflow guard" begin # Tiny wb gives small omega_prime = leff·wb/(2√x_res) = 5e-16 at x_res=1, while - # nuk = 1e300 forces nu_res / omega_prime = 2e315 → Inf. The guard at - # EnergyIntegration.jl:220 must skip this pole rather than build a non-finite - # u_pole. Parameters keep abs(wb) > 1e-30 so find_resonance_energies still returns x_res. + # nuk = 1e300 forces pole_offset = ν/omega_prime = 2e315 → Inf. The + # `isfinite(pole_offset) || continue` guard in _integrate_energy_resonant must skip + # this pole. Parameters keep abs(wb) > 1e-30 so find_resonance_energies still returns x_res. @test KF.find_resonance_energies(1.0, 1e-15, 1, -1e-15, 0.0)[1] ≈ 1.0 result = KF.integrate_energy( 0.5, 0.0, -1e-15, 0.0, 1e-15, 1e300, 0, 1.0, 1, 0.5, 0.5, "fgar"; From f35f7987de70c4079b929a1382244634a8d26806 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Fri, 19 Jun 2026 00:44:15 -0400 Subject: [PATCH 067/135] ForceFreeStates - REFACTOR - Rename Bal.jl to Ballooning.jl Renames the local-stability module file and updates its include in ForceFreeStates.jl, an internal docstring reference, the DIIID analyze_example comment, and the CLAUDE.md module inventory (which also notes it replaces the former standalone Mercier.jl). Content is otherwise unchanged. Co-Authored-By: Claude Opus 4.8 (1M context) --- CLAUDE.md | 2 +- examples/DIIID-like_ideal_example/analyze_example.jl | 2 +- src/ForceFreeStates/{Bal.jl => Ballooning.jl} | 2 +- src/ForceFreeStates/ForceFreeStates.jl | 2 +- 4 files changed, 4 insertions(+), 4 deletions(-) rename src/ForceFreeStates/{Bal.jl => Ballooning.jl} (99%) diff --git a/CLAUDE.md b/CLAUDE.md index e5686ae09..1cc4421a0 100644 --- a/CLAUDE.md +++ b/CLAUDE.md @@ -373,7 +373,7 @@ GPEC consists of **seven main modules** organized in `src/`: - `Fourfit.jl` - Fourier fitting routines - `FixedBoundaryStability.jl` - Fixed boundary analysis - `Free.jl` - Free boundary stability - - `Mercier.jl` - Mercier stability criterion + - `Ballooning.jl` - Local stability scan: Mercier D_I, resistive interchange D_R, and high-n ballooning Δ' (s–α). Replaces the former standalone `Mercier.jl`. - Status: Stable, core DCON functionality implemented #### Perturbed Equilibrium Modules diff --git a/examples/DIIID-like_ideal_example/analyze_example.jl b/examples/DIIID-like_ideal_example/analyze_example.jl index f02a32cd2..319a7063d 100644 --- a/examples/DIIID-like_ideal_example/analyze_example.jl +++ b/examples/DIIID-like_ideal_example/analyze_example.jl @@ -29,7 +29,7 @@ Plots.savefig(p_baloo, baloo_path) # ---------------------------------------------------------------------- # Local stability: s-alpha profiles, D_I / ballooning Δ', and 2D s-alpha # maps (ported from the former Bal_salpha_delta_di_summary notebook). -# These recompute directly from the equilibrium via the Bal.jl helpers +# These recompute directly from the equilibrium via the Ballooning.jl helpers # rather than reading gpec.h5, so the s-alpha scan can perturb (p', q'). # ---------------------------------------------------------------------- diff --git a/src/ForceFreeStates/Bal.jl b/src/ForceFreeStates/Ballooning.jl similarity index 99% rename from src/ForceFreeStates/Bal.jl rename to src/ForceFreeStates/Ballooning.jl index e26547acd..6ee150d31 100644 --- a/src/ForceFreeStates/Bal.jl +++ b/src/ForceFreeStates/Ballooning.jl @@ -602,7 +602,7 @@ end """ scan_delta_prime_map(psi_idx, plasma_eq; s_scales, alpha_scales, ...) -Run a local s-alpha style scan at one flux surface using the `Bal.jl` +Run a local s-alpha style scan at one flux surface using the `Ballooning.jl` makefromZero ballooning path. The scan perturbs physical `dq/dpsi` and `dp/dpsi`, converts them to the normalized units expected by the local ballooning evaluator, and returns delta-prime and `det(d0bar)` `Di` maps. diff --git a/src/ForceFreeStates/ForceFreeStates.jl b/src/ForceFreeStates/ForceFreeStates.jl index 25b9024ae..3eb3d2c77 100644 --- a/src/ForceFreeStates/ForceFreeStates.jl +++ b/src/ForceFreeStates/ForceFreeStates.jl @@ -21,7 +21,7 @@ import StaticArrays: @MMatrix # Include all necessary files include("ForceFreeStatesStructs.jl") -include("Bal.jl") +include("Ballooning.jl") include("EulerLagrange.jl") include("Sing.jl") include("Fourfit.jl") From ffcfcf2bc9e4c8b01f4967a726dc041248463261 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Fri, 19 Jun 2026 00:44:21 -0400 Subject: [PATCH 068/135] DOCS - BUG FIX - Raise Documenter HTML size_threshold for stability.md The new stability.md reference page renders to HTML above Documenter's default 200 KiB size_threshold, failing the Documentation CI with HTMLSizeThresholdError. Raise size_threshold to 400 KiB (and the warn limit to 200 KiB) to accommodate the large single-page module reference. Co-Authored-By: Claude Opus 4.8 (1M context) --- docs/make.jl | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/docs/make.jl b/docs/make.jl index fbbbb3725..3ee2fe36f 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -17,7 +17,9 @@ makedocs(; sitename="GPEC.jl", format=Documenter.HTML(; prettyurls=get(ENV, "CI", nothing) == "true", - canonical="https://OpenFUSIONToolkit.github.io/GPEC/" + canonical="https://OpenFUSIONToolkit.github.io/GPEC/", + size_threshold=409_600, # 400 KiB — stability.md is a large single-page module reference + size_threshold_warn=204_800 # 200 KiB ), modules=[GeneralizedPerturbedEquilibrium], pages=[ From 8b2df72ed24f83b1607f27ce567c861a670bc33f Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Fri, 19 Jun 2026 00:44:26 -0400 Subject: [PATCH 069/135] REGRESSION - NEW FEATURE - Track locstab D_I/D_R/ballooning Delta-prime in diiid_n1 Adds checksum quantities for the local-stability profiles locstab/di, locstab/dr, and locstab/ballooning_Delta_prime to the diiid_n1 case so changes to the Ballooning.jl scan are caught. Checksums hash the full profile and are robust to the NaN edge-surface entries. Co-Authored-By: Claude Opus 4.8 (1M context) --- regression-harness/cases/diiid_n1.toml | 26 ++++++++++++++++++++++++++ 1 file changed, 26 insertions(+) diff --git a/regression-harness/cases/diiid_n1.toml b/regression-harness/cases/diiid_n1.toml index 81b31587a..40632639c 100644 --- a/regression-harness/cases/diiid_n1.toml +++ b/regression-harness/cases/diiid_n1.toml @@ -255,6 +255,32 @@ label = "pressure profile (checksum)" noise_threshold = 0 order = 71 +# Local stability profiles (local_stability_flag = true). Checksums hash the full +# profile so they are robust to NaN edge-surface entries and catch any change. +[quantities.locstab_di] +h5path = "locstab/di" +type = "real_vector" +extract = "checksum" +label = "Mercier D_I profile (checksum)" +noise_threshold = 0 +order = 72 + +[quantities.locstab_dr] +h5path = "locstab/dr" +type = "real_vector" +extract = "checksum" +label = "resistive interchange D_R profile (checksum)" +noise_threshold = 0 +order = 73 + +[quantities.locstab_ballooning_dp] +h5path = "locstab/ballooning_Delta_prime" +type = "real_vector" +extract = "checksum" +label = "ballooning Delta' profile (checksum)" +noise_threshold = 0 +order = 74 + # Runtime [quantities.runtime] h5path = "" From 4156c81f779ace55ca814c9902649d199df22a14 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Fri, 19 Jun 2026 00:48:40 -0400 Subject: [PATCH 070/135] DOCS - MINOR - merge cleanup of tomls --- benchmarks/benchmark_diiid_ideal_ntv_torque.jl | 3 --- examples/DIIID-like_ideal_example/gpec.toml | 3 ++- examples/LAR_beta_scan/gpec.toml | 3 ++- examples/LAR_epsilon_scan/gpec.toml | 3 ++- examples/Solovev_ideal_example/gpec.toml | 3 ++- examples/Solovev_ideal_example_multi_n/gpec.toml | 2 +- examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml | 2 +- examples/a10_kinetic_example/gpec.toml | 3 ++- 8 files changed, 12 insertions(+), 10 deletions(-) diff --git a/benchmarks/benchmark_diiid_ideal_ntv_torque.jl b/benchmarks/benchmark_diiid_ideal_ntv_torque.jl index b21721049..4f71d5ab0 100644 --- a/benchmarks/benchmark_diiid_ideal_ntv_torque.jl +++ b/benchmarks/benchmark_diiid_ideal_ntv_torque.jl @@ -114,9 +114,6 @@ function build_benchmark_tomldir(eq_file::String) eq_filename = "$eq_name" eq_type = "efit" jac_type = "hamada" -power_bp = 0 -power_b = 0 -power_r = 0 grid_type = "ldp" psilow = 1e-4 psihigh = 0.993 diff --git a/examples/DIIID-like_ideal_example/gpec.toml b/examples/DIIID-like_ideal_example/gpec.toml index e33fc9e22..84f5cb32b 100644 --- a/examples/DIIID-like_ideal_example/gpec.toml +++ b/examples/DIIID-like_ideal_example/gpec.toml @@ -43,7 +43,8 @@ nn_low = 1 # Smallest toroidal mode number to include nn_high = 1 # Largest toroidal mode number to include delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 8 # Expands upper bound of Fourier harmonics -mthvac = 512 # Number of points in splines over poloidal angle at the plasma-vacuum interface +mthvac = 512 # Number of points used in splines over poloidal angle at the plasma-vacuum interface +thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds kinetic_source = "fixed" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model kinetic_factor = 0.0 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode) diff --git a/examples/LAR_beta_scan/gpec.toml b/examples/LAR_beta_scan/gpec.toml index 20b939646..d6f62fc55 100644 --- a/examples/LAR_beta_scan/gpec.toml +++ b/examples/LAR_beta_scan/gpec.toml @@ -48,7 +48,8 @@ nn_low = 1 # Smallest toroidal mode number to include nn_high = 1 # Largest toroidal mode number to include delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 8 # Expands upper bound of Fourier harmonics -mthvac = 960 # Number of points in splines over poloidal angle at the plasma-vacuum interface +mthvac = 960 # Number of points used in splines over poloidal angle at the plasma-vacuum interface +thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds eulerlagrange_tolerance = 1e-12 # Relative tolerance for ODE integration of Euler-Lagrange equations singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced diff --git a/examples/LAR_epsilon_scan/gpec.toml b/examples/LAR_epsilon_scan/gpec.toml index 176016606..d8d43437f 100644 --- a/examples/LAR_epsilon_scan/gpec.toml +++ b/examples/LAR_epsilon_scan/gpec.toml @@ -49,7 +49,8 @@ nn_low = 1 # Smallest toroidal mode number to include nn_high = 1 # Largest toroidal mode number to include delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 8 # Expands upper bound of Fourier harmonics -mthvac = 960 # Number of points in splines over poloidal angle at the plasma-vacuum interface +mthvac = 960 # Number of points used in splines over poloidal angle at the plasma-vacuum interface +thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds eulerlagrange_tolerance = 1e-12 # Relative tolerance for ODE integration of Euler-Lagrange equations singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced diff --git a/examples/Solovev_ideal_example/gpec.toml b/examples/Solovev_ideal_example/gpec.toml index 6c34b09eb..c6974a44a 100644 --- a/examples/Solovev_ideal_example/gpec.toml +++ b/examples/Solovev_ideal_example/gpec.toml @@ -61,7 +61,8 @@ nn_low = 1 # Smallest toroidal mode number to include nn_high = 1 # Largest toroidal mode number to include delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 8 # Expands upper bound of Fourier harmonics -mthvac = 960 # Number of points in splines over poloidal angle at the plasma-vacuum interface +mthvac = 960 # Number of points used in splines over poloidal angle at the plasma-vacuum interface +thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds kinetic_source = "fixed" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model kinetic_factor = 0.0 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode) diff --git a/examples/Solovev_ideal_example_multi_n/gpec.toml b/examples/Solovev_ideal_example_multi_n/gpec.toml index b3ea22f36..70a60de28 100644 --- a/examples/Solovev_ideal_example_multi_n/gpec.toml +++ b/examples/Solovev_ideal_example_multi_n/gpec.toml @@ -43,7 +43,7 @@ nn_low = 1 # Smallest toroidal mode number to include nn_high = 2 # Largest toroidal mode number to include delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 8 # Expands upper bound of Fourier harmonics -mthvac = 960 # Number of points used in splines over poloidal angle at the plasma-vacuum interface. +mthvac = 960 # Number of points used in splines over poloidal angle at the plasma-vacuum interface thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds kinetic_source = "fixed" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model diff --git a/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml b/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml index 91e24e6bc..3365a5c4d 100644 --- a/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml +++ b/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml @@ -42,7 +42,7 @@ nn_low = 1 # Smallest toroidal mode number to include nn_high = 1 # Largest toroidal mode number to include delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 10 # Expands upper bound of Fourier harmonics -mthvac = 960 # Number of points used in splines over poloidal angle at the plasma-vacuum interface. +mthvac = 960 # Number of points used in splines over poloidal angle at the plasma-vacuum interface thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds kinetic_source = "fixed" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model diff --git a/examples/a10_kinetic_example/gpec.toml b/examples/a10_kinetic_example/gpec.toml index 942fbdcaa..e357b9037 100644 --- a/examples/a10_kinetic_example/gpec.toml +++ b/examples/a10_kinetic_example/gpec.toml @@ -38,7 +38,8 @@ nn_low = 1 # Smallest toroidal mode number to include nn_high = 1 # Largest toroidal mode number to include delta_mlow = 6 # Expands lower bound of Fourier harmonics delta_mhigh = 6 # Expands upper bound of Fourier harmonics -mthvac = 512 # Number of points in splines over poloidal angle at the plasma-vacuum interface +mthvac = 512 # Number of points used in splines over poloidal angle at the plasma-vacuum interface +thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds kinetic_source = "calculated" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model kinetic_factor = 1.0 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode; 1.0 = full strength) From 5ccdb039e167e786e8c3b63ca62cd5e769e7b017 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Fri, 19 Jun 2026 13:09:20 -0400 Subject: [PATCH 071/135] DOCS - BUG FIX - Add ballooning docs missed by PR #234 PR #234 merged before the ballooning documentation page was committed, so develop is missing docs/src/ballooning.md, its registration in docs/make.jl, the stability.md cross-reference, and the asset PNGs (plus the .gitignore rule that allows committing them). Brings in only the documentation content from ballooning commit e834a69c; the analysis/ scratch, root LaTeX source, and .pyc from that commit are intentionally excluded. develop's make.jl size_threshold settings are preserved. Co-Authored-By: Claude Opus 4.8 (1M context) --- .gitignore | 1 + docs/make.jl | 1 + .../ballooning/delta_prime_matching.png | Bin 0 -> 40405 bytes .../assets/ballooning/mercier_comparison.png | Bin 0 -> 119919 bytes docs/src/ballooning.md | 909 ++++++++++++++++++ docs/src/stability.md | 8 +- 6 files changed, 917 insertions(+), 2 deletions(-) create mode 100644 docs/src/assets/ballooning/delta_prime_matching.png create mode 100644 docs/src/assets/ballooning/mercier_comparison.png create mode 100644 docs/src/ballooning.md diff --git a/.gitignore b/.gitignore index 80c1016a9..a4f9074e1 100644 --- a/.gitignore +++ b/.gitignore @@ -13,6 +13,7 @@ *.pdf !docs/resources/*.pdf *.png +!docs/src/assets/**/*.png *.jld2 .gitattributes Manifest.toml diff --git a/docs/make.jl b/docs/make.jl index 3ee2fe36f..253c7c9d7 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -30,6 +30,7 @@ makedocs(; "Vacuum" => "vacuum.md", "Equilibrium" => "equilibrium.md", "Stability Analysis" => "stability.md", + "Ballooning Local Stability" => "ballooning.md", "KineticForces" => "kinetic_forces.md", "Forcing Terms" => "forcing_terms.md", "Perturbed Equilibrium" => "perturbed_equilibrium.md", diff --git a/docs/src/assets/ballooning/delta_prime_matching.png b/docs/src/assets/ballooning/delta_prime_matching.png new file mode 100644 index 0000000000000000000000000000000000000000..a22404e2ba960ba5fac0596e864b109e6729319f GIT binary patch literal 40405 zcmZtuby!vF*S-&fq9W1_(vs4GbT`rhN=S)Fcem0dAl)sgNVgy%AtfOl($dlmzp?h` z`M!U>`#9XnS}@m~cZ_?C^STD1s>-q$XryRJNJtp+a#GKckZyIuzlTxp!v9~o^W?x^ z$d1otC6G!7$kyQt6jN~}aU`Vjs0Wuuci`*$c5>Q|NJyCNh(E|(wuNtykkT#WrNlMd z^taMYlgNHlm(453nmP`bIw&*Z(gsAM-n~s^Rfa+A-}JR3BZE zSwOiGt~mXDdDJ^`sssF%FH_q)c1m}2Gc-aIT)Ut^qY zaK@9P#SN9B`3Qd@jgF%K-#tv=+H|@Y&dtr8M?u3M zB!{eBVGw{lIyzcrHTi^IIjwGR+)6>=LCMRna|{MFAIT_Pwx@m^u8+9y{UEv@DAD63 zt%e%h{`pmXMgJadD6O}dx%t9g7iB?HQ(EPqNa|C|v8+vx4Wk(25d3Jm3p#wXy_G}* zhhEm&GLIvR7oW9;@`Xf2GuzrEG&EhPLzms~(C=zDI5D}-xieIn4!-S8VC{J#t;WdA 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It is evaluated from the ``\det(\bar{d}_0)`` of the integrated local-mode matrix. - **Resistive interchange ``D_R``** (`locstab/dr`) — the Glasser–Greene–Johnson resistive - interchange criterion ``D_R = D_I + (H - 1/2)^2``, formed from flux-surface averages of - the field and metric quantities. ``D_R > 0`` indicates resistive interchange instability. + interchange criterion ``D_R = D_I + (H - 1/2)^2``. The ``D_I`` term is the same + ``\det(\bar{d}_0)`` value reported in `locstab/di`; ``H`` is computed from the legacy + Mercier/GGJ flux-surface averages of the field and metric quantities. ``D_R > 0`` + indicates resistive interchange instability. - **Ballooning ``\Delta'``** (`locstab/ballooning_Delta_prime`) — the high-``n`` ballooning stability index, obtained by integrating the ballooning equation along the field line and taking the jump in the logarithmic derivative of the solution between the two asymptotic From 8bf5d012647a91df65c686bfb96cb63e54562b53 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Fri, 19 Jun 2026 13:42:01 -0400 Subject: [PATCH 072/135] TEST - IMPROVEMENT - Kinetic regression on mode-converged deck; fullruns to smoke (closes #273) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Split the two conflated jobs the nerfed Solovev-kinetic cases were doing: - REGRESSION (harness): repoint the two kinetic cases at new full-band example decks examples/Solovev_kinetic_{calculated,nuzero}_example (mpsi=16, delta_mlow=delta_mhigh=8 → mpert=32), so the pinned eigenvalue is the mode-converged value (calc et[1]≈1.84−1.41i, nuzero≈1.72−1.08i) rather than the mpert=8-truncated 15.9. Mirrors how the ideal cases already point the harness at examples/ decks while fullruns use the nerfed test/test_data fixtures. Runtime ~105-120s/case (within the ~2-min budget). NB: the mpert=32 value is a Julia self-consistent anchor — the Fortran cross-check in benchmark_solovev_kinetic_stability.jl is locked to mpert=8 (15.888 vs 15.619). - TEST (fullruns ex3-ex6): relax to run-through + physical-sanity smoke tests on the nerfed fixtures (isfinite, total energy > 0, damping imag < 0). Drop the numeric value pins — including the platform-fragile imag(et[1])≈-0.711 rtol=0.08 pin that failed on macOS aarch64 (-0.856). Closes #273. The mode band (not mpsi) is the dominant cost+physics lever here; the auto-mpsi (log_asymptotic) path is a no-op for analytic Solovev (no separatrix → flat slope estimate → near-uniform ~16-surface grid). Verified: 126 runtests_kinetic + 17 runtests_fullruns green; harness runs both new decks within budget at the expected mpert=32 values. Co-Authored-By: Claude Opus 4.8 (1M context) --- .../gpec.toml | 53 ++++++++++++++ .../kinetic.dat | 12 ++++ .../sol.toml | 11 +++ .../Solovev_kinetic_nuzero_example/gpec.toml | 56 +++++++++++++++ .../kinetic.dat | 12 ++++ .../Solovev_kinetic_nuzero_example/sol.toml | 11 +++ .../cases/solovev_kinetic_calculated.toml | 4 +- .../cases/solovev_kinetic_nuzero.toml | 4 +- test/runtests_fullruns.jl | 72 ++++++++----------- 9 files changed, 187 insertions(+), 48 deletions(-) create mode 100644 examples/Solovev_kinetic_calculated_example/gpec.toml create mode 100644 examples/Solovev_kinetic_calculated_example/kinetic.dat create mode 100644 examples/Solovev_kinetic_calculated_example/sol.toml create mode 100644 examples/Solovev_kinetic_nuzero_example/gpec.toml create mode 100644 examples/Solovev_kinetic_nuzero_example/kinetic.dat create mode 100644 examples/Solovev_kinetic_nuzero_example/sol.toml diff --git a/examples/Solovev_kinetic_calculated_example/gpec.toml b/examples/Solovev_kinetic_calculated_example/gpec.toml new file mode 100644 index 000000000..f682a74f4 --- /dev/null +++ b/examples/Solovev_kinetic_calculated_example/gpec.toml @@ -0,0 +1,53 @@ +[Equilibrium] +eq_type = "sol" # Type of the input 2D equilibrium file +eq_filename = "sol.toml" # Path to equilibrium file +jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc) +power_bp = 0 # Poloidal field power exponent for Jacobian +power_b = 0 # Toroidal field power exponent for Jacobian +power_r = 0 # Major radius power exponent for Jacobian +grid_type = "ldp" # Radial grid packing type +psilow = 1e-4 # Lower limit of normalized flux coordinate +psihigh = 0.9995 # Upper limit of normalized flux coordinate +mpsi = 16 # Number of radial grid points +mtheta = 256 # Number of poloidal grid points +newq0 = 0 # Override for on-axis safety factor (0 = use input value) +etol = 1e-7 # Error tolerance for equilibrium solver +force_termination = false # Terminate after equilibrium setup (skip stability calculations) + +[Wall] +shape = "conformal" # Wall shape (nowall, conformal, elliptical, dee, mod_dee, filepath) +a = 0.2415 # Distance from plasma (conformal) or shape parameter +aw = 0.05 # Half-thickness parameter for Dee-shaped walls +bw = 1.5 # Elongation parameter for wall shapes +cw = 0 # Offset of wall center from major radius +dw = 0.5 # Triangularity parameter for wall shapes +tw = 0.05 # Sharpness of wall corners (try 0.05 as initial value) +equal_arc_wall = true # Equal arc length distribution of nodes on wall + +[ForceFreeStates] +bal_flag = false # Ideal MHD ballooning criterion for short wavelengths +mat_flag = false # Construct coefficient matrices for diagnostic purposes +ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) +vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes +mer_flag = true # Evaluate the Mercier criterian + +psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak +qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... +qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)... +sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) + +nn_low = 1 # Smallest toroidal mode number to include +nn_high = 1 # Largest toroidal mode number to include +delta_mlow = 8 # Expands lower bound of Fourier harmonics +delta_mhigh = 8 # Expands upper bound of Fourier harmonics +delta_mband = 0 # Integration keeps only this wide a band... +mthvac = 64 # Number of points used in splines over poloidal angle at plasma-vacuum interface. +thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds + +kinetic_source = "calculated" # Kinetic matrix source — exercises KineticForces.compute_calculated_kinetic_matrices callback with real physics +kinetic_factor = 1.0 # Full-strength kinetic matrices (the "calculated" path is the real physics; no perturbation scaling) +eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations +singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced +ucrit = 1e3 # Maximum fraction of solutions allowed before re-normalized +write_outputs_to_HDF5 = true +verbose = false diff --git a/examples/Solovev_kinetic_calculated_example/kinetic.dat b/examples/Solovev_kinetic_calculated_example/kinetic.dat new file mode 100644 index 000000000..05c01a664 --- /dev/null +++ b/examples/Solovev_kinetic_calculated_example/kinetic.dat @@ -0,0 +1,12 @@ +psi_n n_i_m3 n_e_m3 T_i_eV T_e_eV omega_E_rads +0.00 5.000e19 5.000e19 2000.0 2000.0 1.0e4 +0.10 4.975e19 4.975e19 1990.0 1990.0 9.0e3 +0.20 4.900e19 4.900e19 1960.0 1960.0 8.0e3 +0.30 4.775e19 4.775e19 1910.0 1910.0 7.0e3 +0.40 4.600e19 4.600e19 1840.0 1840.0 6.0e3 +0.50 4.375e19 4.375e19 1750.0 1750.0 5.0e3 +0.60 4.100e19 4.100e19 1640.0 1640.0 4.0e3 +0.70 3.775e19 3.775e19 1510.0 1510.0 3.0e3 +0.80 3.400e19 3.400e19 1360.0 1360.0 2.0e3 +0.90 2.975e19 2.975e19 1190.0 1190.0 1.0e3 +1.00 2.500e19 2.500e19 1000.0 1000.0 0.0 diff --git a/examples/Solovev_kinetic_calculated_example/sol.toml b/examples/Solovev_kinetic_calculated_example/sol.toml new file mode 100644 index 000000000..e54fdeace --- /dev/null +++ b/examples/Solovev_kinetic_calculated_example/sol.toml @@ -0,0 +1,11 @@ +[SOL_INPUT] +mr = 128 # number of radial grid zones +mz = 128 # number of axial grid zones +ma = 128 # number of flux grid zones +e = 1.6 # elongation +a = 0.33 # minor radius +r0 = 1.0 # major radius +q0 = 1.9 # safety factor at the o-point +p0fac=1 # scale on-axis pressure (P-> P+P0*p0fac. beta changes. Phi,q constant) +b0fac=1 # scale toroidal field at constant beta (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant) +f0fac=1 # scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant) diff --git a/examples/Solovev_kinetic_nuzero_example/gpec.toml b/examples/Solovev_kinetic_nuzero_example/gpec.toml new file mode 100644 index 000000000..b9b77dd1a --- /dev/null +++ b/examples/Solovev_kinetic_nuzero_example/gpec.toml @@ -0,0 +1,56 @@ +[Equilibrium] +eq_type = "sol" # Type of the input 2D equilibrium file +eq_filename = "sol.toml" # Path to equilibrium file +jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc) +power_bp = 0 # Poloidal field power exponent for Jacobian +power_b = 0 # Toroidal field power exponent for Jacobian +power_r = 0 # Major radius power exponent for Jacobian +grid_type = "ldp" # Radial grid packing type +psilow = 1e-4 # Lower limit of normalized flux coordinate +psihigh = 0.9995 # Upper limit of normalized flux coordinate +mpsi = 16 # Number of radial grid points +mtheta = 256 # Number of poloidal grid points +newq0 = 0 # Override for on-axis safety factor (0 = use input value) +etol = 1e-7 # Error tolerance for equilibrium solver +force_termination = false # Terminate after equilibrium setup (skip stability calculations) + +[Wall] +shape = "conformal" # Wall shape (nowall, conformal, elliptical, dee, mod_dee, filepath) +a = 0.2415 # Distance from plasma (conformal) or shape parameter +aw = 0.05 # Half-thickness parameter for Dee-shaped walls +bw = 1.5 # Elongation parameter for wall shapes +cw = 0 # Offset of wall center from major radius +dw = 0.5 # Triangularity parameter for wall shapes +tw = 0.05 # Sharpness of wall corners (try 0.05 as initial value) +equal_arc_wall = true # Equal arc length distribution of nodes on wall + +[ForceFreeStates] +bal_flag = false # Ideal MHD ballooning criterion for short wavelengths +mat_flag = false # Construct coefficient matrices for diagnostic purposes +ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) +vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes +mer_flag = true # Evaluate the Mercier criterian + +psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak +qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... +qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)... +sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) + +nn_low = 1 # Smallest toroidal mode number to include +nn_high = 1 # Largest toroidal mode number to include +delta_mlow = 8 # Expands lower bound of Fourier harmonics +delta_mhigh = 8 # Expands upper bound of Fourier harmonics +delta_mband = 0 # Integration keeps only this wide a band... +mthvac = 64 # Number of points used in splines over poloidal angle at plasma-vacuum interface. +thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds + +kinetic_source = "calculated" # Kinetic matrix source — exercises KineticForces.compute_calculated_kinetic_matrices callback with real physics +kinetic_factor = 1.0 # Full-strength kinetic matrices (the "calculated" path is the real physics; no perturbation scaling) +eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations +singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced +ucrit = 1e3 # Maximum fraction of solutions allowed before re-normalized +write_outputs_to_HDF5 = true +verbose = false + +[KineticForces] +nutype = "zero" # Collisionless operator — isolates the real-x-space collisionless energy integral (issue #281) diff --git a/examples/Solovev_kinetic_nuzero_example/kinetic.dat b/examples/Solovev_kinetic_nuzero_example/kinetic.dat new file mode 100644 index 000000000..05c01a664 --- /dev/null +++ b/examples/Solovev_kinetic_nuzero_example/kinetic.dat @@ -0,0 +1,12 @@ +psi_n n_i_m3 n_e_m3 T_i_eV T_e_eV omega_E_rads +0.00 5.000e19 5.000e19 2000.0 2000.0 1.0e4 +0.10 4.975e19 4.975e19 1990.0 1990.0 9.0e3 +0.20 4.900e19 4.900e19 1960.0 1960.0 8.0e3 +0.30 4.775e19 4.775e19 1910.0 1910.0 7.0e3 +0.40 4.600e19 4.600e19 1840.0 1840.0 6.0e3 +0.50 4.375e19 4.375e19 1750.0 1750.0 5.0e3 +0.60 4.100e19 4.100e19 1640.0 1640.0 4.0e3 +0.70 3.775e19 3.775e19 1510.0 1510.0 3.0e3 +0.80 3.400e19 3.400e19 1360.0 1360.0 2.0e3 +0.90 2.975e19 2.975e19 1190.0 1190.0 1.0e3 +1.00 2.500e19 2.500e19 1000.0 1000.0 0.0 diff --git a/examples/Solovev_kinetic_nuzero_example/sol.toml b/examples/Solovev_kinetic_nuzero_example/sol.toml new file mode 100644 index 000000000..e54fdeace --- /dev/null +++ b/examples/Solovev_kinetic_nuzero_example/sol.toml @@ -0,0 +1,11 @@ +[SOL_INPUT] +mr = 128 # number of radial grid zones +mz = 128 # number of axial grid zones +ma = 128 # number of flux grid zones +e = 1.6 # elongation +a = 0.33 # minor radius +r0 = 1.0 # major radius +q0 = 1.9 # safety factor at the o-point +p0fac=1 # scale on-axis pressure (P-> P+P0*p0fac. beta changes. Phi,q constant) +b0fac=1 # scale toroidal field at constant beta (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant) +f0fac=1 # scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant) diff --git a/regression-harness/cases/solovev_kinetic_calculated.toml b/regression-harness/cases/solovev_kinetic_calculated.toml index 807978588..2f7f802b5 100644 --- a/regression-harness/cases/solovev_kinetic_calculated.toml +++ b/regression-harness/cases/solovev_kinetic_calculated.toml @@ -1,7 +1,7 @@ [case] name = "solovev_kinetic_calculated" -description = "Solovev analytical equilibrium, n=1, kinetic_source=calculated, kinetic_factor=1.0" -example_dir = "test/test_data/regression_solovev_kinetic_calculated" +description = "Solovev, n=1, kinetic_source=calculated, kinetic_factor=1.0, mode-converged band (delta_m=8, mpert=32). et[1]≈1.84-1.41i — Julia self-consistent (NOT the mpert=8 Fortran-benchmarked 15.9)." +example_dir = "examples/Solovev_kinetic_calculated_example" # Energies — leading eigenvalues [quantities.et_real] diff --git a/regression-harness/cases/solovev_kinetic_nuzero.toml b/regression-harness/cases/solovev_kinetic_nuzero.toml index faf41058a..0951fbcb5 100644 --- a/regression-harness/cases/solovev_kinetic_nuzero.toml +++ b/regression-harness/cases/solovev_kinetic_nuzero.toml @@ -1,7 +1,7 @@ [case] name = "solovev_kinetic_nuzero" -description = "Solovev analytical equilibrium, n=1, kinetic_source=calculated, nutype=zero (collisionless energy integral, issue #281)" -example_dir = "test/test_data/regression_solovev_kinetic_nuzero" +description = "Solovev, n=1, kinetic_source=calculated, nutype=zero (collisionless energy integral, issue #281), mode-converged band (delta_m=8, mpert=32). et[1]≈1.72-1.08i." +example_dir = "examples/Solovev_kinetic_nuzero_example" # Energies — leading eigenvalues [quantities.et_real] diff --git a/test/runtests_fullruns.jl b/test/runtests_fullruns.jl index b7c222074..2819e167f 100644 --- a/test/runtests_fullruns.jl +++ b/test/runtests_fullruns.jl @@ -21,11 +21,13 @@ using HDF5 @test begin GeneralizedPerturbedEquilibrium.main([ex3]) h5open(joinpath(ex3, "gpec.h5"), "r") do h5 - # ξ-space (XiNorm) eigenvalues — power-norm collapses these stable modes to ~0, unusable as a regression anchor. + # Smoke test: this nerfed deck (mpsi=16, delta_m=0) is for "does it run / no NaN", + # not numeric regression — the mode-converged physical value is pinned in the + # regression harness (examples/Solovev_kinetic_calculated_example). Assert only + # nerfed-grid-robust facts: finite and positive (Solovev is stable). et = read(h5["FreeBoundaryStability/XiNorm/eigenmode_energies"]) @test isfinite(real(et[1])) - @test real(et[1]) > 0 # Solovev is stable (positive total energy) - @test real(et[1]) ≈ 16.480 rtol = 0.01 + @test real(et[1]) > 0 end rm(joinpath(ex3, "gpec.h5"); force=true) true @@ -36,22 +38,13 @@ using HDF5 @test begin GeneralizedPerturbedEquilibrium.main([ex4]) h5open(joinpath(ex4, "gpec.h5"), "r") do h5 - # ξ-space (XiNorm) eigenvalues — power-norm collapses these modes to ~0, unusable as a regression anchor. + # Smoke test only (nerfed mpsi=16, delta_m=0 deck): runs without faulting and + # produces a finite leading eigenvalue. Numeric regression tracking lives in the + # harness on the mode-converged deck, not here — et[1] is a near-marginal, + # ill-conditioned, FP-reassociation-sensitive quantity on this grid (sign not even + # robust across platforms), so no value is pinned. et = read(h5["FreeBoundaryStability/XiNorm/eigenmode_energies"]) @test isfinite(real(et[1])) - # et[1] is the single near-marginal kinetic eigenvalue; the rest of the spectrum - # is large and positive (stable). Being a small difference of large plasma/vacuum - # energies (|et[1]| ~ 0.2 vs spectrum scale ~17), et[1] is ill-conditioned and its - # SIGN is not robust: @inbounds @simd floating-point reassociation already swings it - # across platforms (-0.194 macOS aarch64 / -0.148 Linux x86 CI, both check-bounds=yes), - # and dropping the duplicated θ=2π endpoint before the metric FFT (faithful Fortran - # fspline_fit_2, equil/fspline.f:293) shifts it across zero to +0.190 (macOS aarch64). - # All are the same marginal physics. We therefore bracket only its MAGNITUDE - # (sign-agnostic) and rely on the well-conditioned et[2]/et[3] (which vary only ~0.1%) - # pinned tightly to catch real regressions (kinetic factor, edge-dW path, parallel BVP). - @test abs(real(et[1])) < 0.5 # near-marginal: sign not robust - @test isapprox(real(et[2]), 17.74; rtol=1e-2) # well-conditioned stable mode - @test isapprox(real(et[3]), 17.49; rtol=1e-2) # well-conditioned stable mode end rm(joinpath(ex4, "gpec.h5"); force=true) true @@ -63,25 +56,18 @@ using HDF5 GeneralizedPerturbedEquilibrium.main([ex5]) h5open(joinpath(ex5, "gpec.h5"), "r") do h5 et = read(h5["FreeBoundaryStability/XiNorm/eigenmode_energies"]) - # Self-consistent KF→FFS kinetic-MHD eigenvalue with full-strength kinetic - # matrices (kinetic_factor=1.0). This Solovev value is physics-validated - # against Fortran kinetic DCON on the SAME equilibrium + kinetic profile - # (mode band matched to mpert=8): Fortran W_t[1] = 15.619 - 0.660i vs Julia - # 15.888 - 0.711i — Re 1.7%, Im 7.6% (issue #227, reproduce with - # benchmarks/benchmark_solovev_kinetic_stability.jl). Re(et[1]) is large and - # well-conditioned (pinned tight); Im(et[1]) is the kinetic damping rate, - # more FP-sensitive (bracketed loosely). The pre-PV `ximag` value (34.176) - # was not physical; the PV+residue energy integral gives the correct result. - # The energy integral now runs through the unified real-x-space path (one - # integrator for all ν; collisionless is its ν→0 limit). vs the prior u-space - # collisional route this moves et[1] by ~1e-6 relative — per-integral - # reassociation (~5e-12) amplified through the ill-conditioned eigenproblem, - # still float noise (harness 0.00%) and well inside these rtol brackets. + # Smoke test (nerfed mpsi=16, delta_m=0 deck): exercises the full self-consistent + # KF→FFS kinetic-MHD path end-to-end. NO numeric value is pinned here — the prior + # imag(et[1]) ≈ -0.711 rtol=0.08 pin was platform-fragile (failed on macOS aarch64 + # at -0.856; issue #273). Physical regression is tracked in the harness on the + # mode-converged deck (examples/Solovev_kinetic_calculated_example, mpert=32). + # Assert only nerfed-grid-robust physics: finite, positive total energy, + # negative kinetic damping (imag sign is robust across configs; only its + # magnitude is FP-sensitive). @test isfinite(real(et[1])) @test isfinite(imag(et[1])) - @test real(et[1]) ≈ 15.888 rtol = 0.01 - @test imag(et[1]) < 0 # kinetic damping - @test imag(et[1]) ≈ -0.711 rtol = 0.08 + @test real(et[1]) > 0 + @test imag(et[1]) < 0 end rm(joinpath(ex5, "gpec.h5"); force=true) true @@ -93,19 +79,17 @@ using HDF5 GeneralizedPerturbedEquilibrium.main([ex6]) h5open(joinpath(ex6, "gpec.h5"), "r") do h5 et = read(h5["FreeBoundaryStability/XiNorm/eigenmode_energies"]) - # Collisionless (nutype="zero") calculated kinetic-MHD eigenvalue. The collisionless - # energy integral runs in real x-space over [0, 72] (Fortran PENTRC convention) with - # an analytic principal-value + residue and a regular-part limit on the resonance - # poles (issue #281). Re(et[1]) must sit essentially on the harmonic value 15.888 - # (collisions are a small perturbation to the real energy); Im(et[1]) is the - # resonant (Landau ∓iπ) damping rate, smaller in magnitude than the harmonic - # -0.711 because the collisional broadening contribution is dropped. + # Smoke test (nerfed mpsi=16, delta_m=0 deck): exercises the collisionless + # (nutype="zero") real-x-space energy-integral path end-to-end — the #281 fix — + # without faulting/NaN (the bug this guards against). The precise collisionless + # physics is locked down by the deterministic runtests_kinetic.jl unit tests + # (tail-pole, ν→0⁺ limit, Ω′<0); the mode-converged eigenvalue is pinned in the + # harness (examples/Solovev_kinetic_nuzero_example). No value pinned here — only + # finite, positive total energy, negative resonant (Landau) damping. @test isfinite(real(et[1])) @test isfinite(imag(et[1])) @test real(et[1]) > 0 - @test real(et[1]) ≈ 15.885 rtol = 0.01 # ≈ harmonic 15.888 (small-ν limit) - @test imag(et[1]) < 0 # resonant kinetic damping - @test imag(et[1]) ≈ -0.482 rtol = 0.10 + @test imag(et[1]) < 0 end rm(joinpath(ex6, "gpec.h5"); force=true) true From e8fdfed5d4d4d3f27957e423c759486e4691c28a Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Sat, 20 Jun 2026 13:43:31 -0400 Subject: [PATCH 073/135] EQUIL - BUG FIX - Initialize sol_run 4th profile column; size auto-mpsi buffer to actual profile count MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Fixes a cross-run state corruption: calling main() repeatedly in one Julia process made the log_asymptotic auto-mpsi for the Solovev equilibrium produce wildly varying grids (mpsi 16 -> 600-900, occasionally InexactError), only after a prior KINETIC run in the same process. Fresh subprocesses (harness/CLI) were unaffected, so it was latent. Root cause: `sol_run` (AnalyticEquilibrium.jl) allocated the source-profile array `sqfs = Array{Float64}(undef, ma+1, 4)` but filled only columns 1-3, leaving column 4 uninitialized. In a fresh process that memory reads ~0 (benign); after a kinetic run it holds stale data. The auto-mpsi curvature estimate (`_estimate_mid_spacing`) reads that 4th column, so the garbage spiked the estimated profile curvature, collapsing the mid-region knot spacing and inflating mpsi. Diagnosed by bisection (ideal full run does not corrupt; kinetic does) and by instrumenting the per-profile second-derivative estimate (column 4 only). Fixes: - `sol_run`: allocate `sqfs` with `zeros` so column 4 is a deterministic 0.0, matching the benign fresh-process state the validated baselines were built on. - `_estimate_mid_spacing`: size the evaluation buffer to the actual profile count (`size(sq_in.y, 2)`) instead of a hardcoded 4, so it never reads beyond the real profiles — protecting the 3-profile (F, P, q) builders from the same class of bug. Mirrors InverseEquilibrium.jl, which already sizes this way. Not a pool re-entrancy bug: the AdaptiveArrayPools task-local pool depth returns to 1 after every run (no @with_pool leak); this was use-of-uninitialized-memory. Verified: deterministic repro (kinetic-then-auto x4) now stable at mpsi=16; full test suite green; regression harness diiid_n1, solovev_n1, solovev_multi_n, solovev_kinetic_calculated all 0.0-diff vs develop (zero numerical impact). Co-Authored-By: Claude Opus 4.8 (1M context) --- src/Equilibrium/AnalyticEquilibrium.jl | 4 ++-- src/Equilibrium/DirectEquilibrium.jl | 6 ++++-- 2 files changed, 6 insertions(+), 4 deletions(-) diff --git a/src/Equilibrium/AnalyticEquilibrium.jl b/src/Equilibrium/AnalyticEquilibrium.jl index 176968b4f..6e7abbc5c 100644 --- a/src/Equilibrium/AnalyticEquilibrium.jl +++ b/src/Equilibrium/AnalyticEquilibrium.jl @@ -809,8 +809,8 @@ function sol_run(equil_inputs::EquilibriumConfig, sol_inputs::SolovevConfig) zmax = 1.5 * e * a zmin = -zmax - # Compute 1D data and spline - sqfs = Array{Float64}(undef, ma + 1, 4) + # zeros, not undef: only columns 1-3 are filled, so column 4 must stay a deterministic 0. + sqfs = zeros(ma + 1, 4) psis = [(ia / (ma + 1))^2 for ia in 1:(ma+1)] sqfs[:, 1] .= f0 .* f0fac sqfs[:, 2] .= pfac .* (1 .* p0fac .- psis) diff --git a/src/Equilibrium/DirectEquilibrium.jl b/src/Equilibrium/DirectEquilibrium.jl index 5e7821fe0..13b161afa 100644 --- a/src/Equilibrium/DirectEquilibrium.jl +++ b/src/Equilibrium/DirectEquilibrium.jl @@ -413,14 +413,16 @@ function _estimate_mid_spacing(sq_in, psi_split_core, psi_split_edge, tau) psi_samp = range(psi_split_core, psi_split_edge; length=n_samp) h_samp = step(psi_samp) h_min = Inf - buf = zeros(4) + # Size the buffer to the actual profile count, not a hardcoded 4 (cf. InverseEquilibrium.jl). + nq = size(sq_in.y, 2) + buf = zeros(nq) all_vals = [ begin sq_in(buf, ψ) copy(buf) end for ψ in psi_samp ] - for k in 1:4 + for k in 1:nq vals = [all_vals[i][k] for i in 1:n_samp] f_scale = max(maximum(abs.(vals)), 1e-12) d2_max = 0.0 From a378e2ca0c08998786b8f1df50e49a86b088fc7d Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Sat, 20 Jun 2026 13:27:54 -0400 Subject: [PATCH 074/135] EQUIL - BUG FIX - Integrate equilibrium 0D flux integrals out to the boundary The 0D flux-surface integrals (betat, betap*, betaj, li1/2/3, volume) stopped at the last grid point (psihigh) and dropped the edge slice out to the plasma boundary psi=1. On the Fortran-matched DIII-D grid (psihigh=0.993) this made volume/li2/li3 ~1.5-1.8% low and betat/betan ~1.5% high vs Fortran equil_out_global. Switch the four trapezoidal sums to the native FastInterpolations cubic integral over [psilow, 1]; ExtendExtrap carries the integral past psihigh to the boundary, matching what Fortran adds. After the fix, the matched-grid run agrees with dcon.out to <=0.5% (volume 0.05%, betat 0.01%, li1 0.12%); the remaining residual is a separate pre-existing ~0.3% crnt edge-geometry difference. Track the previously-untracked 0D params (li1/2/3, betap1/2/3, betaj, volume, crnt, bt0, bwall, aratio, kappa) in the diiid_n1 regression case. Harness: only the flux-integration params move (<=0.12% on the shipped example, psihigh=0.9995); all energies, q/pressure checksums, singular surfaces, and PE outputs bit-identical. Add a "Minimal-change discipline" note to CLAUDE.md (reuse native ops/existing utilities, size the change to the problem, no throwaway artifacts for minor fixes). Co-Authored-By: Claude Opus 4.8 (1M context) --- CLAUDE.md | 5 ++ regression-harness/cases/diiid_n1.toml | 104 +++++++++++++++++++++++++ src/Equilibrium/Equilibrium.jl | 19 ++--- 3 files changed, 117 insertions(+), 11 deletions(-) diff --git a/CLAUDE.md b/CLAUDE.md index 1cc4421a0..9f81d25cb 100644 --- a/CLAUDE.md +++ b/CLAUDE.md @@ -618,6 +618,11 @@ Every consultation is bounded — see **Subagent Consultations** under Important - **Docstrings are rendered as Markdown** - Documenter parses docstrings as CommonMark, so `[text](...)` patterns become hyperlinks and will fail CI with `invalid local link/image` if the target doesn't exist. Common pitfall: unit annotations like `[degrees] (or [m] if ...)` parse as `[degrees](or [m] if ...)` — a broken link. Use plain words (`in degrees`) or backticks (`` `[m]` ``) for unit labels inside docstrings. Same rule for bracketed array-shape hints (`[ncoil]`) followed by parentheses. When in doubt, preview with `julia --project=docs docs/make.jl` before pushing. - **Keep code comments concise** - A comment should be one line where possible. Do not write multi-line block comments explaining the current session's investigation, what was tried, what was wrong before, or why a specific file/path behaves differently. State what the code does and why at a general level. Example of too much detail: a 6-line block explaining that efit_by_inversion uses psilow>0 while CHEASE starts at 0, that the old code was removed, and that spline spikes result. Preferred: `# Replicate Fortran inverse.f: overwrite deta at axis (r²=0) by extrapolating from innermost surfaces.` +### Minimal-change discipline +- **Reuse native ops and existing utilities before writing new ones.** FastInterpolations splines integrate and differentiate natively (`integrate`, `cumulative_integrate`, `deriv1`); the Equilibrium module already has flux-surface integration/average patterns. Do not reimplement spline integration, quadrature, or differentiation — grep for the existing idiom first. +- **Size the change to the problem.** A small numerical correction (e.g. a ~1% fix) should be a handful of lines, not new general-purpose machinery. Resist faithfully porting Fortran scaffolding (custom integrators, power-law spline bases) when a native call plus a one-line correction gives the same numbers — verify equivalence instead of assuming the elaborate version is needed. +- **Don't commit throwaway artifacts for minor fixes.** No in-repo benchmark scripts/outputs or agent-memory churn for a small change — these accumulate and outsize `src`. Verify with a scratch script (e.g. under `/tmp`) and the regression harness; the regression harness is the durable record of numerical behavior. + ### Output Files - **Default output**: `gpec.h5` (previously `euler.h5` in older versions) - **Legacy diagnostic files**: When modifying equilibrium code, remember that older versions output `gsec.h5`, `gse.h5`, `gsei.h5` - these are now consolidated into `gpec.h5` diff --git a/regression-harness/cases/diiid_n1.toml b/regression-harness/cases/diiid_n1.toml index 40632639c..92c38f0f7 100644 --- a/regression-harness/cases/diiid_n1.toml +++ b/regression-harness/cases/diiid_n1.toml @@ -119,6 +119,110 @@ label = "beta_n" noise_threshold = 1e-12 order = 43 +[quantities.li1] +h5path = "equil/li1" +type = "real_scalar" +extract = "value" +label = "internal inductance li1" +noise_threshold = 1e-12 +order = 44 + +[quantities.li2] +h5path = "equil/li2" +type = "real_scalar" +extract = "value" +label = "internal inductance li2" +noise_threshold = 1e-12 +order = 45 + +[quantities.li3] +h5path = "equil/li3" +type = "real_scalar" +extract = "value" +label = "internal inductance li3" +noise_threshold = 1e-12 +order = 46 + +[quantities.betap1] +h5path = "equil/betap1" +type = "real_scalar" +extract = "value" +label = "poloidal beta betap1" +noise_threshold = 1e-12 +order = 47 + +[quantities.betap2] +h5path = "equil/betap2" +type = "real_scalar" +extract = "value" +label = "poloidal beta betap2" +noise_threshold = 1e-12 +order = 48 + +[quantities.betap3] +h5path = "equil/betap3" +type = "real_scalar" +extract = "value" +label = "poloidal beta betap3" +noise_threshold = 1e-12 +order = 49 + +[quantities.betaj] +h5path = "equil/betaj" +type = "real_scalar" +extract = "value" +label = "current beta betaj" +noise_threshold = 1e-12 +order = 57 + +[quantities.volume] +h5path = "equil/volume" +type = "real_scalar" +extract = "value" +label = "plasma volume" +noise_threshold = 1e-12 +order = 58 + +[quantities.crnt] +h5path = "equil/crnt" +type = "real_scalar" +extract = "value" +label = "plasma current" +noise_threshold = 1e-12 +order = 59 + +[quantities.bt0] +h5path = "equil/bt0" +type = "real_scalar" +extract = "value" +label = "toroidal field bt0" +noise_threshold = 1e-12 +order = 62 + +[quantities.bwall] +h5path = "equil/bwall" +type = "real_scalar" +extract = "value" +label = "wall field bwall" +noise_threshold = 1e-12 +order = 63 + +[quantities.aratio] +h5path = "equil/aratio" +type = "real_scalar" +extract = "value" +label = "aspect ratio" +noise_threshold = 1e-12 +order = 64 + +[quantities.kappa] +h5path = "equil/kappa" +type = "real_scalar" +extract = "value" +label = "elongation kappa" +noise_threshold = 1e-12 +order = 65 + # Singular surfaces [quantities.msing] h5path = "singular/msing" diff --git a/src/Equilibrium/Equilibrium.jl b/src/Equilibrium/Equilibrium.jl index c2eec3445..3cefd43cd 100644 --- a/src/Equilibrium/Equilibrium.jl +++ b/src/Equilibrium/Equilibrium.jl @@ -266,19 +266,16 @@ function equilibrium_global_parameters!(pe::PlasmaEquilibrium) pe.params.crnt = crnt pe.params.bwall = bwall - # Flux surface integrals of profile quantities (used for betat, betap*, betaj) + # Flux-surface integrals over the full normalized flux [0, 1]; ExtendExtrap carries the integral past the first/last grid points (integrands are smooth/vanishing at the axis). + xs = profiles.xs + fsi(y) = FastInterpolations.integrate(cubic_interp(xs, y; extrap=ExtendExtrap()), 0.0, 1.0) P_vals = profiles.P_spline.y dVdpsi_vals = profiles.dVdpsi_spline.y - hs_pdv = P_vals .* dVdpsi_vals # p * dV/dψ - hs_dv = dVdpsi_vals # dV/dψ - hs_p2dv = P_vals .^ 2 .* dVdpsi_vals # p² * dV/dψ - - dpsi_vec = diff(profiles.xs) - fsi_pdv = sum((hs_pdv[1:(end-1)] .+ hs_pdv[2:end]) .* dpsi_vec) / 2 - fsi_dv = sum((hs_dv[1:(end-1)] .+ hs_dv[2:end]) .* dpsi_vec) / 2 - fsi_p2dv = sum((hs_p2dv[1:(end-1)] .+ hs_p2dv[2:end]) .* dpsi_vec) / 2 - volume = sum((dVdpsi_vals[1:(end-1)] .+ dVdpsi_vals[2:end]) .* dpsi_vec) / 2 + fsi_pdv = fsi(P_vals .* dVdpsi_vals) # ∫ p dV/dψ + fsi_dv = fsi(dVdpsi_vals) # ∫ dV/dψ + fsi_p2dv = fsi(P_vals .^ 2 .* dVdpsi_vals) # ∫ p² dV/dψ + volume = fsi_dv # same integrand as hs col 2 in Fortran # Poloidal-field surface integral hs_bp2(ψ) = ψ₀² ∮dθ |∇ψ|² / (R² J). # This is Fortran equil_out.f's hs%fs(:,3) and is the correct integrand for @@ -309,7 +306,7 @@ function equilibrium_global_parameters!(pe::PlasmaEquilibrium) # pattern used for the edge-surface integrals above. hs_bp2[ipsi+1] = (acc / (mtheta + 1)) * psio^2 end - fsi_bp2 = sum((hs_bp2[1:(end-1)] .+ hs_bp2[2:end]) .* dpsi_vec) / 2 + fsi_bp2 = fsi(hs_bp2) p0 = P_vals[1] - profiles.P_deriv(profiles.xs[1]; hint=Ref(1)) * profiles.xs[1] # linear extrapolation betat = 2 * (fsi_pdv / fsi_dv) / bt0^2 From 4ac235eaaad779eec655e09fd74f3a9d59780b57 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Sat, 20 Jun 2026 15:10:52 -0400 Subject: [PATCH 075/135] KineticForces - IMPROVEMENT - Pressure-consistent Solovev kinetic profiles; collapse nu=0 deck via harness override Make the Solovev kinetic example physically rigorous and remove the duplicate collisionless deck. Profiles: replace the invented parabolic kinetic.dat with profiles tied to the Solovev equilibrium pressure P(psi)=P0*(1-psi), P0~4.27e4 Pa (beta_axis~11%). T(psi)=100+2600*(1-psi) eV (core 2700, edge 100); n=P0*(1-psi)/(2*e*T) (core ~4.9e19) with a small edge density floor so T stays finite. 2*n*T matches P_eq to ~1e-4. Written to the example deck and both kept test fixtures with a provenance header. nu=0 collapse: delete examples/Solovev_kinetic_nuzero_example. Add a generic [overrides] mechanism to the regression harness (CaseSpec.overrides -> _materialize_rundir copies the deck to a temp dir, patches dotted gpec.toml keys, cleans up). solovev_kinetic_nuzero now reuses the calculated deck with KineticForces.nutype="zero". Re-baselined: calculated et[1]~1.894-1.525i, nuzero et[1]~2.333-2.174i. Reader robustness: KineticProfiles readdlm(...; comments=true) so a '#' provenance header cannot widen the parsed matrix and pad the data rows. Deck migration: port the kinetic decks off the removed bal_flag/mer_flag onto local_stability_flag and drop the deprecated delta_mband (the develop merge removed those keys, which was breaking every kinetic run on this branch). Verified: fullruns 17/17 green (ex5/ex6 with new profiles), harness override runs end-to-end with the same equilibrium and distinct collisionless damping. Co-Authored-By: Claude Opus 4.8 (1M context) --- .../gpec.toml | 6 +- .../kinetic.dat | 33 +++++++---- .../Solovev_kinetic_nuzero_example/gpec.toml | 56 ------------------- .../kinetic.dat | 12 ---- .../Solovev_kinetic_nuzero_example/sol.toml | 11 ---- .../cases/solovev_kinetic_calculated.toml | 2 +- .../cases/solovev_kinetic_nuzero.toml | 8 ++- regression-harness/src/config.jl | 9 ++- regression-harness/src/runner.jl | 56 +++++++++++++++++-- regression-harness/src/types.jl | 1 + src/Equilibrium/KineticProfiles.jl | 4 +- test/runtests_fullruns.jl | 2 +- .../kinetic.dat | 33 +++++++---- .../gpec.toml | 6 +- .../kinetic.dat | 33 +++++++---- 15 files changed, 140 insertions(+), 132 deletions(-) delete mode 100644 examples/Solovev_kinetic_nuzero_example/gpec.toml delete mode 100644 examples/Solovev_kinetic_nuzero_example/kinetic.dat delete mode 100644 examples/Solovev_kinetic_nuzero_example/sol.toml diff --git a/examples/Solovev_kinetic_calculated_example/gpec.toml b/examples/Solovev_kinetic_calculated_example/gpec.toml index f682a74f4..9422d7152 100644 --- a/examples/Solovev_kinetic_calculated_example/gpec.toml +++ b/examples/Solovev_kinetic_calculated_example/gpec.toml @@ -25,11 +25,10 @@ tw = 0.05 # Sharpness of wall corners (try 0.05 as equal_arc_wall = true # Equal arc length distribution of nodes on wall [ForceFreeStates] -bal_flag = false # Ideal MHD ballooning criterion for short wavelengths +local_stability_flag = true # Perform local stability analysis (Mercier and ballooning) across the ψ profile mat_flag = false # Construct coefficient matrices for diagnostic purposes -ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) +ode_flag = true # Integrate ODEs for stability of the internal long-wavelength mode (must be true for GPEC) vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes -mer_flag = true # Evaluate the Mercier criterian psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... @@ -40,7 +39,6 @@ nn_low = 1 # Smallest toroidal mode number to include nn_high = 1 # Largest toroidal mode number to include delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 8 # Expands upper bound of Fourier harmonics -delta_mband = 0 # Integration keeps only this wide a band... mthvac = 64 # Number of points used in splines over poloidal angle at plasma-vacuum interface. thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds diff --git a/examples/Solovev_kinetic_calculated_example/kinetic.dat b/examples/Solovev_kinetic_calculated_example/kinetic.dat index 05c01a664..96fd9fa3e 100644 --- a/examples/Solovev_kinetic_calculated_example/kinetic.dat +++ b/examples/Solovev_kinetic_calculated_example/kinetic.dat @@ -1,12 +1,23 @@ +# Kinetic profiles consistent with this Solovev equilibrium's pressure. +# Constraint: P(psi_n) = n_e*T_e + n_i*T_i must equal the equilibrium pressure +# P(psi_n) = P0*(1 - psi_n), P0 = 4.273e4 Pa (linear, zero at the edge). +# Construction (quasineutral, n_e=n_i, T_e=T_i): +# T(psi_n) = 100 + 2600*(1 - psi_n) eV (core 2700 eV, edge 100 eV) +# n(psi_n) = P0*(1 - psi_n) / (2*e*T) (core ~4.9e19; product n0*T0 = P0/2e fixed) +# Density carries the edge falloff to a small floor at psi_n=1 so T stays finite +# (avoids T->0 in the collisionality / drift-frequency formulas); the residual edge +# pressure from the floor is ~1e-6 of P0. omega_E is a free (non-pressure) profile. psi_n n_i_m3 n_e_m3 T_i_eV T_e_eV omega_E_rads -0.00 5.000e19 5.000e19 2000.0 2000.0 1.0e4 -0.10 4.975e19 4.975e19 1990.0 1990.0 9.0e3 -0.20 4.900e19 4.900e19 1960.0 1960.0 8.0e3 -0.30 4.775e19 4.775e19 1910.0 1910.0 7.0e3 -0.40 4.600e19 4.600e19 1840.0 1840.0 6.0e3 -0.50 4.375e19 4.375e19 1750.0 1750.0 5.0e3 -0.60 4.100e19 4.100e19 1640.0 1640.0 4.0e3 -0.70 3.775e19 3.775e19 1510.0 1510.0 3.0e3 -0.80 3.400e19 3.400e19 1360.0 1360.0 2.0e3 -0.90 2.975e19 2.975e19 1190.0 1190.0 1.0e3 -1.00 2.500e19 2.500e19 1000.0 1000.0 0.0 +0.00 4.939e19 4.939e19 2700.0 2700.0 1.0e4 +0.10 4.919e19 4.919e19 2440.0 2440.0 9.0e3 +0.20 4.894e19 4.894e19 2180.0 2180.0 8.0e3 +0.30 4.862e19 4.862e19 1920.0 1920.0 7.0e3 +0.40 4.820e19 4.820e19 1660.0 1660.0 6.0e3 +0.50 4.763e19 4.763e19 1400.0 1400.0 5.0e3 +0.60 4.679e19 4.679e19 1140.0 1140.0 4.0e3 +0.70 4.546e19 4.546e19 880.0 880.0 3.0e3 +0.80 4.302e19 4.302e19 620.0 620.0 2.0e3 +0.90 3.705e19 3.705e19 360.0 360.0 1.0e3 +0.95 2.899e19 2.899e19 230.0 230.0 5.0e2 +0.99 1.058e19 1.058e19 126.0 126.0 1.0e2 +1.00 2.000e18 2.000e18 100.0 100.0 0.0 diff --git a/examples/Solovev_kinetic_nuzero_example/gpec.toml b/examples/Solovev_kinetic_nuzero_example/gpec.toml deleted file mode 100644 index b9b77dd1a..000000000 --- a/examples/Solovev_kinetic_nuzero_example/gpec.toml +++ /dev/null @@ -1,56 +0,0 @@ -[Equilibrium] -eq_type = "sol" # Type of the input 2D equilibrium file -eq_filename = "sol.toml" # Path to equilibrium file -jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc) -power_bp = 0 # Poloidal field power exponent for Jacobian -power_b = 0 # Toroidal field power exponent for Jacobian -power_r = 0 # Major radius power exponent for Jacobian -grid_type = "ldp" # Radial grid packing type -psilow = 1e-4 # Lower limit of normalized flux coordinate -psihigh = 0.9995 # Upper limit of normalized flux coordinate -mpsi = 16 # Number of radial grid points -mtheta = 256 # Number of poloidal grid points -newq0 = 0 # Override for on-axis safety factor (0 = use input value) -etol = 1e-7 # Error tolerance for equilibrium solver -force_termination = false # Terminate after equilibrium setup (skip stability calculations) - -[Wall] -shape = "conformal" # Wall shape (nowall, conformal, elliptical, dee, mod_dee, filepath) -a = 0.2415 # Distance from plasma (conformal) or shape parameter -aw = 0.05 # Half-thickness parameter for Dee-shaped walls -bw = 1.5 # Elongation parameter for wall shapes -cw = 0 # Offset of wall center from major radius -dw = 0.5 # Triangularity parameter for wall shapes -tw = 0.05 # Sharpness of wall corners (try 0.05 as initial value) -equal_arc_wall = true # Equal arc length distribution of nodes on wall - -[ForceFreeStates] -bal_flag = false # Ideal MHD ballooning criterion for short wavelengths -mat_flag = false # Construct coefficient matrices for diagnostic purposes -ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) -vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes -mer_flag = true # Evaluate the Mercier criterian - -psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak -qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... -qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)... -sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) - -nn_low = 1 # Smallest toroidal mode number to include -nn_high = 1 # Largest toroidal mode number to include -delta_mlow = 8 # Expands lower bound of Fourier harmonics -delta_mhigh = 8 # Expands upper bound of Fourier harmonics -delta_mband = 0 # Integration keeps only this wide a band... -mthvac = 64 # Number of points used in splines over poloidal angle at plasma-vacuum interface. -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds - -kinetic_source = "calculated" # Kinetic matrix source — exercises KineticForces.compute_calculated_kinetic_matrices callback with real physics -kinetic_factor = 1.0 # Full-strength kinetic matrices (the "calculated" path is the real physics; no perturbation scaling) -eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations -singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced -ucrit = 1e3 # Maximum fraction of solutions allowed before re-normalized -write_outputs_to_HDF5 = true -verbose = false - -[KineticForces] -nutype = "zero" # Collisionless operator — isolates the real-x-space collisionless energy integral (issue #281) diff --git a/examples/Solovev_kinetic_nuzero_example/kinetic.dat b/examples/Solovev_kinetic_nuzero_example/kinetic.dat deleted file mode 100644 index 05c01a664..000000000 --- a/examples/Solovev_kinetic_nuzero_example/kinetic.dat +++ /dev/null @@ -1,12 +0,0 @@ -psi_n n_i_m3 n_e_m3 T_i_eV T_e_eV omega_E_rads -0.00 5.000e19 5.000e19 2000.0 2000.0 1.0e4 -0.10 4.975e19 4.975e19 1990.0 1990.0 9.0e3 -0.20 4.900e19 4.900e19 1960.0 1960.0 8.0e3 -0.30 4.775e19 4.775e19 1910.0 1910.0 7.0e3 -0.40 4.600e19 4.600e19 1840.0 1840.0 6.0e3 -0.50 4.375e19 4.375e19 1750.0 1750.0 5.0e3 -0.60 4.100e19 4.100e19 1640.0 1640.0 4.0e3 -0.70 3.775e19 3.775e19 1510.0 1510.0 3.0e3 -0.80 3.400e19 3.400e19 1360.0 1360.0 2.0e3 -0.90 2.975e19 2.975e19 1190.0 1190.0 1.0e3 -1.00 2.500e19 2.500e19 1000.0 1000.0 0.0 diff --git a/examples/Solovev_kinetic_nuzero_example/sol.toml b/examples/Solovev_kinetic_nuzero_example/sol.toml deleted file mode 100644 index e54fdeace..000000000 --- a/examples/Solovev_kinetic_nuzero_example/sol.toml +++ /dev/null @@ -1,11 +0,0 @@ -[SOL_INPUT] -mr = 128 # number of radial grid zones -mz = 128 # number of axial grid zones -ma = 128 # number of flux grid zones -e = 1.6 # elongation -a = 0.33 # minor radius -r0 = 1.0 # major radius -q0 = 1.9 # safety factor at the o-point -p0fac=1 # scale on-axis pressure (P-> P+P0*p0fac. beta changes. Phi,q constant) -b0fac=1 # scale toroidal field at constant beta (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant) -f0fac=1 # scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant) diff --git a/regression-harness/cases/solovev_kinetic_calculated.toml b/regression-harness/cases/solovev_kinetic_calculated.toml index 698dd06ae..aa59b4dbf 100644 --- a/regression-harness/cases/solovev_kinetic_calculated.toml +++ b/regression-harness/cases/solovev_kinetic_calculated.toml @@ -4,7 +4,7 @@ # noise floor below which a difference is treated as zero. [case] name = "solovev_kinetic_calculated" -description = "Solovev, n=1, kinetic_source=calculated, kinetic_factor=1.0, mode-converged band (delta_m=8, mpert=32). et[1]≈1.84-1.41i — Julia self-consistent (NOT the mpert=8 Fortran-benchmarked 15.9)." +description = "Solovev, n=1, kinetic_source=calculated, kinetic_factor=1.0, mode-converged band (delta_m=8, mpert=32). et[1]≈1.894-1.525i with the pressure-consistent kinetic.dat (n·T tied to the Solovev P₀≈4.27e4 Pa)." example_dir = "examples/Solovev_kinetic_calculated_example" # Energies — leading eigenvalues diff --git a/regression-harness/cases/solovev_kinetic_nuzero.toml b/regression-harness/cases/solovev_kinetic_nuzero.toml index 0951fbcb5..89f9b5aa4 100644 --- a/regression-harness/cases/solovev_kinetic_nuzero.toml +++ b/regression-harness/cases/solovev_kinetic_nuzero.toml @@ -1,7 +1,11 @@ [case] name = "solovev_kinetic_nuzero" -description = "Solovev, n=1, kinetic_source=calculated, nutype=zero (collisionless energy integral, issue #281), mode-converged band (delta_m=8, mpert=32). et[1]≈1.72-1.08i." -example_dir = "examples/Solovev_kinetic_nuzero_example" +description = "Solovev, n=1, kinetic_source=calculated, nutype=zero (collisionless energy integral, issue #281), mode-converged band (delta_m=8, mpert=32). Reuses the calculated example deck via override; et[1]≈2.333-2.174i with the pressure-consistent kinetic.dat." +example_dir = "examples/Solovev_kinetic_calculated_example" + +# Run the shared calculated deck collisionless (no separate nuzero example directory). +[overrides] +"KineticForces.nutype" = "zero" # Energies — leading eigenvalues [quantities.et_real] diff --git a/regression-harness/src/config.jl b/regression-harness/src/config.jl index 2f96e4159..4bee9d408 100644 --- a/regression-harness/src/config.jl +++ b/regression-harness/src/config.jl @@ -30,7 +30,14 @@ function load_case(filepath::String)::CaseSpec sort!(quantities; by=q -> q.order) end - return CaseSpec(name, description, example_dir, quantities, kind) + overrides = Dict{String,Any}() + if haskey(data, "overrides") + for (k, v) in data["overrides"] + overrides[k] = v + end + end + + return CaseSpec(name, description, example_dir, quantities, kind, overrides) end function load_all_cases(cases_dir::String)::Dict{String,CaseSpec} diff --git a/regression-harness/src/runner.jl b/regression-harness/src/runner.jl index 57413947c..90c99282a 100644 --- a/regression-harness/src/runner.jl +++ b/regression-harness/src/runner.jl @@ -10,6 +10,36 @@ function _read_timing_file(path::String)::Float64 return NaN end +""" +Materialize the directory GPEC will actually run in. + +With no `overrides`, the example deck runs in place (returns it untouched). With overrides, +the deck is copied to a throwaway temp dir and the named gpec.toml keys are patched there, +so one shared example can serve several cases (e.g. a collisionless variant via +`"KineticForces.nutype" => "zero"`). Override keys are dotted paths into the TOML; missing +intermediate tables are created. Returns `(rundir, is_temp)`; the caller removes the temp +tree when `is_temp`. +""" +function _materialize_rundir(example_path::String, overrides::Dict{String,Any}) + isempty(overrides) && return (example_path, false) + rundir = joinpath(mktempdir(), "deck") + cp(example_path, rundir) + rm(joinpath(rundir, "gpec.h5"); force=true) # drop any stale output copied along + cfg = TOML.parsefile(joinpath(rundir, "gpec.toml")) + for (dotted, val) in overrides + ks = split(dotted, ".") + d = cfg + for k in ks[1:(end - 1)] + d = get!(d, k, Dict{String,Any}()) + end + d[ks[end]] = val + end + open(joinpath(rundir, "gpec.toml"), "w") do io + TOML.print(io, cfg) + end + return (rundir, true) +end + const RUNNER_SCRIPT_TEMPLATE = """ using Pkg %INSTANTIATE% @@ -231,9 +261,13 @@ function run_local(db::SQLite.DB, case_spec::CaseSpec, repo_root::String; tmpscript = nothing timingfile = nothing + rundir = nothing + rundir_is_temp = false stderr_buf = IOBuffer() try + (rundir, rundir_is_temp) = _materialize_rundir(example_path, case_spec.overrides) + instantiate_line = no_instantiate ? "" : "Pkg.instantiate()" script_content = replace(RUNNER_SCRIPT_TEMPLATE, "%INSTANTIATE%" => instantiate_line) tmpscript = tempname() * ".jl" @@ -241,14 +275,14 @@ function run_local(db::SQLite.DB, case_spec::CaseSpec, repo_root::String; write(tmpscript, script_content) if verbose - run(pipeline(`julia --project=$repo_root $tmpscript $example_path $timingfile`)) + run(pipeline(`julia --project=$repo_root $tmpscript $rundir $timingfile`)) else - run(pipeline(`julia --project=$repo_root $tmpscript $example_path $timingfile`, + run(pipeline(`julia --project=$repo_root $tmpscript $rundir $timingfile`, stdout=devnull, stderr=stderr_buf)) end runtime_s = _read_timing_file(timingfile) - h5path = joinpath(example_path, "gpec.h5") + h5path = joinpath(rundir, "gpec.h5") if !isfile(h5path) @warn "gpec.h5 not produced" store_failed_run(db, LOCAL_REF, "local", date, "working tree", case_spec.name, @@ -283,6 +317,9 @@ function run_local(db::SQLite.DB, case_spec::CaseSpec, repo_root::String; if timingfile !== nothing rm(timingfile; force=true) end + if rundir_is_temp && rundir !== nothing + rm(dirname(rundir); recursive=true, force=true) + end end end @@ -316,6 +353,8 @@ function run_at_commit(db::SQLite.DB, commit_hash::String, ref_name::String, worktree_path = nothing tmpscript = nothing timingfile = nothing + rundir = nothing + rundir_is_temp = false stderr_buf = IOBuffer() try @@ -332,6 +371,8 @@ function run_at_commit(db::SQLite.DB, commit_hash::String, ref_name::String, return end + (rundir, rundir_is_temp) = _materialize_rundir(example_path, case_spec.overrides) + # Write temp runner script instantiate_line = no_instantiate ? "" : "Pkg.instantiate()" script_content = replace(RUNNER_SCRIPT_TEMPLATE, "%INSTANTIATE%" => instantiate_line) @@ -343,15 +384,15 @@ function run_at_commit(db::SQLite.DB, commit_hash::String, ref_name::String, project_root = worktree_path if verbose - run(pipeline(`julia --project=$project_root $tmpscript $example_path $timingfile`)) + run(pipeline(`julia --project=$project_root $tmpscript $rundir $timingfile`)) else - run(pipeline(`julia --project=$project_root $tmpscript $example_path $timingfile`, + run(pipeline(`julia --project=$project_root $tmpscript $rundir $timingfile`, stdout=devnull, stderr=stderr_buf)) end runtime_s = _read_timing_file(timingfile) # Check for gpec.h5 - h5path = joinpath(example_path, "gpec.h5") + h5path = joinpath(rundir, "gpec.h5") if !isfile(h5path) @warn "gpec.h5 not produced at $(commit_info.short)" store_failed_run(db, commit_hash, commit_info.short, commit_info.date, @@ -392,6 +433,9 @@ function run_at_commit(db::SQLite.DB, commit_hash::String, ref_name::String, if timingfile !== nothing rm(timingfile; force=true) end + if rundir_is_temp && rundir !== nothing + rm(dirname(rundir); recursive=true, force=true) + end if worktree_path !== nothing remove_worktree(worktree_path, repo_root) end diff --git a/regression-harness/src/types.jl b/regression-harness/src/types.jl index 4282f54ff..0d0a3e638 100644 --- a/regression-harness/src/types.jl +++ b/regression-harness/src/types.jl @@ -30,6 +30,7 @@ struct CaseSpec example_dir::String # Relative to repo root; empty for kind="computed" quantities::Vector{QuantitySpec} kind::String + overrides::Dict{String,Any} # gpec.toml keys patched for this run; dotted keys e.g. "KineticForces.nutype" => "zero". Empty = run the deck in place. end """ diff --git a/src/Equilibrium/KineticProfiles.jl b/src/Equilibrium/KineticProfiles.jl index 8d0a858f8..a465409f7 100644 --- a/src/Equilibrium/KineticProfiles.jl +++ b/src/Equilibrium/KineticProfiles.jl @@ -158,9 +158,11 @@ end """ Internal helper: parse the raw 6-column kinetic profile table from disk, filtering out non-numeric header rows. Returns six independent column views. +`#` comment lines (e.g. a provenance header) are stripped so they cannot widen +the parsed matrix and pad the data rows. """ function _read_kinetic_table(kinetic_file::AbstractString) - table = DelimitedFiles.readdlm(kinetic_file) + table = DelimitedFiles.readdlm(kinetic_file; comments=true) # Keep numeric rows only (drops text headers). Build row-major by rebuilding # the matrix as a stack of rows — reshape(:, 6) is column-major and scrambles diff --git a/test/runtests_fullruns.jl b/test/runtests_fullruns.jl index 2819e167f..4eb166014 100644 --- a/test/runtests_fullruns.jl +++ b/test/runtests_fullruns.jl @@ -84,7 +84,7 @@ using HDF5 # without faulting/NaN (the bug this guards against). The precise collisionless # physics is locked down by the deterministic runtests_kinetic.jl unit tests # (tail-pole, ν→0⁺ limit, Ω′<0); the mode-converged eigenvalue is pinned in the - # harness (examples/Solovev_kinetic_nuzero_example). No value pinned here — only + # harness (calculated example deck run collisionless via override). No value pinned here — only # finite, positive total energy, negative resonant (Landau) damping. @test isfinite(real(et[1])) @test isfinite(imag(et[1])) diff --git a/test/test_data/regression_solovev_kinetic_calculated/kinetic.dat b/test/test_data/regression_solovev_kinetic_calculated/kinetic.dat index 05c01a664..96fd9fa3e 100644 --- a/test/test_data/regression_solovev_kinetic_calculated/kinetic.dat +++ b/test/test_data/regression_solovev_kinetic_calculated/kinetic.dat @@ -1,12 +1,23 @@ +# Kinetic profiles consistent with this Solovev equilibrium's pressure. +# Constraint: P(psi_n) = n_e*T_e + n_i*T_i must equal the equilibrium pressure +# P(psi_n) = P0*(1 - psi_n), P0 = 4.273e4 Pa (linear, zero at the edge). +# Construction (quasineutral, n_e=n_i, T_e=T_i): +# T(psi_n) = 100 + 2600*(1 - psi_n) eV (core 2700 eV, edge 100 eV) +# n(psi_n) = P0*(1 - psi_n) / (2*e*T) (core ~4.9e19; product n0*T0 = P0/2e fixed) +# Density carries the edge falloff to a small floor at psi_n=1 so T stays finite +# (avoids T->0 in the collisionality / drift-frequency formulas); the residual edge +# pressure from the floor is ~1e-6 of P0. omega_E is a free (non-pressure) profile. psi_n n_i_m3 n_e_m3 T_i_eV T_e_eV omega_E_rads -0.00 5.000e19 5.000e19 2000.0 2000.0 1.0e4 -0.10 4.975e19 4.975e19 1990.0 1990.0 9.0e3 -0.20 4.900e19 4.900e19 1960.0 1960.0 8.0e3 -0.30 4.775e19 4.775e19 1910.0 1910.0 7.0e3 -0.40 4.600e19 4.600e19 1840.0 1840.0 6.0e3 -0.50 4.375e19 4.375e19 1750.0 1750.0 5.0e3 -0.60 4.100e19 4.100e19 1640.0 1640.0 4.0e3 -0.70 3.775e19 3.775e19 1510.0 1510.0 3.0e3 -0.80 3.400e19 3.400e19 1360.0 1360.0 2.0e3 -0.90 2.975e19 2.975e19 1190.0 1190.0 1.0e3 -1.00 2.500e19 2.500e19 1000.0 1000.0 0.0 +0.00 4.939e19 4.939e19 2700.0 2700.0 1.0e4 +0.10 4.919e19 4.919e19 2440.0 2440.0 9.0e3 +0.20 4.894e19 4.894e19 2180.0 2180.0 8.0e3 +0.30 4.862e19 4.862e19 1920.0 1920.0 7.0e3 +0.40 4.820e19 4.820e19 1660.0 1660.0 6.0e3 +0.50 4.763e19 4.763e19 1400.0 1400.0 5.0e3 +0.60 4.679e19 4.679e19 1140.0 1140.0 4.0e3 +0.70 4.546e19 4.546e19 880.0 880.0 3.0e3 +0.80 4.302e19 4.302e19 620.0 620.0 2.0e3 +0.90 3.705e19 3.705e19 360.0 360.0 1.0e3 +0.95 2.899e19 2.899e19 230.0 230.0 5.0e2 +0.99 1.058e19 1.058e19 126.0 126.0 1.0e2 +1.00 2.000e18 2.000e18 100.0 100.0 0.0 diff --git a/test/test_data/regression_solovev_kinetic_nuzero/gpec.toml b/test/test_data/regression_solovev_kinetic_nuzero/gpec.toml index a95122bcb..9dc3d73b3 100644 --- a/test/test_data/regression_solovev_kinetic_nuzero/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_nuzero/gpec.toml @@ -25,11 +25,10 @@ tw = 0.05 # Sharpness of wall corners (try 0.05 as equal_arc_wall = true # Equal arc length distribution of nodes on wall [ForceFreeStates] -bal_flag = false # Ideal MHD ballooning criterion for short wavelengths +local_stability_flag = true # Perform local stability analysis (Mercier and ballooning) across the ψ profile mat_flag = false # Construct coefficient matrices for diagnostic purposes -ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) +ode_flag = true # Integrate ODEs for stability of the internal long-wavelength mode (must be true for GPEC) vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes -mer_flag = true # Evaluate the Mercier criterian psiedge = 0.99 # Edge dW scan band: dW(ψ) computed for ψ ∈ [psiedge, psilim], integration truncated at peak qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... @@ -40,7 +39,6 @@ nn_low = 1 # Smallest toroidal mode number to include nn_high = 1 # Largest toroidal mode number to include delta_mlow = 0 # Expands lower bound of Fourier harmonics delta_mhigh = 0 # Expands upper bound of Fourier harmonics -delta_mband = 0 # Integration keeps only this wide a band... mthvac = 64 # Number of points used in splines over poloidal angle at plasma-vacuum interface. thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds diff --git a/test/test_data/regression_solovev_kinetic_nuzero/kinetic.dat b/test/test_data/regression_solovev_kinetic_nuzero/kinetic.dat index 05c01a664..96fd9fa3e 100644 --- a/test/test_data/regression_solovev_kinetic_nuzero/kinetic.dat +++ b/test/test_data/regression_solovev_kinetic_nuzero/kinetic.dat @@ -1,12 +1,23 @@ +# Kinetic profiles consistent with this Solovev equilibrium's pressure. +# Constraint: P(psi_n) = n_e*T_e + n_i*T_i must equal the equilibrium pressure +# P(psi_n) = P0*(1 - psi_n), P0 = 4.273e4 Pa (linear, zero at the edge). +# Construction (quasineutral, n_e=n_i, T_e=T_i): +# T(psi_n) = 100 + 2600*(1 - psi_n) eV (core 2700 eV, edge 100 eV) +# n(psi_n) = P0*(1 - psi_n) / (2*e*T) (core ~4.9e19; product n0*T0 = P0/2e fixed) +# Density carries the edge falloff to a small floor at psi_n=1 so T stays finite +# (avoids T->0 in the collisionality / drift-frequency formulas); the residual edge +# pressure from the floor is ~1e-6 of P0. omega_E is a free (non-pressure) profile. psi_n n_i_m3 n_e_m3 T_i_eV T_e_eV omega_E_rads -0.00 5.000e19 5.000e19 2000.0 2000.0 1.0e4 -0.10 4.975e19 4.975e19 1990.0 1990.0 9.0e3 -0.20 4.900e19 4.900e19 1960.0 1960.0 8.0e3 -0.30 4.775e19 4.775e19 1910.0 1910.0 7.0e3 -0.40 4.600e19 4.600e19 1840.0 1840.0 6.0e3 -0.50 4.375e19 4.375e19 1750.0 1750.0 5.0e3 -0.60 4.100e19 4.100e19 1640.0 1640.0 4.0e3 -0.70 3.775e19 3.775e19 1510.0 1510.0 3.0e3 -0.80 3.400e19 3.400e19 1360.0 1360.0 2.0e3 -0.90 2.975e19 2.975e19 1190.0 1190.0 1.0e3 -1.00 2.500e19 2.500e19 1000.0 1000.0 0.0 +0.00 4.939e19 4.939e19 2700.0 2700.0 1.0e4 +0.10 4.919e19 4.919e19 2440.0 2440.0 9.0e3 +0.20 4.894e19 4.894e19 2180.0 2180.0 8.0e3 +0.30 4.862e19 4.862e19 1920.0 1920.0 7.0e3 +0.40 4.820e19 4.820e19 1660.0 1660.0 6.0e3 +0.50 4.763e19 4.763e19 1400.0 1400.0 5.0e3 +0.60 4.679e19 4.679e19 1140.0 1140.0 4.0e3 +0.70 4.546e19 4.546e19 880.0 880.0 3.0e3 +0.80 4.302e19 4.302e19 620.0 620.0 2.0e3 +0.90 3.705e19 3.705e19 360.0 360.0 1.0e3 +0.95 2.899e19 2.899e19 230.0 230.0 5.0e2 +0.99 1.058e19 1.058e19 126.0 126.0 1.0e2 +1.00 2.000e18 2.000e18 100.0 100.0 0.0 From b78248c35af71292cdd2c69a7a20a4e7300a42b8 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Sat, 20 Jun 2026 20:22:39 -0400 Subject: [PATCH 076/135] ForcingTerms - IMPROVEMENT - Address PR review: raise pf_hoop nsec floor, guard standoff coils against boundary Per NilsLeuthold's review of #278: - make_pf_hoop: raise nsec floor from >=4 to >=361 (default) so a full poloidal loop has at least ~1 deg resolution instead of a near-square. - make_window_pane_standoff: error when a tilted coil would intersect the plasma boundary (clearance = standoff - half*|sin(tilt)| <= 0), the case Nils flagged (90 deg tilt with standoff shorter than half the leg length). - Tests: sub-floor nsec throw; standoff intersection throw + valid case. Co-Authored-By: Claude Opus 4.8 (1M context) --- src/ForcingTerms/CoilGeometry.jl | 14 +++++++++++++- test/runtests_coils.jl | 9 +++++++++ 2 files changed, 22 insertions(+), 1 deletion(-) diff --git a/src/ForcingTerms/CoilGeometry.jl b/src/ForcingTerms/CoilGeometry.jl index 8a5e5e0fe..cd6bcb17d 100644 --- a/src/ForcingTerms/CoilGeometry.jl +++ b/src/ForcingTerms/CoilGeometry.jl @@ -299,7 +299,7 @@ breaks axisymmetry to produce n≠0 forcing. Currents are zeroed; `load_coil_set """ function make_pf_hoop(; radius::Real, height::Real, nsec::Int=361, name::String="pf_hoop") radius > 0 || error("make_pf_hoop: radius must be > 0 (got $radius)") - nsec >= 4 || error("make_pf_hoop: nsec must be >= 4 (got $nsec)") + nsec >= 361 || error("make_pf_hoop: nsec must be >= 361 (got $nsec); a full poloidal hoop needs at least ~1° resolution to be smooth") phis = range(0; length=nsec, stop=2π) # closed: phis[end] == phis[1] + 2π x = reshape([radius * cos(p) for p in phis], 1, 1, nsec) y = reshape([radius * sin(p) for p in phis], 1, 1, nsec) @@ -395,6 +395,18 @@ function make_window_pane_standoff(equil; standoff::Real, poloidal_angle::Real, uZ = s * tR + c * tZ half = poloidal_length / 2 + + # Guard against a coil that pokes through the plasma boundary (the standoff is too small for + # the tilt/length, e.g. a 90° tilt with standoff < half the leg length). The surface point's + # tangent plane supports the (convex) boundary, so the nearest leg corner's clearance from the + # boundary along the normal is standoff - half*|sin(tilt)| — the tilt tips the legs toward the + # surface, while tangential displacement leaves the normal clearance unchanged. + clearance = standoff - half * abs(sin(deg2rad(poloidal_tilt))) + clearance > 0 || error("make_window_pane_standoff: coil intersects the plasma boundary " * + "(standoff=$standoff, poloidal_length=$poloidal_length, poloidal_tilt=$poloidal_tilt); " * + "an external coil must lie outside the control surface — increase standoff or reduce " * + "poloidal_length/poloidal_tilt") + c1 = [Rc - half * uR, Zc - half * uZ] c2 = [Rc + half * uR, Zc + half * uZ] diff --git a/test/runtests_coils.jl b/test/runtests_coils.jl index 1204582c4..6ae7a0c18 100644 --- a/test/runtests_coils.jl +++ b/test/runtests_coils.jl @@ -325,6 +325,8 @@ end @test abs(By[1]) < 1e-14 @test_throws ErrorException ForcingTerms.make_pf_hoop(; radius=-1.0, height=0.0) + # nsec below the 361 floor (too coarse for a smooth poloidal loop) must error + @test_throws ErrorException ForcingTerms.make_pf_hoop(; radius=a, height=0.0, nsec=100) end @testset "Analytic coils: make_window_pane" begin @@ -421,6 +423,13 @@ end # near the coil (same sense as the corner-built window pane). np_pol = 20 # make_window_pane default @test cs1.z[1, 1, np_pol] > cs1.z[1, 1, 1] + + # Separatrix-touch guard: a 90° tilt with standoff shorter than half the leg length pushes + # one corner back through the boundary, which must error. A normal placement still succeeds. + @test_throws ErrorException ForcingTerms.make_window_pane_standoff(equil; standoff=0.1, + poloidal_angle=0.0, poloidal_length=1.0, poloidal_tilt=90.0, ncoil=1) + @test ForcingTerms.make_window_pane_standoff(equil; standoff=0.3, poloidal_angle=0.0, + poloidal_length=0.4, poloidal_tilt=0.0, ncoil=1) isa ForcingTerms.CoilSet end # --------------------------------------------------------------------------- From 1ce108bf98d2cedd981662a5d2e97b8fcbb6b58f Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Sat, 20 Jun 2026 20:44:40 -0400 Subject: [PATCH 077/135] =?UTF-8?q?ForceFreeStates=20Galerkin=20-=20CLEANU?= =?UTF-8?q?P=20-=20Review=20remediation:=20comments,=20DRY,=20alloc-free?= =?UTF-8?q?=20assembly,=20=CE=94(Q)=20test,=20docs?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Post-review cleanup of the Galerkin resistive-MHD solver (physics, clean-code, performance, regression-guardian). All changes verified bit-identical vs develop (51/51 regression quantities) and the full unit suite passes. - GalerkinMatch: correct the RPEC forced-eigenvalue comments to state the deliberate Hz convention (gal_rotation is f[Hz], γ=2πi·n·f) instead of overstating match.f correspondence; annotate the inner-layer Δ block signs. - DRY: extract gal_resonant_surfaces (GalerkinGrid) used by galerkin_solve and gal_match_rpec; drop the filter-drift guard. Add empty_galerkin_result helper. - Perf (bit-identical): in-place F̄→F scaling, preallocated F/K/G scratch in the Gauss-Lobatto hotspot, tuple Hermite basis (no per-node collect). - Trim multi-line investigation/prior-bug comments to one line each; rename ua2/dua2 slices to ua_cols/dua_cols; add constant rationales. - Docs: add GalerkinSolution.jl and GalerkinMatch.jl to the galerkin.md autodocs. - Test: new test/runtests_innerlayer.jl pins the GGJ inner-layer Δ(Q) on the published glasser_wang_2020_eq55 benchmark (guard, pending Fortran cross-check). Co-Authored-By: Claude Opus 4.8 (1M context) --- .../galerkin_assembly_map.md | 20 ++++++++- docs/src/galerkin.md | 4 +- src/ForceFreeStates/ForceFreeStatesStructs.jl | 4 +- .../Galerkin/GalerkinAssembly.jl | 44 +++++++++---------- src/ForceFreeStates/Galerkin/GalerkinGrid.jl | 14 ++++++ src/ForceFreeStates/Galerkin/GalerkinMatch.jl | 22 +++++----- .../Galerkin/GalerkinSolution.jl | 20 ++++----- src/ForceFreeStates/Galerkin/GalerkinSolve.jl | 18 ++++---- test/runtests.jl | 1 + test/runtests_innerlayer.jl | 29 ++++++++++++ 10 files changed, 118 insertions(+), 58 deletions(-) create mode 100644 test/runtests_innerlayer.jl diff --git a/.claude/agent-memory/fortran-physics-reviewer/galerkin_assembly_map.md b/.claude/agent-memory/fortran-physics-reviewer/galerkin_assembly_map.md index c916e3b00..5f2b93f6d 100644 --- a/.claude/agent-memory/fortran-physics-reviewer/galerkin_assembly_map.md +++ b/.claude/agent-memory/fortran-physics-reviewer/galerkin_assembly_map.md @@ -34,4 +34,22 @@ of sing.f's internal singular-surface handling, not a line port. The ×(-1) chai but worth a dedicated check against sing.f sing_get_ua/dua if Δ′ ever disagrees with Fortran. Lives outside GalerkinAssembly.jl. -## Verdict: PASS WITH REQUIRED ANNOTATIONS (citation comments only; no physics defects found). +## RPEC matching (GalerkinMatch.jl <-> rmatch/match.f match_rpec) — reviewed 2026-06-20 +- match block (mat idx1..idx4, -delta1/delta2 signs) + rmat=-TRANSPOSE(delta coil block) + cout/cin split: EXACT port. PASS. +- matched outer soln Σcout(isol)·sols + sols(:,:,csol): EXACT (match_output_solution L32-41). +- resist.f E/F/H/M/G/K/taua/taur/v1: EXACT (Resist.jl). eta/rho caller-supplied = deliberate documented deviation. +- gal quadrature: jacobi_alloc "gll" = Gauss-Lobatto = Julia gausslobatto. nq1 lower=|nn·q1|, upper=|q1|: match. + +## SUSPECT (should-fix) — RPEC forced eigenvalue γ +GalerkinMatch.jl:66 uses γ = 2π·im·n·gal_rotation. Fortran match_rpec passes `initguess` (namelist, +default 0.0) DIRECTLY to deltac_run — NOT i·n·rotation. The `guess+ifac*ntor*rotation` Doppler form +lives only in match_delta (Newton eigenvalue search), NOT the RPEC path. Two issues: + (1) extra 2π: Fortran eig=ifac*ntor*rotation has NO 2π (rotation is ω[rad/s], eig is 1/time, q0=x0/taua). + (2) RPEC path in Fortran uses initguess (the user forced eigenvalue), not a per-surface i·n·rotation shift. +Confirm intended convention vs Fortran before trusting resistive Δ(Q); ideal_flag path (γ unused) is unaffected. +RESOLUTION 2026-06-20: author confirms the Hz convention is DELIBERATE (gal_rotation is f[Hz], so γ=2πi·n·f); +the overstated comments were corrected. Δ(Q) now guarded by test/runtests_innerlayer.jl (Julia self-pin on +glasser_wang_2020_eq55). Remaining follow-up (mpharr): upgrade that guard to a Fortran deltac_run / paper +cross-check to fully close the convention question. + +## Verdict: PASS WITH REQUIRED ANNOTATIONS for outer solve; RPEC γ convention is SHOULD-FIX (verify vs match.f). diff --git a/docs/src/galerkin.md b/docs/src/galerkin.md index 540bde2c3..d9ac34436 100644 --- a/docs/src/galerkin.md +++ b/docs/src/galerkin.md @@ -19,13 +19,15 @@ The implementation lives in `src/ForceFreeStates/Galerkin/`: | `GalerkinStructs.jl` | Cell, interval, and workspace types mirroring the Fortran derived types | | `GalerkinGrid.jl` | Packed grid construction and local→global DOF mapping | | `GalerkinAssembly.jl` | Element-level assembly: Hermite basis, Gauss-Lobatto stiffness, resonant and extension cells, boundary conditions | +| `GalerkinSolution.jl` | Reconstruct ξ(ψ) and analytic ξ′(ψ) on the gal-native grid | +| `GalerkinMatch.jl` | DRIVEN/RPEC outer↔inner asymptotic matching and the matched `OdeState` for PerturbedEquilibrium | | `GalerkinSolve.jl` | Top-level driver `galerkin_solve`, banded solve, Δ′ extraction, PEST-3 blocks, HDF5 output | ## API Reference ```@autodocs Modules = [GeneralizedPerturbedEquilibrium.ForceFreeStates] -Pages = ["Galerkin/GalerkinStructs.jl", "Galerkin/GalerkinGrid.jl", "Galerkin/GalerkinAssembly.jl", "Galerkin/GalerkinSolve.jl"] +Pages = ["Galerkin/GalerkinStructs.jl", "Galerkin/GalerkinGrid.jl", "Galerkin/GalerkinAssembly.jl", "Galerkin/GalerkinSolution.jl", "Galerkin/GalerkinMatch.jl", "Galerkin/GalerkinSolve.jl"] ``` ## See also diff --git a/src/ForceFreeStates/ForceFreeStatesStructs.jl b/src/ForceFreeStates/ForceFreeStatesStructs.jl index 58faadaaa..970e1f4b4 100644 --- a/src/ForceFreeStates/ForceFreeStatesStructs.jl +++ b/src/ForceFreeStates/ForceFreeStatesStructs.jl @@ -314,10 +314,10 @@ A mutable struct containing control parameters for stability analysis, set by th gal_sing_order::Int = 6 # base power-series order for the Galerkin singular asymptotics gal_sing_order_ceiling::Bool = true # auto-raise order by ceil(2·Re(α)) per surface (high Mercier index) gal_rpec_flag::Bool = false # append mpert coil-response columns to the Δ′ solve (RDCON rpec_flag): unit boundary sources whose plasma response is recorded; needed for the driven (resistive perturbed-equilibrium) Δ_gw - gal_edge_onesided::Bool = false # pack the two end intervals (`[psilow,first rational]`, `[last rational,psihigh]`) one-sided toward their single rational end instead of the Fortran-faithful symmetric "both" pack. Leaves the regular domain boundary at coarse spacing, removing the gratuitous fine edge cell that inflates cond(A) (entry spread ~1/h²) and seeds the downstream edge-derivative artifact. Default false = faithful to gal.f. + gal_edge_onesided::Bool = false # pack the two end intervals one-sided toward their single rational end (vs the Fortran symmetric "both" pack); avoids the fine edge cell that inflates cond(A). Default false = faithful to gal.f. # --- DRIVEN (RPEC) outer↔inner asymptotic matching (rmatch match_rpec port) --- gal_match_flag::Bool = false # enable the RPEC inner-layer matching: solve the coil-driven matched ξ(ψ) from the gal Δ′ + the inner-layer Δ(Q). Requires gal_rpec_flag=true. - gal_ideal_flag::Bool = false # within the match (gal_match_flag), build the IDEAL solution instead of the resistive one: skip the inner-layer Δ and use the bare coil columns (cout=0). Mirrors Fortran rmatch coil%ideal_flag; "physically equivalent to regular DCON" — the EL reference. eta/rho/rotation are ignored. + gal_ideal_flag::Bool = false # within the match, build the IDEAL solution: skip the inner-layer Δ, use bare coil columns (cout=0). Mirrors Fortran rmatch coil%ideal_flag (the EL reference). eta/rho/rotation ignored. gal_eta::Vector{Float64} = Float64[] # per-surface resistivity η (length msing, core→edge); Fortran rmatch `eta` gal_rho::Vector{Float64} = Float64[] # per-surface mass density ρ [kg/m³] (length msing, core→edge); Fortran rmatch `massden` gal_rotation::Vector{Float64} = Float64[] # per-surface rotation frequency f [Hz] (length msing, core→edge); forced eigenvalue γ_s = 2πi·n·f. Fortran rmatch `rotation` diff --git a/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl b/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl index 94b6ddb35..bbde71c92 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl @@ -50,20 +50,22 @@ Evaluate the `mpert×mpert` matrices `F = Q F̄ Qᴴ`, `K = Q K̄`, `G = Ḡ` at Uses the un-factored reduced `ffit.fmats_gal` (F̄), `ffit.kmats` (K̄), `ffit.gmats` (Ḡ). F/K/G are the ideal-MHD Euler–Lagrange coefficient matrices of the outer-region weak form (Glasser 2016, PoP 23, 112506). """ -function gal_get_fkg(ffit::FourFitVars, intr::ForceFreeStatesInternal, x::Float64, q::Float64) +function gal_get_fkg(ffit::FourFitVars, intr::ForceFreeStatesInternal, x::Float64, q::Float64; + Fbuf::Union{Nothing,Matrix{ComplexF64}}=nothing, Kbuf::Union{Nothing,Matrix{ComplexF64}}=nothing, + Gbuf::Union{Nothing,Matrix{ComplexF64}}=nothing) N = intr.numpert_total sf = vec((intr.mlow:intr.mhigh) .- q .* (intr.nlow:intr.nhigh)') - Fbar = Matrix{ComplexF64}(undef, N, N) - K = Matrix{ComplexF64}(undef, N, N) - G = Matrix{ComplexF64}(undef, N, N) - ffit.fmats_gal(vec(Fbar), x; hint=ffit._hint) + F = Fbuf === nothing ? Matrix{ComplexF64}(undef, N, N) : Fbuf + K = Kbuf === nothing ? Matrix{ComplexF64}(undef, N, N) : Kbuf + G = Gbuf === nothing ? Matrix{ComplexF64}(undef, N, N) : Gbuf + ffit.fmats_gal(vec(F), x; hint=ffit._hint) ffit.kmats(vec(K), x; hint=ffit._hint) ffit.gmats(vec(G), x; hint=ffit._hint) - F = Matrix{ComplexF64}(undef, N, N) + # scale F̄→F=Q F̄ Qᴴ and K̄→K=Q K̄ in place (Q = diag(sf)) @inbounds for j in 1:N, i in 1:N - F[i, j] = Fbar[i, j] * sf[i] * sf[j] + F[i, j] = F[i, j] * sf[i] * sf[j] K[i, j] = K[i, j] * sf[i] end return F, K, G @@ -87,19 +89,19 @@ function gal_gauss_quad!(cell::GalCell, ffit::FourFitVars, profiles, intr::Force x0c = (x2 + x1) / 2 dxc = (x2 - x1) / 2 qhint = Ref(1) + Fbuf = Matrix{ComplexF64}(undef, N, N) + Kbuf = Matrix{ComplexF64}(undef, N, N) + Gbuf = Matrix{ComplexF64}(undef, N, N) @inbounds for iq in eachindex(nodes) x = x0c + dxc * nodes[iq] w = dxc * weights[iq] q = profiles.q_spline(x; hint=qhint) - F, K, G = gal_get_fkg(ffit, intr, x, q) + F, K, G = gal_get_fkg(ffit, intr, x, q; Fbuf=Fbuf, Kbuf=Kbuf, Gbuf=Gbuf) pbt, qbt = gal_hermite(x, x1, x2) - pb = collect(pbt) - qb = collect(qbt) - if swap_edge - pb[3], pb[4] = pb[4], pb[3] - qb[3], qb[4] = qb[4], qb[3] - end + # swap the right-node value/slope DOFs (Fortran pb(2)↔pb(3)) for the free-boundary edge + pb = swap_edge ? (pbt[1], pbt[2], pbt[4], pbt[3]) : pbt + qb = swap_edge ? (qbt[1], qbt[2], qbt[4], qbt[3]) : qbt for ip in 0:np, ipert in 1:N, jp in 0:np, jpert in 1:N cell.mat[ipert, jpert, ip+1, jp+1] += w * ( F[ipert, jpert] * qb[ip+1] * qb[jp+1] + @@ -285,11 +287,11 @@ function gal_resonant!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, ua = sing_get_ua_gal(asymp, z) dua = sing_get_dua_gal(asymp, z) q = profiles.q_spline(x; hint=qhint) - ua2 = ua[:, cols, :] - dua2 = dua[:, cols, :] - mv = sing_matvec(ffit, intr, x, q, ua2, dua2) # N×2 (col1=big, col2=small) + ua_cols = ua[:, cols, :] + dua_cols = dua[:, cols, :] + mv = sing_matvec(ffit, intr, x, q, ua_cols, dua_cols) # N×2 (col1=big, col2=small) pbt, _ = gal_hermite(x, x1, x2) - w = conj.(@view ua2[:, 2, 1]) # conj small solution, qty1 + w = conj.(@view ua_cols[:, 2, 1]) # conj small solution, qty1 out = Vector{ComplexF64}(undef, L) out[1] = sum(w .* @view mv[:, 1]) # res1 out[2] = sum(w .* @view mv[:, 2]) # res2 @@ -305,10 +307,8 @@ function gal_resonant!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, return out end - # Numerical-method deviation from gal_lsode_int: adaptive QuadGK (Gauss-Kronrod) replaces Fortran's - # LSODE accumulation over the same integrand/limits, so this path is NOT bit-exact with gal.f. Match - # Fortran's LSODE tolerance (gal_tol) and cap the evaluations at gal_gnstep (Fortran's gnstep limit) - # so a near-singular integrand cannot hang. + # QuadGK (adaptive Gauss-Kronrod) replaces Fortran gal_lsode_int over the same integrand/limits — not + # bit-exact; gal_tol/gal_gnstep cap the evals so a near-singular integrand cannot hang. raw, qerr = quadgk(integrand, x0, x1l; rtol=gal_tol, atol=1e-30, maxevals=gal_gnstep) if verbose @info " resonant jsing=$jsing side=$(cell.extra) qerr=$(qerr) res1=$(raw[1]) res2=$(raw[2])" diff --git a/src/ForceFreeStates/Galerkin/GalerkinGrid.jl b/src/ForceFreeStates/Galerkin/GalerkinGrid.jl index 88bb26782..497e26e70 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinGrid.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinGrid.jl @@ -46,6 +46,20 @@ function gal_pack(nx::Int, pfac::Float64, side::String) return x end +""" + gal_resonant_surfaces(intr, equil) -> (sings, psilow, psihigh) + +Resonant surfaces inside the integration domain, in increasing ψ (Fortran `sing(1:msing)`), with the +domain bounds. `psilow` is raised above the axis by `sing_min!` when `qlow > qmin` (excludes the q 0 ? intr.psilow : equil.profiles.xs[1] + psihigh = intr.psilim + sings = [s for s in intr.sing if psilow < s.psifac < psihigh && intr.mlow <= s.m[1] <= intr.mhigh] + return sings, psilow, psihigh +end + """ gal_make_grid!(intvl::GalInterval, ising::Int, msing::Int, sings::Vector{SingType}, nn::Int, psilow::Float64, psihigh::Float64, ctrl::ForceFreeStatesControl) diff --git a/src/ForceFreeStates/Galerkin/GalerkinMatch.jl b/src/ForceFreeStates/Galerkin/GalerkinMatch.jl index 2bdb1d2d2..2a2b37af9 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinMatch.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinMatch.jl @@ -3,8 +3,9 @@ # DRIVEN (RPEC) outer↔inner asymptotic matching. Port of rmatch `match_rpec` (match.f) and the # outer total-solution construction of `match_output_solution` (match.f). # -# Per rational surface: the forced eigenvalue γ_s = 2πi·n·f_s (rpec, match.f), the inner-layer -# matching data Δ(Q) via the Galerkin GGJ solver (InnerLayer.solve_inner), then the 4·msing matching +# Per rational surface: the forced eigenvalue γ_s = 2πi·n·f_s (gal_rotation is the rotation f in Hz, so γ +# is the layer Doppler frequency), the inner-layer matching data Δ(Q) via the Galerkin GGJ solver +# (InnerLayer.solve_inner), then the 4·msing matching # system mat·[cout;cin] = rmat is assembled (rmat = −transpose of the gal Δ′ coil block) and solved for # the per-coil outer/inner coefficients. The matched outer solution for coil drive j is # ξ_j = Σ_{isol=1}^{2 msing} cout[isol,j]·sols[:,:,isol] + sols[:,:,2 msing+j] @@ -48,13 +49,11 @@ function gal_match_rpec(ctrl::ForceFreeStatesControl, equil, intr::ForceFreeStat length(v) == msing || error("gal_match_rpec: $name has length $(length(v)), expected msing=$msing (one value per surface, core→edge)") end - # Re-derive the gal singular-surface set (must match galerkin_solve's filter) to get the SingType - # objects resist_eval needs; verify alignment with the stored gal Δ′ surfaces. - psilow = intr.psilow > 0 ? intr.psilow : equil.profiles.xs[1] - psihigh = intr.psilim - sings = [s for s in intr.sing if psilow < s.psifac < psihigh && intr.mlow <= s.m[1] <= intr.mhigh] - length(sings) == msing && isapprox([s.psifac for s in sings], gal_result.sing_psi; rtol=1e-8) || - error("gal_match_rpec: re-derived surface set does not match gal Δ′ surfaces (filter drift?)") + # Re-derive the gal singular-surface set (same helper as galerkin_solve) for the SingType objects + # resist_eval needs. + sings, _, _ = gal_resonant_surfaces(intr, equil) + length(sings) == msing || + error("gal_match_rpec: re-derived $(length(sings)) surfaces, expected msing=$msing") # --- inner-layer matching data Δ(Q) per surface (deltac_run; match.f) --- inner = InnerLayer.GGJModel(solver=:galerkin) @@ -63,7 +62,7 @@ function gal_match_rpec(ctrl::ForceFreeStatesControl, equil, intr::ForceFreeStat for i in 1:msing params = resist_eval(sings[i], equil, intr; eta=ctrl.gal_eta[i], rho=ctrl.gal_rho[i], gamma=ctrl.gal_gamma, ising=i) - γ = 2π * im * nn * ctrl.gal_rotation[i] # rpec forced eigenvalue 2πi·n·f + γ = 2π * im * nn * ctrl.gal_rotation[i] # forced eigenvalue; gal_rotation is f [Hz], γ = 2πi·n·f rpec_eig[i] = γ Δ = InnerLayer.solve_inner(inner, params, γ) # (Δ₁, Δ₂) in deltac.f convention deltar[i, 1] = Δ[1] @@ -89,7 +88,8 @@ function gal_match_rpec(ctrl::ForceFreeStatesControl, equil, intr::ForceFreeStat mat[idx1, idx4] = 1 mat[idx2, idx3] = -1 mat[idx2, idx4] = -1 - mat[idx3, idx3] = -delta1 # Δ_in + # inner-layer Δ block signs per match.f match_rpec + mat[idx3, idx3] = -delta1 mat[idx3, idx4] = delta2 mat[idx4, idx3] = -delta1 mat[idx4, idx4] = -delta2 diff --git a/src/ForceFreeStates/Galerkin/GalerkinSolution.jl b/src/ForceFreeStates/Galerkin/GalerkinSolution.jl index dfed6dfe7..e2a1ebbad 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinSolution.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinSolution.jl @@ -5,22 +5,21 @@ # gal_get_solution (gal.f) ξ (and optional ξ′) at one ψ for one solution column # gal_output_solution (gal.f) evaluate (ξ, ξ′) on a gal-native packed grid, all columns # -# The whole point of carrying ξ′ here is to evaluate it analytically from the Hermite derivative basis -# (gal_hermite qb) and the asymptotic-series derivative (sing_get_dua_gal) rather than ever -# spline-differentiating ξ at the packed edge — the spline-endpoint derivative was the root cause of -# GPEC's fake ~100% shielding (fixed in Fortran by RDCON_singcoup commit c3e8c5bc). +# ξ′ is evaluated analytically from the Hermite derivative basis (gal_hermite qb) and the asymptotic-series +# derivative (sing_get_dua_gal), never by spline-differentiating ξ at the packed edge. # # Fortran module flags restore_uh/us/ul default .TRUE. (gal.f); the full reconstruction is always # performed. The cut path (gal.f, used only for the matching diagnostic) is NOT ported here. -# Dense / coarse sampling per cell, matching Fortran interp_np_res / interp_np (gal.f). +# Sampling points per cell, matching Fortran interp_np_res / interp_np (gal.f): coarse in regular cells, +# dense in resonant/extension cells to resolve the near-singular asymptotic series. const GAL_INTERP_NP = 3 const GAL_INTERP_NP_RES = 60 # Advance the monotone (iintvl, icell) cursor to the cell containing x. Port of gal.f. @inline function gal_locate_cell(ws::GalWorkspace, x::Float64, iintvl::Int, icell::Int) msing = length(ws.intvl) - 1 - for _ in 1:((msing+1)*ws.nx+1) + for _ in 1:((msing+1)*ws.nx+1) # bounded scan: at most one full wrap over all cells cell = ws.intvl[iintvl+1].cells[icell] if cell.x[1] <= x <= cell.x[2] return iintvl, icell, cell @@ -59,12 +58,9 @@ function gal_get_solution(ws::GalWorkspace, asymps::Vector{GalSingAsymp}, sings: # --- non-resonant (Hermite) part: same coefficients, value basis pb → ξ, derivative basis qb → ξ′ --- pbt, qbt = gal_hermite(x, cell.x[1], cell.x[2]) - pb = collect(pbt) - qb = collect(qbt) - if iintvl == msing && icell == ws.nx # last edge cell: swap node-2/3 DOFs (gal.f) - pb[3], pb[4] = pb[4], pb[3] - qb[3], qb[4] = qb[4], qb[3] - end + swap = iintvl == msing && icell == ws.nx # last edge cell: swap node-2/3 DOFs (gal.f) + pb = swap ? (pbt[1], pbt[2], pbt[4], pbt[3]) : pbt + qb = swap ? (qbt[1], qbt[2], qbt[4], qbt[3]) : qbt for ip in 0:np u = @view ws.sol[cell.map[:, ip+1], isol] @views sol .+= u .* pb[ip+1] diff --git a/src/ForceFreeStates/Galerkin/GalerkinSolve.jl b/src/ForceFreeStates/Galerkin/GalerkinSolve.jl index 767bc6512..9531b34b6 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinSolve.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinSolve.jl @@ -39,6 +39,13 @@ function gal_make_arrays!(ws::GalWorkspace, ctrl::ForceFreeStatesControl, equil, return ws end +"""Empty `GalerkinResult` for a domain with no resonant surfaces.""" +function empty_galerkin_result() + empty2 = Matrix{ComplexF64}(undef, 0, 0) + return GalerkinResult(empty2, empty2, empty2, empty2, empty2, 0, + Float64[], Float64[], Int[], Int[], Float64[], ComplexF64[], empty2, nothing, nothing) +end + """ galerkin_solve(ctrl::ForceFreeStatesControl, equil, ffit::FourFitVars, intr::ForceFreeStatesInternal; vac_data=nothing) -> GalerkinResult @@ -59,18 +66,11 @@ function galerkin_solve(ctrl::ForceFreeStatesControl, equil, ffit::FourFitVars, mpert = intr.numpert_total np = GAL_NP - # Resonant surfaces inside the integration domain, in increasing ψ (Fortran `sing(1:msing)`). - # psilow is raised above the axis by sing_min! when qlow > qmin (excludes the q 0 ? intr.psilow : equil.profiles.xs[1] - psihigh = intr.psilim - sings = [s for s in intr.sing if psilow < s.psifac < psihigh && intr.mlow <= s.m[1] <= intr.mhigh] + sings, psilow, psihigh = gal_resonant_surfaces(intr, equil) msing = length(sings) if msing == 0 ctrl.verbose && @info "galerkin_solve: no resonant surfaces in domain; skipping Δ′ solve" - empty2 = Matrix{ComplexF64}(undef, 0, 0) - return GalerkinResult(Matrix{ComplexF64}(undef, 0, 0), empty2, empty2, empty2, empty2, 0, - Float64[], Float64[], Int[], Int[], Float64[], ComplexF64[], empty2, nothing, nothing) + return empty_galerkin_result() end ctrl.verbose && @info "Starting outer-region Galerkin Δ′ solve (msing=$msing, solver=$(ctrl.gal_solver))" diff --git a/test/runtests.jl b/test/runtests.jl index f424a7d23..d2b26f9a7 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -28,6 +28,7 @@ else include("./runtests_riccati.jl") include("./runtests_parallel_integration.jl") include("./runtests_sing.jl") + include("./runtests_innerlayer.jl") include("./runtests_tj_analytic.jl") include("./runtests_kinetic.jl") include("./runtests_fullruns.jl") diff --git a/test/runtests_innerlayer.jl b/test/runtests_innerlayer.jl new file mode 100644 index 000000000..25f446c55 --- /dev/null +++ b/test/runtests_innerlayer.jl @@ -0,0 +1,29 @@ +# runtests_innerlayer.jl +# +# Inner-layer GGJ Δ(Q) solver tests on the published Glasser & Wang (2020, Eq. 55) benchmark. +# Pins the Galerkin inner-layer Δ as a numerical guard against accidental drift in the Δ(Q) path +# that gal_match_rpec feeds. The forced eigenvalue is built in the RPEC convention γ = 2πi·n·f +# (gal_rotation is f in Hz), so this also exercises that convention. +# +# The reference Δ values are current Julia outputs (reproducible to machine precision), pinned pending +# a Fortran rmatch deltac_run / paper cross-check. The :shooting solver returns NaN on this benchmark, +# so solver-vs-solver cross-validation is left as a follow-up. + +const IL = GeneralizedPerturbedEquilibrium.InnerLayer + +@testset "InnerLayer GGJ Δ(Q)" begin + p = IL.glasser_wang_2020_eq55() + gal = IL.GGJModel(; solver=:galerkin) + n = 1 + + @testset "f=$(f) Hz" for (f, Δ_ref) in ( + (1.0e3, (-5.9565220175e-06 - 2.9037648679e-08im, -2.7749660199e-05 + 1.0841989446e-05im)), + (1.0e4, (3.7251353050e-08 + 4.0060105204e-07im, 1.0531076405e-07 - 9.4368319597e-08im)) + ) + γ = 2π * im * n * f + Δ = IL.solve_inner(gal, p, γ) + @test all(isfinite, Δ) + @test Δ[1] ≈ Δ_ref[1] rtol = 1e-5 + @test Δ[2] ≈ Δ_ref[2] rtol = 1e-5 + end +end From 3e915d092222ce38375efc1d7d70e036321c1e35 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Sat, 20 Jun 2026 20:54:29 -0400 Subject: [PATCH 078/135] KineticForces - IMPROVEMENT - Extend energy-integral X_ENERGY_MAX to 100 and harden boundary-pole handling MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Manual PR review asked whether the real-x-space energy integral's upper limit X_ENERGY_MAX could be chosen more robustly, and whether the approach is robust to a resonance pole sitting at or within ~1e-15 of that limit (the direct analog of the original u→1 NaN this branch fixed). Findings: the integrand AND every resonance pole decay as x^p·exp(-x) (p ≤ 3.5 with the qt heat-flux factor) — at a simple pole Ω′ is O(the drift frequencies), so a dropped pole's residue scales as xr^2.5·exp(-xr), the same law as the smooth tail. exp(-x) does not underflow until x≈746, so the Fortran default 72 was a tolerance edge, not a precision edge. Benchmarking confirmed a tighter, tolerance-derived limit buys no speed (QuadGK accepts the near-zero tail in a single panel; 72→100 is byte-identical eval count). So extend the fixed limit 72 → 100 (100^3.5·exp(-100) ≈ 4e-37, ~30 orders below any tolerance) and document the real justification. A kept pole (xr < X_ENERGY_MAX) is subtracted analytically/exactly and is robust at any proximity to the limit; the xr >= X_ENERGY_MAX guard prevents the only NaN risk, log(X_ENERGY_MAX - x_pole)=log(0), at the exact endpoint. Near-degenerate poles (Ω′→0) are handled by the SINGULAR_EPS guard, not by the limit. Added a regression testset forcing a resonance to exactly X_ENERGY_MAX and ±1e-13 around it, asserting finiteness, continuity across the boundary, and agreement with the ν→0⁺ limit. All 200 kinetic unit tests pass. Co-Authored-By: Claude Opus 4.8 (1M context) --- src/KineticForces/EnergyIntegration.jl | 25 +++++++++++++++------- test/runtests_kinetic.jl | 29 ++++++++++++++++++++++++-- 2 files changed, 44 insertions(+), 10 deletions(-) diff --git a/src/KineticForces/EnergyIntegration.jl b/src/KineticForces/EnergyIntegration.jl index e3ecda600..5baf48146 100644 --- a/src/KineticForces/EnergyIntegration.jl +++ b/src/KineticForces/EnergyIntegration.jl @@ -5,8 +5,9 @@ Energy-space integration for the kinetic resonance operator. Implements the energy integrand from [Logan, Park, et al., Phys. Plasmas, 2013] Eq. (8). The integral over normalized energy x = E/T is evaluated in real x-space over -`[0, X_ENERGY_MAX]` (Fortran PENTRC convention; `exp(-72) ≈ 5e-32` is negligible -to any tolerance). Resonance poles (where the denominator i·Ω(x) - ν vanishes, +`[0, X_ENERGY_MAX]`. The integrand and every resonance pole decay as `x^p·exp(-x)`, +so the upper limit is set where that tail falls far below any quadrature tolerance +(see `X_ENERGY_MAX`). Resonance poles (where the denominator i·Ω(x) - ν vanishes, shifted off the real axis to x_pole = x_res - i·ν/Ω′ by collisions) are removed analytically by a Sokhotski-Plemelj decomposition, so the remaining integrand is smooth and integrated by QuadGK adaptive Gauss-Kronrod quadrature. One path @@ -171,10 +172,17 @@ function find_resonance_energies(leff::Float64, wb::Float64, n::Int, we::Float64 return roots end -# Upper energy limit for the collisionless real-x-space integral, matching the -# Fortran PENTRC convention (energy.f90, `xmax`). exp(-72) ≈ 5e-32, so the energy -# tail beyond this is negligible to any quadrature tolerance. -const X_ENERGY_MAX = 72.0 +# Upper energy limit for the real-x-space integral. The integrand AND every +# resonance pole decay as x^p·exp(-x) (p ≤ 3.5 with the qt heat-flux factor): a +# dropped pole at xr ≥ X_ENERGY_MAX contributes R·(PV+iπ) with residue +# R = N(xr)·exp(-xr)/(i·Ω′), and at a simple pole Ω′ is O(the drift frequencies), +# so |R| ~ xr^2.5·exp(-xr) — the same law as the smooth tail. At x=100, +# 100^3.5·exp(-100) ≈ 4e-37 is ~30 orders below any quadrature tolerance, so 100 +# bounds both with enormous margin. This is a tolerance edge, not a precision edge: +# exp(-x) underflows to 0 only near x≈746. Near-degenerate poles (Ω′→0) are handled +# by the SINGULAR_EPS guard below, not by this limit. QuadGK is adaptive, so the +# near-zero tail beyond the resonance is accepted in a single panel at no extra cost. +const X_ENERGY_MAX = 100.0 """ _real_pole_regular_part(xr, p, leff, wb, n, wd) → ComplexF64 @@ -292,8 +300,9 @@ end Integrate the kinetic resonance operator over normalized energy x = E/T. The integral ∫₀^∞ N(x)·exp(-x)/denom(x) dx is evaluated in real x-space over -`[0, X_ENERGY_MAX]` (Fortran PENTRC convention; `exp(-72) ≈ 5e-32` is below any -tolerance) via `_integrate_energy_resonant`. Each resonance pole (root of +`[0, X_ENERGY_MAX]` (the integrand and its poles decay as `x^p·exp(-x)`, so the +tail there is far below any tolerance) via `_integrate_energy_resonant`. Each +resonance pole (root of Ω(x) = leff·wb·√x + n·(we + wd·x), shifted off the real axis by collisions to x_pole = x_res - i·ν/Ω′) is removed by subtracting its singular part R/(x - x_pole) and adding back the analytic principal-value + residue. A single formula handles diff --git a/test/runtests_kinetic.jl b/test/runtests_kinetic.jl index c0403ef5c..41aaccf67 100644 --- a/test/runtests_kinetic.jl +++ b/test/runtests_kinetic.jl @@ -252,8 +252,8 @@ end @testset "tail pole beyond X_ENERGY_MAX dropped" begin - # Linear case (wd = 0): s = -c/b = -(n·we)/(leff·wb) = 30 ⟹ x_res = 900 > 72. - # The pole sits past X_ENERGY_MAX where exp(-x_res) underflows; the + # Linear case (wd = 0): s = -c/b = -(n·we)/(leff·wb) = 30 ⟹ x_res = 900, + # well past X_ENERGY_MAX. The pole sits where exp(-x_res) underflows; the # `xr >= X_ENERGY_MAX` check in _integrate_energy_resonant drops it cleanly. @test KF.find_resonance_energies(1.0, 1.0, 1, -30.0, 0.0)[1] ≈ 900.0 result = KF.integrate_energy( @@ -264,6 +264,31 @@ @test isfinite(imag(result)) end + @testset "pole at and within 1e-13 of X_ENERGY_MAX (boundary robustness)" begin + # Direct analog of the original u→1 bug, relocated to x→X_ENERGY_MAX: a + # resonance pole sitting exactly at, just below, and just above the upper + # integration limit. Linear case (wd=0) with leff=wb=n=1 gives + # x_res = (n·we/(leff·wb))² = we², so we = -√x_target places the pole. + xmax = KF.X_ENERGY_MAX + run_xres(x_target) = KF.integrate_energy( + 0.5, 0.3, -sqrt(x_target), 0.0, 1.0, 0.3, 0, 1.0, 1, 0.5, 0.5, "fgar"; + nutype="zero", f0type="maxwellian", atol=1e-12, rtol=1e-10) + below = run_xres(xmax - 1e-13) # pole kept, subtracted analytically + at = run_xres(xmax) # find_resonance rounds to ≤ xmax; >= guard drops at endpoint + above = run_xres(xmax + 1e-13) # pole dropped (outside domain) + @test isfinite(below) && isfinite(at) && isfinite(above) + # Continuous across the boundary: the only term that changes is the pole's + # contribution ∝ exp(-xmax) ~ exp(-100) ~ 4e-44, negligible on the O(1) bulk + # integral. No NaN from log(xmax - x_pole) at the exact endpoint. + @test below ≈ at rtol=1e-9 + @test at ≈ above rtol=1e-9 + # Collisionless result equals the ν→0⁺ (small-ν krook) limit. + small_nu = KF.integrate_energy( + 0.5, 0.3, -sqrt(xmax - 1e-13), 0.0, 1.0, 1e-6, 0, 1.0, 1, 0.5, 0.5, "fgar"; + nutype="krook", f0type="maxwellian", atol=1e-12, rtol=1e-10) + @test below ≈ small_nu rtol=1e-3 + end + @testset "pole_offset overflow guard" begin # Tiny wb gives small omega_prime = leff·wb/(2√x_res) = 5e-16 at x_res=1, while # nuk = 1e300 forces pole_offset = ν/omega_prime = 2e315 → Inf. The From eb677e0f0c3c9cb644927b7d9400ae12b5c74638 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Sun, 21 Jun 2026 00:05:47 -0400 Subject: [PATCH 079/135] KineticForces - IMPROVEMENT - Address PR #280 review: benchmark/comment/perf cleanups, count nstep_total on kinetic paths - benchmark_solovev_kinetic_stability.jl: rename local run->rundir (shadowed Base.run); mirror nufac into the matched Fortran pentrc.in deck. - EnergyIntegration.jl: trim over-long comments (X_ENERGY_MAX, resonant-integral docstring, inline overflow/non-finite notes) to the project conciseness rule; sizehint! the pole/residue buffers and replace the type-unstable breaks... splat into quadgk with an explicit breakpoint-count branch (byte-identical). - GeneralizedPerturbedEquilibrium.jl: shorten the NTV-skip comment to two lines. - Riccati.jl: record integration/nstep_total on the kinetic (Riccati + parallel-FM) paths, which previously reported 0 - count every accepted Riccati callback step and sum each propagator solve's accepted steps from the thread-local proxies after the BVP barrier. Verified: 200/200 kinetic unit tests pass; regression harness et[1] byte-identical on solovev_kinetic_calculated/solovev_kinetic_nuzero; nstep_total now 1808/1815. Co-Authored-By: Claude Opus 4.8 (1M context) --- .../benchmark_solovev_kinetic_stability.jl | 9 +-- src/ForceFreeStates/Riccati.jl | 8 +++ src/GeneralizedPerturbedEquilibrium.jl | 8 +-- src/KineticForces/EnergyIntegration.jl | 58 +++++++------------ 4 files changed, 37 insertions(+), 46 deletions(-) diff --git a/benchmarks/benchmark_solovev_kinetic_stability.jl b/benchmarks/benchmark_solovev_kinetic_stability.jl index 23856cc35..ae98fe02e 100644 --- a/benchmarks/benchmark_solovev_kinetic_stability.jl +++ b/benchmarks/benchmark_solovev_kinetic_stability.jl @@ -120,6 +120,7 @@ function build_matched_fortran_deck(workdir::String) replace_namelist_value!(pentin, "nl", string(get(kf, "nl", 1))) replace_namelist_value!(pentin, "nutype", "\"" * string(get(kf, "nutype", "harmonic")) * "\"") replace_namelist_value!(pentin, "f0type", "\"" * string(get(kf, "f0type", "maxwellian")) * "\"") + replace_namelist_value!(pentin, "nufac", string(get(kf, "nufac", 1))) replace_namelist_value!(pentin, "kinetic_file", "\"kinetic.txt\"") # kinetic.txt — Fortran readtable wants a title line then numeric rows; the @@ -148,14 +149,14 @@ function run_fortran_reference(workdir::String) end function run_julia_reference() - run = mktempdir(; prefix="solovev_kinetic_julia_") + rundir = mktempdir(; prefix="solovev_kinetic_julia_") for f in ("gpec.toml", "sol.toml", "kinetic.dat") - cp(joinpath(JULIA_FIXTURE, f), joinpath(run, f)) + cp(joinpath(JULIA_FIXTURE, f), joinpath(rundir, f)) end t0 = time() - GPE.main([run]) + GPE.main([rundir]) wall = time() - t0 - et = h5open(joinpath(run, "gpec.h5"), "r") do h5 + et = h5open(joinpath(rundir, "gpec.h5"), "r") do h5 read(h5["FreeBoundaryStability/XiNorm/eigenmode_energies"]) end return real(et[1]), imag(et[1]), wall diff --git a/src/ForceFreeStates/Riccati.jl b/src/ForceFreeStates/Riccati.jl index f134b686b..715c6421d 100644 --- a/src/ForceFreeStates/Riccati.jl +++ b/src/ForceFreeStates/Riccati.jl @@ -931,6 +931,8 @@ function riccati_integrator_callback!(integrator) ctrl, _, _, intr, odet, chunk = integrator.p + odet.total_steps += 1 # count every accepted solver step (saved or not), as segment_callback! does + # Use unified tolerance (matches integrate_el_region! on develop) integrator.opts.reltol = ctrl.eulerlagrange_tolerance @@ -1352,6 +1354,7 @@ function integrate_propagator_chunk!( prob = ODEProblem(sing_der!, u_upper, tspan, params) sol = solve(prob, Vern9(); reltol=rtol, save_everystep=false, save_end=true) prop.block_upper_ic .= sol.u[end] + odet_proxy.total_steps += sol.stats.naccept # thread-local; summed into odet after the BVP barrier # Lower block IC: U₁ = 0, U₂ = I u_lower = zeros(ComplexF64, N, N, 2) @@ -1363,6 +1366,7 @@ function integrate_propagator_chunk!( prob = ODEProblem(sing_der!, u_lower, tspan, params) sol = solve(prob, Vern9(); reltol=rtol, save_everystep=false, save_end=true) prop.block_lower_ic .= sol.u[end] + odet_proxy.total_steps += sol.stats.naccept end """ @@ -1563,6 +1567,10 @@ function parallel_eulerlagrange_integration( _run_parallel_bvp_phase!(propagators, chunks, ctrl, equil, ffit, intr, odet_proxies, bvp_threads) + # Harvest solver-step counts accumulated thread-locally in each proxy during the BVP phase. + # The outer re-integration below uses riccati_integrate_chunk!, which counts via its callback. + odet.total_steps += sum(p.total_steps for p in odet_proxies) + S_at_surface_left, last_crossing_step = _assemble_propagators_serially!(odet, propagators, chunks, ctrl, equil, ffit, intr) diff --git a/src/GeneralizedPerturbedEquilibrium.jl b/src/GeneralizedPerturbedEquilibrium.jl index c4fb23f68..6829acc1c 100755 --- a/src/GeneralizedPerturbedEquilibrium.jl +++ b/src/GeneralizedPerturbedEquilibrium.jl @@ -439,12 +439,8 @@ function main(args::Vector{String}=String[]; dd::Union{IMASdd.dd,Nothing}=nothin @info "\n KineticForces\n$_SECTION" kf_start = time() - # The standalone NTV torque diagnostics contract the kinetic operators - # against perturbed-equilibrium displacements (ξ), so they require a PE - # state. The self-consistent kinetic_source="calculated" path folds the - # kinetic physics into the stability solve and produces no PE state, so - # there is nothing for this block to act on — skip it rather than feed - # `compute_torque_all_methods!` empty perturbation interpolants. + # Standalone NTV torque diagnostics need a PE state (they contract kinetic operators + # against ξ). The self-consistent kinetic_source="calculated" path produces none — skip. if !@isdefined(pe_state) @info "Skipping NTV torque diagnostics: no perturbed-equilibrium data (e.g. kinetic_source=\"calculated\")." else diff --git a/src/KineticForces/EnergyIntegration.jl b/src/KineticForces/EnergyIntegration.jl index 5baf48146..7c441582a 100644 --- a/src/KineticForces/EnergyIntegration.jl +++ b/src/KineticForces/EnergyIntegration.jl @@ -172,16 +172,8 @@ function find_resonance_energies(leff::Float64, wb::Float64, n::Int, we::Float64 return roots end -# Upper energy limit for the real-x-space integral. The integrand AND every -# resonance pole decay as x^p·exp(-x) (p ≤ 3.5 with the qt heat-flux factor): a -# dropped pole at xr ≥ X_ENERGY_MAX contributes R·(PV+iπ) with residue -# R = N(xr)·exp(-xr)/(i·Ω′), and at a simple pole Ω′ is O(the drift frequencies), -# so |R| ~ xr^2.5·exp(-xr) — the same law as the smooth tail. At x=100, -# 100^3.5·exp(-100) ≈ 4e-37 is ~30 orders below any quadrature tolerance, so 100 -# bounds both with enormous margin. This is a tolerance edge, not a precision edge: -# exp(-x) underflows to 0 only near x≈746. Near-degenerate poles (Ω′→0) are handled -# by the SINGULAR_EPS guard below, not by this limit. QuadGK is adaptive, so the -# near-zero tail beyond the resonance is accepted in a single panel at no extra cost. +# Upper limit of the real-x energy integral. Integrand and poles decay as x^p·exp(-x) +# (p ≤ 3.5); at x=100 the tail is ~1e-37, far below any quadrature tolerance. const X_ENERGY_MAX = 100.0 """ @@ -210,28 +202,20 @@ end Energy integral in **real x-space** over `[0, X_ENERGY_MAX]`, matching Fortran PENTRC's real-space integration (energy.f90). One path for any collisionality: -each resonance contributes a pole `x_pole = x_res − i·ν/Ω′` (real on the axis when -ν ≡ 0, shifted off it when ν > 0), removed analytically by principal-value + -residue (Sokhotski-Plemelj), leaving a smooth integrand for QuadGK. The -collisionless case is the exact ν→0 limit of this single formula. - -The add-back `R·[log(xmax − x_pole) − log(−x_pole)]` carries the causal branch -automatically: with `pole_offset = ν/Ω′`, the signed zero of `−pole_offset` for -ν ≡ 0 makes `log(−x_pole) = log(x_res) + iπ·sign(Ω′)`, the retarded ν→0⁺ limit of -Fortran's ximag>0 contour. - -For ν > 0 the off-axis pole keeps the integrand bounded (`|denom| ≥ ν > 0`). For -ν ≡ 0 the pole is on the real axis, where `Ω(x) = leff·wb·√x + n·(we+wd·x)` — a -difference of `O(10⁴)` terms — rounds to exactly `0` over a ~ULP-wide window, where -the physical term is `0/0`; there QuadGK is handed the analytic regular-part limit -(`_real_pole_regular_part`) instead. That guard only ever fires for ν ≡ 0. +each resonance contributes a pole `x_pole = x_res − i·ν/Ω′`, removed analytically by +principal-value + residue (Sokhotski-Plemelj), leaving a smooth integrand for QuadGK. +The collisionless case (ν ≡ 0, real-axis pole) is the exact ν→0⁺ limit of this single +formula; its causal branch is carried by the signed zero of `−pole_offset` (see the +add-back below), and its on-axis `0/0` window by the analytic regular-part limit. """ function _integrate_energy_resonant(p::EnergyParams, leff::Float64, wb::Float64, n::Int, we::Float64, wd::Float64, atol::Float64, rtol::Float64)::ComplexF64 - x_res_list = find_resonance_energies(leff, wb, n, we, wd) + x_res_list = find_resonance_energies(leff, wb, n, we, wd) # ≤ 2 roots of a quadratic in √x x_poles = ComplexF64[] residues = ComplexF64[] + sizehint!(x_poles, length(x_res_list)) + sizehint!(residues, length(x_res_list)) pole_contribution = ComplexF64(0.0) for xr in x_res_list @@ -240,9 +224,8 @@ function _integrate_energy_resonant(p::EnergyParams, leff::Float64, wb::Float64, # Ω′(x_res) = d/dx[leff·wb·√x + n·(we + wd·x)] omega_prime = leff * wb / (2.0 * sqrt(xr)) + n * wd abs(omega_prime) < SINGULAR_EPS && continue - # Collisions shift the pole off the real axis: x_pole = x_res - i·ν/Ω′ (real iff ν=0). - # If ν overflows (e.g. harmonic ν at tiny x_res) the pole is infinitely broadened — - # no localized pole; skip and let QuadGK integrate the smooth bounded integrand. + # Collisions shift the pole off-axis: x_pole = x_res - i·ν/Ω′. Skip if ν overflows + # (harmonic ν at tiny x_res): pole infinitely broadened, integrand stays smooth. pole_offset = _energy_collision_frequency(xr, p) / omega_prime isfinite(pole_offset) || continue x_pole = complex(xr, -pole_offset) # signed-zero imag part for ν=0 carries the causal branch @@ -262,9 +245,8 @@ function _integrate_energy_resonant(p::EnergyParams, leff::Float64, wb::Float64, @inbounds for k in 1:npole val -= residues[k] / (x - x_poles[k]) end - # Inside a ν=0 pole's flat-Ω window the physical term is 0/0 → val non-finite. Replace - # it with the analytic regular-part limit of the nearest pole (the other poles' - # subtractions stay finite and are kept). Never reached for ν>0 (integrand bounded). + # At a ν=0 pole Ω rounds to 0 and the physical term is 0/0; substitute the nearest + # pole's analytic regular-part limit, keeping the other (finite) pole subtractions. if !isfinite(val) k = 1 @inbounds for j in 2:npole @@ -284,11 +266,15 @@ function _integrate_energy_resonant(p::EnergyParams, leff::Float64, wb::Float64, return val end - # Resonance locations as QuadGK breakpoints so the smooth-but-sharp integrand - # is resolved near each pole. Sort a copy of the real parts — `x_poles` must stay - # aligned with `residues`, which the integrand pairs by index. + # Pole real parts as QuadGK breakpoints so the smooth-but-sharp integrand is resolved + # near each pole. With ≤ 2 poles, branch on the breakpoint count to pass them as + # positional args — a `breaks...` splat of a runtime-length Vector is type-unstable. breaks = unique(sort(real.(x_poles))) - smooth_val, _ = quadgk(integrand, 0.0, breaks..., X_ENERGY_MAX; atol=atol, rtol=rtol) + smooth_val, _ = if length(breaks) == 1 + quadgk(integrand, 0.0, breaks[1], X_ENERGY_MAX; atol=atol, rtol=rtol) + else + quadgk(integrand, 0.0, breaks[1], breaks[2], X_ENERGY_MAX; atol=atol, rtol=rtol) + end return smooth_val + pole_contribution end From 78e6d4e8d5862c72f4fbf526670071b10523138d Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Sun, 21 Jun 2026 13:31:01 -0400 Subject: [PATCH 080/135] DOCS - MINOR - Human cleanup of sign conventions docs --- docs/src/conventions.md | 87 +++++++++++++++++++++++------------------ 1 file changed, 49 insertions(+), 38 deletions(-) diff --git a/docs/src/conventions.md b/docs/src/conventions.md index fd50e5f9e..8886aee2f 100644 --- a/docs/src/conventions.md +++ b/docs/src/conventions.md @@ -57,7 +57,7 @@ kernel ``\exp(-im\theta)``; the inverse transform reconstructs with ``\exp(+im\t ### Toroidal Coordinate ``\zeta`` and ``\phi`` -- The ignorable toroidal coordinate is ``\zeta = \phi/(2\pi) + \nu(\psi,\theta)``, where ``\nu`` is +- The magnetic cooridante toroidal angle is ``\zeta = \phi/(2\pi) + \nu(\psi,\theta)``, where ``\nu`` is a single-valued straight-field-line offset that depends on the working coordinate. PEST coordinates have ``\nu = 0``. - The physical toroidal angle is reconstructed as @@ -69,18 +69,23 @@ kernel ``\exp(-im\theta)``; the inverse transform reconstructs with ``\exp(+im\t ### Working Coordinate Options Controlled by `jac_type` in the `[Equilibrium]` section of `gpec.toml`. The Jacobian is -``J \propto B_p^{p_{bp}}\, B^{p_b}\, R^{-p_r}``: - -| Name | `power_bp` | `power_b` | `power_r` | -|------|-----------|-----------|-----------| -| Hamada (default) | 0 | 0 | 0 | -| PEST | 0 | 0 | 2 | -| Boozer | 0 | 2 | 0 | -| Equal-arc | 1 | 0 | 0 | +``J \propto B_p^{p_{bp}}\, B^{p_b}\, R^{-p_r}\, r_c^{-p_{rc}}``, where ``B_p`` is the poloidal +field magnitude, ``B`` is the total field magnitude, ``R`` is the major radius, and +``r_c = \sqrt{(R-R_0)^2 + (Z-Z_0)^2}`` is the minor radius (distance from the magnetic axis +``(R_0, Z_0)``): + +| Name | `power_bp` | `power_b` | `power_r` | `power_rc` | +|------|-----------|-----------|-----------|------------| +| Hamada (default) | 0 | 0 | 0 | 0 | +| PEST | 0 | 0 | 2 | 0 | +| Boozer | 0 | 2 | 0 | 0 | +| Equal-arc | 1 | 0 | 0 | 0 | +| Park | 0 | 1 | 0 | 0 | The powers are set automatically from `jac_type` (`EquilibriumConfig` in `src/Equilibrium/EquilibriumTypes.jl`) and applied in the field-line Jacobian -(`direct_fieldline_der!` in `src/Equilibrium/DirectEquilibrium.jl`). +(`direct_fieldline_der!` in `src/Equilibrium/DirectEquilibrium.jl`). Setting `jac_type = "other"` +lets you specify the four exponents manually. ## Helicity and Handedness @@ -111,7 +116,7 @@ The code always works with ``|F|``; the sign of ``B_t`` is carried separately (` ## Safety Factor ``q`` -The direct solver **computes** ``q`` by field-line integration for direct (EFIT) equilibria and +The direct solver **computes** ``q`` by field-line integration for direct (EFIT) equilibria and overwrites the file profile (`direct_run` in `src/Equilibrium/DirectEquilibrium.jl`): ```math @@ -122,8 +127,8 @@ q = \frac{F}{2\pi}\oint \frac{J}{B_p}\,dl_p . positive, **``q`` is positive** in standard operation. The solver emits a warning if the on-axis extrapolation yields ``q_0 \le 0``, treating it as a spline artifact rather than a physical result. -- **Inverse** equilibria instead use the ``q`` profile supplied with the input - (`src/Equilibrium/InverseEquilibrium.jl`). +- **Inverse** equilibria, for which only CHEASE and analytic options are currently supported, instead use the ``q`` profile supplied with the input + (`src/Equilibrium/InverseEquilibrium.jl`). This follows the fortran GPEC CHEASE reading convention. ## Mode Numbers ``m`` and ``n`` @@ -138,11 +143,14 @@ q = \frac{F}{2\pi}\oint \frac{J}{B_p}\,dl_p . The poloidal spectrum spans `mlow` to `mhigh` (`src/GeneralizedPerturbedEquilibrium.jl`): ```math -m_\mathrm{low} = \min(n\,q_\mathrm{min},\,0) - 4 - \Delta m_\mathrm{low}, \qquad -m_\mathrm{high} = n\,q_\mathrm{max} + \Delta m_\mathrm{high}. +m_\mathrm{low} = \min(\lfloor n\,q_\mathrm{min}\rfloor,\,0) - 4 - \Delta m_\mathrm{low}, \qquad +m_\mathrm{high} = \lfloor n\,q_\mathrm{max}\rfloor + 2\,\Delta m_\mathrm{high}. ``` -`delta_mlow` and `delta_mhigh` widen the range beyond the resonant modes. +`delta_mlow` and `delta_mhigh` widen the range beyond the resonant modes. Note the asymmetric +factor of 2 on ``\Delta m_\mathrm{high}``: `delta_mhigh` is doubled before being applied (for +consistency with the Fortran DCON convention), so the user-supplied value adds twice as many +modes on the high side as `delta_mlow` does on the low side. ### Why Positive ``m`` Is Always Resonant @@ -155,7 +163,7 @@ m_\mathrm{res} = n\,q > 0 . ``` Negative-``m`` modes are always non-resonant. This is by design: the ``m = 2`` displacement shows -resonant behavior at ``q = 2``, while ``m = -2`` never does. +resonant behavior at ``q = 2``, etc. ## Spectrum Output Sign Conventions @@ -185,16 +193,20 @@ b_surfmn = real(b_m) - 1j * helicity * imag(b_m) For LH configurations only the sign of ``m`` is flipped; for RH, ``m`` is unchanged but the complex conjugate is taken. -### Interfacing with VACUUM +### Interfacing with Vacuum -The VACUUM code uses CCW ``\phi`` and downward-outboard ``\theta``. GPEC uses the complex conjugate -of RH configurations when interfacing with VACUUM. +The Vacuum code uses CCW ``\phi`` and downward-outboard ``\theta``. GPEC uses the complex conjugate +of RH configurations when interfacing with Vacuum. ## Field Amplitudes and Units GPEC reports perturbed magnetic fields as Fourier spectra on flux surfaces. The spectrum of a field -on a surface depends on in general on the coordinate system used. However, certain resonant components on rational surfaces or the 2-norm of the Fourier coefficient vector on any surface can be made coordinate-independent if the proper area weighting is used within the Fourier decomposition. The -coordinate-invariance of the weightings used in GPEC is established in Pharr (2026) (see [Citations](citations.md)). In each case, we normalize the harmonics by scalar area factors in such a way that the units are always Tesla. +on a surface depends in general on the coordinate system used. However, certain resonant components +on rational surfaces or the 2-norm of the Fourier coefficient vector on any surface can be made +coordinate-independent if the proper area weighting is used within the Fourier decomposition. The +coordinate-invariance of the weightings used in GPEC is established in Pharr (2026) (see +[Citations](citations.md)). In each case, we normalize the harmonics by scalar area factors in such +a way that the units are always Tesla. ### Resonant Field @@ -205,13 +217,19 @@ rational surface, divided by the **scalar area** ``A^r`` of that surface: b^r = \frac{\Phi^r}{A^r} \qquad [\mathrm{T}]. ``` -Dividing the resonant flux ``\Phi^r`` by the surface area turns it into a genuine field amplitude +Dividing the resonant flux ``\Phi^r`` by the surface area turns it into a field amplitude in Tesla that is invariant under changes of the poloidal-angle (working) coordinate. This is the quantity reported as `resonant_flux`. -### Power-Normalized Field +Note that there is strictly NO resonant field in ideal MHD perturbed equilibrium calculations, and +only the effective resonant field is non-zero in these cases. Effective resonant fields are computed +as above but for the resonant component of flux that is being shielded by the shielding current layer +on the rational surface. Resistive and kinetic MHD perturbed equilibria have, in general, finite +resonant fields as well as effective resonant fields. + +### Root-Area Normalized Field -The power-normalized field is the Fourier spectrum of the square-root-area-weighted normal field +The root-area normalized field is the Fourier spectrum of the square-root-area-weighted normal field ``\sqrt{\mathcal{J}\,|\nabla\psi|}\,(\mathbf{b}\cdot\hat{\mathbf{n}})``, divided by the scalar ``\sqrt{A}`` of the surface: @@ -220,7 +238,7 @@ The power-normalized field is the Fourier spectrum of the square-root-area-weigh (\mathbf{b}\cdot\hat{\mathbf{n}})\, e^{-i m\theta}\, d\theta \qquad [\mathrm{T}]. ``` -The name comes from Parseval's theorem: the sum of its squared mode amplitudes equals the +According to Parseval's theorem, the sum of its squared mode amplitudes equals the area-averaged squared normal field — the surface-averaged field "power", ```math @@ -297,8 +315,7 @@ The sign of ``\omega_E`` shifts the resonance location in velocity space. ## COCOS Compatibility The conventions above are GPEC-native and predate the COCOS standard, as defined in -[Sauter, Comp. Phys. Comm. 2013](https://doi.org/10.1016/j.cpc.2012.09.010). What is **certain** -about the internal convention: +[Sauter, Comp. Phys. Comm. 2013](https://doi.org/10.1016/j.cpc.2012.09.010). The internal convention: - Right-handed magnetic coordinates ``(\psi, \theta, \zeta)``. - ``\psi`` excludes the ``2\pi`` factor (poloidal flux per radian) and increases from axis to edge. @@ -312,16 +329,10 @@ imas_cocos = 11 # default: IMAS standard, ψ divided by 2π on read imas_cocos = 2 # data already in the internal convention, no conversion ``` -!!! warning "The COCOS index is not yet certified" - The internal "COCOS 2" label is a working assumption, not a verified index. The IMAS reader - converts COCOS 11 → "COCOS 2" by dividing ``\psi`` by ``2\pi`` **only**, whereas in the COCOS - standard the pure ``2\pi`` partner of COCOS 11 is COCOS **1** (COCOS 2 differs additionally in - the cylindrical/poloidal handedness ``\sigma_{R\phi Z}`` and in ``\mathrm{sign}(q)``). A - rigorous classification would require auditing the ``\sigma_{B_p}``, ``\sigma_{R\phi Z}``, and - ``\sigma_{\rho\theta\phi}`` signs against the GPEC field representation. Until that audit is - done, treat the **practical input requirement** as the reliable statement: provide IMAS - equilibria in COCOS 11 (default) or COCOS 2, selected via `imas_cocos`. Full COCOS conformance - is tracked as a separate effort. +!!! warning "The COCOS indexing is still a beta feature" + Note that the IMAS reader converts COCOS 11 → "COCOS 2" by simply dividing ``\psi`` by ``2\pi`` + (i.e. conversion from COCOS 11 to 1) and relying on the standardly enforced sign conventions + above to eventually conform to the COCOS 2 conventions. ## See also From 8249bbc9d1a76c862d7bd508586336c2fe6c7d9f Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Sun, 21 Jun 2026 16:46:47 -0400 Subject: [PATCH 081/135] DOCS - MINOR - Add Park (2008) spectral-asymmetry reference for the resonant field Add 2008-Park-Spectral_asymmetry_due_to_magnetic_coordinates.pdf to docs/resources, cite it in the Resonant Field section of conventions.md to motivate area-normalization of the resonant harmonic, and add the full entry to the PerturbedEquilibrium citations list. 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z@uGhgv4sy?H48*c$z&Q|_dd9a7}-e&D7xh4{*a8)4*%NZ$Usj^SafO96PyeiG+`P> z2ibLO0B)i-PeW`R0rCSIsGT?D)84Zaq9axH`h|}>vc-T2+=VgB;Wd_{nOc;mt z)iVUCbnnR70;z?t}E6|&r@zel9NM5GK(%A6V zM>jkAveHU*NQhtHjhJ|3z-rRSa7E)8a)szdtTi%VmMA}SZEd^Y4*#b2G(WT6{zmMp zvh;!C*l?uPja^->aIw_&^3$%ao9^~q?fz57{DUizb=iX6)VbfgNSy+P{Al`?jX)(h zs0?Woz|?|RADR2E<>Ns23XXlc!{bBULgt=Rx7~8~zBYN$Fbp}@;C(jfdSmPQ;2iXW zRNq)XnGnQd_?a=V;?wPlzP^9!g33p`fK?rR|CRAeVr21w=*a-ty1|rAA6mHZ-yJgbO*gI5 zUhuwrwho?OS1>8RDZH2ah*xwLJ~36RE2p+CLw|xr;r;z#>p=C<&TolAH_1x!L$YG0 z!&hxo9MYk4SE~UB#8^vM%&Xc)0P5iI=h*Ez$hJAwa(ddv-80`PX;#IZ0QD5 zR_{N8<&Dj&B3)Qd#v>-`TCeFWsGF%|PzD`Kp%X)aC{7KZ52pv3o^dzN=apYc{?E7E b&E4G9-OJVb9Y9FrK@|@SU}aT+DB}MYM0X5s literal 0 HcmV?d00001 diff --git a/docs/src/citations.md b/docs/src/citations.md index 57017a172..a9bc62365 100644 --- a/docs/src/citations.md +++ b/docs/src/citations.md @@ -66,6 +66,14 @@ Establishes the self-consistent plasma response calculation. Derives the permeab --- +> J.-K. Park, A. H. Boozer, and J. E. Menard, "Spectral asymmetry due to magnetic coordinates," +> *Physics of Plasmas* **15**, 064501 (2008). +> DOI: [10.1063/1.2932110](https://doi.org/10.1063/1.2932110) + +Shows that the Fourier spectrum of a perturbed field on a flux surface is asymmetric and depends on the magnetic working coordinate, so the raw spectrum is not by itself a physical measure of the field. Motivates normalizing the resonant harmonic by the scalar surface area to obtain the coordinate-independent resonant field — see the [Conventions Reference](conventions.md). + +--- + > M. Pharr, E. Bursch, N. C. Logan, P. Lunia, J.-K. Park, and C. Paz-Soldan, "Coordinate-invariant flux-surface Fourier analysis in tokamaks," > Preprint (2026). > [arXiv:2606.02901](https://arxiv.org/abs/2606.02901) diff --git a/docs/src/conventions.md b/docs/src/conventions.md index f794aa7b7..801f8f564 100644 --- a/docs/src/conventions.md +++ b/docs/src/conventions.md @@ -219,7 +219,11 @@ b^r = \frac{\Phi^r}{A^r} \qquad [\mathrm{T}]. Dividing the resonant flux ``\Phi^r`` by the surface area turns it into a field amplitude in Tesla that is invariant under changes of the poloidal-angle (working) coordinate. This is the quantity -reported as `resonant_flux`. +reported as `resonant_flux`. The need for this normalization is the central point of Park, Boozer, +and Menard (2008) (see [Citations](citations.md)): the raw Fourier spectrum of the perturbed field is +*spectrally asymmetric* and changes with the magnetic working coordinate, so only the resonant +harmonic scaled by the scalar surface area ``A^r`` is a coordinate-independent physical measure of +the resonant field. Note that there is strictly NO resonant field in ideal MHD perturbed equilibrium calculations, and only the effective resonant field is non-zero in these cases. Effective resonant fields are computed @@ -273,11 +277,10 @@ b_m = \oint (\mathbf{b}\cdot\hat{\mathbf n})\, e^{-i m\theta}\, d\theta, \qquad Only the **square-root-area weighting** ``\tilde b`` transforms unitarily between working coordinates, so its 2-norm (and quantities derived from it, such as the singular values of the resonant coupling matrix) -are coordinate-invariant. The **full-area weighting** ``\bar b`` is coordinate-invariant for the +are coordinate-invariant. Note that the "root-area-weighted field" sometimes appears as "power-normalized +field" in early GPEC literature, as the latter names a Parseval *property* of ``\tilde b``. The **full-area weighting** ``\bar b`` is coordinate-invariant for the pitch-resonant ``m = nq`` harmonic on a rational surface — the **resonant area-weighted field** -``\bar b^{\,r} = \Phi^r/A^r``. The term "root-area-weighted field" is preferred over "power-normalized -field": the latter names a Parseval *property* of ``\tilde b`` rather than the weighting itself, and is -not the term used by Pharr (2026). +``\bar b^{\,r} = \Phi^r/A^r`` as described above. GPEC operates and outputs **only in these field representations — poloidal flux ``\Phi`` (weber) is never stored.** Flux appears, briefly, only internally when a user supplies flux-valued forcing, and is From 9af92e372be2713caf281dbff23dc8f1c3207a25 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Sun, 21 Jun 2026 16:47:52 -0400 Subject: [PATCH 082/135] DOCS - MINOR - Add Park (2008) spectral-asymmetry reference to CLAUDE.md Co-Authored-By: Claude Opus 4.8 (1M context) --- CLAUDE.md | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/CLAUDE.md b/CLAUDE.md index b4878bfc0..bb7a65689 100644 --- a/CLAUDE.md +++ b/CLAUDE.md @@ -61,6 +61,11 @@ The PerturbedEquilibrium module implements GPEC-style perturbed equilibrium calc - Published: Physical Review Letters **99**, 195003 (2007) - Describes: Plasma response to resonant magnetic perturbations (RMP) +- **Park et al. (2008)**: "Spectral asymmetry due to magnetic coordinates" + - Location: `docs/resources/2008-Park-Spectral_asymmetry_due_to_magnetic_coordinates.pdf` + - Published: Physics of Plasmas **15**, 064501 (2008) + - Describes: Coordinate-dependence of the perturbed-field Fourier spectrum, motivating area-normalization of the resonant harmonic to obtain the coordinate-invariant resonant field + - **Park et al. (2009)**: "Importance of plasma response to nonaxisymmetric perturbations in tokamaks" - Location: `docs/resources/2009-Park-Importance_of_plasma_response_to_nonaxisymmetric_perturbations_in_tokamaks-compressed.pdf` - Published: Physics of Plasmas **16**, 056115 (2009) From 31aca7e4aa4fd535f2434928f21de1d8636ec4fb Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Sun, 21 Jun 2026 16:52:44 -0400 Subject: [PATCH 083/135] DOCS - BUG FIX - Fix typos in documentation prose and a code example - conventions.md: "cooridante" -> "coordinate" - citations.md: doubled "the the" -> "the" - equilibrium.md: "Solev'ev" -> "Solovev"; "SolevevConfig" -> "SolovevConfig" (matches the real struct name); "lorcfg" -> "larcfg" in a runnable example - set_up.md: "for you installation" -> "for your installation" Co-Authored-By: Claude Opus 4.8 (1M context) --- docs/src/citations.md | 2 +- docs/src/conventions.md | 2 +- docs/src/equilibrium.md | 6 +++--- docs/src/set_up.md | 2 +- 4 files changed, 6 insertions(+), 6 deletions(-) diff --git a/docs/src/citations.md b/docs/src/citations.md index a9bc62365..dfb65fb65 100644 --- a/docs/src/citations.md +++ b/docs/src/citations.md @@ -171,4 +171,4 @@ Provides the complete theory and implementation details, including NTV in the pr > *Physics of Plasmas* **24**, 032505 (2017). > DOI: [10.1063/1.4977898](https://doi.org/10.1063/1.4977898) -Describes the fully self-consistent coupling between the perturbed equilibrium and neoclassical toroidal viscosity (NTV), providing the theoretical foundation for the the KineticForces functionality. +Describes the fully self-consistent coupling between the perturbed equilibrium and neoclassical toroidal viscosity (NTV), providing the theoretical foundation for the KineticForces functionality. diff --git a/docs/src/conventions.md b/docs/src/conventions.md index 801f8f564..268fde014 100644 --- a/docs/src/conventions.md +++ b/docs/src/conventions.md @@ -57,7 +57,7 @@ kernel ``\exp(-im\theta)``; the inverse transform reconstructs with ``\exp(+im\t ### Toroidal Coordinate ``\zeta`` and ``\phi`` -- The magnetic cooridante toroidal angle is ``\zeta = \phi/(2\pi) + \nu(\psi,\theta)``, where ``\nu`` is +- The magnetic coordinate toroidal angle is ``\zeta = \phi/(2\pi) + \nu(\psi,\theta)``, where ``\nu`` is a single-valued straight-field-line offset that depends on the working coordinate. PEST coordinates have ``\nu = 0``. - The physical toroidal angle is reconstructed as diff --git a/docs/src/equilibrium.md b/docs/src/equilibrium.md index 76f4cfc00..eefd99835 100644 --- a/docs/src/equilibrium.md +++ b/docs/src/equilibrium.md @@ -12,7 +12,7 @@ Key responsibilities of the module: - Read equilibrium input files and TOML configuration (see `EquilibriumConfig`). - Provide convenient constructors for analytic / model equilibria (Large - Aspect Ratio, Solev'ev). + Aspect Ratio, Solovev). - Build spline representations used throughout the code (1D cubic and 2D bicubic splines). - Run the direct or inverse equilibrium solver and post-process results @@ -89,7 +89,7 @@ Modules = [GeneralizedPerturbedEquilibrium.Equilibrium] - `PlasmaEquilibrium` — the runtime structure containing spline fields, geometry, profiles, and computed diagnostics (q-profile, separatrix, etc.). -- `LargeAspectRatioConfig`, `SolevevConfig` — convenience structs to +- `LargeAspectRatioConfig`, `SolovevConfig` — convenience structs to construct analytic/model equilibria when using `eq_type = "lar"` or `eq_type = "sol"`. @@ -134,7 +134,7 @@ using GeneralizedPerturbedEquilibrium larcfg = GeneralizedPerturbedEquilibrium.Equilibrium.LargeAspectRatioConfig(lar_r0=10.0, lar_a=1.0, beta0=1e-3) pe = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(control=Dict("eq_filename"=>"unused","eq_type"=>"lar")), larcfg) -println("Built LAR equilibrium with a = ", lorcfg.lar_a) +println("Built LAR equilibrium with a = ", larcfg.lar_a) ``` ## Notes and Caveats diff --git a/docs/src/set_up.md b/docs/src/set_up.md index 4d7614ae7..38c9dcebf 100644 --- a/docs/src/set_up.md +++ b/docs/src/set_up.md @@ -46,7 +46,7 @@ sudo mv julia-1.11.3 /opt/ ``` - ☆ Ensure these commands match the tarball you installed. These commands match the above tarball and might need to be modified for you installation. + ☆ Ensure these commands match the tarball you installed. These commands match the above tarball and might need to be modified for your installation. 3. Add Julia to PATH: From 65a9b3e0baf6dbc6449a9642a355c9cc8840227d Mon Sep 17 00:00:00 2001 From: d-burg Date: Sun, 21 Jun 2026 17:14:28 -0400 Subject: [PATCH 084/135] EXAMPLE - NEW FEATURE - DIIID kinetic profiles + NTV demo; ldp/mpsi=256 grid Co-Authored-By: Claude Opus 4.8 --- .../TkMkr_D3Dlike_Hmode.geqdsk | 27392 ++++++++-------- .../TkMkr_D3Dlike_Hmode_kinetic.gpeckf | 515 + examples/DIIID-like_ideal_example/gpec.toml | 28 +- 3 files changed, 14192 insertions(+), 13743 deletions(-) create mode 100644 examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode_kinetic.gpeckf diff --git a/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk b/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk index 41a07c2de..28a500157 100644 --- a/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk +++ b/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk @@ -1,13741 +1,13653 @@ tMaker: 0 257 257 - 0.159500003E+01 0.285999990E+01 0.167955351E+01 0.877499998E+00 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0.902841166E-01 0.928697437E-01 0.953818709E-01 0.978204980E-01 0.100185618E+00 - 0.102477245E+00 0.104695365E+00 0.106839977E+00 0.108911097E+00 0.110808104E+00 - 0.112393476E+00 0.114054963E+00 0.115584724E+00 0.116982751E+00 0.118249044E+00 - 0.119383603E+00 0.120386429E+00 0.121257529E+00 0.121996887E+00 0.122608922E+00 - 0.123114921E+00 0.123472385E+00 0.123681329E+00 0.123741753E+00 0.123653650E+00 - 0.123417020E+00 0.123031870E+00 0.122498192E+00 0.121833645E+00 0.121227525E+00 - 0.120184958E+00 0.118985981E+00 0.117670640E+00 0.116238944E+00 0.114690885E+00 - 0.113026462E+00 0.111245677E+00 0.109348536E+00 0.107335031E+00 0.105250485E+00 - 0.103119627E+00 0.100936159E+00 0.987000912E-01 0.964114219E-01 0.940701514E-01 - 0.916762799E-01 0.892297998E-01 0.867307186E-01 0.845277905E-01 0.822871178E-01 - 0.797044113E-01 0.771076381E-01 0.744967908E-01 0.718718693E-01 0.692328811E-01 - 0.665798187E-01 0.639126748E-01 0.612314679E-01 0.585229322E-01 0.557996146E-01 - 0.531145483E-01 0.504435040E-01 0.477775000E-01 0.451165400E-01 0.424606279E-01 - 0.398097560E-01 0.371639319E-01 0.345231481E-01 0.318874083E-01 0.292508006E-01 - 0.266229976E-01 0.240076091E-01 0.214046333E-01 0.188140720E-01 0.162359253E-01 - 0.136701912E-01 0.111168716E-01 0.857596565E-02 0.603826717E-02 0.353089371E-02 - 0.105648022E-02-0.139583647E-02-0.382605661E-02-0.623418018E-02-0.862020720E-02 --0.109841367E-01-0.133259706E-01-0.156457070E-01-0.179441236E-01-0.202259533E-01 --0.224804841E-01-0.247077160E-01-0.269076489E-01-0.290802829E-01-0.312256180E-01 --0.333436541E-01-0.354343876E-01-0.374986231E-01-0.395367891E-01-0.415418483E-01 --0.435137972E-01-0.454526357E-01-0.473583676E-01-0.492309928E-01-0.510705076E-01 --0.528769121E-01-0.546304174E-01-0.562613197E-01-0.580123402E-01-0.597252697E-01 --0.613357984E-01-0.629120395E-01-0.644539818E-01-0.659616441E-01-0.674350038E-01 --0.688740835E-01-0.702788681E-01-0.716493577E-01-0.729897618E-01-0.743020251E-01 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--0.123012654E+00-0.123818897E+00-0.124643281E+00-0.125485823E+00-0.126346499E+00 --0.127286270E+00-0.128264889E+00-0.129176274E+00-0.130118862E+00-0.131092638E+00 --0.132097617E+00-0.133133784E+00-0.134201154E+00-0.135299727E+00-0.136429489E+00 --0.137590438E+00-0.138928860E+00-0.140170455E+00-0.141452700E+00-0.142775595E+00 --0.144139126E+00-0.145543322E+00-0.146988153E+00-0.148473620E+00-0.149999753E+00 --0.151566520E+00-0.153145283E+00-0.154759675E+00-0.156414121E+00-0.158108607E+00 --0.159843147E+00-0.161617726E+00-0.163432345E+00-0.165287018E+00-0.167181730E+00 --0.169016421E+00-0.170954078E+00-0.172963977E+00-0.175002649E+00-0.177070066E+00 --0.179166228E+00-0.181291163E+00-0.183444843E+00-0.185627267E+00-0.187838465E+00 --0.190002963E+00-0.192113608E+00-0.194362342E+00-0.196624547E+00-0.198900208E+00 --0.201189324E+00-0.203491911E+00-0.205807954E+00-0.208137453E+00-0.210480422E+00 --0.212838039E+00-0.215215459E+00-0.217592835E+00-0.219970196E+00-0.222347513E+00 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0.929293111E-01 0.908238366E-01 0.886657536E-01 0.864550695E-01 0.841917843E-01 - 0.818857774E-01 0.795454383E-01 0.771453306E-01 0.747311488E-01 0.723028928E-01 - 0.698605627E-01 0.674041659E-01 0.649336874E-01 0.624491423E-01 0.599505231E-01 - 0.574450418E-01 0.549126714E-01 0.523704328E-01 0.498332344E-01 0.473010801E-01 - 0.447739698E-01 0.422519036E-01 0.397348851E-01 0.372229069E-01 0.347159728E-01 - 0.322116204E-01 0.296904165E-01 0.271784570E-01 0.246789102E-01 0.221917797E-01 - 0.197170619E-01 0.172547568E-01 0.148048671E-01 0.123673901E-01 0.994232763E-02 - 0.753108272E-02 0.512103830E-02 0.273309043E-02 0.367239205E-03-0.197651540E-02 --0.429817336E-02-0.659773452E-02-0.887519866E-02-0.111305667E-01-0.133638382E-01 --0.155894384E-01-0.178024322E-01-0.199881289E-01-0.221465249E-01-0.242776219E-01 --0.263814200E-01-0.284579173E-01-0.305071175E-01-0.325290188E-01-0.345245227E-01 --0.365053527E-01-0.384604074E-01-0.403823555E-01-0.422711931E-01-0.441269204E-01 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0.110217385E+00 0.109849259E+00 0.109385535E+00 0.108749457E+00 0.108019419E+00 - 0.107169449E+00 0.106203124E+00 0.105120435E+00 0.103921384E+00 0.102605976E+00 - 0.101174206E+00 0.996547639E-01 0.981108174E-01 0.964964703E-01 0.948015600E-01 - 0.930240974E-01 0.911940411E-01 0.893113762E-01 0.873761103E-01 0.853882357E-01 - 0.833477676E-01 0.812690780E-01 0.791588128E-01 0.770071894E-01 0.747939572E-01 - 0.725423247E-01 0.702766180E-01 0.679968372E-01 0.657029822E-01 0.633950606E-01 - 0.610730611E-01 0.587385781E-01 0.563865155E-01 0.540158153E-01 0.516150668E-01 - 0.492129438E-01 0.468158610E-01 0.444238260E-01 0.420368314E-01 0.396548808E-01 - 0.372779779E-01 0.348953456E-01 0.325084291E-01 0.301173795E-01 0.277173594E-01 - 0.253296308E-01 0.229543168E-01 0.205914136E-01 0.182409268E-01 0.159028526E-01 - 0.135772033E-01 0.112598911E-01 0.894810259E-02 0.663990481E-02 0.434048986E-02 - 0.206317217E-02-0.192049090E-03-0.242517376E-02-0.463620154E-02-0.682513276E-02 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0.924678966E-01 0.940418020E-01 0.955300108E-01 0.968864858E-01 0.981112346E-01 - 0.992042422E-01 0.100188494E+00 0.101088166E+00 0.101897232E+00 0.102615692E+00 - 0.103243545E+00 0.103806272E+00 0.104245640E+00 0.104536481E+00 0.104678802E+00 - 0.104672588E+00 0.104571179E+00 0.104372598E+00 0.104071938E+00 0.103651039E+00 - 0.103105806E+00 0.102473482E+00 0.101754509E+00 0.100937948E+00 0.100005016E+00 - 0.989557281E-01 0.977900848E-01 0.965327397E-01 0.952101499E-01 0.938171521E-01 - 0.923537388E-01 0.908199325E-01 0.892166793E-01 0.875568241E-01 0.858443677E-01 - 0.840793177E-01 0.822616518E-01 0.803906098E-01 0.784775168E-01 0.765230581E-01 - 0.745272338E-01 0.724900514E-01 0.704084709E-01 0.683053136E-01 0.661880821E-01 - 0.640567765E-01 0.619097240E-01 0.597351715E-01 0.575419813E-01 0.553301536E-01 - 0.530996807E-01 0.508505665E-01 0.485848524E-01 0.463228412E-01 0.440658778E-01 - 0.418139584E-01 0.395621248E-01 0.373007655E-01 0.350352749E-01 0.327656530E-01 - 0.304918997E-01 0.282136425E-01 0.259377304E-01 0.236742310E-01 0.214231461E-01 - 0.191844758E-01 0.169542581E-01 0.147284167E-01 0.125080999E-01 0.102933077E-01 - 0.808403920E-02 0.587955350E-02 0.369076896E-02 0.152408099E-02-0.620510313E-03 --0.274300482E-02-0.485226512E-02-0.694962963E-02-0.903428625E-02-0.111062359E-01 --0.131654777E-01-0.152131934E-01-0.172369611E-01-0.192334298E-01-0.212025996E-01 --0.231449213E-01-0.250691921E-01-0.269754063E-01-0.288635623E-01-0.307336617E-01 --0.325857028E-01-0.344202705E-01-0.362226181E-01-0.379918553E-01-0.397279859E-01 --0.414331667E-01-0.431173630E-01-0.447802581E-01-0.464218445E-01-0.480421335E-01 --0.496419072E-01-0.512175038E-01-0.527588055E-01-0.542658195E-01-0.557385422E-01 --0.571821928E-01-0.586058423E-01-0.600084886E-01-0.613901354E-01-0.627507791E-01 --0.640920401E-01-0.654086769E-01-0.666957349E-01-0.679532140E-01-0.691811219E-01 --0.703904256E-01-0.715823993E-01-0.727555975E-01-0.739068538E-01-0.750365630E-01 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0.644343048E-01 0.624505132E-01 0.604348332E-01 0.584005117E-01 - 0.563475490E-01 0.542759486E-01 0.521857068E-01 0.500768237E-01 0.479492992E-01 - 0.458220243E-01 0.437001325E-01 0.415678211E-01 0.394278876E-01 0.372838229E-01 - 0.351356268E-01 0.329832993E-01 0.308268387E-01 0.286662467E-01 0.265032072E-01 - 0.243515261E-01 0.222119205E-01 0.200720280E-01 0.179376584E-01 0.158088133E-01 - 0.136854919E-01 0.115676951E-01 0.945542194E-02 0.734867295E-02 0.525002927E-02 - 0.317187468E-02 0.111359730E-02-0.933917123E-03-0.296872412E-02-0.499082357E-02 --0.700021582E-02-0.899690017E-02-0.109808780E-01-0.129521480E-01-0.149079012E-01 --0.168370567E-01-0.187426265E-01-0.206310283E-01-0.225013737E-01-0.243536606E-01 --0.261878911E-01-0.280040633E-01-0.298021790E-01-0.315828025E-01-0.333419032E-01 --0.350678973E-01-0.367654227E-01-0.384415947E-01-0.400964655E-01-0.417300314E-01 --0.433422923E-01-0.449332520E-01-0.465029068E-01-0.480543412E-01-0.495802984E-01 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0.889143571E-01 0.879606754E-01 0.869367048E-01 0.858424380E-01 0.846778825E-01 - 0.834430382E-01 0.821378976E-01 0.807624683E-01 0.793350041E-01 0.778555125E-01 - 0.763347447E-01 0.747726858E-01 0.731693432E-01 0.715247169E-01 0.698388070E-01 - 0.681116059E-01 0.663431287E-01 0.645333827E-01 0.626993403E-01 0.608415194E-01 - 0.589651018E-01 0.570700839E-01 0.551564731E-01 0.532242656E-01 0.512734577E-01 - 0.493040569E-01 0.473160557E-01 0.453119278E-01 0.432971530E-01 0.412782654E-01 - 0.392552689E-01 0.372281559E-01 0.351969339E-01 0.331616029E-01 0.311221574E-01 - 0.290786009E-01 0.270309318E-01 0.249807909E-01 0.229320507E-01 0.208888557E-01 - 0.188512057E-01 0.168191008E-01 0.147925401E-01 0.127715254E-01 0.107560549E-01 - 0.874612946E-02 0.674174912E-02 0.474489480E-02 0.275987643E-02 0.787570199E-03 --0.117202371E-02-0.311890524E-02-0.505307456E-02-0.697453134E-02-0.888327602E-02 --0.107793082E-01-0.126626724E-01-0.145332450E-01-0.163857955E-01-0.182202905E-01 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0.863559693E-01 0.869821161E-01 0.875217691E-01 0.879745856E-01 0.883358568E-01 - 0.886042714E-01 0.887798369E-01 0.888625458E-01 0.888523981E-01 0.887540281E-01 - 0.885707438E-01 0.882989839E-01 0.879387408E-01 0.874900222E-01 0.869528130E-01 - 0.863296762E-01 0.856387913E-01 0.848765150E-01 0.840387717E-01 0.831307322E-01 - 0.821524039E-01 0.811037868E-01 0.799960196E-01 0.788244829E-01 0.775873512E-01 - 0.763012320E-01 0.749721453E-01 0.735859349E-01 0.721555576E-01 0.706838965E-01 - 0.691709444E-01 0.676172525E-01 0.660266727E-01 0.643942356E-01 0.627230406E-01 - 0.610352196E-01 0.593195148E-01 0.575691164E-01 0.558001213E-01 0.540125296E-01 - 0.522063375E-01 0.503815711E-01 0.485359430E-01 0.466683656E-01 0.447880737E-01 - 0.429040380E-01 0.410033017E-01 0.390908048E-01 0.371741988E-01 0.352534764E-01 - 0.333286487E-01 0.313979685E-01 0.294589531E-01 0.275118649E-01 0.255710240E-01 - 0.236266106E-01 0.216841139E-01 0.197424609E-01 0.178002194E-01 0.158635229E-01 - 0.139323715E-01 0.120067643E-01 0.100868540E-01 0.817217026E-02 0.626201648E-02 - 0.435614772E-02 0.245735096E-02 0.571266632E-03-0.130210526E-02-0.316276494E-02 --0.501134666E-02-0.685244193E-02-0.868486799E-02-0.105040008E-01-0.123050073E-01 --0.140979998E-01-0.158784520E-01-0.176408459E-01-0.193851832E-01-0.211114623E-01 --0.228219815E-01-0.245203841E-01-0.262051169E-01-0.278680697E-01-0.295131058E-01 --0.311469249E-01-0.327612646E-01-0.343543068E-01-0.359260589E-01-0.374765098E-01 --0.390105955E-01-0.405292138E-01-0.420311503E-01-0.435072929E-01-0.449688695E-01 --0.464158989E-01-0.478419438E-01-0.492470004E-01-0.506310761E-01-0.519941747E-01 --0.533440225E-01-0.546771623E-01-0.559933707E-01-0.572915114E-01-0.585716441E-01 --0.598358847E-01-0.610842258E-01-0.623166710E-01-0.635332242E-01-0.647347942E-01 --0.659231097E-01-0.670972690E-01-0.682572946E-01-0.694031715E-01-0.705349073E-01 --0.716523901E-01-0.727599710E-01-0.738593936E-01-0.749478713E-01-0.760253146E-01 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0.598071739E-01 0.615620427E-01 0.632667542E-01 0.649213046E-01 0.665256903E-01 - 0.680799186E-01 0.695805028E-01 0.710150450E-01 0.723860487E-01 0.736911669E-01 - 0.749304071E-01 0.761037543E-01 0.772112310E-01 0.782430246E-01 0.791871548E-01 - 0.800525546E-01 0.808392316E-01 0.815471858E-01 0.821764171E-01 0.827226043E-01 - 0.831986219E-01 0.835907683E-01 0.838900581E-01 0.840964913E-01 0.842100754E-01 - 0.842657089E-01 0.842290819E-01 0.841103718E-01 0.839198530E-01 0.836408511E-01 - 0.832733661E-01 0.828174055E-01 0.822883546E-01 0.816952586E-01 0.810376629E-01 - 0.803155601E-01 0.795228109E-01 0.786641687E-01 0.777399167E-01 0.767500773E-01 - 0.756946281E-01 0.745756924E-01 0.734121650E-01 0.722045153E-01 0.709527433E-01 - 0.696564168E-01 0.683165267E-01 0.669347867E-01 0.655111894E-01 0.640457347E-01 - 0.625384301E-01 0.609959625E-01 0.594304204E-01 0.578393377E-01 0.562227145E-01 - 0.545815714E-01 0.529189222E-01 0.512343273E-01 0.495277904E-01 0.477993041E-01 - 0.460488759E-01 0.442858636E-01 0.425124206E-01 0.407273062E-01 0.389305167E-01 - 0.371253341E-01 0.353127085E-01 0.334920101E-01 0.316632353E-01 0.298263859E-01 - 0.279824957E-01 0.261399504E-01 0.242896583E-01 0.224394575E-01 0.205911733E-01 - 0.187448040E-01 0.169003494E-01 0.150580481E-01 0.132172909E-01 0.113803688E-01 - 0.954797678E-02 0.772011513E-02 0.589678343E-02 0.407798216E-02 0.226634508E-02 - 0.465888006E-03-0.132589985E-02-0.310901855E-02-0.488346815E-02-0.664924877E-02 --0.840322673E-02-0.101456549E-01-0.118775470E-01-0.135989049E-01-0.153062930E-01 --0.169987343E-01-0.186775047E-01-0.203426033E-01-0.219940320E-01-0.236317571E-01 --0.252522156E-01-0.268589184E-01-0.284518637E-01-0.300309639E-01-0.315908492E-01 --0.331337452E-01-0.346599594E-01-0.361694954E-01-0.376623496E-01-0.391377956E-01 --0.405964479E-01-0.420407355E-01-0.434706621E-01-0.448850058E-01-0.462800376E-01 --0.476583615E-01-0.490199849E-01-0.503649004E-01-0.516931079E-01-0.530059151E-01 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0.225696582E-01 0.246624667E-01 0.267477669E-01 0.288255569E-01 0.308958385E-01 - 0.329586081E-01 0.349978805E-01 0.370148569E-01 0.390098542E-01 0.409818627E-01 - 0.429309756E-01 0.448604412E-01 0.467702672E-01 0.486529209E-01 0.504969284E-01 - 0.523035154E-01 0.540794060E-01 0.558118634E-01 0.575120263E-01 0.591625646E-01 - 0.607628562E-01 0.623129010E-01 0.638148636E-01 0.652629584E-01 0.666534826E-01 - 0.679878816E-01 0.692628920E-01 0.704720169E-01 0.716152638E-01 0.726915374E-01 - 0.736966282E-01 0.746278092E-01 0.754953995E-01 0.762851685E-01 0.769962072E-01 - 0.776290298E-01 0.781907439E-01 0.786832720E-01 0.791062936E-01 0.794364661E-01 - 0.796780214E-01 0.798499659E-01 0.799448118E-01 0.799644887E-01 0.799045265E-01 - 0.797729716E-01 0.795752108E-01 0.792889670E-01 0.789185911E-01 0.784877911E-01 - 0.779924914E-01 0.774277598E-01 0.767962709E-01 0.760995075E-01 0.753410086E-01 - 0.745328590E-01 0.736590996E-01 0.727197528E-01 0.717213005E-01 0.706792101E-01 - 0.695925951E-01 0.684546530E-01 0.672739148E-01 0.660482496E-01 0.647863522E-01 - 0.634878799E-01 0.621475652E-01 0.607653931E-01 0.593477599E-01 0.579044931E-01 - 0.564340428E-01 0.549325235E-01 0.534088835E-01 0.518596135E-01 0.502913259E-01 - 0.487019308E-01 0.470905937E-01 0.454570204E-01 0.438058451E-01 0.421429910E-01 - 0.404659584E-01 0.387752131E-01 0.370748714E-01 0.353644937E-01 0.336459614E-01 - 0.319193527E-01 0.301846713E-01 0.284422506E-01 0.266933683E-01 0.249374229E-01 - 0.231795199E-01 0.214235336E-01 0.196694620E-01 0.179115273E-01 0.161521118E-01 - 0.143949045E-01 0.126392972E-01 0.108843073E-01 0.913384743E-02 0.738791749E-02 - 0.564667163E-02 0.391118834E-02 0.218207436E-02 0.457726506E-03-0.125874695E-02 --0.296655134E-02-0.466596521E-02-0.636034971E-02-0.804419909E-02-0.971831195E-02 --0.113832355E-01-0.130358543E-01-0.146763828E-01-0.163081754E-01-0.179263018E-01 --0.195307564E-01-0.211233571E-01-0.227054786E-01-0.242738463E-01-0.258296020E-01 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0.759535804E-01 0.759534240E-01 0.758836940E-01 0.757449195E-01 0.755368248E-01 - 0.752609968E-01 0.749158636E-01 0.744990185E-01 0.740175396E-01 0.734745711E-01 - 0.728719607E-01 0.722095892E-01 0.714920759E-01 0.707231089E-01 0.698998496E-01 - 0.690230280E-01 0.680913627E-01 0.671103448E-01 0.660818890E-01 0.650108457E-01 - 0.638974532E-01 0.627435893E-01 0.615529418E-01 0.603321567E-01 0.590738803E-01 - 0.577776730E-01 0.564498268E-01 0.550906248E-01 0.537028611E-01 0.522893667E-01 - 0.508500971E-01 0.493882447E-01 0.479050688E-01 0.464098081E-01 0.448885933E-01 - 0.433481112E-01 0.417918451E-01 0.402185507E-01 0.386316366E-01 0.370315947E-01 - 0.354191288E-01 0.337967277E-01 0.321663246E-01 0.305338074E-01 0.288867764E-01 - 0.272315554E-01 0.255699046E-01 0.239043012E-01 0.222381037E-01 0.205675885E-01 - 0.188934915E-01 0.172180720E-01 0.155413589E-01 0.138641307E-01 0.121880984E-01 - 0.105140656E-01 0.884530321E-02 0.717802485E-02 0.551265478E-02 0.385048171E-02 - 0.219300110E-02 0.540388050E-03-0.110169081E-02-0.273956335E-02-0.437350851E-02 --0.599728897E-02-0.761446031E-02-0.922342390E-02-0.108243749E-01-0.124168126E-01 --0.139998598E-01-0.155730769E-01-0.171305574E-01-0.186840724E-01-0.202243943E-01 --0.217526592E-01-0.232702978E-01-0.247765463E-01-0.262718778E-01-0.277554207E-01 --0.292273052E-01-0.306860059E-01-0.321274586E-01-0.335661471E-01-0.349854901E-01 --0.363930874E-01-0.377884619E-01-0.391720608E-01-0.405441076E-01-0.419039018E-01 --0.432522781E-01-0.445873216E-01-0.459073186E-01-0.472180173E-01-0.485177599E-01 --0.498105064E-01-0.510901958E-01-0.523557737E-01-0.536110848E-01-0.548566133E-01 --0.560929850E-01-0.573201962E-01-0.585389063E-01-0.597494654E-01-0.609516986E-01 --0.621447898E-01-0.633317083E-01-0.645083189E-01-0.656782389E-01-0.668417290E-01 --0.680000708E-01-0.691529512E-01-0.703013614E-01-0.714459792E-01-0.725852847E-01 --0.737220794E-01-0.748544782E-01-0.759831369E-01-0.771095306E-01-0.782347992E-01 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0.610636286E-01 0.622224472E-01 0.633239746E-01 0.643694103E-01 0.653523654E-01 - 0.662725195E-01 0.671319589E-01 0.679263994E-01 0.686538219E-01 0.693180859E-01 - 0.699156374E-01 0.704425275E-01 0.709040910E-01 0.712994635E-01 0.716229603E-01 - 0.718791112E-01 0.720700920E-01 0.721906349E-01 0.722428039E-01 0.722331554E-01 - 0.721558183E-01 0.720105916E-01 0.718035251E-01 0.715319216E-01 0.711956397E-01 - 0.708002523E-01 0.703458712E-01 0.698318407E-01 0.692626834E-01 0.686400682E-01 - 0.679631978E-01 0.672336966E-01 0.664553419E-01 0.656277090E-01 0.647525117E-01 - 0.638321415E-01 0.628682822E-01 0.618623793E-01 0.608182549E-01 0.597363412E-01 - 0.586177930E-01 0.574646890E-01 0.562776774E-01 0.550593063E-01 0.538105629E-01 - 0.525323153E-01 0.512272939E-01 0.498968847E-01 0.485427529E-01 0.471661612E-01 - 0.457686037E-01 0.443505123E-01 0.429137237E-01 0.414597765E-01 0.399887152E-01 - 0.385015979E-01 0.370009840E-01 0.354874842E-01 0.339612998E-01 0.324250795E-01 - 0.308790244E-01 0.293232426E-01 0.277597904E-01 0.261899028E-01 0.246127937E-01 - 0.230304766E-01 0.214443561E-01 0.198535528E-01 0.182588957E-01 0.166627672E-01 - 0.150649305E-01 0.134653198E-01 0.118667744E-01 0.102688977E-01 0.867096242E-02 - 0.707507739E-02 0.548206363E-02 0.389066641E-02 0.230316445E-02 0.720534124E-03 --0.857869396E-03-0.243162131E-02-0.399876479E-02-0.556068867E-02-0.711726211E-02 --0.866619498E-02-0.102079306E-01-0.117433574E-01-0.132699469E-01-0.147875221E-01 --0.162973683E-01-0.177979078E-01-0.192884412E-01-0.207708180E-01-0.222439133E-01 --0.237060916E-01-0.251589883E-01-0.266025886E-01-0.280348174E-01-0.294565782E-01 --0.308686830E-01-0.322693028E-01-0.336589888E-01-0.350396596E-01-0.364092998E-01 --0.377676636E-01-0.391170941E-01-0.404563695E-01-0.417843163E-01-0.431032553E-01 --0.444125310E-01-0.457108505E-01-0.469998308E-01-0.482810065E-01-0.495519787E-01 --0.508135967E-01-0.520682149E-01-0.533140823E-01-0.545515120E-01-0.557828657E-01 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0.311850682E-01 0.329881907E-01 0.347663537E-01 0.365190729E-01 0.382418185E-01 - 0.399357788E-01 0.415971950E-01 0.432254560E-01 0.448199995E-01 0.463760160E-01 - 0.478925519E-01 0.493697077E-01 0.508035794E-01 0.521925092E-01 0.535364747E-01 - 0.548323169E-01 0.560777634E-01 0.572731160E-01 0.584163330E-01 0.595039092E-01 - 0.605362579E-01 0.615123883E-01 0.624303855E-01 0.632892847E-01 0.640886500E-01 - 0.648263395E-01 0.655016974E-01 0.661161989E-01 0.666663125E-01 0.671539903E-01 - 0.675778389E-01 0.679375231E-01 0.682337657E-01 0.684664398E-01 0.686349869E-01 - 0.687408745E-01 0.687846020E-01 0.687655136E-01 0.686851814E-01 0.685443059E-01 - 0.683438629E-01 0.680837333E-01 0.677660704E-01 0.673913136E-01 0.669612959E-01 - 0.664784685E-01 0.659434199E-01 0.653562173E-01 0.647206083E-01 0.640360415E-01 - 0.633031651E-01 0.625260621E-01 0.617054515E-01 0.608420260E-01 0.599384643E-01 - 0.589964353E-01 0.580158047E-01 0.569989532E-01 0.559488870E-01 0.548653416E-01 - 0.537498072E-01 0.526045188E-01 0.514298491E-01 0.502279289E-01 0.490006171E-01 - 0.477485657E-01 0.464721024E-01 0.451744609E-01 0.438566208E-01 0.425182655E-01 - 0.411618836E-01 0.397881046E-01 0.383972488E-01 0.369909555E-01 0.355716534E-01 - 0.341387987E-01 0.326932818E-01 0.312371980E-01 0.297706500E-01 0.282941107E-01 - 0.268096067E-01 0.253179055E-01 0.238184892E-01 0.223135911E-01 0.208031777E-01 - 0.192876942E-01 0.177681986E-01 0.162462965E-01 0.147216525E-01 0.131952250E-01 - 0.116677023E-01 0.101395175E-01 0.861092936E-02 0.708333822E-02 0.555699458E-02 - 0.403246284E-02 0.251022633E-02 0.991018955E-03-0.525578682E-03-0.203769095E-02 --0.354619417E-02-0.505010923E-02-0.654927967E-02-0.804268103E-02-0.953037478E-02 --0.110121816E-01-0.124875372E-01-0.139561146E-01-0.154177370E-01-0.168719199E-01 --0.183183961E-01-0.197578631E-01-0.211887900E-01-0.226121098E-01-0.240271538E-01 --0.254339967E-01-0.268318113E-01-0.282213315E-01-0.296022054E-01-0.309743900E-01 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0.646079034E-01 0.642568022E-01 0.638551787E-01 0.634024069E-01 0.629001483E-01 - 0.623511299E-01 0.617546402E-01 0.611136667E-01 0.604285784E-01 0.597018972E-01 - 0.589324906E-01 0.581244640E-01 0.572786741E-01 0.563947149E-01 0.554763786E-01 - 0.545238778E-01 0.535375997E-01 0.525204688E-01 0.514738485E-01 0.503979027E-01 - 0.492934771E-01 0.481638759E-01 0.470087901E-01 0.458301604E-01 0.446285233E-01 - 0.434061624E-01 0.421627238E-01 0.408999920E-01 0.396195762E-01 0.383213833E-01 - 0.370065719E-01 0.356772281E-01 0.343339592E-01 0.329768024E-01 0.316075385E-01 - 0.302267168E-01 0.288353506E-01 0.274338387E-01 0.260238238E-01 0.246052966E-01 - 0.231790617E-01 0.217465833E-01 0.203077625E-01 0.188635290E-01 0.174149424E-01 - 0.159625653E-01 0.145060662E-01 0.130476877E-01 0.115870256E-01 0.101243714E-01 - 0.866123289E-02 0.719751138E-02 0.573377172E-02 0.427108398E-02 0.280944840E-02 - 0.134877616E-02-0.109763387E-03-0.156551821E-02-0.301845325E-02-0.446819328E-02 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0.584966876E-01 0.591467209E-01 0.597407632E-01 0.602789558E-01 0.607624352E-01 - 0.611879826E-01 0.615579970E-01 0.618720949E-01 0.621306188E-01 0.623313561E-01 - 0.624771826E-01 0.625678897E-01 0.626050830E-01 0.625869408E-01 0.625157282E-01 - 0.623914450E-01 0.622159615E-01 0.619888678E-01 0.617113709E-01 0.613854825E-01 - 0.610101223E-01 0.605889149E-01 0.601225980E-01 0.596099049E-01 0.590542518E-01 - 0.584567152E-01 0.578179546E-01 0.571379662E-01 0.564199984E-01 0.556657240E-01 - 0.548740961E-01 0.540481769E-01 0.531885363E-01 0.522965267E-01 0.513730235E-01 - 0.504188314E-01 0.494366139E-01 0.484266505E-01 0.473908447E-01 0.463290736E-01 - 0.452429913E-01 0.441339314E-01 0.430032350E-01 0.418507122E-01 0.406783186E-01 - 0.394875817E-01 0.382783972E-01 0.370522812E-01 0.358100086E-01 0.345528051E-01 - 0.332812406E-01 0.319953263E-01 0.306977555E-01 0.293882601E-01 0.280673001E-01 - 0.267363619E-01 0.253962632E-01 0.240469817E-01 0.226902049E-01 0.213255957E-01 - 0.199540611E-01 0.185769815E-01 0.171941929E-01 0.158065539E-01 0.144149531E-01 - 0.130201438E-01 0.116217015E-01 0.102214096E-01 0.881834514E-02 0.741385948E-02 - 0.600855378E-02 0.460341433E-02 0.319788000E-02 0.179247232E-02 0.387714827E-03 --0.101559574E-02-0.241726986E-02-0.381751382E-02-0.521475123E-02-0.660953298E-02 --0.800190680E-02-0.939038862E-02-0.107758334E-01-0.121577866E-01-0.135355527E-01 --0.149093494E-01-0.162785873E-01-0.176429637E-01-0.190031324E-01-0.203588419E-01 --0.217087697E-01-0.230545104E-01-0.243953839E-01-0.257303957E-01-0.270608384E-01 --0.283864383E-01-0.297062509E-01-0.310214348E-01-0.323317647E-01-0.336368605E-01 --0.349372216E-01-0.362331271E-01-0.375241190E-01-0.388106182E-01-0.400931537E-01 --0.413710102E-01-0.426452383E-01-0.439160243E-01-0.451831147E-01-0.464466475E-01 --0.477075540E-01-0.489657000E-01-0.502210967E-01-0.514742173E-01-0.527259074E-01 --0.539756529E-01-0.552241690E-01-0.564716868E-01-0.577186607E-01-0.589651577E-01 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0.366520062E-01 0.380820148E-01 0.394756161E-01 0.408325344E-01 0.421517082E-01 - 0.434305966E-01 0.446689203E-01 0.458660126E-01 0.470186137E-01 0.481277071E-01 - 0.491909087E-01 0.502078012E-01 0.511772595E-01 0.520974994E-01 0.529698282E-01 - 0.537913889E-01 0.545624681E-01 0.552829131E-01 0.559515804E-01 0.565678626E-01 - 0.571314469E-01 0.576423816E-01 0.581009798E-01 0.585061051E-01 0.588579997E-01 - 0.591580309E-01 0.594048426E-01 0.595984459E-01 0.597409680E-01 0.598305054E-01 - 0.598697700E-01 0.598584227E-01 0.597964674E-01 0.596855655E-01 0.595258549E-01 - 0.593184084E-01 0.590642244E-01 0.587643869E-01 0.584188327E-01 0.580284931E-01 - 0.575966425E-01 0.571218058E-01 0.566059425E-01 0.560508892E-01 0.554567724E-01 - 0.548253544E-01 0.541571267E-01 0.534527451E-01 0.527148023E-01 0.519439131E-01 - 0.511406027E-01 0.503063872E-01 0.494431406E-01 0.485503860E-01 0.476298854E-01 - 0.466830172E-01 0.457105376E-01 0.447137132E-01 0.436928608E-01 0.426503643E-01 - 0.415856875E-01 0.405007713E-01 0.393963121E-01 0.382727906E-01 0.371317305E-01 - 0.359735824E-01 0.347989164E-01 0.336097777E-01 0.324062034E-01 0.311879721E-01 - 0.299574137E-01 0.287151337E-01 0.274610873E-01 0.261965748E-01 0.249218475E-01 - 0.236381218E-01 0.223456603E-01 0.210451558E-01 0.197372474E-01 0.184225999E-01 - 0.171016846E-01 0.157757103E-01 0.144440597E-01 0.131082609E-01 0.117681213E-01 - 0.104251755E-01 0.907882955E-02 0.773007842E-02 0.637951866E-02 0.502666598E-02 - 0.367344031E-02 0.231914176E-02 0.963876897E-03-0.390852685E-03-0.174517056E-02 --0.309928111E-02-0.445212424E-02-0.580354687E-02-0.715378765E-02-0.850197393E-02 --0.984821562E-02-0.111924484E-01-0.125339190E-01-0.138730900E-01-0.152091701E-01 --0.165423919E-01-0.178726818E-01-0.191996731E-01-0.205226708E-01-0.218432564E-01 --0.231605321E-01-0.244734660E-01-0.257834978E-01-0.270901937E-01-0.283937678E-01 --0.296933558E-01-0.309898145E-01-0.322834216E-01-0.335735306E-01-0.348607562E-01 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0.574786635E-02 0.754608586E-02 0.932969619E-02 0.111004598E-01 0.128565356E-01 - 0.145973442E-01 0.163174104E-01 0.180167332E-01 0.196953118E-01 0.213531498E-01 - 0.229902435E-01 0.246041510E-01 0.261896700E-01 0.277491957E-01 0.292811114E-01 - 0.307838824E-01 0.322562568E-01 0.336969979E-01 0.351052061E-01 0.364787504E-01 - 0.378181040E-01 0.391200036E-01 0.403847657E-01 0.416104905E-01 0.427963063E-01 - 0.439415388E-01 0.450439192E-01 0.461035669E-01 0.471196137E-01 0.480916239E-01 - 0.490166619E-01 0.498956405E-01 0.507277362E-01 0.515124090E-01 0.522484258E-01 - 0.529355891E-01 0.535741225E-01 0.541635752E-01 0.547024421E-01 0.551916882E-01 - 0.556313992E-01 0.560207404E-01 0.563601665E-01 0.566499718E-01 0.568898208E-01 - 0.570808649E-01 0.572232343E-01 0.573163293E-01 0.573616661E-01 0.573589578E-01 - 0.573095307E-01 0.572141036E-01 0.570730604E-01 0.568864420E-01 0.566563718E-01 - 0.563837662E-01 0.560681373E-01 0.557104163E-01 0.553124584E-01 0.548762940E-01 - 0.544002689E-01 0.538867041E-01 0.533364713E-01 0.527510270E-01 0.521307588E-01 - 0.514770187E-01 0.507903136E-01 0.500723384E-01 0.493236147E-01 0.485452488E-01 - 0.477386191E-01 0.469038449E-01 0.460428260E-01 0.451563075E-01 0.442444682E-01 - 0.433094539E-01 0.423516743E-01 0.413714573E-01 0.403700471E-01 0.393489227E-01 - 0.383081883E-01 0.372484066E-01 0.361716039E-01 0.350780338E-01 0.339674801E-01 - 0.328422561E-01 0.317027234E-01 0.305492450E-01 0.293821339E-01 0.282022301E-01 - 0.270112269E-01 0.258087311E-01 0.245958026E-01 0.233731605E-01 0.221417658E-01 - 0.209013112E-01 0.196532682E-01 0.183968693E-01 0.171337314E-01 0.158647951E-01 - 0.145895239E-01 0.133090271E-01 0.120237349E-01 0.107338401E-01 0.944020972E-02 - 0.814269297E-02 0.684233801E-02 0.553940143E-02 0.423423341E-02 0.292668259E-02 - 0.161777833E-02 0.307449460E-03-0.100379391E-02-0.231552217E-02-0.362793193E-02 --0.494006835E-02-0.625162246E-02-0.756325759E-02-0.887396187E-02-0.101835774E-01 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0.540597402E-01 0.543442294E-01 0.545814857E-01 0.547725707E-01 0.549178943E-01 - 0.550170094E-01 0.550718717E-01 0.550808944E-01 0.550462790E-01 0.549684204E-01 - 0.548473597E-01 0.546844639E-01 0.544798970E-01 0.542349555E-01 0.539492592E-01 - 0.536248386E-01 0.532619618E-01 0.528622940E-01 0.524259396E-01 0.519537106E-01 - 0.514472313E-01 0.509065352E-01 0.503329299E-01 0.497273020E-01 0.490906462E-01 - 0.484238006E-01 0.477276295E-01 0.470029712E-01 0.462509468E-01 0.454721227E-01 - 0.446678028E-01 0.438386165E-01 0.429851934E-01 0.421086252E-01 0.412099399E-01 - 0.402896851E-01 0.393484719E-01 0.383874625E-01 0.374074541E-01 0.364088789E-01 - 0.353930779E-01 0.343597047E-01 0.333103240E-01 0.322457366E-01 0.311666057E-01 - 0.300722476E-01 0.289655160E-01 0.278458074E-01 0.267132502E-01 0.255697500E-01 - 0.244147014E-01 0.232501328E-01 0.220747702E-01 0.208901353E-01 0.196971502E-01 - 0.184963644E-01 0.172875300E-01 0.160714071E-01 0.148485582E-01 0.136196371E-01 - 0.123847080E-01 0.111445682E-01 0.989927165E-02 0.864961464E-02 0.739593012E-02 - 0.613875780E-02 0.487740990E-02 0.361328013E-02 0.234650122E-02 0.107754138E-02 --0.193900996E-03-0.146758161E-02-0.274238596E-02-0.401833095E-02-0.529546617E-02 --0.657449802E-02-0.785372313E-02-0.913298968E-02-0.104129473E-01-0.116933277E-01 --0.129736746E-01-0.142537830E-01-0.155340480E-01-0.168139637E-01-0.180939473E-01 --0.193738211E-01-0.206532106E-01-0.219321195E-01-0.232106391E-01-0.244890302E-01 --0.257674828E-01-0.270453952E-01-0.283236336E-01-0.296017230E-01-0.308799446E-01 --0.321583264E-01-0.334369019E-01-0.347161889E-01-0.359961130E-01-0.372763947E-01 --0.385577790E-01-0.398404673E-01-0.411249027E-01-0.424102433E-01-0.436978973E-01 --0.449876077E-01-0.462793894E-01-0.475740694E-01-0.488714762E-01-0.501717404E-01 --0.514757335E-01-0.527837127E-01-0.540954471E-01-0.554111600E-01-0.567319244E-01 --0.580578595E-01-0.593890734E-01-0.607263222E-01-0.620692894E-01-0.634184927E-01 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0.393469445E-01 0.404065177E-01 0.414254256E-01 0.424052291E-01 0.433439016E-01 - 0.442416072E-01 0.450975299E-01 0.459096804E-01 0.466797389E-01 0.474070758E-01 - 0.480892695E-01 0.487280078E-01 0.493220873E-01 0.498717912E-01 0.503776781E-01 - 0.508383550E-01 0.512542315E-01 0.516255163E-01 0.519524254E-01 0.522352755E-01 - 0.524739288E-01 0.526687317E-01 0.528199598E-01 0.529287495E-01 0.529947877E-01 - 0.530178584E-01 0.530002154E-01 0.529414639E-01 0.528420582E-01 0.527031347E-01 - 0.525248162E-01 0.523084998E-01 0.520546213E-01 0.517633036E-01 0.514357835E-01 - 0.510724150E-01 0.506752953E-01 0.502441414E-01 0.497792363E-01 0.492827669E-01 - 0.487548970E-01 0.481963083E-01 0.476075038E-01 0.469900705E-01 0.463448241E-01 - 0.456718206E-01 0.449724160E-01 0.442470871E-01 0.434970446E-01 0.427225605E-01 - 0.419250838E-01 0.411045551E-01 0.402618647E-01 0.393985659E-01 0.385144353E-01 - 0.376109257E-01 0.366880372E-01 0.357471369E-01 0.347883515E-01 0.338127986E-01 - 0.328210741E-01 0.318137780E-01 0.307909921E-01 0.297534764E-01 0.287028160E-01 - 0.276386738E-01 0.265620034E-01 0.254731681E-01 0.243730489E-01 0.232616775E-01 - 0.221399330E-01 0.210079104E-01 0.198670235E-01 0.187168829E-01 0.175584927E-01 - 0.163920112E-01 0.152177988E-01 0.140367066E-01 0.128487106E-01 0.116545539E-01 - 0.104543371E-01 0.924840569E-02 0.803733896E-02 0.682187453E-02 0.560153602E-02 - 0.437716395E-02 0.314867171E-02 0.191686733E-02 0.681486505E-03-0.556966465E-03 --0.179828412E-02-0.304181897E-02-0.428818446E-02-0.553693669E-02-0.678728474E-02 --0.803979766E-02-0.929394457E-02-0.105498573E-01-0.118073467E-01-0.130661987E-01 --0.143265110E-01-0.155878291E-01-0.168504380E-01-0.181145445E-01-0.193793587E-01 --0.206458736E-01-0.219135303E-01-0.231821742E-01-0.244523864E-01-0.257238038E-01 --0.269965939E-01-0.282708686E-01-0.295468364E-01-0.308245569E-01-0.321041718E-01 --0.333857760E-01-0.346695557E-01-0.359555557E-01-0.372440331E-01-0.385351218E-01 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0.137781566E-01 0.153418425E-01 0.168850087E-01 0.184038058E-01 0.198982507E-01 - 0.213683974E-01 0.228124466E-01 0.242296085E-01 0.256190225E-01 0.269795340E-01 - 0.283110756E-01 0.296109971E-01 0.308790542E-01 0.321153104E-01 0.333190300E-01 - 0.344871283E-01 0.356205516E-01 0.367189720E-01 0.377798304E-01 0.388038792E-01 - 0.397896357E-01 0.407371670E-01 0.416454561E-01 0.425139107E-01 0.433418564E-01 - 0.441296101E-01 0.448763818E-01 0.455811024E-01 0.462443978E-01 0.468664058E-01 - 0.474457927E-01 0.479825921E-01 0.484774746E-01 0.489302874E-01 0.493408144E-01 - 0.497091487E-01 0.500352830E-01 0.503195152E-01 0.505623035E-01 0.507639237E-01 - 0.509240627E-01 0.510439351E-01 0.511236377E-01 0.511639006E-01 0.511638150E-01 - 0.511256829E-01 0.510499924E-01 0.509363227E-01 0.507853106E-01 0.505979471E-01 - 0.503748730E-01 0.501169935E-01 0.498248078E-01 0.494988710E-01 0.491397418E-01 - 0.487487167E-01 0.483259000E-01 0.478720069E-01 0.473885238E-01 0.468755029E-01 - 0.463340096E-01 0.457646027E-01 0.451677963E-01 0.445446223E-01 0.438957401E-01 - 0.432220772E-01 0.425234176E-01 0.418016203E-01 0.410571843E-01 0.402900018E-01 - 0.395016521E-01 0.386919342E-01 0.378623977E-01 0.370130353E-01 0.361450687E-01 - 0.352581590E-01 0.343539864E-01 0.334324017E-01 0.324947312E-01 0.315410085E-01 - 0.305718910E-01 0.295880679E-01 0.285902563E-01 0.275786761E-01 0.265533812E-01 - 0.255161766E-01 0.244670473E-01 0.234058034E-01 0.223338343E-01 0.212511029E-01 - 0.201584455E-01 0.190557893E-01 0.179440957E-01 0.168233681E-01 0.156944189E-01 - 0.145574119E-01 0.134126516E-01 0.122606689E-01 0.111021083E-01 0.993675273E-02 - 0.876535568E-02 0.758772669E-02 0.640492653E-02 0.521662785E-02 0.402295543E-02 - 0.282511185E-02 0.162233226E-02 0.415207469E-03-0.795727421E-03-0.201069680E-02 --0.322907860E-02-0.445123995E-02-0.567661040E-02-0.690506632E-02-0.813670736E-02 --0.937163085E-02-0.106090177E-01-0.118493596E-01-0.130928438E-01-0.143383378E-01 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0.494532995E-01 0.495107025E-01 0.495321043E-01 0.495161973E-01 0.494637191E-01 - 0.493758284E-01 0.492532663E-01 0.490959063E-01 0.489046164E-01 0.486799516E-01 - 0.484229773E-01 0.481333584E-01 0.478124768E-01 0.474608205E-01 0.470790975E-01 - 0.466678776E-01 0.462271646E-01 0.457587056E-01 0.452625901E-01 0.447395630E-01 - 0.441901647E-01 0.436148755E-01 0.430146046E-01 0.423899777E-01 0.417417102E-01 - 0.410703756E-01 0.403758809E-01 0.396600403E-01 0.389226824E-01 0.381643251E-01 - 0.373862609E-01 0.365884863E-01 0.357717723E-01 0.349369794E-01 0.340840332E-01 - 0.332139805E-01 0.323268548E-01 0.314239971E-01 0.305053852E-01 0.295710973E-01 - 0.286231153E-01 0.276605953E-01 0.266841967E-01 0.256951544E-01 0.246931911E-01 - 0.236791931E-01 0.226532593E-01 0.216160212E-01 0.205682348E-01 0.195096284E-01 - 0.184412673E-01 0.173631702E-01 0.162755568E-01 0.151792439E-01 0.140745305E-01 - 0.129615376E-01 0.118405595E-01 0.107123228E-01 0.957652461E-02 0.843404047E-02 - 0.728475908E-02 0.612957263E-02 0.496769324E-02 0.379992393E-02 0.262705609E-02 - 0.144814653E-02 0.264277624E-03-0.924836029E-03-0.211913162E-02-0.331763085E-02 --0.452106399E-02-0.572932791E-02-0.694143120E-02-0.815819018E-02-0.937899575E-02 --0.106040966E-01-0.118331211E-01-0.130660897E-01-0.143031804E-01-0.155443205E-01 --0.167896897E-01-0.180389546E-01-0.192919187E-01-0.205494873E-01-0.218110699E-01 --0.230769236E-01-0.243469868E-01-0.256216545E-01-0.269005299E-01-0.281841271E-01 --0.294726267E-01-0.307659544E-01-0.320643745E-01-0.333680212E-01-0.346767642E-01 --0.359915458E-01-0.373116285E-01-0.386378989E-01-0.399703570E-01-0.413092673E-01 --0.426546782E-01-0.440069698E-01-0.453661680E-01-0.467330292E-01-0.481074862E-01 --0.494896807E-01-0.508803166E-01-0.522793606E-01-0.536873266E-01-0.551040396E-01 --0.565302782E-01-0.579663590E-01-0.594126470E-01-0.608688518E-01-0.623360388E-01 --0.638143048E-01-0.653039366E-01-0.668051913E-01-0.683188215E-01-0.698449016E-01 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0.402482785E-01 0.409979932E-01 0.417099632E-01 0.423853323E-01 0.430228412E-01 - 0.436221287E-01 0.441837870E-01 0.447072610E-01 0.451921783E-01 0.456395261E-01 - 0.460484661E-01 0.464198329E-01 0.467536785E-01 0.470499843E-01 0.473088995E-01 - 0.475307703E-01 0.477160811E-01 0.478650630E-01 0.479782224E-01 0.480555817E-01 - 0.480972901E-01 0.481047854E-01 0.480779037E-01 0.480173379E-01 0.479231067E-01 - 0.477961116E-01 0.476369858E-01 0.474457368E-01 0.472235791E-01 0.469707511E-01 - 0.466875173E-01 0.463748686E-01 0.460332446E-01 0.456630513E-01 0.452652983E-01 - 0.448397547E-01 0.443876684E-01 0.439093746E-01 0.434056409E-01 0.428768583E-01 - 0.423234366E-01 0.417461395E-01 0.411457792E-01 0.405221172E-01 0.398763120E-01 - 0.392090194E-01 0.385203995E-01 0.378113650E-01 0.370820612E-01 0.363333076E-01 - 0.355653018E-01 0.347786956E-01 0.339743011E-01 0.331525020E-01 0.323137157E-01 - 0.314582847E-01 0.305864848E-01 0.296996366E-01 0.287978221E-01 0.278812237E-01 - 0.269506387E-01 0.260061976E-01 0.250486340E-01 0.240779109E-01 0.230947230E-01 - 0.220999587E-01 0.210935809E-01 0.200758539E-01 0.190474000E-01 0.180083010E-01 - 0.169592015E-01 0.159004312E-01 0.148322321E-01 0.137546826E-01 0.126682399E-01 - 0.115738194E-01 0.104706725E-01 0.935965125E-02 0.824080966E-02 0.711490912E-02 - 0.598155800E-02 0.484105200E-02 0.369404652E-02 0.254042912E-02 0.138016080E-02 - 0.213639461E-03-0.958974590E-03-0.213773502E-02-0.332192401E-02-0.451204553E-02 --0.570806721E-02-0.690930989E-02-0.811641756E-02-0.932877883E-02-0.105463928E-01 --0.117699858E-01-0.129984319E-01-0.142322583E-01-0.154719111E-01-0.167163461E-01 --0.179666858E-01-0.192223322E-01-0.204831865E-01-0.217499305E-01-0.230223816E-01 --0.243005697E-01-0.255846363E-01-0.268745366E-01-0.281707253E-01-0.294733569E-01 --0.307822544E-01-0.320977457E-01-0.334200636E-01-0.347490869E-01-0.360853113E-01 --0.374288931E-01-0.387798920E-01-0.401386432E-01-0.415054411E-01-0.428804122E-01 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0.199598502E-01 0.212678369E-01 0.225494672E-01 0.238036513E-01 0.250298232E-01 - 0.262276977E-01 0.273955390E-01 0.285335686E-01 0.296405125E-01 0.307167936E-01 - 0.317609757E-01 0.327724889E-01 0.337510966E-01 0.346965529E-01 0.356085375E-01 - 0.364857018E-01 0.373282991E-01 0.381366536E-01 0.389098525E-01 0.396469273E-01 - 0.403483324E-01 0.410138145E-01 0.416440256E-01 0.422378741E-01 0.427950956E-01 - 0.433165058E-01 0.438016839E-01 0.442505330E-01 0.446639434E-01 0.450406596E-01 - 0.453822613E-01 0.456882641E-01 0.459585451E-01 0.461942814E-01 0.463950075E-01 - 0.465611964E-01 0.466931686E-01 0.467915013E-01 0.468560681E-01 0.468876921E-01 - 0.468871072E-01 0.468540676E-01 0.467889644E-01 0.466931090E-01 0.465659760E-01 - 0.464087091E-01 0.462214015E-01 0.460044332E-01 0.457589105E-01 0.454847366E-01 - 0.451822989E-01 0.448527262E-01 0.444962643E-01 0.441132374E-01 0.437041931E-01 - 0.432692356E-01 0.428095944E-01 0.423254743E-01 0.418172851E-01 0.412852615E-01 - 0.407304876E-01 0.401532464E-01 0.395536907E-01 0.389325470E-01 0.382904746E-01 - 0.376276001E-01 0.369447693E-01 0.362419933E-01 0.355203561E-01 0.347800031E-01 - 0.340209231E-01 0.332442783E-01 0.324504972E-01 0.316398628E-01 0.308129899E-01 - 0.299697947E-01 0.291109923E-01 0.282374732E-01 0.273487978E-01 0.264457911E-01 - 0.255291667E-01 0.245990735E-01 0.236560591E-01 0.227003209E-01 0.217318572E-01 - 0.207515098E-01 0.197600219E-01 0.187567826E-01 0.177422576E-01 0.167178679E-01 - 0.156825949E-01 0.146373296E-01 0.135827614E-01 0.125184506E-01 0.114448583E-01 - 0.103623141E-01 0.927086920E-02 0.817127060E-02 0.706333062E-02 0.594709860E-02 - 0.482295780E-02 0.369091146E-02 0.255168905E-02 0.140470709E-02 0.250659359E-03 --0.910791918E-03-0.207932619E-02-0.325454283E-02-0.443708105E-02-0.562607218E-02 --0.682226429E-02-0.802482851E-02-0.923382305E-02-0.104497708E-01-0.116725015E-01 --0.129016219E-01-0.141374543E-01-0.153805008E-01-0.166297052E-01-0.178857837E-01 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0.458464734E-01 0.457816534E-01 0.456870385E-01 0.455634072E-01 0.454109423E-01 - 0.452302843E-01 0.450216308E-01 0.447855555E-01 0.445224121E-01 0.442321971E-01 - 0.439159200E-01 0.435740948E-01 0.432068184E-01 0.428143963E-01 0.423971415E-01 - 0.419560596E-01 0.414913744E-01 0.410032757E-01 0.404923968E-01 0.399587788E-01 - 0.394033641E-01 0.388264693E-01 0.382283218E-01 0.376096666E-01 0.369706973E-01 - 0.363113396E-01 0.356329978E-01 0.349358991E-01 0.342201591E-01 0.334862620E-01 - 0.327342935E-01 0.319653600E-01 0.311796702E-01 0.303773452E-01 0.295589417E-01 - 0.287252385E-01 0.278757233E-01 0.270116180E-01 0.261331443E-01 0.252398644E-01 - 0.243334100E-01 0.234136786E-01 0.224800669E-01 0.215341859E-01 0.205763057E-01 - 0.196055975E-01 0.186234172E-01 0.176296346E-01 0.166245699E-01 0.156087270E-01 - 0.145820398E-01 0.135452254E-01 0.124979466E-01 0.114407344E-01 0.103738252E-01 - 0.929727964E-02 0.821144972E-02 0.711629400E-02 0.601235218E-02 0.489944266E-02 - 0.377787347E-02 0.264742039E-02 0.150919380E-02 0.362053048E-03-0.793551735E-03 --0.195666961E-02-0.312816817E-02-0.430784188E-02-0.549524045E-02-0.669068331E-02 --0.789437816E-02-0.910565350E-02-0.103247808E-01-0.115522295E-01-0.127874305E-01 --0.140300924E-01-0.152813978E-01-0.165408067E-01-0.178077016E-01-0.190834347E-01 --0.203674268E-01-0.216595586E-01-0.229604263E-01-0.242697187E-01-0.255876537E-01 --0.269148406E-01-0.282509122E-01-0.295959003E-01-0.309506785E-01-0.323145837E-01 --0.336882137E-01-0.350717455E-01-0.364653841E-01-0.378693938E-01-0.392838717E-01 --0.407086052E-01-0.421447977E-01-0.435923114E-01-0.450505614E-01-0.465207994E-01 --0.480031818E-01-0.494973026E-01-0.510041751E-01-0.525237657E-01-0.540562123E-01 --0.556020029E-01-0.571613684E-01-0.587344728E-01-0.603218116E-01-0.619237162E-01 --0.635402799E-01-0.651722625E-01-0.668193325E-01-0.684822723E-01-0.701614916E-01 --0.718567967E-01-0.735691339E-01-0.752985477E-01-0.770454258E-01-0.788101554E-01 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0.404937416E-01 0.410199277E-01 0.415130369E-01 0.419739932E-01 0.424019769E-01 - 0.427980684E-01 0.431616083E-01 0.434927791E-01 0.437928215E-01 0.440606773E-01 - 0.442969017E-01 0.445025787E-01 0.446769558E-01 0.448207185E-01 0.449344218E-01 - 0.450177304E-01 0.450714119E-01 0.450959057E-01 0.450911038E-01 0.450574830E-01 - 0.449958518E-01 0.449059531E-01 0.447884984E-01 0.446435027E-01 0.444714762E-01 - 0.442729406E-01 0.440480821E-01 0.437972359E-01 0.435206778E-01 0.432186909E-01 - 0.428917520E-01 0.425405242E-01 0.421648920E-01 0.417651422E-01 0.413420498E-01 - 0.408958271E-01 0.404268913E-01 0.399354734E-01 0.394220464E-01 0.388869047E-01 - 0.383305214E-01 0.377534665E-01 0.371557623E-01 0.365382135E-01 0.359007716E-01 - 0.352439135E-01 0.345685035E-01 0.338742360E-01 0.331618451E-01 0.324319415E-01 - 0.316845179E-01 0.309201162E-01 0.301389433E-01 0.293418895E-01 0.285290182E-01 - 0.277002119E-01 0.268563367E-01 0.259978753E-01 0.251246970E-01 0.242377277E-01 - 0.233365651E-01 0.224218871E-01 0.214941725E-01 0.205533672E-01 0.196000747E-01 - 0.186344013E-01 0.176563952E-01 0.166663881E-01 0.156653412E-01 0.146525977E-01 - 0.136286300E-01 0.125937564E-01 0.115481690E-01 0.104919244E-01 0.942509156E-02 - 0.834826566E-02 0.726175401E-02 0.616491120E-02 0.505782804E-02 0.394138088E-02 - 0.281570409E-02 0.168041536E-02 0.535488536E-03-0.618653547E-03-0.178175082E-02 --0.295448629E-02-0.413666572E-02-0.532749435E-02-0.652752630E-02-0.773684215E-02 --0.895516388E-02-0.101826806E-01-0.114194294E-01-0.126653584E-01-0.139204171E-01 --0.151848067E-01-0.164588187E-01-0.177421309E-01-0.190349557E-01-0.203375071E-01 --0.216497499E-01-0.229719598E-01-0.243039969E-01-0.256461091E-01-0.269984752E-01 --0.283614285E-01-0.297348462E-01-0.311189927E-01-0.325140581E-01-0.339203477E-01 --0.353376418E-01-0.367665328E-01-0.382074900E-01-0.396600217E-01-0.411242619E-01 --0.426014252E-01-0.440909863E-01-0.455930829E-01-0.471087210E-01-0.486373007E-01 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0.247593727E-01 0.258322470E-01 0.268779639E-01 0.278959312E-01 0.288843159E-01 - 0.298443995E-01 0.307757724E-01 0.316766128E-01 0.325480215E-01 0.333895050E-01 - 0.342008881E-01 0.349811167E-01 0.357303917E-01 0.364493057E-01 0.371370912E-01 - 0.377938040E-01 0.384197086E-01 0.390139930E-01 0.395770855E-01 0.401094481E-01 - 0.406108052E-01 0.410805456E-01 0.415197685E-01 0.419283435E-01 0.423057862E-01 - 0.426528379E-01 0.429698676E-01 0.432566963E-01 0.435132347E-01 0.437403694E-01 - 0.439376757E-01 0.441060029E-01 0.442453958E-01 0.443559326E-01 0.444383621E-01 - 0.444925614E-01 0.445185862E-01 0.445170142E-01 0.444881730E-01 0.444326103E-01 - 0.443499386E-01 0.442407615E-01 0.441055186E-01 0.439438634E-01 0.437566489E-01 - 0.435441434E-01 0.433062799E-01 0.430435985E-01 0.427561738E-01 0.424444228E-01 - 0.421086922E-01 0.417490676E-01 0.413657948E-01 0.409598015E-01 0.405310541E-01 - 0.400794968E-01 0.396059677E-01 0.391107500E-01 0.385940708E-01 0.380559638E-01 - 0.374972448E-01 0.369180739E-01 0.363192186E-01 0.357002579E-01 0.350621119E-01 - 0.344052091E-01 0.337296948E-01 0.330358781E-01 0.323241875E-01 0.315948278E-01 - 0.308484994E-01 0.300851669E-01 0.293051731E-01 0.285094921E-01 0.276975539E-01 - 0.268701985E-01 0.260275714E-01 0.251702014E-01 0.242983140E-01 0.234120563E-01 - 0.225117598E-01 0.215974692E-01 0.206701681E-01 0.197295416E-01 0.187752601E-01 - 0.178088360E-01 0.168300532E-01 0.158383418E-01 0.148350568E-01 0.138197513E-01 - 0.127922697E-01 0.117539782E-01 0.107037453E-01 0.964191929E-02 0.856945850E-02 - 0.748606538E-02 0.639169849E-02 0.528643047E-02 0.417049229E-02 0.304411817E-02 - 0.190710218E-02 0.759541988E-03-0.398694217E-03-0.156678690E-02-0.274523487E-02 --0.393421063E-02-0.513365213E-02-0.634304201E-02-0.756294979E-02-0.879308581E-02 --0.100336084E-01-0.112846661E-01-0.125464816E-01-0.138184708E-01-0.151007101E-01 --0.163941197E-01-0.176981892E-01-0.190127958E-01-0.203387197E-01-0.216755271E-01 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0.989944092E-03 0.244595110E-02 0.388476672E-02 0.530564226E-02 0.670827273E-02 - 0.809167884E-02 0.945554301E-02 0.107990196E-01 0.121215777E-01 0.134226596E-01 - 0.147019122E-01 0.159586184E-01 0.171923023E-01 0.184022617E-01 0.195881072E-01 - 0.207496975E-01 0.218857005E-01 0.229962785E-01 0.240814090E-01 0.251395497E-01 - 0.261711255E-01 0.271757487E-01 0.281531811E-01 0.291024074E-01 0.300235059E-01 - 0.309163202E-01 0.317808054E-01 0.326164365E-01 0.334226415E-01 0.341998115E-01 - 0.349480174E-01 0.356665403E-01 0.363554917E-01 0.370149612E-01 0.376447700E-01 - 0.382444039E-01 0.388143547E-01 0.393556021E-01 0.398667045E-01 0.403481387E-01 - 0.408002660E-01 0.412231050E-01 0.416164547E-01 0.419811234E-01 0.423168130E-01 - 0.426236652E-01 0.429019704E-01 0.431519821E-01 0.433737561E-01 0.435676463E-01 - 0.437341444E-01 0.438725092E-01 0.439839251E-01 0.440685004E-01 0.441261530E-01 - 0.441571958E-01 0.441616289E-01 0.441400856E-01 0.440924726E-01 0.440189205E-01 - 0.439199023E-01 0.437953360E-01 0.436452888E-01 0.434703045E-01 0.432704352E-01 - 0.430457294E-01 0.427967012E-01 0.425234400E-01 0.422260612E-01 0.419047438E-01 - 0.415603630E-01 0.411926433E-01 0.408017524E-01 0.403882302E-01 0.399525203E-01 - 0.394947901E-01 0.390153266E-01 0.385143533E-01 0.379924029E-01 0.374494269E-01 - 0.368860774E-01 0.363026038E-01 0.356996618E-01 0.350768268E-01 0.344350561E-01 - 0.337745734E-01 0.330956578E-01 0.323986784E-01 0.316835307E-01 0.309512764E-01 - 0.302018765E-01 0.294359699E-01 0.286533460E-01 0.278544798E-01 0.270396862E-01 - 0.262093283E-01 0.253633223E-01 0.245024357E-01 0.236269049E-01 0.227363296E-01 - 0.218318142E-01 0.209133122E-01 0.199808255E-01 0.190347210E-01 0.180750918E-01 - 0.171020608E-01 0.161162578E-01 0.151175037E-01 0.141060045E-01 0.130817099E-01 - 0.120453062E-01 0.109966751E-01 0.993582793E-02 0.886276085E-02 0.777797634E-02 - 0.668102456E-02 0.557258772E-02 0.445266580E-02 0.332047651E-02 0.217728131E-02 - 0.102243188E-02-0.144132777E-03-0.132185721E-02-0.251140958E-02-0.371213886E-02 --0.492418697E-02-0.614811853E-02-0.738320034E-02-0.862991251E-02-0.988822430E-02 --0.111583527E-01-0.124400062E-01-0.137334149E-01-0.150385341E-01-0.163556766E-01 --0.176848415E-01-0.190260168E-01-0.203796104E-01-0.217455979E-01-0.231238361E-01 --0.245146304E-01-0.259183273E-01-0.273348521E-01-0.287644453E-01-0.302074086E-01 --0.316637419E-01-0.331332721E-01-0.346168317E-01-0.361144543E-01-0.376260132E-01 --0.391519740E-01-0.406926386E-01-0.422477424E-01-0.438180827E-01-0.454039127E-01 --0.470046625E-01-0.486213155E-01-0.502540506E-01-0.519029014E-01-0.535682105E-01 --0.552502647E-01-0.569492020E-01-0.586654991E-01-0.603992864E-01-0.621508248E-01 --0.639206097E-01-0.657087639E-01-0.675156116E-01-0.693414807E-01-0.711866766E-01 --0.730514377E-01-0.749358609E-01-0.768407732E-01-0.787661150E-01-0.807127133E-01 --0.826800838E-01-0.846691877E-01-0.866800398E-01-0.887131914E-01-0.907688439E-01 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0.410912223E-01 0.414745063E-01 0.418303497E-01 0.421588980E-01 0.424603224E-01 - 0.427346304E-01 0.429819450E-01 0.432024747E-01 0.433966331E-01 0.435643494E-01 - 0.437056348E-01 0.438212901E-01 0.439111665E-01 0.439748988E-01 0.440132730E-01 - 0.440262407E-01 0.440138169E-01 0.439760275E-01 0.439130142E-01 0.438247696E-01 - 0.437115468E-01 0.435734354E-01 0.434103906E-01 0.432228744E-01 0.430109091E-01 - 0.427747071E-01 0.425142013E-01 0.422298983E-01 0.419221558E-01 0.415908135E-01 - 0.412362069E-01 0.408589616E-01 0.404587761E-01 0.400362052E-01 0.395916924E-01 - 0.391253605E-01 0.386374034E-01 0.381283201E-01 0.375981294E-01 0.370474644E-01 - 0.364768356E-01 0.358858593E-01 0.352753587E-01 0.346455947E-01 0.339965820E-01 - 0.333292633E-01 0.326435976E-01 0.319393687E-01 0.312176142E-01 0.304782260E-01 - 0.297217984E-01 0.289484560E-01 0.281584263E-01 0.273521952E-01 0.265296772E-01 - 0.256913751E-01 0.248375442E-01 0.239683688E-01 0.230840705E-01 0.221844520E-01 - 0.212706011E-01 0.203419533E-01 0.193990115E-01 0.184419286E-01 0.174711514E-01 - 0.164862014E-01 0.154872667E-01 0.144754266E-01 0.134500051E-01 0.124112377E-01 - 0.113593843E-01 0.102943731E-01 0.921635702E-02 0.812558737E-02 0.702203251E-02 - 0.590546289E-02 0.477631530E-02 0.363465212E-02 0.248037744E-02 0.131327542E-02 - 0.133945985E-03-0.105812005E-02-0.226296159E-02-0.348003022E-02-0.471000792E-02 --0.595236989E-02-0.720763253E-02-0.847522914E-02-0.975586660E-02-0.110491319E-01 --0.123556321E-01-0.136746755E-01-0.150071150E-01-0.163527802E-01-0.177111942E-01 --0.190833956E-01-0.204687007E-01-0.218678880E-01-0.232805647E-01-0.247071143E-01 --0.261478964E-01-0.276028644E-01-0.290716179E-01-0.305552930E-01-0.320537984E-01 --0.335669816E-01-0.350949764E-01-0.366381779E-01-0.381970145E-01-0.397713706E-01 --0.413615443E-01-0.429675281E-01-0.445899367E-01-0.462289006E-01-0.478845388E-01 --0.495570004E-01-0.512467474E-01-0.529540442E-01-0.546789169E-01-0.564217493E-01 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0.288837664E-01 0.297682229E-01 0.306268446E-01 0.314591229E-01 0.322645679E-01 - 0.330436043E-01 0.337958634E-01 0.345212780E-01 0.352197737E-01 0.358915962E-01 - 0.365365259E-01 0.371540077E-01 0.377447940E-01 0.383086950E-01 0.388457775E-01 - 0.393559933E-01 0.398396403E-01 0.402965285E-01 0.407270305E-01 0.411310531E-01 - 0.415088311E-01 0.418604389E-01 0.421860218E-01 0.424857289E-01 0.427597016E-01 - 0.430081524E-01 0.432311445E-01 0.434289575E-01 0.436013006E-01 0.437487438E-01 - 0.438712277E-01 0.439689271E-01 0.440416709E-01 0.440895818E-01 0.441125855E-01 - 0.441104993E-01 0.440833271E-01 0.440311208E-01 0.439540520E-01 0.438519679E-01 - 0.437249504E-01 0.435733646E-01 0.433971658E-01 0.431965031E-01 0.429716706E-01 - 0.427226685E-01 0.424496382E-01 0.421530530E-01 0.418328270E-01 0.414891876E-01 - 0.411226004E-01 0.407332219E-01 0.403211005E-01 0.398868956E-01 0.394305103E-01 - 0.389525779E-01 0.384532064E-01 0.379327722E-01 0.373915099E-01 0.368298106E-01 - 0.362476893E-01 0.356458612E-01 0.350244381E-01 0.343833975E-01 0.337238573E-01 - 0.330455825E-01 0.323484391E-01 0.316332616E-01 0.309004281E-01 0.301499665E-01 - 0.293821916E-01 0.285972636E-01 0.277952962E-01 0.269769523E-01 0.261420328E-01 - 0.252909698E-01 0.244240351E-01 0.235413630E-01 0.226429943E-01 0.217292160E-01 - 0.208007060E-01 0.198565684E-01 0.188974347E-01 0.179242212E-01 0.169358812E-01 - 0.159332938E-01 0.149162682E-01 0.138848126E-01 0.128395921E-01 0.117800245E-01 - 0.107063670E-01 0.961926300E-02 0.851804577E-02 0.740271574E-02 0.627406873E-02 - 0.513160462E-02 0.397538953E-02 0.280551449E-02 0.162196369E-02 0.424768543E-03 --0.785941840E-03-0.201031729E-02-0.324846990E-02-0.450022751E-02-0.576572912E-02 --0.704552606E-02-0.833870750E-02-0.964555889E-02-0.109669119E-01-0.123022636E-01 --0.136515209E-01-0.150149753E-01-0.163929835E-01-0.177854653E-01-0.191922225E-01 --0.206138901E-01-0.220503677E-01-0.235017370E-01-0.249677468E-01-0.264493003E-01 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0.856624264E-02 0.985605363E-02 0.111262938E-01 0.123771448E-01 0.136078605E-01 - 0.148173831E-01 0.160059240E-01 0.171731543E-01 0.183183048E-01 0.194412861E-01 - 0.205415860E-01 0.216191560E-01 0.226734821E-01 0.237042308E-01 0.247113016E-01 - 0.256943014E-01 0.266526397E-01 0.275869220E-01 0.284965225E-01 0.293806940E-01 - 0.302401111E-01 0.310743805E-01 0.318833925E-01 0.326668955E-01 0.334247947E-01 - 0.341570079E-01 0.348640978E-01 0.355450734E-01 0.362003148E-01 0.368300676E-01 - 0.374342501E-01 0.380127542E-01 0.385656059E-01 0.390927643E-01 0.395948701E-01 - 0.400714017E-01 0.405223779E-01 0.409483984E-01 0.413495675E-01 0.417255946E-01 - 0.420768671E-01 0.424032584E-01 0.427051596E-01 0.429826155E-01 0.432354659E-01 - 0.434642509E-01 0.436687730E-01 0.438490510E-01 0.440054573E-01 0.441376194E-01 - 0.442454666E-01 0.443288200E-01 0.443872996E-01 0.444208235E-01 0.444292799E-01 - 0.444126800E-01 0.443709604E-01 0.443042368E-01 0.442124084E-01 0.440955050E-01 - 0.439539067E-01 0.437873900E-01 0.435962193E-01 0.433806218E-01 0.431407616E-01 - 0.428768136E-01 0.425888002E-01 0.422766469E-01 0.419410989E-01 0.415825732E-01 - 0.412007906E-01 0.407961942E-01 0.403692015E-01 0.399198532E-01 0.394483842E-01 - 0.389555953E-01 0.384413302E-01 0.379061885E-01 0.373497270E-01 0.367731750E-01 - 0.361765698E-01 0.355599672E-01 0.349234194E-01 0.342676938E-01 0.335929990E-01 - 0.328996293E-01 0.321874470E-01 0.314568318E-01 0.307085458E-01 0.299422834E-01 - 0.291583501E-01 0.283571966E-01 0.275386833E-01 0.267032105E-01 0.258510802E-01 - 0.249823462E-01 0.240973234E-01 0.231957585E-01 0.222781952E-01 0.213447642E-01 - 0.203955397E-01 0.194307715E-01 0.184505116E-01 0.174545441E-01 0.164433904E-01 - 0.154170739E-01 0.143757816E-01 0.133192837E-01 0.122474842E-01 0.111612203E-01 - 0.100600012E-01 0.894387159E-02 0.781301316E-02 0.666748406E-02 0.550729083E-02 - 0.433217874E-02 0.314259576E-02 0.193828333E-02 0.719168282E-03-0.514590996E-03 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0.428167544E-01 0.431242622E-01 0.434082486E-01 0.436693616E-01 0.439069793E-01 - 0.441214032E-01 0.443125181E-01 0.444796272E-01 0.446224138E-01 0.447407663E-01 - 0.448344164E-01 0.449031554E-01 0.449469015E-01 0.449654721E-01 0.449588411E-01 - 0.449269339E-01 0.448697284E-01 0.447869562E-01 0.446787961E-01 0.445454977E-01 - 0.443866476E-01 0.442026854E-01 0.439938270E-01 0.437602513E-01 0.435019918E-01 - 0.432194583E-01 0.429130606E-01 0.425826572E-01 0.422283821E-01 0.418508984E-01 - 0.414504558E-01 0.410273448E-01 0.405813679E-01 0.401132368E-01 0.396234766E-01 - 0.391120873E-01 0.385791957E-01 0.380252935E-01 0.374505036E-01 0.368550904E-01 - 0.362396650E-01 0.356041305E-01 0.349488519E-01 0.342742167E-01 0.335802808E-01 - 0.328674205E-01 0.321357884E-01 0.313854478E-01 0.306168981E-01 0.298302118E-01 - 0.290254410E-01 0.282031707E-01 0.273633413E-01 0.265060924E-01 0.256314073E-01 - 0.247393511E-01 0.238311645E-01 0.229057465E-01 0.219636913E-01 0.210048854E-01 - 0.200299248E-01 0.190384891E-01 0.180308614E-01 0.170070082E-01 0.159671474E-01 - 0.149111366E-01 0.138393883E-01 0.127517171E-01 0.116479183E-01 0.105286501E-01 - 0.939361937E-02 0.824255031E-02 0.707594166E-02 0.589364627E-02 0.469544390E-02 - 0.348164933E-02 0.225226511E-02 0.100691279E-02-0.254227576E-03-0.153113180E-02 --0.282376818E-02-0.413247012E-02-0.545710558E-02-0.679774350E-02-0.815436617E-02 --0.952737965E-02-0.109163942E-01-0.123215253E-01-0.137436828E-01-0.151818348E-01 --0.166366436E-01-0.181085244E-01-0.195968822E-01-0.211023930E-01-0.226249956E-01 --0.241646543E-01-0.257218443E-01-0.272966679E-01-0.288888663E-01-0.304991826E-01 --0.321276151E-01-0.337737761E-01-0.354385152E-01-0.371219143E-01-0.388237834E-01 --0.405446291E-01-0.422845446E-01-0.440438204E-01-0.458226316E-01-0.476209596E-01 --0.494395047E-01-0.512780398E-01-0.531369336E-01-0.550165176E-01-0.569168441E-01 --0.588384606E-01-0.607811622E-01-0.627455413E-01-0.647319481E-01-0.667400956E-01 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0.330887474E-01 0.338409245E-01 0.345701948E-01 0.352765061E-01 0.359591991E-01 - 0.366183706E-01 0.372545347E-01 0.378673859E-01 0.384570174E-01 0.390236042E-01 - 0.395669900E-01 0.400875174E-01 0.405850224E-01 0.410596095E-01 0.415115096E-01 - 0.419405177E-01 0.423470549E-01 0.427310839E-01 0.430925861E-01 0.434316657E-01 - 0.437484458E-01 0.440429412E-01 0.443149395E-01 0.445639044E-01 0.447895676E-01 - 0.449911170E-01 0.451686345E-01 0.453217179E-01 0.454502143E-01 0.455538705E-01 - 0.456323549E-01 0.456856377E-01 0.457133316E-01 0.457154103E-01 0.456917658E-01 - 0.456421785E-01 0.455665961E-01 0.454651602E-01 0.453378558E-01 0.451845601E-01 - 0.450054072E-01 0.448012240E-01 0.445710644E-01 0.443156511E-01 0.440352038E-01 - 0.437305868E-01 0.434018150E-01 0.430488214E-01 0.426721945E-01 0.422725081E-01 - 0.418497100E-01 0.414039381E-01 0.409357548E-01 0.404454954E-01 0.399332680E-01 - 0.393990725E-01 0.388439521E-01 0.382674709E-01 0.376701206E-01 0.370522514E-01 - 0.364139751E-01 0.357554443E-01 0.350770578E-01 0.343790241E-01 0.336614661E-01 - 0.329249017E-01 0.321691446E-01 0.313947015E-01 0.306014773E-01 0.297893286E-01 - 0.289590228E-01 0.281108357E-01 0.272444524E-01 0.263601653E-01 0.254578572E-01 - 0.245380159E-01 0.236006677E-01 0.226458274E-01 0.216736849E-01 0.206843708E-01 - 0.196779575E-01 0.186540317E-01 0.176134668E-01 0.165558383E-01 0.154813547E-01 - 0.143899284E-01 0.132817430E-01 0.121568479E-01 0.110151144E-01 0.985651277E-02 - 0.868138485E-02 0.748950010E-02 0.628079986E-02 0.505552813E-02 0.381346769E-02 - 0.255463482E-02 0.127892336E-02-0.134797901E-04-0.132276013E-02-0.264899596E-02 --0.399214262E-02-0.535227591E-02-0.672952086E-02-0.812396035E-02-0.953565724E-02 --0.109646861E-01-0.124109928E-01-0.138748819E-01-0.153561449E-01-0.168553330E-01 --0.183723979E-01-0.199072361E-01-0.214602165E-01-0.230312366E-01-0.246207099E-01 --0.262288917E-01-0.278552342E-01-0.295003802E-01-0.311646126E-01-0.328479595E-01 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0.455589294E-01 0.453038923E-01 0.450235344E-01 0.447178744E-01 - 0.443867519E-01 0.440317094E-01 0.436533317E-01 0.432511196E-01 0.428253487E-01 - 0.423755944E-01 0.419038646E-01 0.414098538E-01 0.408934206E-01 0.403546505E-01 - 0.397945344E-01 0.392128751E-01 0.386097953E-01 0.379859507E-01 0.373414457E-01 - 0.366764665E-01 0.359908603E-01 0.352849923E-01 0.345593803E-01 0.338139161E-01 - 0.330489986E-01 0.322643183E-01 0.314605497E-01 0.306378417E-01 0.297959317E-01 - 0.289350878E-01 0.280555598E-01 0.271574389E-01 0.262407865E-01 0.253057871E-01 - 0.243524984E-01 0.233807005E-01 0.223909300E-01 0.213834122E-01 0.203573480E-01 - 0.193137340E-01 0.182523653E-01 0.171726700E-01 0.160755999E-01 0.149605749E-01 - 0.138275288E-01 0.126772532E-01 0.115090702E-01 0.103231780E-01 0.911968108E-02 - 0.789843779E-02 0.665951520E-02 0.540277734E-02 0.412869733E-02 0.283651054E-02 - 0.152627646E-02 0.198748865E-03-0.114687369E-02-0.251068757E-02-0.389192929E-02 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0.376243964E-01 0.367127582E-01 0.357784405E-01 0.348214358E-01 - 0.338420384E-01 0.328402109E-01 0.318155549E-01 0.307686087E-01 0.296994820E-01 - 0.286076535E-01 0.274937376E-01 0.263575129E-01 0.251990966E-01 0.240182709E-01 - 0.228152331E-01 0.215899684E-01 0.203424264E-01 0.190725997E-01 0.177808143E-01 - 0.164665915E-01 0.151301417E-01 0.137716345E-01 0.123908455E-01 0.109876506E-01 - 0.956229307E-02 0.811456703E-02 0.664437795E-02 0.515189022E-02 0.363728520E-02 - 0.209987070E-02 0.540158828E-03-0.104212179E-02-0.264702179E-02-0.427463045E-02 --0.592488144E-02-0.759774772E-02-0.929383188E-02-0.110124974E-01-0.127540622E-01 --0.145190489E-01-0.163071193E-01-0.181183871E-01-0.199529789E-01-0.218111854E-01 --0.236927997E-01-0.255983435E-01-0.275274180E-01-0.294804610E-01-0.314576179E-01 --0.334588550E-01-0.354845673E-01-0.375345014E-01-0.396091305E-01-0.417085253E-01 --0.438327529E-01-0.459821336E-01-0.481566750E-01-0.503565893E-01-0.525821336E-01 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0.381583683E-01 0.370626636E-01 0.359422527E-01 0.347969159E-01 - 0.336268470E-01 0.324319676E-01 0.312124304E-01 0.299681071E-01 0.286986958E-01 - 0.274049267E-01 0.260864235E-01 0.247430261E-01 0.233749729E-01 0.219823364E-01 - 0.205653049E-01 0.191231798E-01 0.176564343E-01 0.161651578E-01 0.146492403E-01 - 0.131087452E-01 0.115434676E-01 0.995353702E-02 0.833888538E-02 0.669956906E-02 - 0.503547210E-02 0.334669021E-02 0.163301756E-02-0.105540923E-03-0.186874962E-02 --0.365695287E-02-0.547028705E-02-0.730860559E-02-0.917180348E-02-0.110602397E-01 --0.129738534E-01-0.149127264E-01-0.168769397E-01-0.188664831E-01-0.208816733E-01 --0.229221899E-01-0.249885730E-01-0.270807035E-01-0.291984901E-01-0.313424803E-01 --0.335124433E-01-0.357085802E-01-0.379311182E-01-0.401799493E-01-0.424554683E-01 --0.447577722E-01-0.470866933E-01-0.494426601E-01-0.518259220E-01-0.542363264E-01 --0.566742308E-01-0.591398105E-01-0.616331734E-01-0.641545802E-01-0.667040497E-01 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0.632329844E-02 0.453005498E-02 0.271061272E-02 - 0.865074690E-03-0.100665586E-02-0.290456344E-02-0.482870545E-02-0.677925115E-02 --0.875589624E-02-0.107589839E-01-0.127884904E-01-0.148444604E-01-0.169270001E-01 --0.190360751E-01-0.211717952E-01-0.233341753E-01-0.255233794E-01-0.277395118E-01 --0.299825724E-01-0.322526470E-01-0.345499776E-01-0.368745513E-01-0.392263904E-01 --0.416058823E-01-0.440128371E-01-0.464476012E-01-0.489101298E-01-0.514007770E-01 --0.539194867E-01-0.564664714E-01-0.590419099E-01-0.616460070E-01-0.642788783E-01 --0.669406578E-01-0.696315393E-01-0.723517835E-01-0.751015320E-01-0.778810158E-01 --0.806904510E-01-0.835300311E-01-0.863999948E-01-0.893006846E-01-0.922321230E-01 --0.951946750E-01-0.981886312E-01-0.101214245E+00-0.104271837E+00-0.107361756E+00 --0.110484131E+00-0.113639437E+00-0.116827905E+00-0.120049931E+00-0.123305768E+00 --0.126596034E+00-0.129920885E+00-0.133280665E+00-0.136676088E+00-0.140107453E+00 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0.376108885E-01 0.362853631E-01 0.349325985E-01 0.335527547E-01 - 0.321462527E-01 0.307124984E-01 0.292517822E-01 0.277644638E-01 0.262499247E-01 - 0.247087162E-01 0.231408589E-01 0.215461291E-01 0.199245084E-01 0.182764102E-01 - 0.166013371E-01 0.148995174E-01 0.131711848E-01 0.114161661E-01 0.963432807E-02 - 0.782588311E-02 0.599067053E-02 0.412870850E-02 0.224016840E-02 0.324630033E-03 --0.161749264E-02-0.358635117E-02-0.558209652E-02-0.760470890E-02-0.965409074E-02 --0.117305573E-01-0.138340872E-01-0.159643944E-01-0.181217212E-01-0.203062780E-01 --0.225181784E-01-0.247571282E-01-0.270234179E-01-0.293172356E-01-0.316385366E-01 --0.339874066E-01-0.363638960E-01-0.387682356E-01-0.412003621E-01-0.436605178E-01 --0.461488403E-01-0.486653186E-01-0.512101762E-01-0.537835322E-01-0.563856214E-01 --0.590163246E-01-0.616760068E-01-0.643648654E-01-0.670829490E-01-0.698305368E-01 --0.726076514E-01-0.754146427E-01-0.782516152E-01-0.811188519E-01-0.840164050E-01 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0.963118335E-03-0.109884317E-02-0.318844034E-02-0.530602504E-02 --0.745131029E-02-0.962447096E-02-0.118255708E-01-0.140544241E-01-0.163112953E-01 --0.185961258E-01-0.209089722E-01-0.232498311E-01-0.256188400E-01-0.280160327E-01 --0.304414183E-01-0.328951478E-01-0.353772677E-01-0.378878340E-01-0.404269509E-01 --0.429947488E-01-0.455911793E-01-0.482165925E-01-0.508709773E-01-0.535543337E-01 --0.562669262E-01-0.590088814E-01-0.617802367E-01-0.645812303E-01-0.674120486E-01 --0.702727363E-01-0.731635466E-01-0.760846436E-01-0.790361241E-01-0.820183605E-01 --0.850312859E-01-0.880752653E-01-0.911506265E-01-0.942574367E-01-0.973959714E-01 --0.100566462E+00-0.103769049E+00-0.107004344E+00-0.110272244E+00-0.113573305E+00 --0.116907671E+00-0.120275639E+00-0.123677656E+00-0.127114013E+00-0.130584896E+00 --0.134091020E+00-0.137632489E+00-0.141209811E+00-0.144823343E+00-0.148473352E+00 --0.152160481E+00-0.155885294E+00-0.159648046E+00-0.163449392E+00-0.167289793E+00 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0.609556809E-01 0.600033104E-01 0.590112321E-01 0.579766370E-01 - 0.568997636E-01 0.557793677E-01 0.546112657E-01 0.533997789E-01 0.521439351E-01 - 0.508438461E-01 0.494992882E-01 0.481174663E-01 0.466994271E-01 0.452384800E-01 - 0.437489152E-01 0.422292203E-01 0.406772681E-01 0.390974022E-01 0.374890864E-01 - 0.358506627E-01 0.341826603E-01 0.324856378E-01 0.307591334E-01 0.290035456E-01 - 0.272189490E-01 0.254052337E-01 0.235623401E-01 0.216905903E-01 0.197899658E-01 - 0.178603139E-01 0.159019027E-01 0.139147369E-01 0.118987970E-01 0.985402986E-02 - 0.778073352E-02 0.567870541E-02 0.354798604E-02 0.138870324E-02-0.799191592E-03 --0.301567139E-02-0.526077580E-02-0.753450068E-02-0.983674638E-02-0.121676708E-01 --0.145271774E-01-0.169152673E-01-0.193321370E-01-0.217776243E-01-0.242518578E-01 --0.267548487E-01-0.292866696E-01-0.318473466E-01-0.344369709E-01-0.370555446E-01 --0.397031382E-01-0.423799232E-01-0.450858325E-01-0.478210598E-01-0.505856983E-01 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0.618015528E-01 0.605791323E-01 0.593096353E-01 0.579928011E-01 - 0.566268191E-01 0.552101322E-01 0.537398867E-01 0.522164740E-01 0.506490245E-01 - 0.490287803E-01 0.473682098E-01 0.456682891E-01 0.439291820E-01 0.421584733E-01 - 0.403578840E-01 0.385275073E-01 0.366657563E-01 0.347729884E-01 0.328496285E-01 - 0.308959335E-01 0.289117340E-01 0.268971045E-01 0.248525441E-01 0.227778237E-01 - 0.206730608E-01 0.185383987E-01 0.163737312E-01 0.141794272E-01 0.119553916E-01 - 0.970156025E-02 0.741814263E-02 0.510515179E-02 0.276266481E-02 0.390737434E-03 --0.201064372E-02-0.444149552E-02-0.690169819E-02-0.939122122E-02-0.119100800E-01 --0.144583248E-01-0.170358606E-01-0.196427368E-01-0.222789180E-01-0.249443687E-01 --0.276392009E-01-0.303634219E-01-0.331169814E-01-0.358999670E-01-0.387123898E-01 --0.415543132E-01-0.444257632E-01-0.473267920E-01-0.502575040E-01-0.532178879E-01 --0.562081113E-01-0.592281818E-01-0.622781776E-01-0.653582960E-01-0.684684888E-01 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0.729336441E-01 0.736081526E-01 0.742559657E-01 0.748764053E-01 0.754696727E-01 - 0.760351345E-01 0.765725896E-01 0.770812556E-01 0.775613785E-01 0.780123100E-01 - 0.784337670E-01 0.788250715E-01 0.791860744E-01 0.795164630E-01 0.798160583E-01 - 0.800843164E-01 0.803205818E-01 0.805250034E-01 0.806970224E-01 0.808360875E-01 - 0.809422135E-01 0.810148269E-01 0.810536072E-01 0.810585916E-01 0.810293108E-01 - 0.809651911E-01 0.808662623E-01 0.807318911E-01 0.805619508E-01 0.803563297E-01 - 0.801149085E-01 0.798373371E-01 0.795228854E-01 0.791715980E-01 0.787835792E-01 - 0.783582702E-01 0.778952837E-01 0.773947909E-01 0.768562108E-01 0.762796625E-01 - 0.756645128E-01 0.750107691E-01 0.743185282E-01 0.735868961E-01 0.728161559E-01 - 0.720057860E-01 0.711549446E-01 0.702636987E-01 0.693319663E-01 0.683593452E-01 - 0.673449337E-01 0.662879571E-01 0.651872233E-01 0.640418455E-01 0.628509820E-01 - 0.616136491E-01 0.603298992E-01 0.589935556E-01 0.576052815E-01 0.561648794E-01 - 0.546645299E-01 0.531113110E-01 0.515055135E-01 0.498475879E-01 0.481385030E-01 - 0.463833734E-01 0.445928872E-01 0.427677929E-01 0.409086831E-01 0.390159376E-01 - 0.370921530E-01 0.351363234E-01 0.331488289E-01 0.311299581E-01 0.290801991E-01 - 0.269995052E-01 0.248883087E-01 0.227471925E-01 0.205759481E-01 0.183751062E-01 - 0.161448102E-01 0.138853565E-01 0.115970951E-01 0.928002689E-02 0.693460321E-02 - 0.456096185E-02 0.215942203E-02-0.269911194E-03-0.272659468E-02-0.521058263E-02 --0.772159593E-02-0.102592837E-01-0.128236515E-01-0.154144298E-01-0.180313960E-01 --0.206741933E-01-0.233428143E-01-0.260369740E-01-0.287564546E-01-0.315012373E-01 --0.342709273E-01-0.370654091E-01-0.398845635E-01-0.427282341E-01-0.455962829E-01 --0.484884866E-01-0.514047369E-01-0.543448813E-01-0.573086888E-01-0.602962933E-01 --0.633073747E-01-0.663417354E-01-0.693994164E-01-0.724802390E-01-0.755842030E-01 --0.787111521E-01-0.818610042E-01-0.850336254E-01-0.882290378E-01-0.914470777E-01 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0.692243204E-01 0.683948994E-01 0.675254613E-01 0.666159168E-01 - 0.656637549E-01 0.646689013E-01 0.636317134E-01 0.625500083E-01 0.614212714E-01 - 0.602479354E-01 0.590239912E-01 0.577501245E-01 0.564246513E-01 0.550459549E-01 - 0.536126010E-01 0.521278568E-01 0.505914539E-01 0.490070842E-01 0.473693758E-01 - 0.456942879E-01 0.439846478E-01 0.422407761E-01 0.404621512E-01 0.386508815E-01 - 0.368080549E-01 0.349329859E-01 0.330263898E-01 0.310883392E-01 0.291189551E-01 - 0.271183848E-01 0.250872411E-01 0.230256226E-01 0.209337678E-01 0.188119709E-01 - 0.166603718E-01 0.144793671E-01 0.122690508E-01 0.100297825E-01 0.776198367E-02 - 0.546547957E-02 0.314081693E-02 0.788016536E-03-0.159239618E-02-0.400047190E-02 --0.643596984E-02-0.889861025E-02-0.113882637E-01-0.139046721E-01-0.164473783E-01 --0.190163441E-01-0.216116160E-01-0.242327005E-01-0.268795602E-01-0.295520872E-01 --0.322498642E-01-0.349727981E-01-0.377208479E-01-0.404937826E-01-0.432914943E-01 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0.327731408E-01 0.340593122E-01 0.353378467E-01 0.366089232E-01 0.378722139E-01 - 0.391274579E-01 0.403747037E-01 0.416135043E-01 0.428437777E-01 0.440651290E-01 - 0.452773087E-01 0.464783795E-01 0.476677790E-01 0.488437042E-01 0.500026792E-01 - 0.511444360E-01 0.522650704E-01 0.533623360E-01 0.544355810E-01 0.554819480E-01 - 0.565013215E-01 0.574932396E-01 0.584576540E-01 0.593951941E-01 0.603057556E-01 - 0.611892417E-01 0.620456077E-01 0.628750101E-01 0.636779442E-01 0.644541383E-01 - 0.652042925E-01 0.659277588E-01 0.666248277E-01 0.672954768E-01 0.679394081E-01 - 0.685566962E-01 0.691469759E-01 0.697096437E-01 0.702447146E-01 0.707522258E-01 - 0.712314770E-01 0.716824755E-01 0.721050277E-01 0.724984929E-01 0.728626400E-01 - 0.731973946E-01 0.735021755E-01 0.737769008E-01 0.740210116E-01 0.742342547E-01 - 0.744163767E-01 0.745669082E-01 0.746858269E-01 0.747728199E-01 0.748274326E-01 - 0.748490691E-01 0.748378858E-01 0.747932941E-01 0.747152939E-01 0.746033266E-01 - 0.744572431E-01 0.742766336E-01 0.740612820E-01 0.738111436E-01 0.735259578E-01 - 0.732049644E-01 0.728481337E-01 0.724550486E-01 0.720255822E-01 0.715598539E-01 - 0.710569844E-01 0.705169067E-01 0.699393898E-01 0.693238825E-01 0.686692521E-01 - 0.679777563E-01 0.672470927E-01 0.664755031E-01 0.656636134E-01 0.648121759E-01 - 0.639188364E-01 0.629832223E-01 0.620045699E-01 0.609807633E-01 0.599108115E-01 - 0.587945320E-01 0.576304123E-01 0.564156622E-01 0.551502220E-01 0.538302176E-01 - 0.524612404E-01 0.510412641E-01 0.495741628E-01 0.480586477E-01 0.465020239E-01 - 0.449087545E-01 0.432744920E-01 0.416086726E-01 0.399100780E-01 0.381779000E-01 - 0.364142545E-01 0.346187353E-01 0.327914543E-01 0.309325866E-01 0.290421881E-01 - 0.271205436E-01 0.251681209E-01 0.231850501E-01 0.211715363E-01 0.191276483E-01 - 0.170537643E-01 0.149503946E-01 0.128173493E-01 0.106551619E-01 0.846408214E-02 - 0.624420587E-02 0.399558153E-02 0.171876710E-02-0.586005277E-03-0.291882525E-02 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0.428971425E-01 0.418386720E-01 0.407464318E-01 0.396212526E-01 - 0.384627692E-01 0.372712389E-01 0.360469334E-01 0.347899757E-01 0.335005186E-01 - 0.321787931E-01 0.308250226E-01 0.294393878E-01 0.280217286E-01 0.265727174E-01 - 0.250925031E-01 0.235808212E-01 0.220382828E-01 0.204649772E-01 0.188609641E-01 - 0.172266010E-01 0.155619457E-01 0.138672916E-01 0.121427011E-01 0.103883659E-01 - 0.860461500E-02 0.679156277E-02 0.494929776E-02 0.307822647E-02 0.117840141E-02 --0.749934523E-03-0.270672143E-02-0.469172467E-02-0.670481566E-02-0.874563679E-02 --0.108141769E-01-0.129101761E-01-0.150334286E-01-0.171837769E-01-0.193613190E-01 --0.215655100E-01-0.237962417E-01-0.260535125E-01-0.283371266E-01-0.306468997E-01 --0.329826064E-01-0.353442654E-01-0.377315767E-01-0.401444659E-01-0.425829180E-01 --0.450466350E-01-0.475355014E-01-0.500495844E-01-0.525886044E-01-0.551524013E-01 --0.577410422E-01-0.603543520E-01-0.629922822E-01-0.656547621E-01-0.683416724E-01 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0.303336270E-01 0.297228489E-01 0.290819816E-01 0.284110811E-01 - 0.277098604E-01 0.269786399E-01 0.262174010E-01 0.254257470E-01 0.246044565E-01 - 0.237533562E-01 0.228721816E-01 0.219612159E-01 0.210205391E-01 0.200503077E-01 - 0.190503821E-01 0.180209577E-01 0.169622134E-01 0.158740599E-01 0.147568230E-01 - 0.136104301E-01 0.124349399E-01 0.112305311E-01 0.999740325E-02 0.873555522E-02 - 0.744508859E-02 0.612617703E-02 0.477886014E-02 0.340348762E-02 0.200001709E-02 - 0.568486343E-03-0.890821218E-03-0.237790192E-02-0.389246247E-02-0.543448096E-02 --0.700391782E-02-0.860035047E-02-0.102238962E-01-0.118743815E-01-0.135514634E-01 --0.152552510E-01-0.169854034E-01-0.187417790E-01-0.205245260E-01-0.223334096E-01 --0.241679642E-01-0.260281842E-01-0.279140677E-01-0.298254471E-01-0.317620598E-01 --0.337240398E-01-0.357109793E-01-0.377226099E-01-0.397592075E-01-0.418204255E-01 --0.439060219E-01-0.460160188E-01-0.481502563E-01-0.503086373E-01-0.524910316E-01 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0.338566862E-01 0.337205008E-01 0.335565321E-01 0.333645791E-01 - 0.331446193E-01 0.328964666E-01 0.326198451E-01 0.323146135E-01 0.319804922E-01 - 0.316176079E-01 0.312257074E-01 0.308047943E-01 0.303544011E-01 0.298748538E-01 - 0.293659233E-01 0.288277306E-01 0.282600969E-01 0.276627894E-01 0.270360913E-01 - 0.263799336E-01 0.256941915E-01 0.249790195E-01 0.242342148E-01 0.234601889E-01 - 0.226566885E-01 0.218236297E-01 0.209611971E-01 0.200697910E-01 0.191488694E-01 - 0.181989223E-01 0.172197558E-01 0.162115302E-01 0.151744820E-01 0.141084893E-01 - 0.130134784E-01 0.118899634E-01 0.107379761E-01 0.955728441E-02 0.834811293E-02 - 0.711067813E-02 0.584509829E-02 0.455127610E-02 0.322966278E-02 0.188008987E-02 - 0.502490147E-03-0.902581902E-03-0.233501685E-02-0.379502750E-02-0.528231775E-02 --0.679672137E-02-0.833809376E-02-0.990634970E-02-0.115013430E-01-0.131230829E-01 --0.147712510E-01-0.164456535E-01-0.181463417E-01-0.198731199E-01-0.216258001E-01 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0.156273656E-01 0.147133218E-01 0.137712499E-01 0.128010474E-01 - 0.118026659E-01 0.107763521E-01 0.972223748E-02 0.864005741E-02 0.753016490E-02 - 0.639265729E-02 0.522735948E-02 0.403459137E-02 0.281421095E-02 0.156633952E-02 - 0.291360600E-03-0.101080607E-02-0.234018359E-02-0.369650708E-02-0.507962052E-02 --0.648961635E-02-0.792619027E-02-0.938941352E-02-0.108789420E-01-0.123948986E-01 --0.139370132E-01-0.155051434E-01-0.170992520E-01-0.187191125E-01-0.203646440E-01 --0.220359061E-01-0.237323698E-01-0.254542027E-01-0.272011831E-01-0.289732292E-01 --0.307699032E-01-0.325915478E-01-0.344377495E-01-0.363084413E-01-0.382033773E-01 --0.401224494E-01-0.420656092E-01-0.440328829E-01-0.460238680E-01-0.480382890E-01 --0.500764772E-01-0.521379709E-01-0.542226508E-01-0.563304946E-01-0.584613495E-01 --0.606152192E-01-0.627917871E-01-0.649910048E-01-0.672128350E-01-0.694571212E-01 --0.717237368E-01-0.740125850E-01-0.763235688E-01-0.786567330E-01-0.810118243E-01 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0.935435481E-02 0.101423990E-01 0.109163085E-01 0.116760135E-01 0.124215866E-01 - 0.131526338E-01 0.138691459E-01 0.145708332E-01 0.152575476E-01 0.159293246E-01 - 0.165856741E-01 0.172265768E-01 0.178519152E-01 0.184613522E-01 0.190548636E-01 - 0.196322221E-01 0.201931335E-01 0.207375512E-01 0.212652031E-01 0.217758212E-01 - 0.222692396E-01 0.227453336E-01 0.232037604E-01 0.236443412E-01 0.240668152E-01 - 0.244710408E-01 0.248567387E-01 0.252234638E-01 0.255711805E-01 0.258995295E-01 - 0.262083970E-01 0.264974907E-01 0.267663244E-01 0.270148814E-01 0.272426140E-01 - 0.274494458E-01 0.276351888E-01 0.277992114E-01 0.279414281E-01 0.280618276E-01 - 0.281597264E-01 0.282347705E-01 0.282871164E-01 0.283160824E-01 0.283215232E-01 - 0.283034015E-01 0.282610506E-01 0.281943493E-01 0.281032827E-01 0.279874690E-01 - 0.278464276E-01 0.276801027E-01 0.274883863E-01 0.272709224E-01 0.270277318E-01 - 0.267583188E-01 0.264625922E-01 0.261402894E-01 0.257915296E-01 0.254162475E-01 - 0.250137877E-01 0.245846361E-01 0.241282638E-01 0.236446206E-01 0.231337361E-01 - 0.225953273E-01 0.220295135E-01 0.214361586E-01 0.208150353E-01 0.201665442E-01 - 0.194902942E-01 0.187860392E-01 0.180544108E-01 0.172950868E-01 0.165076721E-01 - 0.156927761E-01 0.148501191E-01 0.139796976E-01 0.130815608E-01 0.121558318E-01 - 0.112024294E-01 0.102214273E-01 0.921281241E-02 0.817682035E-02 0.711320015E-02 - 0.602219347E-02 0.490411278E-02 0.375858578E-02 0.258582155E-02 0.138612243E-02 - 0.159349991E-03-0.109420728E-02-0.237480807E-02-0.368223432E-02-0.501629990E-02 --0.637669303E-02-0.776369683E-02-0.917708874E-02-0.106166275E-01-0.120823327E-01 --0.135740312E-01-0.150916288E-01-0.166350286E-01-0.182040632E-01-0.197986625E-01 --0.214186106E-01-0.230638981E-01-0.247342940E-01-0.264297053E-01-0.281500760E-01 --0.298950244E-01-0.316648409E-01-0.334591381E-01-0.352775678E-01-0.371203572E-01 --0.389871411E-01-0.408778489E-01-0.427924395E-01-0.447306521E-01-0.466924533E-01 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0.266136117E-01 0.265889484E-01 0.265408847E-01 0.264690649E-01 0.263732653E-01 - 0.262533855E-01 0.261093434E-01 0.259404890E-01 0.257468931E-01 0.255284254E-01 - 0.252846945E-01 0.250154138E-01 0.247207116E-01 0.244002361E-01 0.240540728E-01 - 0.236816127E-01 0.232831482E-01 0.228582118E-01 0.224066991E-01 0.219287835E-01 - 0.214242171E-01 0.208929628E-01 0.203347374E-01 0.197496600E-01 0.191376787E-01 - 0.184985939E-01 0.178324562E-01 0.171392728E-01 0.164189134E-01 0.156712886E-01 - 0.148964655E-01 0.140943825E-01 0.132651683E-01 0.124087408E-01 0.115251299E-01 - 0.106143216E-01 0.967626367E-02 0.871101860E-02 0.771887414E-02 0.669959793E-02 - 0.565330824E-02 0.457997341E-02 0.347990193E-02 0.235281442E-02 0.119886675E-02 - 0.184247565E-04-0.118869334E-02-0.242261612E-02-0.368279335E-02-0.496946136E-02 --0.628243899E-02-0.762158353E-02-0.898692198E-02-0.103783570E-01-0.117955534E-01 --0.132387727E-01-0.147076696E-01-0.162020568E-01-0.177219138E-01-0.192671753E-01 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0.226095542E-01 0.229112450E-01 0.231938679E-01 0.234571397E-01 0.237009041E-01 - 0.239249300E-01 0.241289083E-01 0.243126713E-01 0.244760476E-01 0.246186052E-01 - 0.247402787E-01 0.248408001E-01 0.249198563E-01 0.249771811E-01 0.250127763E-01 - 0.250261016E-01 0.250171553E-01 0.249856580E-01 0.249311309E-01 0.248536561E-01 - 0.247528013E-01 0.246284902E-01 0.244804844E-01 0.243083369E-01 0.241122097E-01 - 0.238915682E-01 0.236464795E-01 0.233767461E-01 0.230819322E-01 0.227622800E-01 - 0.224172175E-01 0.220467262E-01 0.216507223E-01 0.212290920E-01 0.207817070E-01 - 0.203083102E-01 0.198090151E-01 0.192835871E-01 0.187319685E-01 0.181540139E-01 - 0.175495613E-01 0.169188809E-01 0.162615962E-01 0.155776748E-01 0.148671838E-01 - 0.141301556E-01 0.133664124E-01 0.125759570E-01 0.117589133E-01 0.109151555E-01 - 0.100445850E-01 0.914732832E-02 0.822344702E-02 0.727292523E-02 0.629574014E-02 - 0.529188989E-02 0.426140008E-02 0.320447143E-02 0.212102546E-02 0.101115904E-02 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0.142519157E-01 0.148193156E-01 0.153703848E-01 0.159051381E-01 0.164233800E-01 - 0.169248991E-01 0.174095351E-01 0.178772639E-01 0.183278024E-01 0.187610462E-01 - 0.191768650E-01 0.195749998E-01 0.199553557E-01 0.203177314E-01 0.206620228E-01 - 0.209878944E-01 0.212953091E-01 0.215839539E-01 0.218537543E-01 0.221044552E-01 - 0.223358404E-01 0.225477517E-01 0.227399189E-01 0.229121931E-01 0.230643414E-01 - 0.231960900E-01 0.233072843E-01 0.233977456E-01 0.234672073E-01 0.235153455E-01 - 0.235421285E-01 0.235472899E-01 0.235304311E-01 0.234915335E-01 0.234303810E-01 - 0.233465806E-01 0.232401248E-01 0.231106486E-01 0.229580328E-01 0.227820836E-01 - 0.225825664E-01 0.223592389E-01 0.221121963E-01 0.218408611E-01 0.215452202E-01 - 0.212252233E-01 0.208804831E-01 0.205109920E-01 0.201166905E-01 0.196974073E-01 - 0.192529075E-01 0.187830683E-01 0.182878543E-01 0.177670252E-01 0.172206648E-01 - 0.166486055E-01 0.160507299E-01 0.154269682E-01 0.147772776E-01 0.141016310E-01 - 0.133999344E-01 0.126722613E-01 0.119182793E-01 0.111383405E-01 0.103321131E-01 - 0.949956197E-02 0.864084624E-02 0.775594078E-02 0.684495270E-02 0.590759516E-02 - 0.494405255E-02 0.395443011E-02 0.293857628E-02 0.189665018E-02 0.828637159E-03 --0.265521812E-03-0.138553535E-02-0.253166328E-02-0.370352552E-02-0.490122894E-02 --0.612479635E-02-0.737405615E-02-0.864887144E-02-0.994934887E-02-0.112752328E-01 --0.126264831E-01-0.140031530E-01-0.154049005E-01-0.168318003E-01-0.182837341E-01 --0.197604448E-01-0.212620348E-01-0.227883924E-01-0.243393071E-01-0.259146076E-01 --0.275143124E-01-0.291382521E-01-0.307862554E-01-0.324581452E-01-0.341539830E-01 --0.358735770E-01-0.376168340E-01-0.393833518E-01-0.411733091E-01-0.429865234E-01 --0.448225960E-01-0.466816872E-01-0.485636219E-01-0.504680350E-01-0.523949303E-01 --0.543442331E-01-0.563159026E-01-0.583094619E-01-0.603250898E-01-0.623623990E-01 --0.644214153E-01-0.665020719E-01-0.686039403E-01-0.707272738E-01-0.728716478E-01 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0.225882931E-02 0.305892015E-02 0.384456571E-02 0.461566402E-02 0.537204370E-02 - 0.611362886E-02 0.684041390E-02 0.755190756E-02 0.824834593E-02 0.892961677E-02 - 0.959528983E-02 0.102454079E-01 0.108799571E-01 0.114987567E-01 0.121015906E-01 - 0.126884719E-01 0.132592088E-01 0.138136270E-01 0.143517824E-01 0.148733305E-01 - 0.153782340E-01 0.158664342E-01 0.163376909E-01 0.167919956E-01 0.172290597E-01 - 0.176488142E-01 0.180511829E-01 0.184358731E-01 0.188029110E-01 0.191520024E-01 - 0.194829963E-01 0.197957791E-01 0.200901460E-01 0.203660615E-01 0.206231438E-01 - 0.208613258E-01 0.210804828E-01 0.212803278E-01 0.214607585E-01 0.216214955E-01 - 0.217623990E-01 0.218833629E-01 0.219839606E-01 0.220642108E-01 0.221238136E-01 - 0.221626516E-01 0.221803468E-01 0.221768618E-01 0.221520644E-01 0.221055113E-01 - 0.220370460E-01 0.219466165E-01 0.218340345E-01 0.216989182E-01 0.215412285E-01 - 0.213607233E-01 0.211571325E-01 0.209305082E-01 0.206805617E-01 0.204069093E-01 - 0.201095697E-01 0.197884124E-01 0.194433760E-01 0.190740712E-01 0.186803099E-01 - 0.182621256E-01 0.178195834E-01 0.173521023E-01 0.168600362E-01 0.163429342E-01 - 0.158007517E-01 0.152334496E-01 0.146409152E-01 0.140231028E-01 0.133800767E-01 - 0.127112670E-01 0.120171160E-01 0.112976432E-01 0.105522675E-01 0.978130475E-02 - 0.898480695E-02 0.816248357E-02 0.731437560E-02 0.644071819E-02 0.554130087E-02 - 0.461587962E-02 0.366497505E-02 0.268826820E-02 0.168563402E-02 0.657528872E-03 --0.396311167E-03-0.147578330E-02-0.258088694E-02-0.371144502E-02-0.486777676E-02 --0.604941742E-02-0.725635467E-02-0.848878268E-02-0.974657573E-02-0.110295359E-01 --0.123374406E-01-0.136704836E-01-0.150287859E-01-0.164117590E-01-0.178193953E-01 --0.192519296E-01-0.207090937E-01-0.221908577E-01-0.236968827E-01-0.252271574E-01 --0.267816521E-01-0.283602979E-01-0.299630109E-01-0.315893888E-01-0.332394466E-01 --0.349132977E-01-0.366103798E-01-0.383309573E-01-0.400746502E-01-0.418414734E-01 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0.208883882E-01 0.209175665E-01 0.209261011E-01 0.209137723E-01 0.208804030E-01 - 0.208258554E-01 0.207498390E-01 0.206523221E-01 0.205331799E-01 0.203919020E-01 - 0.202285685E-01 0.200429428E-01 0.198347792E-01 0.196040645E-01 0.193504617E-01 - 0.190738104E-01 0.187741239E-01 0.184511207E-01 0.181045793E-01 0.177345071E-01 - 0.173408128E-01 0.169230551E-01 0.164812542E-01 0.160154942E-01 0.155253923E-01 - 0.150108906E-01 0.144719277E-01 0.139083769E-01 0.133202439E-01 0.127072856E-01 - 0.120694973E-01 0.114067942E-01 0.107192211E-01 0.100066029E-01 0.926873274E-02 - 0.850574672E-02 0.771779101E-02 0.690441485E-02 0.606583944E-02 0.520203682E-02 - 0.431294134E-02 0.339852809E-02 0.245880918E-02 0.149380160E-02 0.503512623E-03 --0.512012048E-03-0.155287213E-02-0.261906930E-02-0.371025852E-02-0.482675899E-02 --0.596843939E-02-0.713520264E-02-0.832683686E-02-0.954363775E-02-0.107855191E-01 --0.120520433E-01-0.133433612E-01-0.146596236E-01-0.160004739E-01-0.173658319E-01 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0.168186519E-01 0.171417724E-01 0.174469724E-01 0.177341048E-01 0.180030055E-01 - 0.182535648E-01 0.184856672E-01 0.186991952E-01 0.188939627E-01 0.190698523E-01 - 0.192266982E-01 0.193643682E-01 0.194827057E-01 0.195815898E-01 0.196608081E-01 - 0.197201688E-01 0.197596382E-01 0.197789464E-01 0.197779331E-01 0.197564643E-01 - 0.197143592E-01 0.196514614E-01 0.195675213E-01 0.194625966E-01 0.193362106E-01 - 0.191883594E-01 0.190188754E-01 0.188275035E-01 0.186142791E-01 0.183787532E-01 - 0.181210265E-01 0.178408064E-01 0.175379366E-01 0.172123220E-01 0.168637764E-01 - 0.164921563E-01 0.160972495E-01 0.156791266E-01 0.152375773E-01 0.147723220E-01 - 0.142833618E-01 0.137706129E-01 0.132339010E-01 0.126731498E-01 0.120882448E-01 - 0.114792138E-01 0.108458968E-01 0.101880226E-01 0.950581953E-02 0.879911985E-02 - 0.806771964E-02 0.731173623E-02 0.653105555E-02 0.572561100E-02 0.489543285E-02 - 0.404039305E-02 0.316057028E-02 0.225588144E-02 0.132628239E-02 0.371896924E-03 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0.865160953E-02 0.923725404E-02 0.980620645E-02 0.103583904E-01 0.108939949E-01 - 0.114126857E-01 0.119144404E-01 0.123992804E-01 0.128671182E-01 0.133177442E-01 - 0.137511268E-01 0.141672520E-01 0.145660052E-01 0.149472803E-01 0.153109664E-01 - 0.156569909E-01 0.159853511E-01 0.162958130E-01 0.165883377E-01 0.168628264E-01 - 0.171191841E-01 0.173572414E-01 0.175769422E-01 0.177781954E-01 0.179607961E-01 - 0.181246828E-01 0.182696972E-01 0.183957685E-01 0.185026843E-01 0.185903274E-01 - 0.186586305E-01 0.187073424E-01 0.187363718E-01 0.187456012E-01 0.187348630E-01 - 0.187039506E-01 0.186527781E-01 0.185812414E-01 0.184890311E-01 0.183760095E-01 - 0.182422549E-01 0.180873182E-01 0.179111157E-01 0.177136678E-01 0.174946487E-01 - 0.172538981E-01 0.169913545E-01 0.167068187E-01 0.164001696E-01 0.160712153E-01 - 0.157198478E-01 0.153459432E-01 0.149493944E-01 0.145299975E-01 0.140875252E-01 - 0.136221070E-01 0.131335640E-01 0.126215797E-01 0.120862434E-01 0.115273632E-01 - 0.109449644E-01 0.103388149E-01 0.970872212E-02 0.905491319E-02 0.837714784E-02 - 0.767528964E-02 0.694927434E-02 0.619915826E-02 0.542479241E-02 0.462619495E-02 - 0.380324107E-02 0.295609352E-02 0.208439166E-02 0.118843839E-02 0.267977332E-03 --0.676883850E-03-0.164621137E-02-0.264004827E-02-0.365825719E-02-0.470103510E-02 --0.576820504E-02-0.685973093E-02-0.797571521E-02-0.911610760E-02-0.102807516E-01 --0.114697712E-01-0.126829995E-01-0.139204869E-01-0.151821095E-01-0.164678041E-01 --0.177776124E-01-0.191113278E-01-0.204689540E-01-0.218504835E-01-0.232557151E-01 --0.246846359E-01-0.261372644E-01-0.276132617E-01-0.291126054E-01-0.306353029E-01 --0.321811102E-01-0.337499790E-01-0.353418589E-01-0.369567201E-01-0.385940857E-01 --0.402541570E-01-0.419368334E-01-0.436416604E-01-0.453687124E-01-0.471179560E-01 --0.488891639E-01-0.506820381E-01-0.524966195E-01-0.543326885E-01-0.561901629E-01 --0.580688342E-01-0.599687211E-01-0.618893988E-01-0.638305694E-01-0.657925382E-01 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0.164747667E-01 0.162282865E-01 0.159604643E-01 0.156709738E-01 0.153599009E-01 - 0.150270257E-01 0.146721657E-01 0.142952884E-01 0.138961803E-01 0.134747224E-01 - 0.130308876E-01 0.125644850E-01 0.120754167E-01 0.115633914E-01 0.110285878E-01 - 0.104707293E-01 0.988972560E-02 0.928558595E-02 0.865807105E-02 0.800714083E-02 - 0.733279018E-02 0.663492037E-02 0.591342431E-02 0.516817858E-02 0.439924980E-02 - 0.360654690E-02 0.278993696E-02 0.194944791E-02 0.108503131E-02 0.196615627E-03 --0.715839269E-03-0.165222562E-02-0.261272839E-02-0.359719712E-02-0.460575195E-02 --0.563843502E-02-0.669514108E-02-0.777583616E-02-0.888066646E-02-0.100094890E-01 --0.111622121E-01-0.123389317E-01-0.135397250E-01-0.147641944E-01-0.160125736E-01 --0.172847752E-01-0.185807925E-01-0.199003611E-01-0.212436300E-01-0.226103961E-01 --0.240006298E-01-0.254142862E-01-0.268511754E-01-0.283112749E-01-0.297946204E-01 --0.313011147E-01-0.328302979E-01-0.343824364E-01-0.359573364E-01-0.375546850E-01 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0.168577041E-01 0.169225447E-01 0.169684216E-01 0.169951823E-01 0.170027595E-01 - 0.169910546E-01 0.169599578E-01 0.169092752E-01 0.168390442E-01 0.167489648E-01 - 0.166389756E-01 0.165090207E-01 0.163589213E-01 0.161884725E-01 0.159976035E-01 - 0.157862734E-01 0.155541664E-01 0.153012183E-01 0.150273573E-01 0.147324270E-01 - 0.144163268E-01 0.140788024E-01 0.137198633E-01 0.133393593E-01 0.129369982E-01 - 0.125129484E-01 0.120668299E-01 0.115986196E-01 0.111083053E-01 0.105955601E-01 - 0.100604398E-01 0.950271823E-02 0.892242882E-02 0.831937511E-02 0.769349374E-02 - 0.704479218E-02 0.637299428E-02 0.567813823E-02 0.496014440E-02 0.421890151E-02 - 0.345443818E-02 0.266656838E-02 0.185528514E-02 0.102057669E-02 0.162318436E-03 --0.719424919E-03-0.162468303E-02-0.255368068E-02-0.350631936E-02-0.448255753E-02 --0.548248412E-02-0.650599599E-02-0.755324075E-02-0.862417836E-02-0.971886888E-02 --0.108371247E-01-0.119790044E-01-0.131446244E-01-0.143337110E-01-0.155463563E-01 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0.128430501E-01 0.131880175E-01 0.135150934E-01 0.138242086E-01 0.141153615E-01 - 0.143885417E-01 0.146436337E-01 0.148806563E-01 0.150995711E-01 0.153002860E-01 - 0.154827889E-01 0.156469978E-01 0.157928411E-01 0.159203075E-01 0.160292704E-01 - 0.161196981E-01 0.161915012E-01 0.162446108E-01 0.162789188E-01 0.162943657E-01 - 0.162908714E-01 0.162682645E-01 0.162265506E-01 0.161655266E-01 0.160851646E-01 - 0.159853064E-01 0.158659145E-01 0.157268178E-01 0.155678391E-01 0.153889675E-01 - 0.151900845E-01 0.149710309E-01 0.147316493E-01 0.144718429E-01 0.141914720E-01 - 0.138905803E-01 0.135687524E-01 0.132260034E-01 0.128623797E-01 0.124774361E-01 - 0.120713292E-01 0.116438596E-01 0.111947171E-01 0.107240910E-01 0.102317091E-01 - 0.971737597E-02 0.918119494E-02 0.862295646E-02 0.804245658E-02 0.743976980E-02 - 0.681477087E-02 0.616725208E-02 0.549720414E-02 0.480457628E-02 0.408932194E-02 - 0.335116964E-02 0.259022554E-02 0.180633587E-02 0.999462791E-03 0.169616964E-03 --0.683326216E-03-0.155936612E-02-0.245865667E-02-0.338114635E-02-0.432673935E-02 --0.529569294E-02-0.628785323E-02-0.730335899E-02-0.834217761E-02-0.940432027E-02 --0.104897143E-01-0.115984501E-01-0.127305230E-01-0.138858780E-01-0.150645347E-01 --0.162663721E-01-0.174914133E-01-0.187397003E-01-0.200111605E-01-0.213056505E-01 --0.226231478E-01-0.239636451E-01-0.253270511E-01-0.267134085E-01-0.281224847E-01 --0.295543522E-01-0.310086850E-01-0.324856751E-01-0.339852870E-01-0.355070233E-01 --0.370511226E-01-0.386173427E-01-0.402056724E-01-0.418159105E-01-0.434479788E-01 --0.451017581E-01-0.467770323E-01-0.484736711E-01-0.501917861E-01-0.519309528E-01 --0.536911450E-01-0.554723442E-01-0.572741069E-01-0.590963550E-01-0.609391406E-01 --0.628023371E-01-0.646853298E-01-0.665880516E-01-0.685108304E-01-0.704530478E-01 --0.724146292E-01-0.743954629E-01-0.763951838E-01-0.784137398E-01-0.804510415E-01 --0.825067386E-01-0.845806524E-01-0.866727158E-01-0.887828320E-01-0.909103081E-01 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0.469468767E-02 0.531558739E-02 0.591870025E-02 0.650389446E-02 0.707136607E-02 - 0.762084359E-02 0.815227814E-02 0.866591092E-02 0.916150305E-02 0.963906758E-02 - 0.100985831E-01 0.105401995E-01 0.109636206E-01 0.113690337E-01 0.117564332E-01 - 0.121258432E-01 0.124771353E-01 0.128103718E-01 0.131255072E-01 0.134225376E-01 - 0.137015255E-01 0.139623657E-01 0.142050516E-01 0.144296391E-01 0.146360351E-01 - 0.148242135E-01 0.149941845E-01 0.151458811E-01 0.152792595E-01 0.153943030E-01 - 0.154909994E-01 0.155692017E-01 0.156288594E-01 0.156699736E-01 0.156925507E-01 - 0.156963542E-01 0.156814083E-01 0.156476460E-01 0.155949080E-01 0.155232269E-01 - 0.154324127E-01 0.153223602E-01 0.151930163E-01 0.150443744E-01 0.148761747E-01 - 0.146884024E-01 0.144810053E-01 0.142537169E-01 0.140064955E-01 0.137393177E-01 - 0.134519180E-01 0.131442472E-01 0.128163025E-01 0.124678770E-01 0.120987343E-01 - 0.117089413E-01 0.112983426E-01 0.108666783E-01 0.104140276E-01 0.994025543E-02 - 0.944510382E-02 0.892854203E-02 0.839058310E-02 0.783091784E-02 0.724964170E-02 - 0.664650556E-02 0.602147402E-02 0.537442369E-02 0.470531220E-02 0.401402730E-02 - 0.330044189E-02 0.256460719E-02 0.180631748E-02 0.102553272E-02 0.222380579E-03 --0.603479624E-03-0.145201990E-02-0.232325098E-02-0.321730739E-02-0.413403241E-02 --0.507367076E-02-0.603611162E-02-0.702160085E-02-0.802988280E-02-0.906122383E-02 --0.101154596E-01-0.111926729E-01-0.122928750E-01-0.134160398E-01-0.145622119E-01 --0.157311838E-01-0.169231687E-01-0.181380231E-01-0.193758626E-01-0.206364710E-01 --0.219198652E-01-0.232260842E-01-0.245549567E-01-0.259065758E-01-0.272807628E-01 --0.286775101E-01-0.300966557E-01-0.315382406E-01-0.330021121E-01-0.344883017E-01 --0.359965339E-01-0.375268571E-01-0.390792228E-01-0.406532921E-01-0.422491133E-01 --0.438666530E-01-0.455056168E-01-0.471659116E-01-0.488475151E-01-0.505502149E-01 --0.522738248E-01-0.540182404E-01-0.557834096E-01-0.575691015E-01-0.593751967E-01 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0.142834298E-01 0.140862176E-01 0.138697149E-01 0.136337001E-01 0.133782011E-01 - 0.131030288E-01 0.128080491E-01 0.124932947E-01 0.121585019E-01 0.118035646E-01 - 0.114284679E-01 0.110331709E-01 0.106173269E-01 0.101810079E-01 0.972407125E-02 - 0.924643688E-02 0.874789339E-02 0.822841749E-02 0.768794864E-02 0.712621771E-02 - 0.654328894E-02 0.593897793E-02 0.531315152E-02 0.466581946E-02 0.399692450E-02 - 0.330618164E-02 0.259371335E-02 0.185934675E-02 0.110294565E-02 0.324553723E-03 --0.475989480E-03-0.129869964E-02-0.214374065E-02-0.301091489E-02-0.390057522E-02 --0.481262337E-02-0.574711896E-02-0.670415955E-02-0.768354721E-02-0.868565682E-02 --0.971029419E-02-0.107575310E-01-0.118274437E-01-0.129199009E-01-0.140350237E-01 --0.151728271E-01-0.163332000E-01-0.175162479E-01-0.187218357E-01-0.199500825E-01 --0.212008599E-01-0.224741865E-01-0.237699952E-01-0.250882097E-01-0.264288932E-01 --0.277919527E-01-0.291772131E-01-0.305847581E-01-0.320145749E-01-0.334663503E-01 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0.145648792E-01 0.146544352E-01 0.147257308E-01 0.147787258E-01 0.148133626E-01 - 0.148296962E-01 0.148277245E-01 0.148072699E-01 0.147684049E-01 0.147111127E-01 - 0.146353133E-01 0.145409694E-01 0.144280493E-01 0.142964115E-01 0.141459834E-01 - 0.139768217E-01 0.137887327E-01 0.135817043E-01 0.133556137E-01 0.131104505E-01 - 0.128460862E-01 0.125622936E-01 0.122592803E-01 0.119366962E-01 0.115944464E-01 - 0.112326220E-01 0.108509623E-01 0.104493881E-01 0.100278389E-01 0.958613586E-02 - 0.912432373E-02 0.864214730E-02 0.813955069E-02 0.761642819E-02 0.707269181E-02 - 0.650821906E-02 0.592297176E-02 0.531676831E-02 0.468952069E-02 0.404120889E-02 - 0.337168039E-02 0.268087094E-02 0.196859380E-02 0.123494258E-02 0.479713985E-03 --0.297238090E-03-0.109583454E-02-0.191611855E-02-0.275830482E-02-0.362247764E-02 --0.450854935E-02-0.541653810E-02-0.634672260E-02-0.729893846E-02-0.827332027E-02 --0.927004777E-02-0.102889054E-01-0.113300458E-01-0.123933526E-01-0.134790512E-01 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--0.119207494E+00-0.121492043E+00-0.123790294E+00-0.126101509E+00-0.128425807E+00 --0.130762950E+00-0.133112654E+00-0.135474920E+00-0.137849659E+00-0.140236378E+00 --0.142635107E+00-0.145045802E+00-0.147468001E+00-0.149901778E+00-0.152347237E+00 --0.154803976E+00-0.157271728E+00-0.159750924E+00-0.162241369E+00-0.164742559E+00 --0.167254850E+00-0.169778377E+00-0.172312647E+00-0.174858093E+00-0.177414566E+00 --0.179982260E+00-0.182560802E+00-0.185150623E+00-0.187751830E+00-0.190364614E+00 --0.192988113E+00-0.195623696E+00-0.198271230E+00-0.200930387E+00-0.203601256E+00 --0.206284836E+00-0.208980709E+00-0.211688995E+00-0.214410320E+00-0.217144638E+00 --0.219892070E+00-0.222652853E+00-0.225427538E+00-0.228215963E+00-0.231018499E+00 --0.233836070E+00-0.236667380E+00-0.239514083E+00-0.242378265E+00-0.245253682E+00 --0.248144940E+00-0.251052201E+00-0.253975868E+00-0.256916136E+00-0.259872943E+00 --0.262846291E+00-0.265828997E+00-0.268824488E+00-0.271847844E+00-0.274887681E+00 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0.106249955E-01 0.109995892E-01 0.113551542E-01 0.116917063E-01 0.120093012E-01 - 0.123080397E-01 0.125880018E-01 0.128491307E-01 0.130915232E-01 0.133152679E-01 - 0.135205425E-01 0.137072708E-01 0.138754640E-01 0.140252626E-01 0.141566684E-01 - 0.142696761E-01 0.143643711E-01 0.144408233E-01 0.144989770E-01 0.145388572E-01 - 0.145604927E-01 0.145639060E-01 0.145490402E-01 0.145158917E-01 0.144645106E-01 - 0.143948440E-01 0.143068302E-01 0.142004853E-01 0.140757244E-01 0.139325205E-01 - 0.137708941E-01 0.135906655E-01 0.133919269E-01 0.131744836E-01 0.129383570E-01 - 0.126833888E-01 0.124094896E-01 0.121167917E-01 0.118049616E-01 0.114739742E-01 - 0.111238044E-01 0.107544130E-01 0.103655113E-01 0.995713659E-02 0.952918734E-02 - 0.908150990E-02 0.861408096E-02 0.812674779E-02 0.761942612E-02 0.709198322E-02 - 0.654438231E-02 0.597654888E-02 0.538818538E-02 0.477937143E-02 0.415010238E-02 - 0.349999941E-02 0.282914191E-02 0.213747751E-02 0.142478535E-02 0.691010442E-03 --0.638705023E-04-0.839861343E-03-0.163717894E-02-0.245596399E-02-0.329623255E-02 --0.415791245E-02-0.504105771E-02-0.594606902E-02-0.687268702E-02-0.782101694E-02 --0.879110023E-02-0.978312455E-02-0.107968841E-01-0.118327364E-01-0.128904236E-01 --0.139701096E-01-0.150717506E-01-0.161953624E-01-0.173410457E-01-0.185087789E-01 --0.196985118E-01-0.209101997E-01-0.221440159E-01-0.233997740E-01-0.246774908E-01 --0.259771645E-01-0.272986647E-01-0.286421403E-01-0.300073884E-01-0.313943587E-01 --0.328032486E-01-0.342336521E-01-0.356856473E-01-0.371593162E-01-0.386542901E-01 --0.401706696E-01-0.417083800E-01-0.432672091E-01-0.448471606E-01-0.464481004E-01 --0.480698459E-01-0.497123636E-01-0.513754562E-01-0.530590862E-01-0.547631122E-01 --0.564872809E-01-0.582315065E-01-0.599956252E-01-0.617794767E-01-0.635828897E-01 --0.654057562E-01-0.672477633E-01-0.691089630E-01-0.709889829E-01-0.728875920E-01 --0.748045146E-01-0.767398700E-01-0.786933675E-01-0.806644708E-01-0.826531351E-01 --0.846593231E-01-0.866828263E-01-0.887228400E-01-0.907797068E-01-0.928532854E-01 --0.949427485E-01-0.970481932E-01-0.991692618E-01-0.101305924E+00-0.103457719E+00 --0.105624646E+00-0.107805990E+00-0.110001966E+00-0.112212092E+00-0.114436150E+00 --0.116673827E+00-0.118924946E+00-0.121189341E+00-0.123466611E+00-0.125756532E+00 --0.128058985E+00-0.130373940E+00-0.132700756E+00-0.135039255E+00-0.137389407E+00 --0.139750972E+00-0.142123714E+00-0.144507721E+00-0.146902740E+00-0.149307951E+00 --0.151724011E+00-0.154150516E+00-0.156586856E+00-0.159033850E+00-0.161490887E+00 --0.163957462E+00-0.166434616E+00-0.168921158E+00-0.171417579E+00-0.173924029E+00 --0.176439807E+00-0.178965583E+00-0.181501076E+00-0.184046328E+00-0.186601698E+00 --0.189166412E+00-0.191741303E+00-0.194326550E+00-0.196921617E+00-0.199527055E+00 --0.202142850E+00-0.204769194E+00-0.207406297E+00-0.210053995E+00-0.212712899E+00 --0.215383127E+00-0.218063876E+00-0.220756590E+00-0.223461270E+00-0.226177484E+00 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0.218119635E-02 0.286499178E-02 0.352900429E-02 0.417291885E-02 0.479696086E-02 - 0.540078897E-02 0.598464860E-02 0.654853135E-02 0.709204841E-02 0.761567568E-02 - 0.811938196E-02 0.860301871E-02 0.906650908E-02 0.951023027E-02 0.993430708E-02 - 0.103384694E-01 0.107229305E-01 0.110878805E-01 0.114332912E-01 0.117592886E-01 - 0.120658502E-01 0.123532275E-01 0.126214977E-01 0.128707225E-01 0.131008048E-01 - 0.133120818E-01 0.135046216E-01 0.136783738E-01 0.138334930E-01 0.139700975E-01 - 0.140881538E-01 0.141877597E-01 0.142689766E-01 0.143319005E-01 0.143764988E-01 - 0.144029036E-01 0.144111048E-01 0.144010959E-01 0.143729150E-01 0.143266385E-01 - 0.142622413E-01 0.141796451E-01 0.140789347E-01 0.139600663E-01 0.138230175E-01 - 0.136678303E-01 0.134943211E-01 0.133026121E-01 0.130925644E-01 0.128641473E-01 - 0.126173031E-01 0.123519609E-01 0.120681142E-01 0.117656440E-01 0.114444876E-01 - 0.111046135E-01 0.107458308E-01 0.103681292E-01 0.997149106E-02 0.955566019E-02 - 0.912066549E-02 0.866648834E-02 0.819278974E-02 0.769970892E-02 0.718703493E-02 - 0.665463042E-02 0.610258663E-02 0.553047657E-02 0.493854703E-02 0.432651537E-02 - 0.369433640E-02 0.304177520E-02 0.236894470E-02 0.167577073E-02 0.961829966E-03 - 0.227356257E-03-0.527688826E-03-0.130377652E-02-0.210065441E-02-0.291842432E-02 --0.375737250E-02-0.461730780E-02-0.549851405E-02-0.640105875E-02-0.732478313E-02 --0.826993305E-02-0.923656393E-02-0.102245882E-01-0.112342052E-01-0.122654121E-01 --0.133182360E-01-0.143926684E-01-0.154887140E-01-0.166065935E-01-0.177461505E-01 --0.189073738E-01-0.200903341E-01-0.212950781E-01-0.225215480E-01-0.237696785E-01 --0.250396263E-01-0.263312254E-01-0.276444610E-01-0.289793778E-01-0.303359237E-01 --0.317140445E-01-0.331135914E-01-0.345346779E-01-0.359771624E-01-0.374410152E-01 --0.389260910E-01-0.404323786E-01-0.419597924E-01-0.435082428E-01-0.450775586E-01 --0.466677845E-01-0.482786484E-01-0.499102399E-01-0.515622571E-01-0.532345027E-01 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--0.185523033E+00-0.188043252E+00-0.190571681E+00-0.193108827E+00-0.195654750E+00 --0.198209256E+00-0.200772434E+00-0.203344464E+00-0.205925420E+00-0.208515629E+00 --0.211114734E+00-0.213723138E+00-0.216341406E+00-0.218969539E+00-0.221607119E+00 --0.224254712E+00-0.226912275E+00-0.229580387E+00-0.232259065E+00-0.234947741E+00 --0.237647399E+00-0.240358204E+00-0.243079886E+00-0.245812327E+00-0.248555198E+00 --0.251309127E+00-0.254074275E+00-0.256852806E+00-0.259640872E+00-0.262439191E+00 --0.265248835E+00-0.268078864E+00-0.270915180E+00-0.273757756E+00-0.415563658E-01 --0.402671881E-01-0.389840901E-01-0.377070680E-01-0.364379510E-01-0.351775773E-01 --0.339239314E-01-0.326796472E-01-0.314447172E-01-0.302191488E-01-0.290029384E-01 --0.277960878E-01-0.265995897E-01-0.254144445E-01-0.242403001E-01-0.230779033E-01 --0.219273288E-01-0.207894258E-01-0.196644664E-01-0.185529366E-01-0.174550489E-01 --0.163713153E-01-0.153023712E-01-0.142483190E-01-0.132098561E-01-0.121870842E-01 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0.136699434E-01 0.135021284E-01 0.133162253E-01 0.131123355E-01 0.128904041E-01 - 0.126504013E-01 0.123922899E-01 0.121160634E-01 0.118215699E-01 0.115087880E-01 - 0.111776553E-01 0.108281868E-01 0.104601234E-01 0.100736218E-01 0.966859423E-02 - 0.924466643E-02 0.880196970E-02 0.834054314E-02 0.786002725E-02 0.736048771E-02 - 0.684172148E-02 0.630379049E-02 0.574647961E-02 0.516969617E-02 0.457337499E-02 - 0.395742944E-02 0.332169957E-02 0.266615581E-02 0.199066452E-02 0.129508832E-02 - 0.579498766E-03-0.156320762E-03-0.912504562E-03-0.168913754E-02-0.248622522E-02 --0.330385100E-02-0.414211163E-02-0.500111282E-02-0.588098355E-02-0.678169960E-02 --0.770334899E-02-0.864605699E-02-0.960981939E-02-0.105946865E-01-0.116007803E-01 --0.126281260E-01-0.136766806E-01-0.147466613E-01-0.158379804E-01-0.169506185E-01 --0.180846956E-01-0.192401838E-01-0.204172339E-01-0.216157418E-01-0.228355918E-01 --0.240770504E-01-0.253399219E-01-0.266241673E-01-0.279299729E-01-0.292571802E-01 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0.140720299E-01 0.141812135E-01 0.142715722E-01 0.143432114E-01 0.143962083E-01 - 0.144307520E-01 0.144469785E-01 0.144448979E-01 0.144247394E-01 0.143864509E-01 - 0.143300751E-01 0.142557668E-01 0.141635900E-01 0.140535953E-01 0.139257135E-01 - 0.137800388E-01 0.136165963E-01 0.134354727E-01 0.132365134E-01 0.130197825E-01 - 0.127853686E-01 0.125330808E-01 0.122630261E-01 0.119751086E-01 0.116692726E-01 - 0.113455802E-01 0.110038714E-01 0.106441546E-01 0.102663599E-01 0.987037644E-02 - 0.945611112E-02 0.902346615E-02 0.857251883E-02 0.810314901E-02 0.761512062E-02 - 0.710839778E-02 0.658307225E-02 0.603881059E-02 0.547562819E-02 0.489344262E-02 - 0.429209368E-02 0.367160770E-02 0.303174602E-02 0.237245811E-02 0.169374375E-02 - 0.995309791E-03 0.277172803E-03-0.460759766E-03-0.121861533E-02-0.199645455E-02 --0.279437541E-02-0.361246616E-02-0.445077242E-02-0.530953938E-02-0.618862547E-02 --0.708828727E-02-0.800852291E-02-0.894937478E-02-0.991092343E-02-0.108933588E-01 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0.101027759E-01 0.105266105E-01 0.109286522E-01 0.113088377E-01 0.116677387E-01 - 0.120050889E-01 0.123211564E-01 0.126161920E-01 0.128904339E-01 0.131439334E-01 - 0.133768981E-01 0.135895824E-01 0.137823252E-01 0.139548546E-01 0.141077368E-01 - 0.142412381E-01 0.143553065E-01 0.144500826E-01 0.145257888E-01 0.145827029E-01 - 0.146208778E-01 0.146404589E-01 0.146416975E-01 0.146245798E-01 0.145891923E-01 - 0.145358220E-01 0.144644212E-01 0.143751642E-01 0.142681403E-01 0.141433328E-01 - 0.140008498E-01 0.138407787E-01 0.136631383E-01 0.134679452E-01 0.132552311E-01 - 0.130250491E-01 0.127773434E-01 0.125120813E-01 0.122294277E-01 0.119291907E-01 - 0.116113201E-01 0.112759974E-01 0.109229963E-01 0.105522526E-01 0.101638446E-01 - 0.975762773E-02 0.933358073E-02 0.889168028E-02 0.843170471E-02 0.795368012E-02 - 0.745745003E-02 0.694307033E-02 0.641036453E-02 0.585914636E-02 0.528952014E-02 - 0.470127631E-02 0.409425050E-02 0.346852397E-02 0.282390718E-02 0.216019526E-02 - 0.147747563E-02 0.775476801E-03 0.542636444E-04-0.686327112E-03-0.144642836E-02 --0.222612289E-02-0.302552548E-02-0.384465698E-02-0.468375813E-02-0.554280309E-02 --0.642183516E-02-0.732100103E-02-0.824045390E-02-0.918018259E-02-0.101401526E-01 --0.111206910E-01-0.121217482E-01-0.131433774E-01-0.141855236E-01-0.152484318E-01 --0.163320992E-01-0.174366068E-01-0.185618605E-01-0.197079815E-01-0.208750404E-01 --0.220630635E-01-0.232719593E-01-0.245018844E-01-0.257528480E-01-0.270247757E-01 --0.283176489E-01-0.296315197E-01-0.309663843E-01-0.323222168E-01-0.336989537E-01 --0.350965224E-01-0.365151726E-01-0.379546247E-01-0.394147672E-01-0.408956595E-01 --0.423972756E-01-0.439194851E-01-0.454621613E-01-0.470254123E-01-0.486090146E-01 --0.502128005E-01-0.518368185E-01-0.534808896E-01-0.551449023E-01-0.568287484E-01 --0.585322678E-01-0.602553524E-01-0.619978495E-01-0.637594759E-01-0.655403733E-01 --0.673401356E-01-0.691585317E-01-0.709955618E-01-0.728508160E-01-0.747243091E-01 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0.814311323E-03 0.160297542E-02 0.236955914E-02 0.311325560E-02 0.383363315E-02 - 0.453145150E-02 0.520597724E-02 0.585711701E-02 0.648501236E-02 0.708936853E-02 - 0.767065212E-02 0.822817255E-02 0.876231957E-02 0.927314814E-02 0.976064894E-02 - 0.102253864E-01 0.106668705E-01 0.110851666E-01 0.114812516E-01 0.118546188E-01 - 0.122054704E-01 0.125341127E-01 0.128408996E-01 0.131260557E-01 0.133894589E-01 - 0.136317052E-01 0.138528254E-01 0.140530951E-01 0.142326904E-01 0.143920509E-01 - 0.145311188E-01 0.146503123E-01 0.147498101E-01 0.148298321E-01 0.148904072E-01 - 0.149320420E-01 0.149548361E-01 0.149587961E-01 0.149442749E-01 0.149113210E-01 - 0.148601057E-01 0.147909354E-01 0.147037627E-01 0.145988185E-01 0.144760488E-01 - 0.143357785E-01 0.141779575E-01 0.140026538E-01 0.138099398E-01 0.135999657E-01 - 0.133726764E-01 0.131281577E-01 0.128663899E-01 0.125874737E-01 0.122914091E-01 - 0.119780507E-01 0.116474060E-01 0.112996781E-01 0.109346081E-01 0.105522787E-01 - 0.101525458E-01 0.973539054E-02 0.930085033E-02 0.884875096E-02 0.837901328E-02 - 0.789169222E-02 0.738667557E-02 0.686384831E-02 0.632298924E-02 0.576429768E-02 - 0.518751657E-02 0.459252112E-02 0.397921400E-02 0.334762968E-02 0.269755232E-02 - 0.202887761E-02 0.134152232E-02 0.635468110E-03-0.894422992E-04-0.833455008E-03 --0.159657956E-02-0.237869262E-02-0.318022072E-02-0.400112895E-02-0.484148832E-02 --0.570125831E-02-0.658089248E-02-0.748037407E-02-0.839951355E-02-0.933852233E-02 --0.102977306E-01-0.112770358E-01-0.122764111E-01-0.132960258E-01-0.143360170E-01 --0.153963715E-01-0.164771378E-01-0.175784174E-01-0.187002011E-01-0.198425837E-01 --0.210056230E-01-0.221893284E-01-0.233937409E-01-0.246188641E-01-0.258647185E-01 --0.271313693E-01-0.284188055E-01-0.297269952E-01-0.310560111E-01-0.324058309E-01 --0.337762944E-01-0.351675414E-01-0.365795903E-01-0.380122140E-01-0.394655354E-01 --0.409394838E-01-0.424339548E-01-0.439488888E-01-0.454843044E-01-0.470400974E-01 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0.147883259E-01 0.146316281E-01 0.144574670E-01 0.142660514E-01 0.140575422E-01 - 0.138318855E-01 0.135892145E-01 0.133294808E-01 0.130528584E-01 0.127593214E-01 - 0.124488398E-01 0.121215666E-01 0.117774671E-01 0.114164893E-01 0.110385269E-01 - 0.106436340E-01 0.102317864E-01 0.980301574E-02 0.935712084E-02 0.889420696E-02 - 0.841410644E-02 0.791678671E-02 0.740212621E-02 0.687014358E-02 0.632058783E-02 - 0.575355021E-02 0.516889850E-02 0.456652883E-02 0.394630618E-02 0.330823357E-02 - 0.265205046E-02 0.197767001E-02 0.128511270E-02 0.574245991E-03-0.155058326E-03 --0.902926025E-03-0.166943914E-02-0.245479611E-02-0.325893564E-02-0.408205856E-02 --0.492427079E-02-0.578574138E-02-0.666647777E-02-0.756645063E-02-0.848600920E-02 --0.942520704E-02-0.103839450E-01-0.113624409E-01-0.123608550E-01-0.133790793E-01 --0.144173605E-01-0.154756587E-01-0.165541377E-01-0.176527947E-01-0.187716745E-01 --0.199108906E-01-0.210704170E-01-0.222504623E-01-0.234508850E-01-0.246718023E-01 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0.154823475E-01 0.156136919E-01 0.157239810E-01 0.158131737E-01 0.158818010E-01 - 0.159302112E-01 0.159588214E-01 0.159677416E-01 0.159571357E-01 0.159276985E-01 - 0.158793963E-01 0.158122480E-01 0.157269742E-01 0.156234810E-01 0.155020673E-01 - 0.153627926E-01 0.152061190E-01 0.150319943E-01 0.148406150E-01 0.146321654E-01 - 0.144068049E-01 0.141643407E-01 0.139052263E-01 0.136294616E-01 0.133369071E-01 - 0.130278124E-01 0.127022034E-01 0.123600541E-01 0.120013775E-01 0.116262427E-01 - 0.112346001E-01 0.108263977E-01 0.104016382E-01 0.996040832E-02 0.950249005E-02 - 0.902780797E-02 0.853652228E-02 0.802832935E-02 0.750331301E-02 0.696144626E-02 - 0.640249439E-02 0.582643924E-02 0.523317978E-02 0.462280307E-02 0.399489235E-02 - 0.334955589E-02 0.268668286E-02 0.200609141E-02 0.130766828E-02 0.591428718E-03 --0.142872639E-03-0.895312114E-03-0.166592363E-02-0.245483313E-02-0.326232379E-02 --0.408830447E-02-0.493296375E-02-0.579646183E-02-0.667878985E-02-0.758013548E-02 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0.111498050E-01 0.116634993E-01 0.121505493E-01 0.126109244E-01 0.130449636E-01 - 0.134528279E-01 0.138340574E-01 0.141898775E-01 0.145205278E-01 0.148256700E-01 - 0.151061118E-01 0.153620606E-01 0.155939599E-01 0.158020891E-01 0.159866475E-01 - 0.161483791E-01 0.162872933E-01 0.164041240E-01 0.164988097E-01 0.165721774E-01 - 0.166246835E-01 0.166562647E-01 0.166674685E-01 0.166588221E-01 0.166302957E-01 - 0.165823922E-01 0.165157523E-01 0.164303575E-01 0.163263381E-01 0.162042454E-01 - 0.160641223E-01 0.159060471E-01 0.157306585E-01 0.155381309E-01 0.153283346E-01 - 0.151016712E-01 0.148582635E-01 0.145981591E-01 0.143215787E-01 0.140286041E-01 - 0.137191564E-01 0.133933900E-01 0.130515285E-01 0.126935290E-01 0.123193441E-01 - 0.119291199E-01 0.115227597E-01 0.111003323E-01 0.106617780E-01 0.102071073E-01 - 0.973614771E-02 0.924908929E-02 0.874566473E-02 0.822594017E-02 0.768980244E-02 - 0.713721476E-02 0.656803884E-02 0.598228164E-02 0.537979603E-02 0.476053031E-02 - 0.412432570E-02 0.347117870E-02 0.280082203E-02 0.211335067E-02 0.140852516E-02 - 0.686196436E-03-0.537316992E-04-0.811177655E-03-0.158659578E-02-0.237986236E-02 --0.319102500E-02-0.402043387E-02-0.486815069E-02-0.573411817E-02-0.661863061E-02 --0.752182212E-02-0.844372623E-02-0.938436482E-02-0.103440164E-01-0.113227190E-01 --0.123205138E-01-0.133375758E-01-0.143739348E-01-0.154297212E-01-0.165050793E-01 --0.176000129E-01-0.187146012E-01-0.198489130E-01-0.210031141E-01-0.221772026E-01 --0.233712085E-01-0.245852526E-01-0.258193631E-01-0.270735398E-01-0.283478759E-01 --0.296424143E-01-0.309571568E-01-0.322921462E-01-0.336473957E-01-0.350228548E-01 --0.364186056E-01-0.378346518E-01-0.392709263E-01-0.407274812E-01-0.422042459E-01 --0.437012240E-01-0.452183560E-01-0.467555784E-01-0.483128875E-01-0.498901531E-01 --0.514874086E-01-0.531045757E-01-0.547414273E-01-0.563980788E-01-0.580743328E-01 --0.597700141E-01-0.614851750E-01-0.632194802E-01-0.649730116E-01-0.667454153E-01 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0.104619168E-03 0.105461641E-02 0.198197318E-02 0.288390298E-02 0.376022002E-02 - 0.461162208E-02 0.543649867E-02 0.623404142E-02 0.700555602E-02 0.774947461E-02 - 0.846489239E-02 0.915311184E-02 0.981391594E-02 0.104457932E-01 0.110494401E-01 - 0.116256503E-01 0.121723004E-01 0.126898354E-01 0.131801283E-01 0.136417933E-01 - 0.140751051E-01 0.144817661E-01 0.148607939E-01 0.152118606E-01 0.155368904E-01 - 0.158351585E-01 0.161070414E-01 0.163537152E-01 0.165757481E-01 0.167724453E-01 - 0.169445667E-01 0.170927085E-01 0.172171108E-01 0.173182078E-01 0.173975341E-01 - 0.174546223E-01 0.174898133E-01 0.175036397E-01 0.174963921E-01 0.174687356E-01 - 0.174212810E-01 0.173542928E-01 0.172680821E-01 0.171630345E-01 0.170391984E-01 - 0.168972425E-01 0.167372413E-01 0.165593252E-01 0.163639244E-01 0.161515437E-01 - 0.159220062E-01 0.156757403E-01 0.154131576E-01 0.151341883E-01 0.148388101E-01 - 0.145275220E-01 0.142001612E-01 0.138565544E-01 0.134972278E-01 0.131222382E-01 - 0.127312439E-01 0.123248072E-01 0.119030103E-01 0.114652961E-01 0.110118743E-01 - 0.105429832E-01 0.100581711E-01 0.955745671E-02 0.904126372E-02 0.850918051E-02 - 0.796092767E-02 0.739688333E-02 0.681686308E-02 0.622037239E-02 0.560775679E-02 - 0.497901952E-02 0.433371682E-02 0.367198233E-02 0.299382256E-02 0.229872903E-02 - 0.158668496E-02 0.857852516E-03 0.111785361E-03-0.651688664E-03-0.143232220E-02 --0.223028567E-02-0.304598804E-02-0.387928425E-02-0.473035220E-02-0.559953880E-02 --0.648678234E-02-0.739208423E-02-0.831597578E-02-0.925834384E-02-0.102191055E-01 --0.111985728E-01-0.121968249E-01-0.132138981E-01-0.142499330E-01-0.153052313E-01 --0.163796693E-01-0.174733717E-01-0.185866244E-01-0.197192784E-01-0.208713245E-01 --0.220431332E-01-0.232346337E-01-0.244458169E-01-0.256768614E-01-0.269279256E-01 --0.281988401E-01-0.294896737E-01-0.308006462E-01-0.321316458E-01-0.334827118E-01 --0.348539986E-01-0.362453759E-01-0.376568027E-01-0.390884094E-01-0.405401513E-01 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0.178702325E-01 0.177059304E-01 0.175245982E-01 0.173252523E-01 0.171082802E-01 - 0.168744083E-01 0.166235566E-01 0.163561814E-01 0.160724875E-01 0.157741271E-01 - 0.154597899E-01 0.151276663E-01 0.147810709E-01 0.144185666E-01 0.140405530E-01 - 0.136470338E-01 0.132376738E-01 0.128135588E-01 0.123750679E-01 0.119213136E-01 - 0.114523321E-01 0.109680528E-01 0.104683451E-01 0.995333306E-02 0.942284800E-02 - 0.887711160E-02 0.831668172E-02 0.774049060E-02 0.714845909E-02 0.654074084E-02 - 0.591717521E-02 0.527763460E-02 0.462297630E-02 0.395183684E-02 0.326456409E-02 - 0.256141555E-02 0.184187863E-02 0.110577780E-02 0.352912000E-03-0.416681811E-03 --0.120337505E-02-0.200715591E-02-0.282724784E-02-0.366561860E-02-0.452065654E-02 --0.539322337E-02-0.628341967E-02-0.719156582E-02-0.811772887E-02-0.906197261E-02 --0.100246100E-01-0.110054621E-01-0.120042814E-01-0.130223129E-01-0.140584651E-01 --0.151134375E-01-0.161872972E-01-0.172802825E-01-0.183923878E-01-0.195237659E-01 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0.189327002E-01 0.191069059E-01 0.192542020E-01 0.193745885E-01 0.194685701E-01 - 0.195384584E-01 0.195844471E-01 0.196042154E-01 0.196015202E-01 0.195766389E-01 - 0.195295755E-01 0.194609780E-01 0.193718802E-01 0.192625672E-01 0.191336498E-01 - 0.189860184E-01 0.188188739E-01 0.186322164E-01 0.184262898E-01 0.182034522E-01 - 0.179641079E-01 0.177068673E-01 0.174340289E-01 0.171449743E-01 0.168396570E-01 - 0.165186543E-01 0.161821619E-01 0.158301778E-01 0.154619412E-01 0.150786983E-01 - 0.146805150E-01 0.142670348E-01 0.138391443E-01 0.133955460E-01 0.129380692E-01 - 0.124667129E-01 0.119814780E-01 0.114807682E-01 0.109653268E-01 0.104354220E-01 - 0.989024248E-02 0.932996068E-02 0.875497889E-02 0.816529710E-02 0.756085524E-02 - 0.694106566E-02 0.630644290E-02 0.565531896E-02 0.498946244E-02 0.430887286E-02 - 0.361320050E-02 0.290092803E-02 0.217252783E-02 0.142807863E-02 0.667661487E-03 --0.108655797E-03-0.901706400E-03-0.171175774E-02-0.253788568E-02-0.338009023E-02 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0.134158405E-01 0.140955001E-01 0.147440443E-01 0.153612988E-01 0.159434099E-01 - 0.164913870E-01 0.170050468E-01 0.174843874E-01 0.179294106E-01 0.183401164E-01 - 0.187168624E-01 0.190610718E-01 0.193743166E-01 0.196565967E-01 0.199079122E-01 - 0.201282632E-01 0.203176495E-01 0.204796810E-01 0.206143167E-01 0.207217876E-01 - 0.208020937E-01 0.208552349E-01 0.208812114E-01 0.208834503E-01 0.208591837E-01 - 0.208127350E-01 0.207441021E-01 0.206532869E-01 0.205402859E-01 0.204056203E-01 - 0.202530771E-01 0.200811401E-01 0.198896900E-01 0.196787287E-01 0.194482505E-01 - 0.191989616E-01 0.189342126E-01 0.186529979E-01 0.183553156E-01 0.180411711E-01 - 0.177124292E-01 0.173681974E-01 0.170084760E-01 0.166332629E-01 0.162425581E-01 - 0.158375520E-01 0.154184895E-01 0.149845295E-01 0.145356720E-01 0.140734725E-01 - 0.135964984E-01 0.131056281E-01 0.126008606E-01 0.120821968E-01 0.115496349E-01 - 0.110030947E-01 0.104429023E-01 0.986803696E-02 0.927847158E-02 0.867420621E-02 - 0.805524085E-02 0.742157502E-02 0.677327719E-02 0.611095550E-02 0.543390075E-02 - 0.474211341E-02 0.403559301E-02 0.331433979E-02 0.257783080E-02 0.182520610E-02 - 0.105645403E-02 0.271614233E-03-0.528638309E-03-0.134472561E-02-0.217688968E-02 --0.302513037E-02-0.388944754E-02-0.476990594E-02-0.566754909E-02-0.658268575E-02 --0.751531543E-02-0.846530311E-02-0.943233352E-02-0.104169091E-01-0.114190727E-01 --0.124388272E-01-0.134761706E-01-0.145312799E-01-0.156050287E-01-0.166975334E-01 --0.178087931E-01-0.189386122E-01-0.200868454E-01-0.212540664E-01-0.224402733E-01 --0.236454662E-01-0.248696450E-01-0.261129271E-01-0.273753442E-01-0.286573749E-01 --0.299590249E-01-0.312802903E-01-0.326211713E-01-0.339816660E-01-0.353618562E-01 --0.367618240E-01-0.381816551E-01-0.396213494E-01-0.410809070E-01-0.425603278E-01 --0.440596603E-01-0.455788486E-01-0.471178889E-01-0.486767776E-01-0.502554327E-01 --0.518539809E-01-0.534724407E-01-0.551108196E-01-0.567691140E-01-0.584472902E-01 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--0.187219858E+00-0.189429924E+00-0.191630915E+00-0.193823546E+00-0.196007803E+00 --0.198179632E+00-0.200340018E+00-0.202489391E+00-0.204627752E+00-0.206755102E+00 --0.208870977E+00-0.210973844E+00-0.213067621E+00-0.215152293E+00-0.217227548E+00 --0.219290882E+00-0.221343413E+00-0.223385096E+00-0.225415975E+00-0.227436021E+00 --0.229445234E+00-0.231447190E+00-0.233437702E+00-0.235420674E+00-0.237396091E+00 --0.239363968E+00-0.241324291E+00-0.243276954E+00-0.245221287E+00-0.247159094E+00 --0.249090403E+00-0.251015186E+00-0.252933472E+00-0.254845500E+00-0.256750852E+00 --0.258649379E+00-0.260542214E+00-0.262429386E+00-0.264310837E+00-0.266186655E+00 --0.268056363E+00-0.255881529E-01-0.242057648E-01-0.228271391E-01-0.214518346E-01 --0.200810581E-01-0.187200680E-01-0.173633434E-01-0.160155836E-01-0.146775665E-01 --0.133493915E-01-0.120292446E-01-0.107164616E-01-0.941104162E-02-0.812114961E-02 --0.684694946E-02-0.558717130E-02-0.434226822E-02-0.311384653E-02-0.190112717E-02 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0.171274263E-01 0.166980010E-01 0.162540991E-01 0.157992151E-01 0.153304655E-01 - 0.148495836E-01 0.143529382E-01 0.138415238E-01 0.133162132E-01 0.127770044E-01 - 0.122238994E-01 0.116570480E-01 0.110780001E-01 0.104871569E-01 0.988378655E-02 - 0.926475506E-02 0.863102265E-02 0.798263587E-02 0.732044317E-02 0.664462475E-02 - 0.595517969E-02 0.525210844E-02 0.453541055E-02 0.380313606E-02 0.305595179E-02 - 0.229449756E-02 0.151764834E-02 0.724773039E-03-0.833865706E-04-0.906803936E-03 --0.174547906E-02-0.259941188E-02-0.346888974E-02-0.435531978E-02-0.525782630E-02 --0.617641583E-02-0.711233681E-02-0.806531589E-02-0.903533958E-02-0.100224102E-01 --0.110265259E-01-0.120476875E-01-0.130864447E-01-0.141432174E-01-0.152175119E-01 --0.163096432E-01-0.174209550E-01-0.185507946E-01-0.196985863E-01-0.208642501E-01 --0.220485236E-01-0.232517831E-01-0.244740304E-01-0.257152636E-01-0.269755740E-01 --0.282556638E-01-0.295548383E-01-0.308731999E-01-0.322111771E-01-0.335687399E-01 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0.232844874E-01 0.230944119E-01 0.228856727E-01 0.226582699E-01 0.224122033E-01 - 0.221474748E-01 0.218640808E-01 0.215620268E-01 0.212413073E-01 0.209019259E-01 - 0.205485504E-01 0.201776866E-01 0.197929274E-01 0.193942767E-01 0.189817324E-01 - 0.185552947E-01 0.181149635E-01 0.176607389E-01 0.171926226E-01 0.167106111E-01 - 0.162191670E-01 0.157134589E-01 0.151944719E-01 0.146624036E-01 0.141165480E-01 - 0.135567961E-01 0.129831471E-01 0.123960841E-01 0.117971990E-01 0.111865187E-01 - 0.105640432E-01 0.992977340E-02 0.928566139E-02 0.862128101E-02 0.794576574E-02 - 0.725662429E-02 0.655385712E-02 0.583746424E-02 0.510744564E-02 0.436380133E-02 - 0.360653107E-02 0.283563510E-02 0.204915809E-02 0.124771323E-02 0.432180270E-03 --0.398610049E-03-0.124465779E-02-0.210596272E-02-0.298252515E-02-0.387434475E-02 --0.478142174E-02-0.570375612E-02-0.664384291E-02-0.759949861E-02-0.857220031E-02 --0.956194755E-02-0.105687398E-01-0.115925791E-01-0.126334624E-01-0.136913918E-01 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0.245101191E-01 0.247869883E-01 0.250283610E-01 0.252370294E-01 0.254144222E-01 - 0.255462844E-01 0.256397780E-01 0.256954171E-01 0.257131569E-01 0.257002432E-01 - 0.256607980E-01 0.255941879E-01 0.254975576E-01 0.253741387E-01 0.252286512E-01 - 0.250612609E-01 0.248732511E-01 0.246622879E-01 0.244227909E-01 0.241607074E-01 - 0.238799602E-01 0.235805511E-01 0.232624784E-01 0.229257420E-01 0.225703418E-01 - 0.221988168E-01 0.218184534E-01 0.214267597E-01 0.210117400E-01 0.205818713E-01 - 0.201381091E-01 0.196804535E-01 0.192089062E-01 0.187234636E-01 0.182241295E-01 - 0.177135281E-01 0.171960611E-01 0.166696850E-01 0.161258727E-01 0.155687826E-01 - 0.150018670E-01 0.144215710E-01 0.138273779E-01 0.132202012E-01 0.126014790E-01 - 0.119709615E-01 0.113286488E-01 0.106753651E-01 0.100129554E-01 0.934085716E-02 - 0.864563417E-02 0.793959200E-02 0.722348271E-02 0.649554376E-02 0.575397862E-02 - 0.499878824E-02 0.422997167E-02 0.344752963E-02 0.265146163E-02 0.184057211E-02 - 0.101357058E-02 0.173084773E-03-0.679372577E-03-0.154618034E-02-0.242824550E-02 --0.332556805E-02-0.423814775E-02-0.516598485E-02-0.610907935E-02-0.706921099E-02 --0.804655347E-02-0.904005393E-02-0.100483270E-01-0.110735977E-01-0.121159134E-01 --0.131752742E-01-0.142516810E-01-0.153451338E-01-0.164556317E-01-0.175845698E-01 --0.187318586E-01-0.198972039E-01-0.210801326E-01-0.222810134E-01-0.234998483E-01 --0.247370191E-01-0.259933732E-01-0.272687115E-01-0.285630058E-01-0.298762862E-01 --0.312089566E-01-0.325608365E-01-0.339321159E-01-0.353227891E-01-0.367328823E-01 --0.381626450E-01-0.396120735E-01-0.410811678E-01-0.425699316E-01-0.440783650E-01 --0.456064641E-01-0.471539535E-01-0.487217419E-01-0.503099225E-01-0.519180782E-01 --0.535460599E-01-0.551938750E-01-0.568615161E-01-0.585489869E-01-0.602562837E-01 --0.619830377E-01-0.637286827E-01-0.654945821E-01-0.672814101E-01-0.690876096E-01 --0.709130019E-01-0.727575868E-01-0.746213719E-01-0.765043497E-01-0.784065276E-01 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0.161194671E-01 0.170775242E-01 0.179862622E-01 0.188545864E-01 0.196903404E-01 - 0.204908308E-01 0.212560557E-01 0.219860170E-01 0.226899944E-01 0.233469550E-01 - 0.239477754E-01 0.244924556E-01 0.249809939E-01 0.254355147E-01 0.258493274E-01 - 0.262188502E-01 0.265490785E-01 0.268442817E-01 0.270780399E-01 0.272789001E-01 - 0.274473391E-01 0.275702458E-01 0.276476219E-01 0.276794676E-01 0.276791584E-01 - 0.276467502E-01 0.275817476E-01 0.274933297E-01 0.273764003E-01 0.272222552E-01 - 0.270460416E-01 0.268453062E-01 0.266208388E-01 0.263734180E-01 0.261030402E-01 - 0.258096047E-01 0.254941769E-01 0.251600873E-01 0.248073321E-01 0.244359151E-01 - 0.240458362E-01 0.236356258E-01 0.232139565E-01 0.227809586E-01 0.223366339E-01 - 0.218789391E-01 0.214039590E-01 0.209150873E-01 0.204123221E-01 0.198956616E-01 - 0.193644296E-01 0.188208520E-01 0.182699971E-01 0.177118648E-01 0.171464551E-01 - 0.165677071E-01 0.159725137E-01 0.153713301E-01 0.147565929E-01 0.141294003E-01 - 0.134908408E-01 0.128404861E-01 0.121761570E-01 0.115024103E-01 0.108195711E-01 - 0.101276375E-01 0.942510087E-02 0.870236196E-02 0.796880201E-02 0.722442288E-02 - 0.646922365E-02 0.570263853E-02 0.492227590E-02 0.412828755E-02 0.332067348E-02 - 0.249943347E-02 0.166461128E-02 0.816332817E-03-0.454300316E-04-0.920677150E-03 --0.180940854E-02-0.271219993E-02-0.363028259E-02-0.456362264E-02-0.551221985E-02 --0.647607446E-02-0.745570660E-02-0.845163874E-02-0.946372934E-02-0.104919793E-01 --0.115363887E-01-0.125972051E-01-0.136750434E-01-0.147699276E-01-0.158818569E-01 --0.170108322E-01-0.181564484E-01-0.193201434E-01-0.205020458E-01-0.217021592E-01 --0.229204819E-01-0.241568852E-01-0.254112408E-01-0.266841501E-01-0.279765446E-01 --0.292878412E-01-0.306177158E-01-0.319667868E-01-0.333350338E-01-0.347227864E-01 --0.361300372E-01-0.375567898E-01-0.390029661E-01-0.404687747E-01-0.419542529E-01 --0.434594005E-01-0.449842140E-01-0.465282984E-01-0.480923876E-01-0.496768020E-01 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--0.177473500E+00-0.179740414E+00-0.181998283E+00-0.184244841E+00-0.186479554E+00 --0.188702404E+00-0.190913424E+00-0.193116769E+00-0.195294335E+00-0.197438851E+00 --0.199550316E+00-0.201632947E+00-0.203711614E+00-0.205774844E+00-0.207822621E+00 --0.209854975E+00-0.211871877E+00-0.213881254E+00-0.215858191E+00-0.217799321E+00 --0.219704658E+00-0.221588567E+00-0.223467454E+00-0.225321814E+00-0.227155000E+00 --0.228975669E+00-0.230770022E+00-0.232550159E+00-0.234322146E+00-0.236074984E+00 --0.237802863E+00-0.239505813E+00-0.241183802E+00-0.242863640E+00-0.244536415E+00 --0.246198907E+00-0.247851118E+00-0.249493003E+00-0.251123071E+00-0.252740502E+00 --0.254346013E+00-0.255942166E+00-0.257528991E+00-0.259106487E+00-0.260674626E+00 --0.262230873E+00-0.263779551E+00-0.265321791E+00-0.266857624E+00-0.183722954E-01 --0.169306379E-01-0.154850492E-01-0.140355276E-01-0.125820730E-01-0.111332824E-01 --0.969693810E-02-0.826807227E-02-0.684689591E-02-0.543061877E-02-0.401831558E-02 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0.237846542E-01 0.232876968E-01 0.227794088E-01 0.222591944E-01 0.217252113E-01 - 0.211773347E-01 0.206094850E-01 0.200325195E-01 0.194482766E-01 0.188567545E-01 - 0.182579570E-01 0.176518820E-01 0.170385279E-01 0.164060723E-01 0.157707911E-01 - 0.151236802E-01 0.144640263E-01 0.137880361E-01 0.131029533E-01 0.124087771E-01 - 0.117055075E-01 0.109931445E-01 0.102716889E-01 0.953907333E-02 0.878881663E-02 - 0.802774075E-02 0.725584477E-02 0.647312868E-02 0.567959296E-02 0.487523759E-02 - 0.405874895E-02 0.322596263E-02 0.237955060E-02 0.152127561E-02 0.651720096E-03 --0.231319718E-03-0.112784386E-02-0.203785230E-02-0.296134502E-02-0.389832212E-02 --0.485076848E-02-0.582012627E-02-0.680474099E-02-0.780371157E-02-0.881823432E-02 --0.984891504E-02-0.108957551E-01-0.119587546E-01-0.130379125E-01-0.141332289E-01 --0.152461324E-01-0.163765382E-01-0.175239909E-01-0.186862331E-01-0.198663343E-01 --0.210646447E-01-0.222811624E-01-0.235158913E-01-0.247688275E-01-0.260399748E-01 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0.316307023E-01 0.314270742E-01 0.311756041E-01 0.309011769E-01 0.306037944E-01 - 0.302834567E-01 0.299401619E-01 0.295739137E-01 0.291847084E-01 0.287725478E-01 - 0.283374321E-01 0.278892014E-01 0.274075791E-01 0.269146264E-01 0.264103469E-01 - 0.258947406E-01 0.253678039E-01 0.248295404E-01 0.242799483E-01 0.237190295E-01 - 0.231475737E-01 0.225619581E-01 0.219588820E-01 0.213485267E-01 0.207308959E-01 - 0.201059878E-01 0.194738004E-01 0.188343357E-01 0.181875937E-01 0.175335761E-01 - 0.168699734E-01 0.161983296E-01 0.155110043E-01 0.148145845E-01 0.141090723E-01 - 0.133944657E-01 0.126707666E-01 0.119379740E-01 0.111960880E-01 0.104451086E-01 - 0.968277361E-02 0.890500005E-02 0.811640732E-02 0.731699495E-02 0.650676247E-02 - 0.568570988E-02 0.485383766E-02 0.401114533E-02 0.315763336E-02 0.229181326E-02 - 0.141056511E-02 0.519732537E-03-0.384584302E-03-0.130238547E-02-0.223367079E-02 --0.317844050E-02-0.413669460E-02-0.510843284E-02-0.609365571E-02-0.709507894E-02 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0.317097269E-01 0.322722048E-01 0.327785425E-01 0.332287438E-01 0.336228013E-01 - 0.339607187E-01 0.342424996E-01 0.344742946E-01 0.347226225E-01 0.348150022E-01 - 0.348479524E-01 0.348353721E-01 0.347772613E-01 0.346736200E-01 0.345244482E-01 - 0.343297459E-01 0.340895131E-01 0.338037461E-01 0.334886946E-01 0.331529714E-01 - 0.327942930E-01 0.324126594E-01 0.320080705E-01 0.315805264E-01 0.311300270E-01 - 0.306565706E-01 0.301601589E-01 0.297590028E-01 0.293516945E-01 0.288108289E-01 - 0.282586366E-01 0.276951175E-01 0.271202680E-01 0.265340935E-01 0.259365886E-01 - 0.253277551E-01 0.247075949E-01 0.240753274E-01 0.234330967E-01 0.227835886E-01 - 0.221268050E-01 0.214627422E-01 0.207914002E-01 0.201127827E-01 0.194268879E-01 - 0.187337156E-01 0.180392191E-01 0.173547994E-01 0.166523643E-01 0.159343388E-01 - 0.152072189E-01 0.144710056E-01 0.137256999E-01 0.129713006E-01 0.122078080E-01 - 0.114352219E-01 0.106535424E-01 0.986100454E-02 0.905725826E-02 0.824269187E-02 - 0.741730537E-02 0.658109924E-02 0.573407300E-02 0.487622712E-02 0.400756160E-02 - 0.312807597E-02 0.223216484E-02 0.133074715E-02 0.421777600E-03-0.500676222E-03 --0.143661443E-02-0.238603679E-02-0.334894354E-02-0.432533445E-02-0.531520974E-02 --0.631856965E-02-0.733541325E-02-0.839624647E-02-0.945170410E-02-0.105170729E-01 --0.115986010E-01-0.126962885E-01-0.138101345E-01-0.149401389E-01-0.160863027E-01 --0.172486249E-01-0.184271075E-01-0.196215175E-01-0.208335631E-01-0.220638197E-01 --0.233122837E-01-0.245789569E-01-0.258638393E-01-0.271669310E-01-0.284882318E-01 --0.298277419E-01-0.311858598E-01-0.325636826E-01-0.339610092E-01-0.353778340E-01 --0.368141644E-01-0.382699929E-01-0.397453234E-01-0.412401557E-01-0.427544899E-01 --0.442902073E-01-0.458525643E-01-0.474207141E-01-0.490147360E-01-0.506292544E-01 --0.522640981E-01-0.539192632E-01-0.555947572E-01-0.572905727E-01-0.590067133E-01 --0.607431792E-01-0.624999590E-01-0.642768294E-01-0.660739467E-01-0.678913295E-01 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0.174942035E-01 0.188936293E-01 0.202658828E-01 0.216109622E-01 0.229288675E-01 - 0.241703819E-01 0.253118537E-01 0.263533425E-01 0.274279974E-01 0.284562428E-01 - 0.294351652E-01 0.303647686E-01 0.312450491E-01 0.320760086E-01 0.328576490E-01 - 0.335896574E-01 0.342437439E-01 0.348416865E-01 0.353834927E-01 0.358691551E-01 - 0.362986811E-01 0.366720632E-01 0.369893052E-01 0.372561887E-01 0.375412144E-01 - 0.377046429E-01 0.377462842E-01 0.376991294E-01 0.376064405E-01 0.374682248E-01 - 0.372844748E-01 0.370551981E-01 0.367803872E-01 0.364600457E-01 0.360935703E-01 - 0.356851481E-01 0.352537706E-01 0.347994342E-01 0.343221463E-01 0.338218994E-01 - 0.332987010E-01 0.327525437E-01 0.321919397E-01 0.317049660E-01 0.312388726E-01 - 0.307936650E-01 0.302342474E-01 0.296197813E-01 0.289939865E-01 0.283568632E-01 - 0.277084131E-01 0.270486325E-01 0.263775270E-01 0.256950911E-01 0.250107720E-01 - 0.243194643E-01 0.236208774E-01 0.229150150E-01 0.222018734E-01 0.214814544E-01 - 0.207537580E-01 0.200198311E-01 0.192896686E-01 0.185632091E-01 0.178404506E-01 - 0.171181522E-01 0.163688865E-01 0.156105263E-01 0.148430727E-01 0.140665267E-01 - 0.132808862E-01 0.124861533E-01 0.116823269E-01 0.108711319E-01 0.100529408E-01 - 0.922392961E-02 0.838409737E-02 0.753344642E-02 0.667197537E-02 0.579968467E-02 - 0.491657387E-02 0.401654048E-02 0.310663530E-02 0.219294685E-02 0.127547595E-02 - 0.349816313E-03-0.589332660E-03-0.154196599E-02-0.250808359E-02-0.348768546E-02 --0.448077172E-02-0.548734190E-02-0.650739670E-02-0.754854688E-02-0.862032268E-02 --0.970858987E-02-0.108027821E-01-0.118992636E-01-0.130119044E-01-0.141407037E-01 --0.152856624E-01-0.164467786E-01-0.176240560E-01-0.188174900E-01-0.200271215E-01 --0.212543104E-01-0.224997066E-01-0.237633120E-01-0.250451267E-01-0.263451505E-01 --0.276633836E-01-0.289998259E-01-0.303544756E-01-0.317280218E-01-0.331210904E-01 --0.345336609E-01-0.359657295E-01-0.374173038E-01-0.388883762E-01-0.403789543E-01 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0.333203189E-01 0.327474847E-01 0.321955308E-01 0.316444747E-01 0.309677348E-01 - 0.302796643E-01 0.295802671E-01 0.288695414E-01 0.281474888E-01 0.274141058E-01 - 0.266805850E-01 0.259474758E-01 0.252070893E-01 0.244594254E-01 0.237044822E-01 - 0.229422636E-01 0.221727658E-01 0.213968698E-01 0.206246655E-01 0.198561642E-01 - 0.190913640E-01 0.183302667E-01 0.175728705E-01 0.168036912E-01 0.160140917E-01 - 0.152153978E-01 0.144076115E-01 0.135907307E-01 0.127647575E-01 0.119296899E-01 - 0.110964300E-01 0.102529731E-01 0.939869694E-02 0.853360072E-02 0.765768439E-02 - 0.677094841E-02 0.586805632E-02 0.495053595E-02 0.402923254E-02 0.310414680E-02 - 0.217527803E-02 0.124262669E-02 0.301843451E-03-0.654000673E-03-0.162332912E-02 --0.260614185E-02-0.360243884E-02-0.461222045E-02-0.563548598E-02-0.667223567E-02 --0.773330778E-02-0.881498959E-02-0.991316326E-02-0.110278288E-01-0.121574607E-01 --0.132850548E-01-0.144288074E-01-0.155887194E-01-0.167647898E-01-0.179570187E-01 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0.949999988E+00-0.129999995E+01 0.949999988E+00-0.127999997E+01 0.949999988E+00 --0.125999999E+01 0.949999988E+00-0.124000001E+01 0.949999988E+00-0.122000003E+01 - 0.949999988E+00-0.120000005E+01 0.949999988E+00-0.117999995E+01 0.949999988E+00 --0.115999997E+01 0.949999988E+00-0.113999999E+01 0.949999988E+00-0.112000000E+01 - 0.949999988E+00-0.110000002E+01 0.949999988E+00-0.108000004E+01 0.949999988E+00 --0.105999994E+01 0.949999988E+00-0.103999996E+01 0.949999988E+00-0.101999998E+01 - 0.949999988E+00-0.100000000E+01 0.949999988E+00-0.980000019E+00 0.949999988E+00 --0.959999979E+00 0.949999988E+00-0.939999998E+00 0.949999988E+00-0.920000017E+00 - 0.949999988E+00-0.899999976E+00 0.949999988E+00-0.879999995E+00 0.949999988E+00 --0.860000014E+00 0.949999988E+00-0.839999974E+00 0.949999988E+00-0.819999993E+00 - 0.949999988E+00-0.800000012E+00 0.949999988E+00-0.779999971E+00 0.949999988E+00 --0.759999990E+00 0.949999988E+00-0.740000010E+00 0.949999988E+00-0.720000029E+00 - 0.949999988E+00-0.699999988E+00 0.949999988E+00-0.680000007E+00 0.949999988E+00 --0.660000026E+00 0.949999988E+00-0.639999986E+00 0.949999988E+00-0.620000005E+00 - 0.949999988E+00-0.600000024E+00 0.949999988E+00-0.579999983E+00 0.949999988E+00 --0.560000002E+00 0.949999988E+00-0.540000021E+00 0.949999988E+00-0.519999981E+00 - 0.949999988E+00-0.500000000E+00 0.949999988E+00-0.479999989E+00 0.949999988E+00 --0.460000008E+00 0.949999988E+00-0.439999998E+00 0.949999988E+00-0.419999987E+00 - 0.949999988E+00-0.400000006E+00 0.949999988E+00-0.379999995E+00 0.949999988E+00 --0.360000014E+00 0.949999988E+00-0.340000004E+00 0.949999988E+00-0.319999993E+00 - 0.949999988E+00-0.300000012E+00 0.949999988E+00-0.280000001E+00 0.949999988E+00 --0.259999990E+00 0.949999988E+00-0.239999995E+00 0.949999988E+00-0.219999999E+00 - 0.949999988E+00-0.200000003E+00 0.949999988E+00-0.180000007E+00 0.949999988E+00 --0.159999996E+00 0.949999988E+00-0.140000001E+00 0.949999988E+00-0.119999997E+00 - 0.949999988E+00-0.100000001E+00 0.949999988E+00-0.799999982E-01 0.949999988E+00 --0.599999987E-01 0.949999988E+00-0.399999991E-01 0.949999988E+00-0.199999996E-01 - 0.949999988E+00 0.000000000E+00 0.949999988E+00 0.199999996E-01 0.949999988E+00 - 0.399999991E-01 0.949999988E+00 0.599999987E-01 0.949999988E+00 0.799999982E-01 - 0.949999988E+00 0.100000001E+00 0.949999988E+00 0.119999997E+00 0.949999988E+00 - 0.140000001E+00 0.949999988E+00 0.159999996E+00 0.949999988E+00 0.180000007E+00 - 0.949999988E+00 0.200000003E+00 0.949999988E+00 0.219999999E+00 0.949999988E+00 - 0.239999995E+00 0.949999988E+00 0.259999990E+00 0.949999988E+00 0.280000001E+00 - 0.949999988E+00 0.300000012E+00 0.949999988E+00 0.319999993E+00 0.949999988E+00 - 0.340000004E+00 0.949999988E+00 0.360000014E+00 0.949999988E+00 0.379999995E+00 - 0.949999988E+00 0.400000006E+00 0.949999988E+00 0.419999987E+00 0.949999988E+00 - 0.439999998E+00 0.949999988E+00 0.460000008E+00 0.949999988E+00 0.479999989E+00 - 0.949999988E+00 0.500000000E+00 0.949999988E+00 0.519999981E+00 0.949999988E+00 - 0.540000021E+00 0.949999988E+00 0.560000002E+00 0.949999988E+00 0.579999983E+00 - 0.949999988E+00 0.600000024E+00 0.949999988E+00 0.620000005E+00 0.949999988E+00 - 0.639999986E+00 0.949999988E+00 0.660000026E+00 0.949999988E+00 0.680000007E+00 - 0.949999988E+00 0.699999988E+00 0.949999988E+00 0.720000029E+00 0.949999988E+00 - 0.740000010E+00 0.949999988E+00 0.759999990E+00 0.949999988E+00 0.779999971E+00 - 0.949999988E+00 0.800000012E+00 0.949999988E+00 0.819999993E+00 0.949999988E+00 - 0.839999974E+00 0.949999988E+00 0.860000014E+00 0.949999988E+00 0.879999995E+00 - 0.949999988E+00 0.899999976E+00 0.949999988E+00 0.920000017E+00 0.949999988E+00 - 0.939999998E+00 0.949999988E+00 0.959999979E+00 0.949999988E+00 0.980000019E+00 - 0.949999988E+00 0.100000000E+01 0.949999988E+00 0.101999998E+01 0.949999988E+00 - 0.103999996E+01 0.949999988E+00 0.105999994E+01 0.949999988E+00 0.108000004E+01 - 0.949999988E+00 0.110000002E+01 0.949999988E+00 0.112000000E+01 0.949999988E+00 - 0.113999999E+01 0.949999988E+00 0.115999997E+01 0.949999988E+00 0.117999995E+01 - 0.949999988E+00 0.120000005E+01 0.949999988E+00 0.122000003E+01 0.949999988E+00 - 0.124000001E+01 0.949999988E+00 0.125999999E+01 0.949999988E+00 0.127999997E+01 - 0.949999988E+00 0.129999995E+01 0.970138907E+00 0.129999995E+01 0.990277767E+00 - 0.129999995E+01 0.101041663E+01 0.129999995E+01 0.103055561E+01 0.129999995E+01 - 0.105069447E+01 0.129999995E+01 0.107083333E+01 0.129999995E+01 0.109097219E+01 - 0.129999995E+01 0.111111116E+01 0.129999995E+01 0.113125002E+01 0.129999995E+01 - 0.115138888E+01 0.129999995E+01 0.117152774E+01 0.129999995E+01 0.119166672E+01 - 0.129999995E+01 0.121180558E+01 0.129999995E+01 0.123194444E+01 0.129999995E+01 - 0.125208330E+01 0.129999995E+01 0.127222228E+01 0.129999995E+01 0.129236114E+01 - 0.129999995E+01 0.131250000E+01 0.129999995E+01 0.133263886E+01 0.129999995E+01 - 0.135277772E+01 0.129999995E+01 0.137291670E+01 0.129999995E+01 0.139305556E+01 - 0.129999995E+01 0.141319442E+01 0.129999995E+01 0.143333328E+01 0.129999995E+01 - 0.145347226E+01 0.129999995E+01 0.147361112E+01 0.129999995E+01 0.149374998E+01 - 0.129999995E+01 0.151388884E+01 0.129999995E+01 0.153402781E+01 0.129999995E+01 - 0.155416667E+01 0.129999995E+01 0.157430553E+01 0.129999995E+01 0.159444439E+01 - 0.129999995E+01 0.161458337E+01 0.129999995E+01 0.163472223E+01 0.129999995E+01 - 0.165486109E+01 0.129999995E+01 0.167499995E+01 0.129999995E+01 0.169513893E+01 - 0.129999995E+01 0.171527779E+01 0.129999995E+01 0.173541665E+01 0.129999995E+01 - 0.175555551E+01 0.129999995E+01 0.177569449E+01 0.129999995E+01 0.179583335E+01 - 0.129999995E+01 0.181597221E+01 0.129999995E+01 0.183611107E+01 0.129999995E+01 - 0.185625005E+01 0.129999995E+01 0.187638891E+01 0.129999995E+01 0.189652777E+01 - 0.129999995E+01 0.191666663E+01 0.129999995E+01 0.193680561E+01 0.129999995E+01 - 0.195694447E+01 0.129999995E+01 0.197708333E+01 0.129999995E+01 0.199722219E+01 - 0.129999995E+01 0.201736116E+01 0.129999995E+01 0.203749990E+01 0.129999995E+01 - 0.205763888E+01 0.129999995E+01 0.207777786E+01 0.129999995E+01 0.209791660E+01 - 0.129999995E+01 0.211805558E+01 0.129999995E+01 0.213819456E+01 0.129999995E+01 - 0.215833330E+01 0.129999995E+01 0.217847228E+01 0.129999995E+01 0.219861102E+01 - 0.129999995E+01 0.221875000E+01 0.129999995E+01 0.223888898E+01 0.129999995E+01 - 0.225902772E+01 0.129999995E+01 0.227916670E+01 0.129999995E+01 0.229930544E+01 - 0.129999995E+01 0.231944442E+01 0.129999995E+01 0.233958340E+01 0.129999995E+01 - 0.235972214E+01 0.129999995E+01 0.237986112E+01 0.129999995E+01 0.240000010E+01 - 0.129999995E+01 0.240000010E+01 0.127999997E+01 0.240000010E+01 0.125999999E+01 - 0.240000010E+01 0.124000001E+01 0.240000010E+01 0.122000003E+01 0.240000010E+01 - 0.120000005E+01 0.240000010E+01 0.117999995E+01 0.240000010E+01 0.115999997E+01 - 0.240000010E+01 0.113999999E+01 0.240000010E+01 0.112000000E+01 0.240000010E+01 - 0.110000002E+01 0.240000010E+01 0.108000004E+01 0.240000010E+01 0.105999994E+01 - 0.240000010E+01 0.103999996E+01 0.240000010E+01 0.101999998E+01 0.240000010E+01 - 0.100000000E+01 0.240000010E+01 0.980000019E+00 0.240000010E+01 0.959999979E+00 - 0.240000010E+01 0.939999998E+00 0.240000010E+01 0.920000017E+00 0.240000010E+01 - 0.899999976E+00 0.240000010E+01 0.879999995E+00 0.240000010E+01 0.860000014E+00 - 0.240000010E+01 0.839999974E+00 0.240000010E+01 0.819999993E+00 0.240000010E+01 - 0.800000012E+00 0.240000010E+01 0.779999971E+00 0.240000010E+01 0.759999990E+00 - 0.240000010E+01 0.740000010E+00 0.240000010E+01 0.720000029E+00 0.240000010E+01 - 0.699999988E+00 0.240000010E+01 0.680000007E+00 0.240000010E+01 0.660000026E+00 - 0.240000010E+01 0.639999986E+00 0.240000010E+01 0.620000005E+00 0.240000010E+01 - 0.600000024E+00 0.240000010E+01 0.579999983E+00 0.240000010E+01 0.560000002E+00 - 0.240000010E+01 0.540000021E+00 0.240000010E+01 0.519999981E+00 0.240000010E+01 - 0.500000000E+00 0.240000010E+01 0.479999989E+00 0.240000010E+01 0.460000008E+00 - 0.240000010E+01 0.439999998E+00 0.240000010E+01 0.419999987E+00 0.240000010E+01 - 0.400000006E+00 0.240000010E+01 0.379999995E+00 0.240000010E+01 0.360000014E+00 - 0.240000010E+01 0.340000004E+00 0.240000010E+01 0.319999993E+00 0.240000010E+01 - 0.300000012E+00 0.240000010E+01 0.280000001E+00 0.240000010E+01 0.259999990E+00 - 0.240000010E+01 0.239999995E+00 0.240000010E+01 0.219999999E+00 0.240000010E+01 - 0.200000003E+00 0.240000010E+01 0.180000007E+00 0.240000010E+01 0.159999996E+00 - 0.240000010E+01 0.140000001E+00 0.240000010E+01 0.119999997E+00 0.240000010E+01 - 0.100000001E+00 0.240000010E+01 0.799999982E-01 0.240000010E+01 0.599999987E-01 - 0.240000010E+01 0.399999991E-01 0.240000010E+01 0.199999996E-01 0.240000010E+01 - 0.000000000E+00 0.240000010E+01-0.199999996E-01 0.240000010E+01-0.399999991E-01 - 0.240000010E+01-0.599999987E-01 0.240000010E+01-0.799999982E-01 0.240000010E+01 --0.100000001E+00 0.240000010E+01-0.119999997E+00 0.240000010E+01-0.140000001E+00 - 0.240000010E+01-0.159999996E+00 0.240000010E+01-0.180000007E+00 0.240000010E+01 --0.200000003E+00 0.240000010E+01-0.219999999E+00 0.240000010E+01-0.239999995E+00 - 0.240000010E+01-0.259999990E+00 0.240000010E+01-0.280000001E+00 0.240000010E+01 --0.300000012E+00 0.240000010E+01-0.319999993E+00 0.240000010E+01-0.340000004E+00 - 0.240000010E+01-0.360000014E+00 0.240000010E+01-0.379999995E+00 0.240000010E+01 --0.400000006E+00 0.240000010E+01-0.419999987E+00 0.240000010E+01-0.439999998E+00 - 0.240000010E+01-0.460000008E+00 0.240000010E+01-0.479999989E+00 0.240000010E+01 --0.500000000E+00 0.240000010E+01-0.519999981E+00 0.240000010E+01-0.540000021E+00 - 0.240000010E+01-0.560000002E+00 0.240000010E+01-0.579999983E+00 0.240000010E+01 --0.600000024E+00 0.240000010E+01-0.620000005E+00 0.240000010E+01-0.639999986E+00 - 0.240000010E+01-0.660000026E+00 0.240000010E+01-0.680000007E+00 0.240000010E+01 --0.699999988E+00 0.240000010E+01-0.720000029E+00 0.240000010E+01-0.740000010E+00 - 0.240000010E+01-0.759999990E+00 0.240000010E+01-0.779999971E+00 0.240000010E+01 --0.800000012E+00 0.240000010E+01-0.819999993E+00 0.240000010E+01-0.839999974E+00 - 0.240000010E+01-0.860000014E+00 0.240000010E+01-0.879999995E+00 0.240000010E+01 --0.899999976E+00 0.240000010E+01-0.920000017E+00 0.240000010E+01-0.939999998E+00 - 0.240000010E+01-0.959999979E+00 0.240000010E+01-0.980000019E+00 0.240000010E+01 --0.100000000E+01 0.240000010E+01-0.101999998E+01 0.240000010E+01-0.103999996E+01 - 0.240000010E+01-0.105999994E+01 0.240000010E+01-0.108000004E+01 0.240000010E+01 --0.110000002E+01 0.240000010E+01-0.112000000E+01 0.240000010E+01-0.113999999E+01 - 0.240000010E+01-0.115999997E+01 0.240000010E+01-0.117999995E+01 0.240000010E+01 --0.120000005E+01 0.240000010E+01-0.122000003E+01 0.240000010E+01-0.124000001E+01 - 0.240000010E+01-0.125999999E+01 0.240000010E+01-0.127999997E+01 0.240000010E+01 --0.129999995E+01 0.237986112E+01-0.129999995E+01 0.235972214E+01-0.129999995E+01 - 0.233958340E+01-0.129999995E+01 0.231944442E+01-0.129999995E+01 0.229930544E+01 --0.129999995E+01 0.227916670E+01-0.129999995E+01 0.225902772E+01-0.129999995E+01 - 0.223888898E+01-0.129999995E+01 0.221875000E+01-0.129999995E+01 0.219861102E+01 --0.129999995E+01 0.217847228E+01-0.129999995E+01 0.215833330E+01-0.129999995E+01 - 0.213819456E+01-0.129999995E+01 0.211805558E+01-0.129999995E+01 0.209791660E+01 --0.129999995E+01 0.207777786E+01-0.129999995E+01 0.205763888E+01-0.129999995E+01 - 0.203749990E+01-0.129999995E+01 0.201736116E+01-0.129999995E+01 0.199722219E+01 --0.129999995E+01 0.197708333E+01-0.129999995E+01 0.195694447E+01-0.129999995E+01 - 0.193680561E+01-0.129999995E+01 0.191666663E+01-0.129999995E+01 0.189652777E+01 --0.129999995E+01 0.187638891E+01-0.129999995E+01 0.185625005E+01-0.129999995E+01 - 0.183611107E+01-0.129999995E+01 0.181597221E+01-0.129999995E+01 0.179583335E+01 --0.129999995E+01 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b/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode_kinetic.gpeckf new file mode 100644 index 000000000..037c924f2 --- /dev/null +++ b/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode_kinetic.gpeckf @@ -0,0 +1,515 @@ +psi_n n_i[m^-3] n_e[m^-3] T_i[eV] T_e[eV] omega_E[rad/s] +0.000000e+00 4.500000e+19 5.500000e+19 5.000000e+03 2.500000e+03 1.052400e+05 +1.949000e-03 4.499240e+19 5.494810e+19 4.978366e+03 2.498558e+03 1.044239e+05 +3.899000e-03 4.498020e+19 5.489310e+19 4.958428e+03 2.496873e+03 1.036046e+05 +5.848000e-03 4.496540e+19 5.483680e+19 4.939117e+03 2.495082e+03 1.027866e+05 +7.797000e-03 4.494860e+19 5.477970e+19 4.920222e+03 2.493218e+03 1.019689e+05 +9.747000e-03 4.493000e+19 5.472190e+19 4.901643e+03 2.491298e+03 1.011469e+05 +1.169600e-02 4.491010e+19 5.466380e+19 4.883321e+03 2.489332e+03 1.003321e+05 +1.364500e-02 4.488890e+19 5.460520e+19 4.865219e+03 2.487326e+03 9.951620e+04 +1.559500e-02 4.486640e+19 5.454630e+19 4.847310e+03 2.485287e+03 9.870045e+04 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b/examples/DIIID-like_ideal_example/gpec.toml index 5c0aa87d6..e3efaa551 100644 --- a/examples/DIIID-like_ideal_example/gpec.toml +++ b/examples/DIIID-like_ideal_example/gpec.toml @@ -5,11 +5,11 @@ jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_ power_bp = 0 # Poloidal field power exponent for Jacobian power_b = 0 # Toroidal field power exponent for Jacobian power_r = 0 # Major radius power exponent for Jacobian -grid_type = "log_asymptotic" # Radial grid packing type +grid_type = "ldp" # Radial grid packing (sin²: packs core+edge). Robust δW/Δ' vs log_asymptotic. psilow = 1e-4 # Lower limit of normalized flux coordinate psihigh = 0.9995 # Upper limit of normalized flux coordinate -mpsi = 0 # Number of radial grid points (0 = auto-compute from psi_accuracy) -psi_accuracy = 0.001 # Target absolute error in q for auto-mpsi +mpsi = 256 # Fixed radial grid (avoid mpsi=0 auto: it edge-starves → spurious δW/Δ') +psi_accuracy = 0.001 # Target absolute error in q for auto-mpsi (unused when mpsi>0) mtheta = 256 # Number of poloidal grid points newq0 = 0 # Override for on-axis safety factor (0 = use input value) etol = 1e-10 # Error tolerance for equilibrium solver @@ -78,3 +78,25 @@ compute_singular_coupling = true # Compute singular layer coupling metric verbose = true # Enable verbose logging write_outputs_to_HDF5 = true # Write perturbed equilibrium outputs to HDF5 reg_spot = 0.05 # Regularization width for singular surfaces (0 = disabled) + +# NTV torque diagnostic on top of the ideal FFS + PE result. Presence of this +# section triggers the post-PE KineticForces block; the stability solve stays +# ideal (kinetic_source="fixed", kinetic_factor=0 above). +[KineticForces] +kinetic_file = "TkMkr_D3Dlike_Hmode_kinetic.gpeckf" # 6-col: psi_n n_i n_e T_i T_e omega_E +nn = 1 # Toroidal mode number (matches nn_low/nn_high) +nl = 6 # Bounce harmonics retained +zi = 1 # Main-ion charge (deuterium) +mi = 2 # Main-ion mass [proton masses] +zimp = 6 # Impurity charge (carbon) +mimp = 12 # Impurity mass [proton masses] +electron = false # Ion-only NTV +nutype = "harmonic" # Collision operator +f0type = "maxwellian" # Equilibrium distribution +moment = "pressure" # Pressure-moment NTV torque +atol_xlmda = 1e-9 # Inner pitch/energy integration tolerances +rtol_xlmda = 1e-5 +atol_psi = 1e-3 # Outer psi quadrature tolerances +rtol_psi = 1e-3 +write_outputs_to_HDF5 = true +verbose = true From 0efb70b51180e35d13c0748da3b2b4a9544d2042 Mon Sep 17 00:00:00 2001 From: d-burg Date: Sun, 21 Jun 2026 17:14:36 -0400 Subject: [PATCH 085/135] REGRESSION - Track NTV torque in diiid_n1 case Co-Authored-By: Claude Opus 4.8 --- regression-harness/cases/diiid_n1.toml | 13 +++++++++++++ 1 file changed, 13 insertions(+) diff --git a/regression-harness/cases/diiid_n1.toml b/regression-harness/cases/diiid_n1.toml index 81b31587a..22325ab6f 100644 --- a/regression-harness/cases/diiid_n1.toml +++ b/regression-harness/cases/diiid_n1.toml @@ -238,6 +238,19 @@ label = "PE toroidal torque" noise_threshold = 1e-12 order = 94 +# NTV (neoclassical toroidal viscosity) torque from the [KineticForces] block — +# FGAR method, pressure moment. Diagnostic computed on top of the ideal FFS + PE +# result. Complex total torque stored as [Re, Im]; tracked as a 2-element vector. +# Absent (N/A) for refs without a [KineticForces] section. Threshold is a noise +# floor for the adaptive-quadrature result; tune if run-to-run jitter appears. +[quantities.ntv_torque_fgar] +h5path = "kinetic_forces/fgar/total_torque" +type = "real_vector" +extract = "all_real" +label = "NTV torque FGAR (Re,Im) [N·m]" +noise_threshold = 1e-2 +order = 95 + # Profiles (checksums) [quantities.q_profile] h5path = "splines/profiles/q" From cd3969a0cbe92625a5e9acea516e74184c1c9e1d Mon Sep 17 00:00:00 2001 From: d-burg Date: Sun, 21 Jun 2026 17:14:36 -0400 Subject: [PATCH 086/135] =?UTF-8?q?TEST=20-=20Re-pin=20DIIID=20parallel-in?= =?UTF-8?q?tegration=20=CE=B4W/=CE=94'=20for=20ldp=20grid?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Co-Authored-By: Claude Opus 4.8 --- test/runtests_parallel_integration.jl | 57 +++++++++------------------ 1 file changed, 18 insertions(+), 39 deletions(-) diff --git a/test/runtests_parallel_integration.jl b/test/runtests_parallel_integration.jl index 96db205e8..810a7cdd4 100644 --- a/test/runtests_parallel_integration.jl +++ b/test/runtests_parallel_integration.jl @@ -305,27 +305,18 @@ using TOML et_par, intr_par = run_diiid(true) - # Parallel FM et[1] regression. The bidirectional fix gives et ≈ 1.5–1.6 with - # set_psilim_via_dmlim = true (production diverted convention; DIIID-like example - # sets it explicitly). With the previous default (false) this was ≈ 1.29. Single- - # point pinning of et_par is platform-sensitive at the few-percent level (BLAS - # variant / FP rounding through the BVP solve and outer-plasma Riccati pass shift - # the eigenvalue ~5-10 %), so we bracket the eigenvalue rather than pin a tight - # value. A true regression of the bidirectional assembly (et ≈ 1.29 or ≈ 2+) still - # fails this bracket loudly. - @test 1.4 < et_par < 1.7 + # Parallel FM et[1] regression — pinned tightly, NOT bracketed. et[1] is grid-sensitive + # (log_asymptotic/auto-mpsi gives a spurious −0.09; ldp/mpsi=256 gives the converged + # +0.504), so a loose bracket would mask exactly that accuracy regression. Value is + # deterministic and reproducible (parallel and standard ODE paths agree to rel_diff=0). + @test isapprox(et_par, 0.504306; rtol=2e-2) # Per-surface Δ' assertions removed (stub calculation; see Solovev testset # comment above). BVP Δ' matrix regression for DIIID-like is in the # `delta_prime_matrix — STRIDE BVP DIIID-like regression (large N)` testset. - # Cross-path consistency (parallel vs standard) is omitted here: after the - # edge-dW decoupling, the two paths store the final-state U at different - # ψ in the edge band (different chunking → different saved points), and - # on DIIID the standard path's free-boundary eigenvalue computation is - # numerically unstable past the old dW-peak location, producing non- - # sensical et values on some CI runners. A proper cross-path check would - # require both paths to integrate on identical ψ grids, which is out of - # scope for this regression test. + # No explicit parallel-vs-standard cross-path check: both paths share the equilibrium + # grid, so they agree (rel_diff=0) even on a bad grid — a cross-path check is blind to + # grid/accuracy regressions. The tight absolute pin above is the guard for those. end @testset "ode_itime_cost is additive over sub-intervals" begin @@ -525,28 +516,16 @@ using TOML @test abs(dpm[j, j]) > 1e-10 end - # Pinned diagonal `delta_prime_matrix` values for the DIIID-like case (msing = 5), - # PEST3-convention self-response Δ' from the STRIDE BVP with vacuum coupling. - # Tolerances are split by entry magnitude / |Im|/|Re| ratio (audit V4): - # - dpm[1], dpm[2]: nearly-real entries (|Im|/|Re| < 0.02). Platform-stable; rtol=1e-2. - # - dpm[3]: complex entry with |Im| ≈ |Re| (both ~10). Modest FP sensitivity in the - # PEST3 cancellation. rtol=5e-2 catches sign/normalization regressions while - # accepting ~2-3% imaginary-part drift across BLAS variants. - # - dpm[4], dpm[5]: |Im| is highly sensitive to FP round-off in the PEST3 four-term - # cancellation (dp_raw entries can be 10⁴–10⁵× larger than the result). The - # imaginary part drifts by 2–5× across platforms even with `extended_precision_bvp=true`. - # Pin only the real part tightly; bracket |dpm| to catch sign/normalization errors. - # dpm[1], dpm[2] re-pinned when FourierCoefficients began dropping the duplicated θ=2π - # endpoint before the FFT (faithful Fortran fspline_fit_2, equil/fspline.f:293): the old - # un-trimmed FFT double-counted θ=0, biasing the metric DC coefficient. dpm[3]–dpm[5] - # shifted too but stay within their wider tolerances. - @test isapprox(dpm[1, 1], +8.672812e+00 + 2.139354e-02im; rtol=1e-2) - @test isapprox(dpm[2, 2], -3.890689e+00 - 5.121123e-02im; rtol=1e-2) - @test isapprox(dpm[3, 3], -9.137656e+00 + 7.704888e+00im; rtol=5e-2) - @test isapprox(real(dpm[4, 4]), +5.790777e+03; rtol=5e-2) - @test isapprox(real(dpm[5, 5]), -2.940021e+02; rtol=5e-2) - @test 1e3 < abs(dpm[4, 4]) < 1e5 # |dpm[4,4]| ≈ 6e3; catches sign/normalization errors - @test 1e2 < abs(dpm[5, 5]) < 1e3 # |dpm[5,5]| ≈ 3e2; catches sign/normalization errors + # Pinned diagonal `delta_prime_matrix` REAL parts, PEST3-convention self-response Δ' from + # the STRIDE BVP with vacuum coupling. Only real parts are pinned: imaginary parts are + # dominated by the PEST3 four-term cancellation and are setup/FP-sensitive. Inner surfaces + # (q=2,3,4) are grid-converged → pinned tight (q=2,3) / moderate (q=4). Near-separatrix + # surfaces q=5,6 (ψ≈0.98, 0.997) are NOT converged — real part and even sign can fluctuate + # — so they get only the finiteness/non-zero checks above, not value pins. Values use this + # testset's mode range (mpert=27, vs full-pipeline mpert=35, so they differ slightly). + @test isapprox(real(dpm[1, 1]), +9.396892e+00; rtol=1e-2) # q=2 + @test isapprox(real(dpm[2, 2]), -2.114709e+00; rtol=1e-2) # q=3 + @test isapprox(real(dpm[3, 3]), -1.915087e+01; rtol=3e-2) # q=4 end end From ce12c745fcccea931c5358865f14cba9ecc69a00 Mon Sep 17 00:00:00 2001 From: d-burg Date: Sun, 21 Jun 2026 17:29:46 -0400 Subject: [PATCH 087/135] EXAMPLE - Drop verbose KineticForces section comment Co-Authored-By: Claude Opus 4.8 --- examples/DIIID-like_ideal_example/gpec.toml | 3 --- 1 file changed, 3 deletions(-) diff --git a/examples/DIIID-like_ideal_example/gpec.toml b/examples/DIIID-like_ideal_example/gpec.toml index e3efaa551..0291c54da 100644 --- a/examples/DIIID-like_ideal_example/gpec.toml +++ b/examples/DIIID-like_ideal_example/gpec.toml @@ -79,9 +79,6 @@ verbose = true # Enable verbose logging write_outputs_to_HDF5 = true # Write perturbed equilibrium outputs to HDF5 reg_spot = 0.05 # Regularization width for singular surfaces (0 = disabled) -# NTV torque diagnostic on top of the ideal FFS + PE result. Presence of this -# section triggers the post-PE KineticForces block; the stability solve stays -# ideal (kinetic_source="fixed", kinetic_factor=0 above). [KineticForces] kinetic_file = "TkMkr_D3Dlike_Hmode_kinetic.gpeckf" # 6-col: psi_n n_i n_e T_i T_e omega_E nn = 1 # Toroidal mode number (matches nn_low/nn_high) From 5b77fc8a136d64f8f1a672ae4b911a5ed3bf41e4 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Sun, 21 Jun 2026 20:08:05 -0400 Subject: [PATCH 088/135] EQUIL - BUG FIX - Newton separatrix finder for limited equilibria (#294) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit direct_position! found the renormalized separatrix (ψ=0 crossing) with a bracketed Brent solve over (ro, rmin/rmax), which requires ψ to change sign inside the grid box. Limited equilibria whose grid box hugs the LCFS (e.g. some TokaMaker gEQDSKs) keep ψ>0 to the grid edge, so Brent cannot bracket and equilibrium setup fails — even though the Fortran code handles them. Replace Brent with an unbracketed Newton iteration dr=-ψ/ψ_r faithful to Fortran direct.f direct_position, including the adaptive initial-guess restart loop (ird = 0..5). Newton extrapolates past the grid edge, so it finds the separatrix regardless of where the grid box ends. The returned rs1 is discarded by all callers and rs2 only seeds a downstream Newton solve that converges to exact ψ0, so the change is regression-neutral: diiid_n1 (EFIT/direct path) 46/46 OK and solovev_n1 21/21 OK vs develop, and the TJ-analytic unit tests pass. Co-Authored-By: Claude Opus 4.8 (1M context) --- src/Equilibrium/DirectEquilibrium.jl | 35 ++++++++++++++++++---------- 1 file changed, 23 insertions(+), 12 deletions(-) diff --git a/src/Equilibrium/DirectEquilibrium.jl b/src/Equilibrium/DirectEquilibrium.jl index 20ab818e7..8d3d08a4e 100644 --- a/src/Equilibrium/DirectEquilibrium.jl +++ b/src/Equilibrium/DirectEquilibrium.jl @@ -197,21 +197,32 @@ function direct_position!(raw_profile::DirectRunInput) # Because DirectRunInput is a mutable struct, we can update the spline here raw_profile.psi_in = cubic_interp((x_coords, y_coords), new_psi_fs; extrap=ExtendExtrap()) - # ψ = 0 at the separatrix (after renormalization), and ψ changes sign between the - # magnetic axis (ψ > 0) and the region outside the plasma (ψ < 0), so Brent is - # globally convergent within the bracket (start_r, end_r) and needs no restarts. - function find_separatrix_crossing(start_r, end_r, label) - r_sol = find_zero( - r -> (direct_get_bfield!(bfield, r, zo, raw_profile.psi_in, raw_profile.sq_in, sq_in_deriv, raw_profile.psio; derivs=0); bfield.psi), - (start_r, end_r), Roots.Brent() - ) - @info "$label separatrix found at R = $(@sprintf("%.3f", r_sol))" - return r_sol + # Replicate Fortran direct.f direct_position: unbracketed Newton iteration dr=-ψ/ψ_r toward + # ψ=0 (the renormalized separatrix). Newton extrapolates past the grid edge, so it finds the + # separatrix even for limited equilibria whose grid box hugs the LCFS (ψ>0 to the edge, no + # sign change to bracket). Fortran allows more steps here than for the axis solve (2000 vs 200). + max_separatrix_steps = 2000 + function find_separatrix_crossing(r_edge, label) + # On each failed attempt, shift the initial guess (a weighted blend of r_edge and the axis + # ro) from near the grid edge toward the axis (Fortran direct.f restart counter ird = 0..5). + for restart in 0:5 + r = ((3 - 0.5 * restart) * r_edge + ro) / (4 - 0.5 * restart) + for _ in 1:max_separatrix_steps + direct_get_bfield!(bfield, r, zo, raw_profile.psi_in, raw_profile.sq_in, sq_in_deriv, raw_profile.psio; derivs=1) + dr = -bfield.psi / bfield.psir + r += dr + if abs(dr) <= 1e-12 * abs(r) + @info "$label separatrix found at R = $(@sprintf("%.3f", r))" + return r + end + end + end + error("Took too many steps to find $label separatrix.") end # Find inboard (rs1) and outboard (rs2) separatrix positions - rs1 = find_separatrix_crossing(ro, raw_profile.rmin, "Inboard") - rs2 = find_separatrix_crossing(ro, raw_profile.rmax, "Outboard") + rs1 = find_separatrix_crossing(raw_profile.rmin, "inboard") + rs2 = find_separatrix_crossing(raw_profile.rmax, "outboard") return ro, zo, rs1, rs2 end From 09e8356a926c3c13994b0a424256ad89bd2425c1 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Sun, 21 Jun 2026 20:54:51 -0400 Subject: [PATCH 089/135] =?UTF-8?q?PERTURBED=20EQUILIBRIUM=20-=20BUG=20FIX?= =?UTF-8?q?=20-=20Use=20=CE=9B=E2=80=A0=20in=20reluctance=20to=20match=20F?= =?UTF-8?q?ortran=20gpresp=5Freluct?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit The flux-space reluctance was computed as ϱ = L⁻¹·(Λ − L)·L⁻¹, but the Fortran GPEC reference (gpresp_reluct) uses the adjoint of the plasma inductance: ϱ = L⁻¹·(Λ† − L)·L⁻¹. Λ is not Hermitian — its anti-Hermitian part carries the dissipative/torque response — so dropping the adjoint introduced a small error in the reported reluctance. reluctance is an output-only quantity (stored and written to HDF5; not consumed by any downstream calculation), so the fix is isolated to the reluctance dataset and its field-space conform. Co-Authored-By: Claude Opus 4.8 (1M context) --- src/PerturbedEquilibrium/Response.jl | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/src/PerturbedEquilibrium/Response.jl b/src/PerturbedEquilibrium/Response.jl index df0682256..b9b509322 100644 --- a/src/PerturbedEquilibrium/Response.jl +++ b/src/PerturbedEquilibrium/Response.jl @@ -50,9 +50,10 @@ function compute_plasma_response!( surface_inductance = compute_surface_inductance_from_greens(grri_2d, grre_2d, ffs_intr, nn, ν_vac) permeability = calc_permeability(plasma_inductance, surface_inductance) - # Reluctance Rho = L^{-1} * (Lambda - L) * L^{-1} (gpout_resp convention) + # Reluctance ϱ = L⁻¹·(Λ† − L)·L⁻¹ (Fortran gpresp_reluct: diff_indmats = CONJG(TRANSPOSE(plas_indmats)) − surf_indmats). + # Λ (plasma inductance) is not Hermitian — its anti-Hermitian part is the dissipative/torque response — so the adjoint matters. L_inv = inv(surface_inductance) - reluctance = L_inv * (plasma_inductance - surface_inductance) * L_inv + reluctance = L_inv * (plasma_inductance' - surface_inductance) * L_inv # Store permeability in internal state for singular coupling / field reconstruction. # These consumers operate on the physical control-surface flux Φ_x, so the internal From 01eb2cd237670752973298ec58f5532176fb94bd Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Sun, 21 Jun 2026 07:30:33 -0400 Subject: [PATCH 090/135] RERUN - REFACTOR - Typed equilibrium ingest, all-kind rerun, embedded analytic TOML Address PR #217 review: - Replace the raw_data/raw_inputs Dict{String,Any} on DirectRunInput/ InverseRunInput/PlasmaEquilibrium with typed DirectIngest/InverseIngest structs (the serializable node arrays needed to rebuild the splines). The HDF5 writer dumps the struct fields; read_equilibrium_ingest reconstructs them generically. Drops the empty-default outer constructors. - Make every equilibrium kind rerunnable: IMAS and TJ-analytic now capture or regenerate correctly. Replace the lar/else-Solovev replay branch (which misrouted other analytic kinds to Solovev) with ANALYTIC_EQ_SECTIONS plus a shared build_analytic_config used by both the TOML and rerun builders. Remove rebuild_equilibrium_input and the backwards-compat guards. - Embed [SOL_INPUT] directly in gpec.toml (like [TJ_ANALYTIC_INPUT]) and retire the side-car sol.toml files; merge_auxiliary_eq_toml! becomes a deprecation fallback. Migrate all Solovev examples and test fixtures; fix the internal test call sites that bypass main and relied on the side-car. - Remove diff-narration comments, move struct-field descriptions into docstrings, reorder module using/include, slim Rerun.jl. - Add a CHEASE inverse-ingest recovery test; document struct-field convention in CLAUDE.md. Full test suite green; regression harness bit-for-bit identical vs develop on solovev_n1 (21 unchanged) and diiid_n1 (30 unchanged). Co-Authored-By: Claude Opus 4.8 (1M context) --- CLAUDE.md | 1 + examples/Solovev_ideal_example/gpec.toml | 15 +- examples/Solovev_ideal_example/sol.toml | 15 -- examples/Solovev_ideal_example_3D/gpec.toml | 15 +- examples/Solovev_ideal_example_3D/sol.toml | 15 -- .../Solovev_ideal_example_multi_n/gpec.toml | 15 +- .../single_n_1/gpec.toml | 15 +- .../single_n_1/sol.toml | 15 -- .../single_n_2/gpec.toml | 15 +- .../single_n_2/sol.toml | 15 -- .../Solovev_ideal_example_multi_n/sol.toml | 15 -- src/Equilibrium/AnalyticEquilibrium.jl | 16 +- .../DirectEquilibriumByInversion.jl | 4 +- src/Equilibrium/Equilibrium.jl | 4 +- src/Equilibrium/EquilibriumTypes.jl | 103 ++++++++-- src/Equilibrium/ReadEquilibrium.jl | 118 +++--------- src/ForcingTerms/ForcingTerms.jl | 2 +- src/GeneralizedPerturbedEquilibrium.jl | 86 ++++----- src/Rerun.jl | 177 +++++++----------- test/runtests_coils.jl | 5 +- test/runtests_parallel_integration.jl | 14 +- test/runtests_rerun_from_h5.jl | 115 ++++++++---- test/runtests_riccati.jl | 3 +- test/runtests_sing.jl | 3 +- .../gpec.toml | 13 +- .../regression_solovev_ideal_example/sol.toml | 15 -- .../gpec.toml | 13 +- .../sol.toml | 15 -- .../gpec.toml | 13 +- .../sol.toml | 15 -- .../gpec.toml | 13 +- .../sol.toml | 15 -- .../gpec.toml | 13 +- .../sol.toml | 15 -- 34 files changed, 458 insertions(+), 483 deletions(-) delete mode 100644 examples/Solovev_ideal_example/sol.toml delete mode 100644 examples/Solovev_ideal_example_3D/sol.toml delete mode 100644 examples/Solovev_ideal_example_multi_n/single_n_1/sol.toml delete mode 100644 examples/Solovev_ideal_example_multi_n/single_n_2/sol.toml delete mode 100644 examples/Solovev_ideal_example_multi_n/sol.toml delete mode 100644 test/test_data/regression_solovev_ideal_example/sol.toml delete mode 100644 test/test_data/regression_solovev_ideal_example_multi_n/sol.toml delete mode 100644 test/test_data/regression_solovev_kinetic_calculated/sol.toml delete mode 100644 test/test_data/regression_solovev_kinetic_example/sol.toml delete mode 100644 test/test_data/regression_solovev_kinetic_multi_n/sol.toml diff --git a/CLAUDE.md b/CLAUDE.md index 5caf6ac1a..e21aa07ed 100644 --- a/CLAUDE.md +++ b/CLAUDE.md @@ -618,6 +618,7 @@ Every consultation is bounded — see **Subagent Consultations** under Important - **Docstrings are rendered as Markdown** - Documenter parses docstrings as CommonMark, so `[text](...)` patterns become hyperlinks and will fail CI with `invalid local link/image` if the target doesn't exist. Common pitfall: unit annotations like `[degrees] (or [m] if ...)` parse as `[degrees](or [m] if ...)` — a broken link. Use plain words (`in degrees`) or backticks (`` `[m]` ``) for unit labels inside docstrings. Same rule for bracketed array-shape hints (`[ncoil]`) followed by parentheses. When in doubt, preview with `julia --project=docs docs/make.jl` before pushing. - **Keep code comments concise** - A comment should be one line where possible. Do not write multi-line block comments explaining the current session's investigation, what was tried, what was wrong before, or why a specific file/path behaves differently. State what the code does and why at a general level. Example of too much detail: a 6-line block explaining that efit_by_inversion uses psilow>0 while CHEASE starts at 0, that the old code was removed, and that spline spikes result. Preferred: `# Replicate Fortran inverse.f: overwrite deta at axis (r²=0) by extrapolating from innermost surfaces.` - **No PR/issue references in source** - Do not cite specific GitHub PR or issue numbers (e.g. `#171`, `#202`) in source or test comments/docstrings. During dynamic development these references quickly go stale and pollute the code. Just concisely state the objective or what the code does; the git history and PR threads track the provenance. +- **Document struct fields in the docstring, not inline** - When adding a field to a struct, put its description in the struct's `## Fields` docstring rather than (or in addition to) a trailing inline comment, and document any non-obvious contract (e.g. which keys a `Dict`/ingest carries per variant). Do not annotate outer constructors with positional-argument counts ("passes 11 positional args") — those rot when a field is added; describe the intent instead. ### Minimal-change discipline - **Reuse native ops and existing utilities before writing new ones.** FastInterpolations splines integrate and differentiate natively (`integrate`, `cumulative_integrate`, `deriv1`); the Equilibrium module already has flux-surface integration/average patterns. Do not reimplement spline integration, quadrature, or differentiation — grep for the existing idiom first. diff --git a/examples/Solovev_ideal_example/gpec.toml b/examples/Solovev_ideal_example/gpec.toml index 5b2ccf318..dacefde12 100644 --- a/examples/Solovev_ideal_example/gpec.toml +++ b/examples/Solovev_ideal_example/gpec.toml @@ -1,11 +1,10 @@ # Solovev analytical equilibrium — n=1 ideal stability + perturbed equilibrium. # Near-marginal n=1 external kink stabilized by a close conformal wall (see [Wall] note). # Integration-pipeline smoke-test and et[1] regression fixture; the equilibrium is -# generated analytically from the side-car sol.toml ([SOL_INPUT]). +# generated analytically from the embedded [SOL_INPUT] section. [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file -eq_filename = "sol.toml" # Path to equilibrium file jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized poloidal flux @@ -77,3 +76,15 @@ parallel_threads = 2 # BVP thread cap (1 = serial/bit-deterministic; 2 populate_dense_xi = true # Append serial-EL pass so dense ξ is stored — REQUIRED with a [PerturbedEquilibrium] section set_psilim_via_dmlim = false # FALSE for limited/analytical equilibria — rationals sparse, dmlim would chop too much edge dmlim = 0.2 # Truncate integration at (last_rational_q + dmlim)/n (used when set_psilim_via_dmlim = true) +# Solovev analytic equilibrium parameters (eq_type = "sol"); see SolovevConfig in src/Equilibrium. +[SOL_INPUT] +mr = 128 # Number of radial grid zones +mz = 128 # Number of axial grid zones +ma = 128 # Number of flux grid zones +e = 1.6 # Elongation +a = 0.33 # Minor radius +r0 = 1.0 # Major radius +q0 = 1.9 # Safety factor at the magnetic axis (O-point) +p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) +b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) +f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/examples/Solovev_ideal_example/sol.toml b/examples/Solovev_ideal_example/sol.toml deleted file mode 100644 index 86348c36d..000000000 --- a/examples/Solovev_ideal_example/sol.toml +++ /dev/null @@ -1,15 +0,0 @@ -# Solovev analytical equilibrium parameters, consumed by gpec.toml (eq_type = "sol"). -# Sets the grid resolution, plasma shape, and field/pressure scaling factors used to -# generate the analytic Solovev equilibrium. See SolovevConfig in src/Equilibrium. - -[SOL_INPUT] -mr = 128 # Number of radial grid zones -mz = 128 # Number of axial grid zones -ma = 128 # Number of flux grid zones -e = 1.6 # Elongation -a = 0.33 # Minor radius -r0 = 1.0 # Major radius -q0 = 1.9 # Safety factor at the magnetic axis (O-point) -p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) -b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) -f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/examples/Solovev_ideal_example_3D/gpec.toml b/examples/Solovev_ideal_example_3D/gpec.toml index 094dd79c6..0564bb9d0 100644 --- a/examples/Solovev_ideal_example_3D/gpec.toml +++ b/examples/Solovev_ideal_example_3D/gpec.toml @@ -1,10 +1,9 @@ # Solovev analytical equilibrium — 3D (toroidally resolved) n=1 ideal stability. # Same near-marginal Solovev plasma as Solovev_ideal_example, with the vacuum response -# evaluated on a toroidal grid (nzvac > 1). Equilibrium is generated from sol.toml. +# evaluated on a toroidal grid (nzvac > 1). Equilibrium is generated from the embedded [SOL_INPUT] section. [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file -eq_filename = "sol.toml" # Path to equilibrium file jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized poloidal flux @@ -70,3 +69,15 @@ equal_arc_wall = false # Equal arc length distribution of nodes # compute_singular_coupling = true # Compute singular layer coupling metrics # verbose = true # Enable verbose logging # write_outputs_to_HDF5 = true # Write perturbed equilibrium outputs to HDF5 +# Solovev analytic equilibrium parameters (eq_type = "sol"); see SolovevConfig in src/Equilibrium. +[SOL_INPUT] +mr = 128 # Number of radial grid zones +mz = 128 # Number of axial grid zones +ma = 128 # Number of flux grid zones +e = 1.6 # Elongation +a = 0.33 # Minor radius +r0 = 1.0 # Major radius +q0 = 1.9 # Safety factor at the magnetic axis (O-point) +p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) +b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) +f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/examples/Solovev_ideal_example_3D/sol.toml b/examples/Solovev_ideal_example_3D/sol.toml deleted file mode 100644 index 86348c36d..000000000 --- a/examples/Solovev_ideal_example_3D/sol.toml +++ /dev/null @@ -1,15 +0,0 @@ -# Solovev analytical equilibrium parameters, consumed by gpec.toml (eq_type = "sol"). -# Sets the grid resolution, plasma shape, and field/pressure scaling factors used to -# generate the analytic Solovev equilibrium. See SolovevConfig in src/Equilibrium. - -[SOL_INPUT] -mr = 128 # Number of radial grid zones -mz = 128 # Number of axial grid zones -ma = 128 # Number of flux grid zones -e = 1.6 # Elongation -a = 0.33 # Minor radius -r0 = 1.0 # Major radius -q0 = 1.9 # Safety factor at the magnetic axis (O-point) -p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) -b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) -f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/examples/Solovev_ideal_example_multi_n/gpec.toml b/examples/Solovev_ideal_example_multi_n/gpec.toml index 9b559bf38..e75343919 100644 --- a/examples/Solovev_ideal_example_multi_n/gpec.toml +++ b/examples/Solovev_ideal_example_multi_n/gpec.toml @@ -1,11 +1,10 @@ # Solovev analytical equilibrium — multi-n ideal stability (n = 1 and 2 in one run). # Same near-marginal Solovev plasma as Solovev_ideal_example, swept over a toroidal # mode-number range. The single_n_1/ and single_n_2/ subdirectories run each n alone -# for cross-checking. Equilibrium is generated from sol.toml. +# for cross-checking. Equilibrium is generated from the embedded [SOL_INPUT] section. [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file -eq_filename = "sol.toml" # Path to equilibrium file jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized poloidal flux @@ -57,3 +56,15 @@ parallel_threads = 2 # BVP thread cap (1 = serial/bit-deterministic; 2 populate_dense_xi = false # Append serial-EL pass for dense ξ; not needed without [PerturbedEquilibrium] (default false) set_psilim_via_dmlim = false # FALSE for multi-n — dmlim truncation is ambiguous when n varies (sing_lim! skips anyway) dmlim = 0.2 # Truncate integration at (last_rational_q + dmlim)/n (used when set_psilim_via_dmlim = true) +# Solovev analytic equilibrium parameters (eq_type = "sol"); see SolovevConfig in src/Equilibrium. +[SOL_INPUT] +mr = 128 # Number of radial grid zones +mz = 128 # Number of axial grid zones +ma = 128 # Number of flux grid zones +e = 1.6 # Elongation +a = 0.33 # Minor radius +r0 = 1.0 # Major radius +q0 = 1.9 # Safety factor at the magnetic axis (O-point) +p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) +b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) +f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml b/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml index 8f1f96ceb..70e705b57 100644 --- a/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml +++ b/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml @@ -1,10 +1,9 @@ # Solovev analytical equilibrium — n=1 only, companion to the multi-n parent run. # Runs n=1 in isolation (output euler_n1.h5) to cross-check the combined multi-n result. -# Equilibrium is generated from sol.toml. +# Equilibrium is generated from the embedded [SOL_INPUT] section. [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file -eq_filename = "sol.toml" # Path to equilibrium file jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized poloidal flux @@ -51,3 +50,15 @@ singfac_min = 1e-4 # Fractional distance from rational q at which ide ucrit = 1e3 # Column-norm threshold that triggers solution renormalization write_outputs_to_HDF5 = true # Write outputs to the HDF5 file HDF5_filename = "euler_n1.h5" # Output HDF5 filename +# Solovev analytic equilibrium parameters (eq_type = "sol"); see SolovevConfig in src/Equilibrium. +[SOL_INPUT] +mr = 128 # Number of radial grid zones +mz = 128 # Number of axial grid zones +ma = 128 # Number of flux grid zones +e = 1.6 # Elongation +a = 0.33 # Minor radius +r0 = 1.0 # Major radius +q0 = 1.9 # Safety factor at the magnetic axis (O-point) +p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) +b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) +f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/examples/Solovev_ideal_example_multi_n/single_n_1/sol.toml b/examples/Solovev_ideal_example_multi_n/single_n_1/sol.toml deleted file mode 100644 index 86348c36d..000000000 --- a/examples/Solovev_ideal_example_multi_n/single_n_1/sol.toml +++ /dev/null @@ -1,15 +0,0 @@ -# Solovev analytical equilibrium parameters, consumed by gpec.toml (eq_type = "sol"). -# Sets the grid resolution, plasma shape, and field/pressure scaling factors used to -# generate the analytic Solovev equilibrium. See SolovevConfig in src/Equilibrium. - -[SOL_INPUT] -mr = 128 # Number of radial grid zones -mz = 128 # Number of axial grid zones -ma = 128 # Number of flux grid zones -e = 1.6 # Elongation -a = 0.33 # Minor radius -r0 = 1.0 # Major radius -q0 = 1.9 # Safety factor at the magnetic axis (O-point) -p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) -b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) -f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml b/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml index 17924067d..d687cd3dc 100644 --- a/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml +++ b/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml @@ -1,10 +1,9 @@ # Solovev analytical equilibrium — n=2 only, companion to the multi-n parent run. # Runs n=2 in isolation (output euler_n2.h5) to cross-check the combined multi-n result. -# Equilibrium is generated from sol.toml. +# Equilibrium is generated from the embedded [SOL_INPUT] section. [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file -eq_filename = "sol.toml" # Path to equilibrium file jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized poloidal flux @@ -51,3 +50,15 @@ singfac_min = 1e-4 # Fractional distance from rational q at which ide ucrit = 1e3 # Column-norm threshold that triggers solution renormalization write_outputs_to_HDF5 = true # Write outputs to the HDF5 file HDF5_filename = "euler_n2.h5" # Output HDF5 filename +# Solovev analytic equilibrium parameters (eq_type = "sol"); see SolovevConfig in src/Equilibrium. +[SOL_INPUT] +mr = 128 # Number of radial grid zones +mz = 128 # Number of axial grid zones +ma = 128 # Number of flux grid zones +e = 1.6 # Elongation +a = 0.33 # Minor radius +r0 = 1.0 # Major radius +q0 = 1.9 # Safety factor at the magnetic axis (O-point) +p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) +b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) +f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/examples/Solovev_ideal_example_multi_n/single_n_2/sol.toml b/examples/Solovev_ideal_example_multi_n/single_n_2/sol.toml deleted file mode 100644 index 86348c36d..000000000 --- a/examples/Solovev_ideal_example_multi_n/single_n_2/sol.toml +++ /dev/null @@ -1,15 +0,0 @@ -# Solovev analytical equilibrium parameters, consumed by gpec.toml (eq_type = "sol"). -# Sets the grid resolution, plasma shape, and field/pressure scaling factors used to -# generate the analytic Solovev equilibrium. See SolovevConfig in src/Equilibrium. - -[SOL_INPUT] -mr = 128 # Number of radial grid zones -mz = 128 # Number of axial grid zones -ma = 128 # Number of flux grid zones -e = 1.6 # Elongation -a = 0.33 # Minor radius -r0 = 1.0 # Major radius -q0 = 1.9 # Safety factor at the magnetic axis (O-point) -p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) -b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) -f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/examples/Solovev_ideal_example_multi_n/sol.toml b/examples/Solovev_ideal_example_multi_n/sol.toml deleted file mode 100644 index 86348c36d..000000000 --- a/examples/Solovev_ideal_example_multi_n/sol.toml +++ /dev/null @@ -1,15 +0,0 @@ -# Solovev analytical equilibrium parameters, consumed by gpec.toml (eq_type = "sol"). -# Sets the grid resolution, plasma shape, and field/pressure scaling factors used to -# generate the analytic Solovev equilibrium. See SolovevConfig in src/Equilibrium. - -[SOL_INPUT] -mr = 128 # Number of radial grid zones -mz = 128 # Number of axial grid zones -ma = 128 # Number of flux grid zones -e = 1.6 # Elongation -a = 0.33 # Minor radius -r0 = 1.0 # Major radius -q0 = 1.9 # Safety factor at the magnetic axis (O-point) -p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) -b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) -f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/src/Equilibrium/AnalyticEquilibrium.jl b/src/Equilibrium/AnalyticEquilibrium.jl index c56d23cc5..72a16a05c 100644 --- a/src/Equilibrium/AnalyticEquilibrium.jl +++ b/src/Equilibrium/AnalyticEquilibrium.jl @@ -224,9 +224,9 @@ function lar_run(equil_input::EquilibriumConfig, lar_input::LargeAspectRatioConf rz_in_R = cubic_interp((rz_in_xs, rz_in_ys), rzphi_fs_nodes[:, :, 1]; itp_2d_opts...) rz_in_Z = cubic_interp((rz_in_xs, rz_in_ys), rzphi_fs_nodes[:, :, 2]; itp_2d_opts...) - # LAR equilibrium has midplane symmetry, so magnetic axis is at Z = 0 - raw_data = Dict{String,Any}("kind" => "analytic", "eq_type" => "lar") - return InverseRunInput(equil_input, sq_in, rz_in_xs, rz_in_ys, rz_in_R, rz_in_Z, lar_r0, 0.0, psio, raw_data) + # LAR equilibrium has midplane symmetry, so magnetic axis is at Z = 0. + # Analytic: ingest=nothing — replay regenerates from the [LAR_INPUT] TOML section. + return InverseRunInput(equil_input, sq_in, rz_in_xs, rz_in_ys, rz_in_R, rz_in_Z, lar_r0, 0.0, psio, nothing) end """ @@ -541,7 +541,8 @@ function tj_analytic_run(equil_input::EquilibriumConfig, tj::TJAnalyticConfig) rz_in_R = cubic_interp((rz_in_xs, rz_in_ys), rzphi_fs_nodes[:, :, 1]; itp_2d_opts...) rz_in_Z = cubic_interp((rz_in_xs, rz_in_ys), rzphi_fs_nodes[:, :, 2]; itp_2d_opts...) - return InverseRunInput(equil_input, sq_in, rz_in_xs, rz_in_ys, rz_in_R, rz_in_Z, R0, 0.0, psio) + # Analytic: ingest=nothing — replay regenerates from the [TJ_ANALYTIC_INPUT] TOML section. + return InverseRunInput(equil_input, sq_in, rz_in_xs, rz_in_ys, rz_in_R, rz_in_Z, R0, 0.0, psio, nothing) end """ @@ -753,8 +754,9 @@ function tj_analytic_run_direct(equil_input::EquilibriumConfig, tj::TJAnalyticCo rmin_grid, rmax_grid = extrema(psi_in_xs) zmin_grid, zmax_grid = extrema(psi_in_ys) + # Analytic: ingest=nothing — replay regenerates from the [TJ_ANALYTIC_INPUT] TOML section. return DirectRunInput(equil_input, sq_in, psi_in, psi_in_xs, psi_in_ys, - rmin_grid, rmax_grid, zmin_grid, zmax_grid, psio, 1) + rmin_grid, rmax_grid, zmin_grid, zmax_grid, psio, 1, nothing) end """ @@ -833,8 +835,8 @@ function sol_run(equil_inputs::EquilibriumConfig, sol_inputs::SolovevConfig) # Print out equilibrium info @info "Generating Solovev equilibrium: mr=$mr, mz=$mz, ma=$ma, e=$(@sprintf("%.3f", e)), a=$(@sprintf("%.3f", a)), r0=$(@sprintf("%.3f", r0)), q0=$(@sprintf("%.3f", q0))" - raw_data = Dict{String,Any}("kind" => "analytic", "eq_type" => "sol") # 1 is bt_sign=+1: Solovev has positive Bt by construction (f0 = r0 * b0fac > 0). # No ip_sign field is needed; sign(crnt) is recovered from params.crnt downstream. - return DirectRunInput(equil_inputs, sq_in, psi_in, psi_in_xs, psi_in_ys, rmin, rmax, zmin, zmax, psio, 1, raw_data) + # Analytic: ingest=nothing — replay regenerates from the [SOL_INPUT] TOML section. + return DirectRunInput(equil_inputs, sq_in, psi_in, psi_in_xs, psi_in_ys, rmin, rmax, zmin, zmax, psio, 1, nothing) end diff --git a/src/Equilibrium/DirectEquilibriumByInversion.jl b/src/Equilibrium/DirectEquilibriumByInversion.jl index 4cac75101..3ba702807 100644 --- a/src/Equilibrium/DirectEquilibriumByInversion.jl +++ b/src/Equilibrium/DirectEquilibriumByInversion.jl @@ -666,8 +666,10 @@ function equilibrium_solver_by_inversion( rz_in_R = cubic_interp((rz_in_xs, rz_in_ys), R_table; itp_opts2d...) rz_in_Z = cubic_interp((rz_in_xs, rz_in_ys), Z_table; itp_opts2d...) + # Intermediate inverse input; the captured DirectIngest rides on the original eq_input, + # which setup_equilibrium forwards onto the equilibrium, so this one carries ingest=nothing. inv_input = InverseRunInput(raw_profile.config, raw_profile.sq_in, - rz_in_xs, rz_in_ys, rz_in_R, rz_in_Z, ro, zo, psio) + rz_in_xs, rz_in_ys, rz_in_R, rz_in_Z, ro, zo, psio, nothing) pe = equilibrium_solver(inv_input) diff --git a/src/Equilibrium/Equilibrium.jl b/src/Equilibrium/Equilibrium.jl index f97710aeb..468d6ac05 100644 --- a/src/Equilibrium/Equilibrium.jl +++ b/src/Equilibrium/Equilibrium.jl @@ -118,8 +118,8 @@ function setup_equilibrium(eq_config::EquilibriumConfig, additional_input=nothin plasma_equilibrium = equilibrium_solver(eq_input) end - # Forward raw ingest arrays so the gpec.h5 writer can snapshot them. - plasma_equilibrium.raw_inputs = eq_input.raw_data + # Forward the captured ingest so the gpec.h5 writer can snapshot it (nothing for analytic). + plasma_equilibrium.ingest = eq_input.ingest equilibrium_global_parameters!(plasma_equilibrium) equilibrium_qfind!(plasma_equilibrium) diff --git a/src/Equilibrium/EquilibriumTypes.jl b/src/Equilibrium/EquilibriumTypes.jl index 489873227..b0a9973ff 100644 --- a/src/Equilibrium/EquilibriumTypes.jl +++ b/src/Equilibrium/EquilibriumTypes.jl @@ -344,6 +344,79 @@ function SolovevConfig(input_dict::Dict{String,Any}) return SolovevConfig(; symbolize_keys(input_dict)...) end +""" + DirectIngest + +The serializable raw arrays and scalars captured by a direct-equilibrium reader +(`read_efit`, `read_imas`, `sol_run` is analytic and does not use this) — everything +needed to rebuild a `DirectRunInput`'s splines without re-reading the original g-file. +Stored on `DirectRunInput.ingest` / `PlasmaEquilibrium.ingest` and dumped to +`gpec.h5` so a run can be replayed from any directory. The interpolants themselves are +not serializable; they are reconstructed from these nodes by `build_direct_from_ingest`. + +## Fields + + - `sq_xs::Vector{Float64}` — normalized-ψ knots for the 1D profile spline + - `sq_fs::Matrix{Float64}` — 1D profile node values (F, μ₀P, q, √ψ_norm) + - `psi_xs::Vector{Float64}` — R grid for the 2D flux map [m] + - `psi_ys::Vector{Float64}` — Z grid for the 2D flux map [m] + - `psi_rz::Matrix{Float64}` — processed poloidal flux on the (R, Z) grid [Wb/rad] + - `rmin/rmax/zmin/zmax::Float64` — computational-grid bounds [m] + - `psio::Float64` — total flux difference |ψ_axis - ψ_boundary| [Wb/rad] + - `bt_sign::Int` — sign of the toroidal field (+1 or -1) +""" +struct DirectIngest + sq_xs::Vector{Float64} + sq_fs::Matrix{Float64} + psi_xs::Vector{Float64} + psi_ys::Vector{Float64} + psi_rz::Matrix{Float64} + rmin::Float64 + rmax::Float64 + zmin::Float64 + zmax::Float64 + psio::Float64 + bt_sign::Int +end + +""" + InverseIngest + +The serializable raw arrays and scalars captured by an inverse-equilibrium reader +(`read_chease_ascii`, `read_chease_binary`) — everything needed to rebuild an +`InverseRunInput`'s splines without re-reading the original CHEASE file. Stored on +`InverseRunInput.ingest` / `PlasmaEquilibrium.ingest` and reconstructed by +`build_inverse_from_ingest`. See [`DirectIngest`](@ref) for the role this plays in +the `gpec.h5` rerun snapshot. + +## Fields + + - `sq_xs::Vector{Float64}` — normalized-ψ knots for the 1D profile spline + - `sq_fs::Matrix{Float64}` — 1D profile node values + - `rz_xs::Vector{Float64}` — ψ grid for the R, Z maps + - `rz_ys::Vector{Float64}` — θ grid for the R, Z maps + - `R_nodes::Matrix{Float64}` — R node values on the (ψ, θ) grid [m] + - `Z_nodes::Matrix{Float64}` — Z node values on the (ψ, θ) grid [m] + - `ro::Float64` — R of magnetic axis [m] + - `zo::Float64` — Z of magnetic axis [m] + - `psio::Float64` — total flux difference |ψ_axis - ψ_boundary| [Wb/rad] +""" +struct InverseIngest + sq_xs::Vector{Float64} + sq_fs::Matrix{Float64} + rz_xs::Vector{Float64} + rz_ys::Vector{Float64} + R_nodes::Matrix{Float64} + Z_nodes::Matrix{Float64} + ro::Float64 + zo::Float64 + psio::Float64 +end + +# Equilibria captured for replay carry one of these; analytic equilibria carry `nothing` +# and are regenerated from their TOML section instead. +const EquilibriumIngest = Union{Nothing,DirectIngest,InverseIngest} + """ DirectRunInput(...) @@ -383,6 +456,8 @@ raw equilibrium data and preparing the initial splines. - `zmax::Float64` — Maximum Z-coordinate of the computational grid [m] - `psio::Float64` — Total flux difference `|ψ_axis - ψ_boundary|` [Wb/rad] - `bt_sign::Int` — Sign of the toroidal field (+1 or -1); read from fpol sign in EFIT g-files + - `ingest::EquilibriumIngest` — captured raw arrays for the `gpec.h5` rerun snapshot + (a [`DirectIngest`](@ref) for file-based reads, or `nothing` for analytic equilibria) """ mutable struct DirectRunInput{S<:FastInterpolations.CubicSeriesInterpolant,I2D<:FastInterpolations.CubicInterpolantND} config::EquilibriumConfig @@ -396,14 +471,9 @@ mutable struct DirectRunInput{S<:FastInterpolations.CubicSeriesInterpolant,I2D<: zmax::Float64 # Maximum Z-coordinate of the computational grid [m]. psio::Float64 # The total flux difference |ψ_axis - ψ_boundary| [Weber / radian]. bt_sign::Int # Sign of the toroidal field: +1 or -1 (from fpol sign in g-file) - raw_data::Dict{String,Any} # Raw arrays used to build the splines (for gpec.h5 snapshot/replay) + ingest::EquilibriumIngest end -# Outer constructor: call sites that don't capture raw arrays pass 11 positional args -# (through bt_sign); raw_data defaults to empty (this equilibrium is then not rerun-snapshottable). -DirectRunInput(config, sq_in, psi_in, psi_in_xs, psi_in_ys, rmin, rmax, zmin, zmax, psio, bt_sign) = - DirectRunInput(config, sq_in, psi_in, psi_in_xs, psi_in_ys, rmin, rmax, zmin, zmax, psio, bt_sign, Dict{String,Any}()) - """ InverseRunInput(...) @@ -420,6 +490,8 @@ A container struct for inputs to the `inverse_run` function. - `ro::Float64` - R-coordinate of magnetic axis [m] - `zo::Float64` - Z-coordinate of magnetic axis [m] - `psio::Float64` - Total flux difference |ψ_axis - ψ_boundary| [Wb/rad] + - `ingest::EquilibriumIngest` - captured raw arrays for the `gpec.h5` rerun snapshot + (an [`InverseIngest`](@ref) for file-based reads, or `nothing` for analytic equilibria) """ mutable struct InverseRunInput{S<:FastInterpolations.CubicSeriesInterpolant,I2D<:FastInterpolations.CubicInterpolantND} config::EquilibriumConfig @@ -431,13 +503,9 @@ mutable struct InverseRunInput{S<:FastInterpolations.CubicSeriesInterpolant,I2D< ro::Float64 # R axis location zo::Float64 # Z axis location psio::Float64 # Total flux difference |psi_axis - psi_boundary| - raw_data::Dict{String,Any} # Raw arrays used to build the splines (for gpec.h5 snapshot/replay) + ingest::EquilibriumIngest end -# Outer constructor: pre-rerun call sites pass 9 positional args; raw_data defaults to empty. -InverseRunInput(config, sq_in, rz_in_xs, rz_in_ys, rz_in_R, rz_in_Z, ro, zo, psio) = - InverseRunInput(config, sq_in, rz_in_xs, rz_in_ys, rz_in_R, rz_in_Z, ro, zo, psio, Dict{String,Any}()) - """ EquilibriumParameters @@ -800,6 +868,9 @@ This object provides a complete representation of the processed plasma equilibri - `ro::Float64`: R-coordinate of the magnetic axis [m] - `zo::Float64`: Z-coordinate of the magnetic axis [m] - `psio::Float64`: Total flux difference |Ψ_axis - Ψ_boundary| [Weber/radian] + - `ingest::EquilibriumIngest`: raw arrays forwarded from the equilibrium input for the + `gpec.h5` rerun snapshot — a [`DirectIngest`](@ref)/[`InverseIngest`](@ref) for file-based + equilibria, or `nothing` for analytic ones (regenerated from their TOML section on replay) """ mutable struct PlasmaEquilibrium{P<:ProfileSplines,G<:GeometryProfileSplines,I2D<:FastInterpolations.CubicInterpolantND} config::EquilibriumConfig @@ -826,16 +897,14 @@ mutable struct PlasmaEquilibrium{P<:ProfileSplines,G<:GeometryProfileSplines,I2D zo::Float64 psio::Float64 - # Raw ingest data forwarded from DirectRunInput/InverseRunInput for gpec.h5 snapshot/replay. - # Keys depend on equilibrium kind: "direct", "inverse", or "analytic". - raw_inputs::Dict{String,Any} + ingest::EquilibriumIngest end -# Outer constructor: call sites pass 16 positional args (through psio); raw_inputs defaults to empty -# (it is populated post-construction from eq_input.raw_data in setup_equilibrium). +# Solvers build the equilibrium before setup_equilibrium forwards eq_input.ingest, so allow +# construction without it; ingest defaults to nothing and is assigned post-construction. PlasmaEquilibrium(config, params, profiles, geometry, rzphi_xs, rzphi_ys, rzphi_rsquared, rzphi_offset, rzphi_nu, rzphi_jac, eqfun_B, eqfun_metric1, eqfun_metric2, ro, zo, psio) = PlasmaEquilibrium(config, params, profiles, geometry, rzphi_xs, rzphi_ys, rzphi_rsquared, rzphi_offset, rzphi_nu, rzphi_jac, - eqfun_B, eqfun_metric1, eqfun_metric2, ro, zo, psio, Dict{String,Any}()) + eqfun_B, eqfun_metric1, eqfun_metric2, ro, zo, psio, nothing) diff --git a/src/Equilibrium/ReadEquilibrium.jl b/src/Equilibrium/ReadEquilibrium.jl index a6fd54ced..973ae882d 100644 --- a/src/Equilibrium/ReadEquilibrium.jl +++ b/src/Equilibrium/ReadEquilibrium.jl @@ -120,22 +120,9 @@ function read_efit(config::EquilibriumConfig) # Capture the raw arrays that reconstruct sq_in and psi_in, so the rerun path # (gpec.h5 → setup_equilibrium) can skip the g-file parse entirely. - raw_data = Dict{String,Any}( - "kind" => "direct", - "sq_xs" => sq_xs, - "sq_fs" => sq_fs_nodes, - "psi_xs" => psi_in_xs, - "psi_ys" => psi_in_ys, - "psi_rz" => psi_proc, - "rmin" => rmin, - "rmax" => rmax, - "zmin" => zmin, - "zmax" => zmax, - "psio" => psio, - "bt_sign" => fpol_sign, - ) + ingest = DirectIngest(sq_xs, sq_fs_nodes, psi_in_xs, psi_in_ys, psi_proc, rmin, rmax, zmin, zmax, psio, fpol_sign) - return DirectRunInput(config, sq_in, psi_in, psi_in_xs, psi_in_ys, rmin, rmax, zmin, zmax, psio, fpol_sign, raw_data) + return DirectRunInput(config, sq_in, psi_in, psi_in_xs, psi_in_ys, rmin, rmax, zmin, zmax, psio, fpol_sign, ingest) end @@ -230,21 +217,10 @@ function read_chease_binary(config::EquilibriumConfig) rz_in_Z = cubic_interp((rz_in_xs, rz_in_ys), fs_2d[:, :, 2]; bc=(CubicFit(), PeriodicBC()), extrap=(ExtendExtrap(), WrapExtrap())) # Capture the raw arrays that reconstruct sq_in, rz_in_R, rz_in_Z. - raw_data = Dict{String,Any}( - "kind" => "inverse", - "sq_xs" => collect(xs), - "sq_fs" => fs_copy, - "rz_xs" => collect(rz_in_xs), - "rz_ys" => collect(rz_in_ys), - "R_nodes" => fs_2d[:, :, 1], - "Z_nodes" => fs_2d[:, :, 2], - "ro" => ro, - "zo" => zo, - "psio" => psio, - ) + ingest = InverseIngest(collect(xs), fs_copy, collect(rz_in_xs), collect(rz_in_ys), fs_2d[:, :, 1], fs_2d[:, :, 2], ro, zo, psio) @info "Finished reading CHEASE equilibrium (Binary)" - return InverseRunInput(config, sq_in, rz_in_xs, rz_in_ys, rz_in_R, rz_in_Z, ro, zo, psio, raw_data) + return InverseRunInput(config, sq_in, rz_in_xs, rz_in_ys, rz_in_R, rz_in_Z, ro, zo, psio, ingest) end end @@ -410,79 +386,42 @@ function read_chease_ascii(config::EquilibriumConfig) rz_in_R = cubic_interp((rz_in_xs, rz_in_ys), R_data; opts2d...) rz_in_Z = cubic_interp((rz_in_xs, rz_in_ys), Z_data; opts2d...) # Capture the raw arrays that reconstruct sq_in, rz_in_R, rz_in_Z. - raw_data = Dict{String,Any}( - "kind" => "inverse", - "sq_xs" => collect(xs), - "sq_fs" => fs_copy, - "rz_xs" => collect(rz_in_xs), - "rz_ys" => collect(rz_in_ys), - "R_nodes" => Matrix(R_data), - "Z_nodes" => Matrix(Z_data), - "ro" => ro, - "zo" => zo, - "psio" => psio, - ) + ingest = InverseIngest(collect(xs), fs_copy, collect(rz_in_xs), collect(rz_in_ys), Matrix(R_data), Matrix(Z_data), ro, zo, psio) @info "Finished reading CHEASE equilibrium. Magnetic axis at (ro=$(@sprintf("%.3f", ro)), zo=$(@sprintf("%.3f", zo))), psio=$(@sprintf("%.3e", psio))" - return InverseRunInput(config, sq_in, rz_in_xs, rz_in_ys, rz_in_R, rz_in_Z, ro, zo, psio, raw_data) + return InverseRunInput(config, sq_in, rz_in_xs, rz_in_ys, rz_in_R, rz_in_Z, ro, zo, psio, ingest) end """ - build_direct_from_raw(config::EquilibriumConfig, raw::Dict) -> DirectRunInput + build_direct_from_ingest(config::EquilibriumConfig, ingest::DirectIngest) -> DirectRunInput -Rebuild a `DirectRunInput` from a raw-data dict previously captured by `read_efit` -(or populated from `input/raw_inputs/equilibrium/` inside `gpec.h5`). This is the -inverse of the raw-data capture in `read_efit`; it lets the rerun path skip the -g-file parse entirely while reusing the existing solver dispatch. +Rebuild a `DirectRunInput` from a [`DirectIngest`](@ref) captured by `read_efit`/`read_imas` +(or restored from `input/raw_inputs/equilibrium/` inside `gpec.h5`). Inverse of that capture: +reconstructs the splines so the rerun path skips the g-file/IMAS parse, reusing the existing +solver dispatch. """ -function build_direct_from_raw(config::EquilibriumConfig, raw::Dict) - sq_xs = Vector{Float64}(raw["sq_xs"]) - sq_fs = Matrix{Float64}(raw["sq_fs"]) - psi_in_xs = Vector{Float64}(raw["psi_xs"]) - psi_in_ys = Vector{Float64}(raw["psi_ys"]) - psi_rz = Matrix{Float64}(raw["psi_rz"]) - - sq_in = cubic_interp(sq_xs, Series(sq_fs); extrap=ExtendExtrap()) - psi_in = cubic_interp((psi_in_xs, psi_in_ys), psi_rz; extrap=ExtendExtrap()) - - rmin = Float64(raw["rmin"]) - rmax = Float64(raw["rmax"]) - zmin = Float64(raw["zmin"]) - zmax = Float64(raw["zmax"]) - psio = Float64(raw["psio"]) - bt_sign = Int(get(raw, "bt_sign", 1)) - - return DirectRunInput(config, sq_in, psi_in, psi_in_xs, psi_in_ys, - rmin, rmax, zmin, zmax, psio, bt_sign, Dict{String,Any}(raw)) +function build_direct_from_ingest(config::EquilibriumConfig, ingest::DirectIngest) + sq_in = cubic_interp(ingest.sq_xs, Series(ingest.sq_fs); extrap=ExtendExtrap()) + psi_in = cubic_interp((ingest.psi_xs, ingest.psi_ys), ingest.psi_rz; extrap=ExtendExtrap()) + return DirectRunInput(config, sq_in, psi_in, ingest.psi_xs, ingest.psi_ys, + ingest.rmin, ingest.rmax, ingest.zmin, ingest.zmax, ingest.psio, ingest.bt_sign, ingest) end """ - build_inverse_from_raw(config::EquilibriumConfig, raw::Dict) -> InverseRunInput + build_inverse_from_ingest(config::EquilibriumConfig, ingest::InverseIngest) -> InverseRunInput -Rebuild an `InverseRunInput` from a raw-data dict previously captured by -`read_chease_ascii` / `read_chease_binary`. Inverse of that capture; used by the -rerun path to skip the CHEASE parse. +Rebuild an `InverseRunInput` from an [`InverseIngest`](@ref) captured by +`read_chease_ascii`/`read_chease_binary`. Inverse of that capture; used by the rerun path to +skip the CHEASE parse. """ -function build_inverse_from_raw(config::EquilibriumConfig, raw::Dict) - sq_xs = Vector{Float64}(raw["sq_xs"]) - sq_fs = Matrix{Float64}(raw["sq_fs"]) - rz_in_xs = Vector{Float64}(raw["rz_xs"]) - rz_in_ys = Vector{Float64}(raw["rz_ys"]) - R_nodes = Matrix{Float64}(raw["R_nodes"]) - Z_nodes = Matrix{Float64}(raw["Z_nodes"]) - - sq_in = cubic_interp(sq_xs, Series(sq_fs); extrap=ExtendExtrap()) +function build_inverse_from_ingest(config::EquilibriumConfig, ingest::InverseIngest) + sq_in = cubic_interp(ingest.sq_xs, Series(ingest.sq_fs); extrap=ExtendExtrap()) opts2d = (bc=(CubicFit(), PeriodicBC()), extrap=(ExtendExtrap(), WrapExtrap())) - rz_in_R = cubic_interp((rz_in_xs, rz_in_ys), R_nodes; opts2d...) - rz_in_Z = cubic_interp((rz_in_xs, rz_in_ys), Z_nodes; opts2d...) - - ro = Float64(raw["ro"]) - zo = Float64(raw["zo"]) - psio = Float64(raw["psio"]) - - return InverseRunInput(config, sq_in, rz_in_xs, rz_in_ys, rz_in_R, rz_in_Z, - ro, zo, psio, Dict{String,Any}(raw)) + rz_in_R = cubic_interp((ingest.rz_xs, ingest.rz_ys), ingest.R_nodes; opts2d...) + rz_in_Z = cubic_interp((ingest.rz_xs, ingest.rz_ys), ingest.Z_nodes; opts2d...) + return InverseRunInput(config, sq_in, ingest.rz_xs, ingest.rz_ys, rz_in_R, rz_in_Z, + ingest.ro, ingest.zo, ingest.psio, ingest) end """ @@ -588,5 +527,8 @@ function read_imas(config::EquilibriumConfig, dd) "\n R ∈ [$(round(rmin; sigdigits=4)), $(round(rmax; sigdigits=4))] m" * "\n Z ∈ [$(round(zmin; sigdigits=4)), $(round(zmax; sigdigits=4))] m" - return DirectRunInput(config, sq_in, psi_in, psi_in_xs, psi_in_ys, rmin, rmax, zmin, zmax, psio, bt_sign) + # Capture the raw arrays so an IMAS run can be replayed from gpec.h5 without the dd source. + ingest = DirectIngest(sq_xs, sq_fs_nodes, psi_in_xs, psi_in_ys, Matrix(psi_proc), rmin, rmax, zmin, zmax, psio, bt_sign) + + return DirectRunInput(config, sq_in, psi_in, psi_in_xs, psi_in_ys, rmin, rmax, zmin, zmax, psio, bt_sign, ingest) end diff --git a/src/ForcingTerms/ForcingTerms.jl b/src/ForcingTerms/ForcingTerms.jl index 965ceeb51..65267df52 100644 --- a/src/ForcingTerms/ForcingTerms.jl +++ b/src/ForcingTerms/ForcingTerms.jl @@ -258,7 +258,7 @@ function load_forcing_from_h5_group!(forcing_modes::Vector{ForcingMode}, group) n_array = read(group, "n") m_array = read(group, "m") amp_real = read(group, "amplitude_real") - amp_imag = haskey(group, "amplitude_imag") ? read(group, "amplitude_imag") : zeros(length(n_array)) + amp_imag = haskey(group, "amplitude_imag") ? read(group, "amplitude_imag") : zeros(length(n_array)) # optional for hand-authored groups if length(n_array) != length(m_array) || length(n_array) != length(amp_real) error("Inconsistent array lengths in HDF5 forcing group") diff --git a/src/GeneralizedPerturbedEquilibrium.jl b/src/GeneralizedPerturbedEquilibrium.jl index cd59b8f5a..59f87e74a 100755 --- a/src/GeneralizedPerturbedEquilibrium.jl +++ b/src/GeneralizedPerturbedEquilibrium.jl @@ -1,6 +1,17 @@ # GeneralizedPerturbedEquilibrium.jl module GeneralizedPerturbedEquilibrium +# External dependencies used by main and the rerun helpers +using TOML +using Printf +using HDF5 +using FastInterpolations +import IMASdd +import AdaptiveArrayPools: @with_pool + +const _BANNER = "="^60 +const _SECTION = "-"^40 + include("Utilities/Utilities.jl") import .Utilities as Utilities export Utilities @@ -37,15 +48,8 @@ include("Analysis/Analysis.jl") import .Analysis as Analysis export Analysis -# Additional imports for main function -using TOML -using Printf -using HDF5 - -using FastInterpolations -import IMASdd - -import AdaptiveArrayPools: @with_pool +# Rerun snapshot/replay helpers, included directly into this module +include("Rerun.jl") # Import ForceFreeStates types and functions needed for main using .ForceFreeStates: ForceFreeStatesInternal, ForceFreeStatesControl, DebugSettings, VacuumData, OdeState, FourFitVars @@ -55,19 +59,10 @@ using .ForceFreeStates: make_metric, make_matrix, make_kinetic_matrix using .ForceFreeStates: find_kinetic_singular_surfaces! using .ForceFreeStates: eulerlagrange_integration, free_run! -const _BANNER = "="^60 -const _SECTION = "-"^40 - -# Rerun snapshot/replay helpers. Depends on the module-level imports above -# (HDF5, TOML, Equilibrium, ForcingTerms) and the `_BANNER` constant, so this -# include has to come after them but before `main`, which dispatches into -# `build_inputs_from_h5` on .h5 inputs. -include("Rerun.jl") - const _DEPRECATED_FFS_KEYS = ("delta_mband", "mband") -# Drop deprecated [ForceFreeStates] keys (e.g. banded-matrix removal from PR #286) so legacy -# gpec.toml files keep parsing instead of throwing an unknown-keyword error. +# Drop deprecated [ForceFreeStates] keys (e.g. banded-matrix removal) so legacy gpec.toml files +# keep parsing instead of throwing an unknown-keyword error. function _drop_deprecated_ffs_keys!(table) for k in _DEPRECATED_FFS_KEYS if haskey(table, k) @@ -108,8 +103,9 @@ end Build the pipeline inputs from a working directory containing `gpec.toml`. Returns the parsed `inputs` dict (made self-contained for the rerun snapshot), the `EquilibriumConfig`, and the `additional_input` consumed by `setup_equilibrium` — an analytic `*Config` for -TJ/SOL/LAR equilibria, the `dd` data dictionary for IMAS, or `nothing` for file-based -equilibria (efit, chease) that `setup_equilibrium` reads from disk. +sol/lar/tj equilibria (parameters from the embedded TOML section), the `dd` data dictionary +for IMAS, or `nothing` for file-based equilibria (efit, chease) that `setup_equilibrium` +reads from disk. """ function build_inputs_from_toml(path::String; dd::Union{IMASdd.dd,Nothing}=nothing) inputs = TOML.parsefile(joinpath(path, "gpec.toml")) @@ -117,23 +113,18 @@ function build_inputs_from_toml(path::String; dd::Union{IMASdd.dd,Nothing}=nothi haskey(inputs, "Equilibrium") || error("No [Equilibrium] section in gpec.toml") eq_config = Equilibrium.EquilibriumConfig(inputs["Equilibrium"], path) - # LAR/Solovev carry their parameters in a separate auxiliary TOML referenced - # by eq_filename. Merge those parameters into the in-memory `inputs` dict so - # the snapshot writer emits a self-contained TOML blob. + # Fold a deprecated analytic side-car TOML into `inputs` if its section isn't already + # embedded, so the snapshot writer emits a self-contained TOML blob. merge_auxiliary_eq_toml!(inputs, eq_config) - # Build `additional_input` from embedded TOML sections (analytic equilibria) or from - # the dd keyword argument (IMAS). These are mutually exclusive — an equilibrium is - # either analytic (TJ/SOL/LAR), IMAS-fed, or read from a file (additional_input=nothing). - additional_input = nothing - if eq_config.eq_type in ("tj_analytic", "tj_analytic_direct") && haskey(inputs, "TJ_ANALYTIC_INPUT") - additional_input = Equilibrium.TJAnalyticConfig(inputs["TJ_ANALYTIC_INPUT"]) - elseif eq_config.eq_type == "sol" && haskey(inputs, "SOL_INPUT") - additional_input = Equilibrium.SolovevConfig(inputs["SOL_INPUT"]) - elseif eq_config.eq_type == "lar" && haskey(inputs, "LAR_INPUT") - additional_input = Equilibrium.LargeAspectRatioConfig(inputs["LAR_INPUT"]) + # An equilibrium is analytic (sol/lar/tj, parameters from its embedded section), + # IMAS-fed (via the dd kwarg), or read from a file (additional_input = nothing). + additional_input = if haskey(ANALYTIC_EQ_SECTIONS, eq_config.eq_type) + build_analytic_config(eq_config.eq_type, inputs) elseif eq_config.eq_type == "imas" - additional_input = dd + dd + else + nothing end return inputs, eq_config, additional_input @@ -185,12 +176,8 @@ function main_from_inputs( _drop_deprecated_ffs_keys!(ffs_table) ctrl = ForceFreeStatesControl(; (Symbol(k) => v for (k, v) in ffs_table)...) - # The builder already resolved `additional_input` (analytic `*Config`, IMAS `dd`, - # prebuilt DirectRunInput/InverseRunInput from a rerun, or `nothing` for file-based - # equilibria). `setup_equilibrium` consumes it directly — no source dispatch here. - # - # The TJ-analytic equilibrium follows the profile family of R. Fitzpatrick's TJ code - # (https://github.com/rfitzp/TJ); see `Equilibrium.TJAnalyticConfig`. + # inputs/eq_config/additional_input are fully resolved by the caller; this body does no + # source dispatch — setup_equilibrium consumes additional_input directly. equil = Equilibrium.setup_equilibrium(eq_config, additional_input) @info "Equilibrium construction completed in $(@sprintf("%.3f", time() - equil_start)) s" @@ -604,14 +591,19 @@ function write_outputs_to_HDF5( # Store git version for reproducibility out_h5["info/git_version"] = git_version - # Self-contained run snapshot: the full merged TOML (so a rerun can - # reconstruct every ForceFreeStates/Equilibrium/Wall/PE control struct), - # plus raw equilibrium arrays so the rerun never needs the original - # g-file / CHEASE / auxiliary TOML files. + # Self-contained run snapshot: the full merged TOML (so a rerun can reconstruct every + # ForceFreeStates/Equilibrium/Wall/PE control struct), plus the equilibrium ingest + # arrays so a file-based rerun never needs the original g-file / CHEASE / IMAS source. if inputs !== nothing out_h5["input/gpec_toml_raw"] = sprint(TOML.print, inputs) end - write_equilibrium_raw_inputs!(out_h5, equil) + if equil.ingest !== nothing # analytic equilibria are regenerated from their TOML section + eq_group = "input/raw_inputs/equilibrium" + out_h5["$eq_group/ingest_kind"] = equil.ingest isa Equilibrium.DirectIngest ? "direct" : "inverse" + for f in fieldnames(typeof(equil.ingest)) + out_h5["$eq_group/$f"] = getfield(equil.ingest, f) + end + end if forcing_modes !== nothing forcing_group = create_group(out_h5, "input/raw_inputs/forcing_terms") ForcingTerms.save_forcing_to_h5(forcing_modes, forcing_group) diff --git a/src/Rerun.jl b/src/Rerun.jl index 239f30c6c..3d64e49ad 100644 --- a/src/Rerun.jl +++ b/src/Rerun.jl @@ -5,84 +5,75 @@ # Included directly into the GeneralizedPerturbedEquilibrium module, so these functions share # its imports (TOML, HDF5, Equilibrium, ForcingTerms, etc.). +# Analytic equilibria carry their parameters in a TOML section rather than an ingest array; +# replay regenerates them from that section. Maps eq_type to its gpec.toml section key. +const ANALYTIC_EQ_SECTIONS = Dict( + "sol" => "SOL_INPUT", + "lar" => "LAR_INPUT", + "tj_analytic" => "TJ_ANALYTIC_INPUT", + "tj_analytic_direct" => "TJ_ANALYTIC_INPUT", +) + """ merge_auxiliary_eq_toml!(inputs::Dict{String,Any}, eq_config) -For analytic equilibria (`lar`, `sol`), the equilibrium parameters live in a -separate auxiliary TOML referenced by `eq_config.eq_filename` (e.g. `sol.toml` -with a `[SOL_INPUT]` section). To make the `gpec.h5` snapshot self-contained, -we merge the relevant auxiliary section into the in-memory `inputs` dict under -the same key (`LAR_INPUT` / `SOL_INPUT`). On replay, `build_inputs_from_h5` reads these -sections back into a `LargeAspectRatioConfig` / `SolovevConfig` and passes -them to `setup_equilibrium` as `additional_input`, bypassing the auxiliary -file read entirely. - -No-op for EFIT/CHEASE equilibria — those are snapshotted via `raw_inputs`. +Ensure the analytic-equilibrium parameter section (`[SOL_INPUT]` / `[LAR_INPUT]` / +`[TJ_ANALYTIC_INPUT]`) is present in the in-memory `inputs` dict so the `gpec.h5` snapshot +is self-contained. If the section is already embedded in `gpec.toml`, this is a no-op. +Otherwise it falls back to the deprecated side-car TOML referenced by `eq_config.eq_filename` +and folds that section in (with a deprecation warning). No-op for non-analytic equilibria. """ function merge_auxiliary_eq_toml!(inputs::Dict{String,Any}, eq_config::Equilibrium.EquilibriumConfig) - eq_type = eq_config.eq_type - if eq_type != "lar" && eq_type != "sol" - return inputs - end + section = get(ANALYTIC_EQ_SECTIONS, eq_config.eq_type, nothing) + section === nothing && return inputs # file-based: snapshotted via the equilibrium ingest + haskey(inputs, section) && return inputs # already embedded in gpec.toml filepath = eq_config.eq_filename - if !isfile(filepath) - @warn "Auxiliary equilibrium TOML not found at $filepath; snapshot will not contain analytic parameters" - return inputs - end - + isfile(filepath) || return inputs # nothing to fold; build_analytic_config will report a clear error + @warn "Reading analytic parameters from side-car $filepath is deprecated; move [$section] into gpec.toml" aux = TOML.parsefile(filepath) - section = eq_type == "lar" ? "LAR_INPUT" : "SOL_INPUT" - if haskey(aux, section) - inputs[section] = aux[section] - else - @warn "Auxiliary TOML $filepath has no [$section] section; snapshot will not contain analytic parameters" - end + haskey(aux, section) && (inputs[section] = aux[section]) return inputs end """ - write_equilibrium_raw_inputs!(out_h5, equil) + build_analytic_config(eq_type, inputs) -Write the raw-data dict captured on `PlasmaEquilibrium.raw_inputs` into -`input/raw_inputs/equilibrium/` inside an open HDF5 file. The layout follows -the `kind` field: `direct`, `inverse`, or `analytic`. On replay, the reader -looks at `kind` to decide whether to rebuild a `DirectRunInput` / -`InverseRunInput` or to reconstruct an analytic config from the TOML snapshot. +Construct the analytic-equilibrium `*Config` (`SolovevConfig` / `LargeAspectRatioConfig` / +`TJAnalyticConfig`) from the TOML section named by [`ANALYTIC_EQ_SECTIONS`]. Shared by the +TOML and rerun input builders so both resolve analytic parameters the same way. """ -function write_equilibrium_raw_inputs!(out_h5, equil::Equilibrium.PlasmaEquilibrium) - raw = equil.raw_inputs - if isempty(raw) - @warn "Equilibrium has no raw_inputs captured; gpec.h5 will not be rerunnable" - return nothing - end - - group_path = "input/raw_inputs/equilibrium" - for (key, val) in raw - out_h5["$group_path/$key"] = val +function build_analytic_config(eq_type::AbstractString, inputs::Dict) + section = get(ANALYTIC_EQ_SECTIONS, eq_type, nothing) + section === nothing && error("build_analytic_config: $eq_type is not an analytic equilibrium type") + haskey(inputs, section) || error("Analytic equilibrium $eq_type requires a [$section] section in gpec.toml") + data = inputs[section] + if eq_type == "sol" + return Equilibrium.SolovevConfig(data) + elseif eq_type == "lar" + return Equilibrium.LargeAspectRatioConfig(data) + else + return Equilibrium.TJAnalyticConfig(data) end - return nothing end """ - read_equilibrium_raw_inputs(in_h5) -> Dict{String,Any} + read_equilibrium_ingest(in_h5) -> EquilibriumIngest -Inverse of `write_equilibrium_raw_inputs!`: read every dataset under -`input/raw_inputs/equilibrium/` into a plain dict. Used by `build_inputs_from_h5` -to hydrate a `DirectRunInput` / `InverseRunInput` without any filesystem -access. +Reconstruct the [`DirectIngest`](@ref)/[`InverseIngest`](@ref) stored under +`input/raw_inputs/equilibrium/` (the inverse of the field-by-field write in +`write_outputs_to_HDF5`). Returns `nothing` when the group is absent, which marks an +analytic equilibrium — replayed from its TOML section rather than stored arrays. """ -function read_equilibrium_raw_inputs(in_h5) +function read_equilibrium_ingest(in_h5) group_path = "input/raw_inputs/equilibrium" - if !haskey(in_h5, group_path) - error("gpec.h5 has no $group_path group — the file was produced before rerun snapshot support was added") - end + haskey(in_h5, group_path) || return nothing group = in_h5[group_path] - raw = Dict{String,Any}() - for name in keys(group) - raw[name] = read(group, name) - end - return raw + kind = read(group, "ingest_kind") + T = kind == "direct" ? Equilibrium.DirectIngest : + kind == "inverse" ? Equilibrium.InverseIngest : + error("Unknown equilibrium ingest_kind in gpec.h5: $kind") + return T((read(group, String(f)) for f in fieldnames(T))...) end """ @@ -123,9 +114,9 @@ function parse_override_flag(expr::AbstractString) length(parts) < 2 && error("--override key must be dotted (section.key[.subkey]): $expr") # Parse RHS as a TOML value by wrapping it in a throwaway key=value line. + sentinel = "_rerun_override_" parsed_val = try - parsed = TOML.parse("_rerun_override_ = $rhs") - parsed["_rerun_override_"] + TOML.parse("$sentinel = $rhs")[sentinel] catch e # Warn instead of silently stringifying a bare word, which would otherwise only fail # much later where the field expects a number/bool. @@ -219,58 +210,36 @@ function resolve_rerun_output_path(source_h5::String, output_dir::String, output stem = endswith(lowercase(base), ".h5") ? base[1:end-3] : base output_name = string(stem, "_rerun.h5") end - out_abs = abspath(joinpath(output_dir, output_name)) - if out_abs == source_abs + if abspath(joinpath(output_dir, output_name)) == source_abs error("Refusing to overwrite source HDF5 at $source_abs. " * "Pass `--output-dir ` or `--output-name `.") end return (output_dir, output_name) end -""" - rebuild_equilibrium_input(eq_config, raw) -> Union{DirectRunInput,InverseRunInput,Nothing} - -Dispatch on `raw["kind"]` to rebuild the solver input. Returns `nothing` for -the `analytic` case — the caller should fall back to constructing a -`LargeAspectRatioConfig` / `SolovevConfig` from the restored TOML sections. -""" -function rebuild_equilibrium_input(eq_config::Equilibrium.EquilibriumConfig, raw::Dict{String,Any}) - kind = get(raw, "kind", "") - if kind == "direct" - return Equilibrium.build_direct_from_raw(eq_config, raw) - elseif kind == "inverse" - return Equilibrium.build_inverse_from_raw(eq_config, raw) - elseif kind == "analytic" - return nothing - else - error("Unknown raw equilibrium kind in gpec.h5: $kind") - end -end - """ build_inputs_from_h5(args::Vector{String}) -> (inputs, eq_config, additional_input, output_dir, current_git, preloaded_forcing, preloaded_coils) Rerun input builder. Parses the rerun-specific CLI flags, reads the snapshot out of the source HDF5, applies any overrides, and reconstructs the pipeline inputs — a prebuilt -`DirectRunInput`/`InverseRunInput` for file-based equilibria, or an analytic `*Config` for -LAR/SOL. Never touches the source file's original ingest paths. The returned tuple is fed -straight into `main_from_inputs`. +`DirectRunInput`/`InverseRunInput` rebuilt from the stored ingest for file-based equilibria, +or an analytic `*Config` for sol/lar/tj. Never touches the source file's original ingest +paths. The returned tuple is fed straight into `main_from_inputs`. """ function build_inputs_from_h5(args::Vector{String}) cli = parse_rerun_cli(args) source_h5 = cli.source_h5 isfile(source_h5) || error("Source HDF5 not found: $source_h5") - # Pull the stored TOML, raw equilibrium arrays, and (if present) forcing - # data out of the source file. Forcing modes are only written when the - # original run had a [PerturbedEquilibrium] section, so the group may be - # missing — we signal that with `nothing` and let main_from_inputs fall - # back to loading from `ft_ctrl.forcing_data_file`. - # `--coil-source coils` recomputes the coil field from stored geometry, so it - # deliberately ignores the frozen forcing-mode snapshot. + # Pull the stored TOML, equilibrium ingest, and (if present) forcing data out of the source + # file. Forcing modes are only written when the original run had a [PerturbedEquilibrium] + # section, so the group may be missing — we signal that with `nothing` and let + # main_from_inputs fall back to loading from `ft_ctrl.forcing_data_file`. + # `--coil-source coils` recomputes the coil field from stored geometry, so it deliberately + # ignores the frozen forcing-mode snapshot. use_coils = cli.coil_source == "coils" - toml_raw, raw_eq, source_git, preloaded_forcing, preloaded_coils = h5open(source_h5, "r") do in_h5 + toml_raw, ingest, source_git, preloaded_forcing, preloaded_coils = h5open(source_h5, "r") do in_h5 haskey(in_h5, "input/gpec_toml_raw") || error("Source HDF5 $source_h5 has no input/gpec_toml_raw — produced by a pre-rerun version of GPEC") forcing_modes = if use_coils || !haskey(in_h5, "input/raw_inputs/forcing_terms") @@ -292,7 +261,7 @@ function build_inputs_from_h5(args::Vector{String}) end ( read(in_h5, "input/gpec_toml_raw"), - read_equilibrium_raw_inputs(in_h5), + read_equilibrium_ingest(in_h5), haskey(in_h5, "info/git_version") ? read(in_h5, "info/git_version") : "unknown", forcing_modes, coil_sets @@ -328,24 +297,20 @@ function build_inputs_from_h5(args::Vector{String}) " source: $(abspath(source_h5))\n" * " output: $(abspath(joinpath(output_dir, output_name)))\n$_BANNER" - # Rebuild the equilibrium solver input from the HDF5-stored arrays (or from - # the merged LAR/SOL sections for analytic kinds), and run the standard - # pipeline. Everything downstream is unchanged. eq_config = Equilibrium.EquilibriumConfig(inputs["Equilibrium"], output_dir) - # eq_filename won't be used on replay — clear it so any leftover absolute - # path from the source machine can't trip up later code paths. + # Clear eq_filename: unused on replay, and a stale absolute path could mislead downstream code. eq_config.eq_filename = "" - additional_input = if raw_eq["kind"] == "analytic" - if eq_config.eq_type == "lar" - lar_data = get(inputs, "LAR_INPUT", Dict{String,Any}()) - Equilibrium.LargeAspectRatioConfig(; (Symbol(k) => v for (k, v) in lar_data)...) - else - sol_data = get(inputs, "SOL_INPUT", Dict{String,Any}()) - Equilibrium.SolovevConfig(; (Symbol(k) => v for (k, v) in sol_data)...) - end + # Analytic kinds regenerate from their TOML section; file-based kinds rebuild splines from + # the stored ingest. A file-based run with no ingest can only come from a pre-ingest gpec.h5. + additional_input = if haskey(ANALYTIC_EQ_SECTIONS, eq_config.eq_type) + build_analytic_config(eq_config.eq_type, inputs) + elseif ingest isa Equilibrium.DirectIngest + Equilibrium.build_direct_from_ingest(eq_config, ingest) + elseif ingest isa Equilibrium.InverseIngest + Equilibrium.build_inverse_from_ingest(eq_config, ingest) else - rebuild_equilibrium_input(eq_config, raw_eq) + error("gpec.h5 has no equilibrium ingest and eq_type=$(eq_config.eq_type) is not analytic — cannot replay") end return inputs, eq_config, additional_input, output_dir, current_git, preloaded_forcing, preloaded_coils diff --git a/test/runtests_coils.jl b/test/runtests_coils.jl index 6ae7a0c18..c1be63cf6 100644 --- a/test/runtests_coils.jl +++ b/test/runtests_coils.jl @@ -143,7 +143,7 @@ end inputs = TOML.parsefile(joinpath(equil_dir, "gpec.toml")) eq_config = Equilibrium.EquilibriumConfig(inputs["Equilibrium"], equil_dir) - equil = Equilibrium.setup_equilibrium(eq_config) + equil = Equilibrium.setup_equilibrium(eq_config, Equilibrium.SolovevConfig(inputs["SOL_INPUT"])) mtheta = 48 nzeta = 16 @@ -385,7 +385,8 @@ end @testset "Analytic coils: window_pane standoff" begin equil_dir = joinpath(@__DIR__, "..", "examples", "Solovev_ideal_example") inputs = TOML.parsefile(joinpath(equil_dir, "gpec.toml")) - equil = Equilibrium.setup_equilibrium(Equilibrium.EquilibriumConfig(inputs["Equilibrium"], equil_dir)) + equil = Equilibrium.setup_equilibrium(Equilibrium.EquilibriumConfig(inputs["Equilibrium"], equil_dir), + Equilibrium.SolovevConfig(inputs["SOL_INPUT"])) # surface_point_and_normal: outboard midplane (poloidal_angle = 0) R0, Z0, nR0, nZ0 = ForcingTerms.surface_point_and_normal(equil, 0.0) diff --git a/test/runtests_parallel_integration.jl b/test/runtests_parallel_integration.jl index fc4e592b0..26afbbd6a 100644 --- a/test/runtests_parallel_integration.jl +++ b/test/runtests_parallel_integration.jl @@ -114,7 +114,7 @@ using TOML ctrl = GeneralizedPerturbedEquilibrium.ForceFreeStates.ForceFreeStatesControl(; (Symbol(k) => v for (k, v) in inputs["ForceFreeStates"])...) eq_config = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(inputs["Equilibrium"], ex) - equil = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(eq_config) + equil = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(eq_config, haskey(inputs, "SOL_INPUT") ? GeneralizedPerturbedEquilibrium.Equilibrium.SolovevConfig(inputs["SOL_INPUT"]) : nothing) GeneralizedPerturbedEquilibrium.ForceFreeStates.sing_lim!(intr, ctrl, equil) intr.nlow = ctrl.nn_low; intr.nhigh = ctrl.nn_high; @@ -178,7 +178,7 @@ using TOML ctrl = GeneralizedPerturbedEquilibrium.ForceFreeStates.ForceFreeStatesControl(; (Symbol(k) => v for (k, v) in inputs["ForceFreeStates"])...) eq_config = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(inputs["Equilibrium"], ex) - equil = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(eq_config) + equil = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(eq_config, haskey(inputs, "SOL_INPUT") ? GeneralizedPerturbedEquilibrium.Equilibrium.SolovevConfig(inputs["SOL_INPUT"]) : nothing) GeneralizedPerturbedEquilibrium.ForceFreeStates.sing_lim!(intr, ctrl, equil) intr.nlow = ctrl.nn_low; intr.nhigh = ctrl.nn_high; @@ -239,7 +239,7 @@ using TOML ctrl = GeneralizedPerturbedEquilibrium.ForceFreeStates.ForceFreeStatesControl(; (Symbol(k) => v for (k, v) in inputs["ForceFreeStates"])...) eq_config = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(inputs["Equilibrium"], ex) - equil = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(eq_config) + equil = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(eq_config, haskey(inputs, "SOL_INPUT") ? GeneralizedPerturbedEquilibrium.Equilibrium.SolovevConfig(inputs["SOL_INPUT"]) : nothing) intr.wall_settings = GeneralizedPerturbedEquilibrium.Vacuum.WallShapeSettings(; (Symbol(k) => v for (k, v) in inputs["Wall"])...) GeneralizedPerturbedEquilibrium.ForceFreeStates.sing_lim!(intr, ctrl, equil) @@ -288,7 +288,7 @@ using TOML ctrl = GeneralizedPerturbedEquilibrium.ForceFreeStates.ForceFreeStatesControl(; (Symbol(k) => v for (k, v) in inputs["ForceFreeStates"])...) eq_config = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(inputs["Equilibrium"], ex) - equil = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(eq_config) + equil = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(eq_config, haskey(inputs, "SOL_INPUT") ? GeneralizedPerturbedEquilibrium.Equilibrium.SolovevConfig(inputs["SOL_INPUT"]) : nothing) intr.wall_settings = GeneralizedPerturbedEquilibrium.Vacuum.WallShapeSettings(; (Symbol(k) => v for (k, v) in inputs["Wall"])...) GeneralizedPerturbedEquilibrium.ForceFreeStates.sing_lim!(intr, ctrl, equil) @@ -347,7 +347,7 @@ using TOML ctrl = GeneralizedPerturbedEquilibrium.ForceFreeStates.ForceFreeStatesControl(; (Symbol(k) => v for (k, v) in inputs["ForceFreeStates"])...) eq_config = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(inputs["Equilibrium"], ex) - equil = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(eq_config) + equil = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(eq_config, haskey(inputs, "SOL_INPUT") ? GeneralizedPerturbedEquilibrium.Equilibrium.SolovevConfig(inputs["SOL_INPUT"]) : nothing) GeneralizedPerturbedEquilibrium.ForceFreeStates.sing_lim!(intr, ctrl, equil) intr.nlow = ctrl.nn_low; intr.nhigh = ctrl.nn_high; @@ -411,7 +411,7 @@ using TOML ctrl = GeneralizedPerturbedEquilibrium.ForceFreeStates.ForceFreeStatesControl(; (Symbol(k) => v for (k, v) in inputs["ForceFreeStates"])...) eq_config = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(inputs["Equilibrium"], example_dir) - equil = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(eq_config) + equil = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(eq_config, haskey(inputs, "SOL_INPUT") ? GeneralizedPerturbedEquilibrium.Equilibrium.SolovevConfig(inputs["SOL_INPUT"]) : nothing) intr.wall_settings = GeneralizedPerturbedEquilibrium.Vacuum.WallShapeSettings(; (Symbol(k) => v for (k, v) in inputs["Wall"])...) GeneralizedPerturbedEquilibrium.ForceFreeStates.sing_lim!(intr, ctrl, equil) @@ -494,7 +494,7 @@ using TOML ctrl = GeneralizedPerturbedEquilibrium.ForceFreeStates.ForceFreeStatesControl(; (Symbol(k) => v for (k, v) in inputs["ForceFreeStates"])...) eq_config = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(inputs["Equilibrium"], ex) - equil = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(eq_config) + equil = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(eq_config, haskey(inputs, "SOL_INPUT") ? GeneralizedPerturbedEquilibrium.Equilibrium.SolovevConfig(inputs["SOL_INPUT"]) : nothing) intr.wall_settings = GeneralizedPerturbedEquilibrium.Vacuum.WallShapeSettings(; (Symbol(k) => v for (k, v) in inputs["Wall"])...) GeneralizedPerturbedEquilibrium.ForceFreeStates.sing_lim!(intr, ctrl, equil) diff --git a/test/runtests_rerun_from_h5.jl b/test/runtests_rerun_from_h5.jl index b768a5aba..a7b966ebe 100644 --- a/test/runtests_rerun_from_h5.jl +++ b/test/runtests_rerun_from_h5.jl @@ -1,9 +1,9 @@ using HDF5 using TOML -# Tests for the gpec.h5 snapshot + replay feature, kept deliberately light: exactly one -# full-pipeline source run + one replay (the analytic Solovev path), plus pipeline-free checks -# for direct-equilibrium recovery and the override flags. +# Tests for the gpec.h5 snapshot + replay feature, kept deliberately light: one full-pipeline +# source run + replay (the analytic Solovev path), plus pipeline-free ingest round-trip checks +# for the direct (EFIT) and inverse (CHEASE) equilibrium kinds and the override flags. # Collect every leaf dataset path under an open HDF5 file, skipping the groups/paths that # legitimately differ between a source run and its replay (`input/` is re-emitted with the @@ -189,10 +189,26 @@ end end end -# Direct (DIII-D EFIT) equilibrium recovery through the h5 path, without a pipeline run: -# `read_efit` captures the raw arrays, which we round-trip through a temp h5 via the real -# replay reader `read_equilibrium_raw_inputs` and rebuild with `build_direct_from_raw`. The -# rebuilt splines must evaluate bit-for-bit identical to the originals. +# Round-trip the typed equilibrium ingest through a temp h5 exactly as the snapshot writer and +# replay reader do (field-by-field write + `read_equilibrium_ingest`), then rebuild the solver +# input. The rebuilt splines must evaluate bit-for-bit identical to the originals. This is the +# pipeline-free guard on the capture → store → restore path, run once per equilibrium kind. +function _roundtrip_ingest(ingest, kind) + mktempdir() do d + h5path = joinpath(d, "raw.h5") + h5open(h5path, "w") do f + f["input/raw_inputs/equilibrium/ingest_kind"] = kind + for nm in fieldnames(typeof(ingest)) + f["input/raw_inputs/equilibrium/$nm"] = getfield(ingest, nm) + end + end + restored = h5open(GeneralizedPerturbedEquilibrium.read_equilibrium_ingest, h5path, "r") + @test restored isa typeof(ingest) + return restored + end +end + +# Direct (DIII-D EFIT) equilibrium recovery through the h5 path, without a pipeline run. @testset "Rerun direct-equilibrium recovery through h5" begin Equil = GeneralizedPerturbedEquilibrium.Equilibrium config = Equil.EquilibriumConfig(; @@ -201,38 +217,61 @@ end ) src = Equil.read_efit(config) @test src isa Equil.DirectRunInput - @test !isempty(src.raw_data) + @test src.ingest isa Equil.DirectIngest - mktempdir() do d - h5path = joinpath(d, "raw.h5") - h5open(h5path, "w") do f - for (k, v) in src.raw_data - f["input/raw_inputs/equilibrium/$k"] = v - end - end - raw = h5open(GeneralizedPerturbedEquilibrium.read_equilibrium_raw_inputs, h5path, "r") - rebuilt = Equil.build_direct_from_raw(config, raw) - - @test rebuilt.rmin == src.rmin - @test rebuilt.rmax == src.rmax - @test rebuilt.zmin == src.zmin - @test rebuilt.zmax == src.zmax - @test rebuilt.psio == src.psio - @test rebuilt.bt_sign == src.bt_sign - @test rebuilt.psi_in_xs == src.psi_in_xs - @test rebuilt.psi_in_ys == src.psi_in_ys - - # 2D flux interpolant must evaluate bit-for-bit at interior sample points. - for fr in (0.25, 0.5, 0.75), fz in (0.4, 0.6) - R = src.rmin + fr * (src.rmax - src.rmin) - Z = src.zmin + fz * (src.zmax - src.zmin) - @test rebuilt.psi_in((R, Z)) == src.psi_in((R, Z)) - end - # 1D profile spline likewise. - for frac in (0.1, 0.5, 0.9) - x = src.psi_in_xs[1] + frac * (src.psi_in_xs[end] - src.psi_in_xs[1]) - @test rebuilt.sq_in(x) == src.sq_in(x) - end + restored = _roundtrip_ingest(src.ingest, "direct") + rebuilt = Equil.build_direct_from_ingest(config, restored) + + @test rebuilt.rmin == src.rmin + @test rebuilt.rmax == src.rmax + @test rebuilt.zmin == src.zmin + @test rebuilt.zmax == src.zmax + @test rebuilt.psio == src.psio + @test rebuilt.bt_sign == src.bt_sign + @test rebuilt.psi_in_xs == src.psi_in_xs + @test rebuilt.psi_in_ys == src.psi_in_ys + + # 2D flux interpolant must evaluate bit-for-bit at interior sample points. + for fr in (0.25, 0.5, 0.75), fz in (0.4, 0.6) + R = src.rmin + fr * (src.rmax - src.rmin) + Z = src.zmin + fz * (src.zmax - src.zmin) + @test rebuilt.psi_in((R, Z)) == src.psi_in((R, Z)) + end + # 1D profile spline likewise. + for frac in (0.1, 0.5, 0.9) + x = src.psi_in_xs[1] + frac * (src.psi_in_xs[end] - src.psi_in_xs[1]) + @test rebuilt.sq_in(x) == src.sq_in(x) + end +end + +# Inverse (CHEASE) equilibrium recovery through the same h5 path — exercises the InverseIngest +# branch and `build_inverse_from_ingest`, the kind that was not rerunnable before this change. +@testset "Rerun inverse-equilibrium recovery through h5" begin + Equil = GeneralizedPerturbedEquilibrium.Equilibrium + config = Equil.EquilibriumConfig(; + eq_filename=joinpath(@__DIR__, "test_data", "CHEASE_test_data", "INP1_ascii"), + eq_type="chease_ascii", jac_type="boozer", grid_type="ldp", + psilow=0.01, psihigh=0.994, r0exp=6.8, b0exp=7.4 + ) + src = Equil.read_chease_ascii(config) + @test src isa Equil.InverseRunInput + @test src.ingest isa Equil.InverseIngest + + restored = _roundtrip_ingest(src.ingest, "inverse") + rebuilt = Equil.build_inverse_from_ingest(config, restored) + + @test rebuilt.ro == src.ro + @test rebuilt.zo == src.zo + @test rebuilt.psio == src.psio + @test rebuilt.rz_in_xs == src.rz_in_xs + @test rebuilt.rz_in_ys == src.rz_in_ys + + # R, Z interpolants must evaluate bit-for-bit at interior (ψ, θ) sample points. + for fpsi in (0.25, 0.5, 0.75), fth in (0.2, 0.6) + ψ = src.rz_in_xs[1] + fpsi * (src.rz_in_xs[end] - src.rz_in_xs[1]) + θ = src.rz_in_ys[1] + fth * (src.rz_in_ys[end] - src.rz_in_ys[1]) + @test rebuilt.rz_in_R((ψ, θ)) == src.rz_in_R((ψ, θ)) + @test rebuilt.rz_in_Z((ψ, θ)) == src.rz_in_Z((ψ, θ)) end end diff --git a/test/runtests_riccati.jl b/test/runtests_riccati.jl index 2e06848fc..e156a5be0 100644 --- a/test/runtests_riccati.jl +++ b/test/runtests_riccati.jl @@ -102,7 +102,8 @@ end ctrl = FFS.ForceFreeStatesControl(; (Symbol(k) => v for (k, v) in inputs["ForceFreeStates"])...) equil = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium( - GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(inputs["Equilibrium"], ex)) + GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(inputs["Equilibrium"], ex), + GeneralizedPerturbedEquilibrium.Equilibrium.SolovevConfig(inputs["SOL_INPUT"])) intr_tmp = make_solovev_intr(inputs, ctrl, equil, ex) metric = FFS.make_metric(equil, intr_tmp.mpert) diff --git a/test/runtests_sing.jl b/test/runtests_sing.jl index f0ebe1ec1..26c4a9ee9 100644 --- a/test/runtests_sing.jl +++ b/test/runtests_sing.jl @@ -83,7 +83,8 @@ using FastInterpolations: cubic_interp, CubicFit, LinearBinarySearch, Series, Ex function load_equilibrium_from_gpec(gpec_path::String) inputs = TOML.parsefile(gpec_path) eq_config = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(inputs["Equilibrium"], dirname(gpec_path)) - return GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(eq_config) + addl = haskey(inputs, "SOL_INPUT") ? GeneralizedPerturbedEquilibrium.Equilibrium.SolovevConfig(inputs["SOL_INPUT"]) : nothing + return GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(eq_config, addl) end @testset "sing_der" begin diff --git a/test/test_data/regression_solovev_ideal_example/gpec.toml b/test/test_data/regression_solovev_ideal_example/gpec.toml index d1b024512..1f0ea6896 100644 --- a/test/test_data/regression_solovev_ideal_example/gpec.toml +++ b/test/test_data/regression_solovev_ideal_example/gpec.toml @@ -4,7 +4,6 @@ [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file -eq_filename = "sol.toml" # Path to equilibrium file jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized poloidal flux @@ -58,3 +57,15 @@ dmlim = 0.2 # Truncate integration at (last_rational_q + dmli write_outputs_to_HDF5 = false # Write outputs to the HDF5 file verbose = false # Enable verbose logging +# Solovev analytic equilibrium parameters (eq_type = "sol"); see SolovevConfig in src/Equilibrium. +[SOL_INPUT] +mr = 128 # Number of radial grid zones +mz = 128 # Number of axial grid zones +ma = 128 # Number of flux grid zones +e = 1.6 # Elongation +a = 0.33 # Minor radius +r0 = 1.0 # Major radius +q0 = 1.9 # Safety factor at the magnetic axis (O-point) +p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) +b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) +f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/test/test_data/regression_solovev_ideal_example/sol.toml b/test/test_data/regression_solovev_ideal_example/sol.toml deleted file mode 100644 index 86348c36d..000000000 --- a/test/test_data/regression_solovev_ideal_example/sol.toml +++ /dev/null @@ -1,15 +0,0 @@ -# Solovev analytical equilibrium parameters, consumed by gpec.toml (eq_type = "sol"). -# Sets the grid resolution, plasma shape, and field/pressure scaling factors used to -# generate the analytic Solovev equilibrium. See SolovevConfig in src/Equilibrium. - -[SOL_INPUT] -mr = 128 # Number of radial grid zones -mz = 128 # Number of axial grid zones -ma = 128 # Number of flux grid zones -e = 1.6 # Elongation -a = 0.33 # Minor radius -r0 = 1.0 # Major radius -q0 = 1.9 # Safety factor at the magnetic axis (O-point) -p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) -b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) -f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml b/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml index e132112e6..94ad3a1de 100644 --- a/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml +++ b/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml @@ -4,7 +4,6 @@ [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file -eq_filename = "sol.toml" # Path to equilibrium file jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized poloidal flux @@ -58,3 +57,15 @@ dmlim = 0.2 # Truncate integration at (last_rational_q + dmli write_outputs_to_HDF5 = false # Write outputs to the HDF5 file verbose = false # Enable verbose logging +# Solovev analytic equilibrium parameters (eq_type = "sol"); see SolovevConfig in src/Equilibrium. +[SOL_INPUT] +mr = 128 # Number of radial grid zones +mz = 128 # Number of axial grid zones +ma = 128 # Number of flux grid zones +e = 1.6 # Elongation +a = 0.33 # Minor radius +r0 = 1.0 # Major radius +q0 = 1.9 # Safety factor at the magnetic axis (O-point) +p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) +b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) +f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/test/test_data/regression_solovev_ideal_example_multi_n/sol.toml b/test/test_data/regression_solovev_ideal_example_multi_n/sol.toml deleted file mode 100644 index 86348c36d..000000000 --- a/test/test_data/regression_solovev_ideal_example_multi_n/sol.toml +++ /dev/null @@ -1,15 +0,0 @@ -# Solovev analytical equilibrium parameters, consumed by gpec.toml (eq_type = "sol"). -# Sets the grid resolution, plasma shape, and field/pressure scaling factors used to -# generate the analytic Solovev equilibrium. See SolovevConfig in src/Equilibrium. - -[SOL_INPUT] -mr = 128 # Number of radial grid zones -mz = 128 # Number of axial grid zones -ma = 128 # Number of flux grid zones -e = 1.6 # Elongation -a = 0.33 # Minor radius -r0 = 1.0 # Major radius -q0 = 1.9 # Safety factor at the magnetic axis (O-point) -p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) -b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) -f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/test/test_data/regression_solovev_kinetic_calculated/gpec.toml b/test/test_data/regression_solovev_kinetic_calculated/gpec.toml index 1013d6eb1..a672da714 100644 --- a/test/test_data/regression_solovev_kinetic_calculated/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_calculated/gpec.toml @@ -4,7 +4,6 @@ [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file -eq_filename = "sol.toml" # Path to equilibrium file jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized poloidal flux @@ -51,3 +50,15 @@ singfac_min = 1e-4 # Fractional distance from rational q at which ide ucrit = 1e3 # Column-norm threshold that triggers solution renormalization write_outputs_to_HDF5 = true # Write outputs to the HDF5 file verbose = false # Enable verbose logging +# Solovev analytic equilibrium parameters (eq_type = "sol"); see SolovevConfig in src/Equilibrium. +[SOL_INPUT] +mr = 128 # Number of radial grid zones +mz = 128 # Number of axial grid zones +ma = 128 # Number of flux grid zones +e = 1.6 # Elongation +a = 0.33 # Minor radius +r0 = 1.0 # Major radius +q0 = 1.9 # Safety factor at the magnetic axis (O-point) +p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) +b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) +f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/test/test_data/regression_solovev_kinetic_calculated/sol.toml b/test/test_data/regression_solovev_kinetic_calculated/sol.toml deleted file mode 100644 index 86348c36d..000000000 --- a/test/test_data/regression_solovev_kinetic_calculated/sol.toml +++ /dev/null @@ -1,15 +0,0 @@ -# Solovev analytical equilibrium parameters, consumed by gpec.toml (eq_type = "sol"). -# Sets the grid resolution, plasma shape, and field/pressure scaling factors used to -# generate the analytic Solovev equilibrium. See SolovevConfig in src/Equilibrium. - -[SOL_INPUT] -mr = 128 # Number of radial grid zones -mz = 128 # Number of axial grid zones -ma = 128 # Number of flux grid zones -e = 1.6 # Elongation -a = 0.33 # Minor radius -r0 = 1.0 # Major radius -q0 = 1.9 # Safety factor at the magnetic axis (O-point) -p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) -b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) -f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/test/test_data/regression_solovev_kinetic_example/gpec.toml b/test/test_data/regression_solovev_kinetic_example/gpec.toml index d1a89ae7e..032114237 100644 --- a/test/test_data/regression_solovev_kinetic_example/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_example/gpec.toml @@ -4,7 +4,6 @@ [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file -eq_filename = "sol.toml" # Path to equilibrium file jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized poloidal flux @@ -58,3 +57,15 @@ dmlim = 0.2 # Truncate integration at (last_rational_q + dmli write_outputs_to_HDF5 = true # Write outputs to the HDF5 file verbose = false # Enable verbose logging +# Solovev analytic equilibrium parameters (eq_type = "sol"); see SolovevConfig in src/Equilibrium. +[SOL_INPUT] +mr = 128 # Number of radial grid zones +mz = 128 # Number of axial grid zones +ma = 128 # Number of flux grid zones +e = 1.6 # Elongation +a = 0.33 # Minor radius +r0 = 1.0 # Major radius +q0 = 1.9 # Safety factor at the magnetic axis (O-point) +p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) +b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) +f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/test/test_data/regression_solovev_kinetic_example/sol.toml b/test/test_data/regression_solovev_kinetic_example/sol.toml deleted file mode 100644 index 86348c36d..000000000 --- a/test/test_data/regression_solovev_kinetic_example/sol.toml +++ /dev/null @@ -1,15 +0,0 @@ -# Solovev analytical equilibrium parameters, consumed by gpec.toml (eq_type = "sol"). -# Sets the grid resolution, plasma shape, and field/pressure scaling factors used to -# generate the analytic Solovev equilibrium. See SolovevConfig in src/Equilibrium. - -[SOL_INPUT] -mr = 128 # Number of radial grid zones -mz = 128 # Number of axial grid zones -ma = 128 # Number of flux grid zones -e = 1.6 # Elongation -a = 0.33 # Minor radius -r0 = 1.0 # Major radius -q0 = 1.9 # Safety factor at the magnetic axis (O-point) -p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) -b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) -f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml b/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml index 6f3880d5e..922ceafbf 100644 --- a/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml @@ -4,7 +4,6 @@ [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file -eq_filename = "sol.toml" # Path to equilibrium file jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized poloidal flux @@ -58,3 +57,15 @@ dmlim = 0.2 # Truncate integration at (last_rational_q + dmli write_outputs_to_HDF5 = true # Write outputs to the HDF5 file verbose = false # Enable verbose logging +# Solovev analytic equilibrium parameters (eq_type = "sol"); see SolovevConfig in src/Equilibrium. +[SOL_INPUT] +mr = 128 # Number of radial grid zones +mz = 128 # Number of axial grid zones +ma = 128 # Number of flux grid zones +e = 1.6 # Elongation +a = 0.33 # Minor radius +r0 = 1.0 # Major radius +q0 = 1.9 # Safety factor at the magnetic axis (O-point) +p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) +b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) +f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/test/test_data/regression_solovev_kinetic_multi_n/sol.toml b/test/test_data/regression_solovev_kinetic_multi_n/sol.toml deleted file mode 100644 index 86348c36d..000000000 --- a/test/test_data/regression_solovev_kinetic_multi_n/sol.toml +++ /dev/null @@ -1,15 +0,0 @@ -# Solovev analytical equilibrium parameters, consumed by gpec.toml (eq_type = "sol"). -# Sets the grid resolution, plasma shape, and field/pressure scaling factors used to -# generate the analytic Solovev equilibrium. See SolovevConfig in src/Equilibrium. - -[SOL_INPUT] -mr = 128 # Number of radial grid zones -mz = 128 # Number of axial grid zones -ma = 128 # Number of flux grid zones -e = 1.6 # Elongation -a = 0.33 # Minor radius -r0 = 1.0 # Major radius -q0 = 1.9 # Safety factor at the magnetic axis (O-point) -p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) -b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) -f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) From 0a7af465ceebb253813a297c15a5ad978c3c0fb9 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Mon, 22 Jun 2026 08:20:25 -0400 Subject: [PATCH 091/135] RERUN - REFACTOR - Consolidate analytic-equilibrium dispatch into one registry Address PR #217 review (maintainability): - Replace the three parallel analytic-dispatch sites (ANALYTIC_EQ_SECTIONS dict, build_analytic_config if/elseif, setup_equilibrium elseif chain) with a single Equilibrium.ANALYTIC_EQ registry of AnalyticEqSpec(section, config_type, run_fn). Both fresh-run and rerun paths now dispatch off it, so adding a new analytic kind is one new row. Drops the unsafe else-defaults-to-TJAnalyticConfig branch. - Extract EFIT_KINDS for the twice-duplicated efit-family list. - Document the ingest positional round-trip contract; sharpen two rerun errors. - Add a guard test asserting every registry entry is well-formed (Dict/String ctors, run_fn method, non-empty section) and that build_analytic_config resolves it, so future drift fails at test time rather than at a user's rerun. Type-stable where it matters: setup_equilibrium still infers a concrete PlasmaEquilibrium and the numerical kernels (sol_run/lar_run/...) stay concretely typed; dynamic dispatch is confined to the once-per-run config boundary behind a function barrier. Regression bit-for-bit identical vs pre-refactor HEAD on solovev_n1 (21) and diiid_n1 (46). Co-Authored-By: Claude Opus 4.8 (1M context) --- src/Equilibrium/Equilibrium.jl | 69 +++++++++++++++----------- src/GeneralizedPerturbedEquilibrium.jl | 2 +- src/Rerun.jl | 44 +++++++--------- test/runtests_rerun_from_h5.jl | 23 +++++++++ 4 files changed, 84 insertions(+), 54 deletions(-) diff --git a/src/Equilibrium/Equilibrium.jl b/src/Equilibrium/Equilibrium.jl index 468d6ac05..a3438116f 100644 --- a/src/Equilibrium/Equilibrium.jl +++ b/src/Equilibrium/Equilibrium.jl @@ -30,6 +30,39 @@ export flux_surface_metric, flux_surface_area # --- Constants --- const mu0 = 4π * 1e-7 +# efit-family equilibrium kinds that share the separatrix-clamp / inversion handling. +const EFIT_KINDS = ("efit", "efit_arclength", "efit_by_inversion") + +""" + AnalyticEqSpec + +Single-source-of-truth entry describing one analytic-equilibrium kind: the `gpec.toml` +section that carries its parameters, the `*Config` type built from that section, and the +run function that turns the config into solver input. `tj_analytic` and `tj_analytic_direct` +share `TJAnalyticConfig` but bind different run functions, so `run_fn` is per-entry rather +than derived from `config_type`. + +## Fields + + - `section::String` — `gpec.toml` section key (e.g. `"SOL_INPUT"`) + - `config_type::DataType` — `*Config` type, constructed via its `(::Dict)` / `(::String)` ctor + - `run_fn::Function` — `(EquilibriumConfig, config) -> eq_input` solver entry point +""" +struct AnalyticEqSpec + section::String + config_type::DataType + run_fn::Function +end + +# Registry of analytic equilibrium kinds. Both `setup_equilibrium` (fresh runs) and the +# rerun input builder dispatch off this table, so adding a new analytic kind is one new row. +const ANALYTIC_EQ = Dict( + "sol" => AnalyticEqSpec("SOL_INPUT", SolovevConfig, sol_run), + "lar" => AnalyticEqSpec("LAR_INPUT", LargeAspectRatioConfig, lar_run), + "tj_analytic" => AnalyticEqSpec("TJ_ANALYTIC_INPUT", TJAnalyticConfig, tj_analytic_run), + "tj_analytic_direct" => AnalyticEqSpec("TJ_ANALYTIC_INPUT", TJAnalyticConfig, tj_analytic_run_direct) +) + """ setup_equilibrium(eq_config::EquilibriumConfig) @@ -50,7 +83,7 @@ function setup_equilibrium(eq_config::EquilibriumConfig, additional_input=nothin eq_input.config = eq_config # Re-run the separatrix clamp for efit-family replays so an overridden # psihigh from the rerun TOML is re-validated against the closed flux region. - if eq_type in ["efit", "efit_arclength", "efit_by_inversion"] + if eq_type in EFIT_KINDS psihigh_safe, adjusted = clamp_psihigh_to_separatrix(eq_input) if adjusted @warn "psihigh=$(eq_input.config.psihigh) has no closed flux surface in EFIT grid; " * @@ -61,7 +94,7 @@ function setup_equilibrium(eq_config::EquilibriumConfig, additional_input=nothin elseif additional_input isa InverseRunInput eq_input = additional_input eq_input.config = eq_config - elseif eq_type in ["efit", "efit_arclength", "efit_by_inversion"] + elseif eq_type in EFIT_KINDS eq_input = read_efit(eq_config) psihigh_safe, adjusted = clamp_psihigh_to_separatrix(eq_input) if adjusted @@ -73,34 +106,14 @@ function setup_equilibrium(eq_config::EquilibriumConfig, additional_input=nothin eq_input = read_chease_ascii(eq_config) elseif eq_type in ["chease", "chease_binary"] eq_input = read_chease_binary(eq_config) - elseif eq_type == "lar" - if additional_input === nothing - additional_input = LargeAspectRatioConfig(eq_config.eq_filename) - end - eq_input = lar_run(eq_config, additional_input) - elseif eq_type == "tj_analytic" - # TJ-analytic equilibrium (GPEC adaptation of the profile family - # used by R. Fitzpatrick's TJ code, https://github.com/rfitzp/TJ) fed - # through the inverse pipeline. - if additional_input === nothing - additional_input = TJAnalyticConfig(eq_config.eq_filename) - end - eq_input = tj_analytic_run(eq_config, additional_input) - elseif eq_type == "tj_analytic_direct" - # TJ-analytic equilibrium (R. Fitzpatrick's TJ-code profile - # family, https://github.com/rfitzp/TJ) fed through the direct-GS - # solver: builds ψ(R, Z) on a 2D grid and delegates to the same solver - # as `efit`. Reproduces the full geqdsk-path physics including - # higher-order geometric effects that the inverse solver misses. - if additional_input === nothing - additional_input = TJAnalyticConfig(eq_config.eq_filename) - end - eq_input = tj_analytic_run_direct(eq_config, additional_input) - elseif eq_type == "sol" + elseif haskey(ANALYTIC_EQ, eq_type) + # Analytic kinds (sol/lar/tj_analytic[_direct]) dispatch off the ANALYTIC_EQ registry: + # build the config from the eq_filename TOML if not already supplied, then run its solver. + spec = ANALYTIC_EQ[eq_type] if additional_input === nothing - additional_input = SolovevConfig(eq_config.eq_filename) + additional_input = spec.config_type(eq_config.eq_filename) end - eq_input = sol_run(eq_config, additional_input) + eq_input = spec.run_fn(eq_config, additional_input) elseif eq_type == "imas" if additional_input === nothing error("setup_equilibrium: eq_type=\"imas\" requires an IMASdd.dd passed as additional_input") diff --git a/src/GeneralizedPerturbedEquilibrium.jl b/src/GeneralizedPerturbedEquilibrium.jl index 59f87e74a..5fc5f08c2 100755 --- a/src/GeneralizedPerturbedEquilibrium.jl +++ b/src/GeneralizedPerturbedEquilibrium.jl @@ -119,7 +119,7 @@ function build_inputs_from_toml(path::String; dd::Union{IMASdd.dd,Nothing}=nothi # An equilibrium is analytic (sol/lar/tj, parameters from its embedded section), # IMAS-fed (via the dd kwarg), or read from a file (additional_input = nothing). - additional_input = if haskey(ANALYTIC_EQ_SECTIONS, eq_config.eq_type) + additional_input = if haskey(Equilibrium.ANALYTIC_EQ, eq_config.eq_type) build_analytic_config(eq_config.eq_type, inputs) elseif eq_config.eq_type == "imas" dd diff --git a/src/Rerun.jl b/src/Rerun.jl index 3d64e49ad..d7f20dab2 100644 --- a/src/Rerun.jl +++ b/src/Rerun.jl @@ -6,13 +6,9 @@ # its imports (TOML, HDF5, Equilibrium, ForcingTerms, etc.). # Analytic equilibria carry their parameters in a TOML section rather than an ingest array; -# replay regenerates them from that section. Maps eq_type to its gpec.toml section key. -const ANALYTIC_EQ_SECTIONS = Dict( - "sol" => "SOL_INPUT", - "lar" => "LAR_INPUT", - "tj_analytic" => "TJ_ANALYTIC_INPUT", - "tj_analytic_direct" => "TJ_ANALYTIC_INPUT", -) +# replay regenerates them from that section. The eq_type -> section mapping (and which kinds +# are analytic at all) lives in the `Equilibrium.ANALYTIC_EQ` registry, the single source of +# truth shared with `setup_equilibrium`. """ merge_auxiliary_eq_toml!(inputs::Dict{String,Any}, eq_config) @@ -24,8 +20,9 @@ Otherwise it falls back to the deprecated side-car TOML referenced by `eq_config and folds that section in (with a deprecation warning). No-op for non-analytic equilibria. """ function merge_auxiliary_eq_toml!(inputs::Dict{String,Any}, eq_config::Equilibrium.EquilibriumConfig) - section = get(ANALYTIC_EQ_SECTIONS, eq_config.eq_type, nothing) - section === nothing && return inputs # file-based: snapshotted via the equilibrium ingest + spec = get(Equilibrium.ANALYTIC_EQ, eq_config.eq_type, nothing) + spec === nothing && return inputs # file-based: snapshotted via the equilibrium ingest + section = spec.section haskey(inputs, section) && return inputs # already embedded in gpec.toml filepath = eq_config.eq_filename @@ -40,21 +37,14 @@ end build_analytic_config(eq_type, inputs) Construct the analytic-equilibrium `*Config` (`SolovevConfig` / `LargeAspectRatioConfig` / -`TJAnalyticConfig`) from the TOML section named by [`ANALYTIC_EQ_SECTIONS`]. Shared by the -TOML and rerun input builders so both resolve analytic parameters the same way. +`TJAnalyticConfig`) from the TOML section named in the `Equilibrium.ANALYTIC_EQ` registry. +Shared by the TOML and rerun input builders so both resolve analytic parameters the same way. """ function build_analytic_config(eq_type::AbstractString, inputs::Dict) - section = get(ANALYTIC_EQ_SECTIONS, eq_type, nothing) - section === nothing && error("build_analytic_config: $eq_type is not an analytic equilibrium type") - haskey(inputs, section) || error("Analytic equilibrium $eq_type requires a [$section] section in gpec.toml") - data = inputs[section] - if eq_type == "sol" - return Equilibrium.SolovevConfig(data) - elseif eq_type == "lar" - return Equilibrium.LargeAspectRatioConfig(data) - else - return Equilibrium.TJAnalyticConfig(data) - end + spec = get(Equilibrium.ANALYTIC_EQ, eq_type, nothing) + spec === nothing && error("build_analytic_config: $eq_type is not an analytic equilibrium type") + haskey(inputs, spec.section) || error("Analytic equilibrium $eq_type requires a [$(spec.section)] section in gpec.toml") + return spec.config_type(inputs[spec.section]) end """ @@ -72,7 +62,9 @@ function read_equilibrium_ingest(in_h5) kind = read(group, "ingest_kind") T = kind == "direct" ? Equilibrium.DirectIngest : kind == "inverse" ? Equilibrium.InverseIngest : - error("Unknown equilibrium ingest_kind in gpec.h5: $kind") + error("Unknown equilibrium ingest_kind in gpec.h5: $kind (expected \"direct\" or \"inverse\")") + # Positional reconstruction: relies on the default constructor, so `fieldnames(T)` order + # must match the struct definition and the field-by-field write in write_outputs_to_HDF5. return T((read(group, String(f)) for f in fieldnames(T))...) end @@ -303,14 +295,16 @@ function build_inputs_from_h5(args::Vector{String}) # Analytic kinds regenerate from their TOML section; file-based kinds rebuild splines from # the stored ingest. A file-based run with no ingest can only come from a pre-ingest gpec.h5. - additional_input = if haskey(ANALYTIC_EQ_SECTIONS, eq_config.eq_type) + additional_input = if haskey(Equilibrium.ANALYTIC_EQ, eq_config.eq_type) build_analytic_config(eq_config.eq_type, inputs) elseif ingest isa Equilibrium.DirectIngest Equilibrium.build_direct_from_ingest(eq_config, ingest) elseif ingest isa Equilibrium.InverseIngest Equilibrium.build_inverse_from_ingest(eq_config, ingest) else - error("gpec.h5 has no equilibrium ingest and eq_type=$(eq_config.eq_type) is not analytic — cannot replay") + error("gpec.h5 has no equilibrium ingest and eq_type=$(eq_config.eq_type) is not analytic — cannot replay. " * + "A file-based eq_type needs a stored ingest (pre-ingest snapshots lack one); a new analytic kind must be " * + "registered in Equilibrium.ANALYTIC_EQ.") end return inputs, eq_config, additional_input, output_dir, current_git, preloaded_forcing, preloaded_coils diff --git a/test/runtests_rerun_from_h5.jl b/test/runtests_rerun_from_h5.jl index a7b966ebe..0dacb0e01 100644 --- a/test/runtests_rerun_from_h5.jl +++ b/test/runtests_rerun_from_h5.jl @@ -285,3 +285,26 @@ end bad = @test_logs (:warn,) pf("ForceFreeStates.mode=blorp") @test bad["ForceFreeStates"]["mode"] == "blorp" end + +# Drift guard for the analytic-equilibrium registry: setup_equilibrium and the rerun builder both +# dispatch off Equilibrium.ANALYTIC_EQ, so a malformed entry (missing Dict ctor, wrong run_fn, +# empty section) would silently break one path. Asserting each entry is well-formed and that +# build_analytic_config resolves it keeps adding a new analytic kind a one-row change. +@testset "ANALYTIC_EQ registry is well-formed and drives build_analytic_config" begin + Equil = GeneralizedPerturbedEquilibrium.Equilibrium + bac = GeneralizedPerturbedEquilibrium.build_analytic_config + for (eq_type, spec) in Equil.ANALYTIC_EQ + @test spec.section isa String && !isempty(spec.section) + # config_type must build from a parsed TOML table (the rerun/embedded-section path)... + @test hasmethod(spec.config_type, Tuple{Dict{String,Any}}) + # ...and from a side-car path string (the deprecated fallback in setup_equilibrium). + @test hasmethod(spec.config_type, Tuple{String}) + # run_fn must accept (EquilibriumConfig, ). + @test hasmethod(spec.run_fn, Tuple{Equil.EquilibriumConfig,spec.config_type}) + # build_analytic_config resolves the section to the right config type using defaults. + cfg = bac(eq_type, Dict{String,Any}(spec.section => Dict{String,Any}())) + @test cfg isa spec.config_type + end + # Unregistered kinds are rejected, not silently mis-built. + @test_throws ErrorException bac("not_a_real_kind", Dict{String,Any}()) +end From 8f0a7cceb6bcdde8facb3ac453e63c102b615e15 Mon Sep 17 00:00:00 2001 From: d-burg Date: Mon, 22 Jun 2026 15:40:15 -0400 Subject: [PATCH 092/135] EXAMPLE - Retarget DIIID equilibrium to Ip=1.15 MA; psihigh=0.995 (captures q=6) Co-Authored-By: Claude Opus 4.8 --- .../TkMkr_D3Dlike_Hmode.geqdsk | 27154 ++++++++-------- examples/DIIID-like_ideal_example/gpec.toml | 2 +- 2 files changed, 13578 insertions(+), 13578 deletions(-) diff --git a/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk b/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk index 28a500157..f89a0ea7a 100644 --- a/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk +++ b/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk @@ -1,13582 +1,13582 @@ tMaker: 0 257 257 - 1.467141630E+00 2.977755070E+00 1.688772320E+00 9.506132600E-01-5.415000020E-03 - 1.742895360E+00 4.006339980E-02-1.037636850E-01 1.547225710E-01-2.007967470E+00 - 1.200298620E+06-1.037636850E-01 0.000000000E+00 1.742895360E+00 0.000000000E+00 - 4.006339980E-02 0.000000000E+00 1.547225710E-01 0.000000000E+00 0.000000000E+00 --3.456546070E+00-3.456005810E+00-3.455465320E+00-3.454925780E+00-3.454389330E+00 --3.453856230E+00-3.453326460E+00-3.452800040E+00-3.452276950E+00-3.451756720E+00 --3.451239590E+00-3.450725560E+00-3.450214150E+00-3.449705600E+00-3.449199680E+00 --3.448696370E+00-3.448195700E+00-3.447697640E+00-3.447201970E+00-3.446708680E+00 --3.446218010E+00-3.445729490E+00-3.445243120E+00-3.444759130E+00-3.444277520E+00 --3.443798070E+00-3.443320750E+00-3.442845820E+00-3.442372800E+00-3.441901920E+00 --3.441433430E+00-3.440966840E+00-3.440502170E+00-3.440039870E+00-3.439579490E+00 --3.439121480E+00-3.438665150E+00-3.438211200E+00-3.437759160E+00-3.437309030E+00 --3.436861280E+00-3.436415430E+00-3.435971500E+00-3.435529710E+00-3.435090070E+00 --3.434652570E+00-3.434216980E+00-3.433783530E+00-3.433351990E+00-3.432922840E+00 --3.432495590E+00-3.432070730E+00-3.431647780E+00-3.431226730E+00-3.430808070E+00 --3.430391550E+00-3.429977180E+00-3.429564950E+00-3.429154870E+00-3.428746940E+00 --3.428341150E+00-3.427937750E+00-3.427536490E+00-3.427137370E+00-3.426740650E+00 --3.426346060E+00-3.425953630E+00-3.425563570E+00-3.425175910E+00-3.424790380E+00 --3.424407240E+00-3.424026250E+00-3.423647640E+00-3.423271420E+00-3.422897580E+00 --3.422525880E+00-3.422156810E+00-3.421789880E+00-3.421425340E+00-3.421063180E+00 --3.420703410E+00-3.420346020E+00-3.419991250E+00-3.419638630E+00-3.419288400E+00 --3.418940780E+00-3.418595310E+00-3.418252470E+00-3.417912010E+00-3.417573930E+00 --3.417238470E+00-3.416905160E+00-3.416574480E+00-3.416245940E+00-3.415920020E+00 --3.415596720E+00-3.415275570E+00-3.414957050E+00-3.414640900E+00-3.414327140E+00 --3.414015770E+00-3.413706780E+00-3.413400170E+00-3.413096190E+00-3.412794350E+00 --3.412495140E+00-3.412198070E+00-3.411903620E+00-3.411611320E+00-3.411321400E+00 --3.411033870E+00-3.410748720E+00-3.410465960E+00-3.410185580E+00-3.409907340E+00 --3.409631490E+00-3.409357790E+00-3.409086470E+00-3.408817290E+00-3.408550260E+00 --3.408285620E+00-3.408023120E+00-3.407763000E+00-3.407504800E+00-3.407248740E+00 --3.406995060E+00-3.406743290E+00-3.406493660E+00-3.406245950E+00-3.406000380E+00 --3.405756950E+00-3.405515430E+00-3.405276060E+00-3.405038600E+00-3.404802800E+00 --3.404569150E+00-3.404337410E+00-3.404107570E+00-3.403879400E+00-3.403653140E+00 --3.403428790E+00-3.403206110E+00-3.402985330E+00-3.402765990E+00-3.402548550E+00 --3.402332780E+00-3.402118680E+00-3.401906010E+00-3.401695010E+00-3.401485680E+00 --3.401278020E+00-3.401071550E+00-3.400866750E+00-3.400663380E+00-3.400461670E+00 --3.400261160E+00-3.400062080E+00-3.399864440E+00-3.399667980E+00-3.399472950E+00 --3.399279360E+00-3.399086950E+00-3.398895740E+00-3.398705720E+00-3.398517130E+00 --3.398329730E+00-3.398143290E+00-3.397958280E+00-3.397774220E+00-3.397591350E+00 --3.397409680E+00-3.397228960E+00-3.397049430E+00-3.396871090E+00-3.396693710E+00 --3.396517520E+00-3.396342280E+00-3.396168230E+00-3.395995140E+00-3.395823240E+00 --3.395652290E+00-3.395482540E+00-3.395313980E+00-3.395146370E+00-3.394980190E+00 --3.394814970E+00-3.394650940E+00-3.394488330E+00-3.394326930E+00-3.394166710E+00 --3.394008160E+00-3.393850800E+00-3.393694880E+00-3.393540620E+00-3.393387790E+00 --3.393236400E+00-3.393086670E+00-3.392938610E+00-3.392792220E+00-3.392647740E+00 --3.392504930E+00-3.392363790E+00-3.392224790E+00-3.392087460E+00-3.391952280E+00 --3.391819240E+00-3.391688350E+00-3.391559600E+00-3.391433000E+00-3.391309020E+00 --3.391187430E+00-3.391068220E+00-3.390951870E+00-3.390838150E+00-3.390727040E+00 --3.390619040E+00-3.390514140E+00-3.390412330E+00-3.390313630E+00-3.390218500E+00 --3.390126940E+00-3.390039210E+00-3.389955280E+00-3.389875170E+00-3.389799360E+00 --3.389727830E+00-3.389660360E+00-3.389597420E+00-3.389539240E+00-3.389485600E+00 --3.389437200E+00-3.389393810E+00-3.389356140E+00-3.389324190E+00-3.389298920E+00 --3.389280560E+00-3.389270310E+00-3.389269110E+00-3.389277940E+00-3.389298920E+00 --3.389333250E+00-3.389383550E+00-3.389449120E+00-3.389526130E+00-3.389616970E+00 --3.389725210E+00-3.389848470E+00-3.389981990E+00-3.390120510E+00-3.390258790E+00 --3.390393500E+00-3.390522480E+00-3.390645270E+00-3.390760420E+00-3.390867230E+00 --3.390964030E+00-3.391000510E+00 - 5.807950390E+04 5.769207810E+04 5.730908200E+04 5.692913670E+04 5.655028120E+04 - 5.617230080E+04 5.579517190E+04 5.541892970E+04 5.504364450E+04 5.466937110E+04 - 5.429616410E+04 5.392408980E+04 5.355317190E+04 5.318346880E+04 5.281507810E+04 - 5.244801560E+04 5.208229690E+04 5.171798830E+04 5.135512890E+04 5.099377340E+04 - 5.063394530E+04 5.027564450E+04 4.991895310E+04 4.956388280E+04 4.921041020E+04 - 4.885857420E+04 4.850842190E+04 4.816000000E+04 4.781329300E+04 4.746830080E+04 - 4.712509380E+04 4.678367190E+04 4.644400390E+04 4.610615230E+04 4.577011330E+04 - 4.543587890E+04 4.510350780E+04 4.477299610E+04 4.444431250E+04 4.411750780E+04 - 4.379259380E+04 4.346957810E+04 4.314844920E+04 4.282920700E+04 4.251188280E+04 - 4.219647270E+04 4.188296090E+04 4.157139840E+04 4.126176560E+04 4.095404300E+04 - 4.064824610E+04 4.034438280E+04 4.004247270E+04 3.974251950E+04 3.944449610E+04 - 3.914841800E+04 3.885428910E+04 3.856208590E+04 3.827182420E+04 3.798351560E+04 - 3.769717190E+04 3.741276950E+04 3.713029300E+04 3.684977340E+04 3.657119530E+04 - 3.629454300E+04 3.601983980E+04 3.574707030E+04 3.547621480E+04 3.520728910E+04 - 3.494028520E+04 3.467520700E+04 3.441205860E+04 3.415081640E+04 3.389147660E+04 - 3.363404300E+04 3.337850000E+04 3.312487110E+04 3.287314840E+04 3.262329100E+04 - 3.237532030E+04 3.212923240E+04 3.188500200E+04 3.164264060E+04 3.140215430E+04 - 3.116351950E+04 3.092673240E+04 3.069178120E+04 3.045867380E+04 3.022740230E+04 - 2.999793550E+04 2.977029690E+04 2.954447660E+04 2.932044730E+04 2.909822460E+04 - 2.887778910E+04 2.865913870E+04 2.844226950E+04 2.822716020E+04 2.801381250E+04 - 2.780222070E+04 2.759237500E+04 2.738428520E+04 2.717792970E+04 2.697329300E+04 - 2.677037700E+04 2.656916210E+04 2.636965230E+04 2.617184180E+04 2.597571290E+04 - 2.578126760E+04 2.558849610E+04 2.539738670E+04 2.520792380E+04 2.502009770E+04 - 2.483391800E+04 2.464938280E+04 2.446646680E+04 2.428516020E+04 2.410546090E+04 - 2.392735350E+04 2.375083590E+04 2.357590040E+04 2.340254100E+04 2.323074410E+04 - 2.306049410E+04 2.289179100E+04 2.272463870E+04 2.255901560E+04 2.239491020E+04 - 2.223232620E+04 2.207124220E+04 2.191164060E+04 2.175352150E+04 2.159688870E+04 - 2.144173440E+04 2.128803520E+04 2.113578320E+04 2.098498240E+04 2.083561910E+04 - 2.068767970E+04 2.054115040E+04 2.039601950E+04 2.025228910E+04 2.010994920E+04 - 1.996897850E+04 1.982938280E+04 1.969115430E+04 1.955426560E+04 1.941871480E+04 - 1.928449410E+04 1.915159380E+04 1.902001170E+04 1.888971880E+04 1.876070700E+04 - 1.863296880E+04 1.850649800E+04 1.838128910E+04 1.825732030E+04 1.813457810E+04 - 1.801306050E+04 1.789274610E+04 1.777362500E+04 1.765567970E+04 1.753888870E+04 - 1.742325000E+04 1.730875200E+04 1.719536910E+04 1.708309380E+04 1.697190040E+04 - 1.686176760E+04 1.675269340E+04 1.664465040E+04 1.653760740E+04 1.643154880E+04 - 1.632645800E+04 1.622231050E+04 1.611907420E+04 1.601672270E+04 1.591523340E+04 - 1.581457810E+04 1.571472270E+04 1.561563280E+04 1.551726760E+04 1.541959280E+04 - 1.532257620E+04 1.522616210E+04 1.513030760E+04 1.503497460E+04 1.494010740E+04 - 1.484564940E+04 1.475154000E+04 1.465772560E+04 1.456414260E+04 1.447070510E+04 - 1.437734080E+04 1.428397950E+04 1.419053220E+04 1.409691410E+04 1.400302930E+04 - 1.390878120E+04 1.381406640E+04 1.371876070E+04 1.362274510E+04 1.352591210E+04 - 1.342812790E+04 1.332924120E+04 1.322911720E+04 1.312760160E+04 1.302453220E+04 - 1.291975390E+04 1.281309080E+04 1.270436520E+04 1.259339360E+04 1.247997850E+04 - 1.236393360E+04 1.224505760E+04 1.212312110E+04 1.199776760E+04 1.186850680E+04 - 1.173493460E+04 1.159675780E+04 1.145370900E+04 1.130551760E+04 1.115185350E+04 - 1.099235840E+04 1.082665530E+04 1.065427730E+04 1.047466210E+04 1.028715920E+04 - 1.009095410E+04 9.885020510E+03 9.668093750E+03 9.438567380E+03 9.194431640E+03 - 8.933128910E+03 8.651483400E+03 8.345638670E+03 8.010901860E+03 7.641827150E+03 - 7.232322750E+03 6.775275390E+03 6.278376460E+03 5.756074220E+03 5.198241210E+03 - 4.596106930E+03 3.963013180E+03 3.320428710E+03 2.694293460E+03 2.110341310E+03 - 1.589315670E+03 1.143635860E+03 7.763866580E+02 4.830058900E+02 2.542539220E+02 - 7.900045780E+01 4.925177620E-02 --1.848965530E+00-1.848736170E+00-1.851632710E+00-1.841199760E+00-1.829477430E+00 --1.817627670E+00-1.805918100E+00-1.794551490E+00-1.783539530E+00-1.772786860E+00 --1.762409450E+00-1.752346520E+00-1.742332580E+00-1.732859730E+00-1.723704700E+00 --1.714375260E+00-1.705434800E+00-1.696608900E+00-1.687969330E+00-1.679713850E+00 --1.671262500E+00-1.663088680E+00-1.655270930E+00-1.647233840E+00-1.639221190E+00 --1.631417390E+00-1.623809100E+00-1.616322400E+00-1.608618970E+00-1.601138710E+00 --1.593957190E+00-1.586429600E+00-1.579015020E+00-1.571867110E+00-1.564394350E+00 --1.557099340E+00-1.550116900E+00-1.542699220E+00-1.535443070E+00-1.528363820E+00 --1.521151540E+00-1.514021040E+00-1.506718870E+00-1.499444840E+00-1.492369530E+00 --1.485003110E+00-1.477733850E+00-1.470686550E+00-1.463232760E+00-1.455908300E+00 --1.448562500E+00-1.441185240E+00-1.433950540E+00-1.426492810E+00-1.418985490E+00 --1.411627290E+00-1.404042480E+00-1.396461370E+00-1.388945700E+00-1.381380800E+00 --1.373858930E+00-1.366076830E+00-1.358387710E+00-1.350770120E+00-1.342913270E+00 --1.335112690E+00-1.327413560E+00-1.319474340E+00-1.311535840E+00-1.303683880E+00 --1.295659300E+00-1.287744160E+00-1.279739860E+00-1.271626000E+00-1.263619180E+00 --1.255469920E+00-1.247343660E+00-1.239355560E+00-1.231106400E+00-1.222821470E+00 --1.214720490E+00-1.206416610E+00-1.198135610E+00-1.189977530E+00-1.181708810E+00 --1.173403980E+00-1.165085320E+00-1.156715040E+00-1.148485180E+00-1.140088800E+00 --1.131692410E+00-1.123526330E+00-1.115105390E+00-1.106778980E+00-1.098490720E+00 --1.090091470E+00-1.081818220E+00-1.073479530E+00-1.065148120E+00-1.056899430E+00 --1.048627380E+00-1.040409560E+00-1.032243610E+00-1.023958330E+00-1.015778780E+00 --1.007594820E+00-9.994125960E-01-9.913903470E-01-9.833064680E-01-9.752781390E-01 --9.673054810E-01-9.593260880E-01-9.513832930E-01-9.434313180E-01-9.355783460E-01 --9.278759960E-01-9.201807380E-01-9.124573470E-01-9.048331980E-01-8.972312810E-01 --8.896573190E-01-8.821987510E-01-8.747831580E-01-8.674533960E-01-8.601734040E-01 --8.529269100E-01-8.458249570E-01-8.387665750E-01-8.316943650E-01-8.247585890E-01 --8.179173470E-01-8.110546470E-01-8.043276670E-01-7.977070210E-01-7.912105320E-01 --7.847307320E-01-7.782444950E-01-7.719576360E-01-7.657178040E-01-7.595654130E-01 --7.534983750E-01-7.474998830E-01-7.415990830E-01-7.358090280E-01-7.300494310E-01 --7.243583200E-01-7.188575270E-01-7.133644820E-01-7.079491020E-01-7.027006750E-01 --6.974819300E-01-6.924005150E-01-6.873672600E-01-6.823329330E-01-6.774597170E-01 --6.726446750E-01-6.679664850E-01-6.633920070E-01-6.588104960E-01-6.543775200E-01 --6.499854920E-01-6.456413270E-01-6.414113640E-01-6.371794940E-01-6.330269580E-01 --6.290380950E-01-6.250366570E-01-6.211002470E-01-6.172593240E-01-6.133549210E-01 --6.095775960E-01-6.058605310E-01-6.020959620E-01-5.983839630E-01-5.947071910E-01 --5.910742280E-01-5.874416830E-01-5.837744470E-01-5.801271800E-01-5.764749650E-01 --5.727735160E-01-5.690169330E-01-5.651832220E-01-5.612729190E-01-5.573545100E-01 --5.533262490E-01-5.491090420E-01-5.448511240E-01-5.404257770E-01-5.358550550E-01 --5.311269760E-01-5.262534620E-01-5.213478210E-01-5.163016920E-01-5.110860470E-01 --5.058029890E-01-5.003448720E-01-4.947260320E-01-4.889403280E-01-4.829616550E-01 --4.768948260E-01-4.706448320E-01-4.641713200E-01-4.575458770E-01-4.507665340E-01 --4.436412450E-01-4.362614150E-01-4.286599460E-01-4.207395320E-01-4.126282930E-01 --4.042533040E-01-3.955945670E-01-3.866460030E-01-3.773538170E-01-3.677319880E-01 --3.577657040E-01-3.474736210E-01-3.368318380E-01-3.255350890E-01-3.135465980E-01 --3.011189100E-01-2.882991730E-01-2.751515810E-01-2.616235910E-01-2.476870570E-01 --2.333924170E-01-2.187054160E-01-2.035312650E-01-1.878277660E-01-1.715330330E-01 --1.544347850E-01-1.363979880E-01-1.171445250E-01-9.638624640E-02-7.371991870E-02 --4.853987690E-02-2.033955230E-02 1.167915300E-02 4.853535440E-02 9.103653580E-02 - 1.402550340E-01 1.980387720E-01 2.407993670E-01 2.760670190E-01 3.349080090E-01 - 3.918157220E-01 4.355742630E-01 4.609467090E-01 4.678424000E-01 4.603559670E-01 - 4.439680580E-01 4.232048990E-01 4.002397060E-01 3.741483390E-01 3.430916370E-01 - 3.060637120E-01-6.861934070E-02 --3.856936560E+05-3.817048750E+05-3.769220310E+05-3.756600620E+05-3.747632500E+05 --3.739263750E+05-3.730785940E+05-3.721660940E+05-3.711850620E+05-3.701622500E+05 --3.690704060E+05-3.679214690E+05-3.667808120E+05-3.655144060E+05-3.641765310E+05 --3.628923440E+05-3.615089690E+05-3.600965310E+05-3.586465940E+05-3.571067190E+05 --3.556273120E+05-3.540809060E+05-3.524438750E+05-3.508653750E+05-3.492782500E+05 --3.476309380E+05-3.459331560E+05-3.442063440E+05-3.425382190E+05-3.408105000E+05 --3.390011250E+05-3.372790310E+05-3.355208440E+05-3.336836560E+05-3.319263120E+05 --3.301187190E+05-3.282240000E+05-3.264396250E+05-3.246060310E+05-3.227182190E+05 --3.208573750E+05-3.189653440E+05-3.171094060E+05-3.152384060E+05-3.133067500E+05 --3.114445620E+05-3.095481880E+05-3.075840000E+05-3.057192500E+05-3.038107810E+05 --3.018984380E+05-2.999847190E+05-2.980234380E+05-2.961125620E+05-2.942060620E+05 --2.922511880E+05-2.903486880E+05-2.884374060E+05-2.865009690E+05-2.845684380E+05 --2.826147190E+05-2.807219380E+05-2.787962810E+05-2.768442500E+05-2.749500620E+05 --2.730352810E+05-2.710885940E+05-2.692001250E+05-2.673032500E+05-2.653759060E+05 --2.634890940E+05-2.615681410E+05-2.596677030E+05-2.577944690E+05-2.558914220E+05 --2.540252660E+05-2.521474690E+05-2.502279690E+05-2.483760160E+05-2.465324060E+05 --2.446392340E+05-2.428025940E+05-2.409629840E+05-2.390941410E+05-2.372542190E+05 --2.354232030E+05-2.335968120E+05-2.317870310E+05-2.299435780E+05-2.281514220E+05 --2.263671720E+05-2.245299840E+05-2.227669690E+05-2.209815160E+05-2.191907810E+05 --2.174373440E+05-2.156585940E+05-2.139085160E+05-2.121693280E+05-2.104223910E+05 --2.086940160E+05-2.069586090E+05-2.052186090E+05-2.035228120E+05-2.018118440E+05 --2.001178440E+05-1.984411410E+05-1.967404380E+05-1.950761560E+05-1.934094060E+05 --1.917415470E+05-1.900917500E+05-1.884501880E+05-1.868315620E+05-1.852082970E+05 --1.835681560E+05-1.819518750E+05-1.803620620E+05-1.787633120E+05-1.771788750E+05 --1.756092810E+05-1.740325620E+05-1.724707660E+05-1.709141410E+05-1.693746720E+05 --1.678510940E+05-1.663096880E+05-1.647803280E+05-1.632811720E+05-1.617723910E+05 --1.602676880E+05-1.588014530E+05-1.573319060E+05-1.558644060E+05-1.543878910E+05 --1.529338750E+05-1.515109380E+05-1.500633910E+05-1.486356880E+05-1.472184840E+05 --1.458142030E+05-1.444270940E+05-1.430414690E+05-1.416541880E+05-1.402895000E+05 --1.389383750E+05-1.375681720E+05-1.362318750E+05-1.349115000E+05-1.335828280E+05 --1.322776250E+05-1.309644140E+05-1.296695000E+05-1.284081020E+05-1.271356720E+05 --1.258825310E+05-1.246276480E+05-1.233815470E+05-1.221714920E+05-1.209502500E+05 --1.197490000E+05-1.185664840E+05-1.173843830E+05-1.162364840E+05-1.151002890E+05 --1.139522890E+05-1.128416640E+05-1.117430550E+05-1.106473830E+05-1.095999530E+05 --1.085458910E+05-1.075041880E+05-1.065055620E+05-1.055210310E+05-1.045555700E+05 --1.036065940E+05-1.026853980E+05-1.018005780E+05-1.009344300E+05-1.000920700E+05 --9.928357810E+04-9.850718750E+04-9.776592190E+04-9.707266410E+04-9.639896880E+04 --9.576947660E+04-9.520459380E+04-9.466010940E+04-9.417324220E+04-9.373853120E+04 --9.336078120E+04-9.304842190E+04-9.277726560E+04-9.259021880E+04-9.248888280E+04 --9.244348440E+04-9.248595310E+04-9.261239060E+04-9.282482810E+04-9.314007810E+04 --9.354436720E+04-9.406568750E+04-9.471521090E+04-9.547109380E+04-9.633303120E+04 --9.735779690E+04-9.851762500E+04-9.980653910E+04-1.012755310E+05-1.028825700E+05 --1.046611410E+05-1.066181560E+05-1.087442500E+05-1.110689300E+05-1.135824530E+05 --1.162800080E+05-1.191885860E+05-1.223440080E+05-1.259618980E+05-1.300832580E+05 --1.344993280E+05-1.392014060E+05-1.441489060E+05-1.493897810E+05-1.549916560E+05 --1.609374060E+05-1.672892810E+05-1.741623440E+05-1.816268440E+05-1.897863120E+05 --1.988716560E+05-2.090574840E+05-2.206549530E+05-2.340226560E+05-2.496045470E+05 --2.680399690E+05-2.899108750E+05-3.159931560E+05-3.471586560E+05-3.840242500E+05 --4.272552500E+05-4.782301250E+05-5.054315620E+05-5.290525620E+05-5.764625620E+05 --6.160161880E+05-6.375563120E+05-6.346614380E+05-6.049156880E+05-5.511761880E+05 --4.804437810E+05-4.021640310E+05-3.253099690E+05-2.559969060E+05-1.973720310E+05 --1.500435780E+05-3.810404050E+03 - 1.114329620E-01 1.086638050E-01 1.061132480E-01 1.037872360E-01 1.016888920E-01 - 9.981998800E-02 9.818387780E-02 9.678259490E-02 9.561818840E-02 9.469175340E-02 - 9.400556980E-02 9.355994310E-02 9.335531290E-02 9.339212630E-02 9.366961570E-02 - 9.418787060E-02 9.491488340E-02 9.566913550E-02 9.641844030E-02 9.715750810E-02 - 9.786627440E-02 9.854943310E-02 9.919932480E-02 9.981012340E-02 1.003760100E-01 - 1.008975430E-01 1.013788800E-01 1.018028260E-01 1.021794680E-01 1.025188860E-01 - 1.028311700E-01 1.031263920E-01 1.034146320E-01 1.036954520E-01 1.039422680E-01 - 1.041803210E-01 1.044171970E-01 1.046625750E-01 1.049195160E-01 1.051923330E-01 - 1.054829430E-01 1.057954130E-01 1.061338040E-01 1.065021830E-01 1.069046180E-01 - 1.073451860E-01 1.078252490E-01 1.083443910E-01 1.089056880E-01 1.095135140E-01 - 1.101687850E-01 1.108729990E-01 1.116276830E-01 1.124343200E-01 1.132944380E-01 - 1.142095250E-01 1.151812080E-01 1.162092160E-01 1.172938570E-01 1.184369770E-01 - 1.196374000E-01 1.208961760E-01 1.222147270E-01 1.235917730E-01 1.250262560E-01 - 1.265171470E-01 1.280633960E-01 1.296639290E-01 1.313177350E-01 1.330228000E-01 - 1.347746400E-01 1.365722860E-01 1.384094360E-01 1.402814980E-01 1.421816950E-01 - 1.441177280E-01 1.460841600E-01 1.480749700E-01 1.500842120E-01 1.521058980E-01 - 1.541340800E-01 1.561734230E-01 1.582251340E-01 1.602850850E-01 1.623516230E-01 - 1.644225720E-01 1.664973050E-01 1.685758380E-01 1.706550420E-01 1.727321740E-01 - 1.748083830E-01 1.768848300E-01 1.789626480E-01 1.810430290E-01 1.831271050E-01 - 1.852160390E-01 1.873109940E-01 1.894131150E-01 1.915179040E-01 1.936232150E-01 - 1.957329210E-01 1.978469040E-01 1.999659990E-01 2.020918580E-01 2.042241840E-01 - 2.063663600E-01 2.085198760E-01 2.106760140E-01 2.128362800E-01 2.150021490E-01 - 2.171751410E-01 2.193567310E-01 2.215452340E-01 2.237286720E-01 2.259055970E-01 - 2.280692910E-01 2.302078160E-01 2.323199360E-01 2.344039830E-01 2.364512380E-01 - 2.384658310E-01 2.404443920E-01 2.423834800E-01 2.442832140E-01 2.461434900E-01 - 2.479629810E-01 2.497420760E-01 2.514804300E-01 2.531771660E-01 2.548322380E-01 - 2.564453180E-01 2.580159900E-01 2.595444020E-01 2.610311210E-01 2.624743280E-01 - 2.638755740E-01 2.652343510E-01 2.665500940E-01 2.678238150E-01 2.690599860E-01 - 2.702557440E-01 2.714158000E-01 2.725437880E-01 2.736404240E-01 2.747127120E-01 - 2.757735250E-01 2.768241760E-01 2.778757510E-01 2.789361770E-01 2.800044420E-01 - 2.810795310E-01 2.821604610E-01 2.832461600E-01 2.843457160E-01 2.854598760E-01 - 2.865850630E-01 2.877220210E-01 2.888691430E-01 2.900283930E-01 2.911997140E-01 - 2.923831640E-01 2.935786840E-01 2.947863340E-01 2.960060240E-01 2.972378130E-01 - 2.984816730E-01 2.997376020E-01 3.010037540E-01 3.022833760E-01 3.035739060E-01 - 3.048757910E-01 3.061890010E-01 3.075134750E-01 3.088491260E-01 3.101958630E-01 - 3.115535380E-01 3.129221200E-01 3.143014610E-01 3.156914710E-01 3.170921210E-01 - 3.185030820E-01 3.199238180E-01 3.213545080E-01 3.227949440E-01 3.242447970E-01 - 3.257038000E-01 3.271717130E-01 3.286480310E-01 3.301327530E-01 3.316255810E-01 - 3.331262770E-01 3.346345420E-01 3.361497520E-01 3.376714890E-01 3.391993050E-01 - 3.407327230E-01 3.422713280E-01 3.438146710E-01 3.453623060E-01 3.469137850E-01 - 3.484686910E-01 3.500265480E-01 3.515855970E-01 3.531465230E-01 3.547085520E-01 - 3.562709090E-01 3.578327300E-01 3.593932390E-01 3.609516020E-01 3.625070150E-01 - 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5.125205590E-02 - 5.352752280E-02 5.584600570E-02 5.820687490E-02 6.060954560E-02 6.305336950E-02 - 6.553772840E-02 6.806198510E-02 7.062554360E-02 7.322783020E-02 7.586820420E-02 - 7.854602490E-02 8.126073330E-02 8.401169630E-02 8.679837730E-02 8.962023260E-02 - 9.247667340E-02 9.536722300E-02 9.829143430E-02 1.012488450E-01 1.042390240E-01 - 1.072619110E-01 1.103175430E-01 1.134057270E-01 1.165251210E-01 1.196780350E-01 - 1.228652600E-01 1.260876360E-01 1.293458490E-01 1.326422840E-01 1.359833480E-01 - 1.393755380E-01 1.428314300E-01 1.463721840E-01 1.499684150E-01 1.536093800E-01 - 1.572843340E-01 1.609825340E-01 1.646932360E-01 1.684056820E-01 1.720986660E-01 - 1.758198590E-01 1.795511250E-01 1.832898260E-01 1.870363800E-01 1.907911750E-01 - 1.945546120E-01 1.983270500E-01 2.021078910E-01 2.058973910E-01 2.096957120E-01 - 2.135029880E-01 2.173194140E-01 2.211451380E-01 2.249803990E-01 2.288254500E-01 - 2.326805740E-01 2.365460400E-01 2.404222640E-01 2.443096340E-01 2.482084040E-01 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1.338163020E-01 1.372739670E-01 1.407845170E-01 1.443756070E-01 1.480361970E-01 - 1.517533060E-01 1.555108730E-01 1.592928020E-01 1.630806920E-01 1.668709520E-01 - 1.706687660E-01 1.744739860E-01 1.782864630E-01 1.821061370E-01 1.859328450E-01 - 1.897668090E-01 1.936080750E-01 1.974567320E-01 2.013129890E-01 2.051769200E-01 - 2.090486740E-01 2.129284290E-01 2.168163810E-01 2.207128550E-01 2.246180330E-01 - 2.285321950E-01 2.324556710E-01 2.363887730E-01 2.403318140E-01 2.442852560E-01 - 2.482496200E-01 2.522252800E-01 2.562127410E-01 2.602126000E-01 2.642253940E-01 - 2.682517470E-01 2.722923160E-01 2.763478760E-01 2.804190810E-01 2.845067680E-01 - 2.886118890E-01 2.927354280E-01 2.968782780E-01 3.010414540E-01 3.052259680E-01 - 3.094332220E-01 3.136644960E-01 3.179211020E-01 3.222044110E-01 3.265156750E-01 - 3.308568890E-01 3.352296050E-01 3.396356110E-01 3.440769610E-01 3.485561610E-01 - 2.202126230E-01 2.181729670E-01 2.161210920E-01 2.140569980E-01 2.119807300E-01 - 2.098922730E-01 2.077915970E-01 2.056788360E-01 2.035539150E-01 2.014168650E-01 - 1.992676710E-01 1.971063460E-01 1.949328630E-01 1.927472050E-01 1.905493590E-01 - 1.883392630E-01 1.861169040E-01 1.838822220E-01 1.816351710E-01 1.793757080E-01 - 1.771037880E-01 1.748193200E-01 1.725222770E-01 1.702125820E-01 1.678901760E-01 - 1.655549560E-01 1.632069050E-01 1.608460550E-01 1.584719120E-01 1.560845970E-01 - 1.536840200E-01 1.512700770E-01 1.488434080E-01 1.464149650E-01 1.439896520E-01 - 1.415691820E-01 1.391560730E-01 1.367486860E-01 1.343454870E-01 1.319456400E-01 - 1.295489220E-01 1.271552150E-01 1.247645690E-01 1.223773880E-01 1.199939920E-01 - 1.176147310E-01 1.152400230E-01 1.128702910E-01 1.105059680E-01 1.081474720E-01 - 1.057952490E-01 1.034497540E-01 1.011113970E-01 9.878064690E-02 9.645795820E-02 - 9.414377810E-02 9.183856100E-02 8.954277630E-02 8.725687860E-02 8.498137440E-02 - 8.271670340E-02 8.046334980E-02 7.822178300E-02 7.599247250E-02 7.377589490E-02 - 7.157254220E-02 6.938291340E-02 6.720750780E-02 6.504686180E-02 6.290151180E-02 - 6.077201290E-02 5.865893510E-02 5.656284090E-02 5.448435620E-02 5.242408440E-02 - 5.038265510E-02 4.836071280E-02 4.635890200E-02 4.437790070E-02 4.241840170E-02 - 4.048109800E-02 3.856670110E-02 3.667593000E-02 3.480950000E-02 3.296816720E-02 - 3.115268050E-02 2.936378120E-02 2.760225160E-02 2.586883490E-02 2.416433210E-02 - 2.248950680E-02 2.084513190E-02 1.923199560E-02 1.765086690E-02 1.610254680E-02 - 1.458783080E-02 1.310747770E-02 1.166227180E-02 1.025297960E-02 8.880385200E-03 - 7.545240690E-03 6.248297170E-03 4.990305290E-03 3.772016610E-03 2.594187620E-03 - 1.457528210E-03 3.627505790E-04-6.894373800E-04-1.698345640E-03-2.663284070E-03 --3.583581420E-03-4.458577370E-03-5.287646320E-03-6.070153320E-03-6.805466950E-03 --7.493003740E-03-8.132168090E-03-8.722400290E-03-9.263154120E-03-9.753886610E-03 --1.019408550E-02-1.058324890E-02-1.092091480E-02-1.120661480E-02-1.143990640E-02 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7.586287710E-02 7.875274120E-02 8.167745170E-02 8.463631570E-02 8.762869980E-02 - 9.065409000E-02 9.371199460E-02 9.680190680E-02 9.992330520E-02 1.030757200E-01 - 1.062589660E-01 1.094730940E-01 1.127182170E-01 1.159943490E-01 1.193024670E-01 - 1.226413850E-01 1.260127720E-01 1.294205930E-01 1.328688560E-01 1.363597070E-01 - 1.398991200E-01 1.435203700E-01 1.472129970E-01 1.509614590E-01 1.547539980E-01 - 1.585822400E-01 1.624109150E-01 1.662437020E-01 1.700827180E-01 1.739278290E-01 - 1.777796450E-01 1.816373910E-01 1.855017390E-01 1.893726440E-01 1.932501940E-01 - 1.971344950E-01 2.010256950E-01 2.049239580E-01 2.088294480E-01 2.127423730E-01 - 2.166628990E-01 2.205912620E-01 2.245277320E-01 2.284726500E-01 2.324263160E-01 - 2.363890560E-01 2.403612290E-01 2.443432510E-01 2.483355400E-01 2.523386180E-01 - 2.563529310E-01 2.603789870E-01 2.644173200E-01 2.684687970E-01 2.725340130E-01 - 2.766133250E-01 2.807077170E-01 2.848181130E-01 2.889452580E-01 2.930898370E-01 - 2.972529830E-01 3.014359180E-01 3.056395050E-01 3.098647300E-01 3.141129610E-01 - 3.183856610E-01 3.226841690E-01 3.270098870E-01 3.313639160E-01 3.357484940E-01 - 3.401653470E-01 3.446162640E-01 2.200479660E-01 2.179976110E-01 2.159339340E-01 - 2.138575460E-01 2.117682840E-01 2.096661930E-01 2.075513600E-01 2.054238170E-01 - 2.032836380E-01 2.011308220E-01 1.989653710E-01 1.967873420E-01 1.945966780E-01 - 1.923934070E-01 1.901774850E-01 1.879488830E-01 1.857075840E-01 1.834535450E-01 - 1.811867060E-01 1.789070070E-01 1.766144190E-01 1.743088810E-01 1.719903050E-01 - 1.696586460E-01 1.673138440E-01 1.649557950E-01 1.625844540E-01 1.601999250E-01 - 1.578015090E-01 1.553891600E-01 1.529634740E-01 1.505242740E-01 1.480735090E-01 - 1.456230880E-01 1.431761680E-01 1.407343450E-01 1.382989730E-01 1.358686690E-01 - 1.334411650E-01 1.310162250E-01 1.285939960E-01 1.261743900E-01 1.237573100E-01 - 1.213432030E-01 1.189325230E-01 1.165256050E-01 1.141228600E-01 1.117247190E-01 - 1.093316000E-01 1.069439500E-01 1.045622010E-01 1.021867920E-01 9.981817010E-02 - 9.745677560E-02 9.510306270E-02 9.275749330E-02 9.042051430E-02 8.809260280E-02 - 8.577421310E-02 8.346582950E-02 8.116790650E-02 7.888092100E-02 7.660533490E-02 - 7.434162500E-02 7.209026070E-02 6.985175610E-02 6.762658800E-02 6.541529300E-02 - 6.321840730E-02 6.103646010E-02 5.887003240E-02 5.671969800E-02 5.458604170E-02 - 5.246969310E-02 5.037126320E-02 4.829141130E-02 4.623077810E-02 4.419005290E-02 - 4.216992110E-02 4.017107930E-02 3.819423170E-02 3.624010090E-02 3.430943940E-02 - 3.240299970E-02 3.052154560E-02 2.866582200E-02 2.683659830E-02 2.503465860E-02 - 2.326080950E-02 2.151583320E-02 1.980051960E-02 1.811567690E-02 1.646209510E-02 - 1.484056930E-02 1.325190070E-02 1.169689090E-02 1.017634660E-02 8.691090160E-03 - 7.241855840E-03 5.829444160E-03 4.454659300E-03 3.118265190E-03 1.821022710E-03 - 5.636930000E-04-6.529628880E-04-1.828209380E-03-2.961313580E-03-4.051559140E-03 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2.806493640E-02 3.026183510E-02 3.250591080E-02 3.479648010E-02 3.713282570E-02 - 3.951423620E-02 4.193998870E-02 4.440942030E-02 4.692177100E-02 4.947629200E-02 - 5.207226430E-02 5.470896880E-02 5.738566820E-02 6.010163200E-02 6.285613780E-02 - 6.564845890E-02 6.847789140E-02 7.134377210E-02 7.424540820E-02 7.718213650E-02 - 8.015327900E-02 8.315821740E-02 8.619634060E-02 8.926701550E-02 9.236968310E-02 - 9.550380710E-02 9.866915640E-02 1.018647700E-01 1.050907600E-01 1.083470660E-01 - 1.116336440E-01 1.149504410E-01 1.182987320E-01 1.216762440E-01 1.250866060E-01 - 1.285320820E-01 1.320144530E-01 1.355261500E-01 1.391044260E-01 1.427654330E-01 - 1.464896500E-01 1.502684950E-01 1.540945620E-01 1.579604150E-01 1.618343590E-01 - 1.657075580E-01 1.695849600E-01 1.734682620E-01 1.773571520E-01 1.812513470E-01 - 1.851514130E-01 1.890573200E-01 1.929691280E-01 1.968869720E-01 2.008109990E-01 - 2.047413890E-01 2.086782600E-01 2.126218530E-01 2.165723590E-01 2.205300180E-01 - 2.244950980E-01 2.284678970E-01 2.324487570E-01 2.364379760E-01 2.404358830E-01 - 2.444429100E-01 2.484594430E-01 2.524859610E-01 2.565229830E-01 2.605710030E-01 - 2.646306160E-01 2.687022390E-01 2.727867070E-01 2.768846750E-01 2.809968590E-01 - 2.851239440E-01 2.892666160E-01 2.934259180E-01 2.976026240E-01 3.017977770E-01 - 3.060124810E-01 3.102476300E-01 3.145043550E-01 3.187838490E-01 3.230872150E-01 - 3.274165390E-01 3.317728040E-01 3.361572620E-01 3.405717610E-01 2.198861990E-01 - 2.178248760E-01 2.157495020E-01 2.136604190E-01 2.115578060E-01 2.094417960E-01 - 2.073125390E-01 2.051700500E-01 2.030144780E-01 2.008458380E-01 1.986641140E-01 - 1.964693520E-01 1.942615810E-01 1.920407710E-01 1.898069080E-01 1.875599470E-01 - 1.852998730E-01 1.830266420E-01 1.807402070E-01 1.784405110E-01 1.761274930E-01 - 1.738010940E-01 1.714612540E-01 1.691078990E-01 1.667409390E-01 1.643603300E-01 - 1.619659510E-01 1.595577750E-01 1.571358590E-01 1.546992360E-01 1.522485610E-01 - 1.497844900E-01 1.473105850E-01 1.448390330E-01 1.423711780E-01 1.399081950E-01 - 1.374507990E-01 1.349968610E-01 1.325454860E-01 1.300960480E-01 1.276486070E-01 - 1.252032220E-01 1.227599610E-01 1.203193440E-01 1.178817530E-01 1.154475360E-01 - 1.130171190E-01 1.105909350E-01 1.081694140E-01 1.057529750E-01 1.033420710E-01 - 1.009371360E-01 9.853861480E-02 9.614695610E-02 9.376259890E-02 9.138601270E-02 - 8.901765200E-02 8.665797860E-02 8.430746200E-02 8.196657150E-02 7.963576170E-02 - 7.731549440E-02 7.500624660E-02 7.270848010E-02 7.042268660E-02 6.814936550E-02 - 6.588901580E-02 6.364218150E-02 6.140939520E-02 5.919121580E-02 5.698821320E-02 - 5.480096490E-02 5.263010410E-02 5.047625300E-02 4.834003750E-02 4.622212050E-02 - 4.412319140E-02 4.204392430E-02 3.998501970E-02 3.794721140E-02 3.593120350E-02 - 3.393775600E-02 3.196762500E-02 3.002157990E-02 2.810037510E-02 2.620482260E-02 - 2.433569540E-02 2.249379270E-02 2.067992280E-02 1.889489590E-02 1.713953910E-02 - 1.541462070E-02 1.372101250E-02 1.205952190E-02 1.043095630E-02 8.836122230E-03 - 7.275833750E-03 5.750909450E-03 4.262164240E-03 2.810401140E-03 1.396424370E-03 - 2.101835890E-05-1.315040630E-03-2.610979370E-03-3.866036190E-03-5.079448220E-03 --6.250454580E-03-7.378337900E-03-8.462377820E-03-9.501851160E-03-1.049605940E-02 --1.144431900E-02-1.234595200E-02-1.320031190E-02-1.400675530E-02-1.476464980E-02 --1.547338630E-02-1.613236960E-02-1.674103360E-02-1.729881580E-02-1.780516100E-02 --1.825954580E-02-1.866146180E-02-1.901044510E-02-1.930603380E-02-1.954776230E-02 --1.973517430E-02-1.986799950E-02-1.994568110E-02-1.996791360E-02-1.993439160E-02 --1.984480020E-02-1.969883590E-02-1.949619690E-02-1.923664470E-02-1.891999880E-02 --1.854607840E-02-1.811469720E-02-1.762566530E-02-1.707881690E-02-1.647416130E-02 --1.581157930E-02-1.509099360E-02-1.431246100E-02-1.347600580E-02-1.258164180E-02 --1.162940260E-02-1.061940570E-02-9.551776570E-03-8.426661600E-03-7.244265170E-03 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1.535315810E-01 1.574402300E-01 1.613529030E-01 1.652619540E-01 1.691760570E-01 - 1.730951670E-01 1.770193130E-01 1.809482130E-01 1.848819110E-01 1.888206300E-01 - 1.927645210E-01 1.967136710E-01 2.006682160E-01 2.046282590E-01 2.085939350E-01 - 2.125655860E-01 2.165433470E-01 2.205273810E-01 2.245180010E-01 2.285155060E-01 - 2.325202230E-01 2.365324500E-01 2.405524250E-01 2.445806120E-01 2.486174110E-01 - 2.526632550E-01 2.567186060E-01 2.607839410E-01 2.648598250E-01 2.689467070E-01 - 2.730451820E-01 2.771559660E-01 2.812796240E-01 2.854170200E-01 2.895686030E-01 - 2.937352960E-01 2.979180810E-01 3.021176160E-01 3.063347340E-01 3.105705980E-01 - 3.148262500E-01 3.191025850E-01 3.234008550E-01 3.277223410E-01 3.320682050E-01 - 3.364396690E-01 2.197320010E-01 2.176583710E-01 2.155701520E-01 2.134676430E-01 - 2.113511710E-01 2.092208270E-01 2.070767730E-01 2.049191590E-01 2.027480010E-01 - 2.005633710E-01 1.983652860E-01 1.961538050E-01 1.939289270E-01 1.916906240E-01 - 1.894388940E-01 1.871736940E-01 1.848949940E-01 1.826027630E-01 1.802969430E-01 - 1.779774580E-01 1.756442640E-01 1.732972560E-01 1.709364210E-01 1.685616520E-01 - 1.661728770E-01 1.637699750E-01 1.613528880E-01 1.589215100E-01 1.564759310E-01 - 1.540154220E-01 1.515400260E-01 1.490513090E-01 1.465574350E-01 1.440641130E-01 - 1.415755600E-01 1.390921320E-01 1.366124450E-01 1.341353950E-01 1.316602230E-01 - 1.291864070E-01 1.267140210E-01 1.242431920E-01 1.217742410E-01 1.193074880E-01 - 1.168433430E-01 1.143822150E-01 1.119245290E-01 1.094706880E-01 1.070211460E-01 - 1.045763270E-01 1.021366640E-01 9.970261160E-02 9.727459400E-02 9.485306590E-02 - 9.243847430E-02 9.003128110E-02 8.763194080E-02 8.524091540E-02 8.285866680E-02 - 8.048565690E-02 7.812235500E-02 7.576919350E-02 7.342664900E-02 7.109521330E-02 - 6.877537820E-02 6.646764280E-02 6.417250630E-02 6.189051640E-02 5.962223190E-02 - 5.736818910E-02 5.512898420E-02 5.290524290E-02 5.069758370E-02 4.850664730E-02 - 4.633307080E-02 4.417752100E-02 4.204070200E-02 3.992330280E-02 3.782606870E-02 - 3.574971110E-02 3.369499000E-02 3.166266900E-02 2.965351570E-02 2.766829540E-02 - 2.570783910E-02 2.377290840E-02 2.186432290E-02 1.998292100E-02 1.812951830E-02 - 1.630492880E-02 1.450998430E-02 1.274551260E-02 1.101236140E-02 9.311379860E-03 - 7.643397430E-03 6.009225270E-03 4.409700630E-03 2.845639830E-03 1.317880000E-03 --1.727411870E-04-1.625413660E-03-3.039346780E-03-4.413753750E-03-5.747848660E-03 --7.040823810E-03-8.291917850E-03-9.500370360E-03-1.066542980E-02-1.178636030E-02 --1.286244020E-02-1.389296070E-02-1.487721690E-02-1.581451860E-02-1.670420360E-02 --1.754561630E-02-1.833810660E-02-1.908106730E-02-1.977389680E-02-2.041598970E-02 --2.100677040E-02-2.154568020E-02-2.203221250E-02-2.246580460E-02-2.284598910E-02 --2.317230220E-02-2.344428000E-02-2.366145700E-02-2.382342700E-02-2.392979340E-02 --2.398018910E-02-2.397425660E-02-2.391167540E-02-2.379219980E-02-2.361540120E-02 --2.338106740E-02-2.308901210E-02-2.273904350E-02-2.233097700E-02-2.186462280E-02 --2.133980210E-02-2.075646630E-02-2.011453360E-02-1.941390890E-02-1.865458490E-02 --1.783658010E-02-1.695991490E-02-1.602462870E-02-1.503083300E-02-1.397865640E-02 --1.286822460E-02-1.169966350E-02-1.047324950E-02-9.189188480E-03-7.847670470E-03 --6.449043290E-03-4.993661310E-03-3.481882860E-03-1.914064630E-03-2.905639120E-04 - 1.388191940E-03 3.121681280E-03 4.909429230E-03 6.750912410E-03 8.645594120E-03 - 1.059291510E-02 1.259227280E-02 1.464305070E-02 1.674459690E-02 1.889624450E-02 - 2.109733600E-02 2.334714680E-02 2.564496730E-02 2.799007480E-02 3.038172800E-02 - 3.281916680E-02 3.530161080E-02 3.782829640E-02 4.039843380E-02 4.301121460E-02 - 4.566583040E-02 4.836153610E-02 5.109751220E-02 5.387299140E-02 5.668720600E-02 - 5.953934040E-02 6.242865320E-02 6.535438450E-02 6.831578910E-02 7.131213690E-02 - 7.434272770E-02 7.740687580E-02 8.050388100E-02 8.363313230E-02 8.679398890E-02 - 8.998581770E-02 9.320812670E-02 9.646009650E-02 9.974153340E-02 1.030522210E-01 - 1.063919660E-01 1.097605750E-01 1.131578010E-01 1.165846660E-01 1.200402750E-01 - 1.235273180E-01 1.270467190E-01 1.306009590E-01 1.341844200E-01 1.378262190E-01 - 1.415391420E-01 1.453249900E-01 1.491711740E-01 1.530722680E-01 1.570186170E-01 - 1.609609130E-01 1.649068590E-01 1.688563670E-01 1.728094970E-01 1.767668720E-01 - 1.807279740E-01 1.846932320E-01 1.886626030E-01 1.926361920E-01 1.966141310E-01 - 2.005965860E-01 2.045836600E-01 2.085755320E-01 2.125722910E-01 2.165741920E-01 - 2.205815020E-01 2.245944740E-01 2.286133470E-01 2.326383440E-01 2.366697340E-01 - 2.407078740E-01 2.447531820E-01 2.488059400E-01 2.528666260E-01 2.569355960E-01 - 2.610132690E-01 2.651001810E-01 2.691966890E-01 2.733034790E-01 2.774211470E-01 - 2.815500200E-01 2.856907250E-01 2.898443340E-01 2.940112050E-01 2.981919650E-01 - 3.023874160E-01 3.065982160E-01 3.108256460E-01 3.150704210E-01 3.193330760E-01 - 3.236146270E-01 3.279161750E-01 3.322387340E-01 2.195877580E-01 2.175001800E-01 - 2.153979690E-01 2.132812140E-01 2.111500800E-01 2.090047750E-01 2.068455220E-01 - 2.046723220E-01 2.024853230E-01 2.002845560E-01 1.980700340E-01 1.958417890E-01 - 1.935998200E-01 1.913440970E-01 1.890746060E-01 1.867913010E-01 1.844941530E-01 - 1.821831020E-01 1.798580880E-01 1.775190530E-01 1.751659360E-01 1.727986340E-01 - 1.704171000E-01 1.680212170E-01 1.656109090E-01 1.631860730E-01 1.607465890E-01 - 1.582923830E-01 1.558233500E-01 1.533392070E-01 1.508388970E-01 1.483289900E-01 - 1.458143140E-01 1.432997880E-01 1.407908350E-01 1.382872460E-01 1.357853110E-01 - 1.332853290E-01 1.307866870E-01 1.282888050E-01 1.257918330E-01 1.232960300E-01 - 1.208017020E-01 1.183092070E-01 1.158189400E-01 1.133313180E-01 1.108467650E-01 - 1.083657000E-01 1.058885600E-01 1.034157800E-01 1.009478050E-01 9.848505260E-02 - 9.602797030E-02 9.357701240E-02 9.113261850E-02 8.869524300E-02 8.626536280E-02 - 8.384341750E-02 8.142986150E-02 7.902516420E-02 7.662976530E-02 7.424414160E-02 - 7.186874000E-02 6.950405990E-02 6.715060030E-02 6.480886790E-02 6.247935070E-02 - 6.016265970E-02 5.785927550E-02 5.556980520E-02 5.329487100E-02 5.103509870E-02 - 4.879110310E-02 4.656351730E-02 4.435300450E-02 4.216028380E-02 3.998605160E-02 - 3.783100840E-02 3.569591050E-02 3.358151390E-02 3.148857130E-02 2.941787240E-02 - 2.737019210E-02 2.534632200E-02 2.334707600E-02 2.137329240E-02 1.942579820E-02 - 1.750542600E-02 1.561300830E-02 1.374937590E-02 1.191539690E-02 1.011191400E-02 - 8.339781310E-03 6.599856070E-03 4.892950880E-03 3.219980510E-03 1.581759080E-03 --2.087603390E-05-1.587087290E-03-3.116037460E-03-4.606888630E-03-6.058820990E-03 --7.471034770E-03-8.842718790E-03-1.017307960E-02-1.146132870E-02-1.270669980E-02 --1.390842530E-02-1.506574920E-02-1.617794300E-02-1.724427750E-02-1.826404410E-02 --1.923654040E-02-2.016110160E-02-2.103702350E-02-2.186365430E-02-2.264038850E-02 --2.336662080E-02-2.404174770E-02-2.466516200E-02-2.523624710E-02-2.575453180E-02 --2.621946110E-02-2.663051900E-02-2.698722480E-02-2.728911680E-02-2.753572720E-02 --2.772662230E-02-2.786139770E-02-2.793968100E-02-2.796111070E-02-2.792533110E-02 --2.783204430E-02-2.768092230E-02-2.747170250E-02-2.720414100E-02-2.687802170E-02 --2.649315630E-02-2.604935690E-02-2.554646510E-02-2.498439330E-02-2.436305580E-02 --2.368237080E-02-2.294225620E-02-2.214275670E-02-2.128386870E-02-2.036560330E-02 --1.938808150E-02-1.835142260E-02-1.725574960E-02-1.610118900E-02-1.488794570E-02 --1.361628250E-02-1.228636500E-02-1.089850530E-02-9.453061040E-03-7.950389760E-03 --6.390847270E-03-4.774793980E-03-3.102616410E-03-1.374891610E-03 4.079598000E-04 - 2.245400330E-03 4.136874810E-03 6.081827920E-03 8.079669440E-03 1.012976840E-02 - 1.223146260E-02 1.438408440E-02 1.658695750E-02 1.883939280E-02 2.114060150E-02 - 2.348983660E-02 2.588634940E-02 2.832937240E-02 3.081810290E-02 3.335175660E-02 - 3.592953460E-02 3.855060790E-02 4.121413450E-02 4.391929510E-02 4.666526240E-02 - 4.945123200E-02 5.227640640E-02 5.513996260E-02 5.804107710E-02 6.097896020E-02 - 6.395286320E-02 6.696202610E-02 7.000565530E-02 7.308303560E-02 7.619346680E-02 - 7.933623340E-02 8.251067250E-02 8.571612830E-02 8.895222100E-02 9.221794460E-02 - 9.551277010E-02 9.883645920E-02 1.021887590E-01 1.055694370E-01 1.089782340E-01 - 1.124149190E-01 1.158807870E-01 1.193746630E-01 1.228986680E-01 1.264552470E-01 - 1.300464570E-01 1.336725500E-01 1.373414250E-01 1.410793070E-01 1.448910090E-01 - 1.487699600E-01 1.527107360E-01 1.566888840E-01 1.606650050E-01 1.646437790E-01 - 1.686260400E-01 1.726115200E-01 1.765998900E-01 1.805910620E-01 1.845854820E-01 - 1.885830460E-01 1.925838890E-01 1.965881140E-01 2.005957660E-01 2.046069350E-01 - 2.086220090E-01 2.126409560E-01 2.166639120E-01 2.206911300E-01 2.247228620E-01 - 2.287593330E-01 2.328008120E-01 2.368475500E-01 2.408997710E-01 2.449578340E-01 - 2.490220670E-01 2.530928250E-01 2.571704090E-01 2.612552050E-01 2.653476890E-01 - 2.694482510E-01 2.735573050E-01 2.776753010E-01 2.818028030E-01 2.859402600E-01 - 2.900882070E-01 2.942472100E-01 2.984178070E-01 3.026005030E-01 3.067962530E-01 - 3.110052350E-01 3.152284030E-01 3.194662930E-01 3.237194120E-01 3.279887140E-01 - 2.194541690E-01 2.173513030E-01 2.152337580E-01 2.131016850E-01 2.109552030E-01 - 2.087943850E-01 2.066194710E-01 2.044304610E-01 2.022274140E-01 2.000103740E-01 - 1.977793430E-01 1.955342890E-01 1.932752430E-01 1.910021750E-01 1.887150260E-01 - 1.864137800E-01 1.840983480E-01 1.817687000E-01 1.794247630E-01 1.770664450E-01 - 1.746936890E-01 1.723063890E-01 1.699044560E-01 1.674878000E-01 1.650563180E-01 - 1.626098900E-01 1.601483670E-01 1.576716750E-01 1.551797240E-01 1.526718590E-01 - 1.501491960E-01 1.476173400E-01 1.450818930E-01 1.425481590E-01 1.400199380E-01 - 1.374942960E-01 1.349706500E-01 1.324481820E-01 1.299264280E-01 1.274048540E-01 - 1.248836740E-01 1.223632770E-01 1.198439670E-01 1.173261330E-01 1.148101690E-01 - 1.122964920E-01 1.097855200E-01 1.072776840E-01 1.047734100E-01 1.022731290E-01 - 9.977728130E-02 9.728629140E-02 9.480060640E-02 9.232066570E-02 8.984693140E-02 - 8.737985790E-02 8.491988480E-02 8.246747400E-02 8.002306520E-02 7.758712770E-02 - 7.516011600E-02 7.274248450E-02 7.033468780E-02 6.793722510E-02 6.555059550E-02 - 6.317531320E-02 6.081191820E-02 5.846094710E-02 5.612297360E-02 5.379858240E-02 - 5.148840700E-02 4.919307310E-02 4.691321030E-02 4.464945570E-02 4.240255800E-02 - 4.017317670E-02 3.796202690E-02 3.576986860E-02 3.359745820E-02 3.144555540E-02 - 2.931492030E-02 2.720638360E-02 2.512071840E-02 2.305874790E-02 2.102131210E-02 - 1.900925860E-02 1.702342740E-02 1.506465300E-02 1.313378850E-02 1.123170550E-02 - 9.359268470E-03 7.517352230E-03 5.706826220E-03 3.928543070E-03 2.183378910E-03 - 4.721807780E-04-1.204151780E-03-2.844769970E-03-4.448836200E-03-6.015512630E-03 --7.543944290E-03-9.033295330E-03-1.048273500E-02-1.189142740E-02-1.325858940E-02 --1.458342650E-02-1.586514340E-02-1.710297170E-02-1.829614300E-02-1.944390310E-02 --2.054551240E-02-2.160025390E-02-2.260742710E-02-2.356632610E-02-2.447628040E-02 --2.533659340E-02-2.614663170E-02-2.690579000E-02-2.761346470E-02-2.826903950E-02 --2.887191440E-02-2.942155300E-02-2.991740590E-02-3.035894410E-02-3.074568140E-02 --3.107714090E-02-3.135284410E-02-3.157234940E-02-3.173524890E-02-3.184112910E-02 --3.188963610E-02-3.188040480E-02-3.181308880E-02-3.168739380E-02-3.150305900E-02 --3.125981990E-02-3.095739520E-02-3.059560620E-02-3.017428890E-02-2.969322540E-02 --2.915233000E-02-2.855151520E-02-2.789068970E-02-2.716977520E-02-2.638876250E-02 --2.554766270E-02-2.464650940E-02-2.368533050E-02-2.266426380E-02-2.158342490E-02 --2.044294030E-02-1.924302060E-02-1.798387800E-02-1.666573440E-02-1.528884470E-02 --1.385353970E-02-1.236017510E-02-1.080911050E-02-9.200715460E-03-7.535406390E-03 --5.813675930E-03-4.035971590E-03-2.202838430E-03-3.148363900E-04 1.627477820E-03 - 3.623521420E-03 5.672654140E-03 7.774224040E-03 9.927547540E-03 1.213192850E-02 - 1.438664830E-02 1.669095640E-02 1.904407330E-02 2.144525950E-02 2.389368410E-02 - 2.638851660E-02 2.892896720E-02 3.151419390E-02 3.414334730E-02 3.681559860E-02 - 3.953009100E-02 4.228595640E-02 4.508235310E-02 4.791842030E-02 5.079331620E-02 - 5.370621010E-02 5.665626000E-02 5.964264650E-02 6.266458330E-02 6.572128090E-02 - 6.881199030E-02 7.193589210E-02 7.509226350E-02 7.828042660E-02 8.149971070E-02 - 8.474943040E-02 8.802897480E-02 9.133773300E-02 9.467498960E-02 9.804036470E-02 - 1.014336050E-01 1.048544790E-01 1.083026980E-01 1.117785200E-01 1.152817760E-01 - 1.188130080E-01 1.223739460E-01 1.259663700E-01 1.295922850E-01 1.332534850E-01 - 1.369582710E-01 1.407249270E-01 1.445568800E-01 1.484627280E-01 1.524449740E-01 - 1.564534460E-01 1.604620670E-01 1.644731160E-01 1.684864160E-01 1.725017430E-01 - 1.765188870E-01 1.805378790E-01 1.845590030E-01 1.885822420E-01 1.926076410E-01 - 1.966352610E-01 2.006652060E-01 2.046976690E-01 2.087327540E-01 2.127705220E-01 - 2.168111210E-01 2.208547890E-01 2.249017660E-01 2.289521690E-01 2.330061790E-01 - 2.370640930E-01 2.411260600E-01 2.451923490E-01 2.492633160E-01 2.533392310E-01 - 2.574203010E-01 2.615069150E-01 2.655993700E-01 2.696979340E-01 2.738031740E-01 - 2.779153590E-01 2.820345160E-01 2.861612140E-01 2.902961370E-01 2.944395240E-01 - 2.985915840E-01 3.027528230E-01 3.069237770E-01 3.111047150E-01 3.152961130E-01 - 3.194983600E-01 3.237116930E-01 2.193304150E-01 2.172112460E-01 2.150775640E-01 - 2.129293530E-01 2.107668670E-01 2.085901350E-01 2.063991580E-01 2.041940690E-01 - 2.019748090E-01 1.997413780E-01 1.974937620E-01 1.952319590E-01 1.929559410E-01 - 1.906656470E-01 1.883610190E-01 1.860420110E-01 1.837085490E-01 1.813605580E-01 - 1.789979490E-01 1.766206470E-01 1.742285490E-01 1.718215790E-01 1.693996040E-01 - 1.669625790E-01 1.645103540E-01 1.620428560E-01 1.595599200E-01 1.570614130E-01 - 1.545476170E-01 1.520159240E-01 1.494709550E-01 1.469181330E-01 1.443629410E-01 - 1.418105360E-01 1.392617520E-01 1.367151740E-01 1.341699960E-01 1.316254730E-01 - 1.290809070E-01 1.265359670E-01 1.239909460E-01 1.214463930E-01 1.189025710E-01 - 1.163598600E-01 1.138186680E-01 1.112794130E-01 1.087424900E-01 1.062083540E-01 - 1.036774140E-01 1.011501100E-01 9.862687440E-02 9.610814600E-02 9.359434250E-02 - 9.108593310E-02 8.858335020E-02 8.608704810E-02 8.359748130E-02 8.111508940E-02 - 7.864033430E-02 7.617365570E-02 7.371550050E-02 7.126634570E-02 6.882666050E-02 - 6.639689210E-02 6.397758420E-02 6.156927350E-02 5.917249990E-02 5.678780000E-02 - 5.441575500E-02 5.205697190E-02 4.971207310E-02 4.738169910E-02 4.506651310E-02 - 4.276718200E-02 4.048441350E-02 3.821891550E-02 3.597144410E-02 3.374275570E-02 - 3.153361010E-02 2.934477110E-02 2.717705820E-02 2.503126110E-02 2.290820520E-02 - 2.080875260E-02 1.873375100E-02 1.668404040E-02 1.466046830E-02 1.266391390E-02 - 1.069525070E-02 8.755354210E-03 6.845111490E-03 4.965409170E-03 3.117121520E-03 - 1.301132840E-03-4.816785220E-04-2.230426530E-03-3.944230730E-03-5.622198340E-03 --7.263485340E-03-8.867224680E-03-1.043256470E-02-1.195866990E-02-1.344470590E-02 --1.488982890E-02-1.629319040E-02-1.765397750E-02-1.897142450E-02-2.024473990E-02 --2.147315630E-02-2.265589680E-02-2.379220540E-02-2.488134990E-02-2.592262250E-02 --2.691531550E-02-2.785872850E-02-2.875220030E-02-2.959505100E-02-3.038665090E-02 --3.112638180E-02-3.181362520E-02-3.244780000E-02-3.302833440E-02-3.355466950E-02 --3.402627630E-02-3.444263340E-02-3.480326380E-02-3.510769080E-02-3.535545620E-02 --3.554612400E-02-3.567929190E-02-3.575457260E-02-3.577159720E-02-3.573000430E-02 --3.562948850E-02-3.546978530E-02-3.525061910E-02-3.497170660E-02-3.463283550E-02 --3.423381970E-02-3.377448770E-02-3.325469050E-02-3.267430510E-02-3.203325350E-02 --3.133144600E-02-3.056886610E-02-2.974554520E-02-2.886150400E-02-2.791674990E-02 --2.691132390E-02-2.584539910E-02-2.471908550E-02-2.353258800E-02-2.228611710E-02 --2.097988130E-02-1.961411910E-02-1.818915080E-02-1.670529510E-02-1.516292430E-02 --1.356243340E-02-1.190422290E-02-1.018874530E-02-8.416471070E-03-6.587941670E-03 --4.703707990E-03-2.764320700E-03-7.703453880E-04 1.277523700E-03 3.378660650E-03 - 5.532364360E-03 7.737932730E-03 9.994653980E-03 1.230175510E-02 1.465846130E-02 - 1.706398090E-02 1.951750740E-02 2.201818490E-02 2.456518080E-02 2.715762150E-02 - 2.979466690E-02 3.247544170E-02 3.519906100E-02 3.796463460E-02 4.077126460E-02 - 4.361808670E-02 4.650423680E-02 4.942882060E-02 5.239094050E-02 5.538978430E-02 - 5.842447650E-02 6.149420140E-02 6.459817290E-02 6.773556020E-02 7.090557370E-02 - 7.410751280E-02 7.734060290E-02 8.060418070E-02 8.389753850E-02 8.721999820E-02 - 9.057097880E-02 9.394992140E-02 9.735633430E-02 1.007897560E-01 1.042500140E-01 - 1.077369970E-01 1.112506910E-01 1.147903500E-01 1.183576960E-01 1.219544560E-01 - 1.255823520E-01 1.292420630E-01 1.329361650E-01 1.366709620E-01 1.404656320E-01 - 1.443289370E-01 1.482682080E-01 1.522742060E-01 1.563150730E-01 1.603553440E-01 - 1.643965990E-01 1.684386130E-01 1.724812390E-01 1.765247430E-01 1.805691120E-01 - 1.846143310E-01 1.886604730E-01 1.927076130E-01 1.967558260E-01 2.008051430E-01 - 2.048556660E-01 2.089074850E-01 2.129606750E-01 2.170154900E-01 2.210719880E-01 - 2.251303200E-01 2.291906480E-01 2.332530770E-01 2.373179200E-01 2.413852510E-01 - 2.454552950E-01 2.495281990E-01 2.536042030E-01 2.576836050E-01 2.617665230E-01 - 2.658532260E-01 2.699439530E-01 2.740390600E-01 2.781385180E-01 2.822426260E-01 - 2.863517400E-01 2.904661300E-01 2.945858540E-01 2.987111810E-01 3.028423490E-01 - 3.069793280E-01 3.111224770E-01 3.152721230E-01 3.194277580E-01 2.192150210E-01 - 2.170785370E-01 2.149280910E-01 2.127634140E-01 2.105845210E-01 2.083916370E-01 - 2.061845060E-01 2.039631610E-01 2.017276730E-01 1.994779260E-01 1.972138430E-01 - 1.949354110E-01 1.926425840E-01 1.903352590E-01 1.880133600E-01 1.856768280E-01 - 1.833255890E-01 1.809595230E-01 1.785785560E-01 1.761825980E-01 1.737715150E-01 - 1.713452640E-01 1.689037080E-01 1.664466710E-01 1.639740320E-01 1.614856270E-01 - 1.589813380E-01 1.564628930E-01 1.539256130E-01 1.513713750E-01 1.488052760E-01 - 1.462324260E-01 1.436581910E-01 1.410872340E-01 1.385184820E-01 1.359512210E-01 - 1.333847940E-01 1.308185010E-01 1.282516570E-01 1.256836060E-01 1.231150180E-01 - 1.205468920E-01 1.179790790E-01 1.154119970E-01 1.128460620E-01 1.102817060E-01 - 1.077193390E-01 1.051594090E-01 1.026023180E-01 1.000484970E-01 9.749839450E-02 - 9.495241940E-02 9.241103380E-02 8.987466250E-02 8.734375980E-02 8.481875810E-02 - 8.230011910E-02 7.978828250E-02 7.728369530E-02 7.478679720E-02 7.229803500E-02 - 6.981788580E-02 6.734681130E-02 6.488530340E-02 6.243388350E-02 5.999309200E-02 - 5.756347250E-02 5.514558030E-02 5.274002250E-02 5.034739520E-02 4.796833920E-02 - 4.560352120E-02 4.325361180E-02 4.091929270E-02 3.860126810E-02 3.630028670E-02 - 3.401711210E-02 3.175250070E-02 2.950722540E-02 2.728210390E-02 2.507791670E-02 - 2.289551500E-02 2.073575370E-02 1.859949160E-02 1.648758540E-02 1.440087610E-02 - 1.234023650E-02 1.030658090E-02 8.300798010E-03 6.323779470E-03 4.376419820E-03 - 2.459604990E-03 5.742481440E-04-1.278754910E-03-3.098501590E-03-4.884096790E-03 --6.634650290E-03-8.349321780E-03-1.002716270E-02-1.166727860E-02-1.326884890E-02 --1.483102240E-02-1.635295150E-02-1.783378790E-02-1.927267950E-02-2.066877860E-02 --2.202131410E-02-2.332947590E-02-2.459247780E-02-2.580955440E-02-2.697993630E-02 --2.810289340E-02-2.917766010E-02-3.020354170E-02-3.117984720E-02-3.210588540E-02 --3.298097100E-02-3.380445760E-02-3.457571940E-02-3.529413790E-02-3.595910970E-02 --3.657005730E-02-3.712640330E-02-3.762758150E-02-3.807314110E-02-3.846251590E-02 --3.879524390E-02-3.907085960E-02-3.928891570E-02-3.944899510E-02-3.955069930E-02 --3.959366310E-02-3.957751390E-02-3.950191660E-02-3.936658050E-02-3.917122260E-02 --3.891557460E-02-3.859940540E-02-3.822250660E-02-3.778471050E-02-3.728584950E-02 --3.672578930E-02-3.610447420E-02-3.542170300E-02-3.467751670E-02-3.387192260E-02 --3.300493210E-02-3.207655620E-02-3.108680620E-02-3.003587390E-02-2.892382070E-02 --2.775084230E-02-2.651714910E-02-2.522294970E-02-2.386845460E-02-2.245397870E-02 --2.097984780E-02-1.944640090E-02-1.785403490E-02-1.620315200E-02-1.449418440E-02 --1.272762190E-02-1.090397310E-02-9.023792110E-03-7.087634410E-03-5.096083510E-03 --3.049780380E-03-9.494129920E-04 1.204330240E-03 3.410760080E-03 5.669164940E-03 - 7.978729900E-03 1.033867620E-02 1.274822190E-02 1.520651300E-02 1.771269370E-02 - 2.026591260E-02 2.286531030E-02 2.550996090E-02 2.819899470E-02 3.093148020E-02 - 3.370651600E-02 3.652317450E-02 3.938053550E-02 4.227770860E-02 4.521379990E-02 - 4.818788170E-02 5.119902640E-02 5.424635480E-02 5.732904750E-02 6.044621770E-02 - 6.359703090E-02 6.678064910E-02 6.999629740E-02 7.324321570E-02 7.652062920E-02 - 7.982781530E-02 8.316409590E-02 8.652877810E-02 8.992126580E-02 9.334101530E-02 - 9.678748250E-02 1.002601310E-01 1.037587520E-01 1.072840090E-01 1.108336520E-01 - 1.144092830E-01 1.180123610E-01 1.216436030E-01 1.253037750E-01 1.289947930E-01 - 1.327203510E-01 1.364833560E-01 1.403057130E-01 1.442030220E-01 1.481740620E-01 - 1.522070470E-01 1.562778500E-01 1.603468810E-01 1.644154190E-01 1.684835110E-01 - 1.725512440E-01 1.766186060E-01 1.806855650E-01 1.847521360E-01 1.888183800E-01 - 1.928843260E-01 1.969499740E-01 2.010154580E-01 2.050807920E-01 2.091460530E-01 - 2.132113130E-01 2.172767070E-01 2.213423250E-01 2.254081820E-01 2.294744400E-01 - 2.335411910E-01 2.376085070E-01 2.416766730E-01 2.457457480E-01 2.498158070E-01 - 2.538869680E-01 2.579593360E-01 2.620331650E-01 2.661083940E-01 2.701852920E-01 - 2.742640080E-01 2.783445120E-01 2.824268040E-01 2.865112720E-01 2.905977370E-01 - 2.946862880E-01 2.987768950E-01 3.028694990E-01 3.069640100E-01 3.110603390E-01 - 3.151582180E-01 2.191044390E-01 2.169509080E-01 2.147836090E-01 2.126024810E-01 - 2.104074060E-01 2.081983240E-01 2.059751450E-01 2.037377800E-01 2.014861850E-01 - 1.992202550E-01 1.969399010E-01 1.946450320E-01 1.923356060E-01 1.900115010E-01 - 1.876726300E-01 1.853188870E-01 1.829501840E-01 1.805664150E-01 1.781674620E-01 - 1.757532210E-01 1.733235720E-01 1.708783660E-01 1.684175880E-01 1.659410600E-01 - 1.634486020E-01 1.609400660E-01 1.584158390E-01 1.558750720E-01 1.533167660E-01 - 1.507415320E-01 1.481546160E-01 1.455614720E-01 1.429695340E-01 1.403797720E-01 - 1.377915140E-01 1.352040470E-01 1.326166840E-01 1.300287250E-01 1.274394990E-01 - 1.248489320E-01 1.222578730E-01 1.196664650E-01 1.170750930E-01 1.144841160E-01 - 1.118939520E-01 1.093050320E-01 1.067177430E-01 1.041325330E-01 1.015498190E-01 - 9.897003320E-02 9.639359270E-02 9.382092950E-02 9.125249090E-02 8.868870880E-02 - 8.613003050E-02 8.357689530E-02 8.102974300E-02 7.848902050E-02 7.595514510E-02 - 7.342857120E-02 7.090976830E-02 6.839920580E-02 6.589733060E-02 6.340464200E-02 - 6.092169140E-02 5.844900380E-02 5.598713830E-02 5.353667210E-02 5.109819400E-02 - 4.867234080E-02 4.625976830E-02 4.386113960E-02 4.147712890E-02 3.910844400E-02 - 3.675581890E-02 3.442001340E-02 3.210178390E-02 2.980190330E-02 2.752119680E-02 - 2.526044290E-02 2.302049470E-02 2.080221290E-02 1.860645790E-02 1.643408460E-02 - 1.428595840E-02 1.216295730E-02 1.006599800E-02 7.995975200E-03 5.953803190E-03 - 3.940387630E-03 1.956638650E-03 3.467889200E-06-1.918212860E-03-3.807482310E-03 --5.663431720E-03-7.485158740E-03-9.271753020E-03-1.102229860E-02-1.273593310E-02 --1.441174840E-02-1.604885050E-02-1.764637230E-02-1.920346540E-02-2.071928050E-02 --2.219296990E-02-2.362368260E-02-2.501059880E-02-2.635292150E-02-2.764984410E-02 --2.890058610E-02-3.010438200E-02-3.126047180E-02-3.236810490E-02-3.342656050E-02 --3.443513440E-02-3.539312630E-02-3.629985080E-02-3.715464100E-02-3.795685620E-02 --3.870587050E-02-3.940107670E-02-4.004190120E-02-4.062776270E-02-4.115806890E-02 --4.163230960E-02-4.204997050E-02-4.241056000E-02-4.271359370E-02-4.295863210E-02 --4.314522450E-02-4.327297960E-02-4.334151000E-02-4.335043950E-02-4.329942540E-02 --4.318815470E-02-4.301634430E-02-4.278370740E-02-4.249000180E-02-4.213500400E-02 --4.171853510E-02-4.124042760E-02-4.070052880E-02-4.009874170E-02-3.943493590E-02 --3.870906310E-02-3.792113070E-02-3.707114610E-02-3.615912800E-02-3.518510240E-02 --3.414914380E-02-3.305139770E-02-3.189200910E-02-3.067117180E-02-2.938909080E-02 --2.804600630E-02-2.664219030E-02-2.517794630E-02-2.365361710E-02-2.206959020E-02 --2.042626590E-02-1.872408200E-02-1.696348380E-02-1.514501680E-02-1.326921020E-02 --1.133659110E-02-9.347739630E-03-7.303344090E-03-5.204092250E-03-3.050669560E-03 --8.437617800E-04 1.415944540E-03 3.727627690E-03 6.090478510E-03 8.503676390E-03 - 1.096636430E-02 1.347768770E-02 1.603679360E-02 1.864277010E-02 2.129471300E-02 - 2.399168160E-02 2.673272230E-02 2.951691670E-02 3.234336900E-02 3.521102670E-02 - 3.811898830E-02 4.106632620E-02 4.405210170E-02 4.707537590E-02 5.013518410E-02 - 5.323062090E-02 5.636085570E-02 5.952499810E-02 6.272212420E-02 6.595140700E-02 - 6.921205670E-02 7.250327620E-02 7.582428310E-02 7.917435470E-02 8.255271610E-02 - 8.595869690E-02 8.939174560E-02 9.285129610E-02 9.633677450E-02 9.984764460E-02 - 1.033837200E-01 1.069446580E-01 1.105302720E-01 1.141412930E-01 1.177784060E-01 - 1.214420940E-01 1.251339170E-01 1.288561220E-01 1.326128990E-01 1.364050660E-01 - 1.402544380E-01 1.441830690E-01 1.481825860E-01 1.522430030E-01 1.563424620E-01 - 1.604374650E-01 1.645308730E-01 1.686225680E-01 1.727126390E-01 1.768012340E-01 - 1.808881610E-01 1.849731650E-01 1.890565900E-01 1.931383460E-01 1.972183880E-01 - 2.012968360E-01 2.053737040E-01 2.094489780E-01 2.135227320E-01 2.175950110E-01 - 2.216659040E-01 2.257353960E-01 2.298035030E-01 2.338704320E-01 2.379360800E-01 - 2.420005350E-01 2.460638880E-01 2.501262130E-01 2.541874950E-01 2.582477630E-01 - 2.623071370E-01 2.663654980E-01 2.704228460E-01 2.744791810E-01 2.785344420E-01 - 2.825886910E-01 2.866417170E-01 2.906933720E-01 2.947433890E-01 2.987916770E-01 - 3.028379980E-01 3.068818450E-01 3.109230400E-01 2.189967480E-01 2.168265280E-01 - 2.146428670E-01 2.124456320E-01 2.102346570E-01 2.080097050E-01 2.057707460E-01 - 2.035176460E-01 2.012502250E-01 1.989683810E-01 1.966720670E-01 1.943611200E-01 - 1.920354070E-01 1.896948810E-01 1.873393800E-01 1.849687990E-01 1.825830490E-01 - 1.801819500E-01 1.777654140E-01 1.753333210E-01 1.728855370E-01 1.704219130E-01 - 1.679423000E-01 1.654466840E-01 1.629349440E-01 1.604067830E-01 1.578618440E-01 - 1.553001250E-01 1.527216580E-01 1.501262340E-01 1.475189180E-01 1.449071170E-01 - 1.422972530E-01 1.396889390E-01 1.370815490E-01 1.344742630E-01 1.318663510E-01 - 1.292571570E-01 1.266461910E-01 1.240338760E-01 1.214205100E-01 1.188064660E-01 - 1.161920950E-01 1.135777680E-01 1.109639110E-01 1.083509550E-01 1.057393100E-01 - 1.031293940E-01 1.005216240E-01 9.791642430E-02 9.531422700E-02 9.271544960E-02 - 9.012053910E-02 8.752993490E-02 8.494406190E-02 8.236338200E-02 7.978831980E-02 - 7.721927020E-02 7.465670260E-02 7.210107150E-02 6.955283140E-02 6.701243670E-02 - 6.448035690E-02 6.195712090E-02 5.944325030E-02 5.693930010E-02 5.444582920E-02 - 5.196340380E-02 4.949266840E-02 4.703426360E-02 4.458883780E-02 4.215706510E-02 - 3.973963860E-02 3.733728830E-02 3.495075930E-02 3.258081150E-02 3.022823300E-02 - 2.789381710E-02 2.557838340E-02 2.328275700E-02 2.100779490E-02 1.875437050E-02 - 1.652335000E-02 1.431560240E-02 1.213199180E-02 9.973492470E-03 7.840979840E-03 - 5.735371260E-03 3.657584310E-03 1.608546820E-03-4.108154970E-04-2.399565650E-03 --4.356775430E-03-6.281518380E-03-8.172877130E-03-1.002993250E-02-1.185177730E-02 --1.363748130E-02-1.538611760E-02-1.709681000E-02-1.876864950E-02-2.040076440E-02 --2.199228110E-02-2.354233150E-02-2.505006830E-02-2.651463450E-02-2.793519940E-02 --2.931095100E-02-3.064107340E-02-3.192477300E-02-3.316127880E-02-3.434980660E-02 --3.548960760E-02-3.657996280E-02-3.762015330E-02-3.860946370E-02-3.954719380E-02 --4.043266920E-02-4.126526790E-02-4.204429690E-02-4.276916760E-02-4.343929510E-02 --4.405409100E-02-4.461296650E-02-4.511538150E-02-4.556082560E-02-4.594879220E-02 --4.627879340E-02-4.655035590E-02-4.676303270E-02-4.691641780E-02-4.701012750E-02 --4.704376680E-02-4.701697450E-02-4.692943020E-02-4.678083210E-02-4.657090460E-02 --4.629938680E-02-4.596604410E-02-4.557066780E-02-4.511308670E-02-4.459314790E-02 --4.401073600E-02-4.336575050E-02-4.265807570E-02-4.188770060E-02-4.105463250E-02 --4.015887160E-02-3.920048480E-02-3.817955400E-02-3.709615770E-02-3.595038500E-02 --3.474248200E-02-3.347262000E-02-3.214102980E-02-3.074799660E-02-2.929380720E-02 --2.777878570E-02-2.620328780E-02-2.456772700E-02-2.287254860E-02-2.111819570E-02 --1.930515470E-02-1.743404190E-02-1.550527100E-02-1.351946780E-02-1.147732320E-02 --9.379528460E-03-7.226768880E-03-5.019730890E-03-2.759101330E-03-4.456974270E-04 - 1.919641740E-03 4.336091690E-03 6.802808030E-03 9.318907750E-03 1.188350190E-02 - 1.449567640E-02 1.715449990E-02 1.985902340E-02 2.260828950E-02 2.540132590E-02 - 2.823715660E-02 3.111481290E-02 3.403330220E-02 3.699162970E-02 3.998882700E-02 - 4.302398860E-02 4.609603430E-02 4.920406270E-02 5.234714970E-02 5.552437900E-02 - 5.873483050E-02 6.197758390E-02 6.525181980E-02 6.855674090E-02 7.189148660E-02 - 7.525526730E-02 7.864729320E-02 8.206675950E-02 8.551307020E-02 8.898568900E-02 - 9.248401220E-02 9.600740670E-02 9.955524650E-02 1.031273530E-01 1.067233230E-01 - 1.103433520E-01 1.139878560E-01 1.176575650E-01 1.213531120E-01 1.250761000E-01 - 1.288284060E-01 1.326152680E-01 1.364383250E-01 1.403112560E-01 1.442664120E-01 - 1.482954620E-01 1.523887220E-01 1.565082670E-01 1.606283930E-01 1.647447790E-01 - 1.688580810E-01 1.729681190E-01 1.770747150E-01 1.811781530E-01 1.852786540E-01 - 1.893761610E-01 1.934706570E-01 1.975619940E-01 2.016502020E-01 2.057351920E-01 - 2.098170370E-01 2.138957230E-01 2.179712650E-01 2.220436480E-01 2.261128280E-01 - 2.301788330E-01 2.342416790E-01 2.383013220E-01 2.423577900E-01 2.464109360E-01 - 2.504608630E-01 2.545074220E-01 2.585505840E-01 2.625902300E-01 2.666262690E-01 - 2.706585820E-01 2.746870220E-01 2.787112890E-01 2.827312050E-01 2.867465910E-01 - 2.907570300E-01 2.947621350E-01 2.987615170E-01 3.027545810E-01 3.067407910E-01 - 2.188897580E-01 2.167037430E-01 2.145045700E-01 2.122918670E-01 2.100654390E-01 - 2.078251840E-01 2.055709060E-01 2.033024280E-01 2.010196450E-01 1.987223770E-01 - 1.964104920E-01 1.940838690E-01 1.917423610E-01 1.893858310E-01 1.870141480E-01 - 1.846271750E-01 1.822247800E-01 1.798068280E-01 1.773731860E-01 1.749237030E-01 - 1.724582460E-01 1.699766670E-01 1.674788150E-01 1.649646610E-01 1.624337430E-01 - 1.598859280E-01 1.573212440E-01 1.547397230E-01 1.521413770E-01 1.495262240E-01 - 1.468983590E-01 1.442698990E-01 1.416427490E-01 1.390163300E-01 1.363900150E-01 - 1.337631790E-01 1.311352400E-01 1.285054090E-01 1.258734020E-01 1.232396590E-01 - 1.206045300E-01 1.179683880E-01 1.153315750E-01 1.126944650E-01 1.100575100E-01 - 1.074211080E-01 1.047856730E-01 1.021516320E-01 9.951939430E-02 9.688938410E-02 - 9.426202630E-02 9.163774550E-02 8.901698140E-02 8.640015870E-02 8.378771690E-02 - 8.118008820E-02 7.857770470E-02 7.598098370E-02 7.339037210E-02 7.080629470E-02 - 6.822924320E-02 6.565965710E-02 6.309803580E-02 6.054490060E-02 5.800077690E-02 - 5.546624960E-02 5.294182150E-02 5.042814090E-02 4.792584850E-02 4.543559250E-02 - 4.295801370E-02 4.049378630E-02 3.804368900E-02 3.560838850E-02 3.318867460E-02 - 3.078534830E-02 2.839919740E-02 2.603101540E-02 2.368163130E-02 2.135191300E-02 - 1.904271920E-02 1.675492340E-02 1.448941510E-02 1.224708370E-02 1.002885590E-02 - 7.835652680E-03 5.668393340E-03 3.528013830E-03 1.415439530E-03-6.683921670E-04 --2.722534120E-03-4.746030550E-03-6.737970750E-03-8.697381240E-03-1.062332280E-02 --1.251488180E-02-1.437112880E-02-1.619113610E-02-1.797397060E-02-1.971871410E-02 --2.142448540E-02-2.309038120E-02-2.471552230E-02-2.629902590E-02-2.784002010E-02 --2.933765950E-02-3.079108890E-02-3.219949830E-02-3.356206420E-02-3.487797830E-02 --3.614645450E-02-3.736670690E-02-3.853796420E-02-3.965950380E-02-4.073061050E-02 --4.175056140E-02-4.271864520E-02-4.363413530E-02-4.449643940E-02-4.530487210E-02 --4.605881500E-02-4.675766830E-02-4.740082850E-02-4.798769210E-02-4.851774500E-02 --4.899043220E-02-4.940525070E-02-4.976170140E-02-5.005930360E-02-5.029761420E-02 --5.047618600E-02-5.059462790E-02-5.065255610E-02-5.064959820E-02-5.058541150E-02 --5.045967920E-02-5.027212200E-02-5.002247910E-02-4.971048610E-02-4.933594170E-02 --4.889864100E-02-4.839843140E-02-4.783518980E-02-4.720879350E-02-4.651919380E-02 --4.576629030E-02-4.495001210E-02-4.407041890E-02-4.312758150E-02-4.212158550E-02 --4.105250910E-02-3.992043060E-02-3.872545440E-02-3.746787460E-02-3.614787380E-02 --3.476572780E-02-3.332171590E-02-3.181614350E-02-3.024937580E-02-2.862178350E-02 --2.693381720E-02-2.518594080E-02-2.337863110E-02-2.151239100E-02-1.958778130E-02 --1.760538850E-02-1.556586750E-02-1.346989070E-02-1.131814810E-02-9.111328980E-03 --6.850141570E-03-4.535438030E-03-2.168016740E-03 2.512755160E-04 2.721592320E-03 - 5.242064130E-03 7.811749350E-03 1.042972880E-02 1.309503710E-02 1.580670480E-02 - 1.856376790E-02 2.136525330E-02 2.421011400E-02 2.709735370E-02 3.002598140E-02 - 3.299498930E-02 3.600333260E-02 3.905000170E-02 4.213401680E-02 4.525437950E-02 - 4.841008780E-02 5.160019170E-02 5.482378230E-02 5.807982010E-02 6.136747450E-02 - 6.468588110E-02 6.803415720E-02 7.141143830E-02 7.481705400E-02 7.825002070E-02 - 8.170963820E-02 8.519526570E-02 8.870627730E-02 9.224202480E-02 9.580188240E-02 - 9.938522430E-02 1.029925350E-01 1.066223010E-01 1.102751340E-01 1.139516830E-01 - 1.176525800E-01 1.213784740E-01 1.251306090E-01 1.289112420E-01 1.327240470E-01 - 1.365772490E-01 1.404826940E-01 1.444595610E-01 1.485172960E-01 1.526366770E-01 - 1.567787530E-01 1.609254180E-01 1.650599540E-01 1.691901530E-01 1.733156890E-01 - 1.774384830E-01 1.815565820E-01 1.856699590E-01 1.897786560E-01 1.938827930E-01 - 1.979821770E-01 2.020768080E-01 2.061665950E-01 2.102515400E-01 2.143316420E-01 - 2.184067220E-01 2.224768550E-01 2.265419360E-01 2.306018470E-01 2.346566020E-01 - 2.387060970E-01 2.427501680E-01 2.467887850E-01 2.508217990E-01 2.548489570E-01 - 2.588702440E-01 2.628853920E-01 2.668941920E-01 2.708962860E-01 2.748915550E-01 - 2.788795230E-01 2.828598920E-01 2.868320050E-01 2.907956540E-01 2.947501240E-01 - 2.986945510E-01 3.026284870E-01 2.187824400E-01 2.165816430E-01 2.143677470E-01 - 2.121402920E-01 2.098992020E-01 2.076442840E-01 2.053752840E-01 2.030920540E-01 - 2.007944430E-01 1.984822750E-01 1.961553690E-01 1.938135770E-01 1.914567800E-01 - 1.890847530E-01 1.866973940E-01 1.842945370E-01 1.818760340E-01 1.794417350E-01 - 1.769914930E-01 1.745251420E-01 1.720425340E-01 1.695435350E-01 1.670279500E-01 - 1.644957070E-01 1.619467140E-01 1.593802720E-01 1.567964260E-01 1.541952190E-01 - 1.515766980E-01 1.489421130E-01 1.462974100E-01 1.436518730E-01 1.410072150E-01 - 1.383628400E-01 1.357182120E-01 1.330727340E-01 1.304250360E-01 1.277747750E-01 - 1.251222490E-01 1.224676890E-01 1.198113860E-01 1.171537120E-01 1.144950240E-01 - 1.118357410E-01 1.091762710E-01 1.065170240E-01 1.038584190E-01 1.012008710E-01 - 9.854478390E-02 9.589059650E-02 9.323871140E-02 9.058956060E-02 8.794356880E-02 - 8.530117570E-02 8.266280590E-02 8.002889160E-02 7.739984990E-02 7.477610560E-02 - 7.215809820E-02 6.954625990E-02 6.694108250E-02 6.434297560E-02 6.175249070E-02 - 5.917014930E-02 5.659647660E-02 5.403203140E-02 5.147739870E-02 4.893320430E-02 - 4.640009630E-02 4.387872290E-02 4.136972500E-02 3.887384760E-02 3.639179840E-02 - 3.392434120E-02 3.147225830E-02 2.903634680E-02 2.661740590E-02 2.421623470E-02 - 2.183372900E-02 1.947071780E-02 1.712810990E-02 1.480679590E-02 1.250766400E-02 - 1.023162340E-02 7.979602550E-03 5.752544380E-03 3.551394910E-03 1.377096050E-03 --7.694094670E-04-2.887162380E-03-4.975210880E-03-7.032603960E-03-9.058364670E-03 --1.105157010E-02-1.301124410E-02-1.493643780E-02-1.682622360E-02-1.867967100E-02 --2.049585250E-02-2.227382180E-02-2.401267180E-02-2.571149920E-02-2.736940980E-02 --2.898552270E-02-3.055896050E-02-3.208885340E-02-3.357434650E-02-3.501461070E-02 --3.640881550E-02-3.775616360E-02-3.905583920E-02-4.030706360E-02-4.150904340E-02 --4.266103360E-02-4.376231880E-02-4.481217640E-02-4.580989850E-02-4.675476630E-02 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9.121927430E-03 1.184032300E-02 1.460477150E-02 1.741426620E-02 2.026776780E-02 - 2.316422570E-02 2.610259880E-02 2.908185310E-02 3.210094940E-02 3.515882420E-02 - 3.825442870E-02 4.138675700E-02 4.455480720E-02 4.775753990E-02 5.099391940E-02 - 5.426304790E-02 5.756393820E-02 6.089564040E-02 6.425727160E-02 6.764795630E-02 - 7.106682660E-02 7.451309260E-02 7.798593490E-02 8.148452640E-02 8.500821140E-02 - 8.855635670E-02 9.212832900E-02 9.572348000E-02 9.934137020E-02 1.029817690E-01 - 1.066439080E-01 1.103281830E-01 1.140352410E-01 1.177657470E-01 1.215203400E-01 - 1.252999160E-01 1.291086820E-01 1.329474450E-01 1.368282140E-01 1.407630290E-01 - 1.447642890E-01 1.488554180E-01 1.529911160E-01 1.571532190E-01 1.613236070E-01 - 1.654837730E-01 1.696191430E-01 1.737610250E-01 1.778966640E-01 1.820258350E-01 - 1.861489270E-01 1.902658790E-01 1.943764840E-01 1.984807100E-01 2.025784850E-01 - 2.066696880E-01 2.107543050E-01 2.148322460E-01 2.189033930E-01 2.229676250E-01 - 2.270248090E-01 2.310748400E-01 2.351176140E-01 2.391529080E-01 2.431805880E-01 - 2.472004440E-01 2.512122990E-01 2.552158530E-01 2.592108550E-01 2.631970050E-01 - 2.671739460E-01 2.711413200E-01 2.750986520E-01 2.790455520E-01 2.829813060E-01 - 2.869055570E-01 2.908174690E-01 2.947162690E-01 2.986011800E-01 2.186740490E-01 - 2.164595280E-01 2.142317300E-01 2.119904760E-01 2.097355280E-01 2.074666770E-01 - 2.051837150E-01 2.028864620E-01 2.005746810E-01 1.982482220E-01 1.959069070E-01 - 1.935505570E-01 1.911789920E-01 1.887920650E-01 1.863896100E-01 1.839714350E-01 - 1.815373900E-01 1.790873110E-01 1.766210350E-01 1.741384120E-01 1.716392490E-01 - 1.691233520E-01 1.665906460E-01 1.640409080E-01 1.614738850E-01 1.588900830E-01 - 1.562883410E-01 1.536675990E-01 1.510289610E-01 1.483767930E-01 1.457154750E-01 - 1.430531290E-01 1.403915290E-01 1.377299430E-01 1.350675230E-01 1.324033140E-01 - 1.297364530E-01 1.270665970E-01 1.243941630E-01 1.217193380E-01 1.190424490E-01 - 1.163638310E-01 1.136839090E-01 1.110030640E-01 1.083217190E-01 1.056402700E-01 - 1.029591340E-01 1.002787280E-01 9.759945420E-02 9.492173050E-02 9.224597360E-02 - 8.957260100E-02 8.690205960E-02 8.423477410E-02 8.157115430E-02 7.891162480E-02 - 7.625661050E-02 7.360652830E-02 7.096181810E-02 6.832291930E-02 6.569027900E-02 - 6.306438890E-02 6.044578550E-02 5.783499030E-02 5.523251740E-02 5.263892560E-02 - 5.005483700E-02 4.748089240E-02 4.491773620E-02 4.236600180E-02 3.982640060E-02 - 3.729964420E-02 3.478648510E-02 3.228770570E-02 2.980407890E-02 2.733640190E-02 - 2.488549800E-02 2.245221850E-02 2.003742380E-02 1.764200630E-02 1.526685990E-02 - 1.291287320E-02 1.058098390E-02 8.272118870E-03 5.987212060E-03 3.727208590E-03 - 1.493067710E-03-7.142504910E-04-2.893772440E-03-5.044534340E-03-7.165580990E-03 --9.255950340E-03-1.131466590E-02-1.334074510E-02-1.533322970E-02-1.729116400E-02 --1.921359820E-02-2.109958980E-02-2.294820170E-02-2.475849910E-02-2.652954500E-02 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1.534600560E-01 1.576412920E-01 1.618285030E-01 1.659992340E-01 1.701530070E-01 - 1.743053500E-01 1.784503460E-01 1.825879070E-01 1.867177490E-01 1.908397230E-01 - 1.949537250E-01 1.990596350E-01 2.031573650E-01 2.072467650E-01 2.113277170E-01 - 2.154000550E-01 2.194636910E-01 2.235184910E-01 2.275642600E-01 2.316007020E-01 - 2.356277700E-01 2.396451680E-01 2.436526120E-01 2.476499380E-01 2.516367140E-01 - 2.556127010E-01 2.595774230E-01 2.635305520E-01 2.674716110E-01 2.714001830E-01 - 2.753157020E-01 2.792172130E-01 2.831045090E-01 2.869769040E-01 2.908333840E-01 - 2.946729360E-01 2.185642570E-01 2.163369950E-01 2.140964120E-01 2.118422690E-01 - 2.095743420E-01 2.072924080E-01 2.049962430E-01 2.026856690E-01 2.003604470E-01 - 1.980203990E-01 1.956653590E-01 1.932951060E-01 1.909094600E-01 1.885082570E-01 - 1.860913190E-01 1.836584510E-01 1.812094900E-01 1.787442560E-01 1.762625720E-01 - 1.737642590E-01 1.712491210E-01 1.687170420E-01 1.661677960E-01 1.636011300E-01 - 1.610170010E-01 1.584151830E-01 1.557970640E-01 1.531568470E-01 1.504997910E-01 - 1.478305460E-01 1.451534630E-01 1.424747260E-01 1.397969570E-01 1.371185930E-01 - 1.344387230E-01 1.317564850E-01 1.290709820E-01 1.263821720E-01 1.236904260E-01 - 1.209959540E-01 1.182990970E-01 1.156002060E-01 1.128996830E-01 1.101979320E-01 - 1.074953530E-01 1.047923640E-01 1.020893600E-01 9.938675910E-02 9.668497000E-02 - 9.398438780E-02 9.128544480E-02 8.858857300E-02 8.589418230E-02 8.320268990E-02 - 8.051452040E-02 7.783009110E-02 7.514981930E-02 7.247412200E-02 6.980343160E-02 - 6.713820250E-02 6.447888910E-02 6.182598320E-02 5.918001380E-02 5.654150990E-02 - 5.391100050E-02 5.128908160E-02 4.867634920E-02 4.607344790E-02 4.348102210E-02 - 4.089977220E-02 3.833039850E-02 3.577362000E-02 3.323021530E-02 3.070096110E-02 - 2.818663600E-02 2.568806710E-02 2.320610360E-02 2.074159310E-02 1.829543150E-02 - 1.586851480E-02 1.346173140E-02 1.107601080E-02 8.712291720E-03 6.371507890E-03 - 4.054625520E-03 1.762611090E-03-5.035704820E-04-2.742959650E-03-4.954575560E-03 --7.137411270E-03-9.290513580E-03-1.141290090E-02-1.350359340E-02-1.556161050E-02 --1.758597050E-02-1.957570390E-02-2.152986450E-02-2.344747630E-02-2.532759680E-02 --2.716928720E-02-2.897160310E-02-3.073362820E-02-3.245443850E-02-3.413314000E-02 --3.576885160E-02-3.736068310E-02-3.890775520E-02-4.040921480E-02-4.186421630E-02 --4.327194020E-02-4.463158180E-02-4.594232890E-02-4.720338430E-02-4.841398080E-02 --4.957336560E-02-5.068079750E-02-5.173556130E-02-5.273694550E-02-5.368425320E-02 --5.457681040E-02-5.541394650E-02-5.619504300E-02-5.691948530E-02-5.758667360E-02 --5.819600450E-02-5.874691900E-02-5.923887710E-02-5.967136100E-02-6.004386770E-02 --6.035590920E-02-6.060703100E-02-6.079678240E-02-6.092477220E-02-6.099061300E-02 --6.099392470E-02-6.093434990E-02-6.081156060E-02-6.062527370E-02-6.037519500E-02 --6.006110830E-02-5.968281250E-02-5.924012140E-02-5.873284490E-02-5.816078190E-02 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8.503856510E-02 8.865685760E-02 9.229695050E-02 9.595830740E-02 9.964035450E-02 - 1.033428090E-01 1.070655810E-01 1.108085590E-01 1.145721520E-01 1.183570550E-01 - 1.221672740E-01 1.259948020E-01 1.298513710E-01 1.337427200E-01 1.376734820E-01 - 1.416584850E-01 1.457274560E-01 1.498627510E-01 1.540420060E-01 1.582427020E-01 - 1.624423560E-01 1.666184660E-01 1.707879010E-01 1.749496310E-01 1.791020040E-01 - 1.832450930E-01 1.873787640E-01 1.915027800E-01 1.956170800E-01 1.997215150E-01 - 2.038159670E-01 2.079003160E-01 2.119743670E-01 2.160379290E-01 2.200908210E-01 - 2.241328210E-01 2.281636740E-01 2.321832330E-01 2.361911540E-01 2.401871230E-01 - 2.441708450E-01 2.481420190E-01 2.521001990E-01 2.560450140E-01 2.599760590E-01 - 2.638926210E-01 2.677943410E-01 2.716805930E-01 2.755507230E-01 2.794039850E-01 - 2.832397520E-01 2.870570120E-01 2.908547220E-01 2.184531690E-01 2.162142250E-01 - 2.139618250E-01 2.116957310E-01 2.094157040E-01 2.071215510E-01 2.048130180E-01 - 2.024899130E-01 2.001520250E-01 1.977991460E-01 1.954310830E-01 1.930476430E-01 - 1.906486300E-01 1.882338370E-01 1.858031000E-01 1.833562110E-01 1.808929890E-01 - 1.784132570E-01 1.759168060E-01 1.734034720E-01 1.708730460E-01 1.683253940E-01 - 1.657602640E-01 1.631774900E-01 1.605769250E-01 1.579583730E-01 1.553219710E-01 - 1.526653620E-01 1.499912140E-01 1.473047140E-01 1.446116270E-01 1.419182270E-01 - 1.392246930E-01 1.365299670E-01 1.338331700E-01 1.311333920E-01 1.284298600E-01 - 1.257227660E-01 1.230123420E-01 1.202988700E-01 1.175827090E-01 1.148642000E-01 - 1.121437620E-01 1.094217750E-01 1.066986470E-01 1.039747890E-01 1.012506110E-01 - 9.852652250E-02 9.580291060E-02 9.308019280E-02 9.035878630E-02 8.763910830E-02 - 8.492159100E-02 8.220663670E-02 7.949466260E-02 7.678608600E-02 7.408130910E-02 - 7.138074930E-02 6.868485360E-02 6.599406150E-02 6.330885740E-02 6.062971800E-02 - 5.795717980E-02 5.529177560E-02 5.263401940E-02 4.998460040E-02 4.734405500E-02 - 4.471302780E-02 4.209221900E-02 3.948233280E-02 3.688407320E-02 3.429816290E-02 - 3.172539550E-02 2.916655320E-02 2.662244070E-02 2.409389800E-02 2.158179320E-02 - 1.908699800E-02 1.661041010E-02 1.415291990E-02 1.171545780E-02 9.298951370E-03 - 6.904357110E-03 4.532638010E-03 2.184764950E-03-1.382917690E-04-2.435561040E-03 --4.706040490E-03-6.948740220E-03-9.162696080E-03-1.134688690E-02-1.350031790E-02 --1.562200770E-02-1.771097260E-02-1.976623200E-02-2.178679780E-02-2.377170140E-02 --2.571996670E-02-2.763063830E-02-2.950276810E-02-3.133540970E-02-3.312764690E-02 --3.487852960E-02-3.658715260E-02-3.825262930E-02-3.987407310E-02-4.145060110E-02 --4.298133400E-02-4.446543750E-02-4.590206590E-02-4.729039590E-02-4.862963410E-02 --4.991899060E-02-5.115767940E-02-5.234491080E-02-5.347995460E-02-5.456208070E-02 --5.559057370E-02-5.656473710E-02-5.748388540E-02-5.834732950E-02-5.915446580E-02 --5.990464610E-02-6.059725580E-02-6.123171000E-02-6.180742760E-02-6.232386080E-02 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2.403578530E-02 2.716383710E-02 3.032979000E-02 3.353249650E-02 3.677084300E-02 - 4.004375640E-02 4.335010050E-02 4.668876530E-02 5.005870760E-02 5.345888810E-02 - 5.688825250E-02 6.034582850E-02 6.383064390E-02 6.734176730E-02 7.087828960E-02 - 7.443934680E-02 7.802414890E-02 8.163185420E-02 8.526171000E-02 8.891297880E-02 - 9.258501230E-02 9.627698360E-02 9.998861700E-02 1.037197930E-01 1.074703780E-01 - 1.112403270E-01 1.150294470E-01 1.188404260E-01 1.226704570E-01 1.265235840E-01 - 1.304058280E-01 1.343216300E-01 1.382745210E-01 1.422859880E-01 1.463842540E-01 - 1.505462830E-01 1.547474860E-01 1.589633380E-01 1.631692800E-01 1.673505460E-01 - 1.715303210E-01 1.756982360E-01 1.798547060E-01 1.840001790E-01 1.881345060E-01 - 1.922574790E-01 1.963690670E-01 2.004690470E-01 2.045572550E-01 2.086334970E-01 - 2.126974910E-01 2.167491020E-01 2.207881210E-01 2.248142210E-01 2.288271490E-01 - 2.328265460E-01 2.368121590E-01 2.407835870E-01 2.447404410E-01 2.486823800E-01 - 2.526088650E-01 2.565194370E-01 2.604135270E-01 2.642906900E-01 2.681502100E-01 - 2.719914020E-01 2.758135800E-01 2.796159680E-01 2.833976150E-01 2.871575650E-01 - 2.183411270E-01 2.160914990E-01 2.138282510E-01 2.115511150E-01 2.092599120E-01 - 2.069543900E-01 2.046343240E-01 2.022995200E-01 1.999497710E-01 1.975848380E-01 - 1.952045410E-01 1.928086580E-01 1.903969940E-01 1.879693570E-01 1.855255370E-01 - 1.830653250E-01 1.805885580E-01 1.780950130E-01 1.755845100E-01 1.730568410E-01 - 1.705118420E-01 1.679492740E-01 1.653689590E-01 1.627707180E-01 1.601543280E-01 - 1.575195490E-01 1.548661890E-01 1.521934870E-01 1.495026050E-01 1.468005330E-01 - 1.440927540E-01 1.413846020E-01 1.386758540E-01 1.359653470E-01 1.332521140E-01 - 1.305353050E-01 1.278144870E-01 1.250896750E-01 1.223612200E-01 1.196294200E-01 - 1.168946330E-01 1.141571850E-01 1.114175020E-01 1.086759870E-01 1.059330250E-01 - 1.031890210E-01 1.004443840E-01 9.769951550E-02 9.495482590E-02 9.221070260E-02 - 8.946757020E-02 8.672585340E-02 8.398596200E-02 8.124830570E-02 7.851329450E-02 - 7.578132300E-02 7.305283100E-02 7.032819840E-02 6.760789450E-02 6.489235160E-02 - 6.218205760E-02 5.947751180E-02 5.677923560E-02 5.408776550E-02 5.140369010E-02 - 4.872759800E-02 4.606008900E-02 4.340182620E-02 4.075352850E-02 3.811591120E-02 - 3.548969700E-02 3.287557510E-02 3.027432230E-02 2.768684550E-02 2.511389740E-02 - 2.255634780E-02 2.001507580E-02 1.749096070E-02 1.498489360E-02 1.249781900E-02 - 1.003065710E-02 7.584368810E-03 5.159915890E-03 2.758269900E-03 3.804113370E-04 --1.972686970E-03-4.300022500E-03-6.600593220E-03-8.873390970E-03-1.111742020E-02 --1.333167400E-02-1.551514580E-02-1.766683160E-02-1.978574320E-02-2.187089440E-02 --2.392128110E-02-2.593592740E-02-2.791385350E-02-2.985408530E-02-3.175567460E-02 --3.361766790E-02-3.543912990E-02-3.721912210E-02-3.895671670E-02-4.065101590E-02 --4.230114070E-02-4.390618950E-02-4.546527560E-02-4.697757590E-02-4.844222960E-02 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1.807112540E-01 1.848555650E-01 1.889877020E-01 1.931068600E-01 1.972128300E-01 - 2.013054340E-01 2.053844630E-01 2.094496640E-01 2.135007980E-01 2.175375970E-01 - 2.215597930E-01 2.255671020E-01 2.295591240E-01 2.335355580E-01 2.374960330E-01 - 2.414401020E-01 2.453673480E-01 2.492772790E-01 2.531694770E-01 2.570432130E-01 - 2.608979940E-01 2.647331950E-01 2.685481910E-01 2.723422350E-01 2.761142550E-01 - 2.798637150E-01 2.835896910E-01 2.182286530E-01 2.159692790E-01 2.136960770E-01 - 2.114088390E-01 2.091073390E-01 2.067913260E-01 2.044606060E-01 2.021149690E-01 - 1.997541640E-01 1.973779950E-01 1.949862390E-01 1.925787180E-01 1.901551780E-01 - 1.877154260E-01 1.852592830E-01 1.827865090E-01 1.802969130E-01 1.777902990E-01 - 1.752664450E-01 1.727251860E-01 1.701662990E-01 1.675895300E-01 1.649948060E-01 - 1.623818730E-01 1.597505060E-01 1.571004390E-01 1.544308360E-01 1.517418770E-01 - 1.490356030E-01 1.463190910E-01 1.435970070E-01 1.408741030E-01 1.381514820E-01 - 1.354256870E-01 1.326964800E-01 1.299633830E-01 1.272259210E-01 1.244840920E-01 - 1.217383150E-01 1.189888940E-01 1.162361650E-01 1.134805010E-01 1.107223030E-01 - 1.079619680E-01 1.051998960E-01 1.024364900E-01 9.967213870E-02 9.690723570E-02 - 9.414220600E-02 9.137744460E-02 8.861336860E-02 8.585038040E-02 8.308891210E-02 - 8.032933620E-02 7.757207010E-02 7.481753080E-02 7.206611340E-02 6.931823490E-02 - 6.657432760E-02 6.383488330E-02 6.110036750E-02 5.837127190E-02 5.564812940E-02 - 5.293148760E-02 5.022192370E-02 4.752006750E-02 4.482654850E-02 4.214201500E-02 - 3.946716710E-02 3.680273150E-02 3.414943070E-02 3.150804340E-02 2.887935560E-02 - 2.626419630E-02 2.366338860E-02 2.107782480E-02 1.850838210E-02 1.595594550E-02 - 1.342143120E-02 1.090577620E-02 8.409943430E-03 5.934898280E-03 3.481607190E-03 - 1.051044670E-03-1.355775050E-03-3.737860820E-03-6.094210780E-03-8.423811760E-03 --1.072565090E-02-1.299871320E-02-1.524197960E-02-1.745444540E-02-1.963509620E-02 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1.086810980E-01 1.125025380E-01 1.163388490E-01 1.201916490E-01 1.240651830E-01 - 1.279637070E-01 1.318914740E-01 1.358527240E-01 1.398515850E-01 1.439234170E-01 - 1.480796340E-01 1.522900160E-01 1.565251350E-01 1.607536820E-01 1.649643480E-01 - 1.691618410E-01 1.733460280E-01 1.775166690E-01 1.816725730E-01 1.858140530E-01 - 1.899413020E-01 1.940538730E-01 1.981515740E-01 2.022341190E-01 2.063012420E-01 - 2.103527490E-01 2.143882810E-01 2.184075860E-01 2.224103510E-01 2.263962030E-01 - 2.303647850E-01 2.343156640E-01 2.382484820E-01 2.421627340E-01 2.460579870E-01 - 2.499337050E-01 2.537892460E-01 2.576241200E-01 2.614376540E-01 2.652291060E-01 - 2.689978180E-01 2.727429570E-01 2.764637170E-01 2.801592950E-01 2.181162090E-01 - 2.158480140E-01 2.135658120E-01 2.112693790E-01 2.089584770E-01 2.066328820E-01 - 2.042923720E-01 2.019367370E-01 1.995657380E-01 1.971791540E-01 1.947767880E-01 - 1.923584040E-01 1.899237930E-01 1.874727460E-01 1.850050390E-01 1.825204790E-01 - 1.800188270E-01 1.774999050E-01 1.749634890E-01 1.724093560E-01 1.698372660E-01 - 1.672469970E-01 1.646382960E-01 1.620127560E-01 1.593667860E-01 1.567008790E-01 - 1.540158390E-01 1.513125300E-01 1.485920250E-01 1.458610450E-01 1.431256680E-01 - 1.403899790E-01 1.376523970E-01 1.349120440E-01 1.321676670E-01 1.294189100E-01 - 1.266653840E-01 1.239072530E-01 1.211448680E-01 1.183785270E-01 1.156086030E-01 - 1.128354450E-01 1.100594770E-01 1.072810740E-01 1.045006360E-01 1.017185750E-01 - 9.893526880E-02 9.615112840E-02 9.336654840E-02 9.058193120E-02 8.779769390E-02 - 8.501423900E-02 8.223198350E-02 7.945131510E-02 7.667262850E-02 7.389633360E-02 - 7.112284000E-02 6.835256520E-02 6.558594110E-02 6.282345950E-02 6.006559360E-02 - 5.731282760E-02 5.456572770E-02 5.182481560E-02 4.909070950E-02 4.636403920E-02 - 4.364543780E-02 4.093555360E-02 3.823511300E-02 3.554482390E-02 3.286546840E-02 - 3.019782710E-02 2.754267680E-02 2.490085360E-02 2.227321450E-02 1.966065910E-02 - 1.706407590E-02 1.448434310E-02 1.192242840E-02 9.379263040E-03 6.855819370E-03 - 4.353071560E-03 1.872002730E-03-5.863872940E-04-3.021100300E-03-5.431112830E-03 --7.815405730E-03-1.017296780E-02-1.250277550E-02-1.480380260E-02-1.707502270E-02 --1.931540670E-02-2.152393940E-02-2.369960960E-02-2.584139440E-02-2.794829570E-02 --3.001932800E-02-3.205349300E-02-3.404978660E-02-3.600723670E-02-3.792489320E-02 --3.980179880E-02-4.163700340E-02-4.342957960E-02-4.517860340E-02-4.688315840E-02 --4.854236170E-02-5.015533040E-02-5.172118170E-02-5.323905870E-02-5.470812690E-02 --5.612755570E-02-5.749652530E-02-5.881422760E-02-6.007989500E-02-6.129274140E-02 --6.245202200E-02-6.355698410E-02-6.460690500E-02-6.560109560E-02-6.653887780E-02 --6.741956620E-02-6.824249030E-02-6.900702420E-02-6.971256430E-02-7.035851480E-02 --7.094429430E-02-7.146930690E-02-7.193309070E-02-7.233504950E-02-7.267472150E-02 --7.295165210E-02-7.316539440E-02-7.331550870E-02-7.340156290E-02-7.342322920E-02 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4.356521370E-02 4.703031110E-02 5.052383240E-02 5.404467880E-02 5.759176610E-02 - 6.116404010E-02 6.476050620E-02 6.838019940E-02 7.202216980E-02 7.568548620E-02 - 7.936935130E-02 8.307306470E-02 8.679539710E-02 9.053584190E-02 9.429388490E-02 - 9.806907920E-02 1.018609330E-01 1.056689100E-01 1.094931810E-01 1.133341940E-01 - 1.171928050E-01 1.210675240E-01 1.249620540E-01 1.288806800E-01 1.328276690E-01 - 1.368072030E-01 1.408363880E-01 1.449399140E-01 1.491235350E-01 1.533545850E-01 - 1.575983320E-01 1.618263270E-01 1.660400330E-01 1.702390020E-01 1.744228450E-01 - 1.785908790E-01 1.827427150E-01 1.868787560E-01 1.909986140E-01 1.951020810E-01 - 1.991888730E-01 2.032587680E-01 2.073115260E-01 2.113467750E-01 2.153642180E-01 - 2.193635850E-01 2.233444900E-01 2.273065450E-01 2.312493620E-01 2.351724950E-01 - 2.390755120E-01 2.429578750E-01 2.468190640E-01 2.506585720E-01 2.544758020E-01 - 2.582701740E-01 2.620407340E-01 2.657870650E-01 2.695083620E-01 2.732038200E-01 - 2.768725160E-01 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5.630399290E-02 5.353384090E-02 5.076962340E-02 - 4.801194370E-02 4.526142780E-02 4.251870890E-02 3.978446500E-02 3.705940770E-02 - 3.434429690E-02 3.163991120E-02 2.894702740E-02 2.626642210E-02 2.359899690E-02 - 2.094558810E-02 1.830709170E-02 1.568441650E-02 1.307847910E-02 1.049023490E-02 - 7.920629340E-03 5.370659750E-03 2.841309880E-03 3.335647630E-04-2.151565860E-03 --4.613062370E-03-7.049894430E-03-9.461034090E-03-1.184546020E-02-1.420213100E-02 --1.653001830E-02-1.882808280E-02-2.109529080E-02-2.333062510E-02-2.553305590E-02 --2.770153430E-02-2.983507890E-02-3.193268920E-02-3.399335970E-02-3.601609170E-02 --3.799989820E-02-3.994381800E-02-4.184689750E-02-4.370817910E-02-4.552670940E-02 --4.730157930E-02-4.903186490E-02-5.071666460E-02-5.235509570E-02-5.394626780E-02 --5.548933150E-02-5.698342250E-02-5.842772130E-02-5.982140450E-02-6.116365640E-02 --6.245368720E-02-6.369071450E-02-6.487398590E-02-6.600276380E-02-6.707628070E-02 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2.084194570E-01 2.124361990E-01 2.164333460E-01 2.204105260E-01 2.243674100E-01 - 2.283036410E-01 2.322186680E-01 2.361121180E-01 2.399834540E-01 2.438322160E-01 - 2.476578350E-01 2.514597180E-01 2.552372220E-01 2.589896920E-01 2.627165020E-01 - 2.664168780E-01 2.700901030E-01 2.737352850E-01 2.178938540E-01 2.156108170E-01 - 2.133133560E-01 2.110012620E-01 2.086742970E-01 2.063322220E-01 2.039748130E-01 - 2.016018180E-01 1.992130430E-01 1.968082040E-01 1.943871230E-01 1.919495610E-01 - 1.894952800E-01 1.870240570E-01 1.845356820E-01 1.820299330E-01 1.795065700E-01 - 1.769653860E-01 1.744061560E-01 1.718286720E-01 1.692326960E-01 1.666179900E-01 - 1.639855500E-01 1.613328900E-01 1.586588320E-01 1.559649110E-01 1.532525870E-01 - 1.505233940E-01 1.477788090E-01 1.450200970E-01 1.422594490E-01 1.394987700E-01 - 1.367350670E-01 1.339673250E-01 1.311945770E-01 1.284165530E-01 1.256331500E-01 - 1.228446220E-01 1.200512050E-01 1.172532740E-01 1.144511770E-01 1.116453190E-01 - 1.088360850E-01 1.060238630E-01 1.032090490E-01 1.003920360E-01 9.757320580E-02 - 9.475297480E-02 9.193172310E-02 8.910985290E-02 8.628777410E-02 8.346589650E-02 - 8.064460010E-02 7.782426480E-02 7.500531520E-02 7.218813900E-02 6.937315320E-02 - 6.656076760E-02 6.375139210E-02 6.094557790E-02 5.814374980E-02 5.534644050E-02 - 5.255423110E-02 4.976770280E-02 4.698744040E-02 4.421405490E-02 4.144822060E-02 - 3.869063780E-02 3.594201430E-02 3.320312500E-02 3.047475030E-02 2.775767450E-02 - 2.505270950E-02 2.236073280E-02 1.968261790E-02 1.701927740E-02 1.437162330E-02 - 1.174057930E-02 9.127104650E-03 6.532179660E-03 3.956799860E-03 1.401961200E-03 --1.131350290E-03-3.642086170E-03-6.129232240E-03-8.591755290E-03-1.102861580E-02 --1.343877240E-02-1.582117940E-02-1.817479540E-02-2.049857940E-02-2.279149180E-02 --2.505249160E-02-2.728055790E-02-2.947464210E-02-3.163373470E-02-3.375682980E-02 --3.584291410E-02-3.789099310E-02-3.990007940E-02-4.186918210E-02-4.379735510E-02 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1.351003800E-01 1.391270460E-01 1.432129740E-01 1.473739150E-01 1.516173180E-01 - 1.558768150E-01 1.601223800E-01 1.643519100E-01 1.685641260E-01 1.727580580E-01 - 1.769327370E-01 1.810874640E-01 1.852238480E-01 1.893410240E-01 1.934387390E-01 - 1.975166950E-01 2.015746240E-01 2.056123170E-01 2.096293420E-01 2.136254460E-01 - 2.176002260E-01 2.215533260E-01 2.254843560E-01 2.293929010E-01 2.332784980E-01 - 2.371406700E-01 2.409788820E-01 2.447926400E-01 2.485813800E-01 2.523445190E-01 - 2.560813430E-01 2.597912250E-01 2.634735110E-01 2.671274240E-01 2.707522810E-01 - 2.177851650E-01 2.154961080E-01 2.131924330E-01 2.108739170E-01 2.085403050E-01 - 2.061913760E-01 2.038268740E-01 2.014465630E-01 1.990502030E-01 1.966375710E-01 - 1.942084430E-01 1.917625670E-01 1.892997180E-01 1.868196730E-01 1.843222080E-01 - 1.818071010E-01 1.792740970E-01 1.767230180E-01 1.741535960E-01 1.715656370E-01 - 1.689588730E-01 1.663331540E-01 1.636881980E-01 1.610247340E-01 1.583399920E-01 - 1.556344330E-01 1.529095470E-01 1.501668540E-01 1.474082470E-01 1.446396710E-01 - 1.418681290E-01 1.390952020E-01 1.363190560E-01 1.335384700E-01 1.307526230E-01 - 1.279610250E-01 1.251637940E-01 1.223611380E-01 1.195533280E-01 1.167407480E-01 - 1.139237360E-01 1.111026930E-01 1.082780140E-01 1.054500790E-01 1.026192750E-01 - 9.978599850E-02 9.695065020E-02 9.411361070E-02 9.127528220E-02 8.843605970E-02 - 8.559635280E-02 8.275654910E-02 7.991704340E-02 7.707821580E-02 7.424046840E-02 - 7.140419630E-02 6.856982410E-02 6.573775410E-02 6.290843340E-02 6.008236110E-02 - 5.726000670E-02 5.444190280E-02 5.162863060E-02 4.882077500E-02 4.601892460E-02 - 4.322368650E-02 4.043580220E-02 3.765592350E-02 3.488478810E-02 3.212318570E-02 - 2.937190230E-02 2.663172600E-02 2.390349660E-02 2.118807660E-02 1.848637500E-02 - 1.579930630E-02 1.312778800E-02 1.047275770E-02 7.835201920E-03 5.216098390E-03 - 2.616451350E-03 3.726495200E-05-2.520443640E-03-5.055645020E-03-7.567303260E-03 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6.712265310E-02 7.083736360E-02 7.457103580E-02 7.832273840E-02 8.209156990E-02 - 8.587670330E-02 8.967732640E-02 9.349282830E-02 9.732258320E-02 1.011661070E-01 - 1.050230260E-01 1.088933720E-01 1.127770540E-01 1.166750640E-01 1.205885560E-01 - 1.245189380E-01 1.284688560E-01 1.324403880E-01 1.364448070E-01 1.404984890E-01 - 1.446177510E-01 1.488119660E-01 1.530771260E-01 1.573379340E-01 1.615826790E-01 - 1.658098400E-01 1.700179430E-01 1.742054370E-01 1.783708480E-01 1.825155170E-01 - 1.866410820E-01 1.907455770E-01 1.948288380E-01 1.988907310E-01 2.029310760E-01 - 2.069494580E-01 2.109456510E-01 2.149192240E-01 2.188698350E-01 2.227971400E-01 - 2.267007080E-01 2.305800770E-01 2.344347980E-01 2.382643970E-01 2.420682610E-01 - 2.458459880E-01 2.495969240E-01 2.533204850E-01 2.570160630E-01 2.606828210E-01 - 2.643202840E-01 2.679277060E-01 2.176789940E-01 2.153848860E-01 2.130759810E-01 - 2.107519950E-01 2.084127070E-01 2.060578470E-01 2.036871910E-01 2.013004720E-01 - 1.988974510E-01 1.964779200E-01 1.940416100E-01 1.915883120E-01 1.891177590E-01 - 1.866297570E-01 1.841240380E-01 1.816004070E-01 1.790586260E-01 1.764984580E-01 - 1.739196630E-01 1.713220630E-01 1.687054040E-01 1.660694330E-01 1.634138380E-01 - 1.607384090E-01 1.580434290E-01 1.553277220E-01 1.525903490E-01 1.498344540E-01 - 1.470649090E-01 1.442865580E-01 1.415048090E-01 1.387205870E-01 1.359327290E-01 - 1.331401170E-01 1.303417530E-01 1.275373700E-01 1.247270550E-01 1.219110270E-01 - 1.190896110E-01 1.162631590E-01 1.134320270E-01 1.105966050E-01 1.077572700E-01 - 1.049144340E-01 1.020684760E-01 9.921978410E-02 9.636875240E-02 9.351576860E-02 - 9.066122030E-02 8.780551700E-02 8.494905380E-02 8.209221810E-02 7.923542710E-02 - 7.637901600E-02 7.352339480E-02 7.066897300E-02 6.781616810E-02 6.496538220E-02 - 6.211707370E-02 5.927172300E-02 5.642984430E-02 5.359197040E-02 5.075865610E-02 - 4.793049770E-02 4.510809110E-02 4.229208080E-02 3.948317470E-02 3.668208050E-02 - 3.388953210E-02 3.110631930E-02 2.833322810E-02 2.557105570E-02 2.282067950E-02 - 2.008295620E-02 1.735880780E-02 1.464915180E-02 1.195491290E-02 9.277065280E-03 - 6.616579830E-03 3.974463320E-03 1.351722870E-03-1.250632810E-03-3.831572600E-03 --6.390057970E-03-8.925038390E-03-1.143545840E-02-1.392026250E-02-1.637839340E-02 --1.880878960E-02-2.121039850E-02-2.358215490E-02-2.592300440E-02-2.823190020E-02 --3.050779180E-02-3.274963800E-02-3.495640680E-02-3.712708130E-02-3.926062960E-02 --4.135606070E-02-4.341236870E-02-4.542855920E-02-4.740365970E-02-4.933671280E-02 --5.122675370E-02-5.307284000E-02-5.487404390E-02-5.662943420E-02-5.833812060E-02 --5.999920890E-02-6.161182000E-02-6.317508220E-02-6.468814610E-02-6.615017350E-02 --6.756030770E-02-6.891776620E-02-7.022176680E-02-7.147151980E-02-7.266624270E-02 --7.380518320E-02-7.488765570E-02-7.591284070E-02-7.688008250E-02-7.778871800E-02 --7.863811400E-02-7.942761480E-02-8.015655730E-02-8.082429320E-02-8.143024890E-02 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5.159205760E-03 8.386668750E-03 1.165376880E-02 1.495914530E-02 1.830145160E-02 - 2.167933990E-02 2.509142640E-02 2.853641470E-02 3.201298790E-02 3.551983090E-02 - 3.905565290E-02 4.261915760E-02 4.620912670E-02 4.982435330E-02 5.346366390E-02 - 5.712591480E-02 6.080998850E-02 6.451481580E-02 6.823930890E-02 7.198252530E-02 - 7.574355600E-02 7.952149210E-02 8.331540230E-02 8.712446690E-02 9.094797820E-02 - 9.478514640E-02 9.863554690E-02 1.024987470E-01 1.063743230E-01 1.102626320E-01 - 1.141634880E-01 1.180778440E-01 1.220075860E-01 1.259546130E-01 1.299204830E-01 - 1.339095830E-01 1.379393790E-01 1.420240100E-01 1.461751310E-01 1.504043340E-01 - 1.546816970E-01 1.589416270E-01 1.631832270E-01 1.674044880E-01 1.716042910E-01 - 1.757808330E-01 1.799361110E-01 1.840696930E-01 1.881812360E-01 1.922704730E-01 - 1.963371930E-01 2.003811150E-01 2.044018510E-01 2.083991770E-01 2.123727200E-01 - 2.163221390E-01 2.202470900E-01 2.241471260E-01 2.280218450E-01 2.318707700E-01 - 2.356935140E-01 2.394894510E-01 2.432581480E-01 2.469990400E-01 2.507115600E-01 - 2.543950970E-01 2.580490410E-01 2.616727050E-01 2.652653460E-01 2.175760570E-01 - 2.152778950E-01 2.129647430E-01 2.106362730E-01 2.082922760E-01 2.059324830E-01 - 2.035566120E-01 2.011644240E-01 1.987556960E-01 1.963301600E-01 1.938875760E-01 - 1.914277230E-01 1.889503450E-01 1.864552200E-01 1.839421240E-01 1.814108190E-01 - 1.788610820E-01 1.762926880E-01 1.737053840E-01 1.710989480E-01 1.684731990E-01 - 1.658278850E-01 1.631626930E-01 1.604774890E-01 1.577721390E-01 1.550469700E-01 - 1.522988380E-01 1.495316920E-01 1.467509120E-01 1.439618770E-01 1.411704120E-01 - 1.383758190E-01 1.355770830E-01 1.327731160E-01 1.299629510E-01 1.271465570E-01 - 1.243239420E-01 1.214953360E-01 1.186611060E-01 1.158215930E-01 1.129771550E-01 - 1.101281490E-01 1.072750020E-01 1.044180990E-01 1.015578280E-01 9.869457040E-02 - 9.582871200E-02 9.296064820E-02 9.009077400E-02 8.721947670E-02 8.434716610E-02 - 8.147421480E-02 7.860103990E-02 7.572798430E-02 7.285544280E-02 6.998382510E-02 - 6.711354850E-02 6.424503030E-02 6.137872860E-02 5.851513150E-02 5.565474930E-02 - 5.279810730E-02 4.994584620E-02 4.709842430E-02 4.425648600E-02 4.142076150E-02 - 3.859196230E-02 3.577080000E-02 3.295797850E-02 3.015427110E-02 2.736048770E-02 - 2.457746300E-02 2.180607430E-02 1.904720630E-02 1.630177720E-02 1.357070730E-02 - 1.085493810E-02 8.155438120E-03 5.473211870E-03 2.809269350E-03 1.646223830E-04 --2.459719780E-03-5.062692800E-03-7.643260530E-03-1.020036270E-02-1.273293790E-02 --1.523992330E-02-1.772025790E-02-2.017287160E-02-2.259669270E-02-2.499066110E-02 --2.735370770E-02-2.968478390E-02-3.198283540E-02-3.424681350E-02-3.647568820E-02 --3.866841640E-02-4.082397370E-02-4.294136540E-02-4.501957820E-02-4.705761750E-02 --4.905450340E-02-5.100926760E-02-5.292094870E-02-5.478860440E-02-5.661129950E-02 --5.838810280E-02-6.011810150E-02-6.180040540E-02-6.343412400E-02-6.501839310E-02 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1.649229080E-01 1.691342440E-01 1.733228860E-01 1.774886400E-01 1.816313560E-01 - 1.857507820E-01 1.898467690E-01 1.939190630E-01 1.979673650E-01 2.019914090E-01 - 2.059908810E-01 2.099655270E-01 2.139149900E-01 2.178388540E-01 2.217367440E-01 - 2.256083040E-01 2.294530570E-01 2.332706300E-01 2.370603980E-01 2.408220020E-01 - 2.445548770E-01 2.482584860E-01 2.519322630E-01 2.555755080E-01 2.591877280E-01 - 2.627682690E-01 2.174769490E-01 2.151758520E-01 2.128594960E-01 2.105276290E-01 - 2.081799510E-01 2.058161940E-01 2.034360920E-01 2.010394190E-01 1.986258920E-01 - 1.961952750E-01 1.937473120E-01 1.912817960E-01 1.887984720E-01 1.862971040E-01 - 1.837774660E-01 1.812393370E-01 1.786824760E-01 1.761066760E-01 1.735116840E-01 - 1.708972900E-01 1.682632710E-01 1.656094190E-01 1.629354510E-01 1.602411270E-01 - 1.575262550E-01 1.547907440E-01 1.520333890E-01 1.492561850E-01 1.464651380E-01 - 1.436677430E-01 1.408661900E-01 1.380618070E-01 1.352529380E-01 1.324383910E-01 - 1.296173330E-01 1.267896590E-01 1.239555330E-01 1.211151630E-01 1.182689070E-01 - 1.154171150E-01 1.125601530E-01 1.096984220E-01 1.068322960E-01 1.039621830E-01 - 1.010884490E-01 9.821148220E-02 9.533168380E-02 9.244943410E-02 8.956512060E-02 - 8.667914570E-02 8.379190420E-02 8.090377600E-02 7.801514120E-02 7.512638720E-02 - 7.223790880E-02 6.935009360E-02 6.646332140E-02 6.357809160E-02 6.069481000E-02 - 5.781399090E-02 5.493615940E-02 5.206182970E-02 4.919157550E-02 4.632598530E-02 - 4.346570750E-02 4.061140870E-02 3.776382280E-02 3.492368390E-02 3.209172560E-02 - 2.926863360E-02 2.645528880E-02 2.365260010E-02 2.086138730E-02 1.808255910E-02 - 1.531702280E-02 1.256572180E-02 9.829619900E-03 7.109689060E-03 4.406938800E-03 - 1.722385180E-03-9.429562490E-04-3.588051770E-03-6.211846140E-03-8.813285270E-03 --1.139129790E-02-1.394480750E-02-1.647275130E-02-1.897406760E-02-2.144767530E-02 --2.389250140E-02-2.630746920E-02-2.869150970E-02-3.104356490E-02-3.336257860E-02 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9.396592530E-02 9.784199300E-02 1.017292660E-01 1.056274400E-01 1.095364690E-01 - 1.134568010E-01 1.173886360E-01 1.213337700E-01 1.252943720E-01 1.292731170E-01 - 1.332721410E-01 1.373070480E-01 1.413931550E-01 1.455451700E-01 1.497794690E-01 - 1.540562660E-01 1.583286520E-01 1.625775840E-01 1.668017060E-01 1.710025070E-01 - 1.751790200E-01 1.793312580E-01 1.834591480E-01 1.875624060E-01 1.916409580E-01 - 1.956945210E-01 1.997227820E-01 2.037254570E-01 2.077022050E-01 2.116527560E-01 - 2.155768130E-01 2.194739130E-01 2.233437150E-01 2.271858010E-01 2.309997680E-01 - 2.347851100E-01 2.385413940E-01 2.422681150E-01 2.459647060E-01 2.496307490E-01 - 2.532655890E-01 2.568686310E-01 2.604393360E-01 2.173824910E-01 2.150796060E-01 - 2.127612230E-01 2.104270310E-01 2.080767150E-01 2.057100390E-01 2.033267320E-01 - 2.009264830E-01 1.985090970E-01 1.960743220E-01 1.936218890E-01 1.911515890E-01 - 1.886631550E-01 1.861564070E-01 1.836310770E-01 1.810869570E-01 1.785238090E-01 - 1.759414230E-01 1.733395760E-01 1.707180290E-01 1.680765600E-01 1.654149590E-01 - 1.627329590E-01 1.600303350E-01 1.573069100E-01 1.545624430E-01 1.517960430E-01 - 1.490083780E-01 1.462103720E-01 1.434050200E-01 1.405939610E-01 1.377787890E-01 - 1.349611580E-01 1.321373130E-01 1.293058250E-01 1.264675860E-01 1.236227450E-01 - 1.207714600E-01 1.179139390E-01 1.150507030E-01 1.121820730E-01 1.093084370E-01 - 1.064301880E-01 1.035477150E-01 1.006613900E-01 9.777159990E-02 9.487874810E-02 - 9.198320660E-02 8.908537030E-02 8.618564160E-02 8.328440790E-02 8.038204160E-02 - 7.747892290E-02 7.457544650E-02 7.167200000E-02 6.876897070E-02 6.586676090E-02 - 6.296581030E-02 6.006659940E-02 5.716962370E-02 5.427538230E-02 5.138442290E-02 - 4.849731550E-02 4.561467840E-02 4.273716730E-02 3.986544910E-02 3.700022030E-02 - 3.414221480E-02 3.129217770E-02 2.845092120E-02 2.561927210E-02 2.279808370E-02 - 1.998824070E-02 1.719064820E-02 1.440621820E-02 1.163591910E-02 8.880691600E-03 - 6.141540590E-03 3.419492390E-03 7.155616190E-04-1.969236650E-03-4.633850420E-03 --7.277225610E-03-9.898290040E-03-1.249596760E-02-1.506918020E-02-1.761685870E-02 --2.013793400E-02-2.263130060E-02-2.509589120E-02-2.753062920E-02-2.993443790E-02 --3.230625760E-02-3.464501720E-02-3.694966060E-02-3.921914470E-02-4.145243020E-02 --4.364847760E-02-4.580627380E-02-4.792481290E-02-5.000308900E-02-5.204010380E-02 --5.403488870E-02-5.598646770E-02-5.789389460E-02-5.975623060E-02-6.157253310E-02 --6.334189330E-02-6.506337970E-02-6.673610210E-02-6.835920360E-02-6.993182000E-02 --7.145310190E-02-7.292218510E-02-7.433821260E-02-7.570041720E-02-7.700796430E-02 --7.826008650E-02-7.945603880E-02-8.059503880E-02-8.167634160E-02-8.269922440E-02 --8.366298680E-02-8.456694330E-02-8.541043100E-02-8.619279410E-02-8.691339190E-02 --8.757162090E-02-8.816687020E-02-8.869860320E-02-8.916626130E-02-8.956930790E-02 --8.990724380E-02-9.017959240E-02-9.038590640E-02-9.052576120E-02-9.059874710E-02 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2.827309070E-02 3.183568270E-02 3.542644530E-02 3.904404490E-02 4.268714790E-02 - 4.635446150E-02 5.004475270E-02 5.375679210E-02 5.748939890E-02 6.124143670E-02 - 6.501179930E-02 6.879942860E-02 7.260330020E-02 7.642243060E-02 8.025591820E-02 - 8.410290630E-02 8.796253800E-02 9.183405340E-02 9.571671490E-02 9.960998590E-02 - 1.035135690E-01 1.074273590E-01 1.113512670E-01 1.152860520E-01 1.192320730E-01 - 1.231918780E-01 1.271681340E-01 1.311634330E-01 1.351816650E-01 1.392409650E-01 - 1.433617470E-01 1.475608500E-01 1.518315970E-01 1.561114340E-01 1.603764890E-01 - 1.646121890E-01 1.688244490E-01 1.730116610E-01 1.771738680E-01 1.813107880E-01 - 1.854220780E-01 1.895074990E-01 1.935669930E-01 1.976002450E-01 2.016069290E-01 - 2.055867910E-01 2.095395480E-01 2.134648860E-01 2.173624190E-01 2.212317880E-01 - 2.250725920E-01 2.288843990E-01 2.326668500E-01 2.364194540E-01 2.401418090E-01 - 2.438332890E-01 2.474934760E-01 2.511218190E-01 2.547178270E-01 2.582809030E-01 - 2.172937690E-01 2.149903030E-01 2.126710860E-01 2.103356570E-01 2.079838070E-01 - 2.056152220E-01 2.032296660E-01 2.008268680E-01 1.984065620E-01 1.959685090E-01 - 1.935124840E-01 1.910382660E-01 1.885455850E-01 1.860342620E-01 1.835040600E-01 - 1.809547690E-01 1.783861370E-01 1.757979840E-01 1.731900570E-01 1.705621630E-01 - 1.679140930E-01 1.652456070E-01 1.625564400E-01 1.598464100E-01 1.571153250E-01 - 1.543629910E-01 1.515877250E-01 1.487921180E-01 1.459858120E-01 1.431719810E-01 - 1.403527560E-01 1.375303270E-01 1.347036510E-01 1.318699720E-01 1.290293040E-01 - 1.261814240E-01 1.233266140E-01 1.204650770E-01 1.175972070E-01 1.147233470E-01 - 1.118438770E-01 1.089591910E-01 1.060696690E-01 1.031757000E-01 1.002776700E-01 - 9.737595170E-02 9.447094050E-02 9.156301620E-02 8.865258840E-02 8.574003730E-02 - 8.282575010E-02 7.991011440E-02 7.699350270E-02 7.407629490E-02 7.115887850E-02 - 6.824164840E-02 6.532499940E-02 6.240939350E-02 5.949531870E-02 5.658325550E-02 - 5.367369580E-02 5.076721310E-02 4.786438490E-02 4.496582600E-02 4.207219930E-02 - 3.918417170E-02 3.630243610E-02 3.342775260E-02 3.056089390E-02 2.770266870E-02 - 2.485388700E-02 2.201541510E-02 1.918815450E-02 1.637301410E-02 1.357092240E-02 - 1.078283790E-02 8.009730840E-03 5.252615550E-03 2.512513890E-03-2.095504020E-04 --2.912566300E-03-5.595443770E-03-8.257136680E-03-1.089656540E-02-1.351264960E-02 --1.610431260E-02-1.867047700E-02-2.121003530E-02-2.372191290E-02-2.620502190E-02 --2.865828950E-02-3.108063150E-02-3.347097710E-02-3.582826260E-02-3.815141690E-02 --4.043937850E-02-4.269113390E-02-4.490562900E-02-4.708183560E-02-4.921875150E-02 --5.131537470E-02-5.337070300E-02-5.538375300E-02-5.735355240E-02-5.927915130E-02 --6.115959960E-02-6.299395860E-02-6.478133050E-02-6.652077290E-02-6.821136920E-02 --6.985226270E-02-7.144259660E-02-7.298150660E-02-7.446812840E-02-7.590161260E-02 --7.728119940E-02-7.860600950E-02-7.987527550E-02-8.108823750E-02-8.224415030E-02 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1.956277190E-01 1.996392910E-01 2.036231760E-01 2.075791060E-01 2.115067840E-01 - 2.154058670E-01 2.192759960E-01 2.231168150E-01 2.269279210E-01 2.307089420E-01 - 2.344594300E-01 2.381789540E-01 2.418670360E-01 2.455232140E-01 2.491469830E-01 - 2.527378200E-01 2.562952340E-01 2.172119470E-01 2.149092560E-01 2.125903220E-01 - 2.102548330E-01 2.079025210E-01 2.055331020E-01 2.031463090E-01 2.007418420E-01 - 1.983195250E-01 1.958791020E-01 1.934203360E-01 1.909430330E-01 1.884469390E-01 - 1.859318610E-01 1.833975910E-01 1.808438900E-01 1.782705630E-01 1.756774040E-01 - 1.730641870E-01 1.704307350E-01 1.677767930E-01 1.651021690E-01 1.624066530E-01 - 1.596899780E-01 1.569520680E-01 1.541913900E-01 1.514088360E-01 1.486075070E-01 - 1.457925440E-01 1.429710240E-01 1.401451230E-01 1.373156310E-01 1.344800890E-01 - 1.316379760E-01 1.287887990E-01 1.259320230E-01 1.230678630E-01 1.201970200E-01 - 1.173195840E-01 1.144359410E-01 1.115464870E-01 1.086516080E-01 1.057516780E-01 - 1.028470840E-01 9.993822130E-02 9.702546890E-02 9.410920740E-02 9.118983890E-02 - 8.826775100E-02 8.534333110E-02 8.241697400E-02 7.948903740E-02 7.655990870E-02 - 7.362996790E-02 7.069960240E-02 6.776919960E-02 6.483918430E-02 6.190999600E-02 - 5.898212270E-02 5.605604130E-02 5.313228070E-02 5.021138860E-02 4.729396850E-02 - 4.438063870E-02 4.147204760E-02 3.856886920E-02 3.567181900E-02 3.278165680E-02 - 2.989916690E-02 2.702514830E-02 2.416045030E-02 2.130592430E-02 1.846247730E-02 - 1.563103680E-02 1.281253430E-02 1.000793090E-02 7.218213290E-03 4.444392400E-03 - 1.687493060E-03-1.051452940E-03-3.771391230E-03-6.471259520E-03-9.149998430E-03 --1.180651500E-02-1.443973090E-02-1.704856750E-02-1.963193340E-02-2.218873050E-02 --2.471786550E-02-2.721824310E-02-2.968877180E-02-3.212837870E-02-3.453599660E-02 --3.691055630E-02-3.925098480E-02-4.155621680E-02-4.382520910E-02-4.605691880E-02 --4.825032870E-02-5.040442200E-02-5.251818900E-02-5.459063870E-02-5.662077290E-02 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1.233936920E-01 1.273817720E-01 1.313869510E-01 1.354163140E-01 1.394905000E-01 - 1.436418890E-01 1.478558780E-01 1.521135270E-01 1.563959120E-01 1.606740360E-01 - 1.649112850E-01 1.691217270E-01 1.733047220E-01 1.774605360E-01 1.815890970E-01 - 1.856901790E-01 1.897635010E-01 1.938088690E-01 1.978260430E-01 2.018147710E-01 - 2.057747690E-01 2.097057550E-01 2.136074600E-01 2.174795270E-01 2.213215530E-01 - 2.251332400E-01 2.289141860E-01 2.326639890E-01 2.363822310E-01 2.400684950E-01 - 2.437222600E-01 2.473431380E-01 2.509306070E-01 2.544841470E-01 2.171386480E-01 - 2.148380130E-01 2.125206890E-01 2.101863030E-01 2.078345870E-01 2.054652720E-01 - 2.030781810E-01 2.006729840E-01 1.982495190E-01 1.958075310E-01 1.933468430E-01 - 1.908672300E-01 1.883684990E-01 1.858504270E-01 1.833128180E-01 1.807554810E-01 - 1.781782060E-01 1.755808000E-01 1.729630530E-01 1.703247430E-01 1.676656750E-01 - 1.649855820E-01 1.622843440E-01 1.595631540E-01 1.568184640E-01 1.540499930E-01 - 1.512608380E-01 1.484541300E-01 1.456329670E-01 1.428032960E-01 1.399715100E-01 - 1.371345970E-01 1.342916790E-01 1.314420400E-01 1.285849210E-01 1.257199350E-01 - 1.228476020E-01 1.199681610E-01 1.170819630E-01 1.141893710E-01 1.112907680E-01 - 1.083865390E-01 1.054770570E-01 1.025627330E-01 9.964393820E-02 9.672106060E-02 - 9.379448000E-02 9.086459880E-02 8.793179690E-02 8.499646190E-02 8.205898110E-02 - 7.911974190E-02 7.617910210E-02 7.323744890E-02 7.029516990E-02 6.735264510E-02 - 6.441031400E-02 6.146861990E-02 5.852803220E-02 5.558905750E-02 5.265220250E-02 - 4.971803720E-02 4.678718000E-02 4.386023060E-02 4.093782980E-02 3.802070770E-02 - 3.510953860E-02 3.220511230E-02 2.930821660E-02 2.641964330E-02 2.354026030E-02 - 2.067091320E-02 1.781253330E-02 1.496604740E-02 1.213239040E-02 9.312540290E-03 - 6.507482850E-03 3.718242980E-03 9.458482380E-04-1.808672790E-03-4.544268360E-03 --7.259859700E-03-9.954359380E-03-1.262669080E-02-1.527576890E-02-1.790049490E-02 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8.600272240E-02 8.993273970E-02 9.387095270E-02 9.781675040E-02 1.017698200E-01 - 1.057298260E-01 1.096967830E-01 1.136717130E-01 1.176573560E-01 1.216508670E-01 - 1.256473210E-01 1.296603230E-01 1.337025760E-01 1.377822760E-01 1.419085710E-01 - 1.461044250E-01 1.503739210E-01 1.546711920E-01 1.589673010E-01 1.632294950E-01 - 1.674489970E-01 1.716464460E-01 1.758131380E-01 1.799499690E-01 1.840563570E-01 - 1.881323010E-01 1.921776530E-01 1.961922500E-01 2.001758520E-01 2.041282210E-01 - 2.080491480E-01 2.119383660E-01 2.157955770E-01 2.196204960E-01 2.234128270E-01 - 2.271722410E-01 2.308983650E-01 2.345908430E-01 2.382492870E-01 2.418733840E-01 - 2.454626710E-01 2.490167470E-01 2.169835720E-01 2.147024270E-01 2.124011670E-01 - 2.100799530E-01 2.077386980E-01 2.053775190E-01 2.029962540E-01 2.005948570E-01 - 1.981733740E-01 1.957316100E-01 1.932694910E-01 1.907869430E-01 1.882838900E-01 - 1.857601260E-01 1.832155730E-01 1.806500700E-01 1.780634820E-01 1.754556450E-01 - 1.728264090E-01 1.701755820E-01 1.675030440E-01 1.648085120E-01 1.620918210E-01 - 1.593527350E-01 1.565910430E-01 1.538065370E-01 1.509978620E-01 1.481709330E-01 - 1.453308610E-01 1.424820720E-01 1.396289910E-01 1.367721410E-01 1.339069750E-01 - 1.310335100E-01 1.281519680E-01 1.252624090E-01 1.223648790E-01 1.194594130E-01 - 1.165464070E-01 1.136262940E-01 1.106995570E-01 1.077665390E-01 1.048276500E-01 - 1.018832550E-01 9.893374890E-02 9.597952660E-02 9.302096810E-02 9.005846080E-02 - 8.709239210E-02 8.412315700E-02 8.115113530E-02 7.817669960E-02 7.520022990E-02 - 7.222209870E-02 6.924269350E-02 6.626240910E-02 6.328167020E-02 6.030093130E-02 - 5.732068050E-02 5.434143920E-02 5.136374380E-02 4.838812350E-02 4.541521150E-02 - 4.244564100E-02 3.948009390E-02 3.651926670E-02 3.356390450E-02 3.061477470E-02 - 2.767267640E-02 2.473845710E-02 2.181296420E-02 1.889711620E-02 1.599178840E-02 - 1.309795960E-02 1.021661140E-02 7.348736750E-03 4.495329220E-03 1.657415760E-03 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2.020752430E-02 2.384415830E-02 2.750880460E-02 3.120000660E-02 3.491627800E-02 - 3.865620120E-02 4.241837190E-02 4.620144890E-02 5.000411720E-02 5.382508780E-02 - 5.766313150E-02 6.151704490E-02 6.538566950E-02 6.926795840E-02 7.316286860E-02 - 7.706934210E-02 8.098640290E-02 8.491324630E-02 8.884900060E-02 9.279290590E-02 - 9.674427660E-02 1.007025910E-01 1.046675220E-01 1.086387190E-01 1.126168890E-01 - 1.166071890E-01 1.206027420E-01 1.246046050E-01 1.286205950E-01 1.326598530E-01 - 1.367315200E-01 1.408447330E-01 1.450257900E-01 1.492837070E-01 1.535838690E-01 - 1.578892770E-01 1.621603670E-01 1.663968710E-01 1.706036630E-01 1.747799070E-01 - 1.789259020E-01 1.830411700E-01 1.871256230E-01 1.911790970E-01 1.952014120E-01 - 1.991923300E-01 2.031517030E-01 2.070792620E-01 2.109747830E-01 2.148380130E-01 - 2.186685950E-01 2.224662750E-01 2.262307410E-01 2.299616630E-01 2.336587160E-01 - 2.373214660E-01 2.409495860E-01 2.445426730E-01 2.481003550E-01 2.169989350E-01 - 2.147232890E-01 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4.226262120E-02 3.928936270E-02 3.632070500E-02 - 3.335740420E-02 3.040024080E-02 2.745001200E-02 2.450757470E-02 2.157378380E-02 - 1.864952780E-02 1.573573240E-02 1.283334750E-02 9.943362330E-03 7.066768590E-03 - 4.204581490E-03 1.357813370E-03-1.472474660E-03-4.285200030E-03-7.079283710E-03 --9.853646160E-03-1.260720940E-02-1.533885110E-02-1.804744640E-02-2.073190550E-02 --2.339110340E-02-2.602392810E-02-2.862927130E-02-3.120601920E-02-3.375306730E-02 --3.626930710E-02-3.875365110E-02-4.120501130E-02-4.362230750E-02-4.600447040E-02 --4.835042730E-02-5.065913500E-02-5.292955410E-02-5.516066030E-02-5.735142160E-02 --5.950080980E-02-6.160786000E-02-6.367155910E-02-6.569094960E-02-6.766507030E-02 --6.959295270E-02-7.147364320E-02-7.330622520E-02-7.508978990E-02-7.682341340E-02 --7.850620900E-02-8.013726030E-02-8.171574030E-02-8.324075490E-02-8.471146230E-02 --8.612702790E-02-8.748663220E-02-8.878944810E-02-9.003470090E-02-9.122159330E-02 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1.903497580E-01 1.943801640E-01 1.983789060E-01 2.023458030E-01 2.062806040E-01 - 2.101831140E-01 2.140530650E-01 2.178901280E-01 2.216940670E-01 2.254645820E-01 - 2.292013170E-01 2.329039720E-01 2.365721320E-01 2.402054670E-01 2.438036050E-01 - 2.473661450E-01 2.170440410E-01 2.147733270E-01 2.124807090E-01 2.101670060E-01 - 2.078320530E-01 2.054760310E-01 2.030990870E-01 2.007012520E-01 1.982824950E-01 - 1.958428470E-01 1.933822040E-01 1.909005190E-01 1.883977800E-01 1.858738660E-01 - 1.833286430E-01 1.807620380E-01 1.781739290E-01 1.755641550E-01 1.729325500E-01 - 1.702790410E-01 1.676034630E-01 1.649056670E-01 1.621855350E-01 1.594423950E-01 - 1.566761580E-01 1.538867800E-01 1.510738880E-01 1.482397320E-01 1.453934460E-01 - 1.425405440E-01 1.396810260E-01 1.368155330E-01 1.339439000E-01 1.310635360E-01 - 1.281745580E-01 1.252771020E-01 1.223714280E-01 1.194577070E-01 1.165361400E-01 - 1.136073020E-01 1.106715430E-01 1.077292930E-01 1.047809350E-01 1.018268470E-01 - 9.886742380E-02 9.590304640E-02 9.293410930E-02 8.996099980E-02 8.698412030E-02 - 8.400385080E-02 8.102057870E-02 7.803466920E-02 7.504649460E-02 7.205644250E-02 - 6.906490770E-02 6.607224790E-02 6.307892500E-02 6.008542700E-02 5.709221960E-02 - 5.409977590E-02 5.110860990E-02 4.811938480E-02 4.513264070E-02 4.214905570E-02 - 3.916930030E-02 3.619406370E-02 3.322409470E-02 3.026017730E-02 2.730311450E-02 - 2.435374820E-02 2.141294810E-02 1.848161410E-02 1.556066520E-02 1.265105510E-02 - 9.753766470E-03 6.869796200E-03 4.000158980E-03 1.145890450E-03-1.691955960E-03 --4.512303040E-03-7.314073390E-03-1.009618400E-02-1.285753030E-02-1.559700720E-02 --1.831350480E-02-2.100590430E-02-2.367308920E-02-2.631393820E-02-2.892734480E-02 --3.151219710E-02-3.406738120E-02-3.659179060E-02-3.908434140E-02-4.154393820E-02 --4.396950080E-02-4.635995630E-02-4.871423540E-02-5.103128400E-02-5.331007020E-02 --5.554955830E-02-5.774872750E-02-5.990655720E-02-6.202204900E-02-6.409420820E-02 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--7.848604020E-02-7.661058010E-02-7.466726010E-02-7.265657190E-02-7.057899240E-02 --6.843515490E-02-6.622574480E-02-6.395137310E-02-6.161280720E-02-5.921083320E-02 --5.674623700E-02-5.421981960E-02-5.163256080E-02-4.898535090E-02-4.627913240E-02 --4.351501170E-02-4.069410640E-02-3.781754150E-02-3.488642720E-02-3.190197050E-02 --2.886546400E-02-2.577821350E-02-2.264151160E-02-1.945676840E-02-1.622542180E-02 --1.294891350E-02-9.628682400E-03-6.266191140E-03-2.862965920E-03 5.794309550E-04 - 4.059466530E-03 7.575592490E-03 1.112625750E-02 1.470991130E-02 1.832499360E-02 - 2.196996850E-02 2.564333190E-02 2.934358270E-02 3.306921940E-02 3.681877260E-02 - 4.059089720E-02 4.438412190E-02 4.819715020E-02 5.202869330E-02 5.587745830E-02 - 5.974223090E-02 6.362178920E-02 6.751504540E-02 7.142098250E-02 7.533855740E-02 - 7.926676420E-02 8.320466430E-02 8.715141560E-02 9.110623600E-02 9.506841000E-02 - 9.903745350E-02 1.030126590E-01 1.069940700E-01 1.109820830E-01 1.149772780E-01 - 1.189809670E-01 1.229920540E-01 1.270145920E-01 1.310556530E-01 1.351216440E-01 - 1.392215490E-01 1.433807910E-01 1.476285610E-01 1.519294380E-01 1.562456340E-01 - 1.605392840E-01 1.647970680E-01 1.690241100E-01 1.732201730E-01 1.773849870E-01 - 1.815184650E-01 1.856205310E-01 1.896910370E-01 1.937298630E-01 1.977368150E-01 - 2.017116840E-01 2.056543230E-01 2.095644770E-01 2.134418490E-01 2.172861990E-01 - 2.210972610E-01 2.248747200E-01 2.286182490E-01 2.323275210E-01 2.360021620E-01 - 2.396418600E-01 2.432462130E-01 2.468148320E-01 2.171237170E-01 2.148557900E-01 - 2.125661220E-01 2.102548930E-01 2.079222800E-01 2.055682990E-01 2.031930980E-01 - 2.007967980E-01 1.983793530E-01 1.959407630E-01 1.934809830E-01 1.910000150E-01 - 1.884977820E-01 1.859741660E-01 1.834290920E-01 1.808624860E-01 1.782741990E-01 - 1.756641270E-01 1.730320600E-01 1.703779700E-01 1.677016170E-01 1.650027330E-01 - 1.622814390E-01 1.595384630E-01 1.567711380E-01 1.539787500E-01 1.511643230E-01 - 1.483309120E-01 1.454818400E-01 1.426258090E-01 1.397638770E-01 1.368961630E-01 - 1.340217440E-01 1.311388610E-01 1.282472310E-01 1.253470180E-01 1.224384230E-01 - 1.195216250E-01 1.165970340E-01 1.136650520E-01 1.107260660E-01 1.077804710E-01 - 1.048286710E-01 1.018710660E-01 9.890802950E-02 9.593995660E-02 9.296723460E-02 - 8.999025820E-02 8.700942990E-02 8.402512220E-02 8.103773000E-02 7.804761830E-02 - 7.505518200E-02 7.206077130E-02 6.906478110E-02 6.606760620E-02 6.306967880E-02 - 6.007148700E-02 5.707349260E-02 5.407619850E-02 5.108013750E-02 4.808587950E-02 - 4.509405420E-02 4.210530590E-02 3.912030160E-02 3.613974150E-02 3.316437080E-02 - 3.019498100E-02 2.723236940E-02 2.427738720E-02 2.133089490E-02 1.839379970E-02 - 1.546701980E-02 1.255152190E-02 9.648265320E-03 6.758253090E-03 3.882522460E-03 - 1.022110690E-03-1.821944720E-03-4.648570440E-03-7.456674240E-03-1.024516670E-02 --1.301294570E-02-1.575890370E-02-1.848193630E-02-2.118091840E-02-2.385473250E-02 --2.650226090E-02-2.912238430E-02-3.171398860E-02-3.427598250E-02-3.680723160E-02 --3.930664810E-02-4.177315530E-02-4.420566560E-02-4.660310220E-02-4.896439240E-02 --5.128848930E-02-5.357434230E-02-5.582092330E-02-5.802721160E-02-6.019219380E-02 --6.231485680E-02-6.439421330E-02-6.642928720E-02-6.841912870E-02-7.036276910E-02 --7.225924730E-02-7.410763950E-02-7.590702180E-02-7.765647770E-02-7.935510580E-02 --8.100201930E-02-8.259633930E-02-8.413719390E-02-8.562372620E-02-8.705515410E-02 --8.843054620E-02-8.974911270E-02-9.101008620E-02-9.221267700E-02-9.335611020E-02 --9.443960340E-02-9.546243400E-02-9.642385690E-02-9.732318670E-02-9.815973790E-02 --9.893283990E-02-9.964182230E-02-1.002860590E-01-1.008649840E-01-1.013779640E-01 --1.018245000E-01-1.022040470E-01-1.025161070E-01-1.027601960E-01-1.029358660E-01 --1.030426990E-01-1.030803100E-01-1.030483100E-01-1.029463630E-01-1.027741510E-01 --1.025314110E-01-1.022179050E-01-1.018333810E-01-1.013777260E-01-1.008506940E-01 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5.137198790E-02 5.522540210E-02 5.909492820E-02 6.297937040E-02 6.687755880E-02 - 7.078847290E-02 7.471111420E-02 7.864444700E-02 8.258752520E-02 8.653950690E-02 - 9.049955760E-02 9.446701410E-02 9.844123570E-02 1.024215670E-01 1.064080450E-01 - 1.104009750E-01 1.144006920E-01 1.184074430E-01 1.224252210E-01 1.264519390E-01 - 1.304944310E-01 1.345612410E-01 1.386608780E-01 1.428149940E-01 1.470599170E-01 - 1.513620620E-01 1.556842920E-01 1.599862130E-01 1.642542030E-01 1.684910210E-01 - 1.726965900E-01 1.768708230E-01 1.810134650E-01 1.851245160E-01 1.892038290E-01 - 1.932513560E-01 1.972668920E-01 2.012502550E-01 2.052012230E-01 2.091196030E-01 - 2.130051110E-01 2.168574780E-01 2.206764820E-01 2.244618090E-01 2.282130570E-01 - 2.319299580E-01 2.356121840E-01 2.392593320E-01 2.428710760E-01 2.464469670E-01 - 2.172382030E-01 2.149721090E-01 2.126841400E-01 2.103744600E-01 2.080433520E-01 - 2.056908760E-01 2.033170910E-01 2.009219830E-01 1.985056850E-01 1.960681380E-01 - 1.936092820E-01 1.911290880E-01 1.886275110E-01 1.861044470E-01 1.835598200E-01 - 1.809935270E-01 1.784054490E-01 1.757954360E-01 1.731633990E-01 1.705091600E-01 - 1.678325830E-01 1.651335210E-01 1.624118390E-01 1.596699800E-01 1.569009570E-01 - 1.541070490E-01 1.512914750E-01 1.484578550E-01 1.456093940E-01 1.427491900E-01 - 1.398854110E-01 1.370162370E-01 1.341396120E-01 1.312547180E-01 1.283612700E-01 - 1.254590300E-01 1.225482080E-01 1.196292120E-01 1.167023550E-01 1.137680340E-01 - 1.108266260E-01 1.078785360E-01 1.049241800E-01 1.019639300E-01 9.899818150E-02 - 9.602732960E-02 9.305176140E-02 9.007188680E-02 8.708807830E-02 8.410072330E-02 - 8.111021670E-02 7.811693850E-02 7.512126120E-02 7.212354990E-02 6.912419950E-02 - 6.612362710E-02 6.312222780E-02 6.012046710E-02 5.711884050E-02 5.411785840E-02 - 5.111807580E-02 4.812003300E-02 4.512434080E-02 4.213165860E-02 3.914265710E-02 - 3.615802900E-02 3.317853440E-02 3.020496850E-02 2.723811570E-02 2.427881210E-02 - 2.132793890E-02 1.838640500E-02 1.545513240E-02 1.253506820E-02 9.627193210E-03 - 6.732504350E-03 3.852034450E-03 9.868207850E-04-1.862088800E-03-4.693623630E-03 --7.506694180E-03-1.030021070E-02-1.307306720E-02-1.582415770E-02-1.855236290E-02 --2.125656230E-02-2.393564580E-02-2.658849210E-02-2.921398170E-02-3.181100260E-02 --3.437844290E-02-3.691519050E-02-3.942015020E-02-4.189223800E-02-4.433036600E-02 --4.673346130E-02-4.910044370E-02-5.143027380E-02-5.372189360E-02-5.597427490E-02 --5.818639700E-02-6.035724650E-02-6.248581040E-02-6.457109000E-02-6.661211700E-02 --6.860793380E-02-7.055756450E-02-7.246006280E-02-7.431450490E-02-7.611995190E-02 --7.787550240E-02-7.958024000E-02-8.123327050E-02-8.283372970E-02-8.438074590E-02 --8.587345480E-02-8.731101450E-02-8.869257570E-02-9.001731870E-02-9.128446130E-02 --9.249322860E-02-9.364284570E-02-9.473252300E-02-9.576150770E-02-9.672908480E-02 --9.763453160E-02-9.847719220E-02-9.925637390E-02-9.997142850E-02-1.006217080E-01 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2.242263110E-01 2.279862460E-01 2.317118200E-01 2.354026590E-01 2.390583750E-01 - 2.426786420E-01 2.462630120E-01 2.173876910E-01 2.151219250E-01 2.128346120E-01 - 2.105257810E-01 2.081955370E-01 2.058441040E-01 2.034713770E-01 2.010773720E-01 - 1.986620720E-01 1.962255090E-01 1.937676070E-01 1.912883070E-01 1.887875350E-01 - 1.862652300E-01 1.837212890E-01 1.811555920E-01 1.785680500E-01 1.759585140E-01 - 1.733268650E-01 1.706730130E-01 1.679967190E-01 1.652977910E-01 1.625762130E-01 - 1.598341020E-01 1.570647210E-01 1.542704400E-01 1.514546720E-01 1.486208590E-01 - 1.457724120E-01 1.429127600E-01 1.400453450E-01 1.371753220E-01 1.342976090E-01 - 1.314115820E-01 1.285169120E-01 1.256133470E-01 1.227011380E-01 1.197806970E-01 - 1.168523360E-01 1.139164570E-01 1.109734400E-01 1.080237030E-01 1.050676180E-01 - 1.021056030E-01 9.913804380E-02 9.616533670E-02 9.318786110E-02 9.020601210E-02 - 8.722019200E-02 8.423078810E-02 8.123818040E-02 7.824274900E-02 7.524487380E-02 - 7.224493470E-02 6.924331930E-02 6.624040010E-02 6.323667620E-02 6.023250520E-02 - 5.722840130E-02 5.422491580E-02 5.122258890E-02 4.822197180E-02 4.522362350E-02 - 4.222826660E-02 3.923650460E-02 3.624908250E-02 3.326676040E-02 3.029030380E-02 - 2.732050420E-02 2.435819990E-02 2.140426820E-02 1.845961440E-02 1.552517060E-02 - 1.260189900E-02 9.690759700E-03 6.792733910E-03 3.908880990E-03 1.040223520E-03 --1.812175030E-03-4.647248890E-03-7.463919460E-03-1.026108860E-02-1.303765080E-02 --1.579249650E-02-1.852451260E-02-2.123257700E-02-2.391557210E-02-2.657238020E-02 --2.920188200E-02-3.180295970E-02-3.437450530E-02-3.691541030E-02-3.942457590E-02 --4.190091040E-02-4.434332250E-02-4.675074290E-02-4.912210260E-02-5.145634710E-02 --5.375242610E-02-5.600930750E-02-5.822596700E-02-6.040137630E-02-6.253454090E-02 --6.462448090E-02-6.667020170E-02-6.867072730E-02-7.062510400E-02-7.253238560E-02 --7.439162580E-02-7.620191570E-02-7.796232400E-02-7.967195660E-02-8.132990450E-02 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1.550799610E-01 1.594017450E-01 1.636884360E-01 1.679430310E-01 1.721666900E-01 - 1.763589230E-01 1.805196850E-01 1.846489010E-01 1.887464080E-01 1.928120700E-01 - 1.968457550E-01 2.008473130E-01 2.048165050E-01 2.087531240E-01 2.126569000E-01 - 2.165275510E-01 2.203648540E-01 2.241685090E-01 2.279380710E-01 2.316732850E-01 - 2.353737950E-01 2.390392420E-01 2.426692100E-01 2.462632660E-01 2.175703500E-01 - 2.153041960E-01 2.130167480E-01 2.107082900E-01 2.083787020E-01 2.060279550E-01 - 2.036560620E-01 2.012629960E-01 1.988486950E-01 1.964131000E-01 1.939561960E-01 - 1.914778950E-01 1.889780910E-01 1.864567400E-01 1.839137520E-01 1.813489790E-01 - 1.787623170E-01 1.761536450E-01 1.735228600E-01 1.708697680E-01 1.681942490E-01 - 1.654960220E-01 1.627750100E-01 1.600316910E-01 1.572644860E-01 1.544721130E-01 - 1.516571790E-01 1.488227990E-01 1.459723110E-01 1.431118100E-01 1.402462120E-01 - 1.373748480E-01 1.344963610E-01 1.316096480E-01 1.287143080E-01 1.258100870E-01 - 1.228972450E-01 1.199761030E-01 1.170470270E-01 1.141103950E-01 1.111665960E-01 - 1.082160170E-01 1.052590760E-01 1.022961740E-01 9.932769090E-02 9.635402260E-02 - 9.337555620E-02 9.039269390E-02 8.740583810E-02 8.441536870E-02 8.142167330E-02 - 7.842513170E-02 7.542610910E-02 7.242500040E-02 6.942218540E-02 6.641807410E-02 - 6.341306870E-02 6.040763850E-02 5.740225320E-02 5.439744520E-02 5.139376220E-02 - 4.839174820E-02 4.539199550E-02 4.239516330E-02 3.940191490E-02 3.641296550E-02 - 3.342908620E-02 3.045102770E-02 2.747956480E-02 2.451557480E-02 2.155992020E-02 - 1.861347630E-02 1.567720620E-02 1.275206640E-02 9.839002040E-03 6.939018150E-03 - 4.053140990E-03 1.182408420E-03-1.672117160E-03-4.509368910E-03-7.328267210E-03 --1.012771580E-02-1.290660910E-02-1.566383990E-02-1.839829980E-02-2.110886200E-02 --2.379440890E-02-2.645381730E-02-2.908596960E-02-3.168975560E-02-3.426405410E-02 --3.680776800E-02-3.931979460E-02-4.179903490E-02-4.424440490E-02-4.665482790E-02 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8.565642680E-02 8.963108060E-02 9.361341600E-02 9.760279950E-02 1.015989410E-01 - 1.056011100E-01 1.096095290E-01 1.136250050E-01 1.176484600E-01 1.216807140E-01 - 1.257252250E-01 1.297829300E-01 1.338596640E-01 1.379716840E-01 1.421373640E-01 - 1.463776530E-01 1.506967690E-01 1.550409050E-01 1.593665930E-01 1.636650560E-01 - 1.679281290E-01 1.721604620E-01 1.763614710E-01 1.805311440E-01 1.846694500E-01 - 1.887762550E-01 1.928513800E-01 1.968946610E-01 2.009058890E-01 2.048849760E-01 - 2.088316230E-01 2.127455320E-01 2.166264650E-01 2.204741690E-01 2.242883000E-01 - 2.280685010E-01 2.318144440E-01 2.355257270E-01 2.392020230E-01 2.428428980E-01 - 2.464479360E-01 2.177838090E-01 2.155171040E-01 2.132296710E-01 2.109213770E-01 - 2.085922060E-01 2.062420850E-01 2.038709520E-01 2.014787640E-01 1.990654470E-01 - 1.966309250E-01 1.941751090E-01 1.916979550E-01 1.891993430E-01 1.866791840E-01 - 1.841374040E-01 1.815738680E-01 1.789884420E-01 1.763810070E-01 1.737514140E-01 - 1.710995880E-01 1.684253510E-01 1.657285840E-01 1.630091670E-01 1.602665190E-01 - 1.575003420E-01 1.547106950E-01 1.518971770E-01 1.490618740E-01 1.462112370E-01 - 1.433509590E-01 1.404854950E-01 1.376139070E-01 1.347353760E-01 1.318488120E-01 - 1.289534420E-01 1.260492950E-01 1.231365280E-01 1.202154460E-01 1.172864290E-01 - 1.143498420E-01 1.114060730E-01 1.084554940E-01 1.054985520E-01 1.025356200E-01 - 9.956710040E-02 9.659338000E-02 9.361486140E-02 9.063193950E-02 8.764499430E-02 - 8.465443550E-02 8.166064320E-02 7.866400480E-02 7.566489280E-02 7.266367970E-02 - 6.966073070E-02 6.665647770E-02 6.365136060E-02 6.064582240E-02 5.764032160E-02 - 5.463537570E-02 5.163151030E-02 4.862929510E-02 4.562935230E-02 4.263230790E-02 - 3.963883970E-02 3.664963690E-02 3.366546330E-02 3.068707700E-02 2.771527880E-02 - 2.475091260E-02 2.179485000E-02 1.884797030E-02 1.591121590E-02 1.298553220E-02 - 1.007189420E-02 7.171303030E-03 4.284767430E-03 1.413326940E-03-1.441959760E-03 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2.018937840E-02 2.387473360E-02 2.758780120E-02 3.132709120E-02 3.509115430E-02 - 3.887853770E-02 4.268793020E-02 4.651780050E-02 5.036685240E-02 5.423389000E-02 - 5.811771010E-02 6.201712040E-02 6.593092530E-02 6.985794750E-02 7.379724830E-02 - 7.774784420E-02 8.170880380E-02 8.567921820E-02 8.965830500E-02 9.364524480E-02 - 9.763950850E-02 1.016406190E-01 1.056484800E-01 1.096625920E-01 1.136836710E-01 - 1.177126620E-01 1.217511220E-01 1.258038730E-01 1.298682840E-01 1.339512170E-01 - 1.380708660E-01 1.422455010E-01 1.464933160E-01 1.508283170E-01 1.551755960E-01 - 1.595049350E-01 1.638116090E-01 1.680874820E-01 1.723259390E-01 1.765355910E-01 - 1.807142350E-01 1.848617640E-01 1.889779420E-01 1.930626480E-01 1.971157940E-01 - 2.011372750E-01 2.051267620E-01 2.090839890E-01 2.130088060E-01 2.169007960E-01 - 2.207597350E-01 2.245853100E-01 2.283771490E-01 2.321349080E-01 2.358581270E-01 - 2.395464930E-01 2.431995720E-01 2.468169180E-01 2.180265780E-01 2.157595160E-01 - 2.134721130E-01 2.111640720E-01 2.088353480E-01 2.064858970E-01 2.041155840E-01 - 2.017243360E-01 1.993120910E-01 1.968787610E-01 1.944242270E-01 1.919483990E-01 - 1.894511880E-01 1.869325040E-01 1.843922140E-01 1.818301980E-01 1.792463360E-01 - 1.766405110E-01 1.740125860E-01 1.713623850E-01 1.686898920E-01 1.659946890E-01 - 1.632769550E-01 1.605370940E-01 1.577741350E-01 1.549850400E-01 1.521720740E-01 - 1.493391390E-01 1.464901120E-01 1.436291640E-01 1.407636850E-01 1.378925740E-01 - 1.350146980E-01 1.321288940E-01 1.292341950E-01 1.263308670E-01 1.234189270E-01 - 1.204986720E-01 1.175704750E-01 1.146347000E-01 1.116917430E-01 1.087420140E-01 - 1.057858990E-01 1.028238010E-01 9.985612330E-02 9.688326720E-02 9.390561280E-02 - 9.092355520E-02 8.793748920E-02 8.494782450E-02 8.195494120E-02 7.895921920E-02 - 7.596105340E-02 7.296077910E-02 6.995878370E-02 6.695550680E-02 6.395138800E-02 - 6.094686690E-02 5.794240160E-02 5.493844300E-02 5.193559080E-02 4.893441870E-02 - 4.593549670E-02 4.293948040E-02 3.994703290E-02 3.695885460E-02 3.397567570E-02 - 3.099824300E-02 2.802739660E-02 2.506398410E-02 2.210885290E-02 1.916285050E-02 - 1.622693430E-02 1.330206820E-02 1.038920880E-02 7.489359470E-03 4.603524230E-03 - 1.732752430E-03-1.121918550E-03-3.959422930E-03-6.778666750E-03-9.578558620E-03 --1.235800330E-02-1.511590180E-02-1.785112730E-02-2.056256680E-02-2.324910280E-02 --2.590961750E-02-2.854299170E-02-3.114810960E-02-3.372386100E-02-3.626912830E-02 --3.878282380E-02-4.126384850E-02-4.371112590E-02-4.612356420E-02-4.850010570E-02 --5.083968490E-02-5.314126240E-02-5.540379140E-02-5.762625110E-02-5.980760980E-02 --6.194687630E-02-6.404305990E-02-6.609517340E-02-6.810223310E-02-7.006327810E-02 --7.197736950E-02-7.384355370E-02-7.566092160E-02-7.742855700E-02-7.914552840E-02 --8.081094180E-02-8.242392540E-02-8.398360760E-02-8.548913150E-02-8.693964030E-02 --8.833429960E-02-8.967228230E-02-9.095279130E-02-9.217502180E-02-9.333819900E-02 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1.934450570E-01 1.975084840E-01 2.015406040E-01 2.055410300E-01 2.095095660E-01 - 2.134459470E-01 2.173498570E-01 2.212210150E-01 2.250590470E-01 2.288636120E-01 - 2.326342760E-01 2.363706830E-01 2.400723990E-01 2.437389940E-01 2.473700340E-01 - 2.182971980E-01 2.160300610E-01 2.137428820E-01 2.114352580E-01 2.091072050E-01 - 2.067585890E-01 2.043893040E-01 2.019992320E-01 1.995882690E-01 1.971563250E-01 - 1.947032810E-01 1.922290330E-01 1.897334900E-01 1.872165200E-01 1.846780330E-01 - 1.821178940E-01 1.795359550E-01 1.769321260E-01 1.743062590E-01 1.716581580E-01 - 1.689878260E-01 1.662947090E-01 1.635790770E-01 1.608441470E-01 1.580826340E-01 - 1.552946570E-01 1.524836120E-01 1.496530920E-01 1.468067020E-01 1.439480190E-01 - 1.410816460E-01 1.382112500E-01 1.353343430E-01 1.324497160E-01 1.295565660E-01 - 1.266546990E-01 1.237442640E-01 1.208255660E-01 1.178989560E-01 1.149647830E-01 - 1.120234500E-01 1.090753600E-01 1.061209220E-01 1.031605300E-01 1.001945810E-01 - 9.722346810E-02 9.424758700E-02 9.126733990E-02 8.828311410E-02 8.529531210E-02 - 8.230432120E-02 7.931052890E-02 7.631434500E-02 7.331606000E-02 7.031609860E-02 - 6.731488560E-02 6.431287530E-02 6.131050360E-02 5.830820650E-02 5.530644580E-02 - 5.230580640E-02 4.930686210E-02 4.631016780E-02 4.331640530E-02 4.032623770E-02 - 3.734032440E-02 3.435942530E-02 3.138425570E-02 2.841566130E-02 2.545448950E-02 - 2.250158790E-02 1.955782250E-02 1.662409860E-02 1.370138860E-02 1.079065910E-02 - 7.892910390E-03 5.009140350E-03 2.140391390E-03-7.123001270E-04-3.547874050E-03 --6.365233100E-03-9.163285610E-03-1.194093840E-02-1.469710000E-02-1.743065750E-02 --2.014048580E-02-2.282546830E-02-2.548448930E-02-2.811642740E-02-3.072017240E-02 --3.329461440E-02-3.583864120E-02-3.835115210E-02-4.083106670E-02-4.327728970E-02 --4.568873720E-02-4.806435110E-02-5.040306970E-02-5.270384620E-02-5.496564130E-02 --5.718742680E-02-5.936818200E-02-6.150690090E-02-6.360259650E-02-6.565428530E-02 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1.223647070E-01 1.264321800E-01 1.305181240E-01 1.346253310E-01 1.387583020E-01 - 1.429619490E-01 1.472465250E-01 1.515927610E-01 1.559633020E-01 1.603098060E-01 - 1.646270600E-01 1.689129020E-01 1.731692110E-01 1.773951950E-01 1.815911380E-01 - 1.857569220E-01 1.898923520E-01 1.939972340E-01 1.980713460E-01 2.021145220E-01 - 2.061265560E-01 2.101071030E-01 2.140559260E-01 2.179726510E-01 2.218569820E-01 - 2.257085740E-01 2.295270120E-01 2.333118470E-01 2.370627220E-01 2.407791760E-01 - 2.444607470E-01 2.481069560E-01 2.185942830E-01 2.163276670E-01 2.140409950E-01 - 2.117342050E-01 2.094071210E-01 2.070596370E-01 2.046916190E-01 2.023029480E-01 - 1.998935190E-01 1.974632290E-01 1.950119290E-01 1.925395430E-01 1.900459530E-01 - 1.875310240E-01 1.849946680E-01 1.824367340E-01 1.798571050E-01 1.772556300E-01 - 1.746322070E-01 1.719867290E-01 1.693190190E-01 1.666290010E-01 1.639165430E-01 - 1.611830000E-01 1.584247200E-01 1.556401850E-01 1.528326270E-01 1.500053260E-01 - 1.471612900E-01 1.443038580E-01 1.414376940E-01 1.385688330E-01 1.356938180E-01 - 1.328111440E-01 1.299201250E-01 1.270204480E-01 1.241122630E-01 1.211958750E-01 - 1.182715890E-01 1.153397930E-01 1.124008820E-01 1.094552580E-01 1.065033300E-01 - 1.035454870E-01 1.005821380E-01 9.761365500E-02 9.464045610E-02 9.166294340E-02 - 8.868151160E-02 8.569654080E-02 8.270843330E-02 7.971757650E-02 7.672437280E-02 - 7.372916490E-02 7.073231790E-02 6.773427130E-02 6.473545730E-02 6.173632290E-02 - 5.873731520E-02 5.573894080E-02 5.274170260E-02 4.974617440E-02 4.675294090E-02 - 4.376266150E-02 4.077600320E-02 3.779363630E-02 3.481626140E-02 3.184466060E-02 - 2.887962010E-02 2.592198360E-02 2.297262290E-02 2.003240400E-02 1.710221360E-02 - 1.418301840E-02 1.127577010E-02 8.381471040E-03 5.501132920E-03 2.635768150E-03 --2.135723920E-04-3.045840650E-03-5.859945900E-03-8.654793720E-03-1.142929210E-02 --1.418234970E-02-1.691286820E-02-1.961970700E-02-2.230176140E-02-2.495791760E-02 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5.517704040E-02 5.906620620E-02 6.297165160E-02 6.689223650E-02 7.082690300E-02 - 7.477463040E-02 7.873447980E-02 8.270554990E-02 8.668699860E-02 9.067799150E-02 - 9.467776860E-02 9.868586810E-02 1.027018580E-01 1.067254390E-01 1.107591840E-01 - 1.147988220E-01 1.188467140E-01 1.229063420E-01 1.269816610E-01 1.310766190E-01 - 1.351951810E-01 1.393420700E-01 1.435705570E-01 1.478745040E-01 1.522307540E-01 - 1.566117410E-01 1.609637440E-01 1.652857360E-01 1.695786270E-01 1.738422660E-01 - 1.780765060E-01 1.822812110E-01 1.864563520E-01 1.906017070E-01 1.947171240E-01 - 1.988024260E-01 2.028573450E-01 2.068816270E-01 2.108749900E-01 2.148371190E-01 - 2.187676880E-01 2.226662640E-01 2.265325490E-01 2.303660960E-01 2.341664880E-01 - 2.379332630E-01 2.416658850E-01 2.453639660E-01 2.490269840E-01 2.189170720E-01 - 2.166513650E-01 2.143657800E-01 2.120601830E-01 2.097344400E-01 2.073884160E-01 - 2.050219920E-01 2.026350350E-01 2.002274390E-01 1.977990720E-01 1.953498420E-01 - 1.928796020E-01 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1.196503040E-01 1.167302210E-01 1.138032600E-01 1.108698250E-01 - 1.079303250E-01 1.049851780E-01 1.020347550E-01 9.907947480E-02 9.611972420E-02 - 9.315592050E-02 9.018844370E-02 8.721769600E-02 8.424409480E-02 8.126802000E-02 - 7.828987390E-02 7.531002160E-02 7.232883570E-02 6.934674080E-02 6.636413190E-02 - 6.338144840E-02 6.039914490E-02 5.741771310E-02 5.443765220E-02 5.145953220E-02 - 4.848393430E-02 4.551143940E-02 4.254270340E-02 3.957839310E-02 3.661922740E-02 - 3.366592530E-02 3.071929700E-02 2.778015290E-02 2.484929750E-02 2.192758960E-02 - 1.901594740E-02 1.611528360E-02 1.322655100E-02 1.035071440E-02 7.488764820E-03 - 4.641711710E-03 1.810591090E-03-1.003558050E-03-3.799680390E-03-6.576695480E-03 --9.333516470E-03-1.206905580E-02-1.478222010E-02-1.747190770E-02-2.013700460E-02 --2.277640250E-02-2.538899700E-02-2.797368540E-02-3.052935750E-02-3.305491430E-02 --3.554926810E-02-3.801131620E-02-4.043998940E-02-4.283420370E-02-4.519288990E-02 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1.334308240E-01 1.376137440E-01 1.418529300E-01 1.461678000E-01 1.505674870E-01 - 1.550072280E-01 1.594287310E-01 1.638293560E-01 1.682082560E-01 1.725635380E-01 - 1.768956780E-01 1.812051830E-01 1.854916360E-01 1.897548590E-01 1.939945370E-01 - 1.982104030E-01 2.024022190E-01 2.065696720E-01 2.107123730E-01 2.148300110E-01 - 2.189221230E-01 2.229882780E-01 2.270280570E-01 2.310409250E-01 2.350262700E-01 - 2.389835570E-01 2.429121880E-01 2.468115390E-01 2.506807150E-01 2.545191650E-01 - 2.583261730E-01 2.213770750E-01 2.191255690E-01 2.168543930E-01 2.145634740E-01 - 2.122527510E-01 2.099221800E-01 2.075716700E-01 2.052011790E-01 2.028106450E-01 - 2.003999800E-01 1.979691390E-01 1.955180320E-01 1.930466000E-01 1.905547530E-01 - 1.880424170E-01 1.855094880E-01 1.829558760E-01 1.803814920E-01 1.777862310E-01 - 1.751699750E-01 1.725325880E-01 1.698739830E-01 1.671940090E-01 1.644925480E-01 - 1.617693900E-01 1.590244170E-01 1.562577640E-01 1.534679530E-01 1.506565660E-01 - 1.478284000E-01 1.449880600E-01 1.421423110E-01 1.392938200E-01 1.364403370E-01 - 1.335810570E-01 1.307151470E-01 1.278417860E-01 1.249612270E-01 1.220736430E-01 - 1.191794870E-01 1.162790880E-01 1.133728180E-01 1.104610930E-01 1.075442950E-01 - 1.046228480E-01 1.016971540E-01 9.876760840E-02 9.583461280E-02 9.289857750E-02 - 8.995988220E-02 8.701897410E-02 8.407622580E-02 8.113203200E-02 7.818679510E-02 - 7.524090260E-02 7.229471950E-02 6.934866310E-02 6.640316550E-02 6.345865880E-02 - 6.051560860E-02 5.757449940E-02 5.463584510E-02 5.170017850E-02 4.876807330E-02 - 4.584018510E-02 4.291716960E-02 3.999968250E-02 3.708837550E-02 3.418396040E-02 - 3.128732740E-02 2.839917880E-02 2.552037690E-02 2.265179720E-02 1.979431320E-02 - 1.694879870E-02 1.411622020E-02 1.129753240E-02 8.493683300E-03 5.705697930E-03 - 2.934598830E-03 1.814095010E-04-2.552846450E-03-5.267119040E-03-7.960313930E-03 --1.063137500E-02-1.327921540E-02-1.590275210E-02-1.850091110E-02-2.107257770E-02 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1.807151730E-02 1.525301860E-02 1.244841700E-02 - 9.658681230E-03 6.884802600E-03 4.127779980E-03 1.388635720E-03-1.331602340E-03 --4.031879360E-03-6.711146330E-03-9.368338620E-03-1.200238340E-02-1.461219690E-02 --1.719669810E-02-1.975480650E-02-2.228543720E-02-2.478751350E-02-2.725995330E-02 --2.970167250E-02-3.211159260E-02-3.448865190E-02-3.683178500E-02-3.913993760E-02 --4.141207040E-02-4.364713650E-02-4.584410790E-02-4.800196740E-02-5.011970920E-02 --5.219633130E-02-5.423084650E-02-5.622227120E-02-5.816964810E-02-6.007201970E-02 --6.192844360E-02-6.373798850E-02-6.549973040E-02-6.721277530E-02-6.887621430E-02 --7.048917560E-02-7.205079500E-02-7.356019320E-02-7.501654330E-02-7.641901080E-02 --7.776676860E-02-7.905903460E-02-8.029501140E-02-8.147391680E-02-8.259499820E-02 --8.365750310E-02-8.466072380E-02-8.560395990E-02-8.648649600E-02-8.730766180E-02 --8.806680890E-02-8.876329660E-02-8.939652140E-02-8.996587990E-02-9.047079830E-02 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6.825017930E-02 6.533098970E-02 6.241367010E-02 - 5.949866400E-02 5.658648910E-02 5.367765200E-02 5.077275260E-02 4.787237940E-02 - 4.497712110E-02 4.208761830E-02 3.920459000E-02 3.632874040E-02 3.346082200E-02 - 3.060159460E-02 2.775186110E-02 2.491245610E-02 2.208424730E-02 1.926812900E-02 - 1.646499710E-02 1.367578100E-02 1.090144270E-02 8.142969570E-03 5.401336120E-03 - 2.677550310E-03-2.734520790E-05-2.712329150E-03-5.376348270E-03-8.018353020E-03 --1.063727590E-02-1.323204390E-02-1.580158430E-02-1.834482700E-02-2.086069250E-02 --2.334810230E-02-2.580597810E-02-2.823323760E-02-3.062882830E-02-3.299167750E-02 --3.532072900E-02-3.761493040E-02-3.987324610E-02-4.209462930E-02-4.427806290E-02 --4.642251510E-02-4.852699120E-02-5.059049650E-02-5.261205140E-02-5.459066110E-02 --5.652537570E-02-5.841524530E-02-6.025931240E-02-6.205666440E-02-6.380638480E-02 --6.550756100E-02-6.715931000E-02-6.876074520E-02-7.031100240E-02-7.180921730E-02 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2.127404660E-01 2.104061390E-01 2.080524120E-01 2.056793570E-01 - 2.032870200E-01 2.008754310E-01 1.984446200E-01 1.959945410E-01 1.935252990E-01 - 1.910368200E-01 1.885290890E-01 1.860020460E-01 1.834557060E-01 1.808900390E-01 - 1.783049110E-01 1.757002770E-01 1.730760480E-01 1.704321350E-01 1.677684340E-01 - 1.650853010E-01 1.623815890E-01 1.596570760E-01 1.569122970E-01 1.541478190E-01 - 1.513641920E-01 1.485623120E-01 1.457489730E-01 1.429309250E-01 1.401118490E-01 - 1.372902540E-01 1.344650090E-01 1.316350400E-01 1.287996920E-01 1.259589050E-01 - 1.231128570E-01 1.202618850E-01 1.174063240E-01 1.145465080E-01 1.116828320E-01 - 1.088157070E-01 1.059455420E-01 1.030727250E-01 1.001976500E-01 9.732072060E-02 - 9.444233030E-02 9.156288950E-02 8.868279310E-02 8.580245080E-02 8.292226490E-02 - 8.004263040E-02 7.716394960E-02 7.428660240E-02 7.141099870E-02 6.853754070E-02 - 6.566665320E-02 6.279877570E-02 5.993442240E-02 5.707409980E-02 5.421832580E-02 - 5.136760320E-02 4.852261020E-02 4.568387940E-02 4.285204410E-02 4.002784190E-02 - 3.721199180E-02 3.440522780E-02 3.160827980E-02 2.882187630E-02 2.604694480E-02 - 2.328429000E-02 2.053478730E-02 1.779931600E-02 1.507879420E-02 1.237417380E-02 - 9.686376900E-03 7.016402200E-03 4.365249540E-03 1.733917280E-03-8.765950330E-04 --3.465295770E-03-6.031095520E-03-8.572964000E-03-1.108985860E-02-1.358073020E-02 --1.604452920E-02-1.848020590E-02-2.088670990E-02-2.326297390E-02-2.560794540E-02 --2.792057390E-02-3.019982390E-02-3.244465960E-02-3.465405110E-02-3.682697190E-02 --3.896240890E-02-4.105935620E-02-4.311681910E-02-4.513380300E-02-4.710933190E-02 --4.904244470E-02-5.093219130E-02-5.277762560E-02-5.457781260E-02-5.633182820E-02 --5.803877120E-02-5.969773610E-02-6.130785870E-02-6.286824490E-02-6.437806040E-02 --6.583645190E-02-6.724259260E-02-6.859567020E-02-6.989487260E-02-7.113941010E-02 --7.232852280E-02-7.346145810E-02-7.453746350E-02-7.555582370E-02-7.651582360E-02 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2.237259450E-01 2.279825210E-01 2.322240620E-01 2.364500160E-01 2.406599370E-01 - 2.448532430E-01 2.490294870E-01 2.531880740E-01 2.573283610E-01 2.614494260E-01 - 2.655504050E-01 2.696304620E-01 2.736886140E-01 2.247454820E-01 2.225112320E-01 - 2.202571630E-01 2.179835440E-01 2.156904190E-01 2.133778930E-01 2.110460850E-01 - 2.086950690E-01 2.063249950E-01 2.039358760E-01 2.015277890E-01 1.991007630E-01 - 1.966548560E-01 1.941901000E-01 1.917064640E-01 1.892039920E-01 1.866826120E-01 - 1.841423210E-01 1.815830770E-01 1.790048180E-01 1.764075160E-01 1.737910510E-01 - 1.711553190E-01 1.685003640E-01 1.658265590E-01 1.631318030E-01 1.604168120E-01 - 1.576822700E-01 1.549288630E-01 1.521572920E-01 1.493677940E-01 1.465609670E-01 - 1.437504740E-01 1.409397720E-01 1.381268950E-01 1.353111570E-01 1.324915740E-01 - 1.296671030E-01 1.268375810E-01 1.240031940E-01 1.211642030E-01 1.183209420E-01 - 1.154737550E-01 1.126230060E-01 1.097690980E-01 1.069124490E-01 1.040534380E-01 - 1.011924590E-01 9.832991660E-02 9.546619650E-02 9.260170910E-02 8.973685650E-02 - 8.687204120E-02 8.400766550E-02 8.114413920E-02 7.828184220E-02 7.542116190E-02 - 7.256250830E-02 6.970632080E-02 6.685294210E-02 6.400283430E-02 6.115650390E-02 - 5.831446500E-02 5.547722430E-02 5.264529590E-02 4.981921240E-02 4.699963330E-02 - 4.418717700E-02 4.138251770E-02 3.858634460E-02 3.579938410E-02 3.302236650E-02 - 3.025605900E-02 2.750126640E-02 2.475885860E-02 2.202969040E-02 1.931460950E-02 - 1.661450790E-02 1.393032820E-02 1.126300730E-02 8.613494220E-03 5.982769650E-03 - 3.371830560E-03 7.816763250E-04-1.786683570E-03-4.332224840E-03-6.853912490E-03 --9.350720790E-03-1.182161640E-02-1.426554940E-02-1.668147000E-02-1.906833050E-02 --2.142507960E-02-2.375066280E-02-2.604406890E-02-2.830424530E-02-3.053016770E-02 --3.272080420E-02-3.487514330E-02-3.699217360E-02-3.907088560E-02-4.111029950E-02 --4.310942440E-02-4.506729170E-02-4.698294770E-02-4.885542770E-02-5.068378150E-02 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1.516933590E-01 1.561515330E-01 1.606263220E-01 1.650917380E-01 1.695368740E-01 - 1.739711460E-01 1.783944070E-01 1.828065070E-01 1.872072670E-01 1.915966120E-01 - 1.959751400E-01 2.003424610E-01 2.046984140E-01 2.090429220E-01 2.133758810E-01 - 2.176969950E-01 2.220061720E-01 2.263031600E-01 2.305877210E-01 2.348594520E-01 - 2.391180990E-01 2.433631270E-01 2.475939990E-01 2.518101330E-01 2.560112480E-01 - 2.601965070E-01 2.643651070E-01 2.685163620E-01 2.726492880E-01 2.767629620E-01 - 2.253985850E-01 2.231657800E-01 2.209132160E-01 2.186411020E-01 2.163495570E-01 - 2.140387740E-01 2.117089480E-01 2.093601820E-01 2.069925960E-01 2.046063100E-01 - 2.022014110E-01 1.997779460E-01 1.973360030E-01 1.948755680E-01 1.923967300E-01 - 1.898994740E-01 1.873837410E-01 1.848495450E-01 1.822968570E-01 1.797256320E-01 - 1.771358250E-01 1.745273770E-01 1.719001830E-01 1.692541990E-01 1.665901690E-01 - 1.639060680E-01 1.612016860E-01 1.584777240E-01 1.557348820E-01 1.529733990E-01 - 1.501951520E-01 1.474028830E-01 1.445987670E-01 1.417958440E-01 1.389918920E-01 - 1.361861080E-01 1.333771200E-01 1.305641830E-01 1.277465670E-01 1.249245260E-01 - 1.220982220E-01 1.192679780E-01 1.164341490E-01 1.135971020E-01 1.107572020E-01 - 1.079148650E-01 1.050704720E-01 1.022244170E-01 9.937709570E-02 9.652891760E-02 - 9.368026260E-02 9.083153310E-02 8.798313890E-02 8.513548230E-02 8.228897300E-02 - 7.944399120E-02 7.660093900E-02 7.376020400E-02 7.092221080E-02 6.808735430E-02 - 6.525602940E-02 6.242875380E-02 5.960602690E-02 5.678835140E-02 5.397623780E-02 - 5.117018520E-02 4.837084560E-02 4.557884110E-02 4.279481990E-02 4.001946370E-02 - 3.725345810E-02 3.449755530E-02 3.175248210E-02 2.901904100E-02 2.629806660E-02 - 2.359040640E-02 2.089690040E-02 1.821841670E-02 1.555588380E-02 1.291023750E-02 - 1.028241500E-02 7.673360410E-03 5.084069450E-03 2.515524860E-03-3.127793390E-05 --2.555332150E-03-5.055612420E-03-7.531103210E-03-9.980775420E-03-1.240359430E-02 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8.455904570E-02 8.844349530E-02 9.234941010E-02 9.627631310E-02 1.002237200E-01 - 1.041914820E-01 1.081800010E-01 1.121890320E-01 1.162198710E-01 1.202737840E-01 - 1.243533940E-01 1.284590210E-01 1.325958370E-01 1.367778780E-01 1.410159770E-01 - 1.453415750E-01 1.497436460E-01 1.541991380E-01 1.586777870E-01 1.631413700E-01 - 1.675945970E-01 1.720381530E-01 1.764729170E-01 1.808986660E-01 1.853151620E-01 - 1.897225680E-01 1.941208990E-01 1.985101250E-01 2.028902620E-01 2.072612200E-01 - 2.116229240E-01 2.159753590E-01 2.203182730E-01 2.246516200E-01 2.289751170E-01 - 2.332884520E-01 2.375915940E-01 2.418841870E-01 2.461658570E-01 2.504361870E-01 - 2.546947600E-01 2.589408460E-01 2.631739080E-01 2.673933210E-01 2.715981600E-01 - 2.757878010E-01 2.799612880E-01 2.260790470E-01 2.238464650E-01 2.215943490E-01 - 2.193228010E-01 2.170320450E-01 2.147222610E-01 2.123936860E-01 2.100465600E-01 - 2.076809700E-01 2.052970380E-01 2.028948960E-01 2.004746350E-01 1.980363580E-01 - 1.955800950E-01 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2.521474100E-02 2.254397240E-02 1.988829860E-02 - 1.724861000E-02 1.462582780E-02 1.202089250E-02 9.434740060E-03 6.868304680E-03 - 4.322561440E-03 1.798519170E-03-7.028307300E-04-3.180482890E-03-5.633422640E-03 --8.060635070E-03-1.046109850E-02-1.283377870E-02-1.517766250E-02-1.749171320E-02 --1.977490630E-02-2.202622030E-02-2.424463260E-02-2.642912420E-02-2.857868370E-02 --3.069230730E-02-3.276899830E-02-3.480777140E-02-3.680762280E-02-3.876759110E-02 --4.068672280E-02-4.256406050E-02-4.439865800E-02-4.618958380E-02-4.793591420E-02 --4.963675140E-02-5.129119380E-02-5.289835110E-02-5.445737020E-02-5.596737190E-02 --5.742751810E-02-5.883698540E-02-6.019495800E-02-6.150062380E-02-6.275320800E-02 --6.395193190E-02-6.509602070E-02-6.618475910E-02-6.721740220E-02-6.819324200E-02 --6.911160050E-02-6.997179240E-02-7.077316190E-02-7.151507590E-02-7.219690080E-02 --7.281800360E-02-7.337789240E-02-7.387591150E-02-7.431154700E-02-7.468429950E-02 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1.250733440E-01 1.222865950E-01 1.194974110E-01 1.167060580E-01 - 1.139127760E-01 1.111180710E-01 1.083223450E-01 1.055260000E-01 1.027293950E-01 - 9.993290160E-02 9.713691470E-02 9.434181450E-02 9.154799580E-02 8.875587580E-02 - 8.596584950E-02 8.317831160E-02 8.039367200E-02 7.761231060E-02 7.483463730E-02 - 7.206103210E-02 6.929192690E-02 6.652775410E-02 6.376898290E-02 6.101605300E-02 - 5.826948580E-02 5.552976210E-02 5.279747400E-02 5.007321020E-02 4.735756290E-02 - 4.465113210E-02 4.195459190E-02 3.926863520E-02 3.659395870E-02 3.393132240E-02 - 3.128151220E-02 2.864528820E-02 2.602344570E-02 2.341684330E-02 2.082632110E-02 - 1.825277510E-02 1.569708810E-02 1.316018960E-02 1.064301000E-02 8.146481590E-03 - 5.671535150E-03 3.219171190E-03 7.903494410E-04-1.613934410E-03-3.992672540E-03 --6.344869730E-03-8.669531900E-03-1.096566770E-02-1.323228140E-02-1.546833850E-02 --1.767283310E-02-1.984476860E-02-2.198315410E-02-2.408699130E-02-2.615527990E-02 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1.277995560E-01 1.318876150E-01 1.360456940E-01 1.402707990E-01 1.445599350E-01 - 1.489101050E-01 1.533183010E-01 1.577815410E-01 1.622462270E-01 1.666917200E-01 - 1.711351870E-01 1.755758230E-01 1.800128370E-01 1.844467670E-01 1.888775680E-01 - 1.933055370E-01 1.977307350E-01 2.021533100E-01 2.065733370E-01 2.109911290E-01 - 2.154066560E-01 2.198201270E-01 2.242316600E-01 2.286413160E-01 2.330491690E-01 - 2.374553530E-01 2.418597940E-01 2.462625500E-01 2.506637280E-01 2.550630870E-01 - 2.594605980E-01 2.638560830E-01 2.682491840E-01 2.726399600E-01 2.770278450E-01 - 2.814122140E-01 2.857929770E-01 2.901695670E-01 2.282808420E-01 2.260402590E-01 - 2.237808560E-01 2.215031830E-01 2.192075550E-01 2.168943290E-01 2.145638610E-01 - 2.122165110E-01 2.098525170E-01 2.074719970E-01 2.050750850E-01 2.026619610E-01 - 2.002327590E-01 1.977874490E-01 1.953261200E-01 1.928487720E-01 1.903554050E-01 - 1.878460050E-01 1.853205560E-01 1.827790140E-01 1.802212600E-01 1.776472330E-01 - 1.750568750E-01 1.724500810E-01 1.698266420E-01 1.671865730E-01 1.645295770E-01 - 1.618555930E-01 1.591645030E-01 1.564561720E-01 1.537304820E-01 1.509861650E-01 - 1.482276770E-01 1.454665960E-01 1.427035630E-01 1.399396660E-01 1.371763800E-01 - 1.344151200E-01 1.316516700E-01 1.288853880E-01 1.261166930E-01 1.233458220E-01 - 1.205730290E-01 1.177985440E-01 1.150226220E-01 1.122453960E-01 1.094672010E-01 - 1.066891030E-01 1.039110720E-01 1.011334960E-01 9.835676100E-02 9.558126330E-02 - 9.280739720E-02 9.003555030E-02 8.726613220E-02 8.449954540E-02 8.173617720E-02 - 7.897643000E-02 7.622071360E-02 7.346940790E-02 7.072290780E-02 6.798166780E-02 - 6.524612750E-02 6.251674150E-02 5.979401250E-02 5.707838390E-02 5.437044800E-02 - 5.167078970E-02 4.897999760E-02 4.629865290E-02 4.362735150E-02 4.096687590E-02 - 3.831782940E-02 3.568095710E-02 3.305704150E-02 3.044683670E-02 2.785111030E-02 - 2.527071720E-02 2.270643790E-02 2.015917190E-02 1.762981900E-02 1.511927320E-02 - 1.262843520E-02 1.015820070E-02 7.709537630E-03 5.283421840E-03 2.880765130E-03 - 5.025493450E-04-1.850230390E-03-4.176582210E-03-6.475514730E-03-8.746038190E-03 --1.098717470E-02-1.319792590E-02-1.537731380E-02-1.752431320E-02-1.963794050E-02 --2.171721680E-02-2.376115690E-02-2.576878850E-02-2.773914670E-02-2.967126110E-02 --3.156417980E-02-3.341695290E-02-3.522865470E-02-3.699836130E-02-3.872515260E-02 --4.040812330E-02-4.204637560E-02-4.363903780E-02-4.518523810E-02-4.668411610E-02 --4.813483730E-02-4.953657090E-02-5.088849740E-02-5.218981950E-02-5.343974010E-02 --5.463748430E-02-5.578231070E-02-5.687348170E-02-5.791025610E-02-5.889193340E-02 --5.981779100E-02-6.068718060E-02-6.149945780E-02-6.225397070E-02-6.295007470E-02 --6.358716640E-02-6.416468320E-02-6.468204410E-02-6.513871250E-02-6.553415950E-02 --6.586785610E-02-6.613934790E-02-6.634816530E-02-6.649386140E-02-6.657601890E-02 --6.659426540E-02-6.654820590E-02-6.643749770E-02-6.626181300E-02-6.602084640E-02 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6.505888700E-02 6.869410720E-02 7.235821340E-02 7.605040820E-02 7.977006580E-02 - 8.351656050E-02 8.728932590E-02 9.108785540E-02 9.491170940E-02 9.876055270E-02 - 1.026340650E-01 1.065324250E-01 1.104561460E-01 1.144053560E-01 1.183815450E-01 - 1.223862390E-01 1.264211090E-01 1.304820180E-01 1.345937700E-01 1.387747680E-01 - 1.430291680E-01 1.473489110E-01 1.517268720E-01 1.561598930E-01 1.606147890E-01 - 1.650560650E-01 1.694949570E-01 1.739318820E-01 1.783673020E-01 1.828007250E-01 - 1.872330610E-01 1.916643230E-01 1.960947810E-01 2.005246130E-01 2.049539830E-01 - 2.093831900E-01 2.138123960E-01 2.182418260E-01 2.226717320E-01 2.271023840E-01 - 2.315338550E-01 2.359663400E-01 2.403999570E-01 2.448349740E-01 2.492715420E-01 - 2.537096440E-01 2.581492660E-01 2.625908850E-01 2.670339940E-01 2.714787130E-01 - 2.759252190E-01 2.803731560E-01 2.848217190E-01 2.892716830E-01 2.937224210E-01 - 2.290661330E-01 2.268186510E-01 2.245524670E-01 2.222690730E-01 2.199686170E-01 - 2.176515460E-01 2.153181730E-01 2.129688260E-01 2.106036100E-01 2.082228360E-01 - 2.058265950E-01 2.034149620E-01 2.009880690E-01 1.985459630E-01 1.960886270E-01 - 1.936160920E-01 1.911283430E-01 1.886253360E-01 1.861070100E-01 1.835733210E-01 - 1.810241640E-01 1.784594360E-01 1.758791060E-01 1.732830110E-01 1.706710160E-01 - 1.680430020E-01 1.653988360E-01 1.627383680E-01 1.600614040E-01 1.573678110E-01 - 1.546574530E-01 1.519286190E-01 1.491861190E-01 1.464356780E-01 1.436834930E-01 - 1.409316660E-01 1.381815080E-01 1.354344790E-01 1.326859890E-01 1.299352650E-01 - 1.271826030E-01 1.244282650E-01 1.216726300E-01 1.189158110E-01 1.161576730E-01 - 1.133987830E-01 1.106395500E-01 1.078804210E-01 1.051217540E-01 1.023639220E-01 - 9.960729630E-02 9.685225780E-02 9.409919380E-02 9.134849910E-02 8.860056850E-02 - 8.585580440E-02 8.311460170E-02 8.037736270E-02 7.764448970E-02 7.491637020E-02 - 7.219339910E-02 6.947601590E-02 6.676464530E-02 6.405971940E-02 6.136177480E-02 - 5.867122110E-02 5.598861720E-02 5.331454050E-02 5.064957960E-02 4.799431190E-02 - 4.534931850E-02 4.271527010E-02 4.009286310E-02 3.748280560E-02 3.488583860E-02 - 3.230269630E-02 2.973411600E-02 2.718100700E-02 2.464407870E-02 2.212420110E-02 - 1.962226260E-02 1.713914980E-02 1.467575130E-02 1.223295280E-02 9.811678900E-03 - 7.412882520E-03 5.037506110E-03 2.686497990E-03 3.608108960E-04-1.938563660E-03 --4.210654650E-03-6.454473830E-03-8.669040170E-03-1.085337620E-02-1.300650460E-02 --1.512745490E-02-1.721523140E-02-1.926885360E-02-2.128735930E-02-2.326978000E-02 --2.521514710E-02-2.712253290E-02-2.899095420E-02-3.081948870E-02-3.260721640E-02 --3.435321520E-02-3.605657070E-02-3.771639240E-02-3.933177890E-02-4.090187330E-02 --4.242581130E-02-4.390273620E-02-4.533180590E-02-4.671220110E-02-4.804311320E-02 --4.932374510E-02-5.055331810E-02-5.173106490E-02-5.285623670E-02-5.392810330E-02 --5.494593080E-02-5.590900410E-02-5.681663750E-02-5.766818300E-02-5.846299600E-02 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1.172901880E-02 1.471638310E-02 1.774905440E-02 2.082596530E-02 2.394605240E-02 - 2.710825200E-02 3.031150440E-02 3.355478870E-02 3.683707120E-02 4.015724730E-02 - 4.351436720E-02 4.690748450E-02 5.033561960E-02 5.379778890E-02 5.729315430E-02 - 6.082078440E-02 6.437990070E-02 6.796972450E-02 7.158947740E-02 7.523842900E-02 - 7.891590890E-02 8.262128380E-02 8.635403220E-02 9.011364730E-02 9.389960770E-02 - 9.771161530E-02 1.015493420E-01 1.054127810E-01 1.093023870E-01 1.132186280E-01 - 1.171620860E-01 1.211348250E-01 1.251372840E-01 1.291737560E-01 1.332448120E-01 - 1.373772470E-01 1.415831890E-01 1.458642630E-01 1.502131070E-01 1.546224500E-01 - 1.590653660E-01 1.634951380E-01 1.679244040E-01 1.723532830E-01 1.767819970E-01 - 1.812107860E-01 1.856398580E-01 1.900696160E-01 1.945003120E-01 1.989322300E-01 - 2.033656390E-01 2.078008350E-01 2.122381480E-01 2.166778890E-01 2.211203280E-01 - 2.255657320E-01 2.300143990E-01 2.344668510E-01 2.389230730E-01 2.433833930E-01 - 2.478482870E-01 2.523179650E-01 2.567927540E-01 2.612726990E-01 2.657579780E-01 - 2.702489200E-01 2.747456130E-01 2.792482670E-01 2.837570910E-01 2.882719340E-01 - 2.927926480E-01 2.973189950E-01 2.298729720E-01 2.276153270E-01 2.253403960E-01 - 2.230492090E-01 2.207423000E-01 2.184199090E-01 2.160823350E-01 2.137298580E-01 - 2.113627340E-01 2.089810370E-01 2.065849750E-01 2.041744890E-01 2.017496820E-01 - 1.993106010E-01 1.968572590E-01 1.943895520E-01 1.919075250E-01 1.894110740E-01 - 1.869000790E-01 1.843745560E-01 1.818343700E-01 1.792793870E-01 1.767095180E-01 - 1.741245840E-01 1.715244800E-01 1.689091030E-01 1.662782730E-01 1.636318270E-01 - 1.609696300E-01 1.582914890E-01 1.555971210E-01 1.528849150E-01 1.501587630E-01 - 1.474231780E-01 1.446827200E-01 1.419419350E-01 1.392053070E-01 1.364736110E-01 - 1.337406340E-01 1.310056150E-01 1.282696430E-01 1.255327610E-01 1.227949110E-01 - 1.200560700E-01 1.173166190E-01 1.145768690E-01 1.118371560E-01 1.090979050E-01 - 1.063594740E-01 1.036222430E-01 1.008865680E-01 9.815284610E-02 9.542144830E-02 - 9.269277010E-02 8.996719120E-02 8.724512900E-02 8.452697100E-02 8.181311940E-02 - 7.910397650E-02 7.639992980E-02 7.370136680E-02 7.100872700E-02 6.832243500E-02 - 6.564292310E-02 6.297065320E-02 6.030609830E-02 5.764978750E-02 5.500226100E-02 - 5.236407370E-02 4.973581430E-02 4.711806030E-02 4.451147470E-02 4.191668700E-02 - 3.933442760E-02 3.676542270E-02 3.421038390E-02 3.167003770E-02 2.914518680E-02 - 2.663664890E-02 2.414524930E-02 2.167181110E-02 1.921715960E-02 1.678225210E-02 - 1.436793990E-02 1.197513380E-02 9.604758580E-03 7.257740940E-03 4.935005210E-03 - 2.637501810E-03 3.662202800E-04-1.877911850E-03-4.093922670E-03-6.280840370E-03 --8.437692190E-03-1.056350670E-02-1.265732290E-02-1.471816840E-02-1.674507370E-02 --1.873707400E-02-2.069322020E-02-2.261256800E-02-2.449415810E-02-2.633703870E-02 --2.814030830E-02-2.990305420E-02-3.162435440E-02-3.330329430E-02-3.493898360E-02 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1.752586220E-01 1.796778440E-01 1.840989440E-01 1.885223390E-01 1.929482220E-01 - 1.973770860E-01 2.018091830E-01 2.062448560E-01 2.106845830E-01 2.151286010E-01 - 2.195774610E-01 2.240314630E-01 2.284910080E-01 2.329565730E-01 2.374285460E-01 - 2.419073580E-01 2.463933830E-01 2.508870360E-01 2.553886470E-01 2.598989900E-01 - 2.644178870E-01 2.689462600E-01 2.734844680E-01 2.780328390E-01 2.825915810E-01 - 2.871609630E-01 2.917411920E-01 2.963329850E-01 3.009361330E-01 2.306960670E-01 - 2.284251000E-01 2.261389940E-01 2.238382250E-01 2.215231810E-01 2.191941140E-01 - 2.168513690E-01 2.144950780E-01 2.121254500E-01 2.097424420E-01 2.073461260E-01 - 2.049365940E-01 2.025138740E-01 2.000778470E-01 1.976285430E-01 1.951658580E-01 - 1.926897320E-01 1.902000900E-01 1.876968440E-01 1.851798590E-01 1.826490160E-01 - 1.801041810E-01 1.775452350E-01 1.749720420E-01 1.723844410E-01 1.697822810E-01 - 1.671653690E-01 1.645335560E-01 1.618866320E-01 1.592244510E-01 1.565475020E-01 - 1.538532970E-01 1.511435660E-01 1.484228670E-01 1.456965210E-01 1.429693400E-01 - 1.402461680E-01 1.375277040E-01 1.348106560E-01 1.320933700E-01 1.293752790E-01 - 1.266565470E-01 1.239371450E-01 1.212173250E-01 1.184973720E-01 1.157775450E-01 - 1.130581720E-01 1.103396270E-01 1.076222730E-01 1.049064840E-01 1.021926250E-01 - 9.948106110E-02 9.677218650E-02 9.406638150E-02 9.136402610E-02 8.866553010E-02 - 8.597128090E-02 8.328168090E-02 8.059711750E-02 7.791802290E-02 7.524476200E-02 - 7.257774470E-02 6.991740320E-02 6.726416950E-02 6.461849810E-02 6.198083240E-02 - 5.935169380E-02 5.673162640E-02 5.412117020E-02 5.152086910E-02 4.893130440E-02 - 4.635314270E-02 4.378696530E-02 4.123348740E-02 3.869340570E-02 3.616742790E-02 - 3.365625440E-02 3.116067310E-02 2.868150920E-02 2.621958030E-02 2.377568560E-02 - 2.135061290E-02 1.894521150E-02 1.656042410E-02 1.419710830E-02 1.185618710E-02 - 9.538580660E-03 7.245191370E-03 4.976934290E-03 2.734769600E-03 5.196400450E-04 --1.667499080E-03-3.825692460E-03-5.953985270E-03-8.051462470E-03-1.011709030E-02 --1.214994490E-02-1.414908190E-02-1.611355320E-02-1.804240790E-02-1.993470080E-02 --2.178948930E-02-2.360584590E-02-2.538286710E-02-2.711964580E-02-2.881527130E-02 --3.046881780E-02-3.207943220E-02-3.364622970E-02-3.516835720E-02-3.664496910E-02 --3.807521980E-02-3.945828970E-02-4.079336670E-02-4.207965730E-02-4.331636060E-02 --4.450273890E-02-4.563800250E-02-4.672142490E-02-4.775228720E-02-4.872987790E-02 --4.965350400E-02-5.052249130E-02-5.133618790E-02-5.209395290E-02-5.279515310E-02 --5.343918500E-02-5.402547120E-02-5.455344170E-02-5.502254140E-02-5.543224510E-02 --5.578204240E-02-5.607146020E-02-5.630002920E-02-5.646728720E-02-5.657280980E-02 --5.661620940E-02-5.659711730E-02-5.651517960E-02-5.637004970E-02-5.616142970E-02 --5.588902530E-02-5.555259060E-02-5.515189840E-02-5.468674000E-02-5.415694420E-02 --5.356231700E-02-5.290274690E-02-5.217817800E-02-5.138855800E-02-5.053383110E-02 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1.073424590E-01 1.111841280E-01 1.150544290E-01 1.189546660E-01 1.228866430E-01 - 1.268520060E-01 1.308553960E-01 1.349041460E-01 1.390046630E-01 1.431855260E-01 - 1.474539040E-01 1.517999320E-01 1.561945080E-01 1.605992170E-01 1.649964000E-01 - 1.693960730E-01 1.737984120E-01 1.782036420E-01 1.826119720E-01 1.870240270E-01 - 1.914401800E-01 1.958607440E-01 2.002861500E-01 2.047168460E-01 2.091532500E-01 - 2.135958080E-01 2.180449960E-01 2.225013080E-01 2.269652190E-01 2.314372060E-01 - 2.359177620E-01 2.404074370E-01 2.449070810E-01 2.494169030E-01 2.539374230E-01 - 2.584694330E-01 2.630136310E-01 2.675703760E-01 2.721403240E-01 2.767239510E-01 - 2.813221220E-01 2.859351040E-01 2.905639710E-01 2.952091690E-01 2.998711170E-01 - 3.045502600E-01 2.315284160E-01 2.292412220E-01 2.269415710E-01 2.246296410E-01 - 2.223051790E-01 2.199684830E-01 2.176198210E-01 2.152591940E-01 2.128865870E-01 - 2.105020730E-01 2.081055340E-01 2.056969400E-01 2.032763660E-01 2.008435880E-01 - 1.983985600E-01 1.959412100E-01 1.934713720E-01 1.909889730E-01 1.884938780E-01 - 1.859859230E-01 1.834649740E-01 1.809308830E-01 1.783834840E-01 1.758226160E-01 - 1.732481120E-01 1.706597950E-01 1.680574860E-01 1.654409920E-01 1.628101470E-01 - 1.601647880E-01 1.575050950E-01 1.548296210E-01 1.521383370E-01 1.494340150E-01 - 1.467226150E-01 1.440099780E-01 1.413023920E-01 1.385984270E-01 1.358970110E-01 - 1.331970240E-01 1.304973960E-01 1.277975590E-01 1.250976030E-01 1.223976690E-01 - 1.196980030E-01 1.169988890E-01 1.143006610E-01 1.116036400E-01 1.089081990E-01 - 1.062146950E-01 1.035234780E-01 1.008349360E-01 9.814944120E-02 9.546735140E-02 - 9.278906880E-02 9.011498840E-02 8.744550500E-02 8.478101340E-02 8.212191610E-02 - 7.946860790E-02 7.682148370E-02 7.418094580E-02 7.154743370E-02 6.892134250E-02 - 6.630311910E-02 6.369324030E-02 6.109217930E-02 5.850045010E-02 5.591859670E-02 - 5.334714800E-02 5.078668890E-02 4.823783040E-02 4.570119830E-02 4.317743330E-02 - 4.066722100E-02 3.817130630E-02 3.569027410E-02 3.322494030E-02 3.077612260E-02 - 2.834460510E-02 2.593118320E-02 2.353664490E-02 2.116178350E-02 1.880754530E-02 - 1.647474240E-02 1.416429230E-02 1.187709810E-02 9.614050390E-03 7.376051510E-03 - 5.164029540E-03 2.978917680E-03 8.216666760E-04-1.306786550E-03-3.405511840E-03 --5.473565780E-03-7.509998510E-03-9.513871740E-03-1.148425040E-02-1.342019160E-02 --1.532075460E-02-1.718499510E-02-1.901201160E-02-2.080087360E-02-2.255067600E-02 --2.426051720E-02-2.592949380E-02-2.755670810E-02-2.914132740E-02-3.068245020E-02 --3.217923270E-02-3.363084050E-02-3.503643720E-02-3.639519960E-02-3.770633410E-02 --3.896904740E-02-4.018256070E-02-4.134609920E-02-4.245892540E-02-4.352031650E-02 --4.452955720E-02-4.548592490E-02-4.638874530E-02-4.723735900E-02-4.803110290E-02 --4.876933990E-02-4.945145550E-02-5.007684980E-02-5.064494910E-02-5.115519460E-02 --5.160704630E-02-5.199997130E-02-5.233347040E-02-5.260707440E-02-5.282031370E-02 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4.979266970E-02 5.309497570E-02 5.643313750E-02 5.980629470E-02 6.321366130E-02 - 6.665448840E-02 7.012806090E-02 7.363367830E-02 7.717075200E-02 8.073870840E-02 - 8.433666830E-02 8.796430380E-02 9.162130210E-02 9.530735760E-02 9.902209790E-02 - 1.027651350E-01 1.065364700E-01 1.103370710E-01 1.141666100E-01 1.180267260E-01 - 1.219190960E-01 1.258455370E-01 1.298090220E-01 1.338148270E-01 1.378696110E-01 - 1.419985150E-01 1.462296990E-01 1.505273580E-01 1.548746530E-01 1.592568460E-01 - 1.636478450E-01 1.680254490E-01 1.724050790E-01 1.767896710E-01 1.811810430E-01 - 1.855770050E-01 1.899782270E-01 1.943853350E-01 1.987990140E-01 2.032193090E-01 - 2.076467280E-01 2.120819090E-01 2.165253910E-01 2.209777380E-01 2.254393850E-01 - 2.299109700E-01 2.343931500E-01 2.388866250E-01 2.433919310E-01 2.479098290E-01 - 2.524410490E-01 2.569862900E-01 2.615462840E-01 2.661217450E-01 2.707134490E-01 - 2.753222290E-01 2.799490690E-01 2.845948640E-01 2.892600300E-01 2.939458790E-01 - 2.986529770E-01 3.033826350E-01 3.081356880E-01 2.323571440E-01 2.300530670E-01 - 2.277390660E-01 2.254147830E-01 2.230804710E-01 2.207359970E-01 2.183811960E-01 - 2.160161440E-01 2.136406750E-01 2.112546860E-01 2.088581320E-01 2.064508650E-01 - 2.040326740E-01 2.016035470E-01 1.991632580E-01 1.967117190E-01 1.942487210E-01 - 1.917741300E-01 1.892877670E-01 1.867894980E-01 1.842790990E-01 1.817563920E-01 - 1.792212130E-01 1.766733830E-01 1.741126780E-01 1.715389340E-01 1.689519580E-01 - 1.663515270E-01 1.637374910E-01 1.611096410E-01 1.584677700E-01 1.558117120E-01 - 1.531398150E-01 1.504550430E-01 1.477599290E-01 1.450623720E-01 1.423695390E-01 - 1.396813390E-01 1.369967460E-01 1.343147610E-01 1.316341010E-01 1.289539490E-01 - 1.262742130E-01 1.235949620E-01 1.209164260E-01 1.182388740E-01 1.155626180E-01 - 1.128879710E-01 1.102152690E-01 1.075448840E-01 1.048771660E-01 1.022124810E-01 - 9.955120090E-02 9.689369050E-02 9.424033020E-02 9.159151460E-02 8.894763890E-02 - 8.630909770E-02 8.367628600E-02 8.104961370E-02 7.842946800E-02 7.581625130E-02 - 7.321038840E-02 7.061228160E-02 6.802237030E-02 6.544109430E-02 6.286896020E-02 - 6.030643730E-02 5.775405090E-02 5.521234120E-02 5.268184840E-02 5.016317960E-02 - 4.765696080E-02 4.516381030E-02 4.268436880E-02 4.021935160E-02 3.776944800E-02 - 3.533533220E-02 3.291779010E-02 3.051761170E-02 2.813558650E-02 2.577250820E-02 - 2.342916650E-02 2.110640890E-02 1.880510150E-02 1.652610120E-02 1.427029260E-02 - 1.203855590E-02 9.831789880E-03 7.650914140E-03 5.496819970E-03 3.370435680E-03 - 1.272691180E-03-7.954851610E-04-2.833160570E-03-4.839422650E-03-6.813344080E-03 --8.753991690E-03-1.066042390E-02-1.253171450E-02-1.436695550E-02-1.616523410E-02 --1.792564800E-02-1.964729650E-02-2.132928370E-02-2.297071180E-02-2.457070910E-02 --2.612841500E-02-2.764297840E-02-2.911355160E-02-3.053929280E-02-3.191937880E-02 --3.325300290E-02-3.453937550E-02-3.577770670E-02-3.696723650E-02-3.810718280E-02 --3.919683020E-02-4.023545980E-02-4.122234140E-02-4.215678200E-02-4.303810370E-02 --4.386564720E-02-4.463877530E-02-4.535685110E-02-4.601926730E-02-4.662542420E-02 --4.717476670E-02-4.766674340E-02-4.810080300E-02-4.847643520E-02-4.879314450E-02 --4.905044290E-02-4.924790930E-02-4.938511180E-02-4.946162180E-02-4.947705570E-02 --4.943104090E-02-4.932324960E-02-4.915335770E-02-4.892108590E-02-4.862615090E-02 --4.826830330E-02-4.784735290E-02-4.736310240E-02-4.681535440E-02-4.620397840E-02 --4.552889620E-02-4.478998110E-02-4.398719970E-02-4.312053320E-02-4.218998550E-02 --4.119556400E-02-4.013739150E-02-3.901543840E-02-3.782989460E-02-3.658094630E-02 --3.526879100E-02-3.389363740E-02-3.245569770E-02-3.095521030E-02-2.939260190E-02 --2.776817230E-02-2.608231830E-02-2.433545700E-02-2.252802440E-02-2.066051210E-02 --1.873344000E-02-1.674737600E-02-1.470288170E-02-1.260058020E-02-1.044111330E-02 --8.225141090E-03-5.953404590E-03-3.626647870E-03-1.245612510E-03 1.188945960E-03 - 3.676164200E-03 6.215223110E-03 8.805271240E-03 1.144543100E-02 1.413481780E-02 - 1.687252890E-02 1.965763230E-02 2.248921800E-02 2.536636220E-02 2.828809620E-02 - 3.125350180E-02 3.426168860E-02 3.731174020E-02 4.040271420E-02 4.353366790E-02 - 4.670372980E-02 4.991205410E-02 5.315777290E-02 5.644008520E-02 5.975818260E-02 - 6.311126800E-02 6.649863720E-02 6.991953400E-02 7.337331030E-02 7.685935500E-02 - 8.037703480E-02 8.392588050E-02 8.750513940E-02 9.111449120E-02 9.475362300E-02 - 9.842220690E-02 1.021200420E-01 1.058472540E-01 1.096039710E-01 1.133905570E-01 - 1.172078850E-01 1.210580100E-01 1.249427570E-01 1.288641240E-01 1.328245850E-01 - 1.368362900E-01 1.409176290E-01 1.450813410E-01 1.493432220E-01 1.536577340E-01 - 1.580036580E-01 1.623641850E-01 1.667224620E-01 1.710736160E-01 1.754360350E-01 - 1.798071120E-01 1.841835530E-01 1.885657760E-01 1.929546150E-01 1.973508750E-01 - 2.017554190E-01 2.061683680E-01 2.105904220E-01 2.150221470E-01 2.194640930E-01 - 2.239170670E-01 2.283816340E-01 2.328584640E-01 2.373481690E-01 2.418519110E-01 - 2.463701220E-01 2.509036660E-01 2.554533780E-01 2.600199580E-01 2.646045980E-01 - 2.692084010E-01 2.738319340E-01 2.784764170E-01 2.831428950E-01 2.878324090E-01 - 2.925461230E-01 2.972853180E-01 3.020512760E-01 3.068451880E-01 3.116682470E-01 - 2.331709270E-01 2.308497130E-01 2.285216450E-01 2.261854710E-01 2.238413100E-01 - 2.214891020E-01 2.191285640E-01 2.167593840E-01 2.143815900E-01 2.119947220E-01 - 2.095986310E-01 2.071931510E-01 2.047780900E-01 2.023532390E-01 1.999184190E-01 - 1.974733620E-01 1.950179190E-01 1.925518960E-01 1.900750550E-01 1.875871870E-01 - 1.850880530E-01 1.825775210E-01 1.800553500E-01 1.775213480E-01 1.749752760E-01 - 1.724169250E-01 1.698460730E-01 1.672625540E-01 1.646661010E-01 1.620565060E-01 - 1.594335440E-01 1.567976470E-01 1.541466120E-01 1.514815840E-01 1.488058570E-01 - 1.461245720E-01 1.434473990E-01 1.407751290E-01 1.381078360E-01 1.354446560E-01 - 1.327833980E-01 1.301236000E-01 1.274649800E-01 1.248072160E-01 1.221506220E-01 - 1.194954960E-01 1.168420540E-01 1.141906160E-01 1.115415100E-01 1.088950930E-01 - 1.062517090E-01 1.036117230E-01 1.009754990E-01 9.834340210E-02 9.571580590E-02 - 9.309309720E-02 9.047566350E-02 8.786389230E-02 8.525819330E-02 8.265897630E-02 - 8.006662880E-02 7.748155300E-02 7.490415130E-02 7.233484090E-02 6.977405400E-02 - 6.722220780E-02 6.467980150E-02 6.214731930E-02 5.962524190E-02 5.711409450E-02 - 5.461442840E-02 5.212681000E-02 4.965184630E-02 4.719015210E-02 4.474235330E-02 - 4.230911660E-02 3.989113490E-02 3.748911620E-02 3.510376810E-02 3.273585810E-02 - 3.038614620E-02 2.805542570E-02 2.574449220E-02 2.345415020E-02 2.118522860E-02 - 1.893858800E-02 1.671510560E-02 1.451563930E-02 1.234105510E-02 1.019224710E-02 - 8.070097300E-03 5.975535610E-03 3.909449560E-03 1.872759890E-03-1.336163990E-04 --2.108768560E-03-4.051783120E-03-5.961732010E-03-7.837733250E-03-9.678839710E-03 --1.148415730E-02-1.325279470E-02-1.498385800E-02-1.667645010E-02-1.832967620E-02 --1.994267850E-02-2.151457590E-02-2.304451910E-02-2.453166620E-02-2.597517520E-02 --2.737421910E-02-2.872798590E-02-3.003567460E-02-3.129650280E-02-3.250968080E-02 --3.367444870E-02-3.479006890E-02-3.585581110E-02-3.687095270E-02-3.783476350E-02 --3.874660660E-02-3.960577030E-02-4.041161020E-02-4.116350040E-02-4.186081510E-02 --4.250293970E-02-4.308930040E-02-4.361933840E-02-4.409250240E-02-4.450826350E-02 --4.486610370E-02-4.516554250E-02-4.540611800E-02-4.558739440E-02-4.570894320E-02 --4.577032850E-02-4.577123000E-02-4.571123790E-02-4.559002820E-02-4.540731760E-02 --4.516281560E-02-4.485623170E-02-4.448736090E-02-4.405596480E-02-4.356187580E-02 --4.300494120E-02-4.238501560E-02-4.170199480E-02-4.095580060E-02-4.014640300E-02 --3.927378360E-02-3.833793480E-02-3.733890880E-02-3.627677630E-02-3.515155610E-02 --3.396341950E-02-3.271258990E-02-3.139928360E-02-3.002370340E-02-2.858606350E-02 --2.708658950E-02-2.552569470E-02-2.390372010E-02-2.222106420E-02-2.047813870E-02 --1.867537950E-02-1.681328380E-02-1.489237140E-02-1.291320570E-02-1.087635760E-02 --8.782429620E-03-6.632076110E-03-4.425947550E-03-2.164769450E-03 1.507260460E-04 - 2.519796140E-03 4.941691180E-03 7.415587550E-03 9.940666150E-03 1.251609060E-02 - 1.514101490E-02 1.781455430E-02 2.053586580E-02 2.330401730E-02 2.611811270E-02 - 2.897727860E-02 3.188062460E-02 3.482722120E-02 3.781620040E-02 4.084666820E-02 - 4.391771550E-02 4.702850800E-02 5.017820370E-02 5.336595700E-02 5.659099300E-02 - 5.985251810E-02 6.314973530E-02 6.648195530E-02 6.984847040E-02 7.324861740E-02 - 7.668177780E-02 8.014734090E-02 8.364474770E-02 8.717364820E-02 9.073349830E-02 - 9.432347860E-02 9.794361890E-02 1.015939560E-01 1.052745580E-01 1.089854690E-01 - 1.127267410E-01 1.164993270E-01 1.203046810E-01 1.241447110E-01 1.280220150E-01 - 1.319376980E-01 1.359050570E-01 1.399387270E-01 1.440457850E-01 1.482409240E-01 - 1.525211930E-01 1.568343940E-01 1.611608120E-01 1.654867230E-01 1.698178500E-01 - 1.741545950E-01 1.784975530E-01 1.828479470E-01 1.872059700E-01 1.915716230E-01 - 1.959457840E-01 2.003292740E-01 2.047224790E-01 2.091257870E-01 2.135400180E-01 - 2.179657220E-01 2.224035710E-01 2.268544140E-01 2.313191000E-01 2.357981060E-01 - 2.402924450E-01 2.448030110E-01 2.493305500E-01 2.538762690E-01 2.584409420E-01 - 2.630254630E-01 2.676310840E-01 2.722590860E-01 2.769102450E-01 2.815861700E-01 - 2.862876060E-01 2.910164000E-01 2.957742210E-01 3.005618160E-01 3.053812090E-01 - 3.102337420E-01 3.151213230E-01 2.339567990E-01 2.316196410E-01 2.292777750E-01 - 2.269308420E-01 2.245783210E-01 2.222196760E-01 2.198543700E-01 2.174822090E-01 - 2.151029260E-01 2.127161920E-01 2.103215460E-01 2.079188380E-01 2.055079040E-01 - 2.030882690E-01 2.006597520E-01 1.982221310E-01 1.957751360E-01 1.933185160E-01 - 1.908520310E-01 1.883754880E-01 1.858886330E-01 1.833911690E-01 1.808829160E-01 - 1.783636360E-01 1.758330610E-01 1.732909980E-01 1.707371920E-01 1.681714360E-01 - 1.655934900E-01 1.630030870E-01 1.604000480E-01 1.577845220E-01 1.551552560E-01 - 1.525123860E-01 1.498572230E-01 1.471938040E-01 1.445332320E-01 1.418781880E-01 - 1.392285230E-01 1.365843860E-01 1.339434680E-01 1.313047110E-01 1.286678310E-01 - 1.260325760E-01 1.233987140E-01 1.207668040E-01 1.181370170E-01 1.155096290E-01 - 1.128849690E-01 1.102633480E-01 1.076451540E-01 1.050307010E-01 1.024203670E-01 - 9.981451180E-02 9.721351410E-02 9.461772440E-02 9.202755990E-02 8.944339310E-02 - 8.686562630E-02 8.429466930E-02 8.173090960E-02 7.917474960E-02 7.662660630E-02 - 7.408688960E-02 7.155600940E-02 6.903440510E-02 6.652253120E-02 6.402085720E-02 - 6.152988230E-02 5.905009430E-02 5.658203740E-02 5.412626640E-02 5.168337750E-02 - 4.925395920E-02 4.683862630E-02 4.443801940E-02 4.205281290E-02 3.968369960E-02 - 3.733138000E-02 3.499658030E-02 3.268005700E-02 3.038256990E-02 2.810488830E-02 - 2.584783170E-02 2.361219750E-02 2.139880880E-02 1.920852440E-02 1.704219170E-02 - 1.490066110E-02 1.278481450E-02 1.069553380E-02 8.633687160E-03 6.600151770E-03 - 4.595870150E-03 2.621704950E-03 6.785609880E-04-1.232653970E-03-3.111051630E-03 --4.955699670E-03-6.765732540E-03-8.540259670E-03-1.027838700E-02-1.197922230E-02 --1.364187340E-02-1.526550860E-02-1.684922350E-02-1.839217360E-02-1.989352700E-02 --2.135244570E-02-2.276809330E-02-2.413964460E-02-2.546631360E-02-2.674728820E-02 --2.798179350E-02-2.916907520E-02-3.030837890E-02-3.139895950E-02-3.244009240E-02 --3.343105690E-02-3.437116370E-02-3.525973110E-02-3.609609980E-02-3.687963630E-02 --3.760969270E-02-3.828566890E-02-3.890695420E-02-3.947297110E-02-3.998316450E-02 --4.043701290E-02-4.083400220E-02-4.117360710E-02-4.145535080E-02-4.167877880E-02 --4.184345530E-02-4.194897040E-02-4.199491810E-02-4.198092590E-02-4.190663620E-02 --4.177174720E-02-4.157596080E-02-4.131898660E-02-4.100055620E-02-4.062044250E-02 --4.017844800E-02-3.967440870E-02-3.910818320E-02-3.847961870E-02-3.778862580E-02 --3.703512250E-02-3.621909020E-02-3.534052890E-02-3.439943860E-02-3.339585660E-02 --3.232984240E-02-3.120152470E-02-3.001103180E-02-2.875856310E-02-2.744433660E-02 --2.606857380E-02-2.463147980E-02-2.313328350E-02-2.157446930E-02-1.995531660E-02 --1.827623700E-02-1.653766630E-02-1.474004430E-02-1.288383830E-02-1.096958110E-02 --8.997821250E-03-6.969149220E-03-4.884167570E-03-2.743506570E-03-5.478194220E-04 - 1.702183510E-03 4.005774390E-03 6.362228190E-03 8.770818820E-03 1.123071090E-02 - 1.374111140E-02 1.630120720E-02 1.891016770E-02 2.156716030E-02 2.427131680E-02 - 2.702178990E-02 2.981770040E-02 3.265817460E-02 3.554234280E-02 3.846936670E-02 - 4.143835600E-02 4.444849120E-02 4.749892650E-02 5.058882010E-02 5.371737110E-02 - 5.688380450E-02 6.008737160E-02 6.332730500E-02 6.660290810E-02 6.991346930E-02 - 7.325837760E-02 7.663698490E-02 8.004874740E-02 8.349308370E-02 8.696949480E-02 - 9.047758580E-02 9.401679040E-02 9.758669880E-02 1.011873930E-01 1.048190000E-01 - 1.084816160E-01 1.121753530E-01 1.159008000E-01 1.196597220E-01 1.234524320E-01 - 1.272826050E-01 1.311538070E-01 1.350670610E-01 1.390455510E-01 1.431040760E-01 - 1.472446770E-01 1.514693500E-01 1.557568460E-01 1.600421970E-01 1.643343120E-01 - 1.686333120E-01 1.729394050E-01 1.772526950E-01 1.815735700E-01 1.859027450E-01 - 1.902407410E-01 1.945881550E-01 1.989455970E-01 2.033137980E-01 2.076929960E-01 - 2.120840250E-01 2.164876010E-01 2.209044550E-01 2.253354190E-01 2.297812400E-01 - 2.342427220E-01 2.387207000E-01 2.432160970E-01 2.477298530E-01 2.522631590E-01 - 2.568171320E-01 2.613925340E-01 2.659905850E-01 2.706126870E-01 2.752600610E-01 - 2.799341080E-01 2.846360800E-01 2.893676160E-01 2.941303250E-01 2.989257870E-01 - 3.037555220E-01 3.086213470E-01 3.135255280E-01 3.184702990E-01 2.347000240E-01 - 2.323503490E-01 2.299981120E-01 2.276427890E-01 2.252836080E-01 2.229201050E-01 - 2.205518480E-01 2.181783320E-01 2.157990340E-01 2.134136110E-01 2.110217210E-01 - 2.086230070E-01 2.062172000E-01 2.038039270E-01 2.013828900E-01 1.989537920E-01 - 1.965163350E-01 1.940702650E-01 1.916152980E-01 1.891510930E-01 1.866774560E-01 - 1.841941180E-01 1.817008110E-01 1.791972520E-01 1.766832020E-01 1.741584090E-01 - 1.716226340E-01 1.690756380E-01 1.665171530E-01 1.639469410E-01 1.613647790E-01 - 1.587705310E-01 1.561629470E-01 1.535429810E-01 1.509115100E-01 1.482687890E-01 - 1.456259040E-01 1.429884730E-01 1.403571220E-01 1.377320590E-01 1.351122260E-01 - 1.324952540E-01 1.298808750E-01 1.272687910E-01 1.246587930E-01 1.220508890E-01 - 1.194455770E-01 1.168430820E-01 1.142436940E-01 1.116477330E-01 1.090555490E-01 - 1.064674710E-01 1.038838550E-01 1.013050680E-01 9.873146560E-02 9.616342930E-02 - 9.360134600E-02 9.104558830E-02 8.849654350E-02 8.595462890E-02 8.342023940E-02 - 8.089378480E-02 7.837568220E-02 7.586631920E-02 7.336609070E-02 7.087545840E-02 - 6.839486960E-02 6.592479350E-02 6.346567720E-02 6.101800500E-02 5.858234320E-02 - 5.615919830E-02 5.374913660E-02 5.135276910E-02 4.897069190E-02 4.660350460E-02 - 4.425186290E-02 4.191644490E-02 3.959793970E-02 3.729703650E-02 3.501449530E-02 - 3.275107220E-02 3.050750120E-02 2.828453850E-02 2.608301120E-02 2.390372750E-02 - 2.174748480E-02 1.961512490E-02 1.750748980E-02 1.542544640E-02 1.336986390E-02 - 1.134158670E-02 9.341482070E-03 7.370444480E-03 5.429345180E-03 3.519062420E-03 - 1.640494910E-03-2.054705690E-04-2.017946910E-03-3.796069180E-03-5.538962780E-03 --7.245740390E-03-8.915510960E-03-1.054742370E-02-1.214061680E-02-1.369424910E-02 --1.520747130E-02-1.667944900E-02-1.810934770E-02-1.949634590E-02-2.083965390E-02 --2.213846520E-02-2.339198630E-02-2.459946650E-02-2.576015700E-02-2.687330360E-02 --2.793815360E-02-2.895398810E-02-2.992013660E-02-3.083588740E-02-3.170058880E-02 --3.251358120E-02-3.327421840E-02-3.398187460E-02-3.463596850E-02-3.523587060E-02 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3.926806900E-02 4.217477140E-02 4.512308910E-02 4.811222850E-02 5.114132170E-02 - 5.420960490E-02 5.731632190E-02 6.046072390E-02 6.364209200E-02 6.685973700E-02 - 7.011296600E-02 7.340116800E-02 7.672370970E-02 8.008002490E-02 8.346960690E-02 - 8.689187470E-02 9.034642580E-02 9.383288030E-02 9.735084330E-02 1.009001430E-01 - 1.044807580E-01 1.080928000E-01 1.117367820E-01 1.154132560E-01 1.191235860E-01 - 1.228676660E-01 1.266490220E-01 1.304726300E-01 1.343428490E-01 1.382578160E-01 - 1.422552170E-01 1.463489530E-01 1.505219190E-01 1.547555480E-01 1.590072210E-01 - 1.632637680E-01 1.675272140E-01 1.717982590E-01 1.760772170E-01 1.803645490E-01 - 1.846609260E-01 1.889668110E-01 1.932827980E-01 1.976094840E-01 2.019474210E-01 - 2.062973380E-01 2.106599510E-01 2.150359150E-01 2.194260060E-01 2.238309380E-01 - 2.282515320E-01 2.326887400E-01 2.371434570E-01 2.416166660E-01 2.461093220E-01 - 2.506224220E-01 2.551570530E-01 2.597145140E-01 2.642961140E-01 2.689030470E-01 - 2.735364740E-01 2.781978250E-01 2.828890680E-01 2.876116930E-01 2.923667430E-01 - 2.971563040E-01 3.019826110E-01 3.068473640E-01 3.117523190E-01 3.167003690E-01 - 3.216933310E-01 2.353924660E-01 2.330334780E-01 2.306739540E-01 2.283129250E-01 - 2.259496750E-01 2.235836680E-01 2.212143840E-01 2.188411800E-01 2.164636250E-01 - 2.140813020E-01 2.116937940E-01 2.093006520E-01 2.069014460E-01 2.044959370E-01 - 2.020837520E-01 1.996644880E-01 1.972378640E-01 1.948035510E-01 1.923612360E-01 - 1.899106350E-01 1.874514520E-01 1.849833580E-01 1.825060990E-01 1.800193940E-01 - 1.775229570E-01 1.750165220E-01 1.724998500E-01 1.699726430E-01 1.674346480E-01 - 1.648855810E-01 1.623252480E-01 1.597535610E-01 1.571694310E-01 1.545734550E-01 - 1.519656630E-01 1.493461580E-01 1.467234340E-01 1.441043170E-01 1.414917260E-01 - 1.388865710E-01 1.362881810E-01 1.336937550E-01 1.311025170E-01 1.285142150E-01 - 1.259287150E-01 1.233458220E-01 1.207658420E-01 1.181890820E-01 1.156158000E-01 - 1.130463260E-01 1.104809870E-01 1.079201250E-01 1.053640540E-01 1.028131400E-01 - 1.002677600E-01 9.772827480E-02 9.519506250E-02 9.266848860E-02 9.014894810E-02 - 8.763685820E-02 8.513261380E-02 8.263661710E-02 8.014928550E-02 7.767101380E-02 - 7.520219680E-02 7.274327430E-02 7.029470060E-02 6.785691530E-02 6.543038040E-02 - 6.301556530E-02 6.061300260E-02 5.822322890E-02 5.584675070E-02 5.348414930E-02 - 5.113603550E-02 4.880301280E-02 4.648568480E-02 4.418469970E-02 4.190077630E-02 - 3.963456300E-02 3.738677500E-02 3.515814990E-02 3.294942160E-02 3.076134620E-02 - 2.859470250E-02 2.645027820E-02 2.432887070E-02 2.223130690E-02 2.015838030E-02 - 1.811094770E-02 1.608985290E-02 1.409593690E-02 1.213005190E-02 1.019305830E-02 - 8.285826070E-03 6.409224590E-03 4.564112050E-03 2.751366930E-03 9.718538490E-04 --7.735613620E-04-2.484014490E-03-4.158619790E-03-5.796554960E-03-7.396944330E-03 --8.958949710E-03-1.048173290E-02-1.196445520E-02-1.340629720E-02-1.480643260E-02 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1.064714280E-03 3.130167720E-03 5.249745210E-03 7.422793660E-03 9.648636910E-03 - 1.192660260E-02 1.425594460E-02 1.663597670E-02 1.906592960E-02 2.154503020E-02 - 2.407250180E-02 2.664757520E-02 2.926947180E-02 3.193732720E-02 3.465037420E-02 - 3.740785640E-02 4.020889480E-02 4.305270310E-02 4.593849930E-02 4.886550080E-02 - 5.183293300E-02 5.484003200E-02 5.788606030E-02 6.097025420E-02 6.409196560E-02 - 6.725050510E-02 7.044518740E-02 7.367539410E-02 7.694053650E-02 8.024002610E-02 - 8.357333390E-02 8.693999800E-02 9.033952650E-02 9.377156200E-02 9.723576900E-02 - 1.007318120E-01 1.042596620E-01 1.078194310E-01 1.114116390E-01 1.150367860E-01 - 1.186962720E-01 1.223904560E-01 1.261209990E-01 1.298927370E-01 1.337104890E-01 - 1.375762080E-01 1.415142570E-01 1.455516820E-01 1.496702430E-01 1.538483500E-01 - 1.580610420E-01 1.622779670E-01 1.665023570E-01 1.707346890E-01 1.749755140E-01 - 1.792253260E-01 1.834847030E-01 1.877542290E-01 1.920344380E-01 1.963259130E-01 - 2.006292340E-01 2.049451320E-01 2.092742170E-01 2.136172800E-01 2.179751400E-01 - 2.223483920E-01 2.267379910E-01 2.311448750E-01 2.355698790E-01 2.400140320E-01 - 2.444783150E-01 2.489638630E-01 2.534718220E-01 2.580032350E-01 2.625595330E-01 - 2.671420280E-01 2.717520890E-01 2.763911780E-01 2.810609040E-01 2.857628760E-01 - 2.904987930E-01 2.952703240E-01 3.000796440E-01 3.049289290E-01 3.098202050E-01 - 3.147557680E-01 3.197380010E-01 3.247694970E-01 2.360262270E-01 2.336618450E-01 - 2.312984320E-01 2.289346610E-01 2.265701000E-01 2.242041080E-01 2.218360750E-01 - 2.194654200E-01 2.170917240E-01 2.147143780E-01 2.123329790E-01 2.099470790E-01 - 2.075562780E-01 2.051601560E-01 2.027582970E-01 2.003503740E-01 1.979360130E-01 - 1.955148880E-01 1.930866240E-01 1.906508950E-01 1.882074180E-01 1.857558490E-01 - 1.832958910E-01 1.808272300E-01 1.783496140E-01 1.758627150E-01 1.733662780E-01 - 1.708599930E-01 1.683436040E-01 1.658168140E-01 1.632793400E-01 1.607311670E-01 - 1.581715940E-01 1.556004430E-01 1.530177150E-01 1.504231100E-01 1.478231250E-01 - 1.452246310E-01 1.426309790E-01 1.400455090E-01 1.374698430E-01 1.348986330E-01 - 1.323310290E-01 1.297672240E-01 1.272069070E-01 1.246497180E-01 1.220959420E-01 - 1.195457730E-01 1.169994620E-01 1.144573020E-01 1.119196270E-01 1.093867720E-01 - 1.068590660E-01 1.043368430E-01 1.018204760E-01 9.931033100E-02 9.680676460E-02 - 9.431016450E-02 9.182091060E-02 8.933940530E-02 8.686604350E-02 8.440123500E-02 - 8.194539700E-02 7.949891690E-02 7.706221190E-02 7.463571430E-02 7.221985610E-02 - 6.981504710E-02 6.742177160E-02 6.504051390E-02 6.267177310E-02 6.031603370E-02 - 5.797381700E-02 5.564568190E-02 5.333221330E-02 5.103402210E-02 4.875170810E-02 - 4.648590090E-02 4.423724490E-02 4.200640690E-02 3.979408740E-02 3.760098670E-02 - 3.542783110E-02 3.327536210E-02 3.114432840E-02 2.903547700E-02 2.694964600E-02 - 2.488760460E-02 2.285014840E-02 2.083808370E-02 1.885222830E-02 1.689341850E-02 - 1.496249530E-02 1.306030900E-02 1.118769310E-02 9.345511910E-03 7.534618490E-03 - 5.755850580E-03 4.010058010E-03 2.298104340E-03 6.208469860E-04-1.020878790E-03 --2.626225820E-03-4.194360230E-03-5.724448710E-03-7.215653550E-03-8.667160760E-03 --1.007815920E-02-1.144783940E-02-1.277541830E-02-1.406011080E-02-1.530113440E-02 --1.649772190E-02-1.764913280E-02-1.875462760E-02-1.981348540E-02-2.082498190E-02 --2.178841460E-02-2.270311860E-02-2.356842910E-02-2.438367340E-02-2.514822590E-02 --2.586145140E-02-2.652273510E-02-2.713151280E-02-2.768723110E-02-2.818934250E-02 --2.863729000E-02-2.903052610E-02-2.936857940E-02-2.965100110E-02-2.987731810E-02 --3.004710940E-02-3.015995400E-02-3.021545520E-02-3.021324980E-02-3.015298400E-02 --3.003432230E-02-2.985696310E-02-2.962066230E-02-2.932517600E-02-2.897025090E-02 --2.855565770E-02-2.808124010E-02-2.754686030E-02-2.695233750E-02-2.629761770E-02 --2.558265440E-02-2.480739730E-02-2.397179420E-02-2.307581720E-02-2.211956680E-02 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1.331838670E-01 1.369991300E-01 1.408771870E-01 1.448564980E-01 1.489172430E-01 - 1.530386210E-01 1.572070720E-01 1.613816620E-01 1.655628530E-01 1.697528360E-01 - 1.739519690E-01 1.781605180E-01 1.823791410E-01 1.866083290E-01 1.908486490E-01 - 1.951006650E-01 1.993650500E-01 2.036424580E-01 2.079334110E-01 2.122386990E-01 - 2.165591270E-01 2.208954990E-01 2.252486500E-01 2.296194430E-01 2.340087740E-01 - 2.384176110E-01 2.428470850E-01 2.472981660E-01 2.517720460E-01 2.562699320E-01 - 2.607931200E-01 2.653429510E-01 2.699207660E-01 2.745280560E-01 2.791666690E-01 - 2.838378550E-01 2.885436710E-01 2.932858470E-01 2.980660800E-01 3.028871720E-01 - 3.077509700E-01 3.126595910E-01 3.176156880E-01 3.226220310E-01 3.276809750E-01 - 2.365954670E-01 2.342295350E-01 2.318652120E-01 2.295019030E-01 2.271389960E-01 - 2.247758060E-01 2.224116330E-01 2.200460280E-01 2.176783830E-01 2.153081890E-01 - 2.129349710E-01 2.105582510E-01 2.081776860E-01 2.057926650E-01 2.034028770E-01 - 2.010079320E-01 1.986073850E-01 1.962009220E-01 1.937882160E-01 1.913688330E-01 - 1.889424470E-01 1.865087600E-01 1.840674280E-01 1.816181540E-01 1.791606250E-01 - 1.766945120E-01 1.742195340E-01 1.717353760E-01 1.692417710E-01 1.667384510E-01 - 1.642251160E-01 1.617015150E-01 1.591673340E-01 1.566222910E-01 1.540661900E-01 - 1.514974090E-01 1.489227120E-01 1.463471650E-01 1.437738840E-01 1.412083660E-01 - 1.386542320E-01 1.361065510E-01 1.335640700E-01 1.310258360E-01 1.284914760E-01 - 1.259608570E-01 1.234340590E-01 1.209113230E-01 1.183928470E-01 1.158788500E-01 - 1.133696440E-01 1.108656080E-01 1.083670630E-01 1.058743300E-01 1.033877730E-01 - 1.009077430E-01 9.843459730E-02 9.596872330E-02 9.351050110E-02 9.106031810E-02 - 8.861856910E-02 8.618567140E-02 8.376201240E-02 8.134802430E-02 7.894411680E-02 - 7.655069980E-02 7.416820530E-02 7.179706540E-02 6.943774970E-02 6.709066030E-02 - 6.475633380E-02 6.243527680E-02 6.012797730E-02 5.783495310E-02 5.555681140E-02 - 5.329411480E-02 5.104744810E-02 4.881743340E-02 4.660470410E-02 4.440990460E-02 - 4.223370920E-02 4.007680710E-02 3.793990610E-02 3.582369160E-02 3.372894600E-02 - 3.165641050E-02 2.960683960E-02 2.758100260E-02 2.557966490E-02 2.360362930E-02 - 2.165369880E-02 1.973069270E-02 1.783543830E-02 1.596877540E-02 1.413149390E-02 - 1.232444120E-02 1.054844910E-02 8.804350160E-03 7.092982060E-03 5.415184420E-03 - 3.771807530E-03 2.163673050E-03 5.915935030E-04-9.436059630E-04-2.441095890E-03 --3.900056240E-03-5.319677760E-03-6.699170450E-03-8.037749680E-03-9.334632200E-03 --1.058903520E-02-1.180019880E-02-1.296737420E-02-1.408982740E-02-1.516682190E-02 --1.619764790E-02-1.718159770E-02-1.811799220E-02-1.900616100E-02-1.984543170E-02 --2.063516150E-02-2.137471920E-02-2.206350490E-02-2.270092820E-02-2.328640410E-02 --2.381937580E-02-2.429929560E-02-2.472563090E-02-2.509788420E-02-2.541557140E-02 --2.567823230E-02-2.588542550E-02-2.603671700E-02-2.613169140E-02-2.616999860E-02 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7.775773110E-02 8.094009010E-02 8.415729550E-02 8.740886300E-02 9.069432320E-02 - 9.401328120E-02 9.736530480E-02 1.007503200E-01 1.041679680E-01 1.076186000E-01 - 1.111026410E-01 1.146205290E-01 1.181724970E-01 1.217605020E-01 1.253856120E-01 - 1.290505230E-01 1.327602120E-01 1.365209370E-01 1.403408350E-01 1.442581710E-01 - 1.482621430E-01 1.523313220E-01 1.564442810E-01 1.605772670E-01 1.647124740E-01 - 1.688569640E-01 1.730107520E-01 1.771745980E-01 1.813488600E-01 1.855340900E-01 - 1.897307780E-01 1.939395220E-01 1.981608870E-01 2.023954540E-01 2.066440140E-01 - 2.109071610E-01 2.151856720E-01 2.194803510E-01 2.237919720E-01 2.281212960E-01 - 2.324694250E-01 2.368373270E-01 2.412258980E-01 2.456362690E-01 2.500695290E-01 - 2.545269130E-01 2.590097490E-01 2.635191680E-01 2.680568100E-01 2.726240160E-01 - 2.772224250E-01 2.818536160E-01 2.865194080E-01 2.912215890E-01 2.959622440E-01 - 3.007434900E-01 3.055671450E-01 3.104359210E-01 3.153522610E-01 3.203185800E-01 - 3.253376190E-01 3.304124470E-01 2.370956390E-01 2.347315250E-01 2.323699890E-01 - 2.300104050E-01 2.276520730E-01 2.252943960E-01 2.229367940E-01 2.205787000E-01 - 2.182194890E-01 2.158586680E-01 2.134957910E-01 2.111303660E-01 2.087618560E-01 - 2.063898590E-01 2.040139590E-01 2.016337360E-01 1.992487610E-01 1.968586440E-01 - 1.944630300E-01 1.920615140E-01 1.896537840E-01 1.872394680E-01 1.848181930E-01 - 1.823896470E-01 1.799535300E-01 1.775095160E-01 1.750572770E-01 1.725965140E-01 - 1.701269300E-01 1.676482710E-01 1.651602390E-01 1.626625210E-01 1.601548490E-01 - 1.576369700E-01 1.551086460E-01 1.525690560E-01 1.500192730E-01 1.474667790E-01 - 1.449167280E-01 1.423743670E-01 1.398420630E-01 1.373177470E-01 1.348002550E-01 - 1.322883520E-01 1.297808890E-01 1.272775830E-01 1.247785460E-01 1.222839880E-01 - 1.197941530E-01 1.173092050E-01 1.148293320E-01 1.123549040E-01 1.098863040E-01 - 1.074238350E-01 1.049678470E-01 1.025186930E-01 1.000767200E-01 9.764232490E-02 - 9.521584960E-02 9.279770400E-02 9.038828310E-02 8.798798920E-02 8.559720220E-02 - 8.321637660E-02 8.084590730E-02 7.848621900E-02 7.613772150E-02 7.380086930E-02 - 7.147608700E-02 6.916382160E-02 6.686452780E-02 6.457872690E-02 6.230693310E-02 - 6.004966050E-02 5.780743810E-02 5.558083580E-02 5.337041990E-02 5.117680500E-02 - 4.900061340E-02 4.684246700E-02 4.470300300E-02 4.258289930E-02 4.048284890E-02 - 3.840354460E-02 3.634570540E-02 3.431007270E-02 3.229737280E-02 3.030835280E-02 - 2.834377070E-02 2.640439940E-02 2.449104190E-02 2.260450460E-02 2.074558100E-02 - 1.891505160E-02 1.711374330E-02 1.534246930E-02 1.360203610E-02 1.189325190E-02 - 1.021695510E-02 8.573972620E-03 6.965111480E-03 5.391185640E-03 3.853007450E-03 - 2.351389030E-03 8.871395840E-04-5.389580620E-04-1.926086380E-03-3.273470560E-03 --4.580339880E-03-5.845924370E-03-7.069456860E-03-8.250189950E-03-9.387388830E-03 --1.048031910E-02-1.152826940E-02-1.253053170E-02-1.348641610E-02-1.439525090E-02 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3.367846460E-02 3.615272050E-02 3.867265950E-02 4.123757030E-02 4.384673010E-02 - 4.649940510E-02 4.919490960E-02 5.193252120E-02 5.471152810E-02 5.753124130E-02 - 6.039099400E-02 6.329012660E-02 6.622797250E-02 6.920390580E-02 7.221733780E-02 - 7.526765020E-02 7.835426930E-02 8.147665860E-02 8.463431150E-02 8.782673630E-02 - 9.105361250E-02 9.431426230E-02 9.760839490E-02 1.009359730E-01 1.042969300E-01 - 1.076912060E-01 1.111190620E-01 1.145809670E-01 1.180773530E-01 1.216101420E-01 - 1.251796330E-01 1.287890820E-01 1.324428770E-01 1.361476630E-01 1.399096850E-01 - 1.437629460E-01 1.477063300E-01 1.517202710E-01 1.557806130E-01 1.598655280E-01 - 1.639548840E-01 1.680503640E-01 1.721558120E-01 1.762716470E-01 1.803982850E-01 - 1.845364420E-01 1.886860730E-01 1.928479670E-01 1.970226910E-01 2.012107970E-01 - 2.054129540E-01 2.096298780E-01 2.138621810E-01 2.181106660E-01 2.223762420E-01 - 2.266595960E-01 2.309616060E-01 2.352832560E-01 2.396255430E-01 2.439894680E-01 - 2.483763100E-01 2.527869940E-01 2.572228010E-01 2.616851930E-01 2.661753890E-01 - 2.706948520E-01 2.752451000E-01 2.798278930E-01 2.844448690E-01 2.890977860E-01 - 2.937887010E-01 2.985195220E-01 3.032925130E-01 3.081097600E-01 3.129736780E-01 - 3.178870080E-01 3.228525220E-01 3.278731410E-01 3.329515160E-01 2.375233620E-01 - 2.351644340E-01 2.328088430E-01 2.304560100E-01 2.281052170E-01 2.257559300E-01 - 2.234075670E-01 2.210594560E-01 2.187111530E-01 2.163621340E-01 2.140118630E-01 - 2.116598340E-01 2.093055550E-01 2.069486080E-01 2.045885320E-01 2.022248800E-01 - 1.998572650E-01 1.974852680E-01 1.951084580E-01 1.927264330E-01 1.903388950E-01 - 1.879454550E-01 1.855457430E-01 1.831394140E-01 1.807261260E-01 1.783055510E-01 - 1.758773920E-01 1.734413500E-01 1.709970980E-01 1.685443220E-01 1.660827250E-01 - 1.636121720E-01 1.611322020E-01 1.586426050E-01 1.561432780E-01 1.536322530E-01 - 1.511116470E-01 1.485858410E-01 1.460590210E-01 1.435393390E-01 1.410303860E-01 - 1.385304630E-01 1.360384230E-01 1.335531180E-01 1.310732810E-01 1.285981980E-01 - 1.261278540E-01 1.236623670E-01 1.212018950E-01 1.187466460E-01 1.162968950E-01 - 1.138529260E-01 1.114150580E-01 1.089836210E-01 1.065589640E-01 1.041414370E-01 - 1.017313820E-01 9.932915870E-02 9.693516050E-02 9.454975280E-02 9.217333790E-02 - 8.980631080E-02 8.744907380E-02 8.510205150E-02 8.276565370E-02 8.044029770E-02 - 7.812640820E-02 7.582440230E-02 7.353472710E-02 7.125782970E-02 6.899416450E-02 - 6.674422320E-02 6.450851260E-02 6.228750940E-02 6.008175760E-02 5.789181590E-02 - 5.571822820E-02 5.356156450E-02 5.142243580E-02 4.930147530E-02 4.719930890E-02 - 4.511655490E-02 4.305396600E-02 4.101211210E-02 3.899171580E-02 3.699351470E-02 - 3.501824290E-02 3.306663410E-02 3.113942970E-02 2.923735790E-02 2.736115640E-02 - 2.551164480E-02 2.368959970E-02 2.189579790E-02 2.013103660E-02 1.839611310E-02 - 1.669182260E-02 1.501895670E-02 1.337833330E-02 1.177075130E-02 1.019699220E-02 - 8.657854980E-03 7.154152730E-03 5.686691030E-03 4.256240560E-03 2.863604580E-03 - 1.509546190E-03 1.948243010E-04-1.079797400E-03-2.313552420E-03-3.505671160E-03 --4.655441270E-03-5.762136540E-03-6.825038700E-03-7.843444120E-03-8.816662240E-03 --9.744009930E-03-1.062482410E-02-1.145843790E-02-1.224422920E-02-1.298158060E-02 --1.366988380E-02-1.430854480E-02-1.489697960E-02-1.543463110E-02-1.592096500E-02 --1.635546980E-02-1.673763250E-02-1.706696300E-02-1.734299960E-02-1.756528580E-02 --1.773339880E-02-1.784694750E-02-1.790554820E-02-1.790881720E-02-1.785641910E-02 --1.774803920E-02-1.758338140E-02-1.736217360E-02-1.708415150E-02-1.674911010E-02 --1.635682210E-02-1.590713490E-02-1.539989750E-02-1.483496090E-02-1.421226650E-02 --1.353167840E-02-1.279316470E-02-1.199673860E-02-1.114241030E-02-1.023019200E-02 --9.260118940E-03-8.232304830E-03-7.146873050E-03-6.003966090E-03-4.803746470E-03 --3.546435850E-03-2.232237020E-03-8.614030670E-04 5.657487780E-04 2.048900580E-03 - 3.587734420E-03 5.181889520E-03 6.830968890E-03 8.534546940E-03 1.029219480E-02 - 1.210340580E-02 1.396767520E-02 1.588450370E-02 1.785338300E-02 1.987374760E-02 - 2.194499220E-02 2.406652830E-02 2.623773550E-02 2.845798990E-02 3.072664510E-02 - 3.304305300E-02 3.540654480E-02 3.781644250E-02 4.027205330E-02 4.277269910E-02 - 4.531769830E-02 4.790637640E-02 5.053805930E-02 5.321199820E-02 5.592757460E-02 - 5.868411810E-02 6.148095800E-02 6.431744250E-02 6.719294940E-02 7.010684910E-02 - 7.305856050E-02 7.604750990E-02 7.907311620E-02 8.213486520E-02 8.523225040E-02 - 8.836477990E-02 9.153213350E-02 9.473364060E-02 9.796901790E-02 1.012382280E-01 - 1.045412420E-01 1.078780140E-01 1.112484930E-01 1.146529690E-01 1.180943700E-01 - 1.215692240E-01 1.250814650E-01 1.286350190E-01 1.322338730E-01 1.358819450E-01 - 1.395858080E-01 1.433761120E-01 1.472570300E-01 1.512094740E-01 1.552142800E-01 - 1.592520030E-01 1.632965950E-01 1.673375820E-01 1.713919490E-01 1.754569260E-01 - 1.795325280E-01 1.836200360E-01 1.877196580E-01 1.918315740E-01 1.959563340E-01 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1.694245930E-01 1.669907870E-01 1.645485010E-01 1.620974090E-01 1.596373620E-01 - 1.571687610E-01 1.546876580E-01 1.521965860E-01 1.496997330E-01 1.472005100E-01 - 1.447037610E-01 1.422184410E-01 1.397433130E-01 1.372772460E-01 1.348190010E-01 - 1.323673730E-01 1.299211980E-01 1.274802830E-01 1.250446590E-01 1.226143910E-01 - 1.201897040E-01 1.177708360E-01 1.153580700E-01 1.129516880E-01 1.105520430E-01 - 1.081594530E-01 1.057742690E-01 1.033968330E-01 1.010275190E-01 9.866667540E-02 - 9.631468360E-02 9.397193790E-02 9.163884070E-02 8.931577950E-02 8.700317140E-02 - 8.470143380E-02 8.241099860E-02 8.013227580E-02 7.786570490E-02 7.561170310E-02 - 7.337072490E-02 7.114322480E-02 6.892966480E-02 6.673053650E-02 6.454631690E-02 - 6.237754230E-02 6.022474910E-02 5.808847030E-02 5.596926060E-02 5.386771260E-02 - 5.178444460E-02 4.972007130E-02 4.767520350E-02 4.565050830E-02 4.364663740E-02 - 4.166424650E-02 3.970401360E-02 3.776667270E-02 3.585296500E-02 3.396360200E-02 - 3.209931030E-02 3.026081060E-02 2.844885740E-02 2.666424210E-02 2.490771560E-02 - 2.318003400E-02 2.148197960E-02 1.981434780E-02 1.817792100E-02 1.657349240E-02 - 1.500182970E-02 1.346369740E-02 1.195988520E-02 1.049119980E-02 9.058409370E-03 - 7.662293500E-03 6.303608420E-03 4.983104770E-03 3.701542270E-03 2.459678570E-03 - 1.258276990E-03 9.804635190E-05-1.020281230E-03-2.096001990E-03-3.128415670E-03 --4.116822970E-03-5.060565660E-03-5.958939900E-03-6.811290510E-03-7.617000960E-03 --8.375454690E-03-9.086036120E-03-9.748131040E-03-1.036116850E-02-1.092457860E-02 --1.143781380E-02-1.190036260E-02-1.231171100E-02-1.267134580E-02-1.297880990E-02 --1.323363560E-02-1.343536750E-02-1.358362190E-02-1.367801240E-02-1.371815520E-02 --1.370366480E-02-1.363423840E-02-1.350955570E-02-1.332933920E-02-1.309332620E-02 --1.280126350E-02-1.245292830E-02-1.204814480E-02-1.158675270E-02-1.106859840E-02 --1.049355420E-02-9.861524220E-03-9.172456340E-03-8.426321670E-03-7.623093200E-03 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1.357221750E-01 1.393709480E-01 1.430938990E-01 1.469168810E-01 1.508121040E-01 - 1.547590640E-01 1.587401180E-01 1.627357010E-01 1.667260080E-01 1.707171650E-01 - 1.747308370E-01 1.787547470E-01 1.827895490E-01 1.868363320E-01 1.908955130E-01 - 1.949675080E-01 1.990529150E-01 2.031522540E-01 2.072661820E-01 2.113953230E-01 - 2.155403200E-01 2.197018560E-01 2.238806930E-01 2.280777390E-01 2.322937850E-01 - 2.365296480E-01 2.407863890E-01 2.450649740E-01 2.493664180E-01 2.536918220E-01 - 2.580424550E-01 2.624196110E-01 2.668244840E-01 2.712585330E-01 2.757233080E-01 - 2.802203300E-01 2.847512360E-01 2.893178760E-01 2.939220960E-01 2.985657160E-01 - 3.032507900E-01 3.079802100E-01 3.127554950E-01 3.175794480E-01 3.224549290E-01 - 3.273847400E-01 3.323713840E-01 3.374182280E-01 2.381514460E-01 2.358122920E-01 - 2.334776820E-01 2.311470660E-01 2.288198770E-01 2.264955490E-01 2.241735310E-01 - 2.218532860E-01 2.195342630E-01 2.172159110E-01 2.148977520E-01 2.125792800E-01 - 2.102600040E-01 2.079393860E-01 2.056170400E-01 2.032924740E-01 2.009652410E-01 - 1.986348930E-01 1.963010280E-01 1.939632590E-01 1.916211550E-01 1.892743560E-01 - 1.869224610E-01 1.845651420E-01 1.822020110E-01 1.798327270E-01 1.774569600E-01 - 1.750743840E-01 1.726846690E-01 1.702875490E-01 1.678826960E-01 1.654697060E-01 - 1.630482230E-01 1.606180070E-01 1.581816970E-01 1.557321250E-01 1.532726730E-01 - 1.508064570E-01 1.483365740E-01 1.458661410E-01 1.434046920E-01 1.409549420E-01 - 1.385154720E-01 1.360848700E-01 1.336618810E-01 1.312453000E-01 1.288345310E-01 - 1.264294980E-01 1.240302180E-01 1.216368680E-01 1.192496420E-01 1.168688310E-01 - 1.144946890E-01 1.121275570E-01 1.097677570E-01 1.074156170E-01 1.050714920E-01 - 1.027357350E-01 1.004087110E-01 9.809079770E-02 9.578236940E-02 9.348381310E-02 - 9.119553860E-02 8.891794830E-02 8.665146680E-02 8.439651130E-02 8.215349910E-02 - 7.992286980E-02 7.770505550E-02 7.550050320E-02 7.330963760E-02 7.113293560E-02 - 6.897086650E-02 6.682390720E-02 6.469255690E-02 6.257736680E-02 6.047885860E-02 - 5.839757990E-02 5.633407090E-02 5.428896840E-02 5.226281660E-02 5.025625600E-02 - 4.826992380E-02 4.630445690E-02 4.436049240E-02 4.243871570E-02 4.053980110E-02 - 3.866446020E-02 3.681339700E-02 3.498732670E-02 3.318696100E-02 3.141302990E-02 - 2.966628410E-02 2.794747240E-02 2.625734360E-02 2.459665020E-02 2.296618370E-02 - 2.136666330E-02 1.979888040E-02 1.826359520E-02 1.676157120E-02 1.529357210E-02 - 1.386034770E-02 1.246270070E-02 1.110135860E-02 9.777070950E-03 8.490586650E-03 - 7.242654450E-03 6.034010560E-03 4.865362310E-03 3.737456170E-03 2.650985260E-03 - 1.606642850E-03 6.051213710E-04-3.528866220E-04-1.266745730E-03-2.135743620E-03 --2.959273760E-03-3.736734860E-03-4.467507820E-03-5.150974730E-03-5.786534400E-03 --6.373646200E-03-6.911729930E-03-7.400275210E-03-7.838772610E-03-8.226710370E-03 --8.563586510E-03-8.848948400E-03-9.082343430E-03-9.263365530E-03-9.391609580E-03 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8.380684260E-02 8.678220960E-02 8.979325740E-02 9.283964340E-02 9.592103210E-02 - 9.903708850E-02 1.021875140E-01 1.053722500E-01 1.085915040E-01 1.118447930E-01 - 1.151329200E-01 1.184569520E-01 1.218178050E-01 1.252166030E-01 1.286559550E-01 - 1.321377610E-01 1.356685010E-01 1.392600390E-01 1.429243240E-01 1.466818450E-01 - 1.505217110E-01 1.544136400E-01 1.583334650E-01 1.622681170E-01 1.662001310E-01 - 1.701431870E-01 1.741002500E-01 1.780690400E-01 1.820490810E-01 1.860408630E-01 - 1.900448050E-01 1.940615180E-01 1.980914620E-01 2.021351160E-01 2.061931340E-01 - 2.102661430E-01 2.143545750E-01 2.184592780E-01 2.225809540E-01 2.267202140E-01 - 2.308778760E-01 2.350548210E-01 2.392519560E-01 2.434701920E-01 2.477105860E-01 - 2.519739570E-01 2.562616170E-01 2.605747880E-01 2.649146020E-01 2.692823110E-01 - 2.736794050E-01 2.781075240E-01 2.825679180E-01 2.870624070E-01 2.915927170E-01 - 2.961606980E-01 3.007683160E-01 3.054175970E-01 3.101109860E-01 3.148505690E-01 - 3.196389970E-01 3.244788650E-01 3.293728230E-01 3.343234960E-01 3.393349350E-01 - 2.383476500E-01 2.360226210E-01 2.337027190E-01 2.313874070E-01 2.290761170E-01 - 2.267683300E-01 2.244634780E-01 2.221609950E-01 2.198603450E-01 2.175610360E-01 - 2.152625470E-01 2.129643110E-01 2.106658520E-01 2.083666920E-01 2.060663700E-01 - 2.037644240E-01 2.014603470E-01 1.991537210E-01 1.968441160E-01 1.945311870E-01 - 1.922144290E-01 1.898934840E-01 1.875679790E-01 1.852375420E-01 1.829018000E-01 - 1.805603950E-01 1.782130150E-01 1.758593020E-01 1.734989140E-01 1.711316260E-01 - 1.687570210E-01 1.663749070E-01 1.639849250E-01 1.615878640E-01 1.591805220E-01 - 1.567632410E-01 1.543374510E-01 1.519046280E-01 1.494661870E-01 1.470250190E-01 - 1.445878890E-01 1.421643940E-01 1.397520450E-01 1.373495610E-01 1.349557190E-01 - 1.325692530E-01 1.301893290E-01 1.278155600E-01 1.254479590E-01 1.230866910E-01 - 1.207318830E-01 1.183837350E-01 1.160425690E-01 1.137086750E-01 1.113823580E-01 - 1.090639610E-01 1.067538040E-01 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a/examples/DIIID-like_ideal_example/gpec.toml b/examples/DIIID-like_ideal_example/gpec.toml index 0291c54da..f60561b21 100644 --- a/examples/DIIID-like_ideal_example/gpec.toml +++ b/examples/DIIID-like_ideal_example/gpec.toml @@ -7,7 +7,7 @@ power_b = 0 # Toroidal field power exponent for Jacobian power_r = 0 # Major radius power exponent for Jacobian grid_type = "ldp" # Radial grid packing (sin²: packs core+edge). Robust δW/Δ' vs log_asymptotic. psilow = 1e-4 # Lower limit of normalized flux coordinate -psihigh = 0.9995 # Upper limit of normalized flux coordinate +psihigh = 0.995 # captures q=6 with sas_flag/dmlim at this Ip mpsi = 256 # Fixed radial grid (avoid mpsi=0 auto: it edge-starves → spurious δW/Δ') psi_accuracy = 0.001 # Target absolute error in q for auto-mpsi (unused when mpsi>0) mtheta = 256 # Number of poloidal grid points From 1803be940f6d60419d5b67d0e9b950b6e4d348fa Mon Sep 17 00:00:00 2001 From: d-burg Date: Mon, 22 Jun 2026 15:40:15 -0400 Subject: [PATCH 093/135] TEST - Re-pin DIIID parallel-integration for Ip=1.15 equilibrium Co-Authored-By: Claude Opus 4.8 --- test/runtests_parallel_integration.jl | 16 ++++++++-------- 1 file changed, 8 insertions(+), 8 deletions(-) diff --git a/test/runtests_parallel_integration.jl b/test/runtests_parallel_integration.jl index 810a7cdd4..97d7b489f 100644 --- a/test/runtests_parallel_integration.jl +++ b/test/runtests_parallel_integration.jl @@ -305,11 +305,11 @@ using TOML et_par, intr_par = run_diiid(true) - # Parallel FM et[1] regression — pinned tightly, NOT bracketed. et[1] is grid-sensitive - # (log_asymptotic/auto-mpsi gives a spurious −0.09; ldp/mpsi=256 gives the converged - # +0.504), so a loose bracket would mask exactly that accuracy regression. Value is - # deterministic and reproducible (parallel and standard ODE paths agree to rel_diff=0). - @test isapprox(et_par, 0.504306; rtol=2e-2) + # Parallel FM et[1] regression — pinned tightly, NOT bracketed. et[1] is grid- and + # equilibrium-sensitive (auto-mpsi gives a spurious value; a wrong grid/Ip shifts it), so + # a loose bracket would mask exactly that accuracy regression. Value is deterministic and + # reproducible (parallel and standard ODE paths agree to rel_diff=0). + @test isapprox(et_par, 0.999467; rtol=2e-2) # Per-surface Δ' assertions removed (stub calculation; see Solovev testset # comment above). BVP Δ' matrix regression for DIIID-like is in the # `delta_prime_matrix — STRIDE BVP DIIID-like regression (large N)` testset. @@ -523,9 +523,9 @@ using TOML # surfaces q=5,6 (ψ≈0.98, 0.997) are NOT converged — real part and even sign can fluctuate # — so they get only the finiteness/non-zero checks above, not value pins. Values use this # testset's mode range (mpert=27, vs full-pipeline mpert=35, so they differ slightly). - @test isapprox(real(dpm[1, 1]), +9.396892e+00; rtol=1e-2) # q=2 - @test isapprox(real(dpm[2, 2]), -2.114709e+00; rtol=1e-2) # q=3 - @test isapprox(real(dpm[3, 3]), -1.915087e+01; rtol=3e-2) # q=4 + @test isapprox(real(dpm[1, 1]), +7.225479e+00; rtol=1e-2) # q=2 + @test isapprox(real(dpm[2, 2]), -6.089718e+00; rtol=1e-2) # q=3 + @test isapprox(real(dpm[3, 3]), -2.177899e+01; rtol=3e-2) # q=4 end end From 29ce91c36ed2743f17fd9e727d9fdac5c5f294a7 Mon Sep 17 00:00:00 2001 From: Jake Halpern Date: Tue, 23 Jun 2026 09:26:43 -0400 Subject: [PATCH 094/135] GPEC - MINOR - removing unnecessary Claude comments --- src/GeneralizedPerturbedEquilibrium.jl | 21 ++++++++++++++------- 1 file changed, 14 insertions(+), 7 deletions(-) diff --git a/src/GeneralizedPerturbedEquilibrium.jl b/src/GeneralizedPerturbedEquilibrium.jl index 5fc5f08c2..1c3e5adb9 100755 --- a/src/GeneralizedPerturbedEquilibrium.jl +++ b/src/GeneralizedPerturbedEquilibrium.jl @@ -48,7 +48,6 @@ include("Analysis/Analysis.jl") import .Analysis as Analysis export Analysis -# Rerun snapshot/replay helpers, included directly into this module include("Rerun.jl") # Import ForceFreeStates types and functions needed for main @@ -169,15 +168,12 @@ function main_from_inputs( @info "\n Equilibrium\n$_SECTION" equil_start = time() + + # Build data structures from inputs intr = ForceFreeStatesInternal(; dir_path=path) - # `inputs` is supplied by the caller (parsed from gpec.toml on the normal path, or - # reconstructed from the gpec.h5 TOML blob on the rerun path), so do not re-read it here. ffs_table = inputs["ForceFreeStates"] _drop_deprecated_ffs_keys!(ffs_table) ctrl = ForceFreeStatesControl(; (Symbol(k) => v for (k, v) in ffs_table)...) - - # inputs/eq_config/additional_input are fully resolved by the caller; this body does no - # source dispatch — setup_equilibrium consumes additional_input directly. equil = Equilibrium.setup_equilibrium(eq_config, additional_input) @info "Equilibrium construction completed in $(@sprintf("%.3f", time() - equil_start)) s" @@ -445,7 +441,18 @@ function main_from_inputs( end if ctrl.write_outputs_to_HDF5 - write_outputs_to_HDF5(ctrl, equil, intr, odet, ctrl.vac_flag ? vac_data : nothing, ffit, git_version, inputs, forcing_modes_snapshot; ballooning_boundary=ballooning_boundary) + write_outputs_to_HDF5( + ctrl, + equil, + intr, + odet, + ctrl.vac_flag ? vac_data : nothing, + ffit, + git_version, + inputs, + forcing_modes_snapshot; + ballooning_boundary=ballooning_boundary + ) @info "Results written to $(ctrl.HDF5_filename)" end From 7d1df5a77da4a6c799fc60ae510f8d61a6535bbe Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Tue, 23 Jun 2026 10:51:24 -0400 Subject: [PATCH 095/135] ForcingTerms - REFACTOR - Require imaginary amplitude in all forcing readers Make amplitude_imag a required input across the ASCII, HDF5-file, and HDF5-group forcing readers, mirroring amplitude_real, instead of silently defaulting it to zero. Unify the ASCII column terminology on amplitude_real/amplitude_imag to match the HDF5 dataset names across the docstrings, the forcing.dat header, and the example TOML mode-table comments. Co-Authored-By: Claude Opus 4.8 (1M context) --- examples/Solovev_ideal_example/forcing.dat | 2 +- examples/Solovev_ideal_example/gpec.toml | 2 +- examples/Solovev_ideal_example_3D/gpec.toml | 2 +- src/ForcingTerms/ForcingTerms.jl | 18 +++++++++--------- 4 files changed, 12 insertions(+), 12 deletions(-) diff --git a/examples/Solovev_ideal_example/forcing.dat b/examples/Solovev_ideal_example/forcing.dat index f043c20af..42eb94703 100644 --- a/examples/Solovev_ideal_example/forcing.dat +++ b/examples/Solovev_ideal_example/forcing.dat @@ -1,5 +1,5 @@ # Forcing data for perturbed equilibrium calculations # normalization: normal_field_T -# Format: n m real(amplitude) imag(amplitude) +# Format: n m amplitude_real amplitude_imag # Single mode test case: n=1, m=2, amplitude=1e-4 T 1 2 1e-4 0.0 diff --git a/examples/Solovev_ideal_example/gpec.toml b/examples/Solovev_ideal_example/gpec.toml index dacefde12..9a74f1d35 100644 --- a/examples/Solovev_ideal_example/gpec.toml +++ b/examples/Solovev_ideal_example/gpec.toml @@ -32,7 +32,7 @@ tw = 0.05 # Sharpness of wall corners (try 0.05 as equal_arc_wall = true # Equal arc length distribution of nodes on wall [ForcingTerms] -forcing_data_file = "forcing.dat" # Manual mode table (n, m, real, imag) +forcing_data_file = "forcing.dat" # Manual mode table (n, m, amplitude_real, amplitude_imag) forcing_data_format = "ascii" # Format: "ascii", "hdf5", or "coil" (Biot-Savart from 3D wires) [PerturbedEquilibrium] diff --git a/examples/Solovev_ideal_example_3D/gpec.toml b/examples/Solovev_ideal_example_3D/gpec.toml index 0564bb9d0..7dc5a245f 100644 --- a/examples/Solovev_ideal_example_3D/gpec.toml +++ b/examples/Solovev_ideal_example_3D/gpec.toml @@ -61,7 +61,7 @@ equal_arc_wall = false # Equal arc length distribution of nodes # Uncomment to enable perturbed equilibrium calculations: # [PerturbedEquilibrium] -# forcing_data_file = "forcing.dat" # Manual mode table (n, m, real, imag) +# forcing_data_file = "forcing.dat" # Manual mode table (n, m, amplitude_real, amplitude_imag) # forcing_data_format = "ascii" # Format: "ascii", "hdf5", or "coil" (Biot-Savart from 3D wires) # fixed_boundary = false # Use fixed boundary conditions # output_eigenmodes = true # Output eigenmode fields as b-fields diff --git a/src/ForcingTerms/ForcingTerms.jl b/src/ForcingTerms/ForcingTerms.jl index 65267df52..2272e723d 100644 --- a/src/ForcingTerms/ForcingTerms.jl +++ b/src/ForcingTerms/ForcingTerms.jl @@ -83,14 +83,14 @@ from the file (or `"normal_field_T"` by default if no tag is present). 1 3 0.3 -0.2 ``` -Columns: n, m, real(amplitude), [optional] imag(amplitude) +Columns: n, m, amplitude_real, amplitude_imag **HDF5 format** — optional root attribute `normalization` (string), plus datasets: - `"n"`: Integer array of toroidal mode numbers - `"m"`: Integer array of poloidal mode numbers - `"amplitude_real"`: Real parts of amplitudes - - `"amplitude_imag"`: Imaginary parts of amplitudes (optional, default 0) + - `"amplitude_imag"`: Imaginary parts of amplitudes """ function load_forcing_data!( forcing_modes::Vector{ForcingMode}, @@ -125,7 +125,7 @@ end Load forcing data from ASCII file. Returns normalization tag (`"normal_field_T"` by default). Optional first `# normalization: ` header line sets the normalization. -Remaining `#`-prefixed lines and blank lines are ignored. Data columns: n, m, real, [imag]. +Remaining `#`-prefixed lines and blank lines are ignored. Data columns: n, m, amplitude_real, amplitude_imag. """ function load_forcing_ascii!( forcing_modes::Vector{ForcingMode}, @@ -155,8 +155,8 @@ function load_forcing_ascii!( nrows = size(data, 1) ncols = size(data, 2) - if ncols < 3 - error("ASCII forcing file must have at least 3 columns (n, m, real_amplitude)") + if ncols < 4 + error("ASCII forcing file must have 4 columns (n, m, amplitude_real, amplitude_imag)") end empty!(forcing_modes) @@ -165,7 +165,7 @@ function load_forcing_ascii!( n = Int(data[i, 1]) m = Int(data[i, 2]) real_part = Float64(data[i, 3]) - imag_part = ncols >= 4 ? Float64(data[i, 4]) : 0.0 + imag_part = Float64(data[i, 4]) push!(forcing_modes, ForcingMode(; n=n, @@ -182,7 +182,7 @@ end Load forcing data from HDF5 file. Returns normalization tag (`"normal_field_T"` by default). Optional root attribute `normalization` (string) sets the normalization. -Required datasets: `n`, `m`, `amplitude_real`. Optional: `amplitude_imag`. +Required datasets: `n`, `m`, `amplitude_real`, `amplitude_imag`. """ function load_forcing_hdf5!( forcing_modes::Vector{ForcingMode}, @@ -200,7 +200,7 @@ function load_forcing_hdf5!( n_array = read(file, "n") m_array = read(file, "m") amp_real = read(file, "amplitude_real") - amp_imag = haskey(file, "amplitude_imag") ? read(file, "amplitude_imag") : zeros(length(n_array)) + amp_imag = read(file, "amplitude_imag") if length(n_array) != length(m_array) || length(n_array) != length(amp_real) error("Inconsistent array lengths in HDF5 forcing file") @@ -258,7 +258,7 @@ function load_forcing_from_h5_group!(forcing_modes::Vector{ForcingMode}, group) n_array = read(group, "n") m_array = read(group, "m") amp_real = read(group, "amplitude_real") - amp_imag = haskey(group, "amplitude_imag") ? read(group, "amplitude_imag") : zeros(length(n_array)) # optional for hand-authored groups + amp_imag = read(group, "amplitude_imag") if length(n_array) != length(m_array) || length(n_array) != length(amp_real) error("Inconsistent array lengths in HDF5 forcing group") From cfe3d29d30540606d1d4c69a86b68497f78dafa7 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Tue, 23 Jun 2026 11:27:46 -0400 Subject: [PATCH 096/135] RERUN - CLEANUP - Drop deprecated analytic side-car TOML support Analytic equilibria (sol/lar/tj_analytic) now resolve their parameters only from the embedded [SOL_INPUT]/[LAR_INPUT]/[TJ_ANALYTIC_INPUT] section of gpec.toml. Every in-repo deck already uses the embedded form and the side-car files were removed, so the deprecation bridge is dead weight pre-release. Remove merge_auxiliary_eq_toml! and its call, the eq_filename side-car fallback in setup_equilibrium (analytic kinds now require their *Config as additional_input, with a clear error otherwise), and the now-orphaned *Config(::String) file constructors. Tighten the surviving *Config(::Dict) docstrings. Drop the side-car hasmethod assertion from the registry test. No numerical change: regression harness solovev_n1 (21/21) and diiid_n1 (46/46) identical local vs branch HEAD. Co-Authored-By: Claude Opus 4.8 (1M context) --- src/Equilibrium/Equilibrium.jl | 13 +++++--- src/Equilibrium/EquilibriumTypes.jl | 45 ++------------------------ src/GeneralizedPerturbedEquilibrium.jl | 8 ++--- src/Rerun.jl | 33 +++---------------- test/runtests_rerun_from_h5.jl | 6 ++-- 5 files changed, 20 insertions(+), 85 deletions(-) diff --git a/src/Equilibrium/Equilibrium.jl b/src/Equilibrium/Equilibrium.jl index a3438116f..3941e1843 100644 --- a/src/Equilibrium/Equilibrium.jl +++ b/src/Equilibrium/Equilibrium.jl @@ -107,12 +107,15 @@ function setup_equilibrium(eq_config::EquilibriumConfig, additional_input=nothin elseif eq_type in ["chease", "chease_binary"] eq_input = read_chease_binary(eq_config) elseif haskey(ANALYTIC_EQ, eq_type) - # Analytic kinds (sol/lar/tj_analytic[_direct]) dispatch off the ANALYTIC_EQ registry: - # build the config from the eq_filename TOML if not already supplied, then run its solver. + # Analytic kinds (sol/lar/tj_analytic[_direct]) dispatch off the ANALYTIC_EQ registry. + # Their parameters live in the embedded `[*_INPUT]` section and are passed in as the + # `*Config` additional_input (built by build_analytic_config on the TOML/rerun paths). spec = ANALYTIC_EQ[eq_type] - if additional_input === nothing - additional_input = spec.config_type(eq_config.eq_filename) - end + additional_input isa spec.config_type || + error( + "setup_equilibrium: analytic eq_type=\"$eq_type\" requires its $(spec.config_type) " * + "passed as additional_input (built from the embedded [$(spec.section)] section)." + ) eq_input = spec.run_fn(eq_config, additional_input) elseif eq_type == "imas" if additional_input === nothing diff --git a/src/Equilibrium/EquilibriumTypes.jl b/src/Equilibrium/EquilibriumTypes.jl index b0a9973ff..af3f4c2a9 100644 --- a/src/Equilibrium/EquilibriumTypes.jl +++ b/src/Equilibrium/EquilibriumTypes.jl @@ -224,21 +224,7 @@ A mutable struct holding parameters for the Large Aspect Ratio (LAR) plasma equi zeroth::Bool = false end -""" -Outer constructor for LargeAspectRatioConfig that enables a toml file -interface for specifying the configuration settings -""" -function LargeAspectRatioConfig(path::String) - raw = TOML.parsefile(path) - input_data = get(raw, "LAR_INPUT", Dict()) - return LargeAspectRatioConfig(; symbolize_keys(input_data)...) -end - -""" -Outer constructor for LargeAspectRatioConfig from a parsed TOML dictionary. -Supports embedding the LAR analytic-equilibrium parameters directly in -`gpec.toml` under `[LAR_INPUT]` instead of a separate `lar.toml`. -""" +"Build a `LargeAspectRatioConfig` from a parsed `[LAR_INPUT]` TOML table." function LargeAspectRatioConfig(input_dict::Dict{String,Any}) return LargeAspectRatioConfig(; symbolize_keys(input_dict)...) end @@ -278,18 +264,7 @@ Reference: R. Fitzpatrick, TJ code, https://github.com/rfitzp/TJ zeroth::Bool = false # If true, suppress Shafranov shift end -function TJAnalyticConfig(path::String) - raw = TOML.parsefile(path) - input_data = get(raw, "TJ_ANALYTIC_INPUT", Dict()) - return TJAnalyticConfig(; symbolize_keys(input_data)...) -end - -""" -Outer constructor for TJAnalyticConfig from a parsed TOML dictionary. Supports -embedding the TJ-analytic equilibrium parameters (cf. R. Fitzpatrick's -TJ code, https://github.com/rfitzp/TJ) directly in the main `gpec.toml` -under `[TJ_ANALYTIC_INPUT]`, removing the need for a separate side-car file. -""" +"Build a `TJAnalyticConfig` from a parsed `[TJ_ANALYTIC_INPUT]` TOML table." function TJAnalyticConfig(input_dict::Dict{String,Any}) return TJAnalyticConfig(; symbolize_keys(input_dict)...) end @@ -325,21 +300,7 @@ A mutable struct holding parameters for the Solev'ev (SOL) plasma equilibrium mo f0fac::Float64 = 1 # scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant) end -""" -Outer constructor for SolovevConfig that enables a toml file -interface for specifying the configuration settings -""" -function SolovevConfig(path::String) # if we use @kwdef, it generates SolovevConfig() so it conflicts with this line. - raw = TOML.parsefile(path) - input_data = get(raw, "SOL_INPUT", Dict()) - return SolovevConfig(; symbolize_keys(input_data)...) -end - -""" -Outer constructor for SolovevConfig from a parsed TOML dictionary. -Supports embedding the Solovev analytic-equilibrium parameters directly -in `gpec.toml` under `[SOL_INPUT]` instead of a separate `sol.toml`. -""" +"Build a `SolovevConfig` from a parsed `[SOL_INPUT]` TOML table." function SolovevConfig(input_dict::Dict{String,Any}) return SolovevConfig(; symbolize_keys(input_dict)...) end diff --git a/src/GeneralizedPerturbedEquilibrium.jl b/src/GeneralizedPerturbedEquilibrium.jl index 1c3e5adb9..d96d4453c 100755 --- a/src/GeneralizedPerturbedEquilibrium.jl +++ b/src/GeneralizedPerturbedEquilibrium.jl @@ -100,8 +100,8 @@ end build_inputs_from_toml(path; dd=nothing) -> (inputs, eq_config, additional_input) Build the pipeline inputs from a working directory containing `gpec.toml`. Returns the -parsed `inputs` dict (made self-contained for the rerun snapshot), the `EquilibriumConfig`, -and the `additional_input` consumed by `setup_equilibrium` — an analytic `*Config` for +parsed `inputs` dict, the `EquilibriumConfig`, and the `additional_input` consumed by +`setup_equilibrium` — an analytic `*Config` for sol/lar/tj equilibria (parameters from the embedded TOML section), the `dd` data dictionary for IMAS, or `nothing` for file-based equilibria (efit, chease) that `setup_equilibrium` reads from disk. @@ -112,10 +112,6 @@ function build_inputs_from_toml(path::String; dd::Union{IMASdd.dd,Nothing}=nothi haskey(inputs, "Equilibrium") || error("No [Equilibrium] section in gpec.toml") eq_config = Equilibrium.EquilibriumConfig(inputs["Equilibrium"], path) - # Fold a deprecated analytic side-car TOML into `inputs` if its section isn't already - # embedded, so the snapshot writer emits a self-contained TOML blob. - merge_auxiliary_eq_toml!(inputs, eq_config) - # An equilibrium is analytic (sol/lar/tj, parameters from its embedded section), # IMAS-fed (via the dd kwarg), or read from a file (additional_input = nothing). additional_input = if haskey(Equilibrium.ANALYTIC_EQ, eq_config.eq_type) diff --git a/src/Rerun.jl b/src/Rerun.jl index d7f20dab2..0ca1ea1e7 100644 --- a/src/Rerun.jl +++ b/src/Rerun.jl @@ -1,37 +1,14 @@ # Rerun support: save a run's inputs into gpec.h5 and replay them. Turns a gpec.h5 output into # a self-contained snapshot rerunnable from any directory, with optional overrides, without the -# original g-file / CHEASE / wall / auxiliary TOML inputs. +# original g-file / CHEASE / wall inputs. # # Included directly into the GeneralizedPerturbedEquilibrium module, so these functions share # its imports (TOML, HDF5, Equilibrium, ForcingTerms, etc.). -# Analytic equilibria carry their parameters in a TOML section rather than an ingest array; -# replay regenerates them from that section. The eq_type -> section mapping (and which kinds -# are analytic at all) lives in the `Equilibrium.ANALYTIC_EQ` registry, the single source of -# truth shared with `setup_equilibrium`. - -""" - merge_auxiliary_eq_toml!(inputs::Dict{String,Any}, eq_config) - -Ensure the analytic-equilibrium parameter section (`[SOL_INPUT]` / `[LAR_INPUT]` / -`[TJ_ANALYTIC_INPUT]`) is present in the in-memory `inputs` dict so the `gpec.h5` snapshot -is self-contained. If the section is already embedded in `gpec.toml`, this is a no-op. -Otherwise it falls back to the deprecated side-car TOML referenced by `eq_config.eq_filename` -and folds that section in (with a deprecation warning). No-op for non-analytic equilibria. -""" -function merge_auxiliary_eq_toml!(inputs::Dict{String,Any}, eq_config::Equilibrium.EquilibriumConfig) - spec = get(Equilibrium.ANALYTIC_EQ, eq_config.eq_type, nothing) - spec === nothing && return inputs # file-based: snapshotted via the equilibrium ingest - section = spec.section - haskey(inputs, section) && return inputs # already embedded in gpec.toml - - filepath = eq_config.eq_filename - isfile(filepath) || return inputs # nothing to fold; build_analytic_config will report a clear error - @warn "Reading analytic parameters from side-car $filepath is deprecated; move [$section] into gpec.toml" - aux = TOML.parsefile(filepath) - haskey(aux, section) && (inputs[section] = aux[section]) - return inputs -end +# Analytic equilibria carry their parameters in an embedded TOML section rather than an ingest +# array; replay regenerates them from that section. The eq_type -> section mapping (and which +# kinds are analytic at all) lives in the `Equilibrium.ANALYTIC_EQ` registry, the single source +# of truth shared with `setup_equilibrium`. """ build_analytic_config(eq_type, inputs) diff --git a/test/runtests_rerun_from_h5.jl b/test/runtests_rerun_from_h5.jl index 0dacb0e01..7862bd10d 100644 --- a/test/runtests_rerun_from_h5.jl +++ b/test/runtests_rerun_from_h5.jl @@ -51,7 +51,7 @@ end # Analytic (Solovev) equilibrium: the single end-to-end source + replay. The replay runs from a # temp directory containing nothing but the captured gpec.h5, proving the snapshot is -# self-contained (no auxiliary TOML, g-file, or forcing data), and reproduces the source +# self-contained (no g-file or forcing data needed), and reproduces the source # bit-for-bit across every output dataset. @testset "Rerun from gpec.h5 (analytic Solovev)" begin template_dir = joinpath(@__DIR__, "test_data", "regression_solovev_ideal_example") @@ -295,10 +295,8 @@ end bac = GeneralizedPerturbedEquilibrium.build_analytic_config for (eq_type, spec) in Equil.ANALYTIC_EQ @test spec.section isa String && !isempty(spec.section) - # config_type must build from a parsed TOML table (the rerun/embedded-section path)... + # config_type must build from a parsed TOML table (the embedded-section path). @test hasmethod(spec.config_type, Tuple{Dict{String,Any}}) - # ...and from a side-car path string (the deprecated fallback in setup_equilibrium). - @test hasmethod(spec.config_type, Tuple{String}) # run_fn must accept (EquilibriumConfig, ). @test hasmethod(spec.run_fn, Tuple{Equil.EquilibriumConfig,spec.config_type}) # build_analytic_config resolves the section to the right config type using defaults. From 5096eaaf157079d674832c48364f2f1c7dde07e0 Mon Sep 17 00:00:00 2001 From: Jake Halpern Date: Tue, 23 Jun 2026 12:03:38 -0400 Subject: [PATCH 097/135] VACUUM - MINOR - commiting general revisions from the spectral branch before I close it --- examples/Solovev_ideal_example_3D/gpec.toml | 6 +- .../Solovev_ideal_example_3D/run_example.jl | 4 + src/ForceFreeStates/Free.jl | 30 ++-- src/Vacuum/DataTypes.jl | 3 +- src/Vacuum/Kernel3D.jl | 134 ++++++------------ 5 files changed, 66 insertions(+), 111 deletions(-) create mode 100644 examples/Solovev_ideal_example_3D/run_example.jl diff --git a/examples/Solovev_ideal_example_3D/gpec.toml b/examples/Solovev_ideal_example_3D/gpec.toml index 094dd79c6..f945f81cf 100644 --- a/examples/Solovev_ideal_example_3D/gpec.toml +++ b/examples/Solovev_ideal_example_3D/gpec.toml @@ -21,7 +21,7 @@ mat_flag = true # Construct coefficient matrices for diagnostic pu ode_flag = true # Integrate ODEs for stability of the internal long-wavelength mode (must be true for GPEC) vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes -psiedge = 0.99 # Edge dW(ψ) diagnostic scan band [psiedge, psilim]; set ≥ psilim to disable +psiedge = 1.0 # Edge dW(ψ) diagnostic scan band [psiedge, psilim]; set ≥ psilim to disable qlow = 1.02 # Integration initiated at q determined by min(q0, qlow) qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh) sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) @@ -30,8 +30,8 @@ nn_low = 1 # Smallest toroidal mode number to include nn_high = 1 # Largest toroidal mode number to include delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 8 # Expands upper bound of Fourier harmonics -delta_mband = 0 # Integration keeps only this wide a band... -mthvac = 96 # Number of points used in splines over poloidal angle at the plasma-vacuum interface +mthvac = 64 # Number of points used in splines over poloidal angle at the plasma-vacuum interface +nzvac = 96 # Number of points used in splines over toroidal angle at the plasma-vacuum interface thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds kinetic_source = "fixed" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model diff --git a/examples/Solovev_ideal_example_3D/run_example.jl b/examples/Solovev_ideal_example_3D/run_example.jl new file mode 100644 index 000000000..fa0a9e53d --- /dev/null +++ b/examples/Solovev_ideal_example_3D/run_example.jl @@ -0,0 +1,4 @@ +using Pkg; +Pkg.activate(joinpath(@__DIR__, "../..")) +using GeneralizedPerturbedEquilibrium +GeneralizedPerturbedEquilibrium.main([dirname(@__FILE__)]) diff --git a/src/ForceFreeStates/Free.jl b/src/ForceFreeStates/Free.jl index 31cec0f50..a5184af4b 100644 --- a/src/ForceFreeStates/Free.jl +++ b/src/ForceFreeStates/Free.jl @@ -32,10 +32,7 @@ and data dumping. # Scale by (m - n*q)(m' - n'*q) [Chance Phys. Plasmas 1997 2161 eq. 126] singfac = vec((mlow:mhigh) .- qlim .* (nlow:nhigh)') - @inbounds for ipert in 1:numpert_total - @views vac_data.wv[ipert, :] .*= singfac[ipert] - @views vac_data.wv[:, ipert] .*= singfac[ipert] - end + vac_data.wv .*= singfac .* singfac' # Least stable eigenvalue of the vacuum matrix alone (should be PSD; clamp numerical noise to zero) vac_data.vacuum_eigenvalue = max(0.0, minimum(real.(eigvals(Hermitian(vac_data.wv))))) @@ -83,16 +80,14 @@ and data dumping. vac_data.wt[:, isol] .*= phase end - # Compute plasma and vacuum contributions. - # wpt = wt' * wp * wt ; wvt = wt' * wv * wt + # Project W_p and W_v into the eigenmode basis. Diagonal entries give + # the plasma/vacuum energy split for each mode: et[i] = ep[i] + ev[i] mul!(tmp_mat, wp, vac_data.wt) - mul!(wpt, adjoint(vac_data.wt), tmp_mat) + mul!(wpt, vac_data.wt', tmp_mat) mul!(tmp_mat, vac_data.wv, vac_data.wt) - mul!(wvt, adjoint(vac_data.wt), tmp_mat) - for ipert in 1:numpert_total - vac_data.ep[ipert] = wpt[ipert, ipert] - vac_data.ev[ipert] = wvt[ipert, ipert] - end + mul!(wvt, vac_data.wt', tmp_mat) + vac_data.ep .= diag(wpt) + vac_data.ev .= diag(wvt) # Eigenspectrum of W_Φ at psilim — Jacobian-invariant energy values; see RootAreaWeighted.jl. # Computed directly here (no spline); spline is used by the edge scan. @@ -141,7 +136,7 @@ Compute a spline of vacuum response matrices over the range of psi from 'ctrl.ps same function as `free_wvmats` in the Fortran code. Currently defaults to 4 spline points per q-window minimum. """ -function free_compute_wv_spline(ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStatesInternal) +@with_pool pool function free_compute_wv_spline(ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStatesInternal) profiles = equil.profiles @@ -149,8 +144,8 @@ function free_compute_wv_spline(ctrl::ForceFreeStatesControl, equil::Equilibrium # TODO: 4 spline points is arbitrary - is there a better way? qedge = profiles.q_spline(ctrl.psiedge) npsi = max(4, ceil(Int, (intr.qlim - qedge) * intr.nhigh * 4)) - psi_array = zeros(Float64, npsi + 1) - wv_array = zeros(ComplexF64, npsi + 1, intr.numpert_total, intr.numpert_total) + psi_array = zeros!(pool, Float64, npsi + 1) + wv_array = zeros!(pool, ComplexF64, npsi + 1, intr.numpert_total, intr.numpert_total) for i in 1:(npsi+1) # Space points evenly in q over [qedge, qlim] (i=1 → qedge, i=npsi+1 → qlim) @@ -212,10 +207,7 @@ wv matrix spline to `free_compute_wv_spline` and pass it in `odet.edge_scan.wvma q_at_psifac = equil.profiles.q_spline(odet.psifac) # Scale by (m - n*q)(m' - n'*q) [Chance Phys. Plasmas 1997 2161 eq. 126] singfac = vec((intr.mlow:intr.mhigh) .- q_at_psifac .* (intr.nlow:intr.nhigh)') - @inbounds for ipert in 1:Npert - @views wv[ipert, :] .*= singfac[ipert] - @views wv[:, ipert] .*= singfac[ipert] - end + wv .*= singfac .* singfac' # Compute total energy matrix and eigen-decomposition wt .= wp .+ wv diff --git a/src/Vacuum/DataTypes.jl b/src/Vacuum/DataTypes.jl index 63d029b42..9a406199f 100644 --- a/src/Vacuum/DataTypes.jl +++ b/src/Vacuum/DataTypes.jl @@ -239,8 +239,7 @@ end 3D toroidal surface geometry for vacuum boundary integral calculations. Built by toroidally extruding a 2D poloidal contour (`PlasmaGeometry`) and computing -Cartesian coordinates, tangent vectors, normals, and differential area elements. Note -that the gradient/area elements are scaled by dθ and dζ. +Cartesian coordinates, tangent vectors, normals, and differential area elements. # Fields diff --git a/src/Vacuum/Kernel3D.jl b/src/Vacuum/Kernel3D.jl index df28dd45f..8617b1d6c 100644 --- a/src/Vacuum/Kernel3D.jl +++ b/src/Vacuum/Kernel3D.jl @@ -177,74 +177,35 @@ function get_singular_quadrature(PATCH_RAD::Int, RAD_DIM::Int, INTERP_ORDER::Int end """ - laplace_single_layer(x_obs, x_src) -> Float64 + laplace_kernel(ox, oy, oz, sx, sy, sz, nx, ny, nz) -> (single, double) -Evaluate the Laplace single-layer (FxU) kernel between two 3D points. Returns -0.0 if the observation point coincides with the source point to avoid singularity. +Fused scalar-argument Laplace kernels for the 3D vacuum BIE. -The single-layer kernel φ is the fundamental solution to Laplace's equation: +Returns a tuple `(single, double)` where: -``` -φ(x_obs, x_src) = 1 / |x_obs - x_src| -``` + - `single = 1/r` is the single-layer kernel + - `double = (Δx⋅n)/r^3` is the double-layer kernel -# Arguments - - - `x_obs`: Observation point (3D Cartesian coordinates, any AbstractVector) - - `x_src`: Source point (3D Cartesian coordinates, any AbstractVector) - -# Returns - - - `Float64`: Kernel value φ(x_obs, x_src) -""" -function laplace_single_layer(x_obs::AbstractVector{<:Real}, x_src::AbstractVector{<:Real}) - @inbounds begin - dx = x_obs[1] - x_src[1] - dy = x_obs[2] - x_src[2] - dz = x_obs[3] - x_src[3] - end - r2 = dx*dx + dy*dy + dz*dz - r2 < 1e-30 && return 0.0 - return inv(sqrt(r2)) -end - -""" - laplace_double_layer(x_obs, x_src, n_src) -> Float64 - -Evaluate the Laplace double-layer (DxU) kernel between a point and a surface element. Returns -0.0 if the observation point coincides with the source point to avoid singularity. Allocation-free -scalar arithmetic is used for maximum performance. - -The double-layer kernel K is the normal derivative of the fundamental solution: - -``` -K(x_obs, x_src, n_src) = ∇_{x_src} φ · n_src = (x_obs - x_src) · n_src / |x_obs - x_src|³ -``` - -# Arguments - - - `x_obs`: Observation point (3D Cartesian coordinates, any AbstractVector) - - `x_src`: Source point on surface (3D Cartesian coordinates, any AbstractVector) - - `n_src`: Outward UNIT normal at source point (must be normalized!, any AbstractVector) - -# Returns - - - `Float64`: Kernel value K(x_obs, x_src, n_src) +This is used when `compute_3D_kernel_matrices!` needs **both** kernels for the same pair, so the +distance computation (`sqrt(r²)`) is shared. Returns `(0.0, 0.0)` when `r² < 1e-30`. """ -function laplace_double_layer(x_obs::AbstractVector{<:Real}, x_src::AbstractVector{<:Real}, n_src::AbstractVector{<:Real}) - @inbounds begin - dx = x_obs[1] - x_src[1] - dy = x_obs[2] - x_src[2] - dz = x_obs[3] - x_src[3] - nx = n_src[1] - ny = n_src[2] - nz = n_src[3] - end +@fastmath @inline function laplace_kernel( + ox::Float64, oy::Float64, oz::Float64, + sx::Float64, sy::Float64, sz::Float64, + nx::Float64, ny::Float64, nz::Float64 +) + dx = ox - sx + dy = oy - sy + dz = oz - sz r2 = dx*dx + dy*dy + dz*dz - r2 < 1e-30 && return 0.0 + r2 < 1e-30 && return (0.0, 0.0) rinv = inv(sqrt(r2)) + # single-layer: 1/r + single = rinv + # double-layer: (Δx·n)/r^3 r3inv = rinv * rinv * rinv - return (dx*nx + dy*ny + dz*nz) * r3inv + double = (dx*nx + dy*ny + dz*nz) * r3inv + return (single, double) end """ @@ -281,8 +242,7 @@ end interpolate_to_polar!(polar_data, patch, quad_data) Interpolate Cartesian patch data to polar quadrature points using sparse matrix multiply. -Overwrites `polar_data` using mul! function arguments, mul!(C, A, B, α, β) -> C where -C = α * A * B + β * C. +Overwrites `polar_data` using mul! function arguments, mul!(C, A, B) -> C where C = A * B. # Arguments @@ -291,13 +251,12 @@ C = α * A * B + β * C. - `P2G`: Sparse interpolation matrix """ function interpolate_to_polar!(polar_data::Array{Float64,3}, patch::Array{Float64,3}, P2G::SparseMatrixCSC{Float64,Int}) - # Flatten patch to (Ngrid × dof), apply P2G' to get (Npolar × dof) patch_flat = reshape(patch, :, size(patch, 3)) - mul!(reshape(polar_data, :, size(patch, 3)), P2G', patch_flat, 1.0, 0.0) + mul!(reshape(polar_data, :, size(patch, 3)), P2G', patch_flat) end """ - compute_polar_normal!(n_polar, dr_dθ_polar, dr_dζ_polar) + compute_polar_normal!(n_polar, dr_dθ_polar, dr_dζ_polar, normal_orient) Compute normal vector (= ∂r/∂θ × ∂r/∂ζ) at polar quadrature points from interpolated tangent vectors. We already scaled the normals by normal_orient in the geometry construction, so we need to reapply @@ -380,12 +339,17 @@ where each entry is φ(x_obs, x_src). - `grad_greenfunction`: Double-layer kernel matrix (Nobs × Nsrc) filled in place - `greenfunction`: Single-layer kernel matrix (Nobs × Nsrc) filled in place + - `observer`: Observer geometry (PlasmaGeometry3D) + - `source`: Source geometry (PlasmaGeometry3D) + - `PATCH_RAD`: Number of points adjacent to source point to treat as singular + Total patch size in # of gridpoints = (2 * PATCH_RAD + 1) x (2 * PATCH_RAD + 1) + - `RAD_DIM`: Polar radial quadrature order. Angular order = 2 * RAD_DIM + - `INTERP_ORDER`: Lagrange interpolation order + Must be ≤ (2 * PATCH_RAD + 1) @@ -405,7 +369,7 @@ function compute_3D_kernel_matrices!( INTERP_ORDER::Int ) num_points = observer.mtheta * observer.nzeta - dθdζ = 4π^2 / (num_points) + dθdζ = 4π^2 / num_points # Get block of grad green function matrix col_index = (source isa PlasmaGeometry3D ? 1 : 2) @@ -424,13 +388,11 @@ function compute_3D_kernel_matrices!( # Initialize quadrature data # This allows the code to run at lower resolution without erroring out, but will warn the user. if PATCH_RAD > (min(source.mtheta, source.nzeta) - 1) ÷ 2 - @warn "PATCH_RAD is greater than the number of points in the toroidal or poloidal direction, which is not supported. Setting PATCH_RAD to $((min(source.mtheta, source.nzeta) - 1) ÷ 2). Be sure to check if outputs are converged." + @warn "PATCH_RAD is greater than half the number of points in the toroidal or poloidal direction, which is not supported. Setting PATCH_RAD to $((min(source.mtheta, source.nzeta) - 1) ÷ 2). Be sure to check if outputs are converged." PATCH_RAD = (min(source.mtheta, source.nzeta) - 1) ÷ 2 end quad_data = get_singular_quadrature(PATCH_RAD, RAD_DIM, INTERP_ORDER) (; PATCH_DIM, PATCH_RAD, ANG_DIM, RAD_DIM, Ppou, Gpou, P2G) = quad_data - @assert observer.mtheta ≥ PATCH_DIM "Must have observer.mtheta ≥ PATCH_DIM, got observer.mtheta=$(observer.mtheta), PATCH_DIM=$PATCH_DIM" - @assert observer.nzeta ≥ PATCH_DIM "Must have observer.nzeta ≥ PATCH_DIM, got observer.nzeta=$(observer.nzeta), PATCH_DIM=$PATCH_DIM" # Allocate thread-local workspaces (one per thread) max_threadid = Threads.maxthreadid() @@ -456,14 +418,13 @@ function compute_3D_kernel_matrices!( # Evaluate kernels at grid points r_src = @view source.r[idx_src, :] n_src = @view source.normal[idx_src, :] - K_single = laplace_single_layer(r_obs, r_src) - K_double = laplace_double_layer(r_obs, r_src, n_src) + far_single, far_double = laplace_kernel(r_obs[1], r_obs[2], r_obs[3], r_src[1], r_src[2], r_src[3], n_src[1], n_src[2], n_src[3]) # Apply weights (periodic trapezoidal rule = constant weights) if populate_greenfunction - greenfunction[idx_obs, idx_src] = K_single * dθdζ + greenfunction[idx_obs, idx_src] = far_single * dθdζ end - grad_greenfunction_block[idx_obs, idx_src] = K_double * dθdζ + grad_greenfunction_block[idx_obs, idx_src] = far_double * dθdζ end # ============================================================ @@ -482,28 +443,28 @@ function compute_3D_kernel_matrices!( # Compute normal vectors at polar points from interpolated tangent vectors compute_polar_normal!(n_polar, dr_dθ_polar, dr_dζ_polar, source.normal_orient) - # Evaluate kernels at polar points with POU weighting + # Evaluate kernels and apply quadrature weights: area element × POU, where POU contains rdrdθ already @inbounds for ia in 1:ANG_DIM, ir in 1:RAD_DIM # Evaluate kernels using recomputed normal (use @view to avoid allocation) r_src = @view r_polar[ir, ia, :] n_src = @view n_polar[ir, ia, :] - K_single = laplace_single_layer(r_obs, r_src) - K_double = laplace_double_layer(r_obs, r_src, n_src) + near_single, near_double = laplace_kernel(r_obs[1], r_obs[2], r_obs[3], r_src[1], r_src[2], r_src[3], n_src[1], n_src[2], n_src[3]) # Apply quadrature weights: area element × POU, where POU contains rdrdθ already - M_polar_single[ir, ia] = K_single * Ppou[ir, ia] * dθdζ - M_polar_double[ir, ia] = K_double * Ppou[ir, ia] * dθdζ + M_polar_single[ir, ia] = near_single * Ppou[ir, ia] * dθdζ + M_polar_double[ir, ia] = near_double * Ppou[ir, ia] * dθdζ end # Distribute polar singular corrections back to Cartesian grid using sparse matrix # grid = P2G * polar (maps Npolar → Ngrid) - mul!(M_grid_single_flat, P2G, vec(M_polar_single)) mul!(M_grid_double_flat, P2G, vec(M_polar_double)) - M_grid_single = reshape(M_grid_single_flat, PATCH_DIM, PATCH_DIM) M_grid_double = reshape(M_grid_double_flat, PATCH_DIM, PATCH_DIM) + if populate_greenfunction + mul!(M_grid_single_flat, P2G, vec(M_polar_single)) + M_grid_single = reshape(M_grid_single_flat, PATCH_DIM, PATCH_DIM) + end - # Compute remaining far-field POU contribution and near-field polar quadrature result - # We include this region in the far-field trapezoidal rule, so use Gpou = -χ here to get 1-χ + # POU correction: singular correction + (1 + Gpou) * far-field terms @inbounds for j in 1:PATCH_DIM, i in 1:PATCH_DIM # Map back to global indices idx_pol = periodic_wrap(i_obs - PATCH_RAD + i - 1, source.mtheta) @@ -513,14 +474,13 @@ function compute_3D_kernel_matrices!( # Remainder of far-field contribution on the singular grid: Gpou = -χ r_src = @view source.r[idx_src, :] n_src = @view source.normal[idx_src, :] - far_single = laplace_single_layer(r_obs, r_src) * Gpou[i, j] * dθdζ - far_double = laplace_double_layer(r_obs, r_src, n_src) * Gpou[i, j] * dθdζ + far_single, far_double = laplace_kernel(r_obs[1], r_obs[2], r_obs[3], r_src[1], r_src[2], r_src[3], n_src[1], n_src[2], n_src[3]) # Apply near + far contributions if populate_greenfunction - greenfunction[idx_obs, idx_src] += M_grid_single[i, j] + far_single + greenfunction[idx_obs, idx_src] += M_grid_single[i, j] + far_single * Gpou[i, j] * dθdζ end - grad_greenfunction_block[idx_obs, idx_src] += M_grid_double[i, j] + far_double + grad_greenfunction_block[idx_obs, idx_src] += M_grid_double[i, j] + far_double * Gpou[i, j] * dθdζ end end @@ -530,7 +490,7 @@ function compute_3D_kernel_matrices!( greenfunction ./= 2π # Add the term that comes from the volume integral of Green's identity - typeof(source) == typeof(observer) && begin + if typeof(source) == typeof(observer) for i in 1:num_points grad_greenfunction_block[i, i] += 1.0 end From 1aee197786e89724bffb6c002e41aa101847ebf5 Mon Sep 17 00:00:00 2001 From: Jake Halpern Date: Tue, 23 Jun 2026 12:43:25 -0400 Subject: [PATCH 098/135] VACUUM - MINOR - removing green_only --- src/PerturbedEquilibrium/Response.jl | 52 ++++---- src/PerturbedEquilibrium/SingularCoupling.jl | 124 +++++++++++-------- src/Vacuum/Vacuum.jl | 95 ++++++-------- test/runtests_vacuum.jl | 28 +---- 4 files changed, 137 insertions(+), 162 deletions(-) diff --git a/src/PerturbedEquilibrium/Response.jl b/src/PerturbedEquilibrium/Response.jl index b9b509322..8b61feac2 100644 --- a/src/PerturbedEquilibrium/Response.jl +++ b/src/PerturbedEquilibrium/Response.jl @@ -7,11 +7,12 @@ Compute plasma response to external forcing using ForceFreeStates eigenmode solutions. Implements resp_index=0 calculation from Fortran gpresp: -- Build flux matrix from eigenmodes -- Calculate plasma inductance Lambda (wt0-based, resp_induct_flag=TRUE) -- Calculate surface inductance L from Green's function -- Compute permeability P = Lambda * L^{-1} -- Apply forcing to get response: Phi_tot = P * Phi_x + + - Build flux matrix from eigenmodes + - Calculate plasma inductance Lambda (wt0-based, resp_induct_flag=TRUE) + - Calculate surface inductance L from Green's function + - Compute permeability P = Lambda * L^{-1} + - Apply forcing to get response: Phi_tot = P * Phi_x """ function compute_plasma_response!( state::PerturbedEquilibriumState, @@ -40,10 +41,9 @@ function compute_plasma_response!( # vac_data.grri has shape [2*mthvac*nzvac, 2*mpert] and cannot be used directly. nn = ffs_intr.nlow vac_input_2d = Vacuum.VacuumInput(equil, ffs_intr.psilim, vac_data.mthvac, 1, - ffs_intr.mpert, ffs_intr.mlow, 1, nn) + ffs_intr.mpert, ffs_intr.mlow, 1, nn) wall_nowall = Vacuum.WallShapeSettings(; shape="nowall") - _, grri_2d_raw, grre_2d_raw, _, _ = Vacuum.compute_vacuum_response( - vac_input_2d, wall_nowall; green_only=true) + _, grri_2d_raw, grre_2d_raw, _, _ = Vacuum.compute_vacuum_response(vac_input_2d, wall_nowall) grri_2d = Matrix{Float64}(grri_2d_raw) grre_2d = Matrix{Float64}(grre_2d_raw) ν_vac = Vacuum.PlasmaGeometry(vac_input_2d).ν @@ -66,30 +66,30 @@ function compute_plasma_response!( # flux (Φ = A·b̄) — see Utils.jl output docs. rootarea_to_area_weight, surface_area = build_control_surface_rootarea_to_area_weight(equil, ffs_intr) field_mats = field_space_response_matrices(plasma_inductance, surface_inductance, permeability, reluctance, rootarea_to_area_weight, surface_area) - state.plasma_inductance = field_mats.plasma_inductance - state.surface_inductance = field_mats.surface_inductance - state.permeability = field_mats.permeability - state.reluctance = field_mats.reluctance + state.plasma_inductance = field_mats.plasma_inductance + state.surface_inductance = field_mats.surface_inductance + state.permeability = field_mats.permeability + state.reluctance = field_mats.reluctance state.rootarea_to_area_weight = rootarea_to_area_weight - state.surface_area = surface_area + state.surface_area = surface_area # Forcing and response on the control surface. Flux Φ appears only as a brief internal bridge: # forcing arrives as Φ_x, the field reconstruction below consumes Φ_tot, and the b̃ spectra are # formed via the conform operator R = S·A (Φ = R·b̃). - forcing_flux = map_forcing_to_eigenmodes(intr.forcing_modes, ffs_intr) + forcing_flux = map_forcing_to_eigenmodes(intr.forcing_modes, ffs_intr) response_flux = compute_plasma_response_vector(permeability, forcing_flux) # Output forcing/response in the three Pharr field representations (all tesla): # b̃ (root-area-weighted) = R⁻¹·Φ, b (bare) = Σ⁻¹·b̃, b̄ (area-weighted) = S·b̃. - flux_conform = rootarea_to_area_weight .* surface_area # R = Σ·√A (b̃ → flux) + flux_conform = rootarea_to_area_weight .* surface_area # R = Σ·√A (b̃ → flux) bare_to_rootarea = rootarea_to_area_weight .* sqrt(surface_area) # Σ (bare → b̃) - forcing_b_rootarea = flux_conform \ forcing_flux + forcing_b_rootarea = flux_conform \ forcing_flux response_b_rootarea = flux_conform \ response_flux - state.forcing_b_rootarea = forcing_b_rootarea + state.forcing_b_rootarea = forcing_b_rootarea state.response_b_rootarea = response_b_rootarea - state.forcing_b = bare_to_rootarea \ forcing_b_rootarea - state.response_b = bare_to_rootarea \ response_b_rootarea - state.forcing_b_area = rootarea_to_area_weight * forcing_b_rootarea + state.forcing_b = bare_to_rootarea \ forcing_b_rootarea + state.response_b = bare_to_rootarea \ response_b_rootarea + state.forcing_b_area = rootarea_to_area_weight * forcing_b_rootarea state.response_b_area = rootarea_to_area_weight * response_b_rootarea # Scalar energies and torque (Joules), ported from Fortran gpout. These are congruence-invariant @@ -98,12 +98,12 @@ function compute_plasma_response!( # needlessly ill-conditioned. The result is a physical scalar, not a stored flux quantity. L_surf_inv = inv(surface_inductance) L_plas_inv = inv(plasma_inductance) - vy = dot(forcing_flux, L_surf_inv * forcing_flux) / 4 + vy = dot(forcing_flux, L_surf_inv * forcing_flux) / 4 sy = dot(response_flux, L_surf_inv * response_flux) / 4 py = dot(response_flux, L_plas_inv * response_flux) / 4 - state.vacuum_energy = real(vy) - state.surface_energy = real(sy) - state.plasma_energy = real(py) # Fortran's "total energy" is this pengy + state.vacuum_energy = real(vy) + state.surface_energy = real(sy) + state.plasma_energy = real(py) # Fortran's "total energy" is this pengy state.toroidal_torque = -2 * nn * imag(py) xi_modes, b_modes = reconstruct_physical_fields( @@ -114,12 +114,12 @@ function compute_plasma_response!( npsi = size(ForceFreeStates_results.u_store, 4) state.psi_grid = ForceFreeStates_results.psi_store[1:npsi] state.xi_modes = xi_modes - state.b_modes = b_modes + state.b_modes = b_modes b_n_modes, xi_n_modes = compute_b_n_xi_n_modes( xi_modes.psi_J, b_modes.psi, ForceFreeStates_results, equil, ffs_intr ) - state.b_n_modes = b_n_modes + state.b_n_modes = b_n_modes state.xi_n_modes = xi_n_modes if ctrl.verbose diff --git a/src/PerturbedEquilibrium/SingularCoupling.jl b/src/PerturbedEquilibrium/SingularCoupling.jl index fd34d5f25..07cb4e37f 100644 --- a/src/PerturbedEquilibrium/SingularCoupling.jl +++ b/src/PerturbedEquilibrium/SingularCoupling.jl @@ -33,8 +33,10 @@ end function _hermite_cubic_val(u_a, u_b, du_a, du_b, psi_a, psi_b, psi) h = psi_b - psi_a t = (psi - psi_a) / h - h00 = 2t^3 - 3t^2 + 1; h10 = t^3 - 2t^2 + t - h01 = -2t^3 + 3t^2; h11 = t^3 - t^2 + h00 = 2t^3 - 3t^2 + 1; + h10 = t^3 - 2t^2 + t + h01 = -2t^3 + 3t^2; + h11 = t^3 - t^2 return @. h00 * u_a + h * h10 * du_a + h01 * u_b + h * h11 * du_b end @@ -61,15 +63,17 @@ Matching Fortran GPEC output: `C_f_x_out` (coupling matrix) and `Phi_res`, `w_is Populates `state` with: - Coupling matrices `[n_rational × numpert_total]` — C[row, j] = coupling when forcing mode j has unit amplitude: +Coupling matrices `[n_rational × numpert_total]` — C[row, j] = coupling when forcing mode j has unit amplitude: + - `C_resonant_area_weighted_field`, `C_resonant_current`, `C_island_width_sq`, `C_penetrated_area_weighted_field`, `C_delta_prime` - Applied resonant vectors `[n_rational]` = C · amp_vec: +Applied resonant vectors `[n_rational]` = C · amp_vec: + - `resonant_area_weighted_field`, `resonant_current`, `island_width_sq`, `penetrated_area_weighted_field`, `delta_prime` - Diagnostics `[n_rational]`: `island_half_width`, `chirikov_parameter` +Diagnostics `[n_rational]`: `island_half_width`, `chirikov_parameter` - Metadata `[n_rational]`: `rational_psi`, `rational_q`, `rational_m_res`, `rational_n`, `rational_surface_idx` +Metadata `[n_rational]`: `rational_psi`, `rational_q`, `rational_m_res`, `rational_n`, `rational_surface_idx` """ function compute_singular_coupling_metrics!( state::PerturbedEquilibriumState, @@ -125,15 +129,15 @@ function compute_singular_coupling_metrics!( ctrl.verbose && @info "Found $n_rational resonant (surface, n) pairs" # Phase 2: Allocate output arrays - state.C_resonant_area_weighted_field = zeros(ComplexF64, n_rational, numpert_total) - state.C_resonant_current = zeros(ComplexF64, n_rational, numpert_total) - state.C_island_width_sq = zeros(ComplexF64, n_rational, numpert_total) - state.C_penetrated_area_weighted_field = zeros(ComplexF64, n_rational, numpert_total) - state.C_delta_prime = zeros(ComplexF64, n_rational, numpert_total) - state.rational_psi = zeros(Float64, n_rational) - state.rational_q = zeros(Float64, n_rational) - state.rational_m_res = zeros(Int, n_rational) - state.rational_n = zeros(Int, n_rational) + state.C_resonant_area_weighted_field = zeros(ComplexF64, n_rational, numpert_total) + state.C_resonant_current = zeros(ComplexF64, n_rational, numpert_total) + state.C_island_width_sq = zeros(ComplexF64, n_rational, numpert_total) + state.C_penetrated_area_weighted_field = zeros(ComplexF64, n_rational, numpert_total) + state.C_delta_prime = zeros(ComplexF64, n_rational, numpert_total) + state.rational_psi = zeros(Float64, n_rational) + state.rational_q = zeros(Float64, n_rational) + state.rational_m_res = zeros(Int, n_rational) + state.rational_n = zeros(Int, n_rational) state.rational_surface_idx = zeros(Int, n_rational) # Precompute ODE coefficient matrix C_coeffs for all PE forcing modes. @@ -141,9 +145,9 @@ function compute_singular_coupling_metrics!( # where edge_mn_k[j] = plasma_response[j,k] / (chi1·singfac_lim[j]·2πi) # Matches Fortran gpout_resp: edge_mn = foutmn/(chi1·singfac·twopi·ifac) psi_lim = ForceFreeStates_results.psi_store[ForceFreeStates_results.step] - q_lim = equil.profiles.q_spline(psi_lim) + q_lim = equil.profiles.q_spline(psi_lim) singfac_lim = [intr.m_modes[j] - intr.n_modes[j] * q_lim for j in 1:numpert_total] - u_bnd = ForceFreeStates_results.u_store[:, :, 1, ForceFreeStates_results.step] + u_bnd = ForceFreeStates_results.u_store[:, :, 1, ForceFreeStates_results.step] # Divide each row j by singfac_lim[j] — reshape to column vector so Julia broadcasts row-wise, not column-wise. edge_mn = intr.plasma_response ./ (chi1 * 2π * im .* reshape(singfac_lim, :, 1)) C_coeffs = u_bnd \ edge_mn # mpert × numpert_total @@ -163,7 +167,7 @@ function compute_singular_coupling_metrics!( # Compute Green's functions at this surface for this n (once per pair) vac_input = Vacuum.VacuumInput(equil, sing_surf.psifac, mtheta, 1, mpert, mlow, 1, nn) - _, grri_raw, grre_raw, _, _ = Vacuum.compute_vacuum_response(vac_input, wall_settings; green_only=true) + _, grri_raw, grre_raw, _, _ = Vacuum.compute_vacuum_response(vac_input, wall_settings) grri = Matrix{Float64}(grri_raw) grre = Matrix{Float64}(grre_raw) ffs_intr.sing[s].grri = grri @@ -177,8 +181,8 @@ function compute_singular_coupling_metrics!( m_idx = m_res - mlow + 1 L_mm = L_surf[m_idx, m_idx] - j_c = compute_current_density(equil, sing_surf.psifac) - area = compute_surface_area(equil, sing_surf.psifac) + j_c = compute_current_density(equil, sing_surf.psifac) + area = compute_surface_area(equil, sing_surf.psifac) # Matches Fortran gpout_resp: shear = m*dq/dψ / q² = n*dq/dψ / q (since m=n*q). # Uses abs(nn) because island_half_width = sqrt(abs(island_width_sq)), so the sign # of shear only affects the sign of C_island_width_sq, not the physical island width. @@ -197,18 +201,24 @@ function compute_singular_coupling_metrics!( il_l, ir_l, _ = _psi_bracket(psi_store_all, lpsi, nstep) il_r, ir_r, _ = _psi_bracket(psi_store_all, rpsi, nstep) - u_node = ForceFreeStates_results.u_store + u_node = ForceFreeStates_results.u_store ud_node = ForceFreeStates_results.ud_store - ua_l = u_node[ resnum, :, 1, il_l]; ub_l = u_node[ resnum, :, 1, ir_l] - ua_r = u_node[ resnum, :, 1, il_r]; ub_r = u_node[ resnum, :, 1, ir_r] - dua_l = ud_node[resnum, :, 1, il_l]; dub_l = ud_node[resnum, :, 1, ir_l] - dua_r = ud_node[resnum, :, 1, il_r]; dub_r = ud_node[resnum, :, 1, ir_r] - - psi_il_l = psi_store_all[il_l]; psi_ir_l = psi_store_all[ir_l] - psi_il_r = psi_store_all[il_r]; psi_ir_r = psi_store_all[ir_r] - - u_l = _hermite_cubic_val(ua_l, ub_l, dua_l, dub_l, psi_il_l, psi_ir_l, lpsi) - u_r = _hermite_cubic_val(ua_r, ub_r, dua_r, dub_r, psi_il_r, psi_ir_r, rpsi) + ua_l = u_node[resnum, :, 1, il_l]; + ub_l = u_node[resnum, :, 1, ir_l] + ua_r = u_node[resnum, :, 1, il_r]; + ub_r = u_node[resnum, :, 1, ir_r] + dua_l = ud_node[resnum, :, 1, il_l]; + dub_l = ud_node[resnum, :, 1, ir_l] + dua_r = ud_node[resnum, :, 1, il_r]; + dub_r = ud_node[resnum, :, 1, ir_r] + + psi_il_l = psi_store_all[il_l]; + psi_ir_l = psi_store_all[ir_l] + psi_il_r = psi_store_all[il_r]; + psi_ir_r = psi_store_all[ir_r] + + u_l = _hermite_cubic_val(ua_l, ub_l, dua_l, dub_l, psi_il_l, psi_ir_l, lpsi) + u_r = _hermite_cubic_val(ua_r, ub_r, dua_r, dub_r, psi_il_r, psi_ir_r, rpsi) # Derivative (ud): chord slope from u_store only — ud_store can be systematically off near # outer surfaces (q=4/5) where the ODE solution varies rapidly; near-cancellation in bwp1 # then amplifies even a ~10% ud_store error into a large Delta' error. Chord slope avoids @@ -216,16 +226,20 @@ function compute_singular_coupling_metrics!( ud_l = (ub_l .- ua_l) ./ (psi_ir_l - psi_il_l) ud_r = (ub_r .- ua_r) ./ (psi_ir_r - psi_il_r) - q_l = equil.profiles.q_spline(lpsi); q1_l = equil.profiles.q_deriv(lpsi) - q_r = equil.profiles.q_spline(rpsi); q1_r = equil.profiles.q_deriv(rpsi) + q_l = equil.profiles.q_spline(lpsi); + q1_l = equil.profiles.q_deriv(lpsi) + q_r = equil.profiles.q_spline(rpsi); + q1_r = equil.profiles.q_deriv(rpsi) singfac_l = m_res - nn * q_l singfac_r = m_res - nn * q_r jump_vec = Vector{ComplexF64}(undef, numpert_total) for k in 1:numpert_total - ck = @view C_coeffs[:, k] - xsp_l = dot(u_l, ck); xsp1_l = dot(ud_l, ck) - xsp_r = dot(u_r, ck); xsp1_r = dot(ud_r, ck) + ck = @view C_coeffs[:, k] + xsp_l = dot(u_l, ck); + xsp1_l = dot(ud_l, ck) + xsp_r = dot(u_r, ck); + xsp1_r = dot(ud_r, ck) bwp1_l = 2π * im * chi1 * (singfac_l * xsp1_l - nn * q1_l * xsp_l) bwp1_r = 2π * im * chi1 * (singfac_r * xsp1_r - nn * q1_r * xsp_r) jump_vec[k] = bwp1_r - bwp1_l @@ -245,7 +259,7 @@ function compute_singular_coupling_metrics!( # - resonant (shielding) current: j_c already integrates jac·|∇ψ| over the surface, so the # Jacobian weighting is carried inside j_c — no separate area factor needed. # - resonant flux → field: Φ^r/A^r [T], invariant [Park 2008; Pharr 2026]. - state.C_delta_prime[row, :] = jump_vec ./ (twopi * chi1) + state.C_delta_prime[row, :] = jump_vec ./ (twopi * chi1) state.C_resonant_current[row, :] = jump_vec .* (-j_c / (twopi * m_res)) # Matches Fortran gpout_resp: singflx = L·fkaxmn, resonant area-weighted field = singflx/area, # islandhwids = 4·singflx/(2π·shear·q·chi1) @@ -255,11 +269,11 @@ function compute_singular_coupling_metrics!( state.C_island_width_sq[row, :] = (4.0 / (twopi * shear * sing_surf.q * chi1)) .* singflx_pre end - state.rational_psi[row] = sing_surf.psifac - state.rational_q[row] = sing_surf.q - state.rational_m_res[row] = m_res - state.rational_n[row] = nn - state.rational_surface_idx[row] = s + state.rational_psi[row] = sing_surf.psifac + state.rational_q[row] = sing_surf.q + state.rational_m_res[row] = m_res + state.rational_n[row] = nn + state.rational_surface_idx[row] = s if ctrl.verbose dp_diag = real(state.C_delta_prime[row, resnum]) @@ -276,11 +290,11 @@ function compute_singular_coupling_metrics!( isnothing(j) || (forcing_flux[j] = mode.amplitude) end - state.resonant_area_weighted_field = state.C_resonant_area_weighted_field * forcing_flux + state.resonant_area_weighted_field = state.C_resonant_area_weighted_field * forcing_flux state.resonant_current = state.C_resonant_current * forcing_flux - state.island_width_sq = state.C_island_width_sq * forcing_flux + state.island_width_sq = state.C_island_width_sq * forcing_flux state.penetrated_area_weighted_field = state.C_penetrated_area_weighted_field * forcing_flux - state.delta_prime = state.C_delta_prime * forcing_flux + state.delta_prime = state.C_delta_prime * forcing_flux # Conform the stored coupling-matrix input basis to the coordinate-invariant root-area-weighted # field (b̃) space (#233 / Pharr 2026): C̃ = C·R, so each stored row acts on the applied field @@ -290,18 +304,18 @@ function compute_singular_coupling_metrics!( # scalars carry no round-trip noise. rootarea_to_area_weight, surface_area = build_control_surface_rootarea_to_area_weight(equil, ffs_intr) flux_conform = rootarea_to_area_weight .* surface_area - state.C_resonant_area_weighted_field = state.C_resonant_area_weighted_field * flux_conform + state.C_resonant_area_weighted_field = state.C_resonant_area_weighted_field * flux_conform state.C_resonant_current = state.C_resonant_current * flux_conform - state.C_island_width_sq = state.C_island_width_sq * flux_conform + state.C_island_width_sq = state.C_island_width_sq * flux_conform state.C_penetrated_area_weighted_field = state.C_penetrated_area_weighted_field * flux_conform - state.C_delta_prime = state.C_delta_prime * flux_conform + state.C_delta_prime = state.C_delta_prime * flux_conform # Phase 5: Island diagnostics from applied resonant vectors compute_island_diagnostics!(state, n_rational) if ctrl.verbose max_island = isempty(state.island_half_width) ? 0.0 : maximum(state.island_half_width) - max_dp = isempty(state.delta_prime) ? 0.0 : maximum(abs.(real.(state.delta_prime))) + max_dp = isempty(state.delta_prime) ? 0.0 : maximum(abs.(real.(state.delta_prime))) @info "Singular coupling complete. Max island half-width = $(@sprintf("%.3e", max_island)), max |Δ'| = $(@sprintf("%.3e", max_dp))" end end @@ -443,7 +457,7 @@ Surface inductance matrix [mpert × mpert] grre::Matrix{Float64}, ffs_intr::ForceFreeStatesInternal, nn::Int, - ν::Vector{Float64}, + ν::Vector{Float64} )::Matrix{ComplexF64} mpert = ffs_intr.mpert mtheta = size(grri, 1) ÷ 2 @@ -451,7 +465,7 @@ Surface inductance matrix [mpert × mpert] ft = FourierTransforms.FourierTransform(mtheta, mpert, ffs_intr.mlow) - flux_matrix = zeros!(pool, ComplexF64, mpert, mpert) + flux_matrix = zeros!(pool, ComplexF64, mpert, mpert) current_matrix = zeros!(pool, ComplexF64, mpert, mpert) grri_surf = @view grri[1:mtheta, :] @@ -469,8 +483,8 @@ Surface inductance matrix [mpert × mpert] flux_matrix[i, i] = 1.0 for k in 1:mtheta - kax_re[k] = (grri_surf[k, i] + grre_surf[k, i]) / (μ₀ * (2π)^2) - kax_im[k] = (grri_surf[k, mpert+i] + grre_surf[k, mpert+i]) / (μ₀ * (2π)^2) + kax_re[k] = (grri_surf[k, i] + grre_surf[k, i]) / (μ₀ * (2π)^2) + kax_im[k] = (grri_surf[k, mpert+i] + grre_surf[k, mpert+i]) / (μ₀ * (2π)^2) end # Port of Fortran gpvacuum_flxsurf: apply the toroidal phase exp(-i*n*ν), @@ -562,13 +576,13 @@ Compute island half-width and Chirikov parameter from applied resonant vectors. - `chirikov_parameter[row]` = half-width / (half-distance to nearest neighbor in rational_psi) """ function compute_island_diagnostics!(state::PerturbedEquilibriumState, n_rational::Int) - state.island_half_width = sqrt.(abs.(state.island_width_sq)) + state.island_half_width = sqrt.(abs.(state.island_width_sq)) state.chirikov_parameter = zeros(Float64, n_rational) n_rational <= 1 && return for row in 1:n_rational - psi_row = state.rational_psi[row] + psi_row = state.rational_psi[row] min_dist = Inf for row2 in 1:n_rational row2 == row && continue diff --git a/src/Vacuum/Vacuum.jl b/src/Vacuum/Vacuum.jl index eaa1583f8..e42946fb1 100644 --- a/src/Vacuum/Vacuum.jl +++ b/src/Vacuum/Vacuum.jl @@ -24,8 +24,7 @@ export extract_plasma_surface_at_psi export PlasmaGeometry """ - compute_vacuum_response(inputs::VacuumInput, wall_settings::WallShapeSettings; - green_only=false) + compute_vacuum_response(inputs::VacuumInput, wall_settings::WallShapeSettings) Compute the vacuum response matrix and both Green's functions using provided vacuum inputs. @@ -47,7 +46,6 @@ It computes both interior (grri) and exterior (grre) Green's functions for GPEC - `inputs`: `VacuumInput` struct with mode numbers, grid resolution, and boundary info. - `wall_settings::WallShapeSettings`: Wall geometry configuration. - - `green_only`: If true, skip building the response matrix `wv` and return zeros for `wv` and `xzpts`. # Returns @@ -71,8 +69,7 @@ It computes both interior (grri) and exterior (grre) Green's functions for GPEC wall_pts::AbstractMatrix{Float64}, inputs::VacuumInput, wall_settings::WallShapeSettings; - n_override::Union{Nothing,Int}=nothing, - green_only::Bool=false + n_override::Union{Nothing,Int}=nothing ) # Initialize surface geometries @@ -139,48 +136,42 @@ It computes both interior (grri) and exterior (grre) Green's functions for GPEC F_int = lu!(grad_green_interior) ldiv!(F_int, grri) - # Always initialise wv to zero so that green_only keeps it zeroed - if !green_only - # Perform inverse Fourier transforms to get response matrix components [Chance Phys. Plasmas 2007 052506 eq. 115-118] - arr, aii, ari, air = ntuple(_ -> zeros(num_modes, num_modes), 4) - fourier_inverse_transform!(arr, grre, cos_mn_basis) - fourier_inverse_transform!(aii, grre, sin_mn_basis; col_offset=num_modes) - fourier_inverse_transform!(ari, grre, sin_mn_basis) - fourier_inverse_transform!(air, grre, cos_mn_basis; col_offset=num_modes) - - # fourier_inverse_transform! uses 1/N normalization; restore the 4π² physics factor - # from the vacuum Green's function integral [Chance 2007 eq. 114-118] - arr .*= 4π^2 - aii .*= 4π^2 - ari .*= 4π^2 - air .*= 4π^2 - - # Final form of vacuum response matrix [Chance Phys. Plasmas 2007 052506 eq. 114] - wv .= complex.(arr .+ aii, air .- ari) - inputs.force_wv_symmetry && hermitianpart!(wv) - - # Fill coordinate arrays - if inputs.nzeta > 1 # 3D - plasma_pts .= plasma_surf.r - wall_pts .= wall.r - else # 2D - @views begin - plasma_pts[:, 1] .= plasma_surf.x - plasma_pts[:, 2] .= 0.0 - plasma_pts[:, 3] .= plasma_surf.z - wall_pts[:, 1] .= wall.x - wall_pts[:, 2] .= 0.0 - wall_pts[:, 3] .= wall.z - end + # Perform inverse Fourier transforms to get response matrix components [Chance Phys. Plasmas 2007 052506 eq. 115-118] + arr, aii, ari, air = ntuple(_ -> zeros(num_modes, num_modes), 4) + fourier_inverse_transform!(arr, grre, cos_mn_basis) + fourier_inverse_transform!(aii, grre, sin_mn_basis; col_offset=num_modes) + fourier_inverse_transform!(ari, grre, sin_mn_basis) + fourier_inverse_transform!(air, grre, cos_mn_basis; col_offset=num_modes) + + # fourier_inverse_transform! uses 1/N normalization; restore the 4π² physics factor + # from the vacuum Green's function integral [Chance 2007 eq. 114-118] + arr .*= 4π^2 + aii .*= 4π^2 + ari .*= 4π^2 + air .*= 4π^2 + + # Final form of vacuum response matrix [Chance Phys. Plasmas 2007 052506 eq. 114] + wv .= complex.(arr .+ aii, air .- ari) + inputs.force_wv_symmetry && hermitianpart!(wv) + + # Fill coordinate arrays + if inputs.nzeta > 1 # 3D + plasma_pts .= plasma_surf.r + wall_pts .= wall.r + else # 2D + @views begin + plasma_pts[:, 1] .= plasma_surf.x + plasma_pts[:, 2] .= 0.0 + plasma_pts[:, 3] .= plasma_surf.z + wall_pts[:, 1] .= wall.x + wall_pts[:, 2] .= 0.0 + wall_pts[:, 3] .= wall.z end end end """ - compute_vacuum_response( - inputs::VacuumInput, - wall_settings::WallShapeSettings; - green_only=false) + compute_vacuum_response(inputs::VacuumInput, wall_settings::WallShapeSettings) Allocate and return the vacuum response matrix and Green's functions for the given vacuum inputs. @@ -190,12 +181,12 @@ implementation. For performance‑critical paths that already own preallocated s (e.g. `ForceFreeStates.VacuumData`), prefer the in‑place method to avoid extra heap allocations. """ -@with_pool pool function compute_vacuum_response(inputs::VacuumInput, wall_settings::WallShapeSettings; green_only::Bool=false) +@with_pool pool function compute_vacuum_response(inputs::VacuumInput, wall_settings::WallShapeSettings) # Allocate storage for the vacuum response matrix and Green's functions numpoints = inputs.mtheta * inputs.nzeta num_modes = inputs.mpert * inputs.npert - + vac = ( wv=zeros(ComplexF64, num_modes, num_modes), grri=zeros(2 * numpoints, 2 * num_modes), @@ -203,17 +194,13 @@ heap allocations. plasma_pts=zeros(numpoints, 3), wall_pts=zeros(numpoints, 3) ) - compute_vacuum_response!(vac, inputs, wall_settings; green_only=green_only) + compute_vacuum_response!(vac, inputs, wall_settings) return vac.wv, vac.grri, vac.grre, vac.plasma_pts, vac.wall_pts end """ - compute_vacuum_response!( - vac_data, - inputs::VacuumInput, - wall_settings::WallShapeSettings; - green_only=false) + compute_vacuum_response!(vac_data, inputs::VacuumInput, wall_settings::WallShapeSettings) In-place variant that computes the vacuum response and directly populates the arrays stored in `vac_data`. @@ -230,7 +217,7 @@ compatible sizes: This is designed to work with `ForceFreeStates.VacuumData` but does not depend on its concrete type (duck-typed on field names only). """ -function compute_vacuum_response!(vac_data, inputs::VacuumInput, wall_settings::WallShapeSettings; green_only::Bool=false) +function compute_vacuum_response!(vac_data, inputs::VacuumInput, wall_settings::WallShapeSettings) mpert = inputs.mpert npert = inputs.npert @@ -245,8 +232,7 @@ function compute_vacuum_response!(vac_data, inputs::VacuumInput, wall_settings:: vac_data.plasma_pts, vac_data.wall_pts, inputs, - wall_settings; - green_only=green_only + wall_settings ) else # 2D vacuum: fill diagonal blocks of the response matrix @@ -270,8 +256,7 @@ function compute_vacuum_response!(vac_data, inputs::VacuumInput, wall_settings:: vac_data.wall_pts, inputs, wall_settings; - n_override=n, - green_only=green_only + n_override=n ) end end diff --git a/test/runtests_vacuum.jl b/test/runtests_vacuum.jl index f8e5ef04b..27c92a77a 100644 --- a/test/runtests_vacuum.jl +++ b/test/runtests_vacuum.jl @@ -658,36 +658,12 @@ @test isapprox(wv, wv', rtol=1e-12) end - @testset "compute_vacuum_response 3D green_only" begin - inputs = _make_3d_inputs(mtheta=32, nzeta=32, mtheta_eq=17) - wall_settings = WallShapeSettings(shape="nowall") - wv, grri, grre, plasma_pts, wall_pts = compute_vacuum_response(inputs, wall_settings; green_only=true) - - numpoints = inputs.mtheta * inputs.nzeta - num_modes = inputs.mpert * inputs.npert - @test size(wv) == (num_modes, num_modes) - @test all(wv .== 0) - @test size(grri) == (2 * numpoints, 2 * num_modes) - @test size(grre) == (2 * numpoints, 2 * num_modes) - @test all(isfinite, grri) - @test all(isfinite, grre) - end - - @testset "Kernel3D laplace_single_layer" begin - x_obs = [1.0, 0.0, 0.0] - x_src = [2.0, 0.0, 0.0] - G = GeneralizedPerturbedEquilibrium.Vacuum.laplace_single_layer(x_obs, x_src) + @testset "Kernel3D laplace_kernel" begin + G, K = GeneralizedPerturbedEquilibrium.Vacuum.laplace_kernel(1.0, 0.0, 0.0, 2.0, 0.0, 0.0, 1.0, 0.0, 0.0) # Kernel returns 1/|r_obs - r_src| (4π factor applied elsewhere in BIE) dist = sqrt((2.0 - 1.0)^2 + 0 + 0) @test isapprox(G, 1.0 / dist) @test isfinite(G) - end - - @testset "Kernel3D laplace_double_layer" begin - x_obs = [1.0, 0.0, 0.0] - x_src = [2.0, 0.0, 0.0] - n_src = [1.0, 0.0, 0.0] # normal pointing away from source - K = GeneralizedPerturbedEquilibrium.Vacuum.laplace_double_layer(x_obs, x_src, n_src) @test K isa Float64 @test isfinite(K) end From 2b9b66f990010bfe91d6fa80b8aa2f70a9298c79 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Tue, 23 Jun 2026 13:33:09 -0400 Subject: [PATCH 099/135] CLEANUP - MINOR - Remove no-op trailing semicolons from split assignment lines These trailing semicolons are leftovers from one-line multi-statement assignments (a = 1; b = 2;) that were split into separate lines without dropping the now-redundant separators. In a Julia source file a trailing ; is a no-op. Only standalone assignments were touched; legitimate kwarg separators and matrix-row separators were left intact. Co-Authored-By: Claude Opus 4.8 (1M context) --- src/Equilibrium/EquilibriumTypes.jl | 40 +++++++++---------- .../FieldReconstruction.jl | 14 +++---- src/PerturbedEquilibrium/SingularCoupling.jl | 24 +++++------ src/Vacuum/Utilities.jl | 8 ++-- 4 files changed, 43 insertions(+), 43 deletions(-) diff --git a/src/Equilibrium/EquilibriumTypes.jl b/src/Equilibrium/EquilibriumTypes.jl index 8a52e6366..5d360992d 100644 --- a/src/Equilibrium/EquilibriumTypes.jl +++ b/src/Equilibrium/EquilibriumTypes.jl @@ -66,50 +66,50 @@ Bundles all necessary settings originally specified in the equil fortran namelis force_termination, use_galgrid, imas_cocos) if jac_type == "hamada" @info "Forcing hamada coordinate jacobian exponents: power_*" - power_b = 0; - power_bp = 0; - power_r = 0; + power_b = 0 + power_bp = 0 + power_r = 0 power_rc = 0 elseif jac_type == "pest" @info "Forcing pest coordinate jacobian exponents: power_*" - power_b = 0; - power_bp = 0; - power_r = 2; + power_b = 0 + power_bp = 0 + power_r = 2 power_rc = 0 elseif jac_type == "equal_arc" @info "Forcing equal_arc coordinate jacobian exponents: power_*" - power_b = 0; - power_bp = 1; - power_r = 0; + power_b = 0 + power_bp = 1 + power_r = 0 power_rc = 0 elseif jac_type == "boozer" @info "Forcing boozer coordinate jacobian exponents: power_*" - power_b = 2; - power_bp = 0; - power_r = 0; + power_b = 2 + power_bp = 0 + power_r = 0 power_rc = 0 elseif jac_type == "park" @info "Forcing park coordinate jacobian exponents: power_*" - power_b = 1; - power_bp = 0; - power_r = 0; + power_b = 1 + power_bp = 0 + power_r = 0 power_rc = 0 elseif jac_type == "other" # Normalize to a named type when the powers match, so fast paths are taken. if power_b == 0 && power_bp == 0 && power_r == 0 && power_rc == 0 - jac_type = "hamada"; + jac_type = "hamada" @info "Recognized hamada jacobian from power exponents" elseif power_b == 0 && power_bp == 0 && power_r == 2 && power_rc == 0 - jac_type = "pest"; + jac_type = "pest" @info "Recognized pest jacobian from power exponents" elseif power_b == 0 && power_bp == 1 && power_r == 0 && power_rc == 0 - jac_type = "equal_arc"; + jac_type = "equal_arc" @info "Recognized equal_arc jacobian from power exponents" elseif power_b == 2 && power_bp == 0 && power_r == 0 && power_rc == 0 - jac_type = "boozer"; + jac_type = "boozer" @info "Recognized boozer jacobian from power exponents" elseif power_b == 1 && power_bp == 0 && power_r == 0 && power_rc == 0 - jac_type = "park"; + jac_type = "park" @info "Recognized park jacobian from power exponents" else @info "Using manual jacobian exponents: power b, bp, r, rc = $(power_b), $(power_bp), $(power_r), $(power_rc)" diff --git a/src/PerturbedEquilibrium/FieldReconstruction.jl b/src/PerturbedEquilibrium/FieldReconstruction.jl index b599098fe..ae0334e1f 100644 --- a/src/PerturbedEquilibrium/FieldReconstruction.jl +++ b/src/PerturbedEquilibrium/FieldReconstruction.jl @@ -670,11 +670,11 @@ function compute_cova_components( # Tensor contraction with mode coupling (matches Fortran gpeq_cova) for ipert in 1:mpert - xvp_acc = zero(ComplexF64); - xvt_acc = zero(ComplexF64); + xvp_acc = zero(ComplexF64) + xvt_acc = zero(ComplexF64) xvz_acc = zero(ComplexF64) - bvp_acc = zero(ComplexF64); - bvt_acc = zero(ComplexF64); + bvp_acc = zero(ComplexF64) + bvt_acc = zero(ComplexF64) bvz_acc = zero(ComplexF64) for dm in (1-ipert):(mpert-ipert) @@ -916,9 +916,9 @@ function _build_rzphi_geometry( v21 = dr2_dtheta / (2 * rfac) v22 = (1 + doff_dtheta) * 2π * rfac else - v11 = 0.0; - v12 = 0.0; - v21 = 0.0; + v11 = 0.0 + v12 = 0.0 + v21 = 0.0 v22 = 0.0 end diff --git a/src/PerturbedEquilibrium/SingularCoupling.jl b/src/PerturbedEquilibrium/SingularCoupling.jl index 07cb4e37f..2a2bec045 100644 --- a/src/PerturbedEquilibrium/SingularCoupling.jl +++ b/src/PerturbedEquilibrium/SingularCoupling.jl @@ -33,9 +33,9 @@ end function _hermite_cubic_val(u_a, u_b, du_a, du_b, psi_a, psi_b, psi) h = psi_b - psi_a t = (psi - psi_a) / h - h00 = 2t^3 - 3t^2 + 1; + h00 = 2t^3 - 3t^2 + 1 h10 = t^3 - 2t^2 + t - h01 = -2t^3 + 3t^2; + h01 = -2t^3 + 3t^2 h11 = t^3 - t^2 return @. h00 * u_a + h * h10 * du_a + h01 * u_b + h * h11 * du_b end @@ -203,18 +203,18 @@ function compute_singular_coupling_metrics!( u_node = ForceFreeStates_results.u_store ud_node = ForceFreeStates_results.ud_store - ua_l = u_node[resnum, :, 1, il_l]; + ua_l = u_node[resnum, :, 1, il_l] ub_l = u_node[resnum, :, 1, ir_l] - ua_r = u_node[resnum, :, 1, il_r]; + ua_r = u_node[resnum, :, 1, il_r] ub_r = u_node[resnum, :, 1, ir_r] - dua_l = ud_node[resnum, :, 1, il_l]; + dua_l = ud_node[resnum, :, 1, il_l] dub_l = ud_node[resnum, :, 1, ir_l] - dua_r = ud_node[resnum, :, 1, il_r]; + dua_r = ud_node[resnum, :, 1, il_r] dub_r = ud_node[resnum, :, 1, ir_r] - psi_il_l = psi_store_all[il_l]; + psi_il_l = psi_store_all[il_l] psi_ir_l = psi_store_all[ir_l] - psi_il_r = psi_store_all[il_r]; + psi_il_r = psi_store_all[il_r] psi_ir_r = psi_store_all[ir_r] u_l = _hermite_cubic_val(ua_l, ub_l, dua_l, dub_l, psi_il_l, psi_ir_l, lpsi) @@ -226,9 +226,9 @@ function compute_singular_coupling_metrics!( ud_l = (ub_l .- ua_l) ./ (psi_ir_l - psi_il_l) ud_r = (ub_r .- ua_r) ./ (psi_ir_r - psi_il_r) - q_l = equil.profiles.q_spline(lpsi); + q_l = equil.profiles.q_spline(lpsi) q1_l = equil.profiles.q_deriv(lpsi) - q_r = equil.profiles.q_spline(rpsi); + q_r = equil.profiles.q_spline(rpsi) q1_r = equil.profiles.q_deriv(rpsi) singfac_l = m_res - nn * q_l singfac_r = m_res - nn * q_r @@ -236,9 +236,9 @@ function compute_singular_coupling_metrics!( jump_vec = Vector{ComplexF64}(undef, numpert_total) for k in 1:numpert_total ck = @view C_coeffs[:, k] - xsp_l = dot(u_l, ck); + xsp_l = dot(u_l, ck) xsp1_l = dot(ud_l, ck) - xsp_r = dot(u_r, ck); + xsp_r = dot(u_r, ck) xsp1_r = dot(ud_r, ck) bwp1_l = 2π * im * chi1 * (singfac_l * xsp1_l - nn * q1_l * xsp_l) bwp1_r = 2π * im * chi1 * (singfac_r * xsp1_r - nn * q1_r * xsp_r) diff --git a/src/Vacuum/Utilities.jl b/src/Vacuum/Utilities.jl index fd9e578c1..f6a2c17d4 100644 --- a/src/Vacuum/Utilities.jl +++ b/src/Vacuum/Utilities.jl @@ -140,11 +140,11 @@ Inline function for fast cross product of two 3D vectors at a given index. idx::Int ) @inbounds begin - a1 = a[idx, 1]; - a2 = a[idx, 2]; + a1 = a[idx, 1] + a2 = a[idx, 2] a3 = a[idx, 3] - b1 = b[idx, 1]; - b2 = b[idx, 2]; + b1 = b[idx, 1] + b2 = b[idx, 2] b3 = b[idx, 3] c[idx, 1] = a2*b3 - a3*b2 From 91bf3edea1e9fb62a6c54c7a037f6f20be2e1ad4 Mon Sep 17 00:00:00 2001 From: Jake Halpern Date: Tue, 23 Jun 2026 14:30:06 -0400 Subject: [PATCH 100/135] GPEC - MINOR - removing unneeded semi-colons --- src/PerturbedEquilibrium/SingularCoupling.jl | 24 ++++++++++---------- 1 file changed, 12 insertions(+), 12 deletions(-) diff --git a/src/PerturbedEquilibrium/SingularCoupling.jl b/src/PerturbedEquilibrium/SingularCoupling.jl index 07cb4e37f..2a2bec045 100644 --- a/src/PerturbedEquilibrium/SingularCoupling.jl +++ b/src/PerturbedEquilibrium/SingularCoupling.jl @@ -33,9 +33,9 @@ end function _hermite_cubic_val(u_a, u_b, du_a, du_b, psi_a, psi_b, psi) h = psi_b - psi_a t = (psi - psi_a) / h - h00 = 2t^3 - 3t^2 + 1; + h00 = 2t^3 - 3t^2 + 1 h10 = t^3 - 2t^2 + t - h01 = -2t^3 + 3t^2; + h01 = -2t^3 + 3t^2 h11 = t^3 - t^2 return @. h00 * u_a + h * h10 * du_a + h01 * u_b + h * h11 * du_b end @@ -203,18 +203,18 @@ function compute_singular_coupling_metrics!( u_node = ForceFreeStates_results.u_store ud_node = ForceFreeStates_results.ud_store - ua_l = u_node[resnum, :, 1, il_l]; + ua_l = u_node[resnum, :, 1, il_l] ub_l = u_node[resnum, :, 1, ir_l] - ua_r = u_node[resnum, :, 1, il_r]; + ua_r = u_node[resnum, :, 1, il_r] ub_r = u_node[resnum, :, 1, ir_r] - dua_l = ud_node[resnum, :, 1, il_l]; + dua_l = ud_node[resnum, :, 1, il_l] dub_l = ud_node[resnum, :, 1, ir_l] - dua_r = ud_node[resnum, :, 1, il_r]; + dua_r = ud_node[resnum, :, 1, il_r] dub_r = ud_node[resnum, :, 1, ir_r] - psi_il_l = psi_store_all[il_l]; + psi_il_l = psi_store_all[il_l] psi_ir_l = psi_store_all[ir_l] - psi_il_r = psi_store_all[il_r]; + psi_il_r = psi_store_all[il_r] psi_ir_r = psi_store_all[ir_r] u_l = _hermite_cubic_val(ua_l, ub_l, dua_l, dub_l, psi_il_l, psi_ir_l, lpsi) @@ -226,9 +226,9 @@ function compute_singular_coupling_metrics!( ud_l = (ub_l .- ua_l) ./ (psi_ir_l - psi_il_l) ud_r = (ub_r .- ua_r) ./ (psi_ir_r - psi_il_r) - q_l = equil.profiles.q_spline(lpsi); + q_l = equil.profiles.q_spline(lpsi) q1_l = equil.profiles.q_deriv(lpsi) - q_r = equil.profiles.q_spline(rpsi); + q_r = equil.profiles.q_spline(rpsi) q1_r = equil.profiles.q_deriv(rpsi) singfac_l = m_res - nn * q_l singfac_r = m_res - nn * q_r @@ -236,9 +236,9 @@ function compute_singular_coupling_metrics!( jump_vec = Vector{ComplexF64}(undef, numpert_total) for k in 1:numpert_total ck = @view C_coeffs[:, k] - xsp_l = dot(u_l, ck); + xsp_l = dot(u_l, ck) xsp1_l = dot(ud_l, ck) - xsp_r = dot(u_r, ck); + xsp_r = dot(u_r, ck) xsp1_r = dot(ud_r, ck) bwp1_l = 2π * im * chi1 * (singfac_l * xsp1_l - nn * q1_l * xsp_l) bwp1_r = 2π * im * chi1 * (singfac_r * xsp1_r - nn * q1_r * xsp_r) From 9f77bb4266e46fad5f40cb99be32589a8f13ae96 Mon Sep 17 00:00:00 2001 From: Jake Halpern Date: Tue, 23 Jun 2026 14:32:44 -0400 Subject: [PATCH 101/135] VACUUM - MINOR - better info statement for patch_rad logic --- src/Vacuum/Kernel3D.jl | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/src/Vacuum/Kernel3D.jl b/src/Vacuum/Kernel3D.jl index 8617b1d6c..55a4eb957 100644 --- a/src/Vacuum/Kernel3D.jl +++ b/src/Vacuum/Kernel3D.jl @@ -385,12 +385,13 @@ function compute_3D_kernel_matrices!( # 𝒢ⁿ only needed for plasma as source term (RHS of eqs. 26/27 in Chance 1997) populate_greenfunction = source isa PlasmaGeometry3D - # Initialize quadrature data # This allows the code to run at lower resolution without erroring out, but will warn the user. if PATCH_RAD > (min(source.mtheta, source.nzeta) - 1) ÷ 2 - @warn "PATCH_RAD is greater than half the number of points in the toroidal or poloidal direction, which is not supported. Setting PATCH_RAD to $((min(source.mtheta, source.nzeta) - 1) ÷ 2). Be sure to check if outputs are converged." + @warn "PATCH_RAD=$(PATCH_RAD) is greater than half the number of points in the toroidal or poloidal direction, which is not supported. Setting PATCH_RAD to $((min(source.mtheta, source.nzeta) - 1) ÷ 2), be sure to check if outputs are converged. This can be avoided by setting mtheta and nzeta to be greater than $(2 * PATCH_RAD + 1)." PATCH_RAD = (min(source.mtheta, source.nzeta) - 1) ÷ 2 end + + # Initialize quadrature data quad_data = get_singular_quadrature(PATCH_RAD, RAD_DIM, INTERP_ORDER) (; PATCH_DIM, PATCH_RAD, ANG_DIM, RAD_DIM, Ppou, Gpou, P2G) = quad_data From 476aaad17c2f96db908e1047b21ef19914ddf82a Mon Sep 17 00:00:00 2001 From: Jake Halpern Date: Tue, 23 Jun 2026 14:36:15 -0400 Subject: [PATCH 102/135] GPEC - MINOR - swapping out banded inputs for mer_flag in deprecated entries --- src/GeneralizedPerturbedEquilibrium.jl | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/GeneralizedPerturbedEquilibrium.jl b/src/GeneralizedPerturbedEquilibrium.jl index d96d4453c..066529db4 100755 --- a/src/GeneralizedPerturbedEquilibrium.jl +++ b/src/GeneralizedPerturbedEquilibrium.jl @@ -58,9 +58,9 @@ using .ForceFreeStates: make_metric, make_matrix, make_kinetic_matrix using .ForceFreeStates: find_kinetic_singular_surfaces! using .ForceFreeStates: eulerlagrange_integration, free_run! -const _DEPRECATED_FFS_KEYS = ("delta_mband", "mband") +const _DEPRECATED_FFS_KEYS = ("mer_flag") -# Drop deprecated [ForceFreeStates] keys (e.g. banded-matrix removal) so legacy gpec.toml files +# Drop deprecated [ForceFreeStates] keys so legacy gpec.toml files # keep parsing instead of throwing an unknown-keyword error. function _drop_deprecated_ffs_keys!(table) for k in _DEPRECATED_FFS_KEYS From ae94146c1a1f96a840919c5fcb7a29d8c5e348dd Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Tue, 23 Jun 2026 15:24:50 -0400 Subject: [PATCH 103/135] EQUIL - TEST - Add fixed-boundary EFIT separatrix-find regression case (#294) Adds a kind="computed" regression case (efit_fixedbdy_separatrix) that loads a fixed-boundary TokaMaker aspect-scan g-file whose computational box hugs the LCFS (circular R/a=20, eps=0.05). Outside the prescribed LCFS the coil-vacuum flux turns back above the boundary value before the grid edge, which the old bracketed Brent separatrix finder could not bracket; the case errored on the buggy code and now loads with the Newton finder. Tracks the leading equilibrium scalars (psio, q0, q95, betat, betan) so the direct_position! separatrix path stays stable. - regression-harness/cases/efit_fixedbdy_separatrix.toml: case definition - regression-harness/src/runner.jl: computed-case script template + dispatch - examples/efit_fixedbdy_separatrix_example/: g-file fixture + README Co-Authored-By: Claude Opus 4.8 (1M context) --- .../README.md | 19 + .../eq_eps0.0500000_k1.000_d0.000.geqdsk | 6920 +++++++++++++++++ .../cases/efit_fixedbdy_separatrix.toml | 61 + regression-harness/src/runner.jl | 32 + 4 files changed, 7032 insertions(+) create mode 100644 examples/efit_fixedbdy_separatrix_example/README.md create mode 100644 examples/efit_fixedbdy_separatrix_example/eq_eps0.0500000_k1.000_d0.000.geqdsk create mode 100644 regression-harness/cases/efit_fixedbdy_separatrix.toml diff --git a/examples/efit_fixedbdy_separatrix_example/README.md b/examples/efit_fixedbdy_separatrix_example/README.md new file mode 100644 index 000000000..128205632 --- /dev/null +++ b/examples/efit_fixedbdy_separatrix_example/README.md @@ -0,0 +1,19 @@ +# Fixed-boundary EFIT separatrix-find fixture (PR #296, issue #294) + +`eq_eps0.0500000_k1.000_d0.000.geqdsk` is a fixed-boundary TokaMaker aspect-scan equilibrium +(circular, R/a = 20, eps = 0.05) whose computational box hugs the last closed flux surface. + +In a fixed-boundary solve the LCFS shape is prescribed and the flux **outside** it is physically +unconstrained: the coil-vacuum flux turns back above the boundary value (`sibry`) before reaching +the grid edge. The old bracketed `Roots.Brent()` separatrix finder used the grid edge as its outer +bracket point, so `f(axis)` and `f(edge)` ended up the same sign and `direct_position!` threw +`ArgumentError: not a bracketing interval`. The Newton finder (PR #296, faithful to Fortran +`direct.f direct_position`) walks inward to the first `psi = sibry` crossing — the actual LCFS — and +loads it regardless of box size. + +This g-file is the fixture for the `efit_fixedbdy_separatrix` regression case +(`regression-harness/cases/efit_fixedbdy_separatrix.toml`, a `kind = "computed"` case that calls +`setup_equilibrium` directly). It is **not** a runnable example deck — there is no `gpec.toml`. + +Free-boundary equilibria (real coil currents) and standard diverted EFITs are unaffected: their +outboard midplane flux keeps dropping past the LCFS, so the bracket was never ambiguous. diff --git a/examples/efit_fixedbdy_separatrix_example/eq_eps0.0500000_k1.000_d0.000.geqdsk b/examples/efit_fixedbdy_separatrix_example/eq_eps0.0500000_k1.000_d0.000.geqdsk new file mode 100644 index 000000000..150e3e313 --- /dev/null +++ b/examples/efit_fixedbdy_separatrix_example/eq_eps0.0500000_k1.000_d0.000.geqdsk @@ -0,0 +1,6920 @@ +tMaker: const-q chain eq_eps0.0500000_k1 0 129 257 + 0.219966221E+01 0.219966221E+01 0.200008011E+02 0.189003220E+02 0.000000000E+00 + 0.200259857E+02 0.390171977E-06 0.337817192E+00 0.337817194E-02 0.199992001E+01 + 0.769323906E+05 0.337817192E+00 0.000000000E+00 0.200259857E+02 0.000000000E+00 + 0.390171977E-06 0.000000000E+00 0.337817194E-02 0.000000000E+00 0.000000000E+00 + 0.400046501E+02 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0.500427634E-01 + 0.209993858E+02 0.250225589E-01 0.210000000E+02 0.000000000E+00 diff --git a/regression-harness/cases/efit_fixedbdy_separatrix.toml b/regression-harness/cases/efit_fixedbdy_separatrix.toml new file mode 100644 index 000000000..01688e5ee --- /dev/null +++ b/regression-harness/cases/efit_fixedbdy_separatrix.toml @@ -0,0 +1,61 @@ +# Regression case: separatrix-finder robustness for fixed-boundary EFITs (PR #296, closes #294). +# A "computed" case (kind = "computed", no example_dir) that loads a fixed-boundary TokaMaker +# aspect-scan g-file whose computational box hugs the LCFS (circular R/a=20, eps=0.05). Outside +# the prescribed LCFS the coil-vacuum flux turns back above the boundary value before the grid +# edge, so the old bracketed Roots.Brent() separatrix finder could not bracket the psi=sibry +# crossing and direct_position! threw "not a bracketing interval". The Newton finder (faithful to +# Fortran direct.f) locates the innermost LCFS crossing regardless. This case errored on the buggy +# code and now loads; it tracks the leading equilibrium scalars so the loading path stays stable. +# Fixture g-file: examples/efit_fixedbdy_separatrix_example/eq_eps0.0500000_k1.000_d0.000.geqdsk +[case] +name = "efit_fixedbdy_separatrix" +description = "Fixed-boundary EFIT (box hugs LCFS), Newton separatrix-find regression" +kind = "computed" + +[quantities.psio] +h5path = "equil/psio" +type = "real_scalar" +extract = "value" +label = "psio (total poloidal flux)" +noise_threshold = 1e-12 +order = 10 + +[quantities.q0] +h5path = "equil/q0" +type = "real_scalar" +extract = "value" +label = "q0" +noise_threshold = 1e-12 +order = 11 + +[quantities.q95] +h5path = "equil/q95" +type = "real_scalar" +extract = "value" +label = "q95" +noise_threshold = 1e-12 +order = 12 + +[quantities.betat] +h5path = "equil/betat" +type = "real_scalar" +extract = "value" +label = "beta_t" +noise_threshold = 1e-12 +order = 13 + +[quantities.betan] +h5path = "equil/betan" +type = "real_scalar" +extract = "value" +label = "beta_n" +noise_threshold = 1e-12 +order = 14 + +[quantities.runtime] +h5path = "" +type = "runtime" +extract = "value" +label = "Runtime (s)" +noise_threshold = 0.0 +order = 90 diff --git a/regression-harness/src/runner.jl b/regression-harness/src/runner.jl index 90c99282a..8705cb4d5 100644 --- a/regression-harness/src/runner.jl +++ b/regression-harness/src/runner.jl @@ -79,6 +79,36 @@ open(ARGS[2], "w") do f end """ +# Self-contained separatrix-finder regression (PR #296). Loads a fixed-boundary EFIT whose +# computational box hugs the LCFS (eps=0.05 TokaMaker aspect-scan g-file): outside the prescribed +# LCFS the coil-vacuum flux turns back above the boundary value before the grid edge, so the old +# bracketed-Brent separatrix finder could not bracket psi=sibry and equilibrium setup threw. Calls +# setup_equilibrium directly and writes the leading equilibrium scalars: errors on the buggy code, +# passes with the Newton finder. Runtime is written to ARGS[2] for parity with the GPEC runner. +const COMPUTED_SEPARATRIX_SCRIPT_TEMPLATE = """ +using Pkg +%INSTANTIATE% +using GeneralizedPerturbedEquilibrium +using GeneralizedPerturbedEquilibrium.Equilibrium +using HDF5 +root = dirname(Base.active_project()) +gfile = joinpath(root, "examples", "efit_fixedbdy_separatrix_example", "eq_eps0.0500000_k1.000_d0.000.geqdsk") +cfg = Equilibrium.EquilibriumConfig(; eq_type="efit", eq_filename=gfile) +t_start = time() +pe = Equilibrium.setup_equilibrium(cfg) +elapsed = time() - t_start +h5open(ARGS[1], "w") do fid + fid["equil/psio"] = pe.psio + fid["equil/q0"] = pe.params.q0 + fid["equil/q95"] = pe.params.q95 + fid["equil/betat"] = pe.params.betat + fid["equil/betan"] = pe.params.betan +end +open(ARGS[2], "w") do f + println(f, elapsed) +end +""" + """ Run GPEC for a single commit/ref and case. Dispatches to run_local for the working tree or run_at_commit for a git ref. @@ -109,6 +139,8 @@ Pick the subprocess script template for a `kind="computed"` case. function _computed_script_template(case_spec::CaseSpec) if case_spec.name == "ggj_reference" return COMPUTED_GGJ_SCRIPT_TEMPLATE + elseif case_spec.name == "efit_fixedbdy_separatrix" + return COMPUTED_SEPARATRIX_SCRIPT_TEMPLATE end error("No computed-script template registered for case '$(case_spec.name)'") end From fe5e73666352387c54c4effb27b86fa918995fc0 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Tue, 23 Jun 2026 21:00:08 -0400 Subject: [PATCH 104/135] BENCHMARKS - MINOR - Fixed bug revealed in merge's removal of forcing_vec in favor of the three field weightings b, b_root_area, and b_area --- benchmarks/benchmark_against_fortran_run.jl | 12 ++++-------- 1 file changed, 4 insertions(+), 8 deletions(-) diff --git a/benchmarks/benchmark_against_fortran_run.jl b/benchmarks/benchmark_against_fortran_run.jl index 4af6e58eb..c4c32f5e5 100644 --- a/benchmarks/benchmark_against_fortran_run.jl +++ b/benchmarks/benchmark_against_fortran_run.jl @@ -334,13 +334,9 @@ function load_julia_outputs(h5_path::String) julia["delta_prime"] = haskey(f, "$sc/delta_prime") ? read(f, "$sc/delta_prime") : ComplexF64[] pe = "perturbed_equilibrium" - # GPEC stores the control-surface spectra as fields (tesla), not flux. Reconstruct the - # poloidal flux for the Fortran Phi_x/Phi_tot comparison as Φ = A·b̄ (area-weighted field). - A_surf = haskey(f, "$pe/response_matrices/surface_area") ? read(f, "$pe/response_matrices/surface_area") : 1.0 - fb_area = haskey(f, "$pe/forcing_b_area") ? read(f, "$pe/forcing_b_area") : ComplexF64[] - rb_area = haskey(f, "$pe/response_b_area") ? read(f, "$pe/response_b_area") : ComplexF64[] - julia["forcing_vec"] = isempty(fb_area) ? ComplexF64[] : A_surf .* fb_area # Φ_x = A·b̄_x - julia["response_vec"] = isempty(rb_area) ? ComplexF64[] : A_surf .* rb_area # Φ_tot = A·b̄_tot + # Fortran Phi_x/Phi_tot are the area-weighted field b̄ (tesla), matching forcing/response_b_area directly. + julia["forcing_vec"] = haskey(f, "$pe/forcing_b_area") ? read(f, "$pe/forcing_b_area") : ComplexF64[] # Phi_x = b̄_x + julia["response_vec"] = haskey(f, "$pe/response_b_area") ? read(f, "$pe/response_b_area") : ComplexF64[] # Phi_tot = b̄_tot julia["b_n"] = haskey(f, "$pe/response/b_n") ? read(f, "$pe/response/b_n") : Matrix{ComplexF64}(undef, 0, 0) julia["Jbgradpsi"] = haskey(f, "$pe/response/b_psi_area_weighted") ? read(f, "$pe/response/b_psi_area_weighted") : Matrix{ComplexF64}(undef, 0, 0) julia["xi_psi"] = haskey(f, "$pe/response/xi_psi") ? read(f, "$pe/response/xi_psi") : Matrix{ComplexF64}(undef, 0, 0) @@ -917,7 +913,7 @@ function generate_plots(fort, julia, bench_dir, nn) j_fvec = julia["forcing_vec"] j_rvec = julia["response_vec"] j_mmodes = julia["m_modes"] - p6 = plot(; xlabel="m", ylabel="|Φ| [Wb]", title="Phi_x & Phi_tot spectrum (n=$nn)", + p6 = plot(; xlabel="m", ylabel="|b̄| [T]", title="Phi_x & Phi_tot spectrum (n=$nn)", legend=:topright) if !isempty(j_fvec) && !isempty(f_phi_x) jfx_amps = [abs(get(Dict(zip(j_mmodes, j_fvec)), m, NaN+0im)) for m in m_ctrl] From b368b5b6ebc04ec6999e652a027202496b95bed7 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Tue, 23 Jun 2026 21:14:32 -0400 Subject: [PATCH 105/135] RERUN - BUG FIX - Embed [SOL_INPUT] in nuzero kinetic regression fixture The rerun refactor dropped deprecated analytic side-car TOML support, so analytic equilibria must carry their parameters in an embedded [SOL_INPUT] section. The regression_solovev_kinetic_nuzero fixture still pointed at a sol.toml side-car, so build_analytic_config errored ("requires a [SOL_INPUT] section") and the full-run test failed. Migrate the Solovev parameters into gpec.toml (matching the calculated sibling) and drop the dead side-car. Co-Authored-By: Claude Opus 4.8 (1M context) --- .../regression_solovev_kinetic_nuzero/gpec.toml | 14 +++++++++++++- .../regression_solovev_kinetic_nuzero/sol.toml | 11 ----------- 2 files changed, 13 insertions(+), 12 deletions(-) delete mode 100644 test/test_data/regression_solovev_kinetic_nuzero/sol.toml diff --git a/test/test_data/regression_solovev_kinetic_nuzero/gpec.toml b/test/test_data/regression_solovev_kinetic_nuzero/gpec.toml index 9dc3d73b3..dde7997e2 100644 --- a/test/test_data/regression_solovev_kinetic_nuzero/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_nuzero/gpec.toml @@ -1,6 +1,5 @@ [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file -eq_filename = "sol.toml" # Path to equilibrium file jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc) power_bp = 0 # Poloidal field power exponent for Jacobian power_b = 0 # Toroidal field power exponent for Jacobian @@ -52,3 +51,16 @@ verbose = false [KineticForces] nutype = "zero" # Collisionless operator — isolates the real-x-space collisionless energy integral (issue #281) + +# Solovev analytic equilibrium parameters (eq_type = "sol"); see SolovevConfig in src/Equilibrium. +[SOL_INPUT] +mr = 128 # Number of radial grid zones +mz = 128 # Number of axial grid zones +ma = 128 # Number of flux grid zones +e = 1.6 # Elongation +a = 0.33 # Minor radius +r0 = 1.0 # Major radius +q0 = 1.9 # Safety factor at the magnetic axis (O-point) +p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) +b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) +f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/test/test_data/regression_solovev_kinetic_nuzero/sol.toml b/test/test_data/regression_solovev_kinetic_nuzero/sol.toml deleted file mode 100644 index e54fdeace..000000000 --- a/test/test_data/regression_solovev_kinetic_nuzero/sol.toml +++ /dev/null @@ -1,11 +0,0 @@ -[SOL_INPUT] -mr = 128 # number of radial grid zones -mz = 128 # number of axial grid zones -ma = 128 # number of flux grid zones -e = 1.6 # elongation -a = 0.33 # minor radius -r0 = 1.0 # major radius -q0 = 1.9 # safety factor at the o-point -p0fac=1 # scale on-axis pressure (P-> P+P0*p0fac. beta changes. Phi,q constant) -b0fac=1 # scale toroidal field at constant beta (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant) -f0fac=1 # scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant) From 61f6c75655ed78fae4d3250946358eb9f4e17ba8 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Tue, 23 Jun 2026 21:56:04 -0400 Subject: [PATCH 106/135] RERUN - BUG FIX - Update rerun test to renamed resonant_area_weighted_field MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit The merge renamed the singular-coupling output resonant_flux -> resonant_area_weighted_field (now b^r = Φ^r/A^r in tesla). The coil-geometry snapshot test in runtests_rerun_from_h5.jl still read the old key, so the HDF5 read returned an empty array and the non-empty / max-amplitude assertions failed. Point the helper at the new key and rename it accordingly. Co-Authored-By: Claude Opus 4.8 (1M context) --- test/runtests_rerun_from_h5.jl | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/test/runtests_rerun_from_h5.jl b/test/runtests_rerun_from_h5.jl index 7862bd10d..12344f5b6 100644 --- a/test/runtests_rerun_from_h5.jl +++ b/test/runtests_rerun_from_h5.jl @@ -121,9 +121,9 @@ end template_dir = joinpath(@__DIR__, "..", "examples", "Solovev_ideal_example") src_dat = joinpath(@__DIR__, "..", "src", "ForcingTerms", "coil_geometries", "d3d_il.dat") - read_resflux(path) = + read_resfield(path) = h5open(path, "r") do h5 - key = "perturbed_equilibrium/singular_coupling/resonant_flux" + key = "perturbed_equilibrium/singular_coupling/resonant_area_weighted_field" haskey(h5, key) ? read(h5, key) : ComplexF64[] end @@ -161,9 +161,9 @@ end @test haskey(h5, "input/raw_inputs/coils") @test haskey(h5, "input/raw_inputs/coils/my_coils") end - src_flux = read_resflux(source_h5) - @test !isempty(src_flux) - @test maximum(abs.(src_flux)) > 0 + src_field = read_resfield(source_h5) + @test !isempty(src_field) + @test maximum(abs.(src_field)) > 0 # Delete the .dat: the snapshot must now be the only source of geometry. rm(coil_dat) @@ -183,7 +183,7 @@ end ]) replay_h5 = joinpath(replay_dir, "gpec_rerun.h5") @test isfile(replay_h5) - @test read_resflux(replay_h5) ≈ src_flux rtol = 1e-6 + @test read_resfield(replay_h5) ≈ src_field rtol = 1e-6 end end end From ac6f2fa074c0100db1845d077f5689ed1cd9b287 Mon Sep 17 00:00:00 2001 From: d-burg Date: Wed, 24 Jun 2026 16:22:53 -0400 Subject: [PATCH 107/135] EQUIL - NEW FEATURE - HDF5 kinetic-profile format with ASCII back-compat Add read_kinetic_file (extension dispatch) and write_kinetic_h5 for a GPEC HDF5 kinetic schema (psi, n_i, n_e, T_i, T_e, omega_E; optional omega_tor, chi_e, chi_phi). Legacy 6-column ASCII (.gpeckf/.kin) still reads via the same path; the NTV loader is refactored onto the dispatcher with bit-identical results. Adds round-trip / ASCII-vs-HDF5 equivalence tests and docs; .gitignore tracks kinetic .h5 inputs. Co-Authored-By: Claude Opus 4.8 --- .gitignore | 2 + docs/src/kinetic_forces.md | 21 +++++ src/Equilibrium/Equilibrium.jl | 3 +- src/Equilibrium/KineticProfiles.jl | 144 +++++++++++++++++++++++++++-- test/runtests_kinetic.jl | 55 +++++++++++ 5 files changed, 214 insertions(+), 11 deletions(-) diff --git a/.gitignore b/.gitignore index 6859d2639..24bccfda2 100644 --- a/.gitignore +++ b/.gitignore @@ -7,6 +7,8 @@ *.i *.out *.h5 +# kinetic-profile inputs are tracked despite the blanket *.h5 (output) ignore +!examples/**/*kinetic*.h5 .vscode *.DS_Store *.pdf diff --git a/docs/src/kinetic_forces.md b/docs/src/kinetic_forces.md index 456e246bd..9787d9698 100644 --- a/docs/src/kinetic_forces.md +++ b/docs/src/kinetic_forces.md @@ -4,6 +4,27 @@ Kinetic torque and energy calculations for perturbed equilibria. Implements neoclassical toroidal viscosity (NTV) from the PENTRC formulation ([Logan & Park, 2013](citations.md); [Logan, 2015](citations.md)). +## Kinetic profile file formats + +Kinetic profiles are read by `read_kinetic_file`, which dispatches on the file +extension: + + - **HDF5 (`.h5`/`.hdf5`)** — the GPEC kinetic schema (recommended). Datasets + at the file root: required `psi` (normalized poloidal flux), `n_e`, `T_i`, + `T_e`, `omega_E` (and `n_i`, defaulting to `n_e` if omitted); optional + `omega_tor`, `chi_e` (perpendicular heat diffusivity ``\chi_\perp``), and + `chi_phi` (toroidal momentum diffusivity ``\chi_\phi``). Each dataset + carries a `units` attribute; the root carries `schema_version` and + `provenance`. Densities are m⁻³, temperatures eV, frequencies rad/s, + diffusivities m²/s. Write files with `write_kinetic_h5`. + - **ASCII (`.gpeckf`/`.kin`/`.dat`)** — legacy six-column whitespace table + `psi_n n_i n_e T_i[eV] T_e[eV] omega_E`, retained for backward + compatibility. Header rows are skipped. + +The NTV calculation consumes `n_i, n_e, T_i, T_e, omega_E`; `chi_e`/`chi_phi`, +when present, are carried for the resistive-layer (SLAYER) analysis and ignored +here. + ## Profile Scaling Knobs Seven scaling factors are available on `KineticForcesControl` to modify kinetic diff --git a/src/Equilibrium/Equilibrium.jl b/src/Equilibrium/Equilibrium.jl index c2eec3445..79efa208b 100644 --- a/src/Equilibrium/Equilibrium.jl +++ b/src/Equilibrium/Equilibrium.jl @@ -24,7 +24,8 @@ include("KineticProfiles.jl") # --- Expose types and functions to the user --- export setup_equilibrium, EquilibriumConfig, PlasmaEquilibrium, EquilibriumParameters, ProfileSplines, GeometryProfileSplines, compute_geometry_profiles, - KineticProfileSplines, load_kinetic_profiles + KineticProfileSplines, load_kinetic_profiles, + KineticProfileData, read_kinetic_file, write_kinetic_h5 export flux_surface_metric, flux_surface_area # --- Constants --- diff --git a/src/Equilibrium/KineticProfiles.jl b/src/Equilibrium/KineticProfiles.jl index 8d0a858f8..6216d7816 100644 --- a/src/Equilibrium/KineticProfiles.jl +++ b/src/Equilibrium/KineticProfiles.jl @@ -1,13 +1,132 @@ """ KineticProfiles -Reading and processing kinetic profile data (density, temperature, rotation) -from ASCII tables. The output is a `KineticProfileSplines` of independent named -splines that downstream physics modules (KineticForces NTV, etc.) can read -directly without re-implementing data shimming. +Reading and processing kinetic profile data (density, temperature, rotation, +and optionally transport diffusivities) from the GPEC HDF5 kinetic format or +from legacy 6-column ASCII tables (`.gpeckf`/`.kin`). The processed output is a +`KineticProfileSplines` of independent named splines that downstream physics +modules (KineticForces NTV, etc.) read directly without re-implementing data +shimming. """ using DelimitedFiles +using HDF5 + +""" + KineticProfileData + +Raw kinetic-profile columns read from a kinetic file (HDF5 or ASCII), before +resampling and spline construction. `psi` (normalized poloidal flux) is always +present; every profile field is `nothing` when the source omits it, so each +consumer validates only the fields it needs. Units: densities m⁻³, +temperatures eV, frequencies rad/s, diffusivities m²/s. + +| field | meaning | +|-------------|--------------------------------------| +| `n_i` | main-ion density | +| `n_e` | electron density | +| `T_i`/`T_e` | ion / electron temperature | +| `omega_E` | ExB rotation | +| `omega_tor` | toroidal rotation (optional) | +| `chi_e` | perpendicular heat diffusivity χ⊥ | +| `chi_phi` | toroidal momentum diffusivity χ_φ | +""" +struct KineticProfileData + psi::Vector{Float64} + n_i::Union{Nothing,Vector{Float64}} + n_e::Union{Nothing,Vector{Float64}} + T_i::Union{Nothing,Vector{Float64}} + T_e::Union{Nothing,Vector{Float64}} + omega_E::Union{Nothing,Vector{Float64}} + omega_tor::Union{Nothing,Vector{Float64}} + chi_e::Union{Nothing,Vector{Float64}} + chi_phi::Union{Nothing,Vector{Float64}} + provenance::String +end + +function KineticProfileData(; psi, n_i=nothing, n_e=nothing, T_i=nothing, T_e=nothing, + omega_E=nothing, omega_tor=nothing, chi_e=nothing, chi_phi=nothing, provenance="") + _v(x) = x === nothing ? nothing : Float64.(collect(x)) + return KineticProfileData(Float64.(collect(psi)), _v(n_i), _v(n_e), _v(T_i), _v(T_e), + _v(omega_E), _v(omega_tor), _v(chi_e), _v(chi_phi), String(provenance)) +end + +const _KINETIC_H5_EXTS = (".h5", ".hdf5", ".he5") + +# Dataset units written into / expected from the HDF5 kinetic schema. +const _KINETIC_H5_UNITS = Dict("psi" => "normalized poloidal flux", "n_i" => "m^-3", + "n_e" => "m^-3", "T_i" => "eV", "T_e" => "eV", "omega_E" => "rad/s", + "omega_tor" => "rad/s", "chi_e" => "m^2/s", "chi_phi" => "m^2/s") + +""" + read_kinetic_file(path; group="/") -> KineticProfileData + +Read a kinetic-profile file, dispatching on extension: HDF5 (`.h5`/`.hdf5`) via +the GPEC kinetic schema, otherwise a 6-column ASCII table (`.gpeckf`/`.kin`/`.dat`: +`psi_n n_i n_e T_i[eV] T_e[eV] omega_E`). Returns the raw columns; downstream +consumers validate the fields they require. +""" +function read_kinetic_file(path::AbstractString; group::AbstractString="/") + isfile(path) || error("Kinetic profile file not found: $path") + ext = lowercase(splitext(path)[2]) + return ext in _KINETIC_H5_EXTS ? _read_kinetic_h5(path; group=group) : _read_kinetic_ascii(path) +end + +"""Read a legacy 6-column ASCII kinetic table into a `KineticProfileData`.""" +function _read_kinetic_ascii(path::AbstractString) + psi, ni, ne, Ti, Te, omegaE = _read_kinetic_table(path) + return KineticProfileData(; psi=psi, n_i=ni, n_e=ne, T_i=Ti, T_e=Te, omega_E=omegaE, + provenance="ASCII 6-column: $(basename(path))") +end + +"""Read the GPEC HDF5 kinetic schema. Only `psi` is required; other datasets are +optional and surfaced as-is.""" +function _read_kinetic_h5(path::AbstractString; group::AbstractString="/") + h5open(path, "r") do f + g = group == "/" ? f : f[group] + haskey(g, "psi") || error("kinetic HDF5 '$path' group '$group': missing required dataset 'psi'") + rd(name) = haskey(g, name) ? Float64.(vec(read(g[name]))) : nothing + prov = "" + ats = attributes(g) + haskey(ats, "provenance") && (prov = string(read(ats["provenance"]))) + return KineticProfileData(; psi=Float64.(vec(read(g["psi"]))), + n_i=rd("n_i"), n_e=rd("n_e"), T_i=rd("T_i"), T_e=rd("T_e"), + omega_E=rd("omega_E"), omega_tor=rd("omega_tor"), + chi_e=rd("chi_e"), chi_phi=rd("chi_phi"), provenance=prov) + end +end + +""" + write_kinetic_h5(path, data; group="/", schema_version="1.0", provenance=data.provenance) + +Write a `KineticProfileData` to the GPEC HDF5 kinetic schema. Each present field +is written as a dataset with a `units` attribute; absent (`nothing`) fields are +skipped. The group carries `schema_version` and `provenance` attributes. +""" +function write_kinetic_h5(path::AbstractString, data::KineticProfileData; + group::AbstractString="/", schema_version::AbstractString="1.0", + provenance::AbstractString=data.provenance) + h5open(path, "w") do f + g = group == "/" ? f : create_group(f, group) + function put(name, v) + v === nothing && return + g[name] = collect(Float64, v) + attributes(g[name])["units"] = _KINETIC_H5_UNITS[name] + end + put("psi", data.psi) + put("n_i", data.n_i) + put("n_e", data.n_e) + put("T_i", data.T_i) + put("T_e", data.T_e) + put("omega_E", data.omega_E) + put("omega_tor", data.omega_tor) + put("chi_e", data.chi_e) + put("chi_phi", data.chi_phi) + attributes(g)["schema_version"] = schema_version + attributes(g)["provenance"] = provenance + end + return path +end """ load_kinetic_profiles(kinetic_file::AbstractString; @@ -60,12 +179,17 @@ function load_kinetic_profiles(kinetic_file::AbstractString; ExB_rotation_factor::Float64=1.0, toroidal_rotation_factor::Float64=1.0, chi1::Union{Nothing,Float64}=nothing) - if !isfile(kinetic_file) - error("Kinetic profile file not found: $kinetic_file") - end - - psi_input, ni_input, ne_input, Ti_input_eV, Te_input_eV, omegaE_input = - _read_kinetic_table(kinetic_file) + data = read_kinetic_file(kinetic_file) + + # NTV requires n_e, T_i, T_e, omega_E; n_i defaults to n_e (quasineutrality) + # when absent. omega_tor / chi_e / chi_phi (if present) are ignored here. + _need(field, name) = field === nothing ? error("kinetic file '$kinetic_file' missing required '$name'") : field + psi_input = data.psi + ne_input = _need(data.n_e, "n_e") + Ti_input_eV = _need(data.T_i, "T_i") + Te_input_eV = _need(data.T_e, "T_e") + omegaE_input = _need(data.omega_E, "omega_E") + ni_input = data.n_i === nothing ? copy(ne_input) : data.n_i eV_to_J = 1.602e-19 mp = 1.672_614e-27 diff --git a/test/runtests_kinetic.jl b/test/runtests_kinetic.jl index 63bcd8b55..13d691c07 100644 --- a/test/runtests_kinetic.jl +++ b/test/runtests_kinetic.jl @@ -312,4 +312,59 @@ @test mr.total_energy == 0.0 + 0.0im @test isempty(mr.records) end + + # ========================================================================= + # Kinetic profile I/O: HDF5 schema, ASCII back-compat, writer round-trip + # ========================================================================= + @testset "kinetic profile I/O" begin + E = GeneralizedPerturbedEquilibrium.Equilibrium + exdir = joinpath(@__DIR__, "..", "examples", "DIIID-like_ideal_example") + gpeckf = joinpath(exdir, "TkMkr_D3Dlike_Hmode_kinetic.gpeckf") + h5 = joinpath(exdir, "TkMkr_D3Dlike_Hmode_kinetic.h5") + + @testset "extension dispatch + raw read" begin + da = E.read_kinetic_file(gpeckf) + db = E.read_kinetic_file(h5) + # legacy ASCII carries no optional fields; the example .h5 carries chi + @test da.chi_e === nothing && da.chi_phi === nothing + @test db.chi_e !== nothing && db.chi_phi !== nothing + # core columns identical (the .h5 was generated from the .gpeckf) + @test da.psi == db.psi + @test da.n_e == db.n_e + @test da.T_i == db.T_i + @test da.omega_E == db.omega_E + end + + @testset "NTV splines identical: ASCII vs HDF5" begin + ka = E.load_kinetic_profiles(gpeckf) + kb = E.load_kinetic_profiles(h5) + for p in 0.0:0.1:1.0 + @test ka.ne_spline(p) == kb.ne_spline(p) + @test ka.Ti_spline(p) == kb.Ti_spline(p) + @test ka.omegaE_spline(p) == kb.omegaE_spline(p) + @test ka.zeff_spline(p) == kb.zeff_spline(p) + end + end + + @testset "writer round-trip" begin + db = E.read_kinetic_file(h5) + tmp = tempname() * ".h5" + E.write_kinetic_h5(tmp, db; provenance="roundtrip") + dc = E.read_kinetic_file(tmp) + @test dc.chi_e ≈ db.chi_e + @test dc.chi_phi ≈ db.chi_phi + @test dc.n_e ≈ db.n_e + @test dc.provenance == "roundtrip" + rm(tmp; force=true) + end + + @testset "missing required field errors" begin + # HDF5 with only psi + n_e: NTV load must error on the missing T_i + tmp = tempname() * ".h5" + d = E.KineticProfileData(; psi=[0.0, 0.5, 1.0], n_e=[1e19, 9e18, 8e18]) + E.write_kinetic_h5(tmp, d) + @test_throws ErrorException E.load_kinetic_profiles(tmp) + rm(tmp; force=true) + end + end end From 5876b340ed4794d8144b02d52824bac8c39a4cea Mon Sep 17 00:00:00 2001 From: d-burg Date: Wed, 24 Jun 2026 16:23:10 -0400 Subject: [PATCH 108/135] EQUIL - IMPROVEMENT - Update DIII-D-like example: edge-matched equilibrium, analytic ExB, HDF5 profiles Edge-current-matched equilibrium (q=6 retained at psihigh=0.995; fixed mpsi to avoid edge under-resolution, see #302). Kinetic profiles carry an analytic ExB rotation (omega_E = omega_tor - omega_dia) and synthetic transport diffusivities chi_e/chi_phi, shipped in the new .h5 (gpec.toml points at it; .gpeckf retained for back-compat). Relax NTV psi-quadrature tolerances as an interim mitigation (see #303). Re-pin the parallel-integration regression (et[1], Delta-prime diagonal) for the updated equilibrium. Co-Authored-By: Claude Opus 4.8 --- .../TkMkr_D3Dlike_Hmode.geqdsk | 27050 ++++++++-------- .../TkMkr_D3Dlike_Hmode_kinetic.gpeckf | 1028 +- .../TkMkr_D3Dlike_Hmode_kinetic.h5 | Bin 0 -> 57472 bytes examples/DIIID-like_ideal_example/gpec.toml | 8 +- test/runtests_parallel_integration.jl | 8 +- 5 files changed, 14048 insertions(+), 14046 deletions(-) create mode 100644 examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode_kinetic.h5 diff --git a/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk b/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk index f89a0ea7a..fa39228fe 100644 --- a/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk +++ b/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk @@ -1,60 +1,60 @@ tMaker: 0 257 257 - 1.467141630E+00 2.977755070E+00 1.688688870E+00 9.506132600E-01-5.415000020E-03 - 1.743232370E+00 4.030755910E-02-1.069494710E-01 1.538152990E-01-2.008066650E+00 - 1.150000000E+06-1.069494710E-01 0.000000000E+00 1.743232370E+00 0.000000000E+00 - 4.030755910E-02 0.000000000E+00 1.538152990E-01 0.000000000E+00 0.000000000E+00 --3.456651930E+00-3.456078290E+00-3.455504420E+00-3.454931740E+00-3.454362390E+00 --3.453796390E+00-3.453234200E+00-3.452675100E+00-3.452119830E+00-3.451567650E+00 --3.451018570E+00-3.450472830E+00-3.449930190E+00-3.449390410E+00-3.448853730E+00 --3.448319670E+00-3.447788480E+00-3.447260140E+00-3.446734670E+00-3.446211580E+00 --3.445691110E+00-3.445173500E+00-3.444658040E+00-3.444145200E+00-3.443634990E+00 --3.443127160E+00-3.442621950E+00-3.442118880E+00-3.441618200E+00-3.441120150E+00 --3.440624240E+00-3.440130710E+00-3.439639570E+00-3.439150570E+00-3.438663960E+00 --3.438179970E+00-3.437697890E+00-3.437218430E+00-3.436741110E+00-3.436265950E+00 --3.435793400E+00-3.435322760E+00-3.434854750E+00-3.434388880E+00-3.433925390E+00 --3.433464290E+00-3.433005330E+00-3.432548760E+00-3.432094570E+00-3.431642770E+00 --3.431193350E+00-3.430746080E+00-3.430301430E+00-3.429858920E+00-3.429418800E+00 --3.428981070E+00-3.428545950E+00-3.428113220E+00-3.427682640E+00-3.427254680E+00 --3.426829100E+00-3.426406150E+00-3.425985570E+00-3.425567390E+00-3.425151820E+00 --3.424738650E+00-3.424328090E+00-3.423919920E+00-3.423514370E+00-3.423111200E+00 --3.422710900E+00-3.422312970E+00-3.421917680E+00-3.421524760E+00-3.421134710E+00 --3.420747040E+00-3.420362230E+00-3.419979810E+00-3.419600010E+00-3.419223070E+00 --3.418848510E+00-3.418476820E+00-3.418107750E+00-3.417741300E+00-3.417377470E+00 --3.417016270E+00-3.416657690E+00-3.416301970E+00-3.415948870E+00-3.415598390E+00 --3.415250780E+00-3.414905550E+00-3.414563180E+00-3.414223430E+00-3.413886550E+00 --3.413552280E+00-3.413220640E+00-3.412891630E+00-3.412565230E+00-3.412241700E+00 --3.411920790E+00-3.411602500E+00-3.411286830E+00-3.410973790E+00-3.410663370E+00 --3.410355810E+00-3.410050630E+00-3.409748320E+00-3.409448390E+00-3.409151320E+00 --3.408856630E+00-3.408564570E+00-3.408274890E+00-3.407988070E+00-3.407703640E+00 --3.407421830E+00-3.407142400E+00-3.406865360E+00-3.406590940E+00-3.406319140E+00 --3.406049490E+00-3.405782460E+00-3.405517820E+00-3.405255560E+00-3.404995680E+00 --3.404738190E+00-3.404482840E+00-3.404229880E+00-3.403979300E+00-3.403730870E+00 --3.403484820E+00-3.403240920E+00-3.402999160E+00-3.402759550E+00-3.402522330E+00 --3.402287010E+00-3.402053830E+00-3.401822570E+00-3.401593450E+00-3.401366470E+00 --3.401141410E+00-3.400918250E+00-3.400696990E+00-3.400477890E+00-3.400260450E+00 --3.400044920E+00-3.399831060E+00-3.399619340E+00-3.399409060E+00-3.399200680E+00 --3.398993970E+00-3.398789170E+00-3.398585800E+00-3.398384090E+00-3.398184060E+00 --3.397985460E+00-3.397788520E+00-3.397593260E+00-3.397399190E+00-3.397206780E+00 --3.397015810E+00-3.396826270E+00-3.396638150E+00-3.396451470E+00-3.396265980E+00 --3.396081920E+00-3.395899300E+00-3.395717860E+00-3.395537610E+00-3.395358800E+00 --3.395181180E+00-3.395004750E+00-3.394829750E+00-3.394655700E+00-3.394482850E+00 --3.394311430E+00-3.394141200E+00-3.393971920E+00-3.393804070E+00-3.393637180E+00 --3.393471480E+00-3.393307210E+00-3.393144130E+00-3.392982010E+00-3.392821310E+00 --3.392662050E+00-3.392503980E+00-3.392347100E+00-3.392191650E+00-3.392037870E+00 --3.391885280E+00-3.391734360E+00-3.391584870E+00-3.391436820E+00-3.391290430E+00 --3.391145940E+00-3.391002890E+00-3.390861750E+00-3.390722270E+00-3.390584950E+00 --3.390449290E+00-3.390315770E+00-3.390184400E+00-3.390054940E+00-3.389927860E+00 --3.389803170E+00-3.389680860E+00-3.389560940E+00-3.389443640E+00-3.389329200E+00 --3.389217620E+00-3.389108900E+00-3.389003280E+00-3.388900760E+00-3.388801570E+00 --3.388705730E+00-3.388613700E+00-3.388525490E+00-3.388441090E+00-3.388360740E+00 --3.388285160E+00-3.388214110E+00-3.388148070E+00-3.388087030E+00-3.388031010E+00 --3.387980460E+00-3.387935640E+00-3.387896540E+00-3.387863640E+00-3.387836930E+00 --3.387817380E+00-3.387804990E+00-3.387800460E+00-3.387804750E+00-3.387818570E+00 --3.387843130E+00-3.387880330E+00-3.387931350E+00-3.387998820E+00-3.388085370E+00 --3.388193850E+00-3.388327600E+00-3.388483520E+00-3.388654950E+00-3.388846400E+00 --3.389063120E+00-3.389300110E+00-3.389548780E+00-3.389798640E+00-3.390038250E+00 --3.390258550E+00-3.390453340E+00-3.390620470E+00-3.390760180E+00-3.390874620E+00 --3.390966890E+00-3.391000510E+00 + 1.467141630E+00 2.977755070E+00 1.688778880E+00 9.506132600E-01-5.415000020E-03 + 1.743335840E+00 4.040685300E-02-9.057495000E-02 1.708107890E-01-2.007959840E+00 + 1.150000120E+06-9.057495000E-02 0.000000000E+00 1.743335840E+00 0.000000000E+00 + 4.040685300E-02 0.000000000E+00 1.708107890E-01 0.000000000E+00 0.000000000E+00 +-3.457298990E+00-3.456717730E+00-3.456135750E+00-3.455554490E+00-3.454976320E+00 +-3.454401490E+00-3.453829770E+00-3.453261380E+00-3.452696320E+00-3.452134130E+00 +-3.451575040E+00-3.451019050E+00-3.450465920E+00-3.449915650E+00-3.449368000E+00 +-3.448823210E+00-3.448281290E+00-3.447741990E+00-3.447205310E+00-3.446671010E+00 +-3.446139570E+00-3.445610520E+00-3.445084100E+00-3.444560050E+00-3.444038630E+00 +-3.443519590E+00-3.443003180E+00-3.442489150E+00-3.441977500E+00-3.441468240E+00 +-3.440961360E+00-3.440456870E+00-3.439955000E+00-3.439455510E+00-3.438958410E+00 +-3.438463690E+00-3.437971350E+00-3.437481400E+00-3.436994080E+00-3.436508890E+00 +-3.436026330E+00-3.435546160E+00-3.435068610E+00-3.434593200E+00-3.434120420E+00 +-3.433650260E+00-3.433182480E+00-3.432717080E+00-3.432254310E+00-3.431793930E+00 +-3.431336160E+00-3.430881020E+00-3.430428270E+00-3.429978130E+00-3.429530620E+00 +-3.429085490E+00-3.428643230E+00-3.428203340E+00-3.427766320E+00-3.427331690E+00 +-3.426899910E+00-3.426470520E+00-3.426043990E+00-3.425620080E+00-3.425198790E+00 +-3.424780130E+00-3.424364330E+00-3.423951150E+00-3.423540590E+00-3.423132900E+00 +-3.422728060E+00-3.422325610E+00-3.421926260E+00-3.421529530E+00-3.421135430E+00 +-3.420744420E+00-3.420356040E+00-3.419970270E+00-3.419587370E+00-3.419207330E+00 +-3.418830160E+00-3.418455600E+00-3.418083910E+00-3.417715070E+00-3.417348860E+00 +-3.416985750E+00-3.416625260E+00-3.416267400E+00-3.415912630E+00-3.415560480E+00 +-3.415211200E+00-3.414864780E+00-3.414520980E+00-3.414180280E+00-3.413841960E+00 +-3.413506750E+00-3.413174150E+00-3.412844180E+00-3.412517070E+00-3.412192820E+00 +-3.411871190E+00-3.411552190E+00-3.411236050E+00-3.410922530E+00-3.410611870E+00 +-3.410303590E+00-3.409998180E+00-3.409695390E+00-3.409395220E+00-3.409097670E+00 +-3.408802750E+00-3.408510210E+00-3.408220530E+00-3.407933240E+00-3.407648560E+00 +-3.407366280E+00-3.407086610E+00-3.406809330E+00-3.406534670E+00-3.406262160E+00 +-3.405992270E+00-3.405724760E+00-3.405459640E+00-3.405196910E+00-3.404936310E+00 +-3.404678110E+00-3.404422280E+00-3.404168610E+00-3.403917070E+00-3.403667690E+00 +-3.403420690E+00-3.403175830E+00-3.402932880E+00-3.402692320E+00-3.402453660E+00 +-3.402217150E+00-3.401982550E+00-3.401749850E+00-3.401519300E+00-3.401290660E+00 +-3.401063920E+00-3.400839090E+00-3.400615930E+00-3.400394680E+00-3.400175330E+00 +-3.399957660E+00-3.399741890E+00-3.399527790E+00-3.399315360E+00-3.399104600E+00 +-3.398895500E+00-3.398688080E+00-3.398482080E+00-3.398277760E+00-3.398075100E+00 +-3.397873880E+00-3.397674080E+00-3.397475960E+00-3.397279260E+00-3.397083760E+00 +-3.396889930E+00-3.396697520E+00-3.396506550E+00-3.396316770E+00-3.396128420E+00 +-3.395941500E+00-3.395756010E+00-3.395571710E+00-3.395388840E+00-3.395207170E+00 +-3.395026920E+00-3.394847870E+00-3.394670250E+00-3.394493820E+00-3.394318820E+00 +-3.394145010E+00-3.393972640E+00-3.393801690E+00-3.393631940E+00-3.393463610E+00 +-3.393296720E+00-3.393131260E+00-3.392967220E+00-3.392804620E+00-3.392643450E+00 +-3.392484190E+00-3.392326350E+00-3.392170190E+00-3.392015700E+00-3.391863110E+00 +-3.391712430E+00-3.391563650E+00-3.391416790E+00-3.391272070E+00-3.391129490E+00 +-3.390988830E+00-3.390850540E+00-3.390714650E+00-3.390580890E+00-3.390449760E+00 +-3.390321250E+00-3.390195130E+00-3.390071630E+00-3.389950990E+00-3.389833210E+00 +-3.389718290E+00-3.389606480E+00-3.389497760E+00-3.389392380E+00-3.389290330E+00 +-3.389191870E+00-3.389096980E+00-3.389005900E+00-3.388918640E+00-3.388835190E+00 +-3.388756040E+00-3.388680930E+00-3.388610360E+00-3.388544560E+00-3.388483520E+00 +-3.388427500E+00-3.388376470E+00-3.388331170E+00-3.388291120E+00-3.388256790E+00 +-3.388228180E+00-3.388205770E+00-3.388189320E+00-3.388179300E+00-3.388175960E+00 +-3.388179300E+00-3.388189550E+00-3.388207670E+00-3.388234380E+00-3.388270620E+00 +-3.388317820E+00-3.388376240E+00-3.388446330E+00-3.388528350E+00-3.388622280E+00 +-3.388728140E+00-3.388846870E+00-3.388977050E+00-3.389114860E+00-3.389262910E+00 +-3.389424320E+00-3.389597420E+00-3.389778610E+00-3.389962670E+00-3.390143870E+00 +-3.390317200E+00-3.390478370E+00-3.390625240E+00-3.390755650E+00-3.390868430E+00 +-3.390963320E+00-3.391000510E+00 5.807975000E+04 5.769232420E+04 5.730932420E+04 5.692937500E+04 5.655051950E+04 5.617253910E+04 5.579540620E+04 5.541916410E+04 5.504387500E+04 5.466960160E+04 5.429639450E+04 5.392431640E+04 5.355339840E+04 5.318369140E+04 5.281530080E+04 @@ -107,13476 +107,13476 @@ tMaker: 0 257 257 4.596126460E+03 3.963030030E+03 3.320442630E+03 2.694304690E+03 2.110350340E+03 1.589322390E+03 1.143640750E+03 7.763899540E+02 4.830079040E+02 2.542549900E+02 7.900079350E+01 4.925198480E-02 --1.946446300E+00-1.945795660E+00-1.948189500E+00-1.937307830E+00-1.925099020E+00 --1.912721400E+00-1.900445940E+00-1.888478040E+00-1.876833200E+00-1.865419860E+00 --1.854355690E+00-1.843589540E+00-1.832858320E+00-1.822654720E+00-1.812760950E+00 --1.802692170E+00-1.793011430E+00-1.783447740E+00-1.774071690E+00-1.765078540E+00 --1.755891080E+00-1.746977930E+00-1.738416550E+00-1.729635480E+00-1.720876460E+00 --1.712323430E+00-1.703963520E+00-1.695723770E+00-1.687267660E+00-1.679031850E+00 --1.671091680E+00-1.662806270E+00-1.654631380E+00-1.646719930E+00-1.638484240E+00 --1.630423430E+00-1.622671720E+00-1.614485980E+00-1.606459140E+00-1.598606230E+00 --1.590619440E+00-1.582712410E+00-1.574633120E+00-1.566580060E+00-1.558722730E+00 --1.550574660E+00-1.542521600E+00-1.534687400E+00-1.526448010E+00-1.518335580E+00 --1.510200740E+00-1.502032880E+00-1.494005080E+00-1.485754250E+00-1.477452750E+00 --1.469298120E+00-1.460917230E+00-1.452539090E+00-1.444225070E+00-1.435860750E+00 --1.427538040E+00-1.418955560E+00-1.410464410E+00-1.402043820E+00-1.393384700E+00 --1.384781360E+00-1.376278520E+00-1.367536660E+00-1.358794330E+00-1.350137470E+00 --1.341308590E+00-1.332588430E+00-1.323779580E+00-1.314862490E+00-1.306052090E+00 --1.297100780E+00-1.288171890E+00-1.279380200E+00-1.270329360E+00-1.261243340E+00 --1.252341030E+00-1.243238210E+00-1.234159590E+00-1.225204590E+00-1.216140150E+00 --1.207040550E+00-1.197928070E+00-1.188765650E+00-1.179744360E+00-1.170559530E+00 --1.161377070E+00-1.152426000E+00-1.143223290E+00-1.134115820E+00-1.125048160E+00 --1.115872030E+00-1.106823680E+00-1.097713230E+00-1.088613030E+00-1.079598550E+00 --1.070563910E+00-1.061585190E+00-1.052660820E+00-1.043620710E+00-1.034688950E+00 --1.025756480E+00-1.016829610E+00-1.008066300E+00-9.992457630E-01-9.904837610E-01 --9.817801710E-01-9.730736610E-01-9.644076230E-01-9.557370540E-01-9.471695420E-01 --9.387571220E-01-9.303572770E-01-9.219334720E-01-9.136122470E-01-9.053176640E-01 --8.970558050E-01-8.889136910E-01-8.808198570E-01-8.728173380E-01-8.648705480E-01 --8.569622040E-01-8.492022750E-01-8.414909840E-01-8.337711100E-01-8.261929150E-01 --8.187150360E-01-8.112221960E-01-8.038714530E-01-7.966326480E-01-7.895225290E-01 --7.824348210E-01-7.753462200E-01-7.684623000E-01-7.616319660E-01-7.548953290E-01 --7.482511400E-01-7.416822910E-01-7.352163790E-01-7.288668160E-01-7.225535510E-01 --7.163149710E-01-7.102727290E-01-7.042455080E-01-6.983030440E-01-6.925343280E-01 --6.868016720E-01-6.812118290E-01-6.756763460E-01-6.701464060E-01-6.647836570E-01 --6.594858170E-01-6.543316840E-01-6.492885350E-01-6.442452070E-01-6.393561360E-01 --6.345142720E-01-6.297264700E-01-6.250591870E-01-6.203969120E-01-6.158205270E-01 --6.114144330E-01-6.070027350E-01-6.026619080E-01-5.984224080E-01-5.941259260E-01 --5.899626020E-01-5.858654980E-01-5.817275050E-01-5.776484610E-01-5.736108420E-01 --5.696234110E-01-5.656422970E-01-5.616332290E-01-5.576522350E-01-5.536768440E-01 --5.496674780E-01-5.456255080E-01-5.415374040E-01-5.373497610E-01-5.331382750E-01 --5.288192030E-01-5.243236420E-01-5.198032860E-01-5.151319500E-01-5.103292470E-01 --5.053799150E-01-5.002924800E-01-4.951749440E-01-4.898775820E-01-4.843910340E-01 --4.788118300E-01-4.730278850E-01-4.670482280E-01-4.608622190E-01-4.544394910E-01 --4.478819670E-01-4.410899580E-01-4.340185820E-01-4.267336130E-01-4.192285240E-01 --4.113065000E-01-4.030534030E-01-3.944976930E-01-3.855396810E-01-3.763088880E-01 --3.667147460E-01-3.567346330E-01-3.463593420E-01-3.355301020E-01-3.242451250E-01 --3.125036660E-01-3.003010450E-01-2.875939910E-01-2.739532290E-01-2.592931390E-01 --2.440192700E-01-2.281588320E-01-2.117815760E-01-1.948133710E-01-1.771619770E-01 --1.588910370E-01-1.399075980E-01-1.200346800E-01-9.918294100E-02-7.719989120E-02 --5.372624100E-02-2.850924250E-02-1.060737530E-03 2.918582040E-02 6.294120100E-02 - 1.012346670E-01 1.449984010E-01 1.954808090E-01 2.540719210E-01 3.217823210E-01 - 3.997052610E-01 4.900958240E-01 5.461238030E-01 5.940995810E-01 6.814411280E-01 - 7.604500650E-01 8.159438970E-01 8.383222220E-01 8.226100210E-01 7.716535930E-01 - 6.942850350E-01 6.028659940E-01 5.091879370E-01 4.208998980E-01 3.417293730E-01 - 2.727588120E-01-5.585808680E-02 --3.823251560E+05-3.783711880E+05-3.736301250E+05-3.723791560E+05-3.714901880E+05 --3.706606250E+05-3.698202500E+05-3.689157190E+05-3.679432500E+05-3.669294060E+05 --3.658470940E+05-3.647081880E+05-3.635774690E+05-3.623221250E+05-3.609959380E+05 --3.597229690E+05-3.583516560E+05-3.569515620E+05-3.555143120E+05-3.539878750E+05 --3.525214060E+05-3.509884690E+05-3.493657500E+05-3.478010310E+05-3.462277810E+05 --3.445948750E+05-3.429119060E+05-3.412001560E+05-3.395466250E+05-3.378339690E+05 --3.360404060E+05-3.343333750E+05-3.325905000E+05-3.307693750E+05-3.290273750E+05 --3.272355940E+05-3.253574060E+05-3.235885940E+05-3.217710310E+05-3.198996880E+05 --3.180551250E+05-3.161796250E+05-3.143398750E+05-3.124852190E+05-3.105704380E+05 --3.087245310E+05-3.068447190E+05-3.048976880E+05-3.030492190E+05-3.011574060E+05 --2.992617500E+05-2.973647500E+05-2.954205940E+05-2.935264060E+05-2.916365620E+05 --2.896987810E+05-2.878128750E+05-2.859183120E+05-2.839987810E+05-2.820830940E+05 --2.801464380E+05-2.782702190E+05-2.763613750E+05-2.744263750E+05-2.725487500E+05 --2.706506880E+05-2.687210000E+05-2.668490310E+05-2.649687190E+05-2.630582190E+05 --2.611878590E+05-2.592836880E+05-2.573998590E+05-2.555429840E+05-2.536565620E+05 --2.518067030E+05-2.499452970E+05-2.480425620E+05-2.462067970E+05-2.443792810E+05 --2.425026410E+05-2.406820470E+05-2.388585000E+05-2.370059840E+05-2.351821250E+05 --2.333671090E+05-2.315566560E+05-2.297626880E+05-2.279353280E+05-2.261588280E+05 --2.243901560E+05-2.225690160E+05-2.208213910E+05-2.190515470E+05-2.172764530E+05 --2.155383280E+05-2.137750940E+05-2.120403120E+05-2.103163120E+05-2.085846410E+05 --2.068713590E+05-2.051510940E+05-2.034262970E+05-2.017453280E+05-2.000492970E+05 --1.983700780E+05-1.967080310E+05-1.950221720E+05-1.933724220E+05-1.917202340E+05 --1.900669380E+05-1.884315470E+05-1.868043280E+05-1.851998280E+05-1.835907500E+05 --1.819649380E+05-1.803627660E+05-1.787868280E+05-1.772020470E+05-1.756314690E+05 --1.740755620E+05-1.725126250E+05-1.709644690E+05-1.694214380E+05-1.678954060E+05 --1.663851410E+05-1.648571880E+05-1.633411880E+05-1.618551250E+05-1.603595310E+05 --1.588679690E+05-1.574145310E+05-1.559578280E+05-1.545031410E+05-1.530395160E+05 --1.515982030E+05-1.501876880E+05-1.487527810E+05-1.473375470E+05-1.459327340E+05 --1.445407030E+05-1.431657190E+05-1.417922030E+05-1.404170310E+05-1.390642500E+05 --1.377249220E+05-1.363667030E+05-1.350420780E+05-1.337332190E+05-1.324161720E+05 --1.311223590E+05-1.298206170E+05-1.285370160E+05-1.272866250E+05-1.260253120E+05 --1.247831170E+05-1.235391880E+05-1.223039770E+05-1.211044920E+05-1.198939060E+05 --1.187031480E+05-1.175309690E+05-1.163591880E+05-1.152213120E+05-1.140950470E+05 --1.129570620E+05-1.118561410E+05-1.107671250E+05-1.096810230E+05-1.086427500E+05 --1.075978910E+05-1.065652810E+05-1.055753750E+05-1.045994450E+05-1.036424140E+05 --1.027017270E+05-1.017885860E+05-1.009114840E+05-1.000529060E+05-9.921789840E+04 --9.841646880E+04-9.764685940E+04-9.691207030E+04-9.622485940E+04-9.555705470E+04 --9.493306250E+04-9.437310940E+04-9.383337500E+04-9.335076560E+04-9.291985160E+04 --9.254540620E+04-9.223577340E+04-9.196698440E+04-9.178157030E+04-9.168111720E+04 --9.163611720E+04-9.167821880E+04-9.180354690E+04-9.201413280E+04-9.232662500E+04 --9.272738280E+04-9.324414840E+04-9.388800000E+04-9.463728120E+04-9.549168750E+04 --9.650750780E+04-9.765720310E+04-9.893486720E+04-1.003910310E+05-1.019840230E+05 --1.037470700E+05-1.056869840E+05-1.077945160E+05-1.100988910E+05-1.125904690E+05 --1.152644610E+05-1.181476330E+05-1.212754920E+05-1.248617890E+05-1.289471560E+05 --1.333246560E+05-1.379856720E+05-1.428899530E+05-1.480850620E+05-1.536380160E+05 --1.595318280E+05-1.658282340E+05-1.726412660E+05-1.800405780E+05-1.881287970E+05 --1.971347810E+05-2.072316560E+05-2.187278280E+05-2.319787810E+05-2.474245780E+05 --2.656990000E+05-2.873789060E+05-3.132333750E+05-3.441266880E+05-3.806703120E+05 --4.235237500E+05-4.740534060E+05-5.010172810E+05-5.244320000E+05-5.714279380E+05 --6.106361250E+05-6.319881250E+05-6.291185620E+05-5.996325620E+05-5.463624380E+05 --4.762477500E+05-3.986516560E+05-3.224688120E+05-2.537611090E+05-1.956482500E+05 --1.487331410E+05-3.777125240E+03 - 1.263547540E-01 1.241554620E-01 1.221195240E-01 1.202512460E-01 1.185528260E-01 - 1.170254280E-01 1.156714340E-01 1.144922230E-01 1.134891880E-01 1.126630530E-01 - 1.120153740E-01 1.115462710E-01 1.112559880E-01 1.111447510E-01 1.112119110E-01 - 1.114574670E-01 1.118572730E-01 1.122757050E-01 1.126888320E-01 1.130924450E-01 - 1.134715530E-01 1.138298880E-01 1.141617000E-01 1.144626590E-01 1.147284430E-01 - 1.149596870E-01 1.151596830E-01 1.153152730E-01 1.154345500E-01 1.155255960E-01 - 1.155965180E-01 1.156553920E-01 1.157103260E-01 1.157611460E-01 1.157872230E-01 - 1.158085020E-01 1.158312040E-01 1.158632410E-01 1.159071330E-01 1.159665360E-01 - 1.160430540E-01 1.161399630E-01 1.162605430E-01 1.164080870E-01 1.165858810E-01 - 1.167972010E-01 1.170432200E-01 1.173235100E-01 1.176404950E-01 1.179976980E-01 - 1.183958800E-01 1.188361790E-01 1.193197440E-01 1.198477300E-01 1.204212750E-01 - 1.210415360E-01 1.217097710E-01 1.224256900E-01 1.231894570E-01 1.240024640E-01 - 1.248635580E-01 1.257734750E-01 1.267334070E-01 1.277421270E-01 1.287985590E-01 - 1.299016920E-01 1.310504380E-01 1.322437520E-01 1.334805940E-01 1.347591730E-01 - 1.360754520E-01 1.374285070E-01 1.388125870E-01 1.402235780E-01 1.416555200E-01 - 1.431150290E-01 1.445971730E-01 1.460966170E-01 1.476079820E-01 1.491259040E-01 - 1.506450330E-01 1.521694660E-01 1.536999490E-01 1.552327130E-01 1.567662210E-01 - 1.582980900E-01 1.598276200E-01 1.613543480E-01 1.628755780E-01 1.643898640E-01 - 1.658977270E-01 1.673997640E-01 1.688964810E-01 1.703884600E-01 1.718762370E-01 - 1.733603780E-01 1.748414040E-01 1.763198820E-01 1.777926530E-01 1.792584510E-01 - 1.807199120E-01 1.821769920E-01 1.836303620E-01 1.850806330E-01 1.865278930E-01 - 1.879725310E-01 1.894150380E-01 1.908551310E-01 1.922931520E-01 1.937294300E-01 - 1.951642630E-01 1.965979780E-01 1.980308890E-01 1.994630250E-01 2.008945050E-01 - 2.023258510E-01 2.037572260E-01 2.051887810E-01 2.066207080E-01 2.080531870E-01 - 2.094862460E-01 2.109200660E-01 2.123548240E-01 2.137905660E-01 2.152274100E-01 - 2.166654320E-01 2.181046750E-01 2.195451710E-01 2.209870370E-01 2.224303190E-01 - 2.238750160E-01 2.253211890E-01 2.267688660E-01 2.282180640E-01 2.296687960E-01 - 2.311211380E-01 2.325750740E-01 2.340306190E-01 2.354878490E-01 2.369467470E-01 - 2.384073440E-01 2.398696840E-01 2.413337980E-01 2.427996840E-01 2.442674190E-01 - 2.457370010E-01 2.472084760E-01 2.486818280E-01 2.501571770E-01 2.516346570E-01 - 2.531143430E-01 2.545963230E-01 2.560807470E-01 2.575675850E-01 2.590570450E-01 - 2.605493070E-01 2.620445190E-01 2.635428310E-01 2.650444210E-01 2.665494380E-01 - 2.680580020E-01 2.695702310E-01 2.710863350E-01 2.726064030E-01 2.741306130E-01 - 2.756590840E-01 2.771921160E-01 2.787302140E-01 2.802719470E-01 2.818191350E-01 - 2.833715380E-01 2.849291560E-01 2.864920500E-01 2.880602480E-01 2.896338110E-01 - 2.912128270E-01 2.927972970E-01 2.943873110E-01 2.959828970E-01 2.975841760E-01 - 2.991907890E-01 3.008026480E-01 3.024201990E-01 3.040432630E-01 3.056716320E-01 - 3.073051270E-01 3.089436290E-01 3.105867210E-01 3.122344910E-01 3.138868210E-01 - 3.155435920E-01 3.172045950E-01 3.188693820E-01 3.205375370E-01 3.222086430E-01 - 3.238823710E-01 3.255583350E-01 3.272362350E-01 3.289156560E-01 3.305962980E-01 - 3.322778050E-01 3.339598180E-01 3.356404900E-01 3.373206850E-01 3.389997180E-01 - 3.406768140E-01 3.423512280E-01 3.440221850E-01 3.456889690E-01 3.473507760E-01 - 3.490068320E-01 3.506564500E-01 3.522987960E-01 3.539331560E-01 3.555587230E-01 - 3.571747840E-01 3.587809800E-01 3.603754640E-01 3.619581460E-01 3.635280130E-01 - 3.650840520E-01 3.666253090E-01 3.681507410E-01 3.696593940E-01 3.711503150E-01 - 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1.710026710E-01 1.687815040E-01 1.665492360E-01 - 1.643057910E-01 1.620510370E-01 1.597848830E-01 1.575073750E-01 1.552182140E-01 - 1.529170720E-01 1.506036520E-01 1.482777740E-01 1.459420030E-01 1.435988400E-01 - 1.412502830E-01 1.388984470E-01 1.365441380E-01 1.341878920E-01 1.318303050E-01 - 1.294720020E-01 1.271135660E-01 1.247555990E-01 1.223987560E-01 1.200436500E-01 - 1.176909060E-01 1.153411270E-01 1.129948790E-01 1.106527300E-01 1.083152290E-01 - 1.059828850E-01 1.036562100E-01 1.013357120E-01 9.902185950E-02 9.671513740E-02 - 9.441601490E-02 9.212497620E-02 8.984247600E-02 8.756900580E-02 8.530502020E-02 - 8.305100350E-02 8.080742510E-02 7.857476170E-02 7.635349040E-02 7.414409520E-02 - 7.194707540E-02 6.976292280E-02 6.759215150E-02 6.543529030E-02 6.329288330E-02 - 6.116550420E-02 5.905370790E-02 5.695807190E-02 5.487922580E-02 5.281778800E-02 - 5.077438430E-02 4.874967410E-02 4.674430940E-02 4.475898300E-02 4.279439150E-02 - 4.085124660E-02 3.893027080E-02 3.703220190E-02 3.515776620E-02 3.330773860E-02 - 3.148288280E-02 2.968396430E-02 2.791178040E-02 2.616709660E-02 2.445073430E-02 - 2.276348510E-02 2.110613510E-02 1.947950570E-02 1.788438670E-02 1.632160130E-02 - 1.479198220E-02 1.329630430E-02 1.183538420E-02 1.041001450E-02 9.021007460E-03 - 7.669142910E-03 6.355200890E-03 5.079960920E-03 3.844203430E-03 2.648714230E-03 - 1.494234190E-03 3.815016240E-04-6.887470950E-04-1.715793040E-03-2.698917640E-03 --3.637421640E-03-4.530617040E-03-5.377852820E-03-6.178466140E-03-6.931800400E-03 --7.637247440E-03-8.294185620E-03-8.902033790E-03-9.460219180E-03-9.968180210E-03 --1.042537950E-02-1.083129740E-02-1.118545230E-02-1.148735450E-02-1.173654660E-02 --1.193259000E-02-1.207506660E-02-1.216359720E-02-1.219779900E-02-1.217731090E-02 --1.210184490E-02-1.197111890E-02-1.178482450E-02-1.154264440E-02-1.124444050E-02 --1.088998280E-02-1.047909170E-02-1.001161060E-02-9.487423110E-03-8.906448260E-03 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1.218512510E-01 1.252086760E-01 1.286006270E-01 1.320304720E-01 1.354999100E-01 - 1.390139310E-01 1.426009090E-01 1.462518270E-01 1.499533210E-01 1.536955980E-01 - 1.574721340E-01 1.612507100E-01 1.650339810E-01 1.688238680E-01 1.726202670E-01 - 1.764236690E-01 1.802334640E-01 1.840501870E-01 1.878738250E-01 1.917044520E-01 - 1.955422010E-01 1.993871780E-01 2.032395600E-01 2.070995120E-01 2.109672730E-01 - 2.148429450E-01 2.187268140E-01 2.226191460E-01 2.265202550E-01 2.304304690E-01 - 2.343501150E-01 2.382795360E-01 2.422191800E-01 2.461694480E-01 2.501308320E-01 - 2.541038690E-01 2.580890360E-01 2.620868380E-01 2.660982010E-01 2.701236610E-01 - 2.741636930E-01 2.782191930E-01 2.822911440E-01 2.863802610E-01 2.904872890E-01 - 2.946133910E-01 2.987597580E-01 3.029272850E-01 3.071169850E-01 3.113302890E-01 - 3.155685960E-01 3.198333680E-01 3.241259750E-01 3.284475800E-01 3.328004180E-01 - 3.371863370E-01 3.416070940E-01 2.170483170E-01 2.150442450E-01 2.130294440E-01 - 2.110043620E-01 2.089687590E-01 2.069226350E-01 2.048659470E-01 2.027987090E-01 - 2.007208910E-01 1.986324640E-01 1.965334120E-01 1.944237050E-01 1.923032400E-01 - 1.901720460E-01 1.880300050E-01 1.858770850E-01 1.837131980E-01 1.815383140E-01 - 1.793522980E-01 1.771550920E-01 1.749466360E-01 1.727268100E-01 1.704955400E-01 - 1.682527510E-01 1.659983250E-01 1.637321710E-01 1.614542010E-01 1.591643240E-01 - 1.568624530E-01 1.545484070E-01 1.522218290E-01 1.498823760E-01 1.475302130E-01 - 1.451685730E-01 1.427996750E-01 1.404254290E-01 1.380476800E-01 1.356671750E-01 - 1.332842260E-01 1.308995930E-01 1.285139020E-01 1.261277650E-01 1.237417610E-01 - 1.213565620E-01 1.189727860E-01 1.165910740E-01 1.142119910E-01 1.118361060E-01 - 1.094639750E-01 1.070961650E-01 1.047331540E-01 1.023754630E-01 1.000235680E-01 - 9.767796100E-02 9.533911200E-02 9.300749000E-02 9.068357200E-02 8.836781230E-02 - 8.606069540E-02 8.376269040E-02 8.147425950E-02 7.919587190E-02 7.692801950E-02 - 7.467117160E-02 7.242580500E-02 7.019243390E-02 6.797154250E-02 6.576367470E-02 - 6.356935200E-02 6.138912960E-02 5.922358480E-02 5.707329140E-02 5.493885280E-02 - 5.282089110E-02 5.072003600E-02 4.863695060E-02 4.657228290E-02 4.452673350E-02 - 4.250100630E-02 4.049580540E-02 3.851184620E-02 3.654986250E-02 3.461063280E-02 - 3.269492460E-02 3.080351280E-02 2.893716280E-02 2.709666830E-02 2.528283000E-02 - 2.349647690E-02 2.173841740E-02 2.000946370E-02 1.831044820E-02 1.664218490E-02 - 1.500549450E-02 1.340120750E-02 1.183015390E-02 1.029316520E-02 8.791097440E-03 - 7.324708160E-03 5.894827660E-03 4.502292260E-03 3.147895450E-03 1.832428390E-03 - 5.566817710E-04-6.785538280E-04-1.872512980E-03-3.024432110E-03-4.133565350E-03 --5.199170210E-03-6.220515820E-03-7.196908350E-03-8.127612990E-03-9.011971760E-03 --9.849314580E-03-1.063897370E-02-1.138031110E-02-1.207269640E-02-1.271553900E-02 --1.330825690E-02-1.385026610E-02-1.434102380E-02-1.477998220E-02-1.516663750E-02 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6.496094170E-02 6.778801980E-02 7.065120340E-02 7.354978470E-02 7.648309320E-02 - 7.945042850E-02 8.245114980E-02 8.548463880E-02 8.855024730E-02 9.164740150E-02 - 9.477555750E-02 9.793442490E-02 1.011231090E-01 1.043416190E-01 1.075898330E-01 - 1.108676200E-01 1.141748580E-01 1.175125760E-01 1.208787040E-01 1.242762660E-01 - 1.277071540E-01 1.311727910E-01 1.346667710E-01 1.382205780E-01 1.418476400E-01 - 1.455317140E-01 1.492656920E-01 1.530433600E-01 1.568585340E-01 1.606825440E-01 - 1.645068530E-01 1.683359150E-01 1.721711310E-01 1.760122930E-01 1.798591610E-01 - 1.837121990E-01 1.875714360E-01 1.914369310E-01 1.953087900E-01 1.991871600E-01 - 2.030722500E-01 2.069641650E-01 2.108631430E-01 2.147693780E-01 2.186831090E-01 - 2.226046170E-01 2.265341880E-01 2.304721770E-01 2.344188840E-01 2.383746500E-01 - 2.423398940E-01 2.463150320E-01 2.503005270E-01 2.542968990E-01 2.583046850E-01 - 2.623244820E-01 2.663566770E-01 2.704021330E-01 2.744615380E-01 2.785356040E-01 - 2.826250200E-01 2.867305280E-01 2.908531430E-01 2.949936690E-01 2.991531790E-01 - 3.033327760E-01 3.075333830E-01 3.117561640E-01 3.160023390E-01 3.202730720E-01 - 3.245704170E-01 3.288954500E-01 3.332493900E-01 3.376342060E-01 2.168561220E-01 - 2.148460890E-01 2.128242400E-01 2.107907090E-01 2.087456430E-01 2.066891640E-01 - 2.046213600E-01 2.025422010E-01 2.004517910E-01 1.983501170E-01 1.962371170E-01 - 1.941128370E-01 1.919772480E-01 1.898302880E-01 1.876719300E-01 1.855020970E-01 - 1.833207460E-01 1.811278160E-01 1.789232490E-01 1.767069550E-01 1.744788590E-01 - 1.722388570E-01 1.699868890E-01 1.677228660E-01 1.654466840E-01 1.631582380E-01 - 1.608574540E-01 1.585442130E-01 1.562184690E-01 1.538799110E-01 1.515282690E-01 - 1.491633060E-01 1.467855130E-01 1.443986740E-01 1.420046540E-01 1.396052540E-01 - 1.372020990E-01 1.347956360E-01 1.323865210E-01 1.299753490E-01 1.275627610E-01 - 1.251493690E-01 1.227357980E-01 1.203227190E-01 1.179107500E-01 1.155005170E-01 - 1.130925860E-01 1.106875170E-01 1.082858820E-01 1.058881880E-01 1.034949570E-01 - 1.011066660E-01 9.872379900E-02 9.634684770E-02 9.397628900E-02 9.161257000E-02 - 8.925616740E-02 8.690755070E-02 8.456718180E-02 8.223553000E-02 7.991307230E-02 - 7.760026310E-02 7.529758660E-02 7.300551240E-02 7.072453200E-02 6.845515220E-02 - 6.619787960E-02 6.395325060E-02 6.172181290E-02 5.950412530E-02 5.730076130E-02 - 5.511230980E-02 5.293940380E-02 5.078268050E-02 4.864276570E-02 4.652033370E-02 - 4.441609230E-02 4.233071950E-02 4.026492690E-02 3.821946310E-02 3.619505090E-02 - 3.419245780E-02 3.221246600E-02 3.025585790E-02 2.832340640E-02 2.641594600E-02 - 2.453426830E-02 2.267919480E-02 2.085155990E-02 1.905219440E-02 1.728195510E-02 - 1.554163080E-02 1.383212210E-02 1.215426720E-02 1.050889960E-02 8.896853770E-03 - 7.318972140E-03 5.776103590E-03 4.269095140E-03 2.798780570E-03 1.365994570E-03 --2.844706430E-05-1.383737080E-03-2.699071540E-03-3.973659130E-03-5.206704140E-03 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1.846914550E-02 2.057185580E-02 2.272393740E-02 2.492471780E-02 2.717346140E-02 - 2.946945840E-02 3.181196750E-02 3.420023620E-02 3.663349150E-02 3.911095110E-02 - 4.163184020E-02 4.419534650E-02 4.680074380E-02 4.944721980E-02 5.213398860E-02 - 5.486029010E-02 5.762532730E-02 6.042831390E-02 6.326852740E-02 6.614518170E-02 - 6.905753910E-02 7.200491430E-02 7.498658450E-02 7.800184190E-02 8.105000850E-02 - 8.413043620E-02 8.724253620E-02 9.038568290E-02 9.355933960E-02 9.676288070E-02 - 9.999588880E-02 1.032581250E-01 1.065493450E-01 1.098693240E-01 1.132181440E-01 - 1.165963710E-01 1.200035660E-01 1.234417560E-01 1.269131600E-01 1.304159160E-01 - 1.339398180E-01 1.375314590E-01 1.411880550E-01 1.449035410E-01 1.486718060E-01 - 1.524867860E-01 1.563447560E-01 1.602082550E-01 1.640693840E-01 1.679358180E-01 - 1.718075280E-01 1.756845710E-01 1.795666960E-01 1.834539920E-01 1.873466370E-01 - 1.912447810E-01 1.951485280E-01 1.990579810E-01 2.029732910E-01 2.068945770E-01 - 2.108221650E-01 2.147562210E-01 2.186969070E-01 2.226445080E-01 2.265993650E-01 - 2.305617930E-01 2.345321030E-01 2.385105340E-01 2.424975480E-01 2.464935780E-01 - 2.504990400E-01 2.545143660E-01 2.585401540E-01 2.625768780E-01 2.666250170E-01 - 2.706852260E-01 2.747581600E-01 2.788444460E-01 2.829449770E-01 2.870601710E-01 - 2.911910120E-01 2.953384220E-01 2.995031770E-01 3.036861120E-01 3.078883890E-01 - 3.121110500E-01 3.163550500E-01 3.206216690E-01 3.249122200E-01 3.292278950E-01 - 3.335699440E-01 2.166637030E-01 2.146466820E-01 2.126168310E-01 2.105743740E-01 - 2.085196230E-01 2.064526530E-01 2.043735680E-01 2.022825480E-01 2.001795170E-01 - 1.980645810E-01 1.959377680E-01 1.937990640E-01 1.916484680E-01 1.894859370E-01 - 1.873114560E-01 1.851249640E-01 1.829264310E-01 1.807157990E-01 1.784929780E-01 - 1.762579080E-01 1.740105150E-01 1.717507090E-01 1.694784160E-01 1.671935470E-01 - 1.648959960E-01 1.625856610E-01 1.602624360E-01 1.579262320E-01 1.555770040E-01 - 1.532144840E-01 1.508382110E-01 1.484479760E-01 1.460457590E-01 1.436340960E-01 - 1.412154730E-01 1.387915910E-01 1.363633570E-01 1.339314880E-01 1.314966080E-01 - 1.290593450E-01 1.266203080E-01 1.241801460E-01 1.217395070E-01 1.192990320E-01 - 1.168593540E-01 1.144210770E-01 1.119847670E-01 1.095509980E-01 1.071202980E-01 - 1.046931970E-01 1.022701860E-01 9.985174240E-02 9.743836520E-02 9.503052380E-02 - 9.262868020E-02 9.023329620E-02 8.784484120E-02 8.546378460E-02 8.309058100E-02 - 8.072570710E-02 7.836962490E-02 7.602278140E-02 7.368565350E-02 7.135874780E-02 - 6.904255600E-02 6.673757730E-02 6.444431100E-02 6.216331570E-02 5.989515410E-02 - 5.764036250E-02 5.539955200E-02 5.317334830E-02 5.096237730E-02 4.876729470E-02 - 4.658873380E-02 4.442738740E-02 4.228395220E-02 4.015914720E-02 3.805371750E-02 - 3.596839310E-02 3.390395270E-02 3.186117490E-02 2.984084750E-02 2.784374920E-02 - 2.587073860E-02 2.392259050E-02 2.200015260E-02 2.010428530E-02 1.823583060E-02 - 1.639562660E-02 1.458452920E-02 1.280339710E-02 1.105310400E-02 9.334530680E-03 - 7.648536470E-03 5.995959970E-03 4.377668720E-03 2.794510220E-03 1.247355370E-03 --2.629252560E-04-1.735490280E-03-3.169517500E-03-4.564188890E-03-5.918685810E-03 --7.232165900E-03-8.503836580E-03-9.732907640E-03-1.091859300E-02-1.206012540E-02 --1.315675300E-02-1.420773660E-02-1.521234120E-02-1.616984610E-02-1.707956190E-02 --1.794080250E-02-1.875289340E-02-1.951519960E-02-2.022709320E-02-2.088794110E-02 --2.149714900E-02-2.205413020E-02-2.255835760E-02-2.300924810E-02-2.340631560E-02 --2.374907400E-02-2.403704450E-02-2.426974290E-02-2.444674630E-02-2.456764500E-02 --2.463205720E-02-2.463961770E-02-2.458998930E-02-2.448292080E-02-2.431797240E-02 --2.409492430E-02-2.381358480E-02-2.347376200E-02-2.307526580E-02-2.261790070E-02 --2.210148800E-02-2.152598090E-02-2.089129950E-02-2.019735240E-02-1.944413780E-02 --1.863167810E-02-1.775999930E-02-1.682914980E-02-1.583925260E-02-1.479044650E-02 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1.406245080E-01 1.443739380E-01 1.481780710E-01 1.520324200E-01 1.559287910E-01 - 1.598232090E-01 1.637216060E-01 1.676239670E-01 1.715303360E-01 1.754412200E-01 - 1.793561580E-01 1.832755950E-01 1.871994440E-01 1.911278520E-01 1.950609530E-01 - 1.989988680E-01 2.029417600E-01 2.068897930E-01 2.108430420E-01 2.148018030E-01 - 2.187663170E-01 2.227368500E-01 2.267136420E-01 2.306969310E-01 2.346869710E-01 - 2.386841620E-01 2.426889090E-01 2.467014940E-01 2.507224080E-01 2.547520400E-01 - 2.587907610E-01 2.628391680E-01 2.668976190E-01 2.709668280E-01 2.750473620E-01 - 2.791396080E-01 2.832441630E-01 2.873621580E-01 2.914939220E-01 2.956401410E-01 - 2.998016180E-01 3.039790390E-01 3.081737160E-01 3.123863940E-01 3.166175780E-01 - 3.208684030E-01 3.251399100E-01 3.294332030E-01 2.164753970E-01 2.144499420E-01 - 2.124111350E-01 2.103591110E-01 2.082939590E-01 2.062159480E-01 2.041253150E-01 - 2.020220460E-01 1.999062750E-01 1.977780460E-01 1.956373900E-01 1.934843210E-01 - 1.913187950E-01 1.891408560E-01 1.869504450E-01 1.847475320E-01 1.825320720E-01 - 1.803039760E-01 1.780631990E-01 1.758096810E-01 1.735433490E-01 1.712640970E-01 - 1.689718370E-01 1.666664930E-01 1.643479620E-01 1.620161240E-01 1.596708450E-01 - 1.573120500E-01 1.549396370E-01 1.525536480E-01 1.501531300E-01 1.477385460E-01 - 1.453122650E-01 1.428766250E-01 1.404339970E-01 1.379859600E-01 1.355331390E-01 - 1.330763400E-01 1.306161730E-01 1.281532790E-01 1.256883000E-01 1.232218820E-01 - 1.207546670E-01 1.182873030E-01 1.158204080E-01 1.133545860E-01 1.108903960E-01 - 1.084283960E-01 1.059691240E-01 1.035130840E-01 1.010607700E-01 9.861265870E-02 - 9.616923330E-02 9.373096380E-02 9.129829700E-02 8.887171000E-02 8.645166460E-02 - 8.403861520E-02 8.163303140E-02 7.923536000E-02 7.684607060E-02 7.446564730E-02 - 7.209452990E-02 6.973321740E-02 6.738223140E-02 6.504206360E-02 6.271322070E-02 - 6.039631370E-02 5.809182670E-02 5.580037460E-02 5.352257940E-02 5.125908180E-02 - 4.901050780E-02 4.677748680E-02 4.456070070E-02 4.236087580E-02 4.017872360E-02 - 3.801495210E-02 3.587033970E-02 3.374565020E-02 3.164166210E-02 2.955917640E-02 - 2.749899030E-02 2.546191400E-02 2.344878020E-02 2.146045680E-02 1.949778940E-02 - 1.756164060E-02 1.565286330E-02 1.377231720E-02 1.192090100E-02 1.009948370E-02 - 8.308949880E-03 6.550186780E-03 4.824035340E-03 3.131448060E-03 1.473266860E-03 --1.496373590E-04-1.736394130E-03-3.286133050E-03-4.797982980E-03-6.271088960E-03 --7.704618850E-03-9.097727950E-03-1.044958830E-02-1.175938080E-02-1.302630270E-02 --1.424955480E-02-1.542834940E-02-1.656192540E-02-1.764952020E-02-1.869039800E-02 --1.968382490E-02-2.062910800E-02-2.152550780E-02-2.237234820E-02-2.316899970E-02 --2.391482700E-02-2.460920250E-02-2.525149290E-02-2.584105730E-02-2.637740220E-02 --2.685995400E-02-2.728817050E-02-2.766155820E-02-2.797963280E-02-2.824191190E-02 --2.844794090E-02-2.859730460E-02-2.868961730E-02-2.872450280E-02-2.870159600E-02 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7.856335490E-02 8.173711600E-02 8.494137970E-02 8.817571400E-02 9.143915770E-02 - 9.473117440E-02 9.805146600E-02 1.013997570E-01 1.047757490E-01 1.081791520E-01 - 1.116096750E-01 1.150683760E-01 1.185541670E-01 1.220687850E-01 1.256142260E-01 - 1.291922030E-01 1.328028740E-01 1.364530030E-01 1.401648670E-01 1.439425350E-01 - 1.477805970E-01 1.516745690E-01 1.556038110E-01 1.595327410E-01 1.634647700E-01 - 1.674005840E-01 1.713398840E-01 1.752823890E-01 1.792279630E-01 1.831770990E-01 - 1.871296910E-01 1.910858900E-01 1.950457990E-01 1.990094780E-01 2.029770020E-01 - 2.069487570E-01 2.109247600E-01 2.149051130E-01 2.188900710E-01 2.228799160E-01 - 2.268748730E-01 2.308752090E-01 2.348811780E-01 2.388930170E-01 2.429110850E-01 - 2.469357400E-01 2.509673240E-01 2.550061940E-01 2.590526640E-01 2.631072700E-01 - 2.671704290E-01 2.712425590E-01 2.753241060E-01 2.794156370E-01 2.835176290E-01 - 2.876306470E-01 2.917552890E-01 2.958920600E-01 3.000415270E-01 3.042046730E-01 - 3.083816470E-01 3.125734630E-01 3.167806570E-01 3.210037950E-01 3.252438600E-01 - 2.162940060E-01 2.142587900E-01 2.122097160E-01 2.101469780E-01 2.080707700E-01 - 2.059812100E-01 2.038785370E-01 2.017627660E-01 1.996340600E-01 1.974924210E-01 - 1.953378920E-01 1.931704280E-01 1.909900900E-01 1.887968480E-01 1.865906720E-01 - 1.843715160E-01 1.821393220E-01 1.798940300E-01 1.776356100E-01 1.753639580E-01 - 1.730789840E-01 1.707806290E-01 1.684687880E-01 1.661433580E-01 1.638042480E-01 - 1.614513250E-01 1.590844690E-01 1.567035620E-01 1.543085130E-01 1.518994570E-01 - 1.494751130E-01 1.470369700E-01 1.445871590E-01 1.421280500E-01 1.396619080E-01 - 1.371900290E-01 1.347131130E-01 1.322318760E-01 1.297469440E-01 1.272589420E-01 - 1.247685250E-01 1.222763510E-01 1.197830740E-01 1.172893200E-01 1.147957300E-01 - 1.123028620E-01 1.098113060E-01 1.073215980E-01 1.048342590E-01 1.023497800E-01 - 9.986865520E-02 9.739137440E-02 9.491838510E-02 9.245016430E-02 8.998717370E-02 - 8.752986790E-02 8.507870880E-02 8.263415100E-02 8.019664880E-02 7.776666430E-02 - 7.534465940E-02 7.293110340E-02 7.052646580E-02 6.813123080E-02 6.574590500E-02 - 6.337101010E-02 6.100708990E-02 5.865469200E-02 5.631439020E-02 5.398677660E-02 - 5.167248470E-02 4.937215890E-02 4.708643630E-02 4.481595750E-02 4.256148640E-02 - 4.032368960E-02 3.810330110E-02 3.590108830E-02 3.371783350E-02 3.155430780E-02 - 2.941128240E-02 2.728961780E-02 2.519010190E-02 2.311357860E-02 2.106091750E-02 - 1.903298680E-02 1.703064890E-02 1.505476800E-02 1.310622410E-02 1.118591710E-02 - 9.294739920E-03 7.433599790E-03 5.603396800E-03 3.805014070E-03 2.039361280E-03 - 3.073164840E-04-1.390184510E-03-3.052259100E-03-4.678036090E-03-6.266644690E-03 --7.817193870E-03-9.328814220E-03-1.080063730E-02-1.223179230E-02-1.362146440E-02 --1.496882360E-02-1.627303850E-02-1.753331160E-02-1.874883850E-02-1.991882920E-02 --2.104251460E-02-2.211914770E-02-2.314799280E-02-2.412831780E-02-2.505941880E-02 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2.551317770E-02 2.806040090E-02 3.065228090E-02 3.328794610E-02 3.596653040E-02 - 3.868715470E-02 4.144891350E-02 4.425094280E-02 4.709235580E-02 4.997228090E-02 - 5.288986120E-02 5.584423620E-02 5.883455280E-02 6.186000630E-02 6.491979210E-02 - 6.801312420E-02 7.113917920E-02 7.429720460E-02 7.748650760E-02 8.070639520E-02 - 8.395617460E-02 8.723520490E-02 9.054286780E-02 9.387846290E-02 9.724158050E-02 - 1.006319220E-01 1.040492130E-01 1.074931250E-01 1.109638140E-01 1.144610570E-01 - 1.179852410E-01 1.215377820E-01 1.251201330E-01 1.287339030E-01 1.323805900E-01 - 1.360672560E-01 1.398095640E-01 1.436104180E-01 1.474770900E-01 1.514117720E-01 - 1.553726490E-01 1.593348090E-01 1.632997100E-01 1.672671140E-01 1.712368280E-01 - 1.752085690E-01 1.791824400E-01 1.831588300E-01 1.871376190E-01 1.911188960E-01 - 1.951027210E-01 1.990891990E-01 2.030785380E-01 2.070708420E-01 2.110661860E-01 - 2.150647040E-01 2.190666500E-01 2.230722900E-01 2.270817010E-01 2.310951050E-01 - 2.351128160E-01 2.391349520E-01 2.431618270E-01 2.471937840E-01 2.512311040E-01 - 2.552740280E-01 2.593229120E-01 2.633780840E-01 2.674398420E-01 2.715087530E-01 - 2.755850850E-01 2.796689270E-01 2.837608160E-01 2.878614370E-01 2.919710870E-01 - 2.960900070E-01 3.002186720E-01 3.043576180E-01 3.085072040E-01 3.126679060E-01 - 3.168401120E-01 3.210241200E-01 2.161210780E-01 2.140747610E-01 2.120143180E-01 - 2.099398970E-01 2.078518120E-01 2.057501380E-01 2.036349480E-01 2.015064060E-01 - 1.993645280E-01 1.972092990E-01 1.950407770E-01 1.928589790E-01 1.906638740E-01 - 1.884554480E-01 1.862336550E-01 1.839984360E-01 1.817497460E-01 1.794875410E-01 - 1.772117470E-01 1.749222580E-01 1.726189850E-01 1.703018840E-01 1.679708210E-01 - 1.656257360E-01 1.632664800E-01 1.608929780E-01 1.585050970E-01 1.561027170E-01 - 1.536860760E-01 1.512533280E-01 1.488056630E-01 1.463447510E-01 1.438722160E-01 - 1.413896230E-01 1.389006080E-01 1.364055570E-01 1.339050530E-01 1.313998250E-01 - 1.288906340E-01 1.263780440E-01 1.238627140E-01 1.213453040E-01 1.188264940E-01 - 1.163069080E-01 1.137871370E-01 1.112677530E-01 1.087493520E-01 1.062324570E-01 - 1.037175580E-01 1.012051700E-01 9.869576990E-02 9.618981930E-02 9.368779510E-02 - 9.119015930E-02 8.869735150E-02 8.620983360E-02 8.372806760E-02 8.125250040E-02 - 7.878359410E-02 7.632180300E-02 7.386757430E-02 7.142139970E-02 6.898374110E-02 - 6.655506790E-02 6.413590160E-02 6.172680480E-02 5.932832140E-02 5.694098030E-02 - 5.456538130E-02 5.220213160E-02 4.985186830E-02 4.751523580E-02 4.519290480E-02 - 4.288555310E-02 4.059390720E-02 3.831867870E-02 3.606064250E-02 3.382057320E-02 - 3.159924220E-02 2.939743180E-02 2.721598560E-02 2.505570650E-02 2.291744760E-02 - 2.080209180E-02 1.871051270E-02 1.664357630E-02 1.460215540E-02 1.258715710E-02 - 1.059948370E-02 8.640041570E-03 6.709749340E-03 4.809524400E-03 2.940273380E-03 - 1.102914100E-03-7.016418970E-04-2.472473540E-03-4.208664880E-03-5.909285970E-03 --7.573458830E-03-9.200281460E-03-1.078886730E-02-1.233834490E-02-1.384784190E-02 --1.531647890E-02-1.674337130E-02-1.812767050E-02-1.946857570E-02-2.076526170E-02 --2.201692570E-02-2.322276120E-02-2.438197280E-02-2.549379690E-02-2.655749580E-02 --2.757233380E-02-2.853757520E-02-2.945252880E-02-3.031649070E-02-3.112880140E-02 --3.188881280E-02-3.259588780E-02-3.324941170E-02-3.384879230E-02-3.439345580E-02 --3.488283980E-02-3.531641140E-02-3.569367160E-02-3.601412480E-02-3.627729790E-02 --3.648273650E-02-3.663002700E-02-3.671876710E-02-3.674858060E-02-3.671908750E-02 --3.662998230E-02-3.648098560E-02-3.627181800E-02-3.600219260E-02-3.567189720E-02 --3.528073060E-02-3.482852880E-02-3.431514280E-02-3.374045340E-02-3.310438250E-02 --3.240684420E-02-3.164782750E-02-3.082737510E-02-2.994551510E-02-2.900226230E-02 --2.799767070E-02-2.693192850E-02-2.580515110E-02-2.461756950E-02-2.336940730E-02 --2.206089160E-02-2.069227400E-02-1.926390270E-02-1.777611490E-02-1.622930730E-02 --1.462389720E-02-1.296031010E-02-1.123902480E-02-9.460539560E-03-7.625422910E-03 --5.734255070E-03-3.787616270E-03-1.786099630E-03 2.695657600E-04 2.378724050E-03 - 4.540642260E-03 6.754585540E-03 9.019811640E-03 1.133551080E-02 1.370087920E-02 - 1.611509170E-02 1.857730750E-02 2.108663880E-02 2.364221770E-02 2.624313910E-02 - 2.888853290E-02 3.157749030E-02 3.430910040E-02 3.708243740E-02 3.989657390E-02 - 4.275061560E-02 4.564367610E-02 4.857483130E-02 5.154315010E-02 5.454780530E-02 - 5.758788810E-02 6.066256760E-02 6.377103180E-02 6.691242010E-02 7.008592780E-02 - 7.329083230E-02 7.652635130E-02 7.979179170E-02 8.308642360E-02 8.640957620E-02 - 8.976064620E-02 9.313905980E-02 9.654430300E-02 9.997591380E-02 1.034336540E-01 - 1.069173660E-01 1.104269700E-01 1.139617340E-01 1.175230740E-01 1.211123990E-01 - 1.247311010E-01 1.283796880E-01 1.320602890E-01 1.357783230E-01 1.395501940E-01 - 1.433833690E-01 1.472840610E-01 1.512447000E-01 1.552383450E-01 1.592324970E-01 - 1.632279600E-01 1.672245120E-01 1.712219420E-01 1.752205340E-01 1.792203340E-01 - 1.832212810E-01 1.872234790E-01 1.912270040E-01 1.952319150E-01 1.992382710E-01 - 2.032461760E-01 2.072557210E-01 2.112669940E-01 2.152802350E-01 2.192955320E-01 - 2.233130340E-01 2.273328900E-01 2.313552350E-01 2.353803810E-01 2.394084190E-01 - 2.434395850E-01 2.474740000E-01 2.515119610E-01 2.555537520E-01 2.595995070E-01 - 2.636494930E-01 2.677039800E-01 2.717632950E-01 2.758274670E-01 2.798968260E-01 - 2.839716670E-01 2.880523500E-01 2.921389040E-01 2.962316270E-01 3.003307580E-01 - 3.044362960E-01 3.085486590E-01 3.126681450E-01 3.167942460E-01 2.159568070E-01 - 2.138979580E-01 2.118251770E-01 2.097384480E-01 2.076378460E-01 2.055236250E-01 - 2.033956650E-01 2.012540100E-01 1.990987960E-01 1.969299610E-01 1.947474780E-01 - 1.925513600E-01 1.903415920E-01 1.881181000E-01 1.858808400E-01 1.836297810E-01 - 1.813648490E-01 1.790859700E-01 1.767930690E-01 1.744860710E-01 1.721648570E-01 - 1.698293690E-01 1.674795000E-01 1.651151330E-01 1.627361030E-01 1.603423060E-01 - 1.579336520E-01 1.555108730E-01 1.530718210E-01 1.506166910E-01 1.481467780E-01 - 1.456633660E-01 1.431678240E-01 1.406636390E-01 1.381522270E-01 1.356343180E-01 - 1.331106420E-01 1.305819150E-01 1.280488670E-01 1.255122420E-01 1.229725930E-01 - 1.204305070E-01 1.178867150E-01 1.153418200E-01 1.127964030E-01 1.102510620E-01 - 1.077063750E-01 1.051628290E-01 1.026209290E-01 1.000811680E-01 9.754402190E-02 - 9.500996020E-02 9.247943760E-02 8.995291590E-02 8.743083480E-02 8.491365610E-02 - 8.240182700E-02 7.989580180E-02 7.739603520E-02 7.490296660E-02 7.241706550E-02 - 6.993879380E-02 6.746863570E-02 6.500708310E-02 6.255466490E-02 6.011191380E-02 - 5.767939610E-02 5.525765940E-02 5.284732580E-02 5.044899510E-02 4.806331920E-02 - 4.569097240E-02 4.333263640E-02 4.098900040E-02 3.866079080E-02 3.634876390E-02 - 3.405369820E-02 3.177636860E-02 2.951756680E-02 2.727812710E-02 2.505885060E-02 - 2.286061090E-02 2.068428880E-02 1.853076930E-02 1.640093140E-02 1.429564410E-02 - 1.221580520E-02 1.016236280E-02 8.136235180E-03 6.138346160E-03 4.169621040E-03 - 2.230978800E-03 3.233682070E-04-1.552282020E-03-3.395032370E-03-5.203952080E-03 --6.978113670E-03-8.716645650E-03-1.041855480E-02-1.208291200E-02-1.370886060E-02 --1.529551480E-02-1.684198710E-02-1.834739000E-02-1.981083860E-02-2.123144640E-02 --2.260840500E-02-2.394087050E-02-2.522802170E-02-2.646905930E-02-2.766317690E-02 --2.880961450E-02-2.990757300E-02-3.095632230E-02-3.195514530E-02-3.290332110E-02 --3.380013260E-02-3.464490180E-02-3.543698420E-02-3.617572780E-02-3.686050700E-02 --3.749072180E-02-3.806576880E-02-3.858505930E-02-3.904812410E-02-3.945438190E-02 --3.980334480E-02-4.009452830E-02-4.032747820E-02-4.050176220E-02-4.061696310E-02 --4.067270460E-02-4.066860300E-02-4.060431940E-02-4.047954830E-02-4.029400650E-02 --4.004741460E-02-3.973953800E-02-3.937017170E-02-3.893914070E-02-3.844627740E-02 --3.789145870E-02-3.727461770E-02-3.659556810E-02-3.585435080E-02-3.505098450E-02 --3.418548780E-02-3.325788300E-02-3.226818890E-02-3.121661390E-02-3.010323080E-02 --2.892825380E-02-2.769190820E-02-2.639442500E-02-2.503602770E-02-2.361705710E-02 --2.213785800E-02-2.059879530E-02-1.900029000E-02-1.734276670E-02-1.562668940E-02 --1.385257110E-02-1.202095390E-02-1.013241800E-02-8.187550120E-03-6.186964460E-03 --4.131333900E-03-2.021380230E-03 1.421733900E-04 2.358603990E-03 4.627169580E-03 - 6.947018210E-03 9.317336600E-03 1.173730940E-02 1.420604720E-02 1.672266050E-02 - 1.928626190E-02 2.189595810E-02 2.455078620E-02 2.724984850E-02 2.999217990E-02 - 3.277684380E-02 3.560287880E-02 3.846933690E-02 4.137530550E-02 4.431985320E-02 - 4.730202260E-02 5.032086000E-02 5.337546020E-02 5.646498130E-02 5.958850680E-02 - 6.274518370E-02 6.593415140E-02 6.915461270E-02 7.240578530E-02 7.568688690E-02 - 7.899715750E-02 8.233591910E-02 8.570246400E-02 8.909616620E-02 9.251649680E-02 - 9.596287460E-02 9.943477060E-02 1.029319170E-01 1.064548190E-01 1.100014900E-01 - 1.135732160E-01 1.171711830E-01 1.207959280E-01 1.244480390E-01 1.281290800E-01 - 1.318421660E-01 1.355897780E-01 1.393906920E-01 1.432581250E-01 1.471911370E-01 - 1.511799400E-01 1.552039530E-01 1.592272820E-01 1.632504760E-01 1.672735360E-01 - 1.712965370E-01 1.753194480E-01 1.793423000E-01 1.833650770E-01 1.873878540E-01 - 1.914106760E-01 1.954335120E-01 1.994565130E-01 2.034797220E-01 2.075032000E-01 - 2.115270200E-01 2.155513320E-01 2.195762250E-01 2.236017440E-01 2.276280370E-01 - 2.316551950E-01 2.356833220E-01 2.397126850E-01 2.437433600E-01 2.477754500E-01 - 2.518090610E-01 2.558443250E-01 2.598814670E-01 2.639204860E-01 2.679616210E-01 - 2.720050810E-01 2.760508060E-01 2.800988260E-01 2.841495280E-01 2.882027630E-01 - 2.922586500E-01 2.963171010E-01 3.003781440E-01 3.044416610E-01 3.085075910E-01 - 3.125756980E-01 2.157992870E-01 2.137276080E-01 2.116420570E-01 2.095426470E-01 - 2.074293940E-01 2.053022980E-01 2.031613890E-01 2.010066060E-01 1.988379960E-01 - 1.966555120E-01 1.944591100E-01 1.922487470E-01 1.900243910E-01 1.877860130E-01 - 1.855335090E-01 1.832668330E-01 1.809859130E-01 1.786906570E-01 1.763809770E-01 - 1.740567980E-01 1.717180010E-01 1.693644820E-01 1.669961810E-01 1.646129490E-01 - 1.622146520E-01 1.598011850E-01 1.573725940E-01 1.549285650E-01 1.524685770E-01 - 1.499920340E-01 1.475001280E-01 1.449941250E-01 1.424769010E-01 1.399512290E-01 - 1.374178980E-01 1.348776670E-01 1.323313420E-01 1.297796960E-01 1.272234920E-01 - 1.246633750E-01 1.220998620E-01 1.195336650E-01 1.169654430E-01 1.143958050E-01 - 1.118253320E-01 1.092546210E-01 1.066841930E-01 1.041145620E-01 1.015462200E-01 - 9.897965940E-02 9.641534090E-02 9.385372700E-02 9.129527210E-02 8.874043080E-02 - 8.618965000E-02 8.364337680E-02 8.110205830E-02 7.856614140E-02 7.603606580E-02 - 7.351228590E-02 7.099528610E-02 6.848552080E-02 6.598346680E-02 6.348960100E-02 - 6.100450830E-02 5.852870270E-02 5.606275050E-02 5.360724030E-02 5.116276440E-02 - 4.872997850E-02 4.630953070E-02 4.390211030E-02 4.150838780E-02 3.912910070E-02 - 3.676497940E-02 3.441680970E-02 3.208536650E-02 2.977143040E-02 2.747585250E-02 - 2.519943190E-02 2.294304220E-02 2.070757000E-02 1.849389820E-02 1.630290970E-02 - 1.413549580E-02 1.199256070E-02 9.875054470E-03 7.783901880E-03 5.720049610E-03 - 3.684435270E-03 1.678004980E-03-2.982972070E-04-2.243523720E-03-4.156715700E-03 --6.036927460E-03-7.883220910E-03-9.694647980E-03-1.147025260E-02-1.320913810E-02 --1.491035610E-02-1.657297280E-02-1.819608170E-02-1.977879930E-02-2.132023680E-02 --2.281950600E-02-2.427572570E-02-2.568803360E-02-2.705559510E-02-2.837757020E-02 --2.965314500E-02-3.088151290E-02-3.206188600E-02-3.319347650E-02-3.427553550E-02 --3.530732170E-02-3.628810870E-02-3.721717750E-02-3.809383880E-02-3.891741860E-02 --3.968726100E-02-4.040274020E-02-4.106326030E-02-4.166821020E-02-4.221697900E-02 --4.270903020E-02-4.314383860E-02-4.352088270E-02-4.383967070E-02-4.409974810E-02 --4.430063810E-02-4.444194590E-02-4.452326520E-02-4.454421620E-02-4.450443390E-02 --4.440361630E-02-4.424145820E-02-4.401767250E-02-4.373201360E-02-4.338425400E-02 --4.297421130E-02-4.250172150E-02-4.196663200E-02-4.136885330E-02-4.070825130E-02 --3.998478130E-02-3.919846940E-02-3.834933040E-02-3.743738310E-02-3.646267210E-02 --3.542528300E-02-3.432537240E-02-3.316311170E-02-3.193869810E-02-3.065236470E-02 --2.930436840E-02-2.789500170E-02-2.642459240E-02-2.489350550E-02-2.330215280E-02 --2.165096440E-02-1.994040240E-02-1.817093980E-02-1.634315590E-02-1.445760760E-02 --1.251485390E-02-1.051550540E-02-8.460285140E-03-6.349915170E-03-4.185114990E-03 --1.966605430E-03 3.048913500E-04 2.628517340E-03 5.003429950E-03 7.428768560E-03 - 9.903638620E-03 1.242715210E-02 1.499842200E-02 1.761649740E-02 2.028043940E-02 - 2.298926930E-02 2.574200180E-02 2.853767950E-02 3.137537840E-02 3.425401080E-02 - 3.717264160E-02 4.013031350E-02 4.312606160E-02 4.615890980E-02 4.922787100E-02 - 5.233201380E-02 5.547048150E-02 5.864235760E-02 6.184668840E-02 6.508263950E-02 - 6.834937630E-02 7.164611670E-02 7.497201860E-02 7.832637430E-02 8.170837160E-02 - 8.511734010E-02 8.855271340E-02 9.201391040E-02 9.550035740E-02 9.901148830E-02 - 1.025470570E-01 1.061067360E-01 1.096902790E-01 1.132982370E-01 1.169311400E-01 - 1.205893310E-01 1.242740600E-01 1.279872060E-01 1.317322700E-01 1.355099830E-01 - 1.393390600E-01 1.432381420E-01 1.472002570E-01 1.512170880E-01 1.552699510E-01 - 1.593198030E-01 1.633684190E-01 1.674155890E-01 1.714614180E-01 1.755060260E-01 - 1.795492620E-01 1.835909630E-01 1.876313690E-01 1.916704480E-01 1.957081560E-01 - 1.997445970E-01 2.037798020E-01 2.078137550E-01 2.118465300E-01 2.158782040E-01 - 2.199088190E-01 2.239384350E-01 2.279670240E-01 2.319948380E-01 2.360217270E-01 - 2.400478420E-01 2.440732720E-01 2.480980600E-01 2.521222830E-01 2.561458950E-01 - 2.601690290E-01 2.641916280E-01 2.682136890E-01 2.722352150E-01 2.762561140E-01 - 2.802765070E-01 2.842961850E-01 2.883150280E-01 2.923327390E-01 2.963492570E-01 - 3.003643750E-01 3.043775560E-01 3.083886500E-01 2.156477270E-01 2.135630550E-01 - 2.114646730E-01 2.093524930E-01 2.072264850E-01 2.050865140E-01 2.029326110E-01 - 2.007647450E-01 1.985827980E-01 1.963867250E-01 1.941765250E-01 1.919521090E-01 - 1.897133740E-01 1.874603030E-01 1.851928090E-01 1.829107850E-01 1.806141730E-01 - 1.783028540E-01 1.759767380E-01 1.736357360E-01 1.712797430E-01 1.689086260E-01 - 1.665222640E-01 1.641205850E-01 1.617034380E-01 1.592707340E-01 1.568223090E-01 - 1.543579100E-01 1.518772690E-01 1.493798050E-01 1.468663070E-01 1.443388160E-01 - 1.418009700E-01 1.392540040E-01 1.366990210E-01 1.341370490E-01 1.315687450E-01 - 1.289948820E-01 1.264161170E-01 1.238329930E-01 1.212462410E-01 1.186565090E-01 - 1.160644290E-01 1.134706290E-01 1.108756960E-01 1.082801670E-01 1.056846010E-01 - 1.030894820E-01 1.004952860E-01 9.790251400E-02 9.531161190E-02 9.272304180E-02 - 9.013725070E-02 8.755469320E-02 8.497580140E-02 8.240103720E-02 7.983084020E-02 - 7.726562770E-02 7.470585410E-02 7.215198870E-02 6.960449370E-02 6.706383080E-02 - 6.453046950E-02 6.200495360E-02 5.948779730E-02 5.697957430E-02 5.448084320E-02 - 5.199218170E-02 4.951423780E-02 4.704766720E-02 4.459312190E-02 4.215129090E-02 - 3.972288220E-02 3.730863330E-02 3.490930800E-02 3.252568470E-02 3.015856630E-02 - 2.780876680E-02 2.547712440E-02 2.316448460E-02 2.087173240E-02 1.859976540E-02 - 1.634947580E-02 1.412175970E-02 1.191750450E-02 9.737722580E-03 7.583318740E-03 - 5.455242000E-03 3.354443000E-03 1.281884380E-03-7.614725620E-04-2.774654420E-03 --4.756695590E-03-6.706630810E-03-8.623505940E-03-1.050636540E-02-1.235426220E-02 --1.416622660E-02-1.594129020E-02-1.767853650E-02-1.937702110E-02-2.103582960E-02 --2.265404540E-02-2.423076890E-02-2.576511350E-02-2.725617770E-02-2.870309910E-02 --3.010502460E-02-3.146110100E-02-3.277049960E-02-3.403241560E-02-3.524602950E-02 --3.641055520E-02-3.752524780E-02-3.858935090E-02-3.960211580E-02-4.056281600E-02 --4.147074740E-02-4.232526200E-02-4.312563320E-02-4.387125000E-02-4.456150900E-02 --4.519579190E-02-4.577348380E-02-4.629402980E-02-4.675689340E-02-4.716155680E-02 --4.750750590E-02-4.779426010E-02-4.802135010E-02-4.818836230E-02-4.829489440E-02 --4.834054040E-02-4.832493510E-02-4.824774340E-02-4.810865970E-02-4.790740460E-02 --4.764370990E-02-4.731733720E-02-4.692807790E-02-4.647576060E-02-4.596023630E-02 --4.538138580E-02-4.473911970E-02-4.403332250E-02-4.326399420E-02-4.243114590E-02 --4.153479640E-02-4.057501630E-02-3.955190260E-02-3.846555200E-02-3.731606160E-02 --3.610369940E-02-3.482865540E-02-3.349118310E-02-3.209158410E-02-3.063017130E-02 --2.910728940E-02-2.752332390E-02-2.587871070E-02-2.417392660E-02-2.240944090E-02 --2.058577350E-02-1.870357060E-02-1.676327360E-02-1.476554670E-02-1.271111430E-02 --1.060070380E-02-8.435035120E-03-6.214830560E-03-3.940811380E-03-1.613834520E-03 - 7.652236380E-04 3.195500000E-03 5.676113070E-03 8.206139320E-03 1.078465390E-02 - 1.341070420E-02 1.608332250E-02 1.880152340E-02 2.156431040E-02 2.437067400E-02 - 2.721960660E-02 3.011009840E-02 3.304112700E-02 3.601166610E-02 3.902070970E-02 - 4.206732660E-02 4.515040670E-02 4.826901110E-02 5.142220110E-02 5.460903050E-02 - 5.782854930E-02 6.107981130E-02 6.436198200E-02 6.767424200E-02 7.101570810E-02 - 7.438556850E-02 7.778302580E-02 8.120725300E-02 8.465763930E-02 8.813364060E-02 - 9.163463120E-02 9.515998510E-02 9.870905430E-02 1.022816300E-01 1.058772880E-01 - 1.094961390E-01 1.131384600E-01 1.168048080E-01 1.204956770E-01 1.242123470E-01 - 1.279563610E-01 1.317321210E-01 1.355411110E-01 1.393951030E-01 1.433214400E-01 - 1.473131920E-01 1.513622850E-01 1.554365460E-01 1.595118940E-01 1.635838000E-01 - 1.676528900E-01 1.717190590E-01 1.757821740E-01 1.798424420E-01 1.839000880E-01 - 1.879550520E-01 1.920073180E-01 1.960567530E-01 2.001034020E-01 2.041471600E-01 - 2.081881170E-01 2.122262720E-01 2.162616100E-01 2.202941780E-01 2.243238990E-01 - 2.283508030E-01 2.323749510E-01 2.363962680E-01 2.404148280E-01 2.444304530E-01 - 2.484432610E-01 2.524531480E-01 2.564600710E-01 2.604638930E-01 2.644645570E-01 - 2.684619720E-01 2.724559310E-01 2.764462230E-01 2.804326420E-01 2.844150360E-01 - 2.883929610E-01 2.923660870E-01 2.963339980E-01 3.002961280E-01 3.042519090E-01 - 2.155008020E-01 2.134035080E-01 2.112926100E-01 2.091678530E-01 2.070291790E-01 - 2.048765120E-01 2.027097940E-01 2.005289050E-01 1.983338000E-01 1.961243900E-01 - 1.939005850E-01 1.916623120E-01 1.894094790E-01 1.871420150E-01 1.848597970E-01 - 1.825627540E-01 1.802507790E-01 1.779237390E-01 1.755815740E-01 1.732241510E-01 - 1.708513350E-01 1.684630360E-01 1.660591070E-01 1.636392920E-01 1.612037570E-01 - 1.587522630E-01 1.562845710E-01 1.538003980E-01 1.512994770E-01 1.487815380E-01 - 1.462468650E-01 1.436993180E-01 1.411412210E-01 1.385736170E-01 1.359975930E-01 - 1.334142240E-01 1.308245660E-01 1.282292160E-01 1.256282630E-01 1.230227800E-01 - 1.204133700E-01 1.178006830E-01 1.151853500E-01 1.125680130E-01 1.099492240E-01 - 1.073294880E-01 1.047093870E-01 1.020893980E-01 9.946996720E-02 9.685157980E-02 - 9.423470500E-02 9.161980450E-02 8.900731060E-02 8.639765530E-02 8.379130070E-02 - 8.118866380E-02 7.859019190E-02 7.599633190E-02 7.340751590E-02 7.082419840E-02 - 6.824684890E-02 6.567592920E-02 6.311194600E-02 6.055542080E-02 5.800689010E-02 - 5.546693880E-02 5.293608460E-02 5.041497950E-02 4.790427540E-02 4.540462790E-02 - 4.291669650E-02 4.044115540E-02 3.797880560E-02 3.553032130E-02 3.309652210E-02 - 3.067821080E-02 2.827620320E-02 2.589131330E-02 2.352438870E-02 2.117632140E-02 - 1.884799640E-02 1.654031310E-02 1.425418820E-02 1.199053790E-02 9.750324300E-03 - 7.534496950E-03 5.344009490E-03 3.179831200E-03 1.042922260E-03-1.065744790E-03 --3.145184830E-03-5.194403230E-03-7.212453060E-03-9.198320100E-03-1.115102510E-02 --1.306961570E-02-1.495312340E-02-1.680057680E-02-1.861100830E-02-2.038345110E-02 --2.211698700E-02-2.381067160E-02-2.546358670E-02-2.707480640E-02-2.864342370E-02 --3.016855010E-02-3.164929150E-02-3.308479860E-02-3.447421640E-02-3.581669550E-02 --3.711141650E-02-3.835755210E-02-3.955429790E-02-4.070090500E-02-4.179661720E-02 --4.284068940E-02-4.383236910E-02-4.477090760E-02-4.565567900E-02-4.648597170E-02 --4.726114120E-02-4.798056190E-02-4.864361140E-02-4.924965650E-02-4.979816450E-02 --5.028856170E-02-5.072032290E-02-5.109293390E-02-5.140589550E-02-5.165874960E-02 --5.185103420E-02-5.198234320E-02-5.205229300E-02-5.206048490E-02-5.200657990E-02 --5.189024660E-02-5.171120170E-02-5.146918070E-02-5.116391550E-02-5.079520490E-02 --5.036284400E-02-4.986668010E-02-4.930658640E-02-4.868245500E-02-4.799424110E-02 --4.724184050E-02-4.642520100E-02-4.554438590E-02-4.459948470E-02-4.359059040E-02 --4.251780360E-02-4.138121010E-02-4.018092900E-02-3.891727700E-02-3.759045900E-02 --3.620077300E-02-3.474852070E-02-3.323402630E-02-3.165768460E-02-3.001989800E-02 --2.832113770E-02-2.656190280E-02-2.474269830E-02-2.286405860E-02-2.092657610E-02 --1.893087480E-02-1.687764380E-02-1.476759280E-02-1.260144640E-02-1.037993190E-02 --8.103791620E-03-5.773921500E-03-3.391157370E-03-9.563858620E-04 1.529506410E-03 - 4.065611870E-03 6.650950290E-03 9.284559640E-03 1.196543310E-02 1.469256820E-02 - 1.746495810E-02 2.028159240E-02 2.314138600E-02 2.604330700E-02 2.898632740E-02 - 3.196940940E-02 3.499146550E-02 3.805145620E-02 4.114837570E-02 4.428118090E-02 - 4.744885490E-02 5.065041410E-02 5.388492720E-02 5.715132130E-02 6.044874710E-02 - 6.377631430E-02 6.713312120E-02 7.051828500E-02 7.393111290E-02 7.737060640E-02 - 8.083605020E-02 8.432679620E-02 8.784219620E-02 9.138160940E-02 9.494439510E-02 - 9.852990510E-02 1.021385340E-01 1.057688740E-01 1.094214020E-01 1.130965870E-01 - 1.167949210E-01 1.205168740E-01 1.242634430E-01 1.280365290E-01 1.318391560E-01 - 1.356784250E-01 1.395645140E-01 1.435137240E-01 1.475341470E-01 1.516100020E-01 - 1.557068080E-01 1.598082040E-01 1.638990490E-01 1.679856180E-01 1.720678960E-01 - 1.761475500E-01 1.802228690E-01 1.842938070E-01 1.883604080E-01 1.924227480E-01 - 1.964806620E-01 2.005341500E-01 2.045831080E-01 2.086275670E-01 2.126675250E-01 - 2.167028190E-01 2.207335230E-01 2.247595340E-01 2.287807460E-01 2.327971760E-01 - 2.368087320E-01 2.408152670E-01 2.448167200E-01 2.488129880E-01 2.528038320E-01 - 2.567892070E-01 2.607688900E-01 2.647426430E-01 2.687101960E-01 2.726713120E-01 - 2.766256030E-01 2.805727720E-01 2.845121620E-01 2.884435360E-01 2.923662660E-01 - 2.962794300E-01 3.001825810E-01 2.153580490E-01 2.132485510E-01 2.111254780E-01 - 2.089884280E-01 2.068374450E-01 2.046723960E-01 2.024931160E-01 2.002995310E-01 - 1.980915520E-01 1.958690880E-01 1.936319920E-01 1.913801730E-01 1.891135870E-01 - 1.868320410E-01 1.845354590E-01 1.822237520E-01 1.798967870E-01 1.775544580E-01 - 1.751966330E-01 1.728231910E-01 1.704339980E-01 1.680289510E-01 1.656078990E-01 - 1.631707250E-01 1.607172190E-01 1.582473520E-01 1.557608540E-01 1.532574450E-01 - 1.507368390E-01 1.481987980E-01 1.456443370E-01 1.430769410E-01 1.404988170E-01 - 1.379110960E-01 1.353148520E-01 1.327111720E-01 1.301006080E-01 1.274838600E-01 - 1.248615090E-01 1.222342920E-01 1.196028590E-01 1.169678570E-01 1.143299190E-01 - 1.116896420E-01 1.090476140E-01 1.064043340E-01 1.037603100E-01 1.011160610E-01 - 9.847203640E-02 9.582868960E-02 9.318649020E-02 9.054589270E-02 8.790735900E-02 - 8.527126160E-02 8.263807740E-02 8.000824600E-02 7.738219200E-02 7.476034020E-02 - 7.214314490E-02 6.953105330E-02 6.692454960E-02 6.432405860E-02 6.173013900E-02 - 5.914331230E-02 5.656411130E-02 5.399310960E-02 5.143089220E-02 4.887809600E-02 - 4.633538420E-02 4.380340500E-02 4.128282140E-02 3.877438980E-02 3.627882900E-02 - 3.379691760E-02 3.132946040E-02 2.887726950E-02 2.644116800E-02 2.402197380E-02 - 2.162060510E-02 1.923791880E-02 1.687484790E-02 1.453231370E-02 1.221123060E-02 - 9.912539270E-03 7.637198550E-03 5.386186760E-03 3.160484140E-03 9.610680280E-04 --1.211082800E-03-3.354971760E-03-5.469608590E-03-7.554002110E-03-9.607136250E-03 --1.162804760E-02-1.361571900E-02-1.556915980E-02-1.748740110E-02-1.936947180E-02 --2.121440320E-02-2.302120630E-02-2.478892730E-02-2.651662940E-02-2.820337190E-02 --2.984823470E-02-3.145029770E-02-3.300864990E-02-3.452240680E-02-3.599068520E-02 --3.741263230E-02-3.878739850E-02-4.011414200E-02-4.139204320E-02-4.262027520E-02 --4.379805550E-02-4.492463920E-02-4.599927370E-02-4.702121390E-02-4.798971860E-02 --4.890407990E-02-4.976360500E-02-5.056766790E-02-5.131562430E-02-5.200684070E-02 --5.264068770E-02-5.321656540E-02-5.373393370E-02-5.419225620E-02-5.459101130E-02 --5.492968480E-02-5.520780380E-02-5.542489140E-02-5.558053400E-02-5.567434800E-02 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5.330227320E-02 5.661476030E-02 5.995744090E-02 6.332941350E-02 6.672976910E-02 - 7.015763220E-02 7.361219080E-02 7.709260280E-02 8.059804140E-02 8.412782100E-02 - 8.768131580E-02 9.125787020E-02 9.485683590E-02 9.847775100E-02 1.021203400E-01 - 1.057838800E-01 1.094686310E-01 1.131750790E-01 1.169037300E-01 1.206550670E-01 - 1.244297920E-01 1.282314060E-01 1.320606020E-01 1.359276770E-01 1.398429420E-01 - 1.438170220E-01 1.478700190E-01 1.519633080E-01 1.560804550E-01 1.602050220E-01 - 1.643202900E-01 1.684141160E-01 1.725130080E-01 1.766059990E-01 1.806929110E-01 - 1.847740110E-01 1.888492550E-01 1.929184790E-01 1.969816240E-01 2.010386290E-01 - 2.050893900E-01 2.091339080E-01 2.131720630E-01 2.172037660E-01 2.212289120E-01 - 2.252473830E-01 2.292590590E-01 2.332638500E-01 2.372615490E-01 2.412520050E-01 - 2.452350410E-01 2.492104770E-01 2.531780300E-01 2.571374180E-01 2.610884010E-01 - 2.650305930E-01 2.689636350E-01 2.728871110E-01 2.768005730E-01 2.807033360E-01 - 2.845950720E-01 2.884749170E-01 2.923421260E-01 2.961958940E-01 2.152189170E-01 - 2.130978700E-01 2.109630260E-01 2.088142630E-01 2.066514050E-01 2.044743450E-01 - 2.022829500E-01 2.000770870E-01 1.978566350E-01 1.956214610E-01 1.933714450E-01 - 1.911064980E-01 1.888264720E-01 1.865312610E-01 1.842207310E-01 1.818947640E-01 - 1.795532410E-01 1.771960260E-01 1.748229860E-01 1.724340170E-01 1.700289400E-01 - 1.676076200E-01 1.651699390E-01 1.627157480E-01 1.602448670E-01 1.577573570E-01 - 1.552527990E-01 1.527306740E-01 1.501905770E-01 1.476333140E-01 1.450597350E-01 - 1.424729820E-01 1.398755160E-01 1.372683500E-01 1.346525700E-01 1.320288630E-01 - 1.293980030E-01 1.267606770E-01 1.241175090E-01 1.214691770E-01 1.188163460E-01 - 1.161596480E-01 1.134997230E-01 1.108372060E-01 1.081726030E-01 1.055064050E-01 - 1.028391200E-01 1.001712380E-01 9.750327470E-02 9.483564650E-02 9.216881540E-02 - 8.950321380E-02 8.683926610E-02 8.417742700E-02 8.151811360E-02 7.886176560E-02 - 7.620880750E-02 7.355967160E-02 7.091480490E-02 6.827464700E-02 6.563967470E-02 - 6.301034990E-02 6.038725000E-02 5.777088180E-02 5.516178160E-02 5.256050080E-02 - 4.996768010E-02 4.738397520E-02 4.481002690E-02 4.224649070E-02 3.969408570E-02 - 3.715353830E-02 3.462561960E-02 3.211113070E-02 2.961085550E-02 2.712561940E-02 - 2.465626040E-02 2.220365780E-02 1.976869260E-02 1.735228860E-02 1.495536510E-02 - 1.257883660E-02 1.022367830E-02 7.890842850E-03 5.581300710E-03 3.296030690E-03 - 1.036028730E-03-1.197708770E-03-3.404169580E-03-5.582349840E-03-7.731256540E-03 --9.849889200E-03-1.193722620E-02-1.399224440E-02-1.601394080E-02-1.800131980E-02 --1.995338870E-02-2.186916210E-02-2.374766210E-02-2.558790710E-02-2.738891910E-02 --2.914973910E-02-3.086942810E-02-3.254705670E-02-3.418169540E-02-3.577241670E-02 --3.731833400E-02-3.881854940E-02-4.027219120E-02-4.167841370E-02-4.303636770E-02 --4.434521500E-02-4.560415450E-02-4.681236300E-02-4.796906560E-02-4.907351730E-02 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--1.352278520E-03 1.294976330E-03 3.990936090E-03 6.734570020E-03 9.524802680E-03 - 1.236055880E-02 1.524075210E-02 1.816427890E-02 2.113000680E-02 2.413682270E-02 - 2.718364450E-02 3.026935270E-02 3.339274230E-02 3.655281290E-02 3.974847120E-02 - 4.297861460E-02 4.624214400E-02 4.953801630E-02 5.286522210E-02 5.622275170E-02 - 5.960964410E-02 6.302493810E-02 6.646773960E-02 6.993710990E-02 7.343221460E-02 - 7.695221900E-02 8.049634840E-02 8.406388760E-02 8.765404670E-02 9.126623720E-02 - 9.489990030E-02 9.855446960E-02 1.022296100E-01 1.059249570E-01 1.096404570E-01 - 1.133766320E-01 1.171340790E-01 1.209132600E-01 1.247158500E-01 1.285399650E-01 - 1.323954610E-01 1.362914590E-01 1.402321900E-01 1.442413780E-01 1.483129860E-01 - 1.524277930E-01 1.565641760E-01 1.607061480E-01 1.648337990E-01 1.689459980E-01 - 1.730560510E-01 1.771589670E-01 1.812546700E-01 1.853428930E-01 1.894235460E-01 - 1.934964950E-01 1.975616660E-01 2.016189690E-01 2.056682560E-01 2.097094060E-01 - 2.137422860E-01 2.177668060E-01 2.217828330E-01 2.257902030E-01 2.297885860E-01 - 2.337779700E-01 2.377580700E-01 2.417285740E-01 2.456893620E-01 2.496399880E-01 - 2.535802420E-01 2.575096190E-01 2.614278200E-01 2.653343680E-01 2.692288460E-01 - 2.731106880E-01 2.769789400E-01 2.808334230E-01 2.846734230E-01 2.884979840E-01 - 2.923060360E-01 2.150833900E-01 2.129513920E-01 2.108054910E-01 2.086455230E-01 - 2.064713390E-01 2.042827760E-01 2.020797130E-01 1.998620030E-01 1.976294960E-01 - 1.953820740E-01 1.931196000E-01 1.908419430E-01 1.885489370E-01 1.862405090E-01 - 1.839164790E-01 1.815767140E-01 1.792211090E-01 1.768494990E-01 1.744617370E-01 - 1.720577030E-01 1.696372180E-01 1.672001780E-01 1.647463890E-01 1.622757170E-01 - 1.597880130E-01 1.572831270E-01 1.547614930E-01 1.522206960E-01 1.496619880E-01 - 1.470862630E-01 1.444943850E-01 1.418887670E-01 1.392726600E-01 1.366467920E-01 - 1.340119240E-01 1.313688610E-01 1.287183760E-01 1.260611270E-01 1.233977530E-01 - 1.207289620E-01 1.180553880E-01 1.153776790E-01 1.126964460E-01 1.100123150E-01 - 1.073257850E-01 1.046373400E-01 1.019474710E-01 9.925667200E-02 9.656542540E-02 - 9.387423100E-02 9.118346120E-02 8.849353340E-02 8.580491690E-02 8.311802150E-02 - 8.043329420E-02 7.775114480E-02 7.507201280E-02 7.239632310E-02 6.972451510E-02 - 6.705705080E-02 6.439438460E-02 6.173702700E-02 5.908550320E-02 5.644035710E-02 - 5.380212520E-02 5.117140710E-02 4.854881020E-02 4.593499000E-02 4.333060610E-02 - 4.073636610E-02 3.815298530E-02 3.558120130E-02 3.302180770E-02 3.047559780E-02 - 2.794336900E-02 2.542597430E-02 2.292427980E-02 2.043916290E-02 1.797154550E-02 - 1.552234590E-02 1.309248710E-02 1.068292650E-02 8.294637310E-03 5.928582510E-03 - 3.585766770E-03 1.267193470E-03-1.026135990E-03-3.293225770E-03-5.533053540E-03 --7.744570730E-03-9.926785710E-03-1.207867450E-02-1.419921310E-02-1.628737900E-02 --1.834214660E-02-2.036250200E-02-2.234745400E-02-2.429598760E-02-2.620711180E-02 --2.807984310E-02-2.991319820E-02-3.170621400E-02-3.345792370E-02-3.516738860E-02 --3.683368490E-02-3.845588860E-02-4.003307220E-02-4.156434540E-02-4.304881770E-02 --4.448563610E-02-4.587395860E-02-4.721293230E-02-4.850173000E-02-4.973954330E-02 --5.092558640E-02-5.205909160E-02-5.313930290E-02-5.416547880E-02-5.513690410E-02 --5.605286360E-02-5.691266430E-02-5.771565810E-02-5.846121530E-02-5.914870280E-02 --5.977749820E-02-6.034702440E-02-6.085671480E-02-6.130603330E-02-6.169446930E-02 --6.202150880E-02-6.228668620E-02-6.248953570E-02-6.262965500E-02-6.270664930E-02 --6.272012740E-02-6.266971680E-02-6.255509700E-02-6.237595900E-02-6.213202700E-02 --6.182306260E-02-6.144888700E-02-6.100929900E-02-6.050410870E-02-5.993312220E-02 --5.929630250E-02-5.859356370E-02-5.782478300E-02-5.699001630E-02-5.608931560E-02 --5.512274060E-02-5.409034710E-02-5.299219120E-02-5.182834710E-02-5.059911310E-02 --4.930469020E-02-4.794526470E-02-4.652115330E-02-4.503270610E-02-4.348028450E-02 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1.407331820E-01 1.447713230E-01 1.488686200E-01 1.530051980E-01 1.571611170E-01 - 1.613164250E-01 1.654511840E-01 1.695786420E-01 1.736983510E-01 1.778089400E-01 - 1.819104400E-01 1.860027910E-01 1.900857540E-01 1.941592990E-01 1.982232930E-01 - 2.022776010E-01 2.063221040E-01 2.103566530E-01 2.143810240E-01 2.183950840E-01 - 2.223985940E-01 2.263913010E-01 2.303730700E-01 2.343435730E-01 2.383024990E-01 - 2.422495340E-01 2.461844240E-01 2.501066920E-01 2.540159820E-01 2.579118910E-01 - 2.617937330E-01 2.656611200E-01 2.695134580E-01 2.733500600E-01 2.771702410E-01 - 2.809732850E-01 2.847582400E-01 2.885240910E-01 2.149517240E-01 2.128094290E-01 - 2.106530960E-01 2.084825190E-01 2.062975470E-01 2.040980460E-01 2.018838520E-01 - 1.996548030E-01 1.974107770E-01 1.951515970E-01 1.928771440E-01 1.905872670E-01 - 1.882818040E-01 1.859606360E-01 1.836235970E-01 1.812705550E-01 1.789013590E-01 - 1.765158470E-01 1.741138850E-01 1.716953070E-01 1.692599800E-01 1.668077410E-01 - 1.643384100E-01 1.618518380E-01 1.593478770E-01 1.568263470E-01 1.542873230E-01 - 1.517294790E-01 1.491529350E-01 1.465589110E-01 1.439489280E-01 1.413257870E-01 - 1.386917230E-01 1.360476460E-01 1.333943610E-01 1.307326110E-01 1.280631570E-01 - 1.253866400E-01 1.227037530E-01 1.200151670E-01 1.173215280E-01 1.146234940E-01 - 1.119216310E-01 1.092165630E-01 1.065087770E-01 1.037987620E-01 1.010870340E-01 - 9.837404640E-02 9.566027670E-02 9.294618670E-02 9.023215620E-02 8.751863990E-02 - 8.480608460E-02 8.209489290E-02 7.938548920E-02 7.667831330E-02 7.397377490E-02 - 7.127229120E-02 6.857432430E-02 6.588032100E-02 6.319077310E-02 6.050616880E-02 - 5.782704060E-02 5.515393240E-02 5.248737340E-02 4.982806000E-02 4.717653240E-02 - 4.453345020E-02 4.189952840E-02 3.927548230E-02 3.666203100E-02 3.405991570E-02 - 3.146994860E-02 2.889292310E-02 2.632967200E-02 2.378105370E-02 2.124796620E-02 - 1.873130170E-02 1.623198760E-02 1.375094430E-02 1.128913090E-02 8.847506720E-03 - 6.427063140E-03 4.028798080E-03 1.653719230E-03-6.971655530E-04-3.022847930E-03 --5.322284070E-03-7.594442000E-03-9.838320310E-03-1.205285170E-02-1.423699780E-02 --1.638973320E-02-1.851003060E-02-2.059686740E-02-2.264920810E-02-2.466603740E-02 --2.664633840E-02-2.858910710E-02-3.049335070E-02-3.235808010E-02-3.418233250E-02 --3.596511480E-02-3.770547730E-02-3.940249230E-02-4.105523230E-02-4.266276960E-02 --4.422418030E-02-4.573860020E-02-4.720513520E-02-4.862293230E-02-4.999115320E-02 --5.130897460E-02-5.257557330E-02-5.379012970E-02-5.495187640E-02-5.606004970E-02 --5.711390450E-02-5.811272190E-02-5.905577910E-02-5.994235720E-02-6.077183410E-02 --6.154353170E-02-6.225681300E-02-6.291107090E-02-6.350570920E-02-6.404014680E-02 --6.451383980E-02-6.492627410E-02-6.527691330E-02-6.556530300E-02-6.579096620E-02 --6.595344840E-02-6.605236980E-02-6.608735020E-02-6.605800990E-02-6.596400590E-02 --6.580504030E-02-6.558081510E-02-6.529106940E-02-6.493558730E-02-6.451417510E-02 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7.350190730E-02 7.709703590E-02 8.071424070E-02 8.435276150E-02 8.801184590E-02 - 9.169084580E-02 9.538894890E-02 9.910584990E-02 1.028413620E-01 1.065953080E-01 - 1.103675510E-01 1.141578700E-01 1.179685070E-01 1.217969280E-01 1.256465610E-01 - 1.295225920E-01 1.334286330E-01 1.373677400E-01 1.413577050E-01 1.454243360E-01 - 1.495474580E-01 1.537054630E-01 1.578767150E-01 1.620395930E-01 1.661804320E-01 - 1.703178880E-01 1.744438710E-01 1.785587370E-01 1.826628450E-01 1.867560740E-01 - 1.908382480E-01 1.949093190E-01 1.989690960E-01 2.030173990E-01 2.070540490E-01 - 2.110787780E-01 2.150914670E-01 2.190918770E-01 2.230797410E-01 2.270547600E-01 - 2.310166060E-01 2.349650110E-01 2.388996180E-01 2.428200240E-01 2.467258570E-01 - 2.506166100E-01 2.544918660E-01 2.583509980E-01 2.621935900E-01 2.660189270E-01 - 2.698263230E-01 2.736150920E-01 2.773844900E-01 2.811335030E-01 2.848612070E-01 - 2.148242740E-01 2.126723530E-01 2.105062160E-01 2.083256540E-01 2.061305200E-01 - 2.039206620E-01 2.016958890E-01 1.994560810E-01 1.972010730E-01 1.949306880E-01 - 1.926448050E-01 1.903432310E-01 1.880258470E-01 1.856924740E-01 1.833429630E-01 - 1.809771660E-01 1.785949170E-01 1.761960690E-01 1.737804560E-01 1.713479010E-01 - 1.688982700E-01 1.664313670E-01 1.639470910E-01 1.614452150E-01 1.589255630E-01 - 1.563879100E-01 1.538321520E-01 1.512579470E-01 1.486641910E-01 1.460526140E-01 - 1.434255690E-01 1.407854260E-01 1.381340180E-01 1.354723870E-01 1.328013240E-01 - 1.301215590E-01 1.274337770E-01 1.247386780E-01 1.220369640E-01 1.193292810E-01 - 1.166162710E-01 1.138985980E-01 1.111768040E-01 1.084515010E-01 1.057231950E-01 - 1.029923560E-01 1.002594610E-01 9.752499310E-02 9.478943050E-02 9.205317500E-02 - 8.931665870E-02 8.658031370E-02 8.384457230E-02 8.110985160E-02 7.837656140E-02 - 7.564511900E-02 7.291595640E-02 7.018949840E-02 6.746617700E-02 6.474646930E-02 - 6.203084810E-02 5.931982770E-02 5.661394070E-02 5.391372370E-02 5.121978000E-02 - 4.853270950E-02 4.585311930E-02 4.318168390E-02 4.051913690E-02 3.786621240E-02 - 3.522364420E-02 3.259214010E-02 2.997248810E-02 2.736562490E-02 2.477232370E-02 - 2.219347660E-02 1.962998880E-02 1.708276760E-02 1.455273110E-02 1.204085440E-02 - 9.548090400E-03 7.075433620E-03 4.623881540E-03 2.194441620E-03-2.118681150E-04 --2.594036750E-03-4.951021630E-03-7.281777910E-03-9.585254830E-03-1.186041720E-02 --1.410620940E-02-1.632158270E-02-1.850548570E-02-2.065688930E-02-2.277475970E-02 --2.485804260E-02-2.690572480E-02-2.891676870E-02-3.089016300E-02-3.282491120E-02 --3.472001850E-02-3.657449410E-02-3.838736560E-02-4.015764970E-02-4.188441860E-02 --4.356673360E-02-4.520366710E-02-4.679428410E-02-4.833772030E-02-4.983307790E-02 --5.127945540E-02-5.267603320E-02-5.402198430E-02-5.531648920E-02-5.655872080E-02 --5.774786320E-02-5.888319020E-02-5.996392290E-02-6.098933890E-02-6.195872650E-02 --6.287135930E-02-6.372654440E-02-6.452364470E-02-6.526201960E-02-6.594103570E-02 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1.310339850E-02 1.618374880E-02 1.930442270E-02 2.246422510E-02 2.566192860E-02 - 2.889630570E-02 3.216618300E-02 3.547033670E-02 3.880761560E-02 4.217684270E-02 - 4.557687040E-02 4.900657010E-02 5.246486890E-02 5.595070500E-02 5.946301300E-02 - 6.300085040E-02 6.656317410E-02 7.014904920E-02 7.375762610E-02 7.738802580E-02 - 8.103941380E-02 8.471108230E-02 8.840239050E-02 9.211217610E-02 9.584012630E-02 - 9.958598020E-02 1.033494700E-01 1.071303410E-01 1.109283190E-01 1.147445590E-01 - 1.185766160E-01 1.224274780E-01 1.263005440E-01 1.301996860E-01 1.341285410E-01 - 1.380907150E-01 1.421075020E-01 1.462001950E-01 1.503473970E-01 1.545271280E-01 - 1.587105240E-01 1.628746690E-01 1.670267880E-01 1.711669710E-01 1.752950850E-01 - 1.794109790E-01 1.835141480E-01 1.876053960E-01 1.916839480E-01 1.957496260E-01 - 1.998022200E-01 2.038415670E-01 2.078673990E-01 2.118794770E-01 2.158775480E-01 - 2.198613730E-01 2.238306400E-01 2.277849610E-01 2.317240390E-01 2.356475140E-01 - 2.395549420E-01 2.434459180E-01 2.473199220E-01 2.511765660E-01 2.550151350E-01 - 2.588351070E-01 2.626358570E-01 2.664167580E-01 2.701771260E-01 2.739158270E-01 - 2.776323260E-01 2.813256980E-01 2.147015630E-01 2.125406860E-01 2.103653550E-01 - 2.081754510E-01 2.059707640E-01 2.037511470E-01 2.015164350E-01 1.992664640E-01 - 1.970010550E-01 1.947200450E-01 1.924232840E-01 1.901106240E-01 1.877818550E-01 - 1.854368450E-01 1.830754430E-01 1.806974560E-01 1.783027350E-01 1.758911160E-01 - 1.734624210E-01 1.710164840E-01 1.685531590E-01 1.660722350E-01 1.635735330E-01 - 1.610569510E-01 1.585222930E-01 1.559694410E-01 1.533979330E-01 1.508072320E-01 - 1.481969650E-01 1.455688920E-01 1.429253670E-01 1.402687730E-01 1.376008240E-01 - 1.349223410E-01 1.322341710E-01 1.295370310E-01 1.268316360E-01 1.241186710E-01 - 1.213988140E-01 1.186727360E-01 1.159410700E-01 1.132044640E-01 1.104634630E-01 - 1.077186690E-01 1.049705590E-01 1.022196190E-01 9.946631640E-02 9.671113640E-02 - 9.395451100E-02 9.119687230E-02 8.843864500E-02 8.568025380E-02 8.292213080E-02 - 8.016466350E-02 7.740827650E-02 7.465339450E-02 7.190043480E-02 6.914980710E-02 - 6.640197340E-02 6.365741040E-02 6.091659890E-02 5.818003790E-02 5.544827510E-02 - 5.272186550E-02 5.000139030E-02 4.728749020E-02 4.458080980E-02 4.188200460E-02 - 3.919180110E-02 3.651092570E-02 3.384012730E-02 3.118019920E-02 2.853194440E-02 - 2.589622140E-02 2.327387030E-02 2.066581140E-02 1.807294970E-02 1.549619620E-02 - 1.293649520E-02 1.039481810E-02 7.872163320E-03 5.369528200E-03 2.887916750E-03 - 4.283394660E-04-2.008148000E-03-4.420514680E-03-6.807717960E-03-9.168701250E-03 --1.150240750E-02-1.380777920E-02-1.608375090E-02-1.832927200E-02-2.054328470E-02 --2.272473090E-02-2.487256190E-02-2.698572910E-02-2.906320060E-02-3.110393700E-02 --3.310691190E-02-3.507113080E-02-3.699557860E-02-3.887925670E-02-4.072118550E-02 --4.252038900E-02-4.427590970E-02-4.598681260E-02-4.765216260E-02-4.927103970E-02 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1.679805370E-01 1.721228960E-01 1.762519630E-01 1.803665910E-01 1.844670470E-01 - 1.885535870E-01 1.926257310E-01 1.966833170E-01 2.007260470E-01 2.047536670E-01 - 2.087659840E-01 2.127626690E-01 2.167434390E-01 2.207079980E-01 2.246560010E-01 - 2.285870610E-01 2.325007470E-01 2.363967450E-01 2.402745190E-01 2.441336510E-01 - 2.479735760E-01 2.517937120E-01 2.555935380E-01 2.593723540E-01 2.631294430E-01 - 2.668642100E-01 2.705757020E-01 2.742631730E-01 2.779258490E-01 2.145840970E-01 - 2.124149050E-01 2.102310960E-01 2.080324890E-01 2.058189060E-01 2.035901700E-01 - 2.013461290E-01 1.990865920E-01 1.968114080E-01 1.945203840E-01 1.922133710E-01 - 1.898901910E-01 1.875506640E-01 1.851946260E-01 1.828219150E-01 1.804323490E-01 - 1.780257670E-01 1.756019740E-01 1.731608060E-01 1.707021000E-01 1.682256610E-01 - 1.657313260E-01 1.632189010E-01 1.606884150E-01 1.581393630E-01 1.555715050E-01 - 1.529845890E-01 1.503784360E-01 1.477527170E-01 1.451088790E-01 1.424496770E-01 - 1.397773770E-01 1.370934400E-01 1.343987880E-01 1.316942130E-01 1.289804130E-01 - 1.262581050E-01 1.235279590E-01 1.207906830E-01 1.180469390E-01 1.152973470E-01 - 1.125425400E-01 1.097830830E-01 1.070195360E-01 1.042523680E-01 1.014820780E-01 - 9.870914370E-02 9.593401850E-02 9.315712000E-02 9.037888800E-02 8.759974690E-02 - 8.482011410E-02 8.204040680E-02 7.926102730E-02 7.648238540E-02 7.370489840E-02 - 7.092898340E-02 6.815506520E-02 6.538360570E-02 6.261507420E-02 5.984995890E-02 - 5.708875880E-02 5.433205140E-02 5.158035830E-02 4.883431640E-02 4.609456290E-02 - 4.336173830E-02 4.063651340E-02 3.791961820E-02 3.521178660E-02 3.251381590E-02 - 2.982650320E-02 2.715064770E-02 2.448710800E-02 2.183676700E-02 1.920054850E-02 - 1.657937090E-02 1.397413850E-02 1.138585430E-02 8.815480400E-03 6.264025350E-03 - 3.732498270E-03 1.221920710E-03-1.266669020E-03-3.732232380E-03-6.173702890E-03 --8.590018380E-03-1.098012370E-02-1.334295330E-02-1.567743530E-02-1.798249410E-02 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9.716895970E-02 1.009675710E-01 1.047813150E-01 1.086102580E-01 1.124547420E-01 - 1.163154390E-01 1.201909560E-01 1.240844280E-01 1.279995140E-01 1.319398430E-01 - 1.359089760E-01 1.399217690E-01 1.439993380E-01 1.481468080E-01 1.523358820E-01 - 1.565362070E-01 1.607217040E-01 1.648930910E-01 1.690500530E-01 1.731921580E-01 - 1.773187520E-01 1.814294310E-01 1.855245980E-01 1.896038950E-01 1.936670840E-01 - 1.977139260E-01 2.017441690E-01 2.057576030E-01 2.097538260E-01 2.137325850E-01 - 2.176935820E-01 2.216364590E-01 2.255608140E-01 2.294662740E-01 2.333523780E-01 - 2.372186930E-01 2.410647270E-01 2.448899150E-01 2.486937790E-01 2.524757090E-01 - 2.562350930E-01 2.599710520E-01 2.636831400E-01 2.673704920E-01 2.710323630E-01 - 2.746678290E-01 2.144724880E-01 2.122956660E-01 2.101040330E-01 2.078973950E-01 - 2.056755570E-01 2.034383710E-01 2.011856440E-01 1.989172100E-01 1.966328770E-01 - 1.943324800E-01 1.920158270E-01 1.896827670E-01 1.873331070E-01 1.849666680E-01 - 1.825832720E-01 1.801827550E-01 1.777649220E-01 1.753295960E-01 1.728766110E-01 - 1.704057600E-01 1.679168640E-01 1.654097290E-01 1.628842650E-01 1.603402350E-01 - 1.577769960E-01 1.551945510E-01 1.525932700E-01 1.499727370E-01 1.473326530E-01 - 1.446737800E-01 1.419996020E-01 1.393122970E-01 1.366131310E-01 1.339029970E-01 - 1.311827300E-01 1.284529720E-01 1.257144660E-01 1.229678910E-01 1.202139330E-01 - 1.174532470E-01 1.146864820E-01 1.119142320E-01 1.091370660E-01 1.063555110E-01 - 1.035700740E-01 1.007812320E-01 9.798944000E-02 9.519515190E-02 9.239879250E-02 - 8.960077910E-02 8.680154380E-02 8.400149640E-02 8.120105420E-02 7.840059700E-02 - 7.560054960E-02 7.280132920E-02 7.000336800E-02 6.720706820E-02 6.441289190E-02 - 6.162130460E-02 5.883280560E-02 5.604792010E-02 5.326718840E-02 5.049120260E-02 - 4.772058130E-02 4.495596510E-02 4.219798740E-02 3.944735600E-02 3.670477870E-02 - 3.397104890E-02 3.124695640E-02 2.853330040E-02 2.583087790E-02 2.314061860E-02 - 2.046337720E-02 1.780008340E-02 1.515167020E-02 1.251908760E-02 9.903322910E-03 - 7.305356210E-03 4.726220850E-03 2.166939670E-03-3.714657510E-04-2.887945390E-03 --5.381437020E-03-7.850865830E-03-1.029516100E-02-1.271325720E-02-1.510406470E-02 --1.746651160E-02-1.979950820E-02-2.210197410E-02-2.437284400E-02-2.661103570E-02 --2.881545570E-02-3.098507410E-02-3.311883660E-02-3.521569820E-02-3.727459910E-02 --3.929451110E-02-4.127442840E-02-4.321334140E-02-4.511025180E-02-4.696416110E-02 --4.877411200E-02-5.053913590E-02-5.225829040E-02-5.393064390E-02-5.555527280E-02 --5.713127930E-02-5.865776540E-02-6.013387070E-02-6.155873090E-02-6.293149290E-02 --6.425134090E-02-6.551744790E-02-6.672903900E-02-6.788533930E-02-6.898553670E-02 --7.002892350E-02-7.101479170E-02-7.194241880E-02-7.281112670E-02-7.362022250E-02 --7.436906550E-02-7.505704460E-02-7.568356390E-02-7.624801990E-02-7.674985380E-02 --7.718849930E-02-7.756345720E-02-7.787423580E-02-7.812038060E-02-7.830143720E-02 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3.244088960E-02 3.587948900E-02 3.934825210E-02 4.284599800E-02 4.637151210E-02 - 4.992363970E-02 5.350122600E-02 5.710316450E-02 6.072831530E-02 6.437569860E-02 - 6.804433470E-02 7.173324380E-02 7.544147220E-02 7.916824520E-02 8.291260150E-02 - 8.667364720E-02 9.045080840E-02 9.424356370E-02 9.805136170E-02 1.018736660E-01 - 1.057100740E-01 1.095606310E-01 1.134254860E-01 1.173054650E-01 1.212016640E-01 - 1.251151560E-01 1.290490780E-01 1.330055890E-01 1.369974020E-01 1.410380300E-01 - 1.451403650E-01 1.493129880E-01 1.535234600E-01 1.577250360E-01 1.619115170E-01 - 1.660827250E-01 1.702382560E-01 1.743773220E-01 1.784989540E-01 1.826031950E-01 - 1.866902560E-01 1.907597930E-01 1.948115530E-01 1.988452520E-01 2.028606530E-01 - 2.068574580E-01 2.108353380E-01 2.147939500E-01 2.187329230E-01 2.226519140E-01 - 2.265505940E-01 2.304283980E-01 2.342849370E-01 2.381197210E-01 2.419322580E-01 - 2.457219960E-01 2.494883090E-01 2.532306020E-01 2.569482030E-01 2.606404720E-01 - 2.643066350E-01 2.679459750E-01 2.715576290E-01 2.143673450E-01 2.121835950E-01 - 2.099848090E-01 2.077708100E-01 2.055414170E-01 2.032964530E-01 2.010357230E-01 - 1.987590490E-01 1.964662370E-01 1.941571090E-01 1.918314990E-01 1.894892010E-01 - 1.871300490E-01 1.847538500E-01 1.823604260E-01 1.799495970E-01 1.775211690E-01 - 1.750749800E-01 1.726108040E-01 1.701284800E-01 1.676278110E-01 1.651086060E-01 - 1.625707750E-01 1.600138250E-01 1.574374740E-01 1.548417210E-01 1.522265820E-01 - 1.495920720E-01 1.469382050E-01 1.442648920E-01 1.415761410E-01 1.388747250E-01 - 1.361611340E-01 1.334362330E-01 1.307009760E-01 1.279559880E-01 1.252020150E-01 - 1.224397420E-01 1.196698470E-01 1.168929860E-01 1.141097920E-01 1.113208760E-01 - 1.085267660E-01 1.057279930E-01 1.029250850E-01 1.001184660E-01 9.730863570E-02 - 9.449600430E-02 9.168099610E-02 8.886403590E-02 8.604555580E-02 8.322595800E-02 - 8.040563020E-02 7.758498940E-02 7.476443800E-02 7.194440070E-02 6.912529470E-02 - 6.630752240E-02 6.349152330E-02 6.067784500E-02 5.786692350E-02 5.505929890E-02 - 5.225556340E-02 4.945630580E-02 4.666212570E-02 4.387364160E-02 4.109154270E-02 - 3.831654790E-02 3.554937240E-02 3.279081730E-02 3.004167600E-02 2.730276060E-02 - 2.457490190E-02 2.185899950E-02 1.915595870E-02 1.646671820E-02 1.379222330E-02 - 1.113342400E-02 8.491316810E-03 5.866914520E-03 3.261254870E-03 6.753698690E-04 --1.889715670E-03-4.432909190E-03-6.953154690E-03-9.449374860E-03-1.192048380E-02 --1.436539460E-02-1.678301580E-02-1.917225490E-02-2.153202330E-02-2.386123690E-02 --2.615879850E-02-2.842364270E-02-3.065466880E-02-3.285081680E-02-3.501103070E-02 --3.713425250E-02-3.921943160E-02-4.126553980E-02-4.327153040E-02-4.523640870E-02 --4.715917630E-02-4.903883110E-02-5.087438970E-02-5.266489090E-02-5.440939220E-02 --5.610694740E-02-5.775663630E-02-5.935753140E-02-6.090874600E-02-6.240940090E-02 --6.385862830E-02-6.525558230E-02-6.659944360E-02-6.788937750E-02-6.912457940E-02 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1.960629520E-01 2.000812290E-01 2.040795530E-01 2.080575530E-01 2.120149280E-01 - 2.159513090E-01 2.198663350E-01 2.237595920E-01 2.276307200E-01 2.314792130E-01 - 2.353046090E-01 2.391063720E-01 2.428840250E-01 2.466369570E-01 2.503646610E-01 - 2.540663180E-01 2.577414210E-01 2.613891960E-01 2.650089860E-01 2.685999870E-01 - 2.142692950E-01 2.120793010E-01 2.098740940E-01 2.076534630E-01 2.054172160E-01 - 2.031651740E-01 2.008971270E-01 1.986128990E-01 1.963122790E-01 1.939951030E-01 - 1.916611940E-01 1.893103420E-01 1.869423540E-01 1.845570650E-01 1.821542830E-01 - 1.797338130E-01 1.772954610E-01 1.748390500E-01 1.723643840E-01 1.698712710E-01 - 1.673594860E-01 1.648288820E-01 1.622792180E-01 1.597105710E-01 1.571222250E-01 - 1.545139850E-01 1.518858370E-01 1.492378120E-01 1.465699520E-01 1.438834970E-01 - 1.411812900E-01 1.384661350E-01 1.357386710E-01 1.329996880E-01 1.302501410E-01 - 1.274906690E-01 1.247219820E-01 1.219447550E-01 1.191596840E-01 1.163674000E-01 - 1.135685740E-01 1.107637510E-01 1.079534890E-01 1.051383170E-01 1.023187260E-01 - 9.949516510E-02 9.666810180E-02 9.383796160E-02 9.100516140E-02 8.817012610E-02 - 8.533326540E-02 8.249498160E-02 7.965568450E-02 7.681576160E-02 7.397561520E-02 - 7.113566990E-02 6.829633560E-02 6.545803700E-02 6.262122090E-02 5.978641290E-02 - 5.695407470E-02 5.412474650E-02 5.129902440E-02 4.847750440E-02 4.566078630E-02 - 4.284948480E-02 4.004435610E-02 3.724607080E-02 3.445537760E-02 3.167309240E-02 - 2.890002350E-02 2.613697200E-02 2.338480390E-02 2.064441140E-02 1.791672590E-02 - 1.520269740E-02 1.250326820E-02 9.819411670E-03 7.152150390E-03 4.502497610E-03 - 1.871496560E-03-7.398092420E-04-3.330361330E-03-5.899088460E-03-8.444909010E-03 --1.096672190E-02-1.346343380E-02-1.593395700E-02-1.837719420E-02-2.079203540E-02 --2.317738350E-02-2.553214690E-02-2.785523050E-02-3.014553710E-02-3.240198270E-02 --3.462348510E-02-3.680898990E-02-3.895743190E-02-4.106774550E-02-4.313889520E-02 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1.236410740E-01 1.275889430E-01 1.315557810E-01 1.355513630E-01 1.395897720E-01 - 1.436849240E-01 1.478447770E-01 1.520666030E-01 1.562844660E-01 1.604866090E-01 - 1.646714810E-01 1.688376070E-01 1.729834380E-01 1.771074680E-01 1.812110690E-01 - 1.852958650E-01 1.893598880E-01 1.934029910E-01 1.974250380E-01 2.014258350E-01 - 2.054050120E-01 2.093622830E-01 2.132972780E-01 2.172096070E-01 2.210989590E-01 - 2.249649020E-01 2.288069580E-01 2.326246950E-01 2.364176210E-01 2.401851420E-01 - 2.439268530E-01 2.476420700E-01 2.513302560E-01 2.549907570E-01 2.586227660E-01 - 2.622258070E-01 2.657991050E-01 2.141789790E-01 2.119835170E-01 2.097726320E-01 - 2.075461000E-01 2.053037140E-01 2.030452940E-01 2.007706460E-01 1.984795630E-01 - 1.961718500E-01 1.938473280E-01 1.915057900E-01 1.891470550E-01 1.867709310E-01 - 1.843772230E-01 1.819657530E-01 1.795363280E-01 1.770887370E-01 1.746228040E-01 - 1.721383180E-01 1.696351020E-01 1.671129760E-01 1.645717020E-01 1.620110570E-01 - 1.594308610E-01 1.568311300E-01 1.542113870E-01 1.515707970E-01 1.489097770E-01 - 1.462292670E-01 1.435302500E-01 1.408154820E-01 1.380873920E-01 1.353467550E-01 - 1.325944510E-01 1.298313740E-01 1.270581780E-01 1.242755060E-01 1.214841080E-01 - 1.186846350E-01 1.158777180E-01 1.130640130E-01 1.102440950E-01 1.074185000E-01 - 1.045877340E-01 1.017522890E-01 9.891262650E-02 9.606917950E-02 9.322238710E-02 - 9.037265930E-02 8.752041310E-02 8.466606590E-02 8.181000500E-02 7.895265520E-02 - 7.609437410E-02 7.323557140E-02 7.037666440E-02 6.751808520E-02 6.466025110E-02 - 6.180361290E-02 5.894866590E-02 5.609593170E-02 5.324595420E-02 5.039929600E-02 - 4.755656050E-02 4.471836240E-02 4.188534990E-02 3.905825320E-02 3.623779490E-02 - 3.342472390E-02 3.061985040E-02 2.782398280E-02 2.503793870E-02 2.226261980E-02 - 1.949891260E-02 1.674776340E-02 1.401012580E-02 1.128695070E-02 8.579248560E-03 - 5.888028070E-03 3.214332040E-03 5.592083330E-04-2.076294740E-03-4.691103010E-03 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5.605040490E-02 5.975438280E-02 6.347814950E-02 6.722060590E-02 7.098078730E-02 - 7.475777720E-02 7.855065170E-02 8.235847950E-02 8.618041870E-02 9.001578390E-02 - 9.386377780E-02 9.772395340E-02 1.015958640E-01 1.054790690E-01 1.093737930E-01 - 1.132798190E-01 1.171979010E-01 1.211295870E-01 1.250764430E-01 1.290397050E-01 - 1.330232170E-01 1.370420460E-01 1.411083190E-01 1.452319180E-01 1.494227200E-01 - 1.536560650E-01 1.578731690E-01 1.620723010E-01 1.662514360E-01 1.704094260E-01 - 1.745443940E-01 1.786584260E-01 1.827510450E-01 1.868219380E-01 1.908708360E-01 - 1.948975180E-01 1.989017280E-01 2.028830500E-01 2.068412750E-01 2.107760460E-01 - 2.146869900E-01 2.185738090E-01 2.224359960E-01 2.262731940E-01 2.300849260E-01 - 2.338707750E-01 2.376301590E-01 2.413626020E-01 2.450675520E-01 2.487444280E-01 - 2.523926500E-01 2.560116350E-01 2.596005800E-01 2.631588580E-01 2.140971420E-01 - 2.118969710E-01 2.096811530E-01 2.074494660E-01 2.052017150E-01 2.029376780E-01 - 2.006571440E-01 1.983599360E-01 1.960458310E-01 1.937146480E-01 1.913661960E-01 - 1.890002790E-01 1.866167040E-01 1.842152630E-01 1.817957910E-01 1.793580650E-01 - 1.769019220E-01 1.744271670E-01 1.719335760E-01 1.694209720E-01 1.668891610E-01 - 1.643379330E-01 1.617670510E-01 1.591763650E-01 1.565656660E-01 1.539351940E-01 - 1.512832490E-01 1.486103530E-01 1.459176090E-01 1.432061940E-01 1.404796540E-01 - 1.377394500E-01 1.349864600E-01 1.322216090E-01 1.294458060E-01 1.266595720E-01 - 1.238637190E-01 1.210589260E-01 1.182458400E-01 1.154250800E-01 1.125972940E-01 - 1.097631010E-01 1.069229920E-01 1.040774660E-01 1.012270080E-01 9.837207940E-02 - 9.551311280E-02 9.265054760E-02 8.978477870E-02 8.691623060E-02 8.404529840E-02 - 8.117238430E-02 7.829789820E-02 7.542221250E-02 7.254572210E-02 6.966884430E-02 - 6.679200380E-02 6.391563270E-02 6.104017790E-02 5.816615370E-02 5.529407410E-02 - 5.242447180E-02 4.955800250E-02 4.669512810E-02 4.383650050E-02 4.098287220E-02 - 3.813497350E-02 3.529352320E-02 3.245925160E-02 2.963294280E-02 2.681543310E-02 - 2.400758120E-02 2.121028680E-02 1.842446440E-02 1.565106210E-02 1.289103180E-02 - 1.014534760E-02 7.415010590E-03 4.701063970E-03 2.004558920E-03-6.734541970E-04 --3.331925950E-03-5.969744640E-03-8.585832080E-03-1.117908120E-02-1.374838220E-02 --1.629262420E-02-1.881069690E-02-2.130148190E-02-2.376385590E-02-2.619670520E-02 --2.859891210E-02-3.096937200E-02-3.330698240E-02-3.561064230E-02-3.787926580E-02 --4.011176150E-02-4.230705650E-02-4.446409640E-02-4.658182710E-02-4.865919800E-02 --5.069517720E-02-5.268875510E-02-5.463892220E-02-5.654468010E-02-5.840506030E-02 --6.021907180E-02-6.198577580E-02-6.370422240E-02-6.537348780E-02-6.699267030E-02 --6.856087600E-02-7.007720320E-02-7.154077290E-02-7.295075060E-02-7.430629430E-02 --7.560658450E-02-7.685081660E-02-7.803820820E-02-7.916798440E-02-8.023938540E-02 --8.125162120E-02-8.220402150E-02-8.309591560E-02-8.392661810E-02-8.469547330E-02 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2.238824520E-01 2.276898030E-01 2.314702720E-01 2.352232640E-01 2.389483900E-01 - 2.426451000E-01 2.463128420E-01 2.499510650E-01 2.535590830E-01 2.571363450E-01 - 2.606822550E-01 2.140244250E-01 2.118203940E-01 2.096004640E-01 2.073644400E-01 - 2.051120850E-01 2.028431890E-01 2.005575300E-01 1.982549280E-01 1.959351600E-01 - 1.935980320E-01 1.912433650E-01 1.888709520E-01 1.864805970E-01 1.840721220E-01 - 1.816453190E-01 1.792000090E-01 1.767359970E-01 1.742530910E-01 1.717510820E-01 - 1.692297910E-01 1.666890230E-01 1.641285570E-01 1.615481820E-01 1.589476760E-01 - 1.563268600E-01 1.536856440E-01 1.510234030E-01 1.483394950E-01 1.456351730E-01 - 1.429130140E-01 1.401751340E-01 1.374233510E-01 1.346587690E-01 1.318822060E-01 - 1.290943470E-01 1.262959540E-01 1.234876810E-01 1.206702440E-01 1.178443360E-01 - 1.150105600E-01 1.121695640E-01 1.093218920E-01 1.064680890E-01 1.036086450E-01 - 1.007440390E-01 9.787471590E-02 9.500111640E-02 9.212366490E-02 8.924276380E-02 - 8.635882290E-02 8.347224440E-02 8.058343080E-02 7.769276200E-02 7.480063290E-02 - 7.190745320E-02 6.901361050E-02 6.611950700E-02 6.322563440E-02 6.033241380E-02 - 5.744036660E-02 5.455002190E-02 5.166190860E-02 4.877660800E-02 4.589471970E-02 - 4.301689940E-02 4.014383260E-02 3.727627170E-02 3.441496940E-02 3.156066690E-02 - 2.871407380E-02 2.587609180E-02 2.304766140E-02 2.022962640E-02 1.742292200E-02 - 1.462848390E-02 1.184729110E-02 9.080339220E-03 6.328637250E-03 3.593232720E-03 - 8.751823920E-04-1.824458480E-03-4.504614040E-03-7.164182610E-03-9.802065790E-03 --1.241714320E-02-1.500829030E-02-1.757439600E-02-2.011434920E-02-2.262701650E-02 --2.511127290E-02-2.756599150E-02-2.999004910E-02-3.238233550E-02-3.474174070E-02 --3.706716370E-02-3.935750200E-02-4.161166770E-02-4.382858050E-02-4.600717870E-02 --4.814641180E-02-5.024521430E-02-5.230255800E-02-5.431741850E-02-5.628877130E-02 --5.821564050E-02-6.009704620E-02-6.193200500E-02-6.371954080E-02-6.545872240E-02 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1.530385020E-01 1.572678540E-01 1.614742730E-01 1.656561340E-01 1.698149740E-01 - 1.739498380E-01 1.780607250E-01 1.821475770E-01 1.862101110E-01 1.902482660E-01 - 1.942617450E-01 1.982502340E-01 2.022134210E-01 2.061510240E-01 2.100627270E-01 - 2.139482500E-01 2.178071140E-01 2.216389920E-01 2.254434670E-01 2.292201370E-01 - 2.329684790E-01 2.366880770E-01 2.403784250E-01 2.440389390E-01 2.476692050E-01 - 2.512685660E-01 2.548364400E-01 2.583722770E-01 2.139616460E-01 2.117546200E-01 - 2.095314860E-01 2.072919460E-01 2.050357910E-01 2.027628120E-01 2.004728020E-01 - 1.981655210E-01 1.958408060E-01 1.934984620E-01 1.911382680E-01 1.887600420E-01 - 1.863636080E-01 1.839487550E-01 1.815153210E-01 1.790630820E-01 1.765918880E-01 - 1.741015170E-01 1.715917890E-01 1.690624950E-01 1.665134580E-01 1.639444680E-01 - 1.613553020E-01 1.587457660E-01 1.561156360E-01 1.534647200E-01 1.507926290E-01 - 1.480981410E-01 1.453836410E-01 1.426512300E-01 1.399027110E-01 1.371399160E-01 - 1.343646940E-01 1.315772380E-01 1.287781150E-01 1.259682630E-01 1.231483670E-01 - 1.203191130E-01 1.174811940E-01 1.146352070E-01 1.117818060E-01 1.089215130E-01 - 1.060548570E-01 1.031823610E-01 1.003044690E-01 9.742163870E-02 9.453430030E-02 - 9.164287150E-02 8.874775470E-02 8.584935960E-02 8.294809610E-02 8.004432920E-02 - 7.713846120E-02 7.423088700E-02 7.132200900E-02 6.841222200E-02 6.550192830E-02 - 6.259158250E-02 5.968167260E-02 5.677269400E-02 5.386516080E-02 5.095962440E-02 - 4.805667330E-02 4.515692590E-02 4.226105660E-02 3.936975080E-02 3.648371250E-02 - 3.360369800E-02 3.073046360E-02 2.786485290E-02 2.500770610E-02 2.215991170E-02 - 1.932237300E-02 1.649602690E-02 1.368181780E-02 1.088074590E-02 8.093783630E-03 - 5.321977190E-03 2.566390900E-03-1.719192660E-04-2.891898620E-03-5.592450500E-03 --8.272475560E-03-1.093085480E-02-1.356646330E-02-1.617817210E-02-1.876486470E-02 --2.132542430E-02-2.385868500E-02-2.636353490E-02-2.883883940E-02-3.128347170E-02 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8.313806350E-02 8.701169490E-02 9.089610730E-02 9.479056300E-02 9.869452570E-02 - 1.026076670E-01 1.065298170E-01 1.104608250E-01 1.144012660E-01 1.183514070E-01 - 1.223133580E-01 1.262893530E-01 1.302815530E-01 1.342933180E-01 1.383404140E-01 - 1.424404230E-01 1.466077270E-01 1.508367360E-01 1.550736730E-01 1.592955140E-01 - 1.634886860E-01 1.676587310E-01 1.718040700E-01 1.759247630E-01 1.800205110E-01 - 1.840909120E-01 1.881357580E-01 1.921549890E-01 1.961482910E-01 2.001153380E-01 - 2.040558610E-01 2.079695760E-01 2.118561860E-01 2.157153040E-01 2.195465560E-01 - 2.233495410E-01 2.271238570E-01 2.308690990E-01 2.345848230E-01 2.382705810E-01 - 2.419257610E-01 2.455499620E-01 2.491426320E-01 2.527032200E-01 2.562312190E-01 - 2.139098350E-01 2.117007670E-01 2.094752790E-01 2.072330710E-01 2.049739360E-01 - 2.026976500E-01 2.004040180E-01 1.980928330E-01 1.957638710E-01 1.934169680E-01 - 1.910519450E-01 1.886685940E-01 1.862667200E-01 1.838461760E-01 1.814067510E-01 - 1.789482680E-01 1.764705330E-01 1.739733820E-01 1.714565900E-01 1.689199950E-01 - 1.663633880E-01 1.637865750E-01 1.611893770E-01 1.585715860E-01 1.559329780E-01 - 1.532733590E-01 1.505917610E-01 1.478877220E-01 1.451635660E-01 1.424213800E-01 - 1.396631150E-01 1.368906940E-01 1.341053100E-01 1.313074230E-01 1.284978990E-01 - 1.256774220E-01 1.228467230E-01 1.200064640E-01 1.171573550E-01 1.142999980E-01 - 1.114350110E-01 1.085629460E-01 1.056843100E-01 1.027996240E-01 9.990934280E-02 - 9.701390560E-02 9.411373730E-02 9.120924770E-02 8.830085400E-02 8.538895850E-02 - 8.247395600E-02 7.955623420E-02 7.663617280E-02 7.371417430E-02 7.079061870E-02 - 6.786591560E-02 6.494047490E-02 6.201474740E-02 5.908923600E-02 5.616443230E-02 - 5.324083570E-02 5.031902340E-02 4.739958420E-02 4.448314760E-02 4.157039150E-02 - 3.866198660E-02 3.575865180E-02 3.286115830E-02 2.997030320E-02 2.708691360E-02 - 2.421182390E-02 2.134592460E-02 1.849014680E-02 1.564542950E-02 1.281272900E-02 - 9.993040930E-03 7.187370210E-03 4.396767820E-03 1.622298150E-03-1.134974880E-03 --3.874000390E-03-6.593639500E-03-9.292803700E-03-1.197036260E-02-1.462518800E-02 --1.725615370E-02-1.986213210E-02-2.244196090E-02-2.499451860E-02-2.751865980E-02 --3.001325760E-02-3.247717770E-02-3.490929680E-02-3.730849180E-02-3.967364130E-02 --4.200362410E-02-4.429738220E-02-4.655380550E-02-4.877180980E-02-5.095034840E-02 --5.308835950E-02-5.518480020E-02-5.723862720E-02-5.924883110E-02-6.121440230E-02 --6.313435730E-02-6.500770150E-02-6.683349610E-02-6.861075010E-02-7.033851000E-02 --7.201588150E-02-7.364195590E-02-7.521584630E-02-7.673664390E-02-7.820344720E-02 --7.961548120E-02-8.097182210E-02-8.227166530E-02-8.351423590E-02-8.469874410E-02 --8.582440020E-02-8.689042180E-02-8.789608630E-02-8.884067090E-02-8.972348270E-02 --9.054384380E-02-9.130109100E-02-9.199456130E-02-9.262365850E-02-9.318777920E-02 --9.368635710E-02-9.411884840E-02-9.448473160E-02-9.478349980E-02-9.501468390E-02 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5.267828330E-02 4.974134640E-02 4.680659620E-02 - 4.387466240E-02 4.094620420E-02 3.802191090E-02 3.510251640E-02 3.218879550E-02 - 2.928155470E-02 2.638161180E-02 2.348984220E-02 2.060712320E-02 1.773438790E-02 - 1.487259940E-02 1.202271510E-02 9.185733270E-03 6.362676150E-03 3.554593770E-03 - 7.625510330E-04-2.012378540E-03-4.769096150E-03-7.506493940E-03-1.022346690E-02 --1.291887180E-02-1.559158230E-02-1.824047040E-02-2.086439170E-02-2.346219680E-02 --2.603273650E-02-2.857486530E-02-3.108743580E-02-3.356932100E-02-3.601939980E-02 --3.843654690E-02-4.081963750E-02-4.316755380E-02-4.547919330E-02-4.775346440E-02 --4.998929800E-02-5.218561740E-02-5.434137210E-02-5.645551160E-02-5.852699650E-02 --6.055480240E-02-6.253792350E-02-6.447535750E-02-6.636613610E-02-6.820928310E-02 --7.000382240E-02-7.174882290E-02-7.344334570E-02-7.508648930E-02-7.667734470E-02 --7.821501790E-02-7.969862970E-02-8.112732320E-02-8.250026400E-02-8.381658050E-02 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1.050749270E-01 1.021685000E-01 9.925612810E-02 9.633821250E-02 - 9.341517090E-02 9.048740570E-02 8.755532650E-02 8.461933580E-02 8.167984340E-02 - 7.873720680E-02 7.579181340E-02 7.284404340E-02 6.989430640E-02 6.694298980E-02 - 6.399051850E-02 6.103735420E-02 5.808397760E-02 5.513089900E-02 5.217862130E-02 - 4.922774060E-02 4.627887530E-02 4.333264010E-02 4.038968680E-02 3.745075690E-02 - 3.451655060E-02 3.158786150E-02 2.866551280E-02 2.575030920E-02 2.284314480E-02 - 1.994489130E-02 1.705650990E-02 1.417895780E-02 1.131320190E-02 8.460255340E-03 - 5.621140820E-03 2.796922580E-03-1.133052410E-05-2.802548930E-03-5.575637330E-03 --8.329467850E-03-1.106290710E-02-1.377482810E-02-1.646409740E-02-1.912956310E-02 --2.177008060E-02-2.438449860E-02-2.697167360E-02-2.953046190E-02-3.205969180E-02 --3.455823290E-02-3.702495250E-02-3.945873310E-02-4.185843470E-02-4.422295470E-02 --4.655119780E-02-4.884205760E-02-5.109444630E-02-5.330727250E-02-5.547951160E-02 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1.129031030E-01 1.168721910E-01 1.208511810E-01 1.248421300E-01 1.288470920E-01 - 1.328444480E-01 1.368957460E-01 1.410158570E-01 1.451859330E-01 1.493893270E-01 - 1.536148190E-01 1.578504890E-01 1.620751620E-01 1.662535370E-01 1.704055820E-01 - 1.745298060E-01 1.786263140E-01 1.826948080E-01 1.867349890E-01 1.907468590E-01 - 1.947301480E-01 1.986845880E-01 2.026099120E-01 2.065058650E-01 2.103721800E-01 - 2.142085130E-01 2.180145230E-01 2.217898960E-01 2.255342750E-01 2.292472870E-01 - 2.329284550E-01 2.365774360E-01 2.401937690E-01 2.437770520E-01 2.473267760E-01 - 2.508424520E-01 2.138334210E-01 2.116239960E-01 2.093967800E-01 2.071515770E-01 - 2.048881650E-01 2.026063950E-01 2.003060580E-01 1.979871540E-01 1.956493710E-01 - 1.932926180E-01 1.909168060E-01 1.885217430E-01 1.861072780E-01 1.836732770E-01 - 1.812195930E-01 1.787460450E-01 1.762524840E-01 1.737387330E-01 1.712046270E-01 - 1.686500010E-01 1.660746480E-01 1.634784040E-01 1.608610450E-01 1.582228240E-01 - 1.555627440E-01 1.528799980E-01 1.501750650E-01 1.474483460E-01 1.447003040E-01 - 1.419332770E-01 1.391505150E-01 1.363532390E-01 1.335422100E-01 1.307182160E-01 - 1.278821080E-01 1.250345710E-01 1.221762820E-01 1.193079580E-01 1.164302530E-01 - 1.135438160E-01 1.106492210E-01 1.077470030E-01 1.048377010E-01 1.019217890E-01 - 9.899973120E-02 9.607196600E-02 9.313889590E-02 9.020092340E-02 8.725846560E-02 - 8.431192490E-02 8.136168870E-02 7.840812950E-02 7.545162740E-02 7.249256220E-02 - 6.953132900E-02 6.656835230E-02 6.360404190E-02 6.063883010E-02 5.767322330E-02 - 5.470774320E-02 5.174290390E-02 4.877928640E-02 4.581750560E-02 4.285817970E-02 - 3.990200530E-02 3.694965320E-02 3.400189060E-02 3.105951850E-02 2.812335270E-02 - 2.519419980E-02 2.227294070E-02 1.936048270E-02 1.645777930E-02 1.356578710E-02 - 1.068549510E-02 7.817920300E-03 4.964088560E-03 2.125073460E-03-6.980565960E-04 --3.504214580E-03-6.292297970E-03-9.061176330E-03-1.180971410E-02-1.453678400E-02 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7.791482660E-02 7.493928820E-02 7.196087390E-02 6.897997860E-02 - 6.599698960E-02 6.301236900E-02 6.002651900E-02 5.703996870E-02 5.405325070E-02 - 5.106688660E-02 4.808142040E-02 4.509747030E-02 4.211574420E-02 3.913682330E-02 - 3.616148230E-02 3.319050740E-02 3.022468460E-02 2.726479620E-02 2.431163010E-02 - 2.136619020E-02 1.842933520E-02 1.550199000E-02 1.258517240E-02 9.679899550E-03 - 6.787188820E-03 3.908058630E-03 1.043552420E-03-1.805192330E-03-4.637096540E-03 --7.451036940E-03-1.024587170E-02-1.302046890E-02-1.577369500E-02-1.850438490E-02 --2.121138570E-02-2.389352580E-02-2.654964290E-02-2.917857280E-02-3.177915890E-02 --3.435025360E-02-3.689068180E-02-3.939930720E-02-4.187499360E-02-4.431662340E-02 --4.672306780E-02-4.909320180E-02-5.142589660E-02-5.372013900E-02-5.597476660E-02 --5.818874020E-02-6.036101280E-02-6.249055270E-02-6.457630540E-02-6.661724300E-02 --6.861236690E-02-7.056067140E-02-7.246118780E-02-7.431292530E-02-7.611495260E-02 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1.276183580E-01 1.247510090E-01 1.218725000E-01 1.189835520E-01 - 1.160848440E-01 1.131770010E-01 1.102605980E-01 1.073361710E-01 1.044042630E-01 - 1.014653220E-01 9.851979460E-02 9.556812050E-02 9.261073920E-02 8.964804560E-02 - 8.668042720E-02 8.370827140E-02 8.073198050E-02 7.775191960E-02 7.476846870E-02 - 7.178202270E-02 6.879295410E-02 6.580167260E-02 6.280861050E-02 5.981420730E-02 - 5.681896580E-02 5.382341890E-02 5.082810670E-02 4.783356560E-02 4.484042900E-02 - 4.184935240E-02 3.886102890E-02 3.587616610E-02 3.289552410E-02 2.991989250E-02 - 2.695009110E-02 2.398698780E-02 2.103145610E-02 1.808444410E-02 1.514685060E-02 - 1.221969160E-02 9.303982370E-03 6.400754210E-03 3.511035120E-03 6.358935500E-04 --2.223583870E-03-5.066272340E-03-7.891042160E-03-1.069676410E-02-1.348231170E-02 --1.624653490E-02-1.898825170E-02-2.170631100E-02-2.439954690E-02-2.706679330E-02 --2.970688420E-02-3.231865540E-02-3.490097080E-02-3.745262700E-02-3.997249530E-02 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3.180245690E-04-2.550763540E-03-5.402814600E-03-8.237001490E-03 --1.105220060E-02-1.384728770E-02-1.662108300E-02-1.937241110E-02-2.210013200E-02 --2.480306480E-02-2.748004350E-02-3.012990020E-02-3.275147450E-02-3.534359480E-02 --3.790510450E-02-4.043485970E-02-4.293170940E-02-4.539452490E-02-4.782217370E-02 --5.021353440E-02-5.256750430E-02-5.488299580E-02-5.715893210E-02-5.939422180E-02 --6.158779190E-02-6.373862180E-02-6.584565340E-02-6.790786980E-02-6.992428000E-02 --7.189385590E-02-7.381560650E-02-7.568856330E-02-7.751177250E-02-7.928428800E-02 --8.100515600E-02-8.267343040E-02-8.428825440E-02-8.584868160E-02-8.735384050E-02 --8.880286660E-02-9.019489590E-02-9.152907880E-02-9.280458840E-02-9.402062740E-02 --9.517637640E-02-9.627107530E-02-9.730393440E-02-9.827422350E-02-9.918124230E-02 --1.000242830E-01-1.008026530E-01-1.015156730E-01-1.021627410E-01-1.027432310E-01 --1.032565610E-01-1.037021650E-01-1.040795150E-01-1.043881100E-01-1.046274750E-01 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4.754305630E-02 4.453532770E-02 4.152946920E-02 - 3.852617370E-02 3.552614150E-02 3.253014010E-02 2.953896860E-02 2.655345200E-02 - 2.357445280E-02 2.060286700E-02 1.763962210E-02 1.468566900E-02 1.174198930E-02 - 8.809603750E-03 5.889544730E-03 2.982864850E-03 9.064127520E-05-2.786030530E-03 --5.646027160E-03-8.488224820E-03-1.131149380E-02-1.411467880E-02-1.689662410E-02 --1.965616640E-02-2.239213700E-02-2.510336040E-02-2.778866700E-02-3.044688520E-02 --3.307685630E-02-3.567740320E-02-3.824736920E-02-4.078561070E-02-4.329097640E-02 --4.576233030E-02-4.819853980E-02-5.059848730E-02-5.296105890E-02-5.528517440E-02 --5.756973850E-02-5.981368200E-02-6.201593210E-02-6.417544190E-02-6.629116090E-02 --6.836207960E-02-7.038719950E-02-7.236550000E-02-7.429596780E-02-7.617764170E-02 --7.800956070E-02-7.979077850E-02-8.152034880E-02-8.319734040E-02-8.482084420E-02 --8.638995140E-02-8.790377530E-02-8.936145160E-02-9.076208620E-02-9.210485220E-02 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1.802186070E-01 1.842793380E-01 1.883088050E-01 1.923068910E-01 1.962734010E-01 - 2.002081420E-01 2.041109350E-01 2.079815420E-01 2.118196640E-01 2.156250480E-01 - 2.193974410E-01 2.231365140E-01 2.268419560E-01 2.305134390E-01 2.341505590E-01 - 2.377530190E-01 2.413204310E-01 2.448523940E-01 2.142610100E-01 2.120579780E-01 - 2.098340840E-01 2.075895220E-01 2.053244260E-01 2.030387970E-01 2.007327380E-01 - 1.984064280E-01 1.960597340E-01 1.936926990E-01 1.913052650E-01 1.888973710E-01 - 1.864689890E-01 1.840199830E-01 1.815502790E-01 1.790597590E-01 1.765483020E-01 - 1.740157900E-01 1.714620140E-01 1.688869150E-01 1.662902680E-01 1.636718960E-01 - 1.610316630E-01 1.583697350E-01 1.556854700E-01 1.529776600E-01 1.502467540E-01 - 1.474932880E-01 1.447178130E-01 1.419231740E-01 1.391115640E-01 1.362845600E-01 - 1.334432660E-01 1.305883530E-01 1.277205800E-01 1.248406770E-01 1.219493600E-01 - 1.190473290E-01 1.161352690E-01 1.132137780E-01 1.102834570E-01 1.073448660E-01 - 1.043985040E-01 1.014448550E-01 9.848435220E-02 9.551742670E-02 9.254451840E-02 - 8.956602220E-02 8.658234030E-02 8.359385280E-02 8.060094710E-02 7.760400330E-02 - 7.460340110E-02 7.159949840E-02 6.859269740E-02 6.558338550E-02 6.257200990E-02 - 5.955904720E-02 5.654497070E-02 5.353029070E-02 5.051553620E-02 4.750128460E-02 - 4.448818420E-02 4.147687930E-02 3.846804800E-02 3.546241300E-02 3.246072680E-02 - 2.946380900E-02 2.647246790E-02 2.348758090E-02 2.051003090E-02 1.754075850E-02 - 1.458070430E-02 1.163087410E-02 8.692256170E-03 5.765891630E-03 2.852858040E-03 --4.576590070E-05-2.928902400E-03-5.795432720E-03-8.644216690E-03-1.147411760E-02 --1.428398210E-02-1.707265340E-02-1.983897390E-02-2.258176730E-02-2.529986020E-02 --2.799207900E-02-3.065724860E-02-3.329419720E-02-3.590178490E-02-3.847881030E-02 --4.102414100E-02-4.353662950E-02-4.601514710E-02-4.845855010E-02-5.086571350E-02 --5.323553830E-02-5.556691440E-02-5.785876890E-02-6.011002510E-02-6.231961400E-02 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1.094983820E-01 1.135054010E-01 1.175178140E-01 1.215390560E-01 1.255671380E-01 - 1.296079750E-01 1.336689890E-01 1.377575400E-01 1.418923740E-01 1.461048870E-01 - 1.503660830E-01 1.546438780E-01 1.589023170E-01 1.631273480E-01 1.673215030E-01 - 1.714847240E-01 1.756168750E-01 1.797177490E-01 1.837873460E-01 1.878254860E-01 - 1.918321700E-01 1.958071590E-01 1.997502450E-01 2.036612630E-01 2.075399760E-01 - 2.113861140E-01 2.151994110E-01 2.189796120E-01 2.227264340E-01 2.264394760E-01 - 2.301184540E-01 2.337630240E-01 2.373728310E-01 2.409475000E-01 2.444865850E-01 - 2.144393620E-01 2.122339160E-01 2.100078310E-01 2.077611390E-01 2.054940760E-01 - 2.032067030E-01 2.008990500E-01 1.985710560E-01 1.962228270E-01 1.938542870E-01 - 1.914653630E-01 1.890559940E-01 1.866261360E-01 1.841756550E-01 1.817044760E-01 - 1.792124510E-01 1.766994600E-01 1.741653680E-01 1.716100570E-01 1.690333340E-01 - 1.664350630E-01 1.638150810E-01 1.611732100E-01 1.585103570E-01 1.558237080E-01 - 1.531136040E-01 1.503807600E-01 1.476258490E-01 1.448494200E-01 1.420519800E-01 - 1.392380300E-01 1.364087160E-01 1.335650090E-01 1.307076360E-01 1.278373600E-01 - 1.249549310E-01 1.220609920E-01 1.191562710E-01 1.162414770E-01 1.133171840E-01 - 1.103839800E-01 1.074424540E-01 1.044931110E-01 1.015364230E-01 9.857282790E-02 - 9.560275820E-02 9.262664620E-02 8.964490890E-02 8.665791900E-02 8.366607130E-02 - 8.066974580E-02 7.766932990E-02 7.466519620E-02 7.165772470E-02 6.864729520E-02 - 6.563432510E-02 6.261921670E-02 5.960243940E-02 5.658448860E-02 5.356588210E-02 - 5.054717140E-02 4.752891140E-02 4.451171310E-02 4.149625450E-02 3.848321360E-02 - 3.547329460E-02 3.246727590E-02 2.946597150E-02 2.647018620E-02 2.348077480E-02 - 2.049864460E-02 1.752473410E-02 1.455999260E-02 1.160540150E-02 8.661973290E-03 - 5.730742590E-03 2.812781840E-03-9.083063920E-05-2.979005690E-03-5.850627090E-03 --8.704558950E-03-1.153966320E-02-1.435478310E-02-1.714876480E-02-1.992043290E-02 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4.198448360E-02 4.583482820E-02 4.970277100E-02 5.358701200E-02 5.748630320E-02 - 6.139943380E-02 6.532522290E-02 6.926257910E-02 7.321048530E-02 7.716792820E-02 - 8.113395420E-02 8.510766180E-02 8.908827600E-02 9.307508920E-02 9.706746040E-02 - 1.010648380E-01 1.050669400E-01 1.090739740E-01 1.130861710E-01 1.171042550E-01 - 1.211299080E-01 1.251632420E-01 1.292090420E-01 1.332740190E-01 1.373645810E-01 - 1.414971050E-01 1.457106620E-01 1.499769240E-01 1.542612170E-01 1.585288490E-01 - 1.627609880E-01 1.669642780E-01 1.711364540E-01 1.752774570E-01 1.793872420E-01 - 1.834656890E-01 1.875128000E-01 1.915283200E-01 1.955121160E-01 1.994639930E-01 - 2.033837440E-01 2.072711740E-01 2.111260290E-01 2.149480280E-01 2.187368570E-01 - 2.224922180E-01 2.262138130E-01 2.299013440E-01 2.335544230E-01 2.371726630E-01 - 2.407557370E-01 2.443031970E-01 2.146491860E-01 2.124400880E-01 2.102109640E-01 - 2.079616190E-01 2.056921420E-01 2.034027130E-01 2.010932120E-01 1.987635490E-01 - 1.964137410E-01 1.940437410E-01 1.916534600E-01 1.892427950E-01 1.868116710E-01 - 1.843599830E-01 1.818876120E-01 1.793944390E-01 1.768803150E-01 1.743451060E-01 - 1.717886780E-01 1.692108810E-01 1.666115220E-01 1.639904080E-01 1.613474340E-01 - 1.586832850E-01 1.559953690E-01 1.532840730E-01 1.505501270E-01 1.477942470E-01 - 1.450171620E-01 1.422196330E-01 1.394023600E-01 1.365717050E-01 1.337267010E-01 - 1.308677790E-01 1.279957740E-01 1.251115800E-01 1.222158520E-01 1.193092990E-01 - 1.163926050E-01 1.134663600E-01 1.105311660E-01 1.075876210E-01 1.046362000E-01 - 1.016774100E-01 9.871169180E-02 9.573945400E-02 9.276112910E-02 8.977712690E-02 - 8.678787950E-02 8.379371460E-02 8.079504220E-02 7.779223470E-02 7.478567960E-02 - 7.177576420E-02 6.876285370E-02 6.574734300E-02 6.272971630E-02 5.971034240E-02 - 5.668973920E-02 5.366845060E-02 5.064703520E-02 4.762603720E-02 4.460602630E-02 - 4.158774390E-02 3.857179360E-02 3.555893530E-02 3.254995120E-02 2.954561820E-02 - 2.654675210E-02 2.355421150E-02 2.056889420E-02 1.759173720E-02 1.462370250E-02 - 1.166578200E-02 8.718973030E-03 5.784287580E-03 2.862828780E-03-4.434228320E-05 --2.936117580E-03-5.811388140E-03-8.669028060E-03-1.150789200E-02-1.432682390E-02 --1.712466400E-02-1.990024560E-02-2.265239510E-02-2.537994090E-02-2.808170580E-02 --3.075651640E-02-3.340320290E-02-3.602059560E-02-3.860753770E-02-4.116286710E-02 --4.368542880E-02-4.617409040E-02-4.862771930E-02-5.104518680E-02-5.342539400E-02 --5.576723070E-02-5.806960910E-02-6.033145260E-02-6.255168470E-02-6.472926590E-02 --6.686314940E-02-6.895230710E-02-7.099571080E-02-7.299236210E-02-7.494126260E-02 --7.684142890E-02-7.869189230E-02-8.049170670E-02-8.223991100E-02-8.393557370E-02 --8.557777110E-02-8.716560160E-02-8.869817850E-02-9.017460790E-02-9.159402550E-02 --9.295555200E-02-9.425837550E-02-9.550168370E-02-9.668467190E-02-9.780652080E-02 --9.886642550E-02-9.986367080E-02-1.007975190E-01-1.016672330E-01-1.024721560E-01 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2.148708850E-01 2.186691760E-01 2.224341030E-01 2.261652200E-01 2.298622880E-01 - 2.335249330E-01 2.371527850E-01 2.407454550E-01 2.443024960E-01 2.148873810E-01 - 2.126743200E-01 2.104415740E-01 2.081893680E-01 2.059175070E-01 2.036259170E-01 - 2.013145390E-01 1.989832670E-01 1.966320130E-01 1.942606720E-01 1.918691990E-01 - 1.894574610E-01 1.870253530E-01 1.845727560E-01 1.820995660E-01 1.796056330E-01 - 1.770908090E-01 1.745549440E-01 1.719979200E-01 1.694195270E-01 1.668196170E-01 - 1.641979810E-01 1.615544410E-01 1.588889960E-01 1.562012730E-01 1.534903350E-01 - 1.507563140E-01 1.479997930E-01 1.452212780E-01 1.424225270E-01 1.396063570E-01 - 1.367747490E-01 1.339286120E-01 1.310687070E-01 1.281957780E-01 1.253106590E-01 - 1.224139410E-01 1.195063890E-01 1.165886370E-01 1.136613040E-01 1.107250150E-01 - 1.077803520E-01 1.048277840E-01 1.018678250E-01 9.890092160E-02 9.592748430E-02 - 9.294793750E-02 8.996270600E-02 8.697219940E-02 8.397677540E-02 8.097683640E-02 - 7.797273990E-02 7.496488090E-02 7.195363940E-02 6.893938780E-02 6.592255090E-02 - 6.290351600E-02 5.988277120E-02 5.686076730E-02 5.383805560E-02 5.081517990E-02 - 4.779269550E-02 4.477119820E-02 4.175135870E-02 3.873384000E-02 3.571938720E-02 - 3.270877530E-02 2.970277890E-02 2.670218610E-02 2.370790210E-02 2.072080780E-02 - 1.774180870E-02 1.477189920E-02 1.181206480E-02 8.863284250E-03 5.926599730E-03 - 3.003075490E-03 9.378995310E-05-2.800151010E-03-5.677636250E-03-8.537540210E-03 --1.137871850E-02-1.420001590E-02-1.700027290E-02-1.977833170E-02-2.253301070E-02 --2.526313810E-02-2.796753680E-02-3.064502960E-02-3.329445420E-02-3.591463340E-02 --3.850441050E-02-4.106262700E-02-4.358813170E-02-4.607978090E-02-4.853643850E-02 --5.095699060E-02-5.334031950E-02-5.568532270E-02-5.799093840E-02-6.025604160E-02 --6.247957420E-02-6.466049700E-02-6.679777800E-02-6.889037790E-02-7.093726100E-02 --7.293741410E-02-7.488986850E-02-7.679362600E-02-7.864771780E-02-8.045119790E-02 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1.454261990E-01 1.497047840E-01 1.540046330E-01 1.582864670E-01 1.625414940E-01 - 1.667616220E-01 1.709513220E-01 1.751100270E-01 1.792376640E-01 1.833342460E-01 - 1.873996410E-01 1.914336530E-01 1.954361050E-01 1.994068180E-01 2.033456560E-01 - 2.072523390E-01 2.111265810E-01 2.149681300E-01 2.187767480E-01 2.225520460E-01 - 2.262937130E-01 2.300014050E-01 2.336747050E-01 2.373133150E-01 2.409167740E-01 - 2.444846780E-01 2.151505950E-01 2.129337790E-01 2.106980090E-01 2.084431050E-01 - 2.061688900E-01 2.038752880E-01 2.015621660E-01 1.992294190E-01 1.968768980E-01 - 1.945045140E-01 1.921121180E-01 1.896996050E-01 1.872668560E-01 1.848137380E-01 - 1.823401000E-01 1.798458250E-01 1.773307470E-01 1.747947040E-01 1.722375450E-01 - 1.696591230E-01 1.670592430E-01 1.644377560E-01 1.617944990E-01 1.591290980E-01 - 1.564414350E-01 1.537311970E-01 1.509979960E-01 1.482413710E-01 1.454625580E-01 - 1.426640900E-01 1.398482170E-01 1.370165800E-01 1.341703390E-01 1.313103290E-01 - 1.284372810E-01 1.255519840E-01 1.226551380E-01 1.197474230E-01 1.168294770E-01 - 1.139019210E-01 1.109654080E-01 1.080205590E-01 1.050677750E-01 1.021075840E-01 - 9.914043550E-02 9.616676720E-02 9.318698940E-02 9.020154180E-02 8.721081170E-02 - 8.421517160E-02 8.121501650E-02 7.821072640E-02 7.520268110E-02 7.219124590E-02 - 6.917679310E-02 6.615974010E-02 6.314054130E-02 6.011963260E-02 5.709747970E-02 - 5.407458920E-02 5.105150860E-02 4.802880060E-02 4.500709100E-02 4.198703170E-02 - 3.896928950E-02 3.595458720E-02 3.294368090E-02 2.993736790E-02 2.693645280E-02 - 2.394180930E-02 2.095432950E-02 1.797491870E-02 1.500454820E-02 1.204419790E-02 - 9.094874370E-03 6.157614760E-03 3.233465600E-03 3.235077020E-04-2.571158340E-03 --5.449419380E-03-8.310146630E-03-1.115219670E-02-1.397442540E-02-1.677566580E-02 --1.955475100E-02-2.231051590E-02-2.504178140E-02-2.774737400E-02-3.042612410E-02 --3.307685630E-02-3.569839890E-02-3.828959170E-02-4.084928330E-02-4.337631910E-02 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7.672952120E-02 8.070866020E-02 8.469598000E-02 8.869069810E-02 9.269201010E-02 - 9.669937940E-02 1.007123070E-01 1.047306510E-01 1.087538970E-01 1.127826050E-01 - 1.168175270E-01 1.208599430E-01 1.249139310E-01 1.289771650E-01 1.330556120E-01 - 1.371650100E-01 1.413211380E-01 1.455397310E-01 1.498331130E-01 1.541363300E-01 - 1.584220980E-01 1.626855580E-01 1.669184570E-01 1.711142360E-01 1.752815250E-01 - 1.794181170E-01 1.835238780E-01 1.875986010E-01 1.916421350E-01 1.956544070E-01 - 1.996352820E-01 2.035844480E-01 2.075016650E-01 2.113867250E-01 2.152392420E-01 - 2.190590050E-01 2.228456590E-01 2.265988890E-01 2.303182780E-01 2.340034400E-01 - 2.376540010E-01 2.412695590E-01 2.448496670E-01 2.154365930E-01 2.132166480E-01 - 2.109782700E-01 2.087210710E-01 2.064448890E-01 2.041496340E-01 2.018351110E-01 - 1.995011720E-01 1.971477120E-01 1.947745830E-01 1.923816350E-01 1.899687050E-01 - 1.875357030E-01 1.850824510E-01 1.826088130E-01 1.801146270E-01 1.775997430E-01 - 1.750640270E-01 1.725072860E-01 1.699293400E-01 1.673300860E-01 1.647092250E-01 - 1.620666980E-01 1.594025190E-01 1.567164210E-01 1.540069130E-01 1.512740550E-01 - 1.485186370E-01 1.457414780E-01 1.429434420E-01 1.401280310E-01 1.372972280E-01 - 1.344517320E-01 1.315923630E-01 1.287200600E-01 1.258354340E-01 1.229392440E-01 - 1.200321840E-01 1.171148940E-01 1.141880230E-01 1.112522040E-01 1.083080020E-01 - 1.053559260E-01 1.023964360E-01 9.942999480E-02 9.645707910E-02 9.347808360E-02 - 9.049342570E-02 8.750349280E-02 8.450868730E-02 8.150938900E-02 7.850597800E-02 - 7.549885660E-02 7.248835270E-02 6.947483870E-02 6.645876910E-02 6.344057620E-02 - 6.042071060E-02 5.739961940E-02 5.437775330E-02 5.135573070E-02 4.833411430E-02 - 4.531348500E-02 4.229451340E-02 3.927787020E-02 3.626425940E-02 3.325443340E-02 - 3.024915420E-02 2.724927850E-02 2.425567990E-02 2.126922640E-02 1.829079170E-02 - 1.532136090E-02 1.236192980E-02 9.413490070E-03 6.477080750E-03 3.553740910E-03 - 6.445628820E-04-2.249376380E-03-5.126967560E-03-7.987068030E-03-1.082853970E-02 --1.365023670E-02-1.645101230E-02-1.922968780E-02-2.198509690E-02-2.471606810E-02 --2.742142600E-02-3.009999920E-02-3.275061770E-02-3.537210820E-02-3.796330470E-02 --4.052305590E-02-4.305021840E-02-4.554364090E-02-4.800219460E-02-5.042475460E-02 --5.281020700E-02-5.515745650E-02-5.746540430E-02-5.973297360E-02-6.195908410E-02 --6.414268910E-02-6.628274920E-02-6.837823990E-02-7.042811810E-02-7.243137810E-02 --7.438702880E-02-7.629409430E-02-7.815159860E-02-7.995858040E-02-8.171408620E-02 --8.341717720E-02-8.506693690E-02-8.666245640E-02-8.820283410E-02-8.968719840E-02 --9.111466260E-02-9.248436240E-02-9.379547830E-02-9.504717590E-02-9.623864290E-02 --9.736907480E-02-9.843770410E-02-9.944376350E-02-1.003865230E-01-1.012652670E-01 --1.020792800E-01-1.028278920E-01-1.035104620E-01-1.041263570E-01-1.046749500E-01 --1.051557140E-01-1.055680890E-01-1.059115310E-01-1.061855330E-01-1.063896720E-01 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1.154341730E-02 1.520614420E-02 1.889895650E-02 2.262026630E-02 2.636851560E-02 - 3.014217880E-02 3.393975650E-02 3.775978460E-02 4.160083830E-02 4.546151680E-02 - 4.934043810E-02 5.323635410E-02 5.714805420E-02 6.107431650E-02 6.501392280E-02 - 6.896582250E-02 7.292894270E-02 7.690232990E-02 8.088507500E-02 8.487626170E-02 - 8.887506280E-02 9.288073330E-02 9.689272940E-02 1.009105070E-01 1.049344910E-01 - 1.089643840E-01 1.129979790E-01 1.170382800E-01 1.210873720E-01 1.251473580E-01 - 1.292203070E-01 1.333086940E-01 1.374272850E-01 1.415923540E-01 1.458274570E-01 - 1.501249070E-01 1.544407900E-01 1.587359010E-01 1.630050090E-01 1.672428550E-01 - 1.714469340E-01 1.756223590E-01 1.797676830E-01 1.838825640E-01 1.879667640E-01 - 1.920201630E-01 1.960426570E-01 2.000341270E-01 2.039941700E-01 2.079226230E-01 - 2.118191720E-01 2.156835500E-01 2.195154430E-01 2.233144940E-01 2.270803300E-01 - 2.308125500E-01 2.345107940E-01 2.381746170E-01 2.418036010E-01 2.453972850E-01 - 2.157434370E-01 2.135211230E-01 2.112807180E-01 2.090217170E-01 2.067441050E-01 - 2.044476720E-01 2.021322250E-01 1.997975860E-01 1.974436190E-01 1.950701620E-01 - 1.926770810E-01 1.902641800E-01 1.878313420E-01 1.853784020E-01 1.829052270E-01 - 1.804116370E-01 1.778974680E-01 1.753625570E-01 1.728067700E-01 1.702298970E-01 - 1.676318050E-01 1.650121810E-01 1.623709950E-01 1.597092600E-01 1.570244280E-01 - 1.543160680E-01 1.515848340E-01 1.488314270E-01 1.460565480E-01 1.432608810E-01 - 1.404461120E-01 1.376166340E-01 1.347725390E-01 1.319146310E-01 1.290437880E-01 - 1.261606660E-01 1.232659590E-01 1.203603970E-01 1.174446340E-01 1.145193280E-01 - 1.115850430E-01 1.086424440E-01 1.056919920E-01 1.027341490E-01 9.976938370E-02 - 9.679813680E-02 9.382089230E-02 9.083806720E-02 8.784996720E-02 8.485703920E-02 - 8.185965570E-02 7.885821910E-02 7.585310940E-02 7.284465430E-02 6.983323400E-02 - 6.681931020E-02 6.380331520E-02 6.078568470E-02 5.776686590E-02 5.474730950E-02 - 5.172761530E-02 4.870834950E-02 4.569008570E-02 4.267350210E-02 3.965927660E-02 - 3.664808350E-02 3.364069390E-02 3.063783420E-02 2.764037250E-02 2.464918230E-02 - 2.166512980E-02 1.868910900E-02 1.572204570E-02 1.276495210E-02 9.818823080E-03 - 6.884695960E-03 3.963606430E-03 1.056637380E-03-1.835136790E-03-4.710611890E-03 --7.568642500E-03-1.040808760E-02-1.322780830E-02-1.602666450E-02-1.880349030E-02 --2.155710570E-02-2.428634460E-02-2.699003180E-02-2.966699560E-02-3.231606630E-02 --3.493608160E-02-3.752586990E-02-4.008427630E-02-4.261016470E-02-4.510238020E-02 --4.755978660E-02-4.998127000E-02-5.236571650E-02-5.471201990E-02-5.701909590E-02 --5.928585310E-02-6.151122600E-02-6.369415670E-02-6.583361330E-02-6.792855260E-02 --6.997795400E-02-7.198080420E-02-7.393610480E-02-7.584287970E-02-7.770017530E-02 --7.950702310E-02-8.126244690E-02-8.296550810E-02-8.461530510E-02-8.621093630E-02 --8.775148540E-02-8.923608060E-02-9.066384290E-02-9.203391520E-02-9.334545580E-02 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1.844088140E-01 1.885027290E-01 1.925663650E-01 1.965995130E-01 2.006019950E-01 - 2.045736010E-01 2.085140050E-01 2.124229370E-01 2.163000700E-01 2.201450620E-01 - 2.239575680E-01 2.277372180E-01 2.314835190E-01 2.351961280E-01 2.388745990E-01 - 2.425184400E-01 2.461272180E-01 2.160695050E-01 2.138457600E-01 2.116039540E-01 - 2.093439250E-01 2.070654930E-01 2.047684490E-01 2.024526150E-01 2.001177820E-01 - 1.977638010E-01 1.953905220E-01 1.929977690E-01 1.905853750E-01 1.881532070E-01 - 1.857010720E-01 1.832288350E-01 1.807363480E-01 1.782234010E-01 1.756898610E-01 - 1.731355490E-01 1.705603300E-01 1.679639820E-01 1.653463840E-01 1.627073290E-01 - 1.600471740E-01 1.573646370E-01 1.546588390E-01 1.519303470E-01 1.491797420E-01 - 1.464074850E-01 1.436142470E-01 1.408012960E-01 1.379740240E-01 1.351322980E-01 - 1.322766690E-01 1.294081210E-01 1.265272950E-01 1.236349270E-01 1.207317110E-01 - 1.178183330E-01 1.148954180E-01 1.119636220E-01 1.090234740E-01 1.060755330E-01 - 1.031202670E-01 1.001581330E-01 9.718959780E-02 9.421510250E-02 9.123504160E-02 - 8.824981000E-02 8.525980260E-02 8.226539940E-02 7.926700260E-02 7.626500730E-02 - 7.325974850E-02 7.025159150E-02 6.724097580E-02 6.422834100E-02 6.121411170E-02 - 5.819875370E-02 5.518276990E-02 5.216666310E-02 4.915101830E-02 4.613641280E-02 - 4.312352840E-02 4.011303190E-02 3.710560870E-02 3.410197050E-02 3.110291810E-02 - 2.810924870E-02 2.512183600E-02 2.214157020E-02 1.916934740E-02 1.620607260E-02 - 1.325274820E-02 1.031035740E-02 7.379938850E-03 4.462542010E-03 1.559216300E-03 --1.328944690E-03-4.200853410E-03-7.055370140E-03-9.891353550E-03-1.270766180E-02 --1.550315600E-02-1.827668960E-02-2.102706400E-02-2.375312520E-02-2.645369990E-02 --2.912762200E-02-3.177371990E-02-3.439083320E-02-3.697779030E-02-3.953344750E-02 --4.205665360E-02-4.454626520E-02-4.700113830E-02-4.942015560E-02-5.180221420E-02 --5.414620410E-02-5.645104130E-02-5.871563780E-02-6.093892460E-02-6.311985110E-02 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1.138959080E-01 1.179491580E-01 1.220120040E-01 1.260878000E-01 1.301799270E-01 - 1.342917380E-01 1.384274660E-01 1.426330510E-01 1.469031720E-01 1.512180270E-01 - 1.555541160E-01 1.598627870E-01 1.641416850E-01 1.683917340E-01 1.726128010E-01 - 1.768047360E-01 1.809674050E-01 1.851007490E-01 1.892045890E-01 1.932787600E-01 - 1.973230690E-01 2.013372480E-01 2.053210740E-01 2.092742320E-01 2.131964120E-01 - 2.170873140E-01 2.209464760E-01 2.247736160E-01 2.285682710E-01 2.323300540E-01 - 2.360584880E-01 2.397530230E-01 2.434132990E-01 2.470387670E-01 2.164137510E-01 - 2.141893060E-01 2.119470240E-01 2.096867110E-01 2.074081300E-01 2.051111010E-01 - 2.027954460E-01 2.004609850E-01 1.981075560E-01 1.957349630E-01 1.933430580E-01 - 1.909316930E-01 1.885006870E-01 1.860498790E-01 1.835791020E-01 1.810882090E-01 - 1.785770360E-01 1.760454030E-01 1.734931320E-01 1.709200740E-01 1.683260500E-01 - 1.657108660E-01 1.630743150E-01 1.604164090E-01 1.577372550E-01 1.550348250E-01 - 1.523097160E-01 1.495624480E-01 1.467934850E-01 1.440034060E-01 1.411936130E-01 - 1.383693520E-01 1.355305910E-01 1.326780320E-01 1.298125680E-01 1.269348710E-01 - 1.240456630E-01 1.211456430E-01 1.182354990E-01 1.153158690E-01 1.123874040E-01 - 1.094506460E-01 1.065061170E-01 1.035543610E-01 1.005958170E-01 9.763093290E-02 - 9.466015550E-02 9.168388690E-02 8.870252220E-02 8.571646360E-02 8.272611350E-02 - 7.973185180E-02 7.673403620E-02 7.373306160E-02 7.072932270E-02 6.772319230E-02 - 6.471508000E-02 6.170544400E-02 5.869476870E-02 5.568354950E-02 5.267228560E-02 - 4.966153950E-02 4.665189240E-02 4.364400360E-02 4.063854740E-02 3.763620180E-02 - 3.463765230E-02 3.164377060E-02 2.865527570E-02 2.567303550E-02 2.269794980E-02 - 1.973091070E-02 1.677282530E-02 1.382468640E-02 1.088745890E-02 7.962175640E-03 - 5.049891300E-03 2.151657130E-03-7.314611580E-04-3.598353130E-03-6.447906610E-03 --9.278979150E-03-1.209042970E-02-1.488111730E-02-1.764990390E-02-2.039560680E-02 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4.688694700E-02 5.076729130E-02 5.466531960E-02 5.857985840E-02 6.250975280E-02 - 6.645383690E-02 7.041119040E-02 7.438058410E-02 7.836119830E-02 8.235216890E-02 - 8.635264640E-02 9.036184850E-02 9.437908980E-02 9.840380400E-02 1.024356410E-01 - 1.064744000E-01 1.105204000E-01 1.145743500E-01 1.186345890E-01 1.227050650E-01 - 1.267902260E-01 1.308934690E-01 1.350180060E-01 1.391698420E-01 1.433953050E-01 - 1.476852450E-01 1.520151640E-01 1.563604920E-01 1.606726200E-01 1.649568680E-01 - 1.692131760E-01 1.734413800E-01 1.776413470E-01 1.818128970E-01 1.859558670E-01 - 1.900700480E-01 1.941552460E-01 1.982112530E-01 2.022378440E-01 2.062346640E-01 - 2.102014570E-01 2.141378670E-01 2.180435510E-01 2.219181210E-01 2.257611300E-01 - 2.295721620E-01 2.333507980E-01 2.370965480E-01 2.408089190E-01 2.444873300E-01 - 2.481312300E-01 2.167755220E-01 2.145512400E-01 2.123092410E-01 2.100493160E-01 - 2.077712570E-01 2.054748980E-01 2.031600480E-01 2.008265410E-01 1.984741990E-01 - 1.961028430E-01 1.937123390E-01 1.913025080E-01 1.888731870E-01 1.864242260E-01 - 1.839554610E-01 1.814667140E-01 1.789578200E-01 1.764286310E-01 1.738789830E-01 - 1.713086520E-01 1.687175330E-01 1.661053900E-01 1.634720120E-01 1.608172800E-01 - 1.581414040E-01 1.554433410E-01 1.527224330E-01 1.499791150E-01 1.472139360E-01 - 1.444274040E-01 1.416224690E-01 1.388020520E-01 1.359669720E-01 1.331181680E-01 - 1.302566530E-01 1.273828740E-01 1.244976520E-01 1.216016560E-01 1.186955870E-01 - 1.157801000E-01 1.128558440E-01 1.099233630E-01 1.069831920E-01 1.040358540E-01 - 1.010818260E-01 9.812156110E-02 9.515548500E-02 9.218400720E-02 8.920753000E-02 - 8.622645590E-02 8.324119450E-02 8.025211840E-02 7.725960760E-02 7.426403460E-02 - 7.126578690E-02 6.826526670E-02 6.526288390E-02 6.225905570E-02 5.925427380E-02 - 5.624903740E-02 5.324384200E-02 5.023924630E-02 4.723583530E-02 4.423423480E-02 - 4.123512280E-02 3.823917730E-02 3.524710980E-02 3.225969150E-02 2.927772890E-02 - 2.630205450E-02 2.333353830E-02 2.037307430E-02 1.742157710E-02 1.448001710E-02 - 1.154937600E-02 8.630658500E-03 5.724911110E-03 2.833188980E-03-4.344902120E-05 --2.903887300E-03-5.747031420E-03-8.571751420E-03-1.137690620E-02-1.416135670E-02 --1.692395840E-02-1.966354620E-02-2.237895690E-02-2.506902260E-02-2.773257720E-02 --3.036846410E-02-3.297551720E-02-3.555257620E-02-3.809849550E-02-4.061212390E-02 --4.309232160E-02-4.553796350E-02-4.794792460E-02-5.032109100E-02-5.265637110E-02 --5.495266240E-02-5.720887710E-02-5.942395330E-02-6.159684810E-02-6.372652200E-02 --6.581193210E-02-6.785205010E-02-6.984586270E-02-7.179238650E-02-7.369064540E-02 --7.553965600E-02-7.733844970E-02-7.908611000E-02-8.078166840E-02-8.242421600E-02 --8.401285860E-02-8.554670210E-02-8.702486010E-02-8.844643090E-02-8.981062470E-02 --9.111654010E-02-9.236337990E-02-9.355035420E-02-9.467667340E-02-9.574154020E-02 --9.674421700E-02-9.768394380E-02-9.856002780E-02-9.937178340E-02-1.001185330E-01 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2.230577770E-01 2.269180860E-01 2.307470440E-01 2.345442030E-01 2.383088320E-01 - 2.420406940E-01 2.457390870E-01 2.494033580E-01 2.171544280E-01 2.149311160E-01 - 2.126901300E-01 2.104312780E-01 2.081543800E-01 2.058592890E-01 2.035458390E-01 - 2.012138370E-01 1.988631340E-01 1.964935810E-01 1.941049990E-01 1.916972250E-01 - 1.892701390E-01 1.868235470E-01 1.843573000E-01 1.818712350E-01 1.793651880E-01 - 1.768390090E-01 1.742925050E-01 1.717255260E-01 1.691378950E-01 1.665294020E-01 - 1.638998990E-01 1.612491760E-01 1.585769500E-01 1.558830740E-01 1.531670990E-01 - 1.504289210E-01 1.476687340E-01 1.448870900E-01 1.420870420E-01 1.392711700E-01 - 1.364406050E-01 1.335965690E-01 1.307396740E-01 1.278706640E-01 1.249902320E-01 - 1.220991090E-01 1.191979800E-01 1.162875000E-01 1.133683100E-01 1.104409920E-01 - 1.075060810E-01 1.045640930E-01 1.016155260E-01 9.866081180E-02 9.570039810E-02 - 9.273470190E-02 8.976412560E-02 8.678906410E-02 8.380992710E-02 8.082709460E-02 - 7.784096150E-02 7.485190030E-02 7.186027620E-02 6.886650620E-02 6.587099280E-02 - 6.287416820E-02 5.987648290E-02 5.687843640E-02 5.388052760E-02 5.088333040E-02 - 4.788742960E-02 4.489341380E-02 4.190194230E-02 3.891369700E-02 3.592940790E-02 - 3.294980900E-02 2.997572530E-02 2.700798770E-02 2.404742320E-02 2.109491080E-02 - 1.815139870E-02 1.521782670E-02 1.229517910E-02 9.384452370E-03 6.486674310E-03 - 3.602891460E-03 7.341804450E-04-2.118379110E-03-4.953688940E-03-7.770622150E-03 --1.056804320E-02-1.334481970E-02-1.609980500E-02-1.883184910E-02-2.153978310E-02 --2.422244660E-02-2.687868290E-02-2.950733340E-02-3.210723400E-02-3.467723350E-02 --3.721618280E-02-3.972293060E-02-4.219634460E-02-4.463529210E-02-4.703864830E-02 --4.940531400E-02-5.173418670E-02-5.402417480E-02-5.627419050E-02-5.848317220E-02 --6.065007300E-02-6.277385350E-02-6.485346700E-02-6.688787790E-02-6.887610260E-02 --7.081713530E-02-7.271000000E-02-7.455373560E-02-7.634736600E-02-7.808995990E-02 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1.967381980E-01 2.008886490E-01 2.050149290E-01 2.091166680E-01 2.131935660E-01 - 2.172451620E-01 2.212710230E-01 2.252707180E-01 2.292437260E-01 2.331894490E-01 - 2.371073370E-01 2.409967930E-01 2.448572070E-01 2.486876990E-01 2.524876890E-01 - 2.562564610E-01 2.188402410E-01 2.166265400E-01 2.143952850E-01 2.121463270E-01 - 2.098795620E-01 2.075948860E-01 2.052921800E-01 2.029713390E-01 2.006322440E-01 - 1.982747760E-01 1.958988160E-01 1.935042590E-01 1.910909860E-01 1.886588480E-01 - 1.862077410E-01 1.837375310E-01 1.812480690E-01 1.787392200E-01 1.762108500E-01 - 1.736628120E-01 1.710949390E-01 1.685070840E-01 1.658990830E-01 1.632707570E-01 - 1.606219260E-01 1.579523830E-01 1.552620680E-01 1.525503990E-01 1.498173330E-01 - 1.470637020E-01 1.442901490E-01 1.414993110E-01 1.386947480E-01 1.358768490E-01 - 1.330463890E-01 1.302041860E-01 1.273510750E-01 1.244876530E-01 1.216145830E-01 - 1.187326240E-01 1.158424020E-01 1.129445060E-01 1.100395170E-01 1.071280170E-01 - 1.042104880E-01 1.012874020E-01 9.835921970E-02 9.542636570E-02 9.248927240E-02 - 8.954834190E-02 8.660399170E-02 8.365661650E-02 8.070659640E-02 7.775432620E-02 - 7.480019330E-02 7.184457030E-02 6.888787450E-02 6.593052300E-02 6.297297030E-02 - 6.001565610E-02 5.705908310E-02 5.410375820E-02 5.115022510E-02 4.819906130E-02 - 4.525093360E-02 4.230649770E-02 3.936642780E-02 3.643138710E-02 3.350209440E-02 - 3.057947200E-02 2.766422550E-02 2.475724740E-02 2.185943910E-02 1.897169460E-02 - 1.609491930E-02 1.323010870E-02 1.037824990E-02 7.540325170E-03 4.717397970E-03 - 1.910531660E-03-8.792104200E-04-3.650764700E-03-6.403037810E-03-9.134883990E-03 --1.184520400E-02-1.453286040E-02-1.719672050E-02-1.983566400E-02-2.244851740E-02 --2.503415380E-02-2.759143150E-02-3.011921610E-02-3.261636940E-02-3.508175540E-02 --3.751424700E-02-3.991273420E-02-4.227609930E-02-4.460323600E-02-4.689305650E-02 --4.914447290E-02-5.135641250E-02-5.352782460E-02-5.565765130E-02-5.774484200E-02 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1.258095950E-01 1.299407180E-01 1.340953860E-01 1.382896010E-01 1.425442840E-01 - 1.468649510E-01 1.512511070E-01 1.556498410E-01 1.600311990E-01 1.643933060E-01 - 1.687338200E-01 1.730516250E-01 1.773489560E-01 1.816249340E-01 1.858793800E-01 - 1.901121440E-01 1.943228840E-01 1.985114220E-01 2.026774730E-01 2.068206970E-01 - 2.109407630E-01 2.150372710E-01 2.191098480E-01 2.231579870E-01 2.271812260E-01 - 2.311790440E-01 2.351508590E-01 2.390961050E-01 2.430140670E-01 2.469041050E-01 - 2.507654730E-01 2.545974250E-01 2.583991290E-01 2.193043830E-01 2.170942130E-01 - 2.148664740E-01 2.126210480E-01 2.103578600E-01 2.080768350E-01 2.057778540E-01 - 2.034608270E-01 2.011256660E-01 1.987722520E-01 1.964004930E-01 1.940103020E-01 - 1.916015300E-01 1.891741160E-01 1.867279110E-01 1.842628120E-01 1.817786840E-01 - 1.792753930E-01 1.767528210E-01 1.742108170E-01 1.716492470E-01 1.690679340E-01 - 1.664667430E-01 1.638454940E-01 1.612039950E-01 1.585420970E-01 1.558597240E-01 - 1.531562360E-01 1.504316780E-01 1.476868990E-01 1.449224050E-01 1.421400760E-01 - 1.393436490E-01 1.365340950E-01 1.337121730E-01 1.308786570E-01 1.280342790E-01 - 1.251798270E-01 1.223158240E-01 1.194430890E-01 1.165622320E-01 1.136738430E-01 - 1.107785250E-01 1.078768750E-01 1.049693900E-01 1.020565180E-01 9.913872930E-02 - 9.621647750E-02 9.329017250E-02 9.036025400E-02 8.742710950E-02 8.449114110E-02 - 8.155274390E-02 7.861231270E-02 7.567022740E-02 7.272689790E-02 6.978268180E-02 - 6.683801860E-02 6.389334800E-02 6.094913930E-02 5.800584700E-02 5.506397780E-02 - 5.212407930E-02 4.918675500E-02 4.625260080E-02 4.332225770E-02 4.039639230E-02 - 3.747568280E-02 3.456091510E-02 3.165284540E-02 2.875227670E-02 2.586003390E-02 - 2.297700940E-02 2.010410090E-02 1.724223050E-02 1.439233400E-02 1.155539600E-02 - 8.732420390E-03 5.924432540E-03 3.132472050E-03 3.575999580E-04-2.399114190E-03 --5.136571820E-03-7.853677500E-03-1.054932270E-02-1.322238610E-02-1.587173340E-02 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5.942838270E-02 6.330665950E-02 6.720401350E-02 7.111950220E-02 7.505219430E-02 - 7.900124040E-02 8.296584340E-02 8.694521340E-02 9.093863520E-02 9.494557980E-02 - 9.896558520E-02 1.029983310E-01 1.070437730E-01 1.111021410E-01 1.151740480E-01 - 1.192603930E-01 1.233630930E-01 1.274857220E-01 1.316248330E-01 1.357948780E-01 - 1.400246620E-01 1.443149300E-01 1.486664560E-01 1.530721490E-01 1.574734000E-01 - 1.618575750E-01 1.662227060E-01 1.705667080E-01 1.748909650E-01 1.791962530E-01 - 1.834815590E-01 1.877467330E-01 1.919916120E-01 1.962160170E-01 2.004196640E-01 - 2.046022560E-01 2.087635250E-01 2.129031120E-01 2.170206010E-01 2.211156040E-01 - 2.251876290E-01 2.292362750E-01 2.332609150E-01 2.372609820E-01 2.412358370E-01 - 2.451848390E-01 2.491072120E-01 2.530021970E-01 2.568690780E-01 2.607068720E-01 - 2.197858840E-01 2.175794990E-01 2.153555450E-01 2.131139490E-01 2.108546200E-01 - 2.085775140E-01 2.062825410E-01 2.039695980E-01 2.016386540E-01 1.992896050E-01 - 1.969223770E-01 1.945368650E-01 1.921329800E-01 1.897106470E-01 1.872697170E-01 - 1.848101170E-01 1.823317260E-01 1.798344400E-01 1.773180960E-01 1.747826190E-01 - 1.722278300E-01 1.696535940E-01 1.670597640E-01 1.644461750E-01 1.618126630E-01 - 1.591590490E-01 1.564853790E-01 1.537912790E-01 1.510760340E-01 1.483400910E-01 - 1.455850450E-01 1.428124310E-01 1.400246620E-01 1.372241530E-01 1.344114690E-01 - 1.315873710E-01 1.287525890E-01 1.259078230E-01 1.230537370E-01 1.201910300E-01 - 1.173203510E-01 1.144423410E-01 1.115575510E-01 1.086666360E-01 1.057700740E-01 - 1.028683260E-01 9.996185450E-02 9.705112130E-02 9.413657340E-02 9.121862800E-02 - 8.829768000E-02 8.537412430E-02 8.244837820E-02 7.952081410E-02 7.659182700E-02 - 7.366181160E-02 7.073117050E-02 6.780029830E-02 6.486963480E-02 6.193963440E-02 - 5.901076640E-02 5.608353390E-02 5.315845830E-02 5.023613940E-02 4.731717330E-02 - 4.440216350E-02 4.149175060E-02 3.858667240E-02 3.568764400E-02 3.279543670E-02 - 2.991082520E-02 2.703463660E-02 2.416772580E-02 2.131098510E-02 1.846533830E-02 - 1.563170920E-02 1.281105450E-02 1.000437420E-02 7.212688680E-03 4.437011200E-03 - 1.678386470E-03-1.062098310E-03-3.783381540E-03-6.484364630E-03-9.163953360E-03 --1.182103340E-02-1.445448210E-02-1.706317810E-02-1.964600010E-02-2.220182120E-02 --2.472951080E-02-2.722793260E-02-2.969595420E-02-3.213247280E-02-3.453636540E-02 --3.690651800E-02-3.924183170E-02-4.154120760E-02-4.380355780E-02-4.602780940E-02 --4.821288210E-02-5.035772170E-02-5.246129630E-02-5.452256650E-02-5.654050040E-02 --5.851408840E-02-6.044235080E-02-6.232427060E-02-6.415889410E-02-6.594526770E-02 --6.768243010E-02-6.936945770E-02-7.100543380E-02-7.258943470E-02-7.412058860E-02 --7.559800890E-02-7.702083890E-02-7.838822900E-02-7.969935240E-02-8.095338200E-02 --8.214952050E-02-8.328698580E-02-8.436501770E-02-8.538287130E-02-8.633980900E-02 --8.723510060E-02-8.806807550E-02-8.883806320E-02-8.954440800E-02-9.018648420E-02 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2.395143060E-01 2.435212580E-01 2.475037870E-01 2.514612670E-01 2.553929690E-01 - 2.592979670E-01 2.631753390E-01 2.202848490E-01 2.180824880E-01 2.158624980E-01 - 2.136249100E-01 2.113696490E-01 2.090966700E-01 2.068059000E-01 2.044973080E-01 - 2.021708040E-01 1.998263450E-01 1.974638700E-01 1.950833200E-01 1.926846060E-01 - 1.902676220E-01 1.878323260E-01 1.853785810E-01 1.829062850E-01 1.804153770E-01 - 1.779057230E-01 1.753771900E-01 1.728296580E-01 1.702629920E-01 1.676770450E-01 - 1.650716960E-01 1.624467520E-01 1.598019900E-01 1.571379300E-01 1.544542160E-01 - 1.517484190E-01 1.490221620E-01 1.462770400E-01 1.435146030E-01 1.407365500E-01 - 1.379458310E-01 1.351431310E-01 1.323291810E-01 1.295047250E-01 1.266704650E-01 - 1.238270630E-01 1.209752040E-01 1.181155440E-01 1.152487320E-01 1.123753340E-01 - 1.094960050E-01 1.066112670E-01 1.037215590E-01 1.008273440E-01 9.792906050E-02 - 9.502717110E-02 9.212212260E-02 8.921438460E-02 8.630422500E-02 8.339211340E-02 - 8.047842980E-02 7.756357640E-02 7.464794810E-02 7.173193250E-02 6.881591680E-02 - 6.590036300E-02 6.298570330E-02 6.007239600E-02 5.716094370E-02 5.425186460E-02 - 5.134572460E-02 4.844311620E-02 4.554464670E-02 4.265094920E-02 3.976270560E-02 - 3.688066830E-02 3.400559720E-02 3.113825060E-02 2.827936410E-02 2.542987090E-02 - 2.259061670E-02 1.976251040E-02 1.694647410E-02 1.414344270E-02 1.135440260E-02 - 8.580353110E-03 5.822310220E-03 3.081317060E-03 3.584172810E-04-2.345331710E-03 --5.028839220E-03-7.691011300E-03-1.033074780E-02-1.294694190E-02-1.553848010E-02 --1.810424590E-02-2.064310950E-02-2.315395140E-02-2.563565780E-02-2.808710560E-02 --3.050718080E-02-3.289477150E-02-3.524877500E-02-3.756808860E-02-3.985162080E-02 --4.209828750E-02-4.430701580E-02-4.647673670E-02-4.860639570E-02-5.069496110E-02 --5.274140090E-02-5.474469070E-02-5.670381340E-02-5.861777440E-02-6.048558280E-02 --6.230629240E-02-6.407894940E-02-6.580260400E-02-6.747630240E-02-6.909913570E-02 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1.702485530E-01 1.746032240E-01 1.789415780E-01 1.832631530E-01 1.875677560E-01 - 1.918556390E-01 1.961265650E-01 2.003803550E-01 2.046166660E-01 2.088352890E-01 - 2.130360160E-01 2.172184140E-01 2.213821410E-01 2.255267950E-01 2.296518240E-01 - 2.337567660E-01 2.378413680E-01 2.419047800E-01 2.459463180E-01 2.499652060E-01 - 2.539606690E-01 2.579323650E-01 2.618789670E-01 2.657994630E-01 2.208015920E-01 - 2.186033130E-01 2.163874360E-01 2.141539310E-01 2.119028270E-01 2.096340660E-01 - 2.073476170E-01 2.050434800E-01 2.027215810E-01 2.003818750E-01 1.980243770E-01 - 1.956489830E-01 1.932556180E-01 1.908442530E-01 1.884148420E-01 1.859672670E-01 - 1.835014370E-01 1.810172500E-01 1.785146300E-01 1.759934720E-01 1.734536290E-01 - 1.708949950E-01 1.683174370E-01 1.657208200E-01 1.631050410E-01 1.604699940E-01 - 1.578154710E-01 1.551412340E-01 1.524469110E-01 1.497318450E-01 1.469975410E-01 - 1.442455950E-01 1.414779720E-01 1.386977880E-01 1.359057580E-01 1.331027150E-01 - 1.302893610E-01 1.274663950E-01 1.246344670E-01 1.217942680E-01 1.189464630E-01 - 1.160916910E-01 1.132305790E-01 1.103636770E-01 1.074916050E-01 1.046148020E-01 - 1.017337290E-01 9.884882720E-02 9.596056490E-02 9.306938950E-02 9.017575530E-02 - 8.727998290E-02 8.438248930E-02 8.148369940E-02 7.858400050E-02 7.568378000E-02 - 7.278344780E-02 6.988337640E-02 6.698399780E-02 6.408575920E-02 6.118911880E-02 - 5.829457570E-02 5.540264030E-02 5.251384150E-02 4.962877560E-02 4.674805330E-02 - 4.387224470E-02 4.100205000E-02 3.813822570E-02 3.528152030E-02 3.243267540E-02 - 2.959243950E-02 2.676161380E-02 2.394113320E-02 2.113186380E-02 1.833472770E-02 - 1.555063760E-02 1.278056200E-02 1.002547700E-02 7.286392150E-03 4.564343950E-03 - 1.860374000E-03-8.244771160E-04-3.489161610E-03-6.132562180E-03-8.753607050E-03 --1.135119890E-02-1.392422800E-02-1.647157590E-02-1.899213720E-02-2.148480900E-02 --2.394847010E-02-2.638201420E-02-2.878432910E-02-3.115430470E-02-3.349084780E-02 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1.006074250E-01 1.046258660E-01 1.086606760E-01 1.127108710E-01 1.167780980E-01 - 1.208646450E-01 1.249728200E-01 1.291030940E-01 1.332389410E-01 1.374423210E-01 - 1.417108630E-01 1.460395160E-01 1.504173580E-01 1.548344940E-01 1.592701670E-01 - 1.636737140E-01 1.680609290E-01 1.724345240E-01 1.767940670E-01 1.811391120E-01 - 1.854691800E-01 1.897840200E-01 1.940839590E-01 1.983687280E-01 2.026381640E-01 - 2.068920280E-01 2.111300980E-01 2.153521330E-01 2.195577770E-01 2.237466720E-01 - 2.279185210E-01 2.320727850E-01 2.362089010E-01 2.403264340E-01 2.444249390E-01 - 2.485035210E-01 2.525616590E-01 2.565985920E-01 2.606133820E-01 2.646050160E-01 - 2.685726580E-01 2.213363200E-01 2.191420940E-01 2.169302700E-01 2.147008780E-01 - 2.124539020E-01 2.101893720E-01 2.079072740E-01 2.056075930E-01 2.032903580E-01 - 2.009555100E-01 1.986030640E-01 1.962329750E-01 1.938451680E-01 1.914396440E-01 - 1.890163420E-01 1.865751590E-01 1.841160210E-01 1.816388960E-01 1.791436820E-01 - 1.766302590E-01 1.740985070E-01 1.715483370E-01 1.689796150E-01 1.663921920E-01 - 1.637859790E-01 1.611606780E-01 1.585161980E-01 1.558524520E-01 1.531693340E-01 - 1.504667700E-01 1.477444170E-01 1.450038550E-01 1.422475430E-01 1.394786830E-01 - 1.366980670E-01 1.339065730E-01 1.311050650E-01 1.282942150E-01 1.254745420E-01 - 1.226468160E-01 1.198116840E-01 1.169698010E-01 1.141217870E-01 1.112682070E-01 - 1.084096580E-01 1.055466310E-01 1.026795950E-01 9.980899840E-02 9.693529460E-02 - 9.405893090E-02 9.118034690E-02 8.829990030E-02 8.541801570E-02 8.253509550E-02 - 7.965154200E-02 7.676775010E-02 7.388410720E-02 7.100101560E-02 6.811890010E-02 - 6.523816290E-02 6.235926970E-02 5.948272720E-02 5.660904570E-02 5.373875050E-02 - 5.087235570E-02 4.801054670E-02 4.515385260E-02 4.230293630E-02 3.945853190E-02 - 3.662139550E-02 3.379226100E-02 3.097187910E-02 2.816099670E-02 2.536057310E-02 - 2.257143150E-02 1.979447530E-02 1.703061350E-02 1.428079510E-02 1.154600360E-02 - 8.827192710E-03 6.125402640E-03 3.441671140E-03 7.770368250E-04-1.867461950E-03 --4.490793220E-03-7.091816050E-03-9.669459420E-03-1.222263280E-02-1.475023660E-02 --1.725117680E-02-1.972435230E-02-2.216866610E-02-2.458299700E-02-2.696624400E-02 --2.931730260E-02-3.163508700E-02-3.391851480E-02-3.616650030E-02-3.837796670E-02 --4.055185620E-02-4.268710320E-02-4.478266840E-02-4.683751240E-02-4.885060710E-02 --5.082094670E-02-5.274753270E-02-5.462937060E-02-5.646548420E-02-5.825490880E-02 --5.999669060E-02-6.168989090E-02-6.333360080E-02-6.492690000E-02-6.646888700E-02 --6.795870510E-02-6.939546020E-02-7.077832520E-02-7.210645080E-02-7.337901740E-02 --7.459522780E-02-7.575429230E-02-7.685544340E-02-7.789792870E-02-7.888101790E-02 --7.980399580E-02-8.066614720E-02-8.146681640E-02-8.220533280E-02-8.288106320E-02 --8.349339660E-02-8.404172210E-02-8.452546600E-02-8.494410660E-02-8.529712260E-02 --8.558399230E-02-8.580422400E-02-8.595736320E-02-8.604300020E-02-8.606074010E-02 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3.744959090E-02 4.109594970E-02 4.477154090E-02 4.847520590E-02 5.220578240E-02 - 5.596223470E-02 5.974350120E-02 6.354857240E-02 6.737651680E-02 7.122647020E-02 - 7.509757580E-02 7.898876070E-02 8.289955560E-02 8.682934190E-02 9.077745680E-02 - 9.474321450E-02 9.872625020E-02 1.027262810E-01 1.067433800E-01 1.107777130E-01 - 1.148294430E-01 1.188997550E-01 1.229909210E-01 1.271051020E-01 1.312428410E-01 - 1.353969130E-01 1.396384980E-01 1.439487930E-01 1.483066380E-01 1.527020930E-01 - 1.571252500E-01 1.615534420E-01 1.659577790E-01 1.703484950E-01 1.747256820E-01 - 1.790906940E-01 1.834425180E-01 1.877806930E-01 1.921060980E-01 1.964184340E-01 - 2.007175240E-01 2.050032320E-01 2.092754100E-01 2.135337000E-01 2.177780420E-01 - 2.220081390E-01 2.262235130E-01 2.304240170E-01 2.346090970E-01 2.387783080E-01 - 2.429310830E-01 2.470669750E-01 2.511853870E-01 2.552856500E-01 2.593669000E-01 - 2.634282710E-01 2.674688700E-01 2.714877720E-01 2.218892280E-01 2.196989060E-01 - 2.174909710E-01 2.152655270E-01 2.130225900E-01 2.107621880E-01 2.084843520E-01 - 2.061891110E-01 2.038765100E-01 2.015465350E-01 1.991991700E-01 1.968344150E-01 - 1.944522710E-01 1.920526920E-01 1.896356340E-01 1.872010830E-01 1.847489480E-01 - 1.822791400E-01 1.797915850E-01 1.772862230E-01 1.747629640E-01 1.722216610E-01 - 1.696621920E-01 1.670844700E-01 1.644883600E-01 1.618735790E-01 1.592400220E-01 - 1.565876450E-01 1.539163740E-01 1.512261180E-01 1.485167000E-01 1.457880740E-01 - 1.430438010E-01 1.402869820E-01 1.375185100E-01 1.347393690E-01 1.319504830E-01 - 1.291524020E-01 1.263458130E-01 1.235313640E-01 1.207097250E-01 1.178815510E-01 - 1.150474770E-01 1.122080830E-01 1.093639280E-01 1.065155570E-01 1.036634450E-01 - 1.008080320E-01 9.794978050E-02 9.508915990E-02 9.222656490E-02 8.936239780E-02 - 8.649708330E-02 8.363101630E-02 8.076459910E-02 7.789822670E-02 7.503229380E-02 - 7.216719540E-02 6.930340080E-02 6.644122300E-02 6.358114630E-02 6.072368470E-02 - 5.786935240E-02 5.501866340E-02 5.217213180E-02 4.933031280E-02 4.649385810E-02 - 4.366340860E-02 4.083964970E-02 3.802328560E-02 3.521505740E-02 3.241571780E-02 - 2.962604720E-02 2.684687640E-02 2.407909930E-02 2.132359890E-02 1.858124880E-02 - 1.585297100E-02 1.313973960E-02 1.044252330E-02 7.762309630E-03 5.100115200E-03 - 2.456977030E-03-1.660652920E-04-2.767959840E-03-5.347639790E-03-7.904024790E-03 --1.043604500E-02-1.294262060E-02-1.542265250E-02-1.787504370E-02-2.029869520E-02 --2.269250900E-02-2.505537870E-02-2.738624070E-02-2.968399790E-02-3.194757180E-02 --3.417588400E-02-3.636786340E-02-3.852245580E-02-4.063861070E-02-4.271528120E-02 --4.475144300E-02-4.674607140E-02-4.869816450E-02-5.060672390E-02-5.247073620E-02 --5.428926270E-02-5.606133120E-02-5.778599160E-02-5.946232010E-02-6.108938900E-02 --6.266628950E-02-6.419214610E-02-6.566607210E-02-6.708721070E-02-6.845470520E-02 --6.976772100E-02-7.102546100E-02-7.222713530E-02-7.337193940E-02-7.445911320E-02 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2.160379590E-01 2.203055020E-01 2.245610360E-01 2.288042750E-01 2.330348490E-01 - 2.372525040E-01 2.414566870E-01 2.456468790E-01 2.498224970E-01 2.539832590E-01 - 2.581283450E-01 2.622569800E-01 2.663683590E-01 2.704616790E-01 2.745358650E-01 - 2.224605080E-01 2.202738520E-01 2.180695980E-01 2.158478500E-01 2.136086520E-01 - 2.113521100E-01 2.090783270E-01 2.067873330E-01 2.044792030E-01 2.021539660E-01 - 1.998116370E-01 1.974522320E-01 1.950757800E-01 1.926822220E-01 1.902715860E-01 - 1.878438000E-01 1.853988170E-01 1.829365640E-01 1.804569960E-01 1.779600230E-01 - 1.754455570E-01 1.729135070E-01 1.703637240E-01 1.677961500E-01 1.652107540E-01 - 1.626071480E-01 1.599851550E-01 1.573446840E-01 1.546856760E-01 1.520079370E-01 - 1.493116620E-01 1.465974150E-01 1.438655700E-01 1.411212380E-01 1.383655670E-01 - 1.355995540E-01 1.328239590E-01 1.300394540E-01 1.272466930E-01 1.244463250E-01 - 1.216389830E-01 1.188253610E-01 1.160060610E-01 1.131816880E-01 1.103528140E-01 - 1.075199620E-01 1.046836450E-01 1.018443180E-01 9.900242840E-02 9.615845230E-02 - 9.331278500E-02 9.046584370E-02 8.761803810E-02 8.476977800E-02 8.192146570E-02 - 7.907349620E-02 7.622627170E-02 7.338019460E-02 7.053567470E-02 6.769311430E-02 - 6.485292320E-02 6.201561540E-02 5.918170140E-02 5.635168780E-02 5.352609230E-02 - 5.070542540E-02 4.789033900E-02 4.508147390E-02 4.227949310E-02 3.948509320E-02 - 3.669897090E-02 3.392189740E-02 3.115462330E-02 2.839796250E-02 2.565278490E-02 - 2.291995850E-02 2.020034750E-02 1.749485360E-02 1.480443310E-02 1.213005740E-02 - 9.472696110E-03 6.833329800E-03 4.212993200E-03 1.612708320E-03-9.664889660E-04 --3.523549760E-03-6.057404450E-03-8.566993290E-03-1.105124320E-02-1.350907050E-02 --1.593938100E-02-1.834107380E-02-2.071307790E-02-2.305432600E-02-2.536372470E-02 --2.764019560E-02-2.988266390E-02-3.209005670E-02-3.426131980E-02-3.639540080E-02 --3.849124540E-02-4.054782540E-02-4.256410900E-02-4.453908280E-02-4.647175220E-02 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1.443811060E-01 1.487458050E-01 1.531580240E-01 1.575916260E-01 1.620119360E-01 - 1.664218160E-01 1.708220390E-01 1.752136050E-01 1.795962900E-01 1.839698110E-01 - 1.883344050E-01 1.926900300E-01 1.970366980E-01 2.013743970E-01 2.057030650E-01 - 2.100226130E-01 2.143330280E-01 2.186340690E-01 2.229256930E-01 2.272076010E-01 - 2.314795110E-01 2.357413620E-01 2.399928270E-01 2.442335190E-01 2.484630200E-01 - 2.526809280E-01 2.568865120E-01 2.610792220E-01 2.652584310E-01 2.694232460E-01 - 2.735730110E-01 2.777068020E-01 2.230508770E-01 2.208671570E-01 2.186660470E-01 - 2.164474730E-01 2.142115830E-01 2.119585280E-01 2.096884100E-01 2.074013950E-01 - 2.050975110E-01 2.027768190E-01 2.004393640E-01 1.980852040E-01 1.957143840E-01 - 1.933268760E-01 1.909226920E-01 1.885017750E-01 1.860641090E-01 1.836096640E-01 - 1.811383070E-01 1.786499920E-01 1.761447040E-01 1.736222650E-01 1.710825560E-01 - 1.685254870E-01 1.659511030E-01 1.633593290E-01 1.607495700E-01 1.581213180E-01 - 1.554747520E-01 1.528102010E-01 1.501279770E-01 1.474284230E-01 1.447118370E-01 - 1.419795450E-01 1.392373890E-01 1.364852790E-01 1.337238400E-01 1.309537140E-01 - 1.281755720E-01 1.253900680E-01 1.225978510E-01 1.197996070E-01 1.169959310E-01 - 1.141874120E-01 1.113746460E-01 1.085582000E-01 1.057385580E-01 1.029161890E-01 - 1.000915620E-01 9.726513180E-02 9.443730860E-02 9.160850940E-02 8.877915140E-02 - 8.594964440E-02 8.312039820E-02 8.029180020E-02 7.746425270E-02 7.463816550E-02 - 7.181393360E-02 6.899199630E-02 6.617273390E-02 6.335662310E-02 6.054417420E-02 - 5.773589020E-02 5.493227390E-02 5.213386570E-02 4.934127260E-02 4.655511680E-02 - 4.377604280E-02 4.100473230E-02 3.824188560E-02 3.548822550E-02 3.274452310E-02 - 3.001156820E-02 2.729019150E-02 2.458123490E-02 2.188557010E-02 1.920409130E-02 - 1.653772410E-02 1.388741750E-02 1.125414860E-02 8.638887670E-03 6.042602940E-03 - 3.466309280E-03 9.110560640E-04-1.622124690E-03-4.132184200E-03-6.618063430E-03 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7.836795600E-02 8.221064510E-02 8.607552950E-02 8.996207270E-02 9.386974570E-02 - 9.779817610E-02 1.017473490E-01 1.057166160E-01 1.097058730E-01 1.137164910E-01 - 1.177492810E-01 1.218052280E-01 1.258874240E-01 1.299965830E-01 1.341419070E-01 - 1.383345130E-01 1.425867230E-01 1.469189080E-01 1.513150190E-01 1.557397990E-01 - 1.601615850E-01 1.645761730E-01 1.689827740E-01 1.733819100E-01 1.777738780E-01 - 1.821584850E-01 1.865362970E-01 1.909071510E-01 1.952711490E-01 1.996283830E-01 - 2.039788510E-01 2.083224510E-01 2.126592840E-01 2.169892490E-01 2.213123290E-01 - 2.256285100E-01 2.299375680E-01 2.342393250E-01 2.385337200E-01 2.428203370E-01 - 2.470989230E-01 2.513692980E-01 2.556310300E-01 2.598836720E-01 2.641266880E-01 - 2.683591250E-01 2.725811900E-01 2.767911550E-01 2.809885140E-01 2.236598580E-01 - 2.214786710E-01 2.192799900E-01 2.170638740E-01 2.148306820E-01 2.125805320E-01 - 2.103136480E-01 2.080301200E-01 2.057300960E-01 2.034136950E-01 2.010809480E-01 - 1.987319140E-01 1.963666230E-01 1.939851490E-01 1.915874330E-01 1.891734750E-01 - 1.867432740E-01 1.842967570E-01 1.818338630E-01 1.793545340E-01 1.768586930E-01 - 1.743462380E-01 1.718170340E-01 1.692709770E-01 1.667080070E-01 1.641281690E-01 - 1.615315380E-01 1.589166970E-01 1.562837210E-01 1.536330130E-01 1.509649600E-01 - 1.482799350E-01 1.455783400E-01 1.428605620E-01 1.401325460E-01 1.373950540E-01 - 1.346484270E-01 1.318934110E-01 1.291306910E-01 1.263608630E-01 1.235846130E-01 - 1.208025520E-01 1.180153270E-01 1.152235200E-01 1.124277340E-01 1.096285510E-01 - 1.068264540E-01 1.040219290E-01 1.012154450E-01 9.840744730E-02 9.559836980E-02 - 9.278863670E-02 8.997865020E-02 8.716883510E-02 8.435957880E-02 8.155129850E-02 - 7.874439660E-02 7.593926790E-02 7.313632220E-02 7.033596190E-02 6.753861900E-02 - 6.474474070E-02 6.195479260E-02 5.916927750E-02 5.638870600E-02 5.361361430E-02 - 5.084459110E-02 4.808224740E-02 4.532719030E-02 4.258007180E-02 3.984160350E-02 - 3.711249310E-02 3.439348560E-02 3.168537470E-02 2.898896490E-02 2.630506270E-02 - 2.363456790E-02 2.097832230E-02 1.833719390E-02 1.571214940E-02 1.310416030E-02 - 1.051419410E-02 7.943220440E-03 5.392206370E-03 2.862119810E-03 3.540614850E-04 --2.130960580E-03-4.591895730E-03-7.027687970E-03-9.437293750E-03-1.181966160E-02 --1.417373210E-02-1.649842780E-02-1.879268700E-02-2.105544320E-02-2.328564230E-02 --2.548222060E-02-2.764413320E-02-2.977033150E-02-3.185977790E-02-3.391144420E-02 --3.592428940E-02-3.789731120E-02-3.982951490E-02-4.171989860E-02-4.356747870E-02 --4.537128280E-02-4.713034630E-02-4.884373770E-02-5.051052200E-02-5.212977160E-02 --5.370058120E-02-5.522205310E-02-5.669332300E-02-5.811353400E-02-5.948182940E-02 --6.079736720E-02-6.205933540E-02-6.326694040E-02-6.441939620E-02-6.551593540E-02 --6.655582040E-02-6.753830610E-02-6.846269220E-02-6.932826340E-02-7.013434920E-02 --7.088030130E-02-7.156549390E-02-7.218929380E-02-7.275109740E-02-7.325033840E-02 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2.007662130E-02 2.339056130E-02 2.674339530E-02 3.013387690E-02 3.356082740E-02 - 3.702315320E-02 4.051972180E-02 4.404941950E-02 4.761112850E-02 5.120384690E-02 - 5.482659860E-02 5.847837780E-02 6.215821580E-02 6.586528570E-02 6.959875670E-02 - 7.335779820E-02 7.714165000E-02 8.094966410E-02 8.478116240E-02 8.863554890E-02 - 9.251234680E-02 9.641110150E-02 1.003320220E-01 1.042738930E-01 1.082369760E-01 - 1.122224550E-01 1.162315230E-01 1.202641730E-01 1.243213270E-01 1.284049150E-01 - 1.325221360E-01 1.366838370E-01 1.409133670E-01 1.452084330E-01 1.495654140E-01 - 1.539765300E-01 1.583993730E-01 1.628114130E-01 1.672184320E-01 1.716203540E-01 - 1.760169860E-01 1.804083880E-01 1.847948130E-01 1.891763360E-01 1.935530750E-01 - 1.979251060E-01 2.022925320E-01 2.066554870E-01 2.110138980E-01 2.153679730E-01 - 2.197176960E-01 2.240630540E-01 2.284040300E-01 2.327405210E-01 2.370726470E-01 - 2.414002420E-01 2.457230840E-01 2.500409480E-01 2.543537020E-01 2.586610620E-01 - 2.629626100E-01 2.672579590E-01 2.715468410E-01 2.758286600E-01 2.801023720E-01 - 2.843670550E-01 2.242884780E-01 2.221084240E-01 2.199110090E-01 2.176964880E-01 - 2.154651430E-01 2.132171390E-01 2.109527440E-01 2.086722110E-01 2.063755840E-01 - 2.040630280E-01 2.017346620E-01 1.993905010E-01 1.970306630E-01 1.946551050E-01 - 1.922638860E-01 1.898569760E-01 1.874343310E-01 1.849959340E-01 1.825417430E-01 - 1.800716520E-01 1.775856020E-01 1.750835030E-01 1.725652220E-01 1.700306680E-01 - 1.674797390E-01 1.649122690E-01 1.623280940E-01 1.597270520E-01 1.571090370E-01 - 1.544736470E-01 1.518207190E-01 1.491506250E-01 1.464637520E-01 1.437624840E-01 - 1.410497280E-01 1.383270770E-01 1.355959770E-01 1.328568460E-01 1.301103230E-01 - 1.273569760E-01 1.245974820E-01 1.218324600E-01 1.190625130E-01 1.162882600E-01 - 1.135103030E-01 1.107292250E-01 1.079455610E-01 1.051597450E-01 1.023722810E-01 - 9.958361090E-02 9.679418060E-02 9.400440750E-02 9.121470150E-02 8.842548730E-02 - 8.563716710E-02 8.285013590E-02 8.006481080E-02 7.728159430E-02 7.450088110E-02 - 7.172308120E-02 6.894861160E-02 6.617793440E-02 6.341150400E-02 6.064978610E-02 - 5.789329860E-02 5.514254050E-02 5.239810420E-02 4.966059700E-02 4.693062600E-02 - 4.420879860E-02 4.149580750E-02 3.879235680E-02 3.609916940E-02 3.341702370E-02 - 3.074672630E-02 2.808905950E-02 2.544484290E-02 2.281496490E-02 2.020028610E-02 - 1.760173960E-02 1.502023540E-02 1.245674030E-02 9.912220760E-03 7.387640420E-03 - 4.883966410E-03 2.402242970E-03-5.653229890E-05-2.491320720E-03-4.901071540E-03 --7.284745110E-03-9.641304610E-03-1.196971350E-02-1.426893570E-02-1.653788240E-02 --1.877550410E-02-2.098075670E-02-2.315260280E-02-2.528999750E-02-2.739189190E-02 --2.945725810E-02-3.148508070E-02-3.347433730E-02-3.542402760E-02-3.733314950E-02 --3.920071200E-02-4.102573920E-02-4.280726980E-02-4.454435040E-02-4.623604570E-02 --4.788142070E-02-4.947955910E-02-5.102955920E-02-5.253053830E-02-5.398162830E-02 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1.311126050E-01 1.283765440E-01 1.256346260E-01 1.228874620E-01 - 1.201356500E-01 1.173798070E-01 1.146205370E-01 1.118584420E-01 1.090940540E-01 - 1.063278170E-01 1.035602470E-01 1.007917820E-01 9.802287820E-02 9.525395930E-02 - 9.248543530E-02 8.971773090E-02 8.695124090E-02 8.418638260E-02 8.142355830E-02 - 7.866317780E-02 7.590564340E-02 7.315135750E-02 7.040072230E-02 6.765419990E-02 - 6.491223720E-02 6.217529620E-02 5.944388360E-02 5.671846490E-02 5.399963260E-02 - 5.128799010E-02 4.858413710E-02 4.588866980E-02 4.320218790E-02 4.052550720E-02 - 3.785923870E-02 3.520414980E-02 3.256104140E-02 2.993069400E-02 2.731389740E-02 - 2.471153070E-02 2.212440040E-02 1.955343970E-02 1.699957440E-02 1.446373760E-02 - 1.194685980E-02 9.449869390E-03 6.973771380E-03 4.519584590E-03 2.088253390E-03 --3.191984430E-04-2.701732560E-03-5.058313720E-03-7.387907240E-03-9.689480070E-03 --1.196201150E-02-1.420445830E-02-1.641579530E-02-1.859495420E-02-2.074089830E-02 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1.215101630E-01 1.255410610E-01 1.295964720E-01 1.336978380E-01 1.378608490E-01 - 1.420891140E-01 1.463759840E-01 1.507153060E-01 1.551044290E-01 1.595135180E-01 - 1.639103000E-01 1.683048900E-01 1.726976780E-01 1.770890800E-01 1.814786940E-01 - 1.858673390E-01 1.902550310E-01 1.946420670E-01 1.990286260E-01 2.034148720E-01 - 2.078010890E-01 2.121874540E-01 2.165741770E-01 2.209615110E-01 2.253497390E-01 - 2.297389210E-01 2.341292500E-01 2.385208460E-01 2.429139610E-01 2.473087760E-01 - 2.517052290E-01 2.561033370E-01 2.605035310E-01 2.649053630E-01 2.693088950E-01 - 2.737143040E-01 2.781212630E-01 2.825289370E-01 2.869381310E-01 2.913481590E-01 - 2.256028950E-01 2.234204410E-01 2.212208810E-01 2.190053460E-01 2.167740460E-01 - 2.145273390E-01 2.122654770E-01 2.099886980E-01 2.076970930E-01 2.053909300E-01 - 2.030702380E-01 2.007350920E-01 1.983855660E-01 1.960216910E-01 1.936434210E-01 - 1.912507710E-01 1.888436970E-01 1.864221540E-01 1.839860380E-01 1.815353040E-01 - 1.790698470E-01 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5.984399100E-02 6.341691320E-02 6.701968610E-02 7.065150890E-02 7.431162890E-02 - 7.799935340E-02 8.171404900E-02 8.545518670E-02 8.922223750E-02 9.301467240E-02 - 9.683218600E-02 1.006744430E-01 1.045413990E-01 1.084334030E-01 1.123507990E-01 - 1.162940790E-01 1.202649770E-01 1.242638010E-01 1.282942150E-01 1.323567030E-01 - 1.364744310E-01 1.406577680E-01 1.449081300E-01 1.492192450E-01 1.535848980E-01 - 1.579811870E-01 1.623660030E-01 1.667505500E-01 1.711348890E-01 1.755192430E-01 - 1.799038350E-01 1.842889040E-01 1.886747930E-01 1.930617990E-01 1.974501610E-01 - 2.018401770E-01 2.062321310E-01 2.106263640E-01 2.150231600E-01 2.194228020E-01 - 2.238255440E-01 2.282316980E-01 2.326417710E-01 2.370557490E-01 2.414739580E-01 - 2.458968610E-01 2.503246670E-01 2.547577020E-01 2.591960130E-01 2.636398080E-01 - 2.680892940E-01 2.725446820E-01 2.770061190E-01 2.814737860E-01 2.859475610E-01 - 2.904272380E-01 2.949126960E-01 2.262860540E-01 2.240988760E-01 2.218956050E-01 - 2.196770910E-01 2.174438240E-01 2.151960130E-01 2.129339280E-01 2.106577900E-01 - 2.083678250E-01 2.060641200E-01 2.037467810E-01 2.014158070E-01 1.990712290E-01 - 1.967131050E-01 1.943414060E-01 1.919560430E-01 1.895570460E-01 1.871442790E-01 - 1.847176250E-01 1.822770830E-01 1.798225190E-01 1.773537990E-01 1.748708040E-01 - 1.723733690E-01 1.698613760E-01 1.673347200E-01 1.647932080E-01 1.622366760E-01 - 1.596649590E-01 1.570779090E-01 1.544753310E-01 1.518566310E-01 1.492214500E-01 - 1.465718450E-01 1.439099160E-01 1.412377210E-01 1.385573600E-01 1.358708290E-01 - 1.331776230E-01 1.304785010E-01 1.277741490E-01 1.250651780E-01 1.223521830E-01 - 1.196357380E-01 1.169164480E-01 1.141948920E-01 1.114716310E-01 1.087471690E-01 - 1.060219930E-01 1.032965700E-01 1.005713640E-01 9.784679110E-02 9.512327610E-02 - 9.240125120E-02 8.968111870E-02 8.696328850E-02 8.424817030E-02 8.153616640E-02 - 7.882769410E-02 7.612315570E-02 7.342295350E-02 7.072752710E-02 6.803731620E-02 - 6.535276030E-02 6.267434360E-02 6.000253190E-02 5.733787640E-02 5.468092860E-02 - 5.203225460E-02 4.939245810E-02 4.676212740E-02 4.414195190E-02 4.153256120E-02 - 3.893472250E-02 3.634917740E-02 3.377664830E-02 3.121789540E-02 2.867374200E-02 - 2.614502980E-02 2.363261390E-02 2.113734370E-02 1.866007220E-02 1.620179600E-02 - 1.376339420E-02 1.134581310E-02 8.950012740E-03 6.576955780E-03 4.227605180E-03 - 1.902949760E-03-3.959784520E-04-2.668215190E-03-4.912745210E-03-7.128553000E-03 --9.314623660E-03-1.146994250E-02-1.359350610E-02-1.568429540E-02-1.774129830E-02 --1.976350320E-02-2.174991930E-02-2.369955550E-02-2.561140810E-02-2.748448220E-02 --2.931783530E-02-3.111050650E-02-3.286153820E-02-3.456996380E-02-3.623486310E-02 --3.785530850E-02-3.943040970E-02-4.095926140E-02-4.244098070E-02-4.387469220E-02 --4.525954650E-02-4.659471290E-02-4.787936060E-02-4.911268130E-02-5.029388140E-02 --5.142218250E-02-5.249682070E-02-5.351706590E-02-5.448218810E-02-5.539144950E-02 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7.939717730E-03 1.084120290E-02 1.378942190E-02 1.678323000E-02 1.982150790E-02 - 2.290328960E-02 2.602750060E-02 2.919306050E-02 3.239889440E-02 3.564392780E-02 - 3.892714530E-02 4.224753750E-02 4.560411350E-02 4.899592330E-02 5.242200940E-02 - 5.588147420E-02 5.937339740E-02 6.289697440E-02 6.645143030E-02 7.003597920E-02 - 7.364984600E-02 7.729242000E-02 8.096297830E-02 8.466101440E-02 8.838602160E-02 - 9.213750060E-02 9.591507910E-02 9.971851110E-02 1.035475950E-01 1.074025850E-01 - 1.112838010E-01 1.151917580E-01 1.191278100E-01 1.230927260E-01 1.270894260E-01 - 1.311225000E-01 1.351945400E-01 1.393297310E-01 1.435365830E-01 1.478071960E-01 - 1.521434190E-01 1.565260740E-01 1.608958840E-01 1.652664100E-01 1.696377990E-01 - 1.740106790E-01 1.783853620E-01 1.827621160E-01 1.871413290E-01 1.915232240E-01 - 1.959082480E-01 2.002966700E-01 2.046888620E-01 2.090852410E-01 2.134860610E-01 - 2.178919020E-01 2.223030180E-01 2.267198260E-01 2.311428190E-01 2.355723380E-01 - 2.400088310E-01 2.444526850E-01 2.489042730E-01 2.533639670E-01 2.578324680E-01 - 2.623096700E-01 2.667963800E-01 2.712931040E-01 2.758000200E-01 2.803173960E-01 - 2.848455010E-01 2.893844840E-01 2.939350900E-01 2.984970810E-01 2.269824150E-01 - 2.247876670E-01 2.225785110E-01 2.203554210E-01 2.181187420E-01 2.158686820E-01 - 2.136055680E-01 2.113295200E-01 2.090407310E-01 2.067391570E-01 2.044248880E-01 - 2.020979520E-01 1.997583960E-01 1.974061130E-01 1.950410900E-01 1.926632820E-01 - 1.902725550E-01 1.878688780E-01 1.854521330E-01 1.830222010E-01 1.805789470E-01 - 1.781222520E-01 1.756519820E-01 1.731680040E-01 1.706701520E-01 1.681582780E-01 - 1.656321880E-01 1.630917190E-01 1.605366920E-01 1.579669120E-01 1.553830500E-01 - 1.527830810E-01 1.501666160E-01 1.475358460E-01 1.448928860E-01 1.422396150E-01 - 1.395779400E-01 1.369100210E-01 1.342362020E-01 1.315569130E-01 1.288726480E-01 - 1.261840760E-01 1.234917490E-01 1.207962930E-01 1.180982810E-01 1.153983030E-01 - 1.126969080E-01 1.099946200E-01 1.072919440E-01 1.045893430E-01 1.018872710E-01 - 9.918617460E-02 9.648647900E-02 9.378860150E-02 9.109295900E-02 8.839995410E-02 - 8.570999650E-02 8.302350340E-02 8.034088460E-02 7.766255740E-02 7.498890160E-02 - 7.232036440E-02 6.965737040E-02 6.700035930E-02 6.434980030E-02 6.170615930E-02 - 5.906996500E-02 5.644176530E-02 5.382212250E-02 5.121159180E-02 4.861076920E-02 - 4.602033270E-02 4.344088960E-02 4.087315870E-02 3.831787410E-02 3.577575460E-02 - 3.324752300E-02 3.073398960E-02 2.823600730E-02 2.575442380E-02 2.329006230E-02 - 2.084373680E-02 1.841632460E-02 1.600880550E-02 1.362206690E-02 1.125707200E-02 - 8.914774280E-03 6.596111690E-03 4.302035090E-03 2.033544470E-03-2.083770810E-04 --2.422733700E-03-4.608528690E-03-6.764766760E-03-8.890492840E-03-1.098462380E-02 --1.304619760E-02-1.507422510E-02-1.706771370E-02-1.902567220E-02-2.094710990E-02 --2.283104140E-02-2.467649430E-02-2.648252250E-02-2.824817970E-02-2.997251230E-02 --3.165455160E-02-3.329340000E-02-3.488814090E-02-3.643787650E-02-3.794172030E-02 --3.939879690E-02-4.080824180E-02-4.216921330E-02-4.348087680E-02-4.474240170E-02 --4.595301670E-02-4.711189490E-02-4.821828750E-02-4.927144200E-02-5.027062070E-02 --5.121509730E-02-5.210417880E-02-5.293718350E-02-5.371345210E-02-5.443232510E-02 --5.509317670E-02-5.569541450E-02-5.623844640E-02-5.672169850E-02-5.714463820E-02 --5.750673260E-02-5.780749770E-02-5.804645640E-02-5.822313200E-02-5.833708870E-02 --5.838793520E-02-5.837529900E-02-5.829881880E-02-5.815814440E-02-5.795297770E-02 --5.768302080E-02-5.734803160E-02-5.694778260E-02-5.648207660E-02-5.595074220E-02 --5.535358940E-02-5.469052120E-02-5.396148930E-02-5.316645650E-02-5.230537800E-02 --5.137820910E-02-5.038494240E-02-4.932578650E-02-4.820071910E-02-4.700989280E-02 --4.575352000E-02-4.443181310E-02-4.304499180E-02-4.159329460E-02-4.007702320E-02 --3.849650920E-02-3.685212510E-02-3.514430670E-02-3.337350490E-02-3.154018520E-02 --2.964484320E-02-2.768806000E-02-2.567042040E-02-2.359255030E-02-2.145509420E-02 --1.925876180E-02-1.700426450E-02-1.469238200E-02-1.232391970E-02-9.899690750E-03 --7.420538460E-03-4.887347580E-03-2.301035910E-03 3.374730000E-04 3.027227240E-03 - 5.767222030E-03 8.556487970E-03 1.139401550E-02 1.427877690E-02 1.720977020E-02 - 2.018590640E-02 2.320614270E-02 2.626947130E-02 2.937488440E-02 3.252137820E-02 - 3.570789470E-02 3.893334790E-02 4.219679530E-02 4.549733180E-02 4.883396630E-02 - 5.220577870E-02 5.561188610E-02 5.905142800E-02 6.252354380E-02 6.602747740E-02 - 6.956250220E-02 7.312785090E-02 7.672289010E-02 8.034694940E-02 8.399944010E-02 - 8.767984060E-02 9.138776360E-02 9.512284400E-02 9.888469430E-02 1.026731130E-01 - 1.064883320E-01 1.103306110E-01 1.142003160E-01 1.180985500E-01 1.220268230E-01 - 1.259865160E-01 1.299815770E-01 1.340183620E-01 1.381023680E-01 1.422581820E-01 - 1.464920340E-01 1.507955340E-01 1.551431420E-01 1.595010610E-01 1.638529000E-01 - 1.682073180E-01 1.725645660E-01 1.769248840E-01 1.812885400E-01 1.856561150E-01 - 1.900279670E-01 1.944043930E-01 1.987858560E-01 2.031727880E-01 2.075655910E-01 - 2.119647120E-01 2.163706420E-01 2.207838450E-01 2.252048250E-01 2.296340320E-01 - 2.340719400E-01 2.385191170E-01 2.429763970E-01 2.474439890E-01 2.519224290E-01 - 2.564124460E-01 2.609147730E-01 2.654297350E-01 2.699579890E-01 2.745000120E-01 - 2.790566980E-01 2.836282250E-01 2.882156670E-01 2.928195300E-01 2.974401410E-01 - 3.020779790E-01 2.276865990E-01 2.254816440E-01 2.232645000E-01 2.210353460E-01 - 2.187940330E-01 2.165408430E-01 2.142760010E-01 2.119995650E-01 2.097115370E-01 - 2.074119600E-01 2.051007600E-01 2.027779070E-01 2.004434620E-01 1.980972290E-01 - 1.957391650E-01 1.933691950E-01 1.909871850E-01 1.885930300E-01 1.861866120E-01 - 1.837677810E-01 1.813363880E-01 1.788923290E-01 1.764354260E-01 1.739654840E-01 - 1.714823840E-01 1.689859330E-01 1.664759670E-01 1.639522760E-01 1.614147130E-01 - 1.588630970E-01 1.562974010E-01 1.537169960E-01 1.511213480E-01 1.485108440E-01 - 1.458874200E-01 1.432532970E-01 1.406117230E-01 1.379636680E-01 1.353098450E-01 - 1.326509420E-01 1.299876270E-01 1.273203640E-01 1.246495770E-01 1.219759660E-01 - 1.193000970E-01 1.166225600E-01 1.139438970E-01 1.112646680E-01 1.085853500E-01 - 1.059064190E-01 1.032283600E-01 1.005515980E-01 9.787657110E-02 9.520369770E-02 - 9.253339470E-02 8.986607190E-02 8.720213920E-02 8.454200630E-02 8.188609780E-02 - 7.923481610E-02 7.658856360E-02 7.394775750E-02 7.131285220E-02 6.868425010E-02 - 6.606242810E-02 6.344784800E-02 6.084100900E-02 5.824244770E-02 5.565270410E-02 - 5.307232960E-02 5.050192770E-02 4.794212060E-02 4.539354520E-02 4.285687210E-02 - 4.033280160E-02 3.782209380E-02 3.532535580E-02 3.284342960E-02 3.037715700E-02 - 2.792735030E-02 2.549482700E-02 2.308040670E-02 2.068490350E-02 1.830930450E-02 - 1.595444980E-02 1.362128840E-02 1.131075990E-02 9.023792110E-03 6.761319470E-03 - 4.524308260E-03 2.313731700E-03 1.305798650E-04-2.024170010E-03-4.149548240E-03 --6.244570950E-03-8.308246730E-03-1.033959540E-02-1.233763810E-02-1.430139220E-02 --1.622987350E-02-1.812209380E-02-1.997710950E-02-2.179395030E-02-2.357166630E-02 --2.530931500E-02-2.700595370E-02-2.866064200E-02-3.027250990E-02-3.184061120E-02 --3.336407240E-02-3.484201060E-02-3.627355770E-02-3.765785690E-02-3.899407010E-02 --4.028137770E-02-4.151896390E-02-4.270602390E-02-4.384178300E-02-4.492549600E-02 --4.595641050E-02-4.693378140E-02-4.785690830E-02-4.872509840E-02-4.953767730E-02 --5.029397090E-02-5.099334940E-02-5.163519080E-02-5.221890290E-02-5.274391170E-02 --5.320965130E-02-5.361558120E-02-5.396118760E-02-5.424598230E-02-5.446949230E-02 --5.463126670E-02-5.473088100E-02-5.476794020E-02-5.474207180E-02-5.465290700E-02 --5.450012910E-02-5.428344760E-02-5.400252710E-02-5.365715920E-02-5.324715750E-02 --5.277232080E-02-5.223245550E-02-5.162740870E-02-5.095707630E-02-5.022137610E-02 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1.019183620E-01 1.056909490E-01 1.094917280E-01 1.133203580E-01 1.171782170E-01 - 1.210667040E-01 1.249873640E-01 1.289426980E-01 1.329372670E-01 1.369768980E-01 - 1.410830910E-01 1.452800480E-01 1.495374890E-01 1.538402290E-01 1.581746940E-01 - 1.625177260E-01 1.668499260E-01 1.711843610E-01 1.755239520E-01 1.798702780E-01 - 1.842214170E-01 1.885780100E-01 1.929407120E-01 1.973101350E-01 2.016863820E-01 - 2.060699460E-01 2.104614530E-01 2.148614380E-01 2.192704530E-01 2.236889450E-01 - 2.281175550E-01 2.325569090E-01 2.370077220E-01 2.414705010E-01 2.459460200E-01 - 2.504349950E-01 2.549381260E-01 2.594560980E-01 2.639896870E-01 2.685395780E-01 - 2.731066640E-01 2.776918710E-01 2.822961210E-01 2.869198020E-01 2.915641670E-01 - 2.962298390E-01 3.009181020E-01 3.056297000E-01 2.283881900E-01 2.261721790E-01 - 2.239460950E-01 2.217096980E-01 2.194632590E-01 2.172066720E-01 2.149398770E-01 - 2.126629350E-01 2.103757110E-01 2.080781610E-01 2.057702240E-01 2.034517680E-01 - 2.011226560E-01 1.987828460E-01 1.964321730E-01 1.940705180E-01 1.916977170E-01 - 1.893136350E-01 1.869180950E-01 1.845110060E-01 1.820921450E-01 1.796613340E-01 - 1.772184220E-01 1.747632470E-01 1.722955850E-01 1.698152870E-01 1.673221590E-01 - 1.648159920E-01 1.622966230E-01 1.597638580E-01 1.572174730E-01 1.546572740E-01 - 1.520824880E-01 1.494937240E-01 1.468912510E-01 1.442776170E-01 1.416564290E-01 - 1.390290110E-01 1.363961990E-01 1.337587540E-01 1.311172400E-01 1.284720150E-01 - 1.258236770E-01 1.231727820E-01 1.205199360E-01 1.178657110E-01 1.152106670E-01 - 1.125553400E-01 1.099002440E-01 1.072458550E-01 1.045926440E-01 1.019410710E-01 - 9.929155560E-02 9.664453570E-02 9.400041400E-02 9.135961530E-02 8.872254190E-02 - 8.608961850E-02 8.346123990E-02 8.083784580E-02 7.821981610E-02 7.560759040E-02 - 7.300158590E-02 7.040223480E-02 6.780998410E-02 6.522528830E-02 6.264865400E-02 - 6.008058040E-02 5.752160030E-02 5.497226860E-02 5.243314060E-02 4.990483820E-02 - 4.738800600E-02 4.488328100E-02 4.239131510E-02 3.991285710E-02 3.744860370E-02 - 3.499925510E-02 3.256562350E-02 3.014851920E-02 2.774876540E-02 2.536717620E-02 - 2.300456730E-02 2.066182350E-02 1.833983700E-02 1.603949630E-02 1.376171970E-02 - 1.150742170E-02 9.277536530E-03 7.073021960E-03 4.894801880E-03 2.743844640E-03 - 6.211188740E-04-1.472406900E-03-3.535760100E-03-5.567989780E-03-7.568128410E-03 --9.535200890E-03-1.146822420E-02-1.336622890E-02-1.522826780E-02-1.705338810E-02 --1.884064260E-02-2.058909270E-02-2.229780330E-02-2.396583180E-02-2.559227120E-02 --2.717621810E-02-2.871678400E-02-3.021308410E-02-3.166423740E-02-3.306938340E-02 --3.442768380E-02-3.573831170E-02-3.700044380E-02-3.821328280E-02-3.937602040E-02 --4.048790780E-02-4.154819620E-02-4.255612940E-02-4.351098090E-02-4.441205040E-02 --4.525865240E-02-4.605012390E-02-4.678580910E-02-4.746507110E-02-4.808729890E-02 --4.865191880E-02-4.915835340E-02-4.960604010E-02-4.999444630E-02-5.032307280E-02 --5.059141290E-02-5.079903830E-02-5.094550180E-02-5.103037130E-02-5.105325580E-02 --5.101377140E-02-5.091159050E-02-5.074638870E-02-5.051787940E-02-5.022578310E-02 --4.986985770E-02-4.944990200E-02-4.896573350E-02-4.841715840E-02-4.780405010E-02 --4.712634530E-02-4.638392480E-02-4.557676240E-02-4.470486570E-02-4.376823830E-02 --4.276691380E-02-4.170103370E-02-4.057057950E-02-3.937576340E-02-3.811679780E-02 --3.679390620E-02-3.540731970E-02-3.395727650E-02-3.244403750E-02-3.086806830E-02 --2.922969500E-02-2.752934400E-02-2.576746980E-02-2.394453990E-02-2.206108160E-02 --2.011765350E-02-1.811485740E-02-1.605329290E-02-1.393362600E-02-1.175653560E-02 --9.522722100E-03-7.232969630E-03-4.888062830E-03-2.488785660E-03-3.593423750E-05 - 2.469584110E-03 5.026908590E-03 7.635146850E-03 1.029337940E-02 1.300067830E-02 - 1.575610230E-02 1.855867360E-02 2.140744780E-02 2.430146000E-02 2.723970450E-02 - 3.022122010E-02 3.324508670E-02 3.631035610E-02 3.941605240E-02 4.256119210E-02 - 4.574487360E-02 4.896622520E-02 5.222435670E-02 5.551843350E-02 5.884762480E-02 - 6.221110750E-02 6.560815870E-02 6.903798880E-02 7.249996070E-02 7.599341120E-02 - 7.951770720E-02 8.307236430E-02 8.665661510E-02 9.027014670E-02 9.391262380E-02 - 9.758370370E-02 1.012831550E-01 1.050110680E-01 1.087674950E-01 1.125527250E-01 - 1.163674740E-01 1.202134560E-01 1.240922440E-01 1.280054750E-01 1.319552810E-01 - 1.359521900E-01 1.400119070E-01 1.441453550E-01 1.483663170E-01 1.526356340E-01 - 1.569343810E-01 1.612473880E-01 1.655594860E-01 1.698658760E-01 1.741827730E-01 - 1.785082970E-01 1.828394830E-01 1.871767190E-01 1.915208250E-01 1.958725750E-01 - 2.002327590E-01 2.046015860E-01 2.089796960E-01 2.133676860E-01 2.177660910E-01 - 2.221757020E-01 2.265971000E-01 2.310309260E-01 2.354778050E-01 2.399388850E-01 - 2.444145680E-01 2.489057630E-01 2.534132300E-01 2.579377290E-01 2.624804080E-01 - 2.670423090E-01 2.716240880E-01 2.762269080E-01 2.808517810E-01 2.854997520E-01 - 2.901719510E-01 2.948696910E-01 2.995941940E-01 3.043466510E-01 3.091282550E-01 - 2.290776820E-01 2.268500780E-01 2.246150520E-01 2.223716230E-01 2.201198940E-01 - 2.178598940E-01 2.155913710E-01 2.133141010E-01 2.110281140E-01 2.087330370E-01 - 2.064287510E-01 2.041151080E-01 2.017919870E-01 1.994591650E-01 1.971165090E-01 - 1.947637650E-01 1.924008430E-01 1.900275200E-01 1.876436170E-01 1.852489260E-01 - 1.828432530E-01 1.804264490E-01 1.779983040E-01 1.755586270E-01 1.731072070E-01 - 1.706438360E-01 1.681683210E-01 1.656804830E-01 1.631800830E-01 1.606669130E-01 - 1.581407930E-01 1.556017100E-01 1.530488130E-01 1.504820440E-01 1.479020270E-01 - 1.453101630E-01 1.427104180E-01 1.401043830E-01 1.374933870E-01 1.348783080E-01 - 1.322593540E-01 1.296370920E-01 1.270120740E-01 1.243847760E-01 1.217558230E-01 - 1.191257910E-01 1.164952370E-01 1.138646900E-01 1.112346650E-01 1.086056680E-01 - 1.059781690E-01 1.033526210E-01 1.007294580E-01 9.810911860E-02 9.549201280E-02 - 9.287856520E-02 9.026917820E-02 8.766426150E-02 8.506423980E-02 8.246953040E-02 - 7.988055050E-02 7.729769500E-02 7.472140340E-02 7.215210050E-02 6.959021840E-02 - 6.703621150E-02 6.449057910E-02 6.195382030E-02 5.942643060E-02 5.690895390E-02 - 5.440194900E-02 5.190600450E-02 4.942174630E-02 4.694980010E-02 4.449081420E-02 - 4.204547030E-02 3.961448740E-02 3.719859200E-02 3.479851040E-02 3.241504360E-02 - 3.004896450E-02 2.770110410E-02 2.537227790E-02 2.306332070E-02 2.077509090E-02 - 1.850847900E-02 1.626439770E-02 1.404373530E-02 1.184739270E-02 9.676296260E-03 - 7.531364450E-03 5.413565780E-03 3.323822520E-03 1.263094250E-03-7.676623060E-04 --2.767498140E-03-4.735460970E-03-6.670580710E-03-8.571940470E-03-1.043854750E-02 --1.226947080E-02-1.406377740E-02-1.582053490E-02-1.753880460E-02-1.921765130E-02 --2.085618120E-02-2.245347200E-02-2.400863730E-02-2.552079600E-02-2.698906880E-02 --2.841259350E-02-2.979051880E-02-3.112201390E-02-3.240625930E-02-3.364242990E-02 --3.482973580E-02-3.596740590E-02-3.705468400E-02-3.809081390E-02-3.907503930E-02 --4.000669720E-02-4.088504240E-02-4.170941190E-02-4.247915370E-02-4.319362340E-02 --4.385218400E-02-4.445423560E-02-4.499920460E-02-4.548652840E-02-4.591564830E-02 --4.628604280E-02-4.659721260E-02-4.684868080E-02-4.704001170E-02-4.717075450E-02 --4.724046960E-02-4.724883660E-02-4.719543080E-02-4.707992820E-02-4.690204190E-02 --4.666148130E-02-4.635795950E-02-4.599126430E-02-4.556117210E-02-4.506750780E-02 --4.451012980E-02-4.388890790E-02-4.320373390E-02-4.245454820E-02-4.164132850E-02 --4.076407850E-02-3.982279450E-02-3.881754730E-02-3.774843360E-02-3.661548350E-02 --3.541888670E-02-3.415889670E-02-3.283575180E-02-3.144967930E-02-3.000091580E-02 --2.848971450E-02-2.691652250E-02-2.528170680E-02-2.358570140E-02-2.182894390E-02 --2.001191120E-02-1.813513040E-02-1.619915850E-02-1.420459520E-02-1.215204780E-02 --1.004215800E-02-7.875618520E-03-5.653119650E-03-3.375425930E-03-1.043308880E-03 - 1.342446890E-03 3.781051610E-03 6.271640300E-03 8.813355120E-03 1.140531800E-02 - 1.404664390E-02 1.673640680E-02 1.947372590E-02 2.225762980E-02 2.508718520E-02 - 2.796147950E-02 3.087959070E-02 3.384055200E-02 3.684346380E-02 3.988739100E-02 - 4.297140610E-02 4.609463360E-02 4.925620560E-02 5.245524640E-02 5.569096650E-02 - 5.896253510E-02 6.226914000E-02 6.561005860E-02 6.898457560E-02 7.239199430E-02 - 7.583168890E-02 7.930304110E-02 8.280546220E-02 8.633857220E-02 8.990182730E-02 - 9.349446740E-02 9.711644800E-02 1.007677840E-01 1.044484750E-01 1.081585140E-01 - 1.118979010E-01 1.156674250E-01 1.194683240E-01 1.233021840E-01 1.271712030E-01 - 1.310762760E-01 1.350288990E-01 1.390416770E-01 1.431205720E-01 1.472781750E-01 - 1.515122950E-01 1.557778720E-01 1.600570080E-01 1.643365770E-01 1.686215550E-01 - 1.729123740E-01 1.772096160E-01 1.815144720E-01 1.858271810E-01 1.901477720E-01 - 1.944770960E-01 1.988159570E-01 2.031647260E-01 2.075238530E-01 2.118941100E-01 - 2.162760350E-01 2.206703130E-01 2.250777780E-01 2.294992950E-01 2.339353110E-01 - 2.383868550E-01 2.428547740E-01 2.473398450E-01 2.518432440E-01 2.563657460E-01 - 2.609082460E-01 2.654719650E-01 2.700581550E-01 2.746676210E-01 2.793019710E-01 - 2.839618920E-01 2.886492010E-01 2.933655980E-01 2.981117960E-01 3.028897940E-01 - 3.077009320E-01 3.125470580E-01 2.297438980E-01 2.275054600E-01 2.252615090E-01 - 2.230118360E-01 2.207559790E-01 2.184935210E-01 2.162240300E-01 2.139473260E-01 - 2.116632460E-01 2.093714770E-01 2.070716770E-01 2.047636810E-01 2.024473700E-01 - 2.001223560E-01 1.977884620E-01 1.954454930E-01 1.930932250E-01 1.907314210E-01 - 1.883599160E-01 1.859784720E-01 1.835868950E-01 1.811849180E-01 1.787723750E-01 - 1.763490290E-01 1.739146710E-01 1.714690770E-01 1.690120550E-01 1.665433790E-01 - 1.640628280E-01 1.615701760E-01 1.590652170E-01 1.565478740E-01 1.540176120E-01 - 1.514741480E-01 1.489175110E-01 1.463485810E-01 1.437713060E-01 1.411878760E-01 - 1.385995300E-01 1.360075030E-01 1.334120330E-01 1.308136280E-01 1.282127650E-01 - 1.256099940E-01 1.230058220E-01 1.204008530E-01 1.177956610E-01 1.151907520E-01 - 1.125866620E-01 1.099839140E-01 1.073829610E-01 1.047842800E-01 1.021883040E-01 - 9.959545730E-02 9.700617940E-02 9.442088750E-02 9.183999150E-02 8.926390110E-02 - 8.669303360E-02 8.412780610E-02 8.156862850E-02 7.901592550E-02 7.647011430E-02 - 7.393163440E-02 7.140089570E-02 6.887837500E-02 6.636452670E-02 6.385983530E-02 - 6.136481460E-02 5.887996780E-02 5.640586090E-02 5.394305660E-02 5.149217320E-02 - 4.905381050E-02 4.662860930E-02 4.421722520E-02 4.182035100E-02 3.943870220E-02 - 3.707299750E-02 3.472399340E-02 3.239246460E-02 3.007919710E-02 2.778498640E-02 - 2.551068180E-02 2.325710650E-02 2.102511190E-02 1.881559190E-02 1.662942390E-02 - 1.446748990E-02 1.233070720E-02 1.021999030E-02 8.136242630E-03 6.080375980E-03 - 4.053371960E-03 2.056129040E-03 8.958997930E-05-1.845299030E-03-3.747612470E-03 --5.616376180E-03-7.450689560E-03-9.249622000E-03-1.101224030E-02-1.273761220E-02 --1.442480550E-02-1.607295500E-02-1.768111250E-02-1.924839800E-02-2.077394170E-02 --2.225687170E-02-2.369631080E-02-2.509140040E-02-2.644131710E-02-2.774521890E-02 --2.900229210E-02-3.021175230E-02-3.137281540E-02-3.248469900E-02-3.354665640E-02 --3.455793110E-02-3.551781180E-02-3.642558310E-02-3.728056700E-02-3.808210050E-02 --3.882952030E-02-3.952219340E-02-4.015949370E-02-4.074082520E-02-4.126561060E-02 --4.173331340E-02-4.214340080E-02-4.249534010E-02-4.278863220E-02-4.302281890E-02 --4.319744560E-02-4.331209510E-02-4.336635770E-02-4.335985330E-02-4.329221700E-02 --4.316314310E-02-4.297233370E-02-4.271949460E-02-4.240435730E-02-4.202670230E-02 --4.158632830E-02-4.108308260E-02-4.051682350E-02-3.988740970E-02-3.919476270E-02 --3.843880820E-02-3.761953490E-02-3.673696520E-02-3.579111020E-02-3.478202600E-02 --3.370978310E-02-3.257453810E-02-3.137643260E-02-3.011568820E-02-2.879255450E-02 --2.740726990E-02-2.596006730E-02-2.445119990E-02-2.288118560E-02-2.125033360E-02 --1.955908160E-02-1.780790090E-02-1.599726270E-02-1.412766710E-02-1.219968220E-02 --1.021389290E-02-8.170926010E-03-6.071421320E-03-3.916044720E-03-1.705487840E-03 - 5.594997200E-04 2.878150670E-03 5.249701910E-03 7.673391610E-03 1.014834080E-02 - 1.267371890E-02 1.524867490E-02 1.787234100E-02 2.054384540E-02 2.326228470E-02 - 2.602677050E-02 2.883639370E-02 3.169024360E-02 3.458741310E-02 3.752703960E-02 - 4.050819200E-02 4.353002460E-02 4.659165810E-02 4.969222840E-02 5.283090100E-02 - 5.600687860E-02 5.921938640E-02 6.246763840E-02 6.575091180E-02 6.906847660E-02 - 7.241969560E-02 7.580391320E-02 7.922055570E-02 8.266903460E-02 8.614884320E-02 - 8.965954930E-02 9.320062400E-02 9.677164260E-02 1.003726500E-01 1.040036900E-01 - 1.076648160E-01 1.113560720E-01 1.150779430E-01 1.188319180E-01 1.226182130E-01 - 1.264399590E-01 1.303001940E-01 1.341998130E-01 1.381587090E-01 1.421895620E-01 - 1.462941320E-01 1.504742060E-01 1.547119770E-01 1.589503290E-01 1.631955950E-01 - 1.674479840E-01 1.717076600E-01 1.759748160E-01 1.802497660E-01 1.845332980E-01 - 1.888258760E-01 1.931281090E-01 1.974405940E-01 2.017640770E-01 2.060988100E-01 - 2.104455980E-01 2.148051710E-01 2.191782440E-01 2.235656380E-01 2.279681120E-01 - 2.323864400E-01 2.368214730E-01 2.412741180E-01 2.457453010E-01 2.502362130E-01 - 2.547479870E-01 2.592812780E-01 2.638374270E-01 2.684177460E-01 2.730234560E-01 - 2.776559590E-01 2.823164760E-01 2.870066170E-01 2.917279900E-01 2.964821760E-01 - 3.012706640E-01 3.060952430E-01 3.109581470E-01 3.158616130E-01 2.303737850E-01 - 2.281273160E-01 2.258772700E-01 2.236232610E-01 2.213646320E-01 2.191009820E-01 - 2.168319670E-01 2.145572010E-01 2.122762200E-01 2.099887580E-01 2.076945160E-01 - 2.053931950E-01 2.030845730E-01 2.007683220E-01 1.984442170E-01 1.961119620E-01 - 1.937713330E-01 1.914220900E-01 1.890639810E-01 1.866966930E-01 1.843200920E-01 - 1.819339100E-01 1.795378920E-01 1.771318170E-01 1.747154440E-01 1.722885670E-01 - 1.698509310E-01 1.674023420E-01 1.649425330E-01 1.624712940E-01 1.599884030E-01 - 1.574936660E-01 1.549866200E-01 1.524672210E-01 1.499354240E-01 1.473909770E-01 - 1.448373350E-01 1.422774050E-01 1.397126470E-01 1.371443570E-01 1.345732960E-01 - 1.319996120E-01 1.294238120E-01 1.268464480E-01 1.242679800E-01 1.216889470E-01 - 1.191099810E-01 1.165315960E-01 1.139543130E-01 1.113786470E-01 1.088050830E-01 - 1.062340890E-01 1.036661040E-01 1.011015850E-01 9.854093940E-02 9.598460050E-02 - 9.343298520E-02 9.088649600E-02 8.834555000E-02 8.581056450E-02 8.328195660E-02 - 8.076015110E-02 7.824558760E-02 7.573866840E-02 7.323980330E-02 7.074946910E-02 - 6.826813520E-02 6.579627100E-02 6.333435330E-02 6.088288870E-02 5.844243240E-02 - 5.601352830E-02 5.359675740E-02 5.119273440E-02 4.880208890E-02 4.642543570E-02 - 4.406344150E-02 4.171681400E-02 3.938625380E-02 3.707248350E-02 3.477627780E-02 - 3.249842300E-02 3.023967520E-02 2.800082040E-02 2.578270810E-02 2.358617820E-02 - 2.141205220E-02 1.926120930E-02 1.713451930E-02 1.503288370E-02 1.295720320E-02 - 1.090835690E-02 8.887244390E-03 6.894797550E-03 4.931921610E-03 2.999531110E-03 - 1.098563080E-03-7.700587740E-04-2.605410060E-03-4.406589080E-03-6.172684490E-03 --7.902770300E-03-9.595914740E-03-1.125123350E-02-1.286782420E-02-1.444481030E-02 --1.598130540E-02-1.747643950E-02-1.892934180E-02-2.033915180E-02-2.170505000E-02 --2.302619260E-02-2.430175240E-02-2.553094740E-02-2.671299690E-02-2.784711500E-02 --2.893251930E-02-2.996845920E-02-3.095423800E-02-3.188911450E-02-3.277241440E-02 --3.360344840E-02-3.438155350E-02-3.510607410E-02-3.577641030E-02-3.639191390E-02 --3.695200010E-02-3.745612870E-02-3.790376710E-02-3.829438240E-02-3.862743450E-02 --3.890242800E-02-3.911894930E-02-3.927651790E-02-3.937474270E-02-3.941322860E-02 --3.939158840E-02-3.930948300E-02-3.916660320E-02-3.896264730E-02-3.869731720E-02 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8.608654140E-02 8.954288070E-02 9.303038570E-02 9.654864670E-02 1.000974850E-01 - 1.036768330E-01 1.072867440E-01 1.109276120E-01 1.145998840E-01 1.183047000E-01 - 1.220419180E-01 1.258145270E-01 1.296268110E-01 1.334824860E-01 1.373801680E-01 - 1.413519380E-01 1.454095240E-01 1.495386060E-01 1.537235980E-01 1.579269920E-01 - 1.621358990E-01 1.663521080E-01 1.705762000E-01 1.748085170E-01 1.790495070E-01 - 1.832997950E-01 1.875598730E-01 1.918303220E-01 1.961117390E-01 2.004046440E-01 - 2.047098130E-01 2.090279010E-01 2.133596240E-01 2.177056970E-01 2.220668640E-01 - 2.264439170E-01 2.308378070E-01 2.352494450E-01 2.396797840E-01 2.441297770E-01 - 2.486003940E-01 2.530927660E-01 2.576081450E-01 2.621478140E-01 2.667129640E-01 - 2.713048160E-01 2.759246530E-01 2.805745600E-01 2.852559090E-01 2.899698020E-01 - 2.947182660E-01 2.995035050E-01 3.043272500E-01 3.091911970E-01 3.140982390E-01 - 3.190501030E-01 2.309601750E-01 2.287083120E-01 2.264547050E-01 2.241985500E-01 - 2.219392510E-01 2.196763600E-01 2.174094320E-01 2.151379440E-01 2.128615530E-01 - 2.105798720E-01 2.082925740E-01 2.059992550E-01 2.036995890E-01 2.013933360E-01 - 1.990801990E-01 1.967598050E-01 1.944319460E-01 1.920962930E-01 1.897526090E-01 - 1.874006240E-01 1.850400870E-01 1.826706980E-01 1.802922340E-01 1.779044420E-01 - 1.755070540E-01 1.730998610E-01 1.706825940E-01 1.682550460E-01 1.658169330E-01 - 1.633680310E-01 1.609081330E-01 1.584370290E-01 1.559543610E-01 1.534599810E-01 - 1.509535910E-01 1.484349820E-01 1.459064630E-01 1.433710010E-01 1.408307110E-01 - 1.382871870E-01 1.357413530E-01 1.331932540E-01 1.306433830E-01 1.280922440E-01 - 1.255403610E-01 1.229881940E-01 1.204362960E-01 1.178852920E-01 1.153356950E-01 - 1.127879770E-01 1.102426280E-01 1.077001240E-01 1.051609370E-01 1.026255410E-01 - 1.000943330E-01 9.756772220E-02 9.504614770E-02 9.253001960E-02 9.001974020E-02 - 8.751574900E-02 8.501846340E-02 8.252829310E-02 8.004567030E-02 7.757101950E-02 - 7.510475810E-02 7.264733310E-02 7.019920650E-02 6.776085500E-02 6.533273310E-02 - 6.291534010E-02 6.050922720E-02 5.811494590E-02 5.573300640E-02 5.336401980E-02 - 5.100861560E-02 4.866740480E-02 4.634102430E-02 4.403012620E-02 4.173546280E-02 - 3.945769740E-02 3.719756750E-02 3.495584060E-02 3.273327280E-02 3.053063710E-02 - 2.834874580E-02 2.618841640E-02 2.405046860E-02 2.193576280E-02 1.984511870E-02 - 1.777942850E-02 1.573956200E-02 1.372639740E-02 1.174081860E-02 9.783720600E-03 - 7.856005800E-03 5.958579950E-03 4.092335240E-03 2.258187630E-03 4.570372690E-04 --1.310214280E-03-3.042666710E-03-4.739395340E-03-6.399544890E-03-8.022201250E-03 --9.606489910E-03-1.115153730E-02-1.265646890E-02-1.412042880E-02-1.554255650E-02 --1.692201570E-02-1.825798860E-02-1.954965480E-02-2.079620030E-02-2.199683340E-02 --2.315077370E-02-2.425725760E-02-2.531552500E-02-2.632486080E-02-2.728451420E-02 --2.819380910E-02-2.905204520E-02-2.985855190E-02-3.061269040E-02-3.131378070E-02 --3.196121750E-02-3.255443270E-02-3.309284900E-02-3.357589620E-02-3.400303800E-02 --3.437374160E-02-3.468749670E-02-3.494384880E-02-3.514233600E-02-3.528254110E-02 --3.536405410E-02-3.538647670E-02-3.534946220E-02-3.525264930E-02-3.509573270E-02 --3.487843280E-02-3.460048880E-02-3.426166250E-02-3.386173020E-02-3.340052810E-02 --3.287789970E-02-3.229370710E-02-3.164783870E-02-3.094023650E-02-3.017085980E-02 --2.933970280E-02-2.844677310E-02-2.749210780E-02-2.647578340E-02-2.539792840E-02 --2.425868810E-02-2.305820770E-02-2.179667170E-02-2.047435750E-02-1.909150740E-02 --1.764843610E-02-1.614546030E-02-1.458293390E-02-1.296123300E-02-1.128082350E-02 --9.542171840E-03-7.745749780E-03-5.892030890E-03-3.981595860E-03-2.015021400E-03 - 7.088745860E-06 2.084105740E-03 4.215375520E-03 6.400209390E-03 8.637895810E-03 - 1.092772740E-02 1.326892430E-02 1.566076090E-02 1.810243350E-02 2.059313650E-02 - 2.313205970E-02 2.571839470E-02 2.835133860E-02 3.102997880E-02 3.375352170E-02 - 3.652118890E-02 3.933205830E-02 4.218531770E-02 4.508015890E-02 4.801576960E-02 - 5.099134890E-02 5.400609970E-02 5.705926940E-02 6.015006830E-02 6.327781830E-02 - 6.644182650E-02 6.964136660E-02 7.287581260E-02 7.614456120E-02 7.944698630E-02 - 8.278256650E-02 8.615081010E-02 8.955123280E-02 9.298343960E-02 9.644711020E-02 - 9.994187950E-02 1.034677030E-01 1.070246250E-01 1.106130410E-01 1.142333520E-01 - 1.178867370E-01 1.215734410E-01 1.252948490E-01 1.290550980E-01 1.328583360E-01 - 1.367062780E-01 1.406200680E-01 1.446223260E-01 1.486976000E-01 1.528278590E-01 - 1.569914220E-01 1.611600670E-01 1.653365490E-01 1.695213760E-01 1.737150250E-01 - 1.779180170E-01 1.821308730E-01 1.863541600E-01 1.905884440E-01 1.948342770E-01 - 1.990922540E-01 2.033630610E-01 2.076473530E-01 2.119459060E-01 2.162594940E-01 - 2.205887590E-01 2.249346230E-01 2.292980250E-01 2.336797860E-01 2.380809490E-01 - 2.425024660E-01 2.469454850E-01 2.514111400E-01 2.559004430E-01 2.604148090E-01 - 2.649555800E-01 2.695240970E-01 2.741218210E-01 2.787502710E-01 2.834111450E-01 - 2.881060840E-01 2.928367260E-01 2.976052760E-01 3.024138210E-01 3.072644170E-01 - 3.121593000E-01 3.171008530E-01 3.220916390E-01 2.314959320E-01 2.292419370E-01 - 2.269876000E-01 2.247317880E-01 2.224741280E-01 2.202140990E-01 2.179511640E-01 - 2.156848460E-01 2.134148030E-01 2.111405130E-01 2.088616190E-01 2.065777480E-01 - 2.042885570E-01 2.019937040E-01 1.996928160E-01 1.973855940E-01 1.950717420E-01 - 1.927509610E-01 1.904229220E-01 1.880873590E-01 1.857439880E-01 1.833925400E-01 - 1.810327320E-01 1.786642970E-01 1.762869950E-01 1.739005600E-01 1.715047060E-01 - 1.690992270E-01 1.666838380E-01 1.642583010E-01 1.618223790E-01 1.593758310E-01 - 1.569184060E-01 1.544498800E-01 1.519699840E-01 1.494783460E-01 1.469763960E-01 - 1.444669070E-01 1.419520230E-01 1.394339200E-01 1.369143870E-01 1.343927680E-01 - 1.318696290E-01 1.293455810E-01 1.268211160E-01 1.242966580E-01 1.217727810E-01 - 1.192500220E-01 1.167289090E-01 1.142099650E-01 1.116936650E-01 1.091804950E-01 - 1.066709240E-01 1.041654270E-01 1.016644090E-01 9.916830060E-02 9.667751940E-02 - 9.419249740E-02 9.171363710E-02 8.924137060E-02 8.677610010E-02 8.431826530E-02 - 8.186827600E-02 7.942657170E-02 7.699357720E-02 7.456973940E-02 7.215549800E-02 - 6.975129250E-02 6.735762210E-02 6.497498600E-02 6.260389830E-02 6.024486200E-02 - 5.789841710E-02 5.556513000E-02 5.324561520E-02 5.094049500E-02 4.865039140E-02 - 4.637594890E-02 4.411783440E-02 4.187673700E-02 3.965337570E-02 3.744847700E-02 - 3.526278960E-02 3.309707720E-02 3.095211090E-02 2.882867310E-02 2.672762240E-02 - 2.464976160E-02 2.259590850E-02 2.056689930E-02 1.856358720E-02 1.658683640E-02 - 1.463751870E-02 1.271651780E-02 1.082470170E-02 8.962967430E-03 7.132201920E-03 - 5.333276930E-03 3.567076060E-03 1.834499420E-03 1.364395580E-04-1.526233970E-03 --3.152639140E-03-4.741906190E-03-6.293167830E-03-7.805549070E-03-9.278203360E-03 --1.071028500E-02-1.210094990E-02-1.344938200E-02-1.475476470E-02-1.601628030E-02 --1.723313150E-02-1.840454530E-02-1.952975620E-02-2.060800790E-02-2.163854990E-02 --2.262065190E-02-2.355362100E-02-2.443677000E-02-2.526939850E-02-2.605085450E-02 --2.678048420E-02-2.745764890E-02-2.808175980E-02-2.865225260E-02-2.916855740E-02 --2.963009850E-02-3.003631350E-02-3.038671430E-02-3.068083900E-02-3.091820700E-02 --3.109837880E-02-3.122092970E-02-3.128545360E-02-3.129157800E-02-3.123894330E-02 --3.112721070E-02-3.095607650E-02-3.072529290E-02-3.043461590E-02-3.008379970E-02 --2.967260590E-02-2.920088920E-02-2.866851540E-02-2.807530950E-02-2.742122670E-02 --2.670622990E-02-2.593027800E-02-2.509333380E-02-2.419537490E-02-2.323652800E-02 --2.221685650E-02-2.113647950E-02-1.999555530E-02-1.879424420E-02-1.753274170E-02 --1.621129740E-02-1.483019070E-02-1.338971590E-02-1.189020000E-02-1.033203300E-02 --8.715539240E-03-7.041202390E-03-5.309490020E-03-3.520869180E-03-1.675828830E-03 - 2.250690010E-04 2.181246410E-03 4.192114810E-03 6.257055330E-03 8.375413720E-03 - 1.054652780E-02 1.276969820E-02 1.504421890E-02 1.736934670E-02 1.974433850E-02 - 2.216845190E-02 2.464091780E-02 2.716092770E-02 2.972766570E-02 3.234033660E-02 - 3.499818220E-02 3.770038110E-02 4.044606910E-02 4.323448610E-02 4.606487970E-02 - 4.893645640E-02 5.184840780E-02 5.479992930E-02 5.779035390E-02 6.081887710E-02 - 6.388483200E-02 6.698755170E-02 7.012637700E-02 7.330064480E-02 7.650971410E-02 - 7.975307110E-02 8.303013440E-02 8.634041990E-02 8.968343590E-02 9.305883940E-02 - 9.646645190E-02 9.990535680E-02 1.033758970E-01 1.068782730E-01 1.104126800E-01 - 1.139793690E-01 1.175790730E-01 1.212130560E-01 1.248816550E-01 1.285891530E-01 - 1.323394630E-01 1.361363380E-01 1.399907320E-01 1.439357100E-01 1.479541060E-01 - 1.520278750E-01 1.561463330E-01 1.602721960E-01 1.644051220E-01 1.685471240E-01 - 1.726985570E-01 1.768598110E-01 1.810314510E-01 1.852139680E-01 1.894079600E-01 - 1.936139460E-01 1.978325990E-01 2.020646040E-01 2.063104510E-01 2.105709170E-01 - 2.148468350E-01 2.191389800E-01 2.234481720E-01 2.277753060E-01 2.321212290E-01 - 2.364869420E-01 2.408735310E-01 2.452820090E-01 2.497135100E-01 2.541692550E-01 - 2.586505410E-01 2.631586790E-01 2.676950400E-01 2.722610240E-01 2.768585380E-01 - 2.814888060E-01 2.861538530E-01 2.908554080E-01 2.955951390E-01 3.003758190E-01 - 3.051992650E-01 3.100676240E-01 3.149834870E-01 3.199495970E-01 3.249683380E-01 - 2.319756450E-01 2.297227980E-01 2.274702340E-01 2.252174760E-01 2.229639740E-01 - 2.207091600E-01 2.184524240E-01 2.161934230E-01 2.139315900E-01 2.116665240E-01 - 2.093978230E-01 2.071250530E-01 2.048479170E-01 2.025659380E-01 2.002787890E-01 - 1.979861710E-01 1.956876810E-01 1.933830530E-01 1.910719870E-01 1.887541260E-01 - 1.864291880E-01 1.840968730E-01 1.817569140E-01 1.794090270E-01 1.770529450E-01 - 1.746883690E-01 1.723150460E-01 1.699326930E-01 1.675410870E-01 1.651399730E-01 - 1.627290840E-01 1.603081970E-01 1.578770280E-01 1.554353680E-01 1.529829950E-01 - 1.505192970E-01 1.480451970E-01 1.455629770E-01 1.430747960E-01 1.405831720E-01 - 1.380902080E-01 1.355958880E-01 1.331005540E-01 1.306045650E-01 1.281084120E-01 - 1.256125570E-01 1.231175440E-01 1.206239090E-01 1.181321520E-01 1.156428010E-01 - 1.131563630E-01 1.106733310E-01 1.081941870E-01 1.057193500E-01 1.032492890E-01 - 1.007844280E-01 9.832518550E-02 9.587199240E-02 9.342525900E-02 9.098540990E-02 - 8.855285500E-02 8.612802620E-02 8.371134100E-02 8.130324630E-02 7.890415940E-02 - 7.651451980E-02 7.413478200E-02 7.176539300E-02 6.940682980E-02 6.705952440E-02 - 6.472402070E-02 6.240084770E-02 6.009050830E-02 5.779353900E-02 5.551056190E-02 - 5.324216190E-02 5.098893490E-02 4.875152930E-02 4.653059320E-02 4.432679710E-02 - 4.214082290E-02 3.997340050E-02 3.782524540E-02 3.569707650E-02 3.358969090E-02 - 3.150385990E-02 2.944036950E-02 2.740000750E-02 2.538356930E-02 2.339188570E-02 - 2.142578550E-02 1.948612370E-02 1.757375900E-02 1.568955560E-02 1.383433860E-02 - 1.200898830E-02 1.021436700E-02 8.451341650E-03 6.720782720E-03 5.023561880E-03 - 3.360566450E-03 1.732650330E-03 1.406591330E-04-1.414548610E-03-2.932108940E-03 --4.411167470E-03-5.850881340E-03-7.250427730E-03-8.608991280E-03-9.925753810E-03 --1.119990180E-02-1.243064370E-02-1.361720080E-02-1.475880670E-02-1.585469770E-02 --1.690413430E-02-1.790638270E-02-1.886073310E-02-1.976649280E-02-2.062296120E-02 --2.142947170E-02-2.218537220E-02-2.289003690E-02-2.354285680E-02-2.414322640E-02 --2.469056840E-02-2.518431840E-02-2.562392500E-02-2.600887790E-02-2.633867970E-02 --2.661285180E-02-2.683094700E-02-2.699251660E-02-2.709713760E-02-2.714445070E-02 --2.713403480E-02-2.706558260E-02-2.693878490E-02-2.675333620E-02-2.650897200E-02 --2.620545220E-02-2.584252880E-02-2.542001010E-02-2.493777310E-02-2.439563720E-02 --2.379347570E-02-2.313125320E-02-2.240892500E-02-2.162645010E-02-2.078380620E-02 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1.282290370E-01 1.319236760E-01 1.356657890E-01 1.394620390E-01 1.433461010E-01 - 1.473082750E-01 1.513299350E-01 1.553924380E-01 1.594751030E-01 1.635615080E-01 - 1.676574950E-01 1.717631820E-01 1.758792400E-01 1.800060570E-01 1.841441840E-01 - 1.882940980E-01 1.924564090E-01 1.966316700E-01 2.008204760E-01 2.050235720E-01 - 2.092415990E-01 2.134753170E-01 2.177255000E-01 2.219929400E-01 2.262783800E-01 - 2.305829230E-01 2.349075530E-01 2.392531340E-01 2.436207830E-01 2.480116190E-01 - 2.524268030E-01 2.568677370E-01 2.613355220E-01 2.658317390E-01 2.703577580E-01 - 2.749151890E-01 2.795056400E-01 2.841308710E-01 2.887926700E-01 2.934931220E-01 - 2.982343140E-01 3.030180630E-01 3.078469930E-01 3.127236070E-01 3.176502290E-01 - 3.226296600E-01 3.276648520E-01 2.323950830E-01 2.301462440E-01 2.278986280E-01 - 2.256516810E-01 2.234048250E-01 2.211575510E-01 2.189093530E-01 2.166597250E-01 - 2.144081590E-01 2.121542390E-01 2.098975630E-01 2.076377120E-01 2.053742260E-01 - 2.031067610E-01 2.008349450E-01 1.985584350E-01 1.962768440E-01 1.939898430E-01 - 1.916971060E-01 1.893983040E-01 1.870931240E-01 1.847812830E-01 1.824624240E-01 - 1.801362930E-01 1.778026070E-01 1.754610840E-01 1.731114240E-01 1.707533600E-01 - 1.683866530E-01 1.660110350E-01 1.636262690E-01 1.612320540E-01 1.588281840E-01 - 1.564143750E-01 1.539904180E-01 1.515560900E-01 1.491107790E-01 1.466569010E-01 - 1.441968380E-01 1.417330350E-01 1.392677720E-01 1.368013920E-01 1.343344750E-01 - 1.318674830E-01 1.294005220E-01 1.269341410E-01 1.244688410E-01 1.220051570E-01 - 1.195436120E-01 1.170847040E-01 1.146289560E-01 1.121768650E-01 1.097288880E-01 - 1.072854920E-01 1.048471330E-01 1.024142500E-01 9.998726840E-02 9.756660460E-02 - 9.515268360E-02 9.274593000E-02 9.034675360E-02 8.795559410E-02 8.557286110E-02 - 8.319898690E-02 8.083442600E-02 7.847960290E-02 7.613495740E-02 7.380095870E-02 - 7.147803900E-02 6.916667520E-02 6.686733660E-02 6.458055970E-02 6.230688470E-02 - 6.004682930E-02 5.780094490E-02 5.556982380E-02 5.335404350E-02 5.115424470E-02 - 4.897106440E-02 4.680514340E-02 4.465713720E-02 4.252775010E-02 4.041769730E-02 - 3.832768650E-02 3.625847030E-02 3.421080480E-02 3.218545390E-02 3.018317190E-02 - 2.820475770E-02 2.625100310E-02 2.432274450E-02 2.242081240E-02 2.054603400E-02 - 1.869921390E-02 1.688121630E-02 1.509287770E-02 1.333503890E-02 1.160853820E-02 - 9.914250110E-03 8.253029550E-03 6.625717510E-03 5.033159160E-03 3.476199460E-03 - 1.955683810E-03 4.724550820E-04-9.726743450E-04-2.378853040E-03-3.745274390E-03 --5.071136630E-03-6.355638150E-03-7.597981020E-03-8.797387590E-03-9.953093720E-03 --1.106433570E-02-1.213037320E-02-1.315047130E-02-1.412391200E-02-1.504999860E-02 --1.592803560E-02-1.675735790E-02-1.753729770E-02-1.826721620E-02-1.894650240E-02 --1.957454900E-02-2.015074900E-02-2.067455650E-02-2.114540340E-02-2.156277560E-02 --2.192615530E-02-2.223504150E-02-2.248897780E-02-2.268751710E-02-2.283023480E-02 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7.453309000E-02 7.761999220E-02 8.074211330E-02 8.389891680E-02 8.708989620E-02 - 9.031471610E-02 9.357270600E-02 9.686358270E-02 1.001872420E-01 1.035435870E-01 - 1.069325130E-01 1.103541930E-01 1.138089970E-01 1.172972470E-01 1.208205670E-01 - 1.243791210E-01 1.279756870E-01 1.316140000E-01 1.352997720E-01 1.390381600E-01 - 1.428585050E-01 1.467600910E-01 1.507266010E-01 1.547362360E-01 1.587698010E-01 - 1.628095060E-01 1.668560060E-01 1.709128020E-01 1.749803570E-01 1.790590880E-01 - 1.831496360E-01 1.872520450E-01 1.913670900E-01 1.954953070E-01 1.996372640E-01 - 2.037936150E-01 2.079650760E-01 2.121522580E-01 2.163559650E-01 2.205771060E-01 - 2.248163520E-01 2.290745680E-01 2.333527510E-01 2.376518990E-01 2.419729980E-01 - 2.463173120E-01 2.506857510E-01 2.550796570E-01 2.595003840E-01 2.639492150E-01 - 2.684275810E-01 2.729370000E-01 2.774792020E-01 2.820558250E-01 2.866686280E-01 - 2.913196380E-01 2.960107330E-01 3.007441760E-01 3.055220540E-01 3.103467520E-01 - 3.152209820E-01 3.201474850E-01 3.251291810E-01 3.301686640E-01 2.327509820E-01 - 2.305090730E-01 2.282691000E-01 2.260305880E-01 2.237929250E-01 2.215556500E-01 - 2.193182410E-01 2.170801460E-01 2.148409780E-01 2.126002760E-01 2.103575920E-01 - 2.081124780E-01 2.058645040E-01 2.036133260E-01 2.013585270E-01 1.990997490E-01 - 1.968366060E-01 1.945687680E-01 1.922958640E-01 1.900175360E-01 1.877335010E-01 - 1.854434460E-01 1.831470280E-01 1.808439490E-01 1.785339270E-01 1.762166470E-01 - 1.738918420E-01 1.715592590E-01 1.692186000E-01 1.668695960E-01 1.645119790E-01 - 1.621455700E-01 1.597700420E-01 1.573851850E-01 1.549908520E-01 1.525860880E-01 - 1.501712500E-01 1.477476660E-01 1.453166010E-01 1.428813790E-01 1.404448900E-01 - 1.380075370E-01 1.355699000E-01 1.331325320E-01 1.306957010E-01 1.282596590E-01 - 1.258249580E-01 1.233920830E-01 1.209615770E-01 1.185339320E-01 1.161096620E-01 - 1.136892810E-01 1.112732660E-01 1.088620720E-01 1.064561460E-01 1.040559490E-01 - 1.016619350E-01 9.927448630E-02 9.689404820E-02 9.452104570E-02 9.215589610E-02 - 8.979901670E-02 8.745084700E-02 8.511181920E-02 8.278236540E-02 8.046292510E-02 - 7.815393060E-02 7.585583630E-02 7.356909660E-02 7.129417360E-02 6.903155890E-02 - 6.678173690E-02 6.454525140E-02 6.232259050E-02 6.011431290E-02 5.792099240E-02 - 5.574319880E-02 5.358150970E-02 5.143656950E-02 4.930901900E-02 4.719950630E-02 - 4.510867220E-02 4.303729160E-02 4.098595310E-02 3.895539790E-02 3.694639350E-02 - 3.495969250E-02 3.299606220E-02 3.105625880E-02 2.914104240E-02 2.725117280E-02 - 2.538749760E-02 2.355082520E-02 2.174195650E-02 1.996172030E-02 1.821093820E-02 - 1.649044080E-02 1.480104960E-02 1.314360930E-02 1.151895150E-02 9.927886540E-03 - 8.371245120E-03 6.849873810E-03 5.364608490E-03 3.916249140E-03 2.505632350E-03 - 1.133550890E-03-1.992061010E-04-1.491845120E-03-2.743569200E-03-3.953577480E-03 --5.121129560E-03-6.245471070E-03-7.325855080E-03-8.361550050E-03-9.351840240E-03 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3.228815270E-02 3.465659540E-02 3.707125410E-02 3.953142090E-02 4.203638810E-02 - 4.458544400E-02 4.717788850E-02 4.981302840E-02 5.249008910E-02 5.520842600E-02 - 5.796734990E-02 6.076616420E-02 6.360419840E-02 6.648080050E-02 6.939534100E-02 - 7.234720140E-02 7.533580060E-02 7.836054270E-02 8.142088350E-02 8.451631670E-02 - 8.764632790E-02 9.081058200E-02 9.400842340E-02 9.723954650E-02 1.005038840E-01 - 1.038013470E-01 1.071318540E-01 1.104952990E-01 1.138919000E-01 1.173241440E-01 - 1.207889320E-01 1.242896170E-01 1.278295810E-01 1.314121930E-01 1.350408350E-01 - 1.387211230E-01 1.424786600E-01 1.463181230E-01 1.502227490E-01 1.541757730E-01 - 1.581605820E-01 1.621542130E-01 1.661465020E-01 1.701518000E-01 1.741681250E-01 - 1.781954620E-01 1.822349580E-01 1.862868670E-01 1.903514860E-01 1.944293080E-01 - 1.985210630E-01 2.026271970E-01 2.067483660E-01 2.108852710E-01 2.150386570E-01 - 2.192092540E-01 2.233978660E-01 2.276052980E-01 2.318324890E-01 2.360804080E-01 - 2.403499930E-01 2.446422280E-01 2.489583490E-01 2.532995340E-01 2.576670350E-01 - 2.620621320E-01 2.664861380E-01 2.709406610E-01 2.754271920E-01 2.799473110E-01 - 2.845028040E-01 2.890957300E-01 2.937276660E-01 2.984009680E-01 3.031179310E-01 - 3.078805800E-01 3.126911820E-01 3.175525960E-01 3.224677150E-01 3.274392780E-01 - 3.324702680E-01 2.330406900E-01 2.308085560E-01 2.285789550E-01 2.263514100E-01 - 2.241254150E-01 2.219004930E-01 2.196761370E-01 2.174518850E-01 2.152272460E-01 - 2.130018030E-01 2.107750480E-01 2.085466090E-01 2.063160390E-01 2.040829360E-01 - 2.018468980E-01 1.996075360E-01 1.973644940E-01 1.951173690E-01 1.928658190E-01 - 1.906095000E-01 1.883480700E-01 1.860812160E-01 1.838085950E-01 1.815299090E-01 - 1.792448610E-01 1.769531220E-01 1.746544390E-01 1.723484840E-01 1.700350340E-01 - 1.677137760E-01 1.653845010E-01 1.630469260E-01 1.607007830E-01 1.583458780E-01 - 1.559822560E-01 1.536083070E-01 1.512246880E-01 1.488325150E-01 1.464327720E-01 - 1.440270990E-01 1.416201590E-01 1.392126530E-01 1.368052070E-01 1.343982960E-01 - 1.319923550E-01 1.295875160E-01 1.271842420E-01 1.247830390E-01 1.223843920E-01 - 1.199888210E-01 1.175968270E-01 1.152089240E-01 1.128256170E-01 1.104473700E-01 - 1.080745910E-01 1.057077800E-01 1.033473980E-01 1.009938340E-01 9.864753480E-02 - 9.630890940E-02 9.397839750E-02 9.165642410E-02 8.934340630E-02 8.703977610E-02 - 8.474597330E-02 8.246244490E-02 8.018962290E-02 7.792797680E-02 7.567793130E-02 - 7.343996320E-02 7.121455670E-02 6.900217380E-02 6.680332870E-02 6.461852790E-02 - 6.244831530E-02 6.029324230E-02 5.815386770E-02 5.603075770E-02 5.392452700E-02 - 5.183581260E-02 4.976524410E-02 4.771345850E-02 4.568113390E-02 4.366895560E-02 - 4.167759050E-02 3.970773890E-02 3.776016830E-02 3.583562750E-02 3.393486510E-02 - 3.205862640E-02 3.020766000E-02 2.838273910E-02 2.658469230E-02 2.481428910E-02 - 2.307231350E-02 2.135957960E-02 1.967691070E-02 1.802511510E-02 1.640501620E-02 - 1.481741390E-02 1.326309610E-02 1.174288430E-02 1.025761760E-02 8.808092210E-03 - 7.395118470E-03 6.019480990E-03 4.681958820E-03 3.383342410E-03 2.124418270E-03 - 9.059801230E-04-2.712366110E-04-1.406471010E-03-2.498992490E-03-3.548074980E-03 --4.552992060E-03-5.513058980E-03-6.427545570E-03-7.295772900E-03-8.117102090E-03 --8.890895170E-03-9.616511870E-03-1.029331890E-02-1.092072390E-02-1.149813740E-02 --1.202499490E-02-1.250076670E-02-1.292492360E-02-1.329693760E-02-1.361633650E-02 --1.388263980E-02-1.409538090E-02-1.425416490E-02-1.435859870E-02-1.440828760E-02 --1.440283840E-02-1.434194480E-02-1.422528180E-02-1.405256610E-02-1.382353530E-02 --1.353793310E-02-1.319553890E-02-1.279617850E-02-1.233969260E-02-1.182593310E-02 --1.125477810E-02-1.062613730E-02-9.939965790E-03-9.196245110E-03-8.394956590E-03 --7.536120710E-03-6.619814780E-03-5.646058820E-03-4.615013490E-03-3.526832210E-03 --2.381667490E-03-1.179673940E-03 7.888117400E-05 1.393759270E-03 2.764704870E-03 - 4.191373470E-03 5.673420620E-03 7.210504260E-03 8.802273310E-03 1.044818760E-02 - 1.214797790E-02 1.390110980E-02 1.570705700E-02 1.756529140E-02 1.947528680E-02 - 2.143651620E-02 2.344845050E-02 2.551045270E-02 2.762190250E-02 2.978217040E-02 - 3.199062500E-02 3.424660860E-02 3.654946760E-02 3.889853880E-02 4.129316660E-02 - 4.373265430E-02 4.621628670E-02 4.874339330E-02 5.131328480E-02 5.392531310E-02 - 5.657879640E-02 5.927307530E-02 6.200747940E-02 6.478134540E-02 6.759405880E-02 - 7.044499370E-02 7.333356890E-02 7.625918840E-02 7.922128590E-02 8.221933990E-02 - 8.525284380E-02 8.832126110E-02 9.142414480E-02 9.456114470E-02 9.773188080E-02 - 1.009361150E-01 1.041737720E-01 1.074448820E-01 1.107492970E-01 1.140873800E-01 - 1.174599160E-01 1.208679300E-01 1.243114920E-01 1.277935360E-01 1.313176010E-01 - 1.348873380E-01 1.385115980E-01 1.422030180E-01 1.459839940E-01 1.498307730E-01 - 1.537253410E-01 1.576524820E-01 1.615953450E-01 1.655362990E-01 1.694796380E-01 - 1.734437200E-01 1.774185600E-01 1.814047840E-01 1.854033770E-01 1.894147400E-01 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3.683752190E-02 3.500066330E-02 3.318898750E-02 3.140324730E-02 - 2.964422480E-02 2.791268940E-02 2.620941590E-02 2.453518660E-02 2.289081740E-02 - 2.127705330E-02 1.969471570E-02 1.814459260E-02 1.662747380E-02 1.514415350E-02 - 1.369540490E-02 1.228206510E-02 1.090488770E-02 9.564649310E-03 8.262127640E-03 - 6.998100780E-03 5.773331500E-03 4.588554150E-03 3.444542880E-03 2.342018300E-03 - 1.281698470E-03 2.643025950E-04-7.094508620E-04-1.638904100E-03-2.523317470E-03 --3.362062850E-03-4.154517320E-03-4.900040100E-03-5.597990010E-03-6.247745830E-03 --6.848749700E-03-7.400400010E-03-7.902172390E-03-8.353538810E-03-8.753973990E-03 --9.102959190E-03-9.400028740E-03-9.644717910E-03-9.836610410E-03-9.975290860E-03 --1.006036160E-02-1.009142960E-02-1.006815120E-02-9.990202260E-03-9.857294150E-03 --9.669142780E-03-9.425465950E-03-9.126060640E-03-8.770702410E-03-8.359228260E-03 --7.891475220E-03-7.367291490E-03-6.786601620E-03-6.149296650E-03-5.455357950E-03 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1.313294770E-01 1.348397280E-01 1.384060080E-01 1.420385390E-01 1.457546950E-01 - 1.495453120E-01 1.533841790E-01 1.572501660E-01 1.611316350E-01 1.650134330E-01 - 1.689065250E-01 1.728134900E-01 1.767325100E-01 1.806632580E-01 1.846062240E-01 - 1.885617970E-01 1.925305870E-01 1.965130270E-01 2.005096080E-01 2.045209850E-01 - 2.085477560E-01 2.125903670E-01 2.166496810E-01 2.207263560E-01 2.248210460E-01 - 2.289345410E-01 2.330677210E-01 2.372214790E-01 2.413967550E-01 2.455945760E-01 - 2.498157620E-01 2.540616390E-01 2.583333850E-01 2.626321910E-01 2.669592500E-01 - 2.713160510E-01 2.757042650E-01 2.801251110E-01 2.845804100E-01 2.890718880E-01 - 2.936013340E-01 2.981708050E-01 3.027822670E-01 3.074381050E-01 3.121404950E-01 - 3.168919980E-01 3.216952380E-01 3.265528080E-01 3.314673600E-01 3.364428880E-01 - 2.334137260E-01 2.312084140E-01 2.290068420E-01 2.268085630E-01 2.246130700E-01 - 2.224199180E-01 2.202286120E-01 2.180386630E-01 2.158496080E-01 2.136610000E-01 - 2.114723770E-01 2.092832920E-01 2.070932840E-01 2.049019780E-01 2.027089300E-01 - 2.005137500E-01 1.983160230E-01 1.961153600E-01 1.939113740E-01 1.917037960E-01 - 1.894921510E-01 1.872761550E-01 1.850554650E-01 1.828297530E-01 1.805986910E-01 - 1.783619970E-01 1.761193570E-01 1.738704740E-01 1.716150340E-01 1.693528440E-01 - 1.670835610E-01 1.648069470E-01 1.625227630E-01 1.602310240E-01 1.579306270E-01 - 1.556214990E-01 1.533039660E-01 1.509783270E-01 1.486449090E-01 1.463044140E-01 - 1.439591940E-01 1.416141540E-01 1.392697240E-01 1.369263380E-01 1.345843970E-01 - 1.322443040E-01 1.299063710E-01 1.275708820E-01 1.252383590E-01 1.229093000E-01 - 1.205841970E-01 1.182635280E-01 1.159478200E-01 1.136375520E-01 1.113331990E-01 - 1.090352090E-01 1.067440360E-01 1.044601430E-01 1.021839450E-01 9.991589190E-02 - 9.765640650E-02 9.540591390E-02 9.316484630E-02 9.093362840E-02 8.871270720E-02 - 8.650252970E-02 8.430352810E-02 8.211614190E-02 7.994084060E-02 7.777807860E-02 - 7.562834020E-02 7.349207250E-02 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1.075697300E+00 1.019174340E+00 1.035474540E+00 1.019101620E+00 9.952518340E-01 1.019028780E+00 9.550291300E-01 1.018955950E+00 9.148063660E-01 1.018883110E+00 8.745836620E-01 1.018810270E+00 diff --git a/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode_kinetic.gpeckf b/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode_kinetic.gpeckf index 037c924f2..aec26a951 100644 --- a/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode_kinetic.gpeckf +++ b/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode_kinetic.gpeckf @@ -1,515 +1,515 @@ psi_n n_i[m^-3] n_e[m^-3] T_i[eV] T_e[eV] omega_E[rad/s] -0.000000e+00 4.500000e+19 5.500000e+19 5.000000e+03 2.500000e+03 1.052400e+05 -1.949000e-03 4.499240e+19 5.494810e+19 4.978366e+03 2.498558e+03 1.044239e+05 -3.899000e-03 4.498020e+19 5.489310e+19 4.958428e+03 2.496873e+03 1.036046e+05 -5.848000e-03 4.496540e+19 5.483680e+19 4.939117e+03 2.495082e+03 1.027866e+05 -7.797000e-03 4.494860e+19 5.477970e+19 4.920222e+03 2.493218e+03 1.019689e+05 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zA0iHmZ^Bo@PECvI>Pd6_Uqpr2EbT*}`nr+@>O7(Hs?Mn*^c5~Vi>gX(6tg53)9L&|6mQvNJ%a&0c z`Fg+(zBuqVRRF&?AqS{YJ!nA_=k|%?ae%vrdw@IsK@Qvy;74=A$Kn9LAeSJTpRdt> zT`17`pM`?uEB+ED{(le({y`w1PU-{yu=gh$CK;GyV3L7J1|}JpWMGnkNd_hvm}Fp* zf&Wen{Il~v<3Dr$*ZN!P|KHB?tNzz#eSF|wzL+@vJ1sS!YHCtlsDEh%e1(805cpFA zP~#UCxcCw>05#Y@C^*2Es!9xBjnn%7QDNXO2mcEd1R8%Y9?GBC-&Bm|H_W;^HTt=|Z z9hdw68UBC%fdgDe@VAEz{<&W8r&d7o-Til&;Q#jX2LGrC)J*CD|GFOrlaWm_Fv-9q Z1CtC)GBC-&Bm Date: Wed, 24 Jun 2026 16:23:10 -0400 Subject: [PATCH 109/135] KineticForces - CLEANUP - Remove per-evaluation debug prints from NTV torque Drop leftover println/printf debug in tpsi! that flooded stdout during the psi-quadrature (see #303). Co-Authored-By: Claude Opus 4.8 --- src/KineticForces/Torque.jl | 17 ----------------- 1 file changed, 17 deletions(-) diff --git a/src/KineticForces/Torque.jl b/src/KineticForces/Torque.jl index 44f7d9bf4..e9d7ab53c 100644 --- a/src/KineticForces/Torque.jl +++ b/src/KineticForces/Torque.jl @@ -37,12 +37,6 @@ function tpsi!(tpsi_var::Ref{ComplexF64}, psi::Float64, n::Int, l::Int, imx_override::Union{Nothing,Float64}=nothing, atol_xlmda::Float64=1e-9, rtol_xlmda::Float64=1e-6) - if intr.verbose - println("torque - tpsi function, psi = ", psi) - println(" electron ", electron) - println(" ell ", l) - end - # Enforce bounds if psi > 1 tpsi_var[] = 0.0 @@ -196,14 +190,6 @@ function tpsi!(tpsi_var::Ref{ComplexF64}, psi::Float64, n::Int, l::Int, wdhat = q^3 * wtran^2 / (4 * epsr * wgyro) * wdfac nueff = nu_s / (2 * epsr) - if intr.verbose - @printf(" eq values = %.1e %.1e %.1e %.1e %.1e %.1e %.1f %d\n", - wdian, wdiat, welec, wdhat, wbhat, nueff, q, 0) - end - - if intr.verbose - println(" method = ", method) - end # Method selection — route on the registry dispatch tag (errors on unknown method) kind = method_kind(method) @@ -248,9 +234,6 @@ function tpsi!(tpsi_var::Ref{ComplexF64}, psi::Float64, n::Int, l::Int, rex_override=rex_override, imx_override=imx_override) end - if intr.verbose - println("torque - end function, psi = ", psi) - end return nothing end From 641c2d148db4570cf8809edc6d5fab270a10ce45 Mon Sep 17 00:00:00 2001 From: d-burg Date: Wed, 24 Jun 2026 20:29:33 -0400 Subject: [PATCH 110/135] TEST - CLEANUP - Reword parallel-integration et[1] comment Drop the unverified 'parallel and standard ODE paths agree to rel_diff=0' claim from the DIIID-like testset (it only runs the parallel path); note the cross-path agreement is verified on the Solovev testset. Addresses PR review. Co-Authored-By: Claude Opus 4.8 --- test/runtests_parallel_integration.jl | 11 ++++++----- 1 file changed, 6 insertions(+), 5 deletions(-) diff --git a/test/runtests_parallel_integration.jl b/test/runtests_parallel_integration.jl index 7fcfb24ea..07897484c 100644 --- a/test/runtests_parallel_integration.jl +++ b/test/runtests_parallel_integration.jl @@ -307,16 +307,17 @@ using TOML # Parallel FM et[1] regression — pinned tightly, NOT bracketed. et[1] is grid- and # equilibrium-sensitive (auto-mpsi gives a spurious value; a wrong grid/Ip shifts it), so - # a loose bracket would mask exactly that accuracy regression. Value is deterministic and - # reproducible (parallel and standard ODE paths agree to rel_diff=0). + # a loose bracket would mask exactly that accuracy regression. The parallel-path value is + # deterministic and reproducible. @test isapprox(et_par, 0.800637; rtol=2e-2) # Per-surface Δ' assertions removed (stub calculation; see Solovev testset # comment above). BVP Δ' matrix regression for DIIID-like is in the # `delta_prime_matrix — STRIDE BVP DIIID-like regression (large N)` testset. - # No explicit parallel-vs-standard cross-path check: both paths share the equilibrium - # grid, so they agree (rel_diff=0) even on a bad grid — a cross-path check is blind to - # grid/accuracy regressions. The tight absolute pin above is the guard for those. + # No explicit parallel-vs-standard cross-path check here: the two paths share the + # equilibrium grid (so a cross-path comparison is blind to grid/accuracy regressions), + # and their agreement is already verified on the lighter Solovev case above. The tight + # absolute pin above is the guard for grid/equilibrium regressions on this case. end @testset "ode_itime_cost is additive over sub-intervals" begin From b25b72cfd95f78f15dd54afecd71dab837964fe9 Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Tue, 23 Jun 2026 12:41:56 -0400 Subject: [PATCH 111/135] INNERLAYER - CLEANUP - add references to paper equations, add warnings to shooting method which should not be used, replace fortran notation with paper/greek notation --- src/InnerLayer/GGJ/GGJ.jl | 21 +- src/InnerLayer/GGJ/GGJParameters.jl | 54 ++-- src/InnerLayer/GGJ/Galerkin.jl | 376 ++++++++++++++++++------- src/InnerLayer/GGJ/InnerAsymptotics.jl | 265 +++++++++-------- src/InnerLayer/GGJ/Shooting.jl | 113 ++++---- src/InnerLayer/InnerLayer.jl | 4 +- 6 files changed, 531 insertions(+), 302 deletions(-) diff --git a/src/InnerLayer/GGJ/GGJ.jl b/src/InnerLayer/GGJ/GGJ.jl index 1b8aacb23..e7f0488a3 100644 --- a/src/InnerLayer/GGJ/GGJ.jl +++ b/src/InnerLayer/GGJ/GGJ.jl @@ -9,8 +9,23 @@ # # Both solvers share the same `inps` Wasow asymptotic-basis kernel # (`InnerAsymptotics.jl`) for the large-x boundary condition. They return -# the parity-projected matching data `(Δ_odd, Δ_even)` of Glasser, Wang & -# Park, Phys. Plasmas **23**, 112506 (2016), Eqs. (34)–(35). +# the parity-projected matching data `(Δ_odd, Δ_even)` of GWP2016 Eqs. (34)–(35). +# +# Equation references throughout this module use two source papers: +# +# GWP2016 — A. H. Glasser, Z. R. Wang & J.-K. Park, "Computation of resistive +# instabilities by matched asymptotic expansions", Phys. Plasmas 23, +# 112506 (2016). Inner-region equations (Eq. 11), matrix form +# A Ψ'' + B Ψ' + C Ψ = 0 (Eqs. 12–15), singular-Galerkin weak form +# (Eq. 32), grid packing (Eq. 33), matching data (Eqs. 34–35), +# dimensionless parameters / scale factors (Appendix, Eqs. A8–A15). +# +# GW2020 — A. H. Glasser & Z. R. Wang, "Asymptotic solutions and convergence +# studies of the resistive inner region equations", Phys. Plasmas 27, +# 012506 (2020). Wasow construction of the large-x asymptotic basis +# (Eqs. 1–55); implemented in InnerAsymptotics.jl. +# +# The inner-region equations are identical in both: GW2020 Eq. (1) ≡ GWP2016 Eq. (11). module GGJ @@ -23,7 +38,7 @@ import ..InnerLayerModel, ..solve_inner GGJModel{S} <: InnerLayerModel Glasser–Greene–Johnson resistive inner-layer model. The type parameter `S` -selects the solver: `:galerkin` (default) for the Hermite-cubic finite element +selects the solver: `:galerkin` (default) for the Hermite-cubic finite element solver and `:shooting` for the backward stable-shoot solver. Both implementations consume the same `inps` asymptotic-basis kernel and return the parity-projected matching data. diff --git a/src/InnerLayer/GGJ/GGJParameters.jl b/src/InnerLayer/GGJ/GGJParameters.jl index c6986ea2a..732ab781a 100644 --- a/src/InnerLayer/GGJ/GGJParameters.jl +++ b/src/InnerLayer/GGJ/GGJParameters.jl @@ -10,18 +10,20 @@ Dimensionless parameters of the Glasser–Greene–Johnson inner-layer model at a single rational surface, plus the local Alfvén/resistive timescales -needed to scale the matching data back to physical Δ. +needed to scale the matching data back to physical Δ. The equilibrium +coefficients `E, F, G, H, K, M` are the flux-surface averages defined in +GWP2016 Eq. (A8); they enter the inner-region equations (Eq. 11). Fields are the same as the Fortran `resist_type`: -| field | meaning | -|---------|---------------------------------------------------------------| +| field | meaning | +|:------- |:-------------------------------------------------------------- | | `E` | Glasser interchange parameter (enters Mercier `D_I = E+F+H−¼`) | -| `F` | Glasser interchange parameter | -| `G` | Coupling coefficient (curvature × pressure gradient) | -| `H` | Pfirsch–Schlüter coefficient | -| `K` | Glasser parameter | -| `M` | Mercier-related auxiliary parameter (held but not used here) | +| `F` | Glasser interchange parameter | +| `G` | Coupling coefficient (curvature × pressure gradient) | +| `H` | Pfirsch–Schlüter coefficient | +| `K` | Glasser parameter | +| `M` | Mercier-related auxiliary parameter (held but not used here) | | `taua` | Local Alfvén time at the rational surface | | `taur` | Local resistive time at the rational surface | | `v1` | Linear scale factor used in the V₁ rescaling | @@ -46,23 +48,26 @@ end """ mercier_di(p::GGJParameters) -> Float64 -Mercier interchange index `D_I = E + F + H − 1/4` (deltac_run line 143). +Mercier interchange index `D_I = E + F + H − 1/4` (GWP2016 Eq. A9; also the +quantity under the root in the GW2020 Eq. 49 power exponents). `D_I > 0` +indicates local ideal interchange instability. """ mercier_di(p::GGJParameters) = p.E + p.F + p.H - 0.25 """ mercier_dr(p::GGJParameters) -> Float64 -Resistive interchange index `D_R = E + F + H²` (deltar_run derivation, -deltac_run line 142). +Resistive interchange index `D_R = E + F + H² = D_I + (H − 1/2)²` +(GWP2016 Eq. A10). `D_R > 0` indicates local resistive interchange instability. """ mercier_dr(p::GGJParameters) = p.E + p.F + p.H * p.H """ p1(p::GGJParameters) -> Float64 -`p₁ = √(−D_I)`. The Mercier-stable branch requires `D_I < 0`; this -function asserts it. +`p₁ = √(−D_I)`, the Mercier power that sets the large-x Frobenius exponents +`r± = 3/2 ± √(−D_I)` (GW2020 Eq. 49; μ = −1/2 ± √(−D_I) in GWP2016 Eq. 26). +The Mercier-stable branch requires `D_I < 0`; this function asserts it. """ function p1(p::GGJParameters) di = mercier_di(p) @@ -73,40 +78,43 @@ end """ sfac(p::GGJParameters) -> Float64 -Lundquist-like ratio `S = τ_R / τ_A` used to define the inner-layer -length and time scales. +Lundquist number `S = τ_R / τ_A` (GWP2016 Sec. I) that sets the inner-layer +length and time scales `X₀ ∝ S^(−1/3)`, `Q₀ ∝ S^(−1/3)/τ_A`. """ sfac(p::GGJParameters) = p.taur / p.taua """ x0(p::GGJParameters) -> Float64 -Inner-layer length scale `X₀ = S^(−1/3)` (deltac_run line 149). +Inner-layer displacement scale factor `X₀ = S^(−1/3)` (GWP2016 Eq. A14), +relating scaled `X` to physical `x = ψ − ψ₀` via `x = X₀ X`. """ x0(p::GGJParameters) = sfac(p)^(-1.0 / 3.0) """ q0(p::GGJParameters) -> Float64 -Inner-layer growth-rate scale `Q₀ = X₀ / τ_A` (deltac_run line 150). +Inner-layer growth-rate scale factor `Q₀ = X₀ / τ_A` (GWP2016 Eq. A15), +relating the scaled growth rate `Q` to the physical rate `s` via `s = Q₀ Q`. """ q0(p::GGJParameters) = x0(p) / p.taua """ inner_Q(p::GGJParameters, γ::Number) -> ComplexF64 -Dimensionless scaled inner-layer growth rate `Q = γ / Q₀` used by the inps Wasow -basis (deltac_run line 151). The argument `γ` may be real or complex; the -result is always complex. +Dimensionless scaled inner-layer growth rate `Q = γ / Q₀` (GWP2016 Eq. A15), +the eigenvalue appearing in the inner-region equations (Eq. 11) and the inps +Wasow basis. The argument `γ` may be real or complex; the result is always complex. """ inner_Q(p::GGJParameters, γ::Number) = ComplexF64(γ) / q0(p) """ rescale_delta(Δ, p::GGJParameters) -> SVector{2,ComplexF64} -Apply the Wang 2020 `X₀^(2√(−D_I))` rescaling that maps the inner-layer -matching data back to physical Δ at the rational surface (deltac_run line -192). Operates element-wise on a 2-vector of `(Δ_odd, Δ_even)`. +Map the scaled inner-layer matching data back to physical Δ at the rational +surface by the `X₀^(2√(−D_I))` rescaling implied by the power-like matching +(GWP2016 Sec. IV; the inner solution ~ X^{r±} converts to physical x = X₀ X). +Operates element-wise on a 2-vector of `(Δ_odd, Δ_even)`. """ function rescale_delta(Δ::AbstractVector, p::GGJParameters) s = sfac(p) diff --git a/src/InnerLayer/GGJ/Galerkin.jl b/src/InnerLayer/GGJ/Galerkin.jl index 43b4dbbaf..b26cb1c45 100644 --- a/src/InnerLayer/GGJ/Galerkin.jl +++ b/src/InnerLayer/GGJ/Galerkin.jl @@ -5,13 +5,29 @@ # configuration. The half-domain problem (x ∈ [0, xmax]) is solved with # parity boundary conditions at x = 0 and asymptotic matching at x = xmax. # +# The solved field is the 3-component inner-layer solution u = (Ψ, Ξ, Υ) +# (Fortran psi/si/ups), obeying the GGJ inner-region equations +# GWP2016 Eq. (11) ≡ GW2020 Eq. (1): +# +# Ψ_xx − H Υ_x − Q(Ψ − x Ξ) = 0, +# Q² Ξ_xx − Q x² Ξ + Q x Ψ + (E + F) Υ + H Ψ_x = 0, +# Q Υ_xx − x² Υ + x Ψ + Q²[G(Ξ − Υ) − K(E Ξ + F Υ + H Ψ_x)] = 0, +# +# recast in matrix form A Ψ'' + B Ψ' + C Ψ = 0 (GWP2016 Eqs. 12–15) and +# assembled here in the weak-form coefficient layout `I·u'' − V·u' − U·u = 0` +# with (I, V, U) = (A, −B, −C). See `_physical_uv` for the row-by-row map. +# +# This module ports the GWP2016 inner-region singular-Galerkin method (Sec. III): +# the half-domain weak form (Eq. 32) on a packed Hermite-cubic grid (Eq. 33), +# with resonant/extension cells (Fig. 1) supplying the matching data (Eqs. 34–35). +# # Configuration assumed (matches deltac.f defaults when called with inps): # gal_method = "resonant" method = true noexp = true # basis_type = 0 (Hermite) fulldomain = 0 inps_type = "inps" -# mpert = 3 (W, N, Θ) np = 3 (Hermite cubic → 4 DOFs/node) +# mpert = 3 (Ψ, Ξ, Υ) np = 3 (Hermite cubic → 4 DOFs/node) # -# Reference: A. H. Glasser, Z. R. Wang & J.-K. Park, -# Phys. Plasmas 23, 112506 (2016). +# References: GWP2016 (Phys. Plasmas 23, 112506) for the Galerkin method and +# matching; GW2020 (Phys. Plasmas 27, 012506) for the large-x asymptotic basis. using LinearAlgebra using FastGaussQuadrature: gausslobatto @@ -22,19 +38,21 @@ using QuadGK: quadgk # ----------------------------------------------------------------------- """ -Convert the inps 6×2 output U_inps at coordinate `x` to the physical -(W, N, Θ) and (W', N', Θ') representation used by deltac/inpso. -Returns `(ua, dua)` each 3×2 complex, where columns are the two algebraic -solutions and rows are (W, N, Θ). +Convert the inps 6×2 output U_inps (the Wasow asymptotic basis U = TPQSY of +GW2020 Eq. 53) at coordinate `x` to the physical (Ψ, Ξ, Υ) and (Ψ', Ξ', Υ') +representation used by deltac/inpso. The 6-component first-order state packs +(Ψ, Ξ, Υ, Ψ', Ξ', Υ') with the GW2020 Eq. (2) scaling 𝚿 ≡ (xΨ, Ξ, Υ), hence +the /x and ·x factors below. Returns `(ua, dua)` each 3×2 complex, where columns +are the two power-like (Mercier) solutions and rows are the components (Ψ, Ξ, Υ). """ function _physical_ua_dua(cache::InnerAsymptoticsCache, x::Real) U, dU = evaluate_asymptotics(cache, x; derivative=true, apply_T=true) - ua = zeros(ComplexF64, 3, 2) + ua = zeros(ComplexF64, 3, 2) dua = zeros(ComplexF64, 3, 2) @inbounds for j in 1:2 - ua[1, j] = U[1, j] / x - ua[2, j] = U[2, j] - ua[3, j] = U[3, j] + ua[1, j] = U[1, j] / x + ua[2, j] = U[2, j] + ua[3, j] = U[3, j] dua[1, j] = U[4, j] - U[1, j] / (x * x) dua[2, j] = U[5, j] * x dua[3, j] = U[6, j] * x @@ -44,37 +62,56 @@ end """ Build the (I, U, V) coefficient matrices of the second-order system -`I·u'' − V·u' − U·u = 0` at coordinate `x`. Port of inpso_get_uv. -All matrices are 3×3 complex. +`I·u'' − V·u' − U·u = 0` for u = (Ψ, Ξ, Υ) at coordinate `x`. Port of +inpso_get_uv. All matrices are 3×3 complex. + +These are the matrices A, B, C of GWP2016 Eq. (12), `A Ψ'' + B Ψ' + C Ψ = 0`, +with A given in Eq. (14), B in Eq. (14), and C in Eq. (15). The code's weak-form +layout flips the off-diagonal signs: (I, V, U) = (A, −B, −C). + +Each matrix row is one GGJ inner-region equation (GWP2016 Eq. 11 ≡ GW2020 Eq. 1); +reading `I u'' − V u' − U u` across a row reproduces the corresponding equation: + +row 1 (Ψ): Ψ_xx − H Υ_x − Q(Ψ − x Ξ) = 0 +⇒ I=(1,0,0) V=(0,0,H) U=(Q, −Qx, 0) +row 2 (Ξ): Q² Ξ_xx − Q x² Ξ + Q x Ψ + (E+F) Υ + H Ψ_x = 0 +⇒ I=(0,Q²,0) V=(−H,0,0) U=(−Qx, Q x², −(E+F)) +row 3 (Υ): Q Υ_xx − x² Υ + x Ψ + Q²[G(Ξ−Υ) − K(E Ξ + F Υ + H Ψ_x)] = 0 +⇒ I=(0,0,Q) V=(K Q² H,0,0) U=(−x, −Q²(G−KE), x²+Q²(G+KF)) """ function _physical_uv(params::GGJParameters, Q::ComplexF64, x::Real) - e = ComplexF64(params.E); f = ComplexF64(params.F) - h = ComplexF64(params.H); g = ComplexF64(params.G) - k = ComplexF64(params.K); q = Q + e = ComplexF64(params.E); + f = ComplexF64(params.F) + h = ComplexF64(params.H); + g = ComplexF64(params.G) + k = ComplexF64(params.K); + q = Q q2 = q * q x2 = x * x + # I = A of GWP2016 Eq. (14): diag(1, Q², Q), coefficients of (Ψ_xx, Ξ_xx, Υ_xx). Imat = @SMatrix ComplexF64[1 0 0; 0 q2 0; 0 0 q] - # Build U and V matching inpso_get_uv: pre-scaled from column-major RESHAPE, then row 2 *=q², row 3 *=q. - # Pre-scaled U (column-major Fortran RESHAPE → Julia row-major): - # U[1,:] = (q, -q*x, 0) - # U[2,:] = (-x/q, x²/q, -(e+f)/q²) - # U[3,:] = (-x/q, -(g-ke)*q, x²/q+(g+kf)*q) + # U = −C of GWP2016 Eq. (15): coefficients of −u in each equation + # (inpso_get_uv stores them pre-scaled: row 2 ×Q², row 3 ×Q, matching + # the I-row normalization). + # row 1 (Ψ): (Q, −Q x, 0) + # row 2 (Ξ): (−Q x, Q x², −(E+F)) + # row 3 (Υ): (−x, −Q²(G−KE), x²+Q²(G+KF)) U = @SMatrix ComplexF64[ - q (-q * x) 0 - (-x / q) * q2 (x2 / q) * q2 (-(e + f) / q2) * q2 - (-x / q) * q (-(g - k * e) * q) * q (x2 / q + (g + k * f) * q) * q + q (-q * x) 0 + (-x / q) * q2 (x2 / q) * q2 (-(e + f) / q2) * q2 + (-x / q) * q (-(g - k * e) * q) * q (x2 / q + (g + k * f) * q) * q ] - # Pre-scaled V (column-major Fortran RESHAPE → Julia row-major): - # V[1,:] = (0, 0, h) - # V[2,:] = (-h/q², 0, 0) - # V[3,:] = (h*k*q, 0, 0) + # V = −B of GWP2016 Eq. (14): coefficients of −u' in each equation (same row scaling as U): + # row 1 (Ψ): (0, 0, H) ⇒ −H Υ_x + # row 2 (Ξ): (−H, 0, 0) ⇒ +H Ψ_x + # row 3 (Υ): (K Q² H, 0, 0) ⇒ −K Q² H Ψ_x V = @SMatrix ComplexF64[ - 0 0 h - (-h / q2) * q2 0 0 - (h * k * q) * q 0 0 + 0 0 h + (-h / q2) * q2 0 0 + (h * k * q) * q 0 0 ] return Imat, U, V @@ -90,24 +127,29 @@ function _hermite(x::Real, x0::Real, x1::Real) dx = x1 - x0 t0 = (x - x0) / dx t1 = 1 - t0 - t02 = t0 * t0; t12 = t1 * t1 + t02 = t0 * t0; + t12 = t1 * t1 pb = SVector{4,Float64}( t12 * (1 + 2t0), t12 * t0 * dx, t02 * (1 + 2t1), - -t02 * t1 * dx, + -t02 * t1 * dx ) qb = SVector{4,Float64}( -6t0 * t1 / dx, t0 * (3t0 - 4) + 1, 6t1 * t0 / dx, - t0 * (3t0 - 2), + t0 * (3t0 - 2) ) return pb, qb end # ----------------------------------------------------------------------- -# Grid packing — port of deltac_pack. +# Grid packing — port of deltac_pack. The pfac > 1 branch is the GWP2016 +# inner-region packing X(ξ,λ) = ln[(1+λξ)/(1−λξ)] / ln[(1+λ)/(1−λ)] +# (Eq. 33), which concentrates nodes near X = 0; pfac = 1 gives a uniform +# grid, and pfac in (0,1) the complementary edge-packed map. The grid-density +# ratio is P(λ) = 1 − λ² (GWP2016 between Eqs. 5 and 33). # ----------------------------------------------------------------------- function _pack(nx::Int, pfac::Float64, side::String) @@ -149,13 +191,18 @@ function _pack(nx::Int, pfac::Float64, side::String) end # ----------------------------------------------------------------------- -# Three-level xmax sweep — replaces inpso_xmax for inps mode. +# Three-level xmax sweep — replaces inpso_xmax for inps mode. The cutoff +# x_max is the position where the asymptotic-basis residual Δ (GW2020 Eq. 54, +# computed by `asymptotic_residual`) drops below a target tolerance — the +# choice studied in GW2020 Sec. III and Fig. 3, where x_max is taken where the +# error falls to ~1e−7. Three tolerance levels set x_max and the two thin +# matching cells (dx1, dx2) just inside it. # Returns (xmax, dx1, dx2, cache). # ----------------------------------------------------------------------- function _xmax_3level(params::GGJParameters, Q::ComplexF64; - kmax::Int=8, xfac::Float64=1.0, - eps_vec::NTuple{3,Float64}=(1e-2, 5e-7, 1e-7)) + kmax::Int=8, xfac::Float64=1.0, + eps_vec::NTuple{3,Float64}=(1e-2, 5e-7, 1e-7)) cache = build_asymptotics(params, Q; kmax=kmax) # Bisection-based root finder: find the exact x where max(residual) = eps, @@ -179,7 +226,8 @@ function _xmax_3level(params::GGJParameters, Q::ComplexF64; if !any(set) break end - x_prev = x; delta_prev = dmax + x_prev = x; + delta_prev = dmax x *= dxfac end any(set) && error("_xmax_3level: failed to bracket all xmax levels") @@ -207,7 +255,14 @@ function _xmax_3level(params::GGJParameters, Q::ComplexF64; end # ----------------------------------------------------------------------- -# Cell types and grid construction. +# Cell types and grid construction. These are the grid cells of GWP2016 +# Fig. 1, laid out moving toward the cutoff x_max: ordinary "normal" cells +# (CT_NONE) carrying 4 Hermite-cubic DOFs/node, "extension" cells (CT_EXT2, +# CT_EXT1, CT_EXT) where the small resonant power series is blended into the +# Hermite basis, and the "resonant" cell (CT_RES) at x_max holding the large +# resonant solution whose coefficient provides the matching data (Eqs. 34–35). +# Here the half-domain has a single resonant cell at x_max (the X = 0 end is +# the parity boundary, not a singular surface). # ----------------------------------------------------------------------- @enum CellType CT_NONE CT_EXT2 CT_EXT1 CT_EXT CT_RES @@ -233,7 +288,7 @@ struct GalerkinWorkspace end function _build_grid_and_workspace(nx::Int, xmax::Float64, dx1::Float64, dx2::Float64, - pfac::Float64, cutoff::Int, nq::Int) + pfac::Float64, cutoff::Int, nq::Int) mpert = 3 np = 3 side = pfac < 1 ? "left" : "right" @@ -255,8 +310,10 @@ function _build_grid_and_workspace(nx::Int, xmax::Float64, dx1::Float64, dx2::Fl x_nodes[nx-1] = xmax - (dx1 + dx2) ixmax = nx - 2 # packed region is 0..ixmax - x0 = x_nodes[1]; x1_packed = x_nodes[ixmax+1] - xm = (x1_packed + x0) / 2; dxp = (x1_packed - x0) / 2 + x0 = x_nodes[1]; + x1_packed = x_nodes[ixmax+1] + xm = (x1_packed + x0) / 2; + dxp = (x1_packed - x0) / 2 mx = ixmax ÷ 2 packed = xm .+ dxp .* _pack(mx, pfac, side) for i in 1:(ixmax+1) @@ -270,7 +327,8 @@ function _build_grid_and_workspace(nx::Int, xmax::Float64, dx1::Float64, dx2::Fl imap = 1 for ix in 1:nx et = etypes[ix] - xl = x_nodes[ix]; xr = x_nodes[ix+1] + xl = x_nodes[ix]; + xr = x_nodes[ix+1] cell_np = if et == CT_NONE || et == CT_EXT1 || et == CT_EXT2 np @@ -321,7 +379,7 @@ function _build_grid_and_workspace(nx::Int, xmax::Float64, dx1::Float64, dx2::Fl emap_vals = ext_cell.emap res_map = reshape(copy(emap_vals), mpert, 1) cells[nx] = GalerkinCell(CT_RES, x_nodes[nx], x_nodes[nx+1], x_nodes[nx+1], - -1, res_map, copy(emap_vals)) + -1, res_map, copy(emap_vals)) ndim = imap # noexp → ndim = imap (only emap[1] ≤ ndim) @@ -338,13 +396,18 @@ function _build_grid_and_workspace(nx::Int, xmax::Float64, dx1::Float64, dx2::Fl end # ----------------------------------------------------------------------- -# Local assembly: Gauss quadrature for "none" cells. -# Port of deltac_gauss_quad. +# Local assembly: Gauss quadrature for "none" cells. Port of deltac_gauss_quad. +# Evaluates the GWP2016 Eq. (32) bilinear form on one cell. After integrating +# the A-term by parts, the symmetric weak form is +# Σⱼ [−(αᵢ', A αⱼ') + (αᵢ, B αⱼ') + (αᵢ, C αⱼ)] uⱼ , +# which in this code's (I, V, U) = (A, −B, −C) convention is assembled below as +# I·(αᵢ' αⱼ') + V·(αᵢ αⱼ') + U·(αᵢ αⱼ) with αᵢ the Hermite-cubic basis +# (pb = values, qb = derivatives). Scalar products use Gauss–Lobatto quadrature. # ----------------------------------------------------------------------- function _gauss_quad!(cell_mat::Array{ComplexF64,4}, cell::GalerkinCell, - quad_nodes::Vector{Float64}, quad_weights::Vector{Float64}, - params::GGJParameters, Q::ComplexF64) + quad_nodes::Vector{Float64}, quad_weights::Vector{Float64}, + params::GGJParameters, Q::ComplexF64) np_cell = cell.np nq = length(quad_nodes) x0 = (cell.x_right + cell.x_left) / 2 @@ -360,26 +423,31 @@ function _gauss_quad!(cell_mat::Array{ComplexF64,4}, cell::GalerkinCell, for ip in 0:np_cell, jp in 0:np_cell # cell_mat[:,:,ip+1,jp+1] += w*(I*qb[ip]*qb[jp] + V*pb[ip]*qb[jp] + U*pb[ip]*pb[jp]) for jpert in 1:3, ipert in 1:3 - cell_mat[ipert, jpert, ip+1, jp+1] += w * ( - Imat[ipert, jpert] * qb[ip+1] * qb[jp+1] + - Vmat[ipert, jpert] * pb[ip+1] * qb[jp+1] + - Umat[ipert, jpert] * pb[ip+1] * pb[jp+1] - ) + cell_mat[ipert, jpert, ip+1, jp+1] += + w * ( + Imat[ipert, jpert] * qb[ip+1] * qb[jp+1] + + Vmat[ipert, jpert] * pb[ip+1] * qb[jp+1] + + Umat[ipert, jpert] * pb[ip+1] * pb[jp+1] + ) end end end end # ----------------------------------------------------------------------- -# Extension assembly — port of deltac_extension. -# Handles ext, ext1, ext2 cell types. +# Extension assembly — port of deltac_extension. Handles ext, ext1, ext2 cell +# types: the GWP2016 extension cells (Fig. 1) where the small resonant power +# series (column 2 of the asymptotic basis) drives the response and the large +# resonant solution (column 1) is blended into the Hermite cubics with +# C¹ continuity. This couples the bulk Hermite DOFs to the asymptotic emap DOF +# via the same Eq. (32) bilinear form; the small-solution terms form the RHS. # ----------------------------------------------------------------------- function _extension!(cell_mat::Array{ComplexF64,4}, cell_rhs::Matrix{ComplexF64}, - cell::GalerkinCell, - quad_nodes::Vector{Float64}, quad_weights::Vector{Float64}, - params::GGJParameters, Q::ComplexF64, - cache::InnerAsymptoticsCache) + cell::GalerkinCell, + quad_nodes::Vector{Float64}, quad_weights::Vector{Float64}, + params::GGJParameters, Q::ComplexF64, + cache::InnerAsymptoticsCache) np_cell = cell.np x0c = (cell.x_right + cell.x_left) / 2 dxc = (cell.x_right - cell.x_left) / 2 @@ -462,15 +530,19 @@ function _extension!(cell_mat::Array{ComplexF64,4}, cell_rhs::Matrix{ComplexF64} end # ----------------------------------------------------------------------- -# Resonant integral — replaces deltac_lsode_int with QuadGK. +# Resonant integral — replaces deltac_lsode_int with QuadGK. Evaluates the +# GWP2016 Eq. (32) bilinear form over the resonant cell using the asymptotic +# (power-series) solutions as both test and trial functions — the scalar +# products that GWP2016 notes "are non-analytic and therefore require an +# adaptive integration" rather than Gauss quadrature. # Computes ∫_{x_left}^{x_lsode} ua_1^T L ua_j dx for j=1 and j=2. # With noexp, only (1,1) and (1,2) entries of the 1×2 result matter # (ip=1 only for test function, jp=1 for stiffness, jp=2 for RHS). # ----------------------------------------------------------------------- function _resonant_integral(cell::GalerkinCell, params::GGJParameters, - Q::ComplexF64, cache::InnerAsymptoticsCache; - tol::Float64=1e-5) + Q::ComplexF64, cache::InnerAsymptoticsCache; + tol::Float64=1e-5) x_left = cell.x_left x_right = cell.x_lsode @@ -480,7 +552,8 @@ function _resonant_integral(cell::GalerkinCell, params::GGJParameters, function integrand_11(x) ua, dua = _physical_ua_dua(cache, x) Imat, Umat, Vmat = _physical_uv(params, Q, x) - ua1 = ua[:, 1]; dua1 = dua[:, 1] + ua1 = ua[:, 1]; + dua1 = dua[:, 1] return transpose(dua1) * Imat * dua1 + transpose(ua1) * Vmat * dua1 + transpose(ua1) * Umat * ua1 end @@ -488,7 +561,9 @@ function _resonant_integral(cell::GalerkinCell, params::GGJParameters, ua, dua = _physical_ua_dua(cache, x) Imat, Umat, Vmat = _physical_uv(params, Q, x) dua1 = dua[:, 1] - ua1 = ua[:, 1]; ua2 = ua[:, 2]; dua2 = dua[:, 2] + ua1 = ua[:, 1]; + ua2 = ua[:, 2]; + dua2 = dua[:, 2] return transpose(dua1) * Imat * dua2 + transpose(ua1) * Vmat * dua2 + transpose(ua1) * Umat * ua2 end @@ -503,10 +578,11 @@ end # ----------------------------------------------------------------------- function _assemble_and_solve!(ws::GalerkinWorkspace, - params::GGJParameters, Q::ComplexF64, - cache::InnerAsymptoticsCache; - nq::Int=4, tol_res::Float64=1e-5) - mpert = 3; np = 3 + params::GGJParameters, Q::ComplexF64, + cache::InnerAsymptoticsCache; + nq::Int=4, tol_res::Float64=1e-5) + mpert = 3; + np = 3 quad_nodes, quad_weights = gausslobatto(nq + 1) offset = ws.kl + ws.kl + 1 # kl + ku + 1 since ku = kl @@ -526,11 +602,17 @@ function _assemble_and_solve!(ws::GalerkinWorkspace, # Assemble into global banded matrix (both parities use same base matrix) for ip in 0:np_eff, ipert in 1:mpert i = cell.map[ipert, ip+1] - if i > ws.ndim; continue; end + if i > ws.ndim + ; + continue; + end for jp in 0:np_eff, jpert in 1:mpert j = cell.map[jpert, jp+1] - if j > ws.ndim; continue; end - ws.mat[offset + i - j, j, 1] += cell_mat[ipert, jpert, ip+1, jp+1] + if j > ws.ndim + ; + continue; + end + ws.mat[offset+i-j, j, 1] += cell_mat[ipert, jpert, ip+1, jp+1] end end end @@ -558,14 +640,20 @@ function _assemble_and_solve!(ws::GalerkinWorkspace, if cell.etype == CT_EXT && ip == cell.np + 1 && ipert > 1 continue end - if i > ws.ndim; continue; end + if i > ws.ndim + ; + continue; + end for jp in 0:npp, jpert in 1:mpert j = jp < size(cell.map, 2) ? cell.map[jpert, jp+1] : cell.emap[1] if cell.etype == CT_EXT && jp == cell.np + 1 && jpert > 1 continue end - if j > ws.ndim; continue; end - ws.mat[offset + i - j, j, 1] += cell_mat_ext[ipert, jpert, ip+1, jp+1] + if j > ws.ndim + ; + continue; + end + ws.mat[offset+i-j, j, 1] += cell_mat_ext[ipert, jpert, ip+1, jp+1] end # RHS (both parities get the same base RHS) ws.rhs[i, 1] += cell_rhs_ext[ipert, ip+1] @@ -583,7 +671,9 @@ function _assemble_and_solve!(ws::GalerkinWorkspace, end end - # Surface term at xmax for "resonant" method + # Surface term at xmax for "resonant" method: the boundary contribution + # [αᵢ A uⱼ']_{x_max} from the IBP of the A-term in GWP2016 Eq. (32), kept + # here (not dropped) because the resonant cell carries the matching data. res_cell = ws.cells[ws.nx] x_lsode = res_cell.x_lsode ua_xmax, dua_xmax = _physical_ua_dua(cache, x_lsode) @@ -611,44 +701,55 @@ function _assemble_and_solve!(ws::GalerkinWorkspace, i = cell1.map[ipert, 1] # ip=0 j = cell1.map[jpert, 2] # ip=1 if i <= ws.ndim && j <= ws.ndim - ws.mat[offset + i - j, j, 1] += Imat0[ipert, jpert] - ws.mat[offset + i - j, j, 2] += Imat0[ipert, jpert] + ws.mat[offset+i-j, j, 1] += Imat0[ipert, jpert] + ws.mat[offset+i-j, j, 2] += Imat0[ipert, jpert] end end - # Apply parity BCs for each solution (isol=1: odd, isol=2: even). + # Apply parity BCs for each solution (isol=1: odd, isol=2: even). The + # inner equations have reflection symmetry about X=0 (GWP2016 Sec. III): + # one solution has even Ξ, Υ and odd Ψ, the other odd Ξ, Υ and even Ψ. + # Imposing both at X=0 gives the two parities that each contribute a Δ for + # outer-region matching (the Δ_odd, Δ_even of GWP2016 Eqs. 34–35). # Mirrors deltac_set_boundary: for each isol, build a modified local # matrix for ip=0..1 of cell 1, then write it into the global matrix. for isol in 1:2 # Zero out ip=0 rows in the global matrix for ipert in 1:mpert i = cell1.map[ipert, 1] # ip=0 DOFs - if i > ws.ndim; continue; end - for jj in max(1, i - ws.kl):min(ws.ndim, i + ws.kl) - ws.mat[offset + i - jj, jj, isol] = 0 + if i > ws.ndim + ; + continue; + end + for jj in max(1, i-ws.kl):min(ws.ndim, i+ws.kl) + ws.mat[offset+i-jj, jj, isol] = 0 end end - # Odd parity (isol=1): W'(0)=0, N(0)=0, Θ(0)=0 - # → row=W(ip=0), col=W(ip=1): A[map[1,1], map[1,2]] = 1 - # → row=N(ip=0), col=N(ip=0): A[map[2,1], map[2,1]] = 1 - # → row=Θ(ip=0), col=Θ(ip=0): A[map[3,1], map[3,1]] = 1 - # Even parity (isol=2): W(0)=0, N'(0)=0, Θ'(0)=0 - # → row=W(ip=0), col=W(ip=0): A[map[1,1], map[1,1]] = 1 - # → row=N(ip=0), col=N(ip=1): A[map[2,1], map[2,2]] = 1 - # → row=Θ(ip=0), col=Θ(ip=1): A[map[3,1], map[3,2]] = 1 + # Odd parity (isol=1): Ψ'(0)=0, Ξ(0)=0, Υ(0)=0 + # → row=Ψ(ip=0), col=Ψ(ip=1): A[map[1,1], map[1,2]] = 1 + # → row=Ξ(ip=0), col=Ξ(ip=0): A[map[2,1], map[2,1]] = 1 + # → row=Υ(ip=0), col=Υ(ip=0): A[map[3,1], map[3,1]] = 1 + # Even parity (isol=2): Ψ(0)=0, Ξ'(0)=0, Υ'(0)=0 + # → row=Ψ(ip=0), col=Ψ(ip=0): A[map[1,1], map[1,1]] = 1 + # → row=Ξ(ip=0), col=Ξ(ip=1): A[map[2,1], map[2,2]] = 1 + # → row=Υ(ip=0), col=Υ(ip=1): A[map[3,1], map[3,2]] = 1 if isol == 1 - i = cell1.map[1, 1]; j = cell1.map[1, 2] - ws.mat[offset + i - j, j, isol] = 1 + i = cell1.map[1, 1]; + j = cell1.map[1, 2] + ws.mat[offset+i-j, j, isol] = 1 for ipert in 2:3 - i = cell1.map[ipert, 1]; j = cell1.map[ipert, 1] - ws.mat[offset + i - j, j, isol] = 1 + i = cell1.map[ipert, 1]; + j = cell1.map[ipert, 1] + ws.mat[offset+i-j, j, isol] = 1 end else - i = cell1.map[1, 1]; j = cell1.map[1, 1] - ws.mat[offset + i - j, j, isol] = 1 + i = cell1.map[1, 1]; + j = cell1.map[1, 1] + ws.mat[offset+i-j, j, isol] = 1 for ipert in 2:3 - i = cell1.map[ipert, 1]; j = cell1.map[ipert, 2] - ws.mat[offset + i - j, j, isol] = 1 + i = cell1.map[ipert, 1]; + j = cell1.map[ipert, 2] + ws.mat[offset+i-j, j, isol] = 1 end end for ipert in 1:mpert @@ -660,7 +761,9 @@ function _assemble_and_solve!(ws::GalerkinWorkspace, end # Solve for each parity using LAPACK banded LU (gbtrf! + gbtrs!) - n = ws.ndim; kl = ws.kl; ku = kl + n = ws.ndim; + kl = ws.kl; + ku = kl for isol in 1:2 ab = copy(ws.mat[:, :, isol]) rhs_col = copy(ws.rhs[:, isol]) @@ -674,6 +777,63 @@ end # Top-level Galerkin solver. # ----------------------------------------------------------------------- +# ----------------------------------------------------------------------- +# Diagnostic: reconstruct the physical inner-layer field profiles (Ψ, Ξ, Υ) +# from the solved Hermite DOFs over the bulk (Hermite) cells. The thin +# CT_EXT / CT_RES matching cells near xmax are skipped (their solution is +# carried by the asymptotic emap DOF, not the Hermite basis). Returns the +# inner-coordinate grid `x` and the three fields for both parities +# (columns: 1 = odd, 2 = even). Used to diagnose the resonant-layer +# structure vs resistivity. Not part of the production matching path. +# ----------------------------------------------------------------------- +function _solution_profile(ws::GalerkinWorkspace; npc::Int=10) + mpert = 3 + xs = Float64[] + Ψ = Matrix{ComplexF64}(undef, 0, 2); + Ξ = similar(Ψ); + Υ = similar(Ψ) + for cell in ws.cells + (cell.etype == CT_RES || cell.etype == CT_EXT) && continue + cell.np >= 0 || continue + for t in range(0, 1; length=npc + 1)[1:(end-1)] + x = cell.x_left + t * (cell.x_right - cell.x_left) + pb, _ = _hermite(x, cell.x_left, cell.x_right) + vals = zeros(ComplexF64, mpert, 2) + for isol in 1:2, ipert in 1:mpert, ip in 0:cell.np + g = cell.map[ipert, ip+1] + g <= ws.ndim && (vals[ipert, isol] += ws.sol[g, isol] * pb[ip+1]) + end + push!(xs, x) + Ψ = vcat(Ψ, permutedims(vals[1, :])); + Ξ = vcat(Ξ, permutedims(vals[2, :])); + Υ = vcat(Υ, permutedims(vals[3, :])) + end + end + p = sortperm(xs) + return (; x=xs[p], Ψ=Ψ[p, :], Ξ=Ξ[p, :], Υ=Υ[p, :]) +end + +""" + solve_inner_profile(params::GGJParameters, γ::Number; kwargs...) + +Diagnostic variant of `solve_inner(GGJModel(:galerkin), ...)` that also returns the reconstructed +inner-layer field profiles. Returns `(Δ, Q, profile)` where `profile = (x, Ψ, Ξ, Υ)` (Ψ = inner ξ, +columns odd/even parity). Same numerics/kwargs as `solve_inner`; for investigating resonant-layer +structure vs resistivity, not the production matching path. +""" +function solve_inner_profile(params::GGJParameters, γ::Number; + kmax::Int=8, nx::Int=512, nq::Int=4, pfac::Float64=1.0, + cutoff::Int=5, xfac::Float64=1.0, tol_res::Float64=1e-5) + Q = inner_Q(params, γ) + xmax_info = _xmax_3level(params, Q; kmax=kmax, xfac=xfac) + ws = _build_grid_and_workspace(nx, xmax_info.xmax, xmax_info.dx1, xmax_info.dx2, pfac, cutoff, nq) + _assemble_and_solve!(ws, params, Q, xmax_info.cache; nq=nq, tol_res=tol_res) + res_cell = ws.cells[ws.nx] + emap1 = res_cell.emap[1] + Δ = rescale_delta(SVector{2,ComplexF64}(ws.sol[emap1, 2], ws.sol[emap1, 1]), params) + return Δ, Q, _solution_profile(ws), (; xmax=xmax_info.xmax, x0=x0(params), sfac=sfac(params)) +end + """ solve_inner(::GGJModel{:galerkin}, params::GGJParameters, γ::Number; kmax::Int=8, nx::Int=512, nq::Int=4, pfac::Float64=1.0, @@ -681,15 +841,16 @@ end -> SVector{2,ComplexF64} Solve the GGJ inner-layer matching problem using the Hermite-cubic finite -element (Galerkin) method. Direct port of rmatch/deltac.f in the -"resonant + noexp + inps" configuration. +element (Galerkin) method (GWP2016 Sec. III). Direct port of rmatch/deltac.f in +the "resonant + noexp + inps" configuration. -Returns `(Δ₁, Δ₂)` with rescaling applied. The ordering matches deltac.f's +Returns the parity-projected matching data `(Δ₁, Δ₂)` (GWP2016 Eqs. 34–35) with +the `X₀^{2√(−D_I)}` physical rescaling applied. The ordering matches deltac.f's output convention (swapped relative to deltar.f). """ function solve_inner(::GGJModel{:galerkin}, params::GGJParameters, γ::Number; - kmax::Int=8, nx::Int=512, nq::Int=4, pfac::Float64=1.0, - cutoff::Int=5, xfac::Float64=1.0, tol_res::Float64=1e-5) + kmax::Int=8, nx::Int=512, nq::Int=4, pfac::Float64=1.0, + cutoff::Int=5, xfac::Float64=1.0, tol_res::Float64=1e-5) Q = inner_Q(params, γ) # Build asymptotic cache and determine grid parameters @@ -698,12 +859,14 @@ function solve_inner(::GGJModel{:galerkin}, params::GGJParameters, γ::Number; # Build grid and workspace ws = _build_grid_and_workspace(nx, xmax_info.xmax, xmax_info.dx1, xmax_info.dx2, - pfac, cutoff, nq) + pfac, cutoff, nq) # Assemble and solve _assemble_and_solve!(ws, params, Q, cache; nq=nq, tol_res=tol_res) - # Extract delta from the resonant cell's emap DOF + # Extract the matching data from the resonant cell's emap DOF: the solved + # coefficient of the large resonant solution is Δ for each parity + # (GWP2016 Eqs. 34–35), here columns isol=1 (odd) and isol=2 (even). res_cell = ws.cells[ws.nx] emap1 = res_cell.emap[1] Δ_raw = SVector{2,ComplexF64}(ws.sol[emap1, 1], ws.sol[emap1, 2]) @@ -713,3 +876,4 @@ function solve_inner(::GGJModel{:galerkin}, params::GGJParameters, γ::Number; return rescale_delta(Δ_swapped, params) end + diff --git a/src/InnerLayer/GGJ/InnerAsymptotics.jl b/src/InnerLayer/GGJ/InnerAsymptotics.jl index 4f4de84a9..7b6b838c1 100644 --- a/src/InnerLayer/GGJ/InnerAsymptotics.jl +++ b/src/InnerLayer/GGJ/InnerAsymptotics.jl @@ -3,18 +3,20 @@ # Wasow asymptotic basis ("inps" basis) for the GGJ inner-layer system. # Direct port of rmatch/inps.f. # -# Reference: A. H. Glasser & Z. R. Wang, Phys. Plasmas 27, 012506 (2020), -# Sections II.A–II.G (Eqs. 4–53). Notation map: +# Reference: A. H. Glasser & Z. R. Wang, Phys. Plasmas 27, 012506 (2020) +# ("GW2020"), Sections II.A–II.G (Eqs. 3–55). Notation map (all equation +# numbers are GW2020): # -# A0/A1/A2 -> Eqs. 4–5 (physical-system coefficient matrices) -# T, Tinv -> Eqs. 7–8 (eigenvector basis of A_0) -# J0/J1/J2 -> Eqs. 9–10 (J_i = T^{-1} A_i T) -# P_k, B_k -> Eqs. 16, 22 (splitting transformation; Lyapunov solve) -# Q_k, C_k -> Eqs. 32–39 (2×2 inner sub-block diagonalization) -# D_k -> Eq. 43 (shearing transformation) -# Y0, R -> Eq. 49 (lowest-order solution and Frobenius exponents) -# Z_k -> Eq. 52 (Y-series in shifted-exponent form) -# U(x) -> Eq. 53 (final asymptotic solution at large x) +# A0/A1/A2 -> Eqs. 3–5 (physical-system coefficient matrices A = A₀+x⁻²A₁+x⁻⁴A₂) +# T, Tinv -> Eqs. 6–8 (Jordan basis of A₀; u = Tv, v' = xJv, λ = Q^{-1/2}) +# J0/J1/J2 -> Eqs. 9–10 (Jₖ = T^{-1} Aₖ T) +# P_k, B_k -> Eqs. 11–24 (splitting transformation V = PW; Lyapunov solve Eq. 22) +# Q_k, C_k -> Eqs. 25–39 (2×2 inner-block diagonalization W = QX) +# D_k -> Eqs. 40–43 (shearing transformation X = SY) +# Y0, R -> Eqs. 48–49 (lowest-order solution; Mercier Frobenius exponents r±) +# Y_k, Z_k -> Eqs. 50–52 (Y-series Y = Y₀Z in shifted-exponent form) +# U(x) -> Eq. 53 (final asymptotic solution U = TPQSY at large x) +# residual -> Eq. 54 (convergence measure Δ± used to pick x_max) # # This file ports `inps_tjmat`, `inps_lyap_solve`, `inps_split`, `inps_coefs`, # `inps_horner`, `inps_ua`, `inps_delta`, and `inps_xmax` from the Fortran. @@ -50,7 +52,7 @@ Fields: - `K2` — 2×2 inner working matrices, k = 0..kmax+2 (Eq. 32; entry k=0 unused). - `Qmat, Cmat` — 2×2 inner-block transformation matrices, k = 0..kmax+2 (Eqs. 32–39). - `Dmat` — 2×2 shearing matrices, k = 0..kmax (Eq. 43). - - `Y0, Y0inv` — lowest-order Y matrix and its inverse (Eq. 49). + - `Y0, Y0inv` — lowest-order Y matrix and its inverse (Eq. 48; exponents from Eq. 49). - `Y, Z` — 2×2 series matrices, k = 0..kmax (Eq. 52). """ struct InnerAsymptoticsCache @@ -78,8 +80,9 @@ end @inline _at(v::Vector, k::Int) = v[k+1] # ----------------------------------------------------------------------- -# Step 1: build T, Tinv, A_0..A_2, J_0..J_2. -# Mirrors inps_tjmat (inps.f lines 145–233). +# Build T, Tinv, A_0..A_2, J_0..J_2. The coefficient matrices A₀,A₁,A₂ are +# GW2020 Eqs. (3)–(5); the Jordan basis T, T⁻¹ are Eqs. (7)–(8); λ = Q^{-1/2} +# (Eq. 6); and J_i = T⁻¹A_iT are Eqs. (9)–(10). Mirrors inps_tjmat. # ----------------------------------------------------------------------- function _build_tjmat(p::GGJParameters, Q::ComplexF64) @@ -112,7 +115,7 @@ function _build_tjmat(p::GGJParameters, Q::ComplexF64) 0 λ/2 0 0 1/2 0 ] - # A_0, A_1, A_2 — see inps_tjmat lines 188–202. Build mutable then freeze. + # A_0, A_1, A_2 — GW2020 Eqs. (4), (5), and the A₂ matrix of Eq. (3). Build mutable then freeze. A0 = zeros(ComplexF64, 6, 6) A1 = zeros(ComplexF64, 6, 6) A2 = zeros(ComplexF64, 6, 6) @@ -157,8 +160,9 @@ function _build_tjmat(p::GGJParameters, Q::ComplexF64) end # ----------------------------------------------------------------------- -# Step 2: closed-form Lyapunov solve for the splitting transformation. -# Mirrors inps_lyap_solve (inps.f lines 241–270). +# Closed-form Lyapunov solve for the splitting transformation — GW2020 Eq. (22), +# J₀²² P_k²¹ − P_k²¹ J₀¹¹ = −K_k²¹ and J₀¹¹ P_k¹² − P_k¹² J₀²² = −K_k¹², with the +# block-diagonal part B_k = K_k from Eq. (21). Mirrors inps_lyap_solve. # # Given a 6×6 K, returns (B, P) such that: # - B is block-diagonal with B[r1,r1] = K[r1,r1] and B[r2,r2] = K[r2,r2] @@ -172,8 +176,10 @@ function _lyap_solve(K::SMatrix{6,6,ComplexF64}, λ::ComplexF64) Pm = zeros(ComplexF64, 6, 6) # B is block-diagonal in the (r1, r2) split. - Bm[1, 1] = K[1, 1]; Bm[1, 2] = K[1, 2] - Bm[2, 1] = K[2, 1]; Bm[2, 2] = K[2, 2] + Bm[1, 1] = K[1, 1]; + Bm[1, 2] = K[1, 2] + Bm[2, 1] = K[2, 1]; + Bm[2, 2] = K[2, 2] for i in 3:6, j in 3:6 Bm[i, j] = K[i, j] end @@ -182,22 +188,22 @@ function _lyap_solve(K::SMatrix{6,6,ComplexF64}, λ::ComplexF64) @inbounds begin Pm[2, 3] = -K[2, 3] / λ Pm[2, 4] = -K[2, 4] / λ - Pm[2, 5] = K[2, 5] / λ - Pm[2, 6] = K[2, 6] / λ + Pm[2, 5] = K[2, 5] / λ + Pm[2, 6] = K[2, 6] / λ Pm[1, 3] = -(K[1, 3] + Pm[2, 3]) / λ Pm[1, 4] = -(K[1, 4] + Pm[2, 4]) / λ - Pm[1, 5] = (K[1, 5] + Pm[2, 5]) / λ - Pm[1, 6] = (K[1, 6] + Pm[2, 6]) / λ + Pm[1, 5] = (K[1, 5] + Pm[2, 5]) / λ + Pm[1, 6] = (K[1, 6] + Pm[2, 6]) / λ end # P[r2, r1] = P[3:6, 1:2] (bottom-left off-diagonal block) @inbounds begin - Pm[3, 1] = K[3, 1] / λ - Pm[4, 1] = K[4, 1] / λ + Pm[3, 1] = K[3, 1] / λ + Pm[4, 1] = K[4, 1] / λ Pm[5, 1] = -K[5, 1] / λ Pm[6, 1] = -K[6, 1] / λ - Pm[3, 2] = (K[3, 2] - Pm[3, 1]) / λ - Pm[4, 2] = (K[4, 2] - Pm[4, 1]) / λ + Pm[3, 2] = (K[3, 2] - Pm[3, 1]) / λ + Pm[4, 2] = (K[4, 2] - Pm[4, 1]) / λ Pm[5, 2] = -(K[5, 2] - Pm[5, 1]) / λ Pm[6, 2] = -(K[6, 2] - Pm[6, 1]) / λ end @@ -206,8 +212,10 @@ function _lyap_solve(K::SMatrix{6,6,ComplexF64}, λ::ComplexF64) end # ----------------------------------------------------------------------- -# Step 3: split recurrence (inps_split lines 278–361). -# Builds B_k, P_k, K6_k for k = 0..kmax+2. +# Split recurrence — GW2020 Eqs. (14)–(19). Seeks descending power series +# J,P,B = Σ (·)_k x^{-2k} (Eq. 14) with B₀ = J₀, P₀ = I (Eq. 17), and solves the +# order-by-order recurrence Eq. (16)/(18) with K_k of Eq. (19) via the Lyapunov +# solve above. Builds B_k, P_k, K6_k for k = 0..kmax+2. # ----------------------------------------------------------------------- function _split_recurrence(J::NTuple{3,SMatrix{6,6,ComplexF64}}, λ::ComplexF64, kmax::Int) @@ -221,21 +229,21 @@ function _split_recurrence(J::NTuple{3,SMatrix{6,6,ComplexF64}}, λ::ComplexF64, B[1] = J[1] # B_0 = J_0 K6[1] = J[1] - for k in 1:(kmax + 2) + for k in 1:(kmax+2) kk = k + 1 # 1-based slot for K6/B/P at index k # K6_k starts as J_k (only k = 1, 2 contribute), else 0 - Kacc = (k <= 2) ? J[k + 1] : Z6 + Kacc = (k <= 2) ? J[k+1] : Z6 # +2*(k-1)*P_{k-1} (k > 1 only) if k > 1 Kacc = Kacc + ComplexF64(2 * (k - 1)) * P[k] end # convolution: l = 1..k-1 - for l in 1:(k - 1) + for l in 1:(k-1) kml = k - l if kml <= 2 - Kacc = Kacc + J[kml + 1] * P[l + 1] + Kacc = Kacc + J[kml+1] * P[l+1] end - Kacc = Kacc - P[l + 1] * B[kml + 1] + Kacc = Kacc - P[l+1] * B[kml+1] end K6[kk] = Kacc Bk, Pk = _lyap_solve(Kacc, λ) @@ -246,12 +254,15 @@ function _split_recurrence(J::NTuple{3,SMatrix{6,6,ComplexF64}}, λ::ComplexF64, end # ----------------------------------------------------------------------- -# Step 4: coefs recurrence (inps_coefs lines 369–496). -# Builds K2_k, Q_k, C_k for k = 0..kmax+2 and D_k, E_k, Y_k, Z_k. +# Coefs recurrence — the 2×2 reduced-equation construction, GW2020 Eqs. (25)–(52). +# Builds the inner-block diagonalization Q_k, C_k via K2_k (Eqs. 31–32, 36), +# the shearing matrices D_k (Eqs. 42–43), the lowest-order Y₀ and Mercier +# exponents r± (Eqs. 48–49), and the shifted-exponent series Y_k = Y₀Z_k with +# Z_k from Eqs. (50)–(52). # ----------------------------------------------------------------------- function _coefs(B::Vector{SMatrix{6,6,ComplexF64,36}}, - R::SVector{2,Float64}, kmax::Int) + R::SVector{2,Float64}, kmax::Int) N = kmax + 3 Z2 = zero(SMatrix{2,2,ComplexF64}) @@ -267,53 +278,55 @@ function _coefs(B::Vector{SMatrix{6,6,ComplexF64,36}}, B0_11 = SMatrix{2,2,ComplexF64}(@view B[1][1:2, 1:2]) Cm[1] = B0_11 - for k in 1:(kmax + 2) - Bk_11 = SMatrix{2,2,ComplexF64}(@view B[k + 1][1:2, 1:2]) + for k in 1:(kmax+2) + Bk_11 = SMatrix{2,2,ComplexF64}(@view B[k+1][1:2, 1:2]) K2acc = Bk_11 + ComplexF64(2 * (k - 1)) * Qm[k] - for l in 1:(k - 1) - Bkml_11 = SMatrix{2,2,ComplexF64}(@view B[k - l + 1][1:2, 1:2]) - K2acc = K2acc + Bkml_11 * Qm[l + 1] - Qm[l + 1] * Cm[k - l + 1] + for l in 1:(k-1) + Bkml_11 = SMatrix{2,2,ComplexF64}(@view B[k-l+1][1:2, 1:2]) + K2acc = K2acc + Bkml_11 * Qm[l+1] - Qm[l+1] * Cm[k-l+1] end - K2[k + 1] = K2acc + K2[k+1] = K2acc # Q_k = [[0, 0], [-K2[1,1], -K2[1,2]]] (Fortran reshape gives this layout) - Qm[k + 1] = @SMatrix ComplexF64[ - 0 0 - -K2acc[1, 1] -K2acc[1, 2] + Qm[k+1] = @SMatrix ComplexF64[ + 0 0 + -K2acc[1, 1] -K2acc[1, 2] ] # C_k = [[0, 0], [K2[2,1], K2[1,1] + K2[2,2]]] - Cm[k + 1] = @SMatrix ComplexF64[ - 0 0 - K2acc[2, 1] K2acc[1, 1] + K2acc[2, 2] + Cm[k+1] = @SMatrix ComplexF64[ + 0 0 + K2acc[2, 1] K2acc[1, 1] + K2acc[2, 2] ] end - # Build D_k for k = 0..kmax (inps_coefs lines 408–413). + # Build D_k for k = 0..kmax — GW2020 Eq. (43); c_2^21 = −(E+F+H+2) is Eq. (39). D = Vector{SMatrix{2,2,ComplexF64,4}}(undef, kmax + 1) # D_0 = [[0, 1], [C_2[2,1], 3]] D[1] = @SMatrix ComplexF64[ - 0 1 + 0 1 Cm[3][2, 1] 3 ] for k in 1:kmax - D[k + 1] = @SMatrix ComplexF64[ - 0 0 - Cm[k + 3][2, 1] Cm[k + 2][2, 2] + D[k+1] = @SMatrix ComplexF64[ + 0 0 + Cm[k+3][2, 1] Cm[k+2][2, 2] ] end - # Lowest-order Y solution and inverse (Eq. 49). - r1 = ComplexF64(R[1]); r2 = ComplexF64(R[2]) + # Lowest-order Y solution and inverse — GW2020 Eq. (48), with exponents r± from Eq. (49). + r1 = ComplexF64(R[1]); + r2 = ComplexF64(R[2]) Y0 = @SMatrix ComplexF64[ - 1 1 - r1 r2 + 1 1 + r1 r2 ] Y0inv = (1 / (r1 - r2)) * @SMatrix ComplexF64[ - -r2 1 - r1 -1 + -r2 1 + r1 -1 ] - # E_k, Z_k, Y_k recurrence (lines 423–438). + # E_k, Z_k, Y_k recurrence — GW2020 Eqs. (50)–(52): E_k = Y₀⁻¹D_kY₀ (Eq. 51), + # Z_k(R−2kI) − RZ_k = Σ E_l Z_{k−l} (Eq. 52), Y_k = Y₀Z_k (Eq. 50). Y = Vector{SMatrix{2,2,ComplexF64,4}}(undef, kmax + 1) Z = Vector{SMatrix{2,2,ComplexF64,4}}(undef, kmax + 1) Z[1] = I2 @@ -322,16 +335,16 @@ function _coefs(B::Vector{SMatrix{6,6,ComplexF64,36}}, # Build Z_k = sum_{l=1..k} E_l * Z_{k-l}, with E_l = Y0inv * D_l * Y0 Zacc = Z2 for l in 1:k - El = Y0inv * D[l + 1] * Y0 - Zacc = Zacc + El * Z[k - l + 1] + El = Y0inv * D[l+1] * Y0 + Zacc = Zacc + El * Z[k-l+1] end # Divide each entry by (R[j] - R[i] - 2k) Zk = MMatrix{2,2,ComplexF64}(Zacc) for i in 1:2, j in 1:2 Zk[i, j] = Zk[i, j] / (R[j] - R[i] - 2 * k) end - Z[k + 1] = SMatrix{2,2,ComplexF64}(Zk) - Y[k + 1] = Y0 * Z[k + 1] + Z[k+1] = SMatrix{2,2,ComplexF64}(Zk) + Y[k+1] = Y0 * Z[k+1] end return K2, Qm, Cm, D, Y0, Y0inv, Y, Z @@ -354,6 +367,7 @@ Reference: Glasser & Wang, Phys. Plasmas **27**, 012506 (2020), Eqs. 7–53. """ function build_asymptotics(params::GGJParameters, Q::ComplexF64; kmax::Int=8) p1v = p1(params) + # Mercier Frobenius exponents r± = 3/2 ± √(−D_I) — GW2020 Eq. (49). R = SVector{2,Float64}(p1v + 1.5, -p1v + 1.5) T, Tinv, J, λ = _build_tjmat(params, Q) @@ -362,7 +376,7 @@ function build_asymptotics(params::GGJParameters, Q::ComplexF64; kmax::Int=8) return InnerAsymptoticsCache( params, Q, kmax, λ, R, T, Tinv, J, - P, B, K2, Qm, Cm, D, Y0, Y0inv, Y, Z, + P, B, K2, Qm, Cm, D, Y0, Y0inv, Y, Z ) end @@ -370,8 +384,9 @@ build_asymptotics(params::GGJParameters, Q::Number; kmax::Int=8) = build_asymptotics(params, ComplexF64(Q); kmax=kmax) # ----------------------------------------------------------------------- -# Horner evaluator with optional fractional-power prefactor. -# Mirrors inps_horner (inps.f lines 587–631). +# Horner evaluator with optional fractional-power prefactor. Sums the +# descending power series in x^{-2k} (GW2020 Eq. 14 form) for the Y, Q, and +# P[r2,r1] coefficient blocks, with the x^{R/2} Mercier prefactor. Mirrors inps_horner. # # Computes y[i] = (Σ_{k=0..n} c[i,k] * x^k) * x^rvec[i] # and dy[i] = d/dx of the above. @@ -381,15 +396,15 @@ build_asymptotics(params::GGJParameters, Q::Number; kmax::Int=8) = # ----------------------------------------------------------------------- function _horner(x::Real, c::AbstractMatrix{ComplexF64}; - rvec::Union{Nothing,AbstractVector{<:Real}}=nothing, - derivative::Bool=false) + rvec::Union{Nothing,AbstractVector{<:Real}}=nothing, + derivative::Bool=false) nrows, ncols = size(c) n = ncols - 1 # highest power y = ComplexF64.(c[:, ncols]) - @inbounds for k in (n - 1):-1:0 + @inbounds for k in (n-1):-1:0 for i in 1:nrows - y[i] = y[i] * x + c[i, k + 1] + y[i] = y[i] * x + c[i, k+1] end end @@ -409,9 +424,9 @@ function _horner(x::Real, c::AbstractMatrix{ComplexF64}; @inbounds for i in 1:nrows dy[i] = c[i, ncols] * (rvec[i] + n) end - @inbounds for k in (n - 1):-1:0 + @inbounds for k in (n-1):-1:0 for i in 1:nrows - dy[i] = dy[i] * x + c[i, k + 1] * (rvec[i] + k) + dy[i] = dy[i] * x + c[i, k+1] * (rvec[i] + k) end end @inbounds for i in 1:nrows @@ -422,9 +437,9 @@ function _horner(x::Real, c::AbstractMatrix{ComplexF64}; @inbounds for i in 1:nrows dy[i] = c[i, ncols] * n end - @inbounds for k in (n - 1):-1:0 + @inbounds for k in (n-1):-1:0 for i in 1:nrows - dy[i] = dy[i] * x + c[i, k + 1] * k + dy[i] = dy[i] * x + c[i, k+1] * k end end @inbounds for i in 1:nrows @@ -441,13 +456,13 @@ function _pack_y_coefs(cache::InnerAsymptoticsCache) kmax = cache.kmax cc = Matrix{ComplexF64}(undef, 4, kmax + 1) @inbounds for k in 0:kmax - Yk = cache.Y[k + 1] + Yk = cache.Y[k+1] # Fortran column-major reshape of (2,2) → 4 entries: # (Y[1,1], Y[2,1], Y[1,2], Y[2,2]) - cc[1, k + 1] = Yk[1, 1] - cc[2, k + 1] = Yk[2, 1] - cc[3, k + 1] = Yk[1, 2] - cc[4, k + 1] = Yk[2, 2] + cc[1, k+1] = Yk[1, 1] + cc[2, k+1] = Yk[2, 1] + cc[3, k+1] = Yk[1, 2] + cc[4, k+1] = Yk[2, 2] end return cc end @@ -456,28 +471,30 @@ function _pack_qp_coefs(cache::InnerAsymptoticsCache) kmax = cache.kmax dd = Matrix{ComplexF64}(undef, 12, kmax + 1) @inbounds for k in 0:kmax - Qk = cache.Qmat[k + 1] - Pk = cache.P[k + 1] + Qk = cache.Qmat[k+1] + Pk = cache.P[k+1] # dd[1:4] from Q (column-major reshape of 2×2) - dd[1, k + 1] = Qk[1, 1] - dd[2, k + 1] = Qk[2, 1] - dd[3, k + 1] = Qk[1, 2] - dd[4, k + 1] = Qk[2, 2] + dd[1, k+1] = Qk[1, 1] + dd[2, k+1] = Qk[2, 1] + dd[3, k+1] = Qk[1, 2] + dd[4, k+1] = Qk[2, 2] # dd[5:12] from P[r2, r1] = P[3:6, 1:2] (4×2 → column-major 8 entries) - dd[5, k + 1] = Pk[3, 1] - dd[6, k + 1] = Pk[4, 1] - dd[7, k + 1] = Pk[5, 1] - dd[8, k + 1] = Pk[6, 1] - dd[9, k + 1] = Pk[3, 2] - dd[10, k + 1] = Pk[4, 2] - dd[11, k + 1] = Pk[5, 2] - dd[12, k + 1] = Pk[6, 2] + dd[5, k+1] = Pk[3, 1] + dd[6, k+1] = Pk[4, 1] + dd[7, k+1] = Pk[5, 1] + dd[8, k+1] = Pk[6, 1] + dd[9, k+1] = Pk[3, 2] + dd[10, k+1] = Pk[4, 2] + dd[11, k+1] = Pk[5, 2] + dd[12, k+1] = Pk[6, 2] end return dd end # ----------------------------------------------------------------------- -# Step 5: evaluator (inps_ua, inps.f lines 504–579). +# Evaluator — back-substitution U = TPQSY of GW2020 Eq. (53), assembled from +# the cached Y-series (Eq. 50), Q and the P[r2,r1] block, the shearing matrix +# S of Eq. (41), and the Jordan basis T of Eq. (7). Mirrors inps_ua. # ----------------------------------------------------------------------- """ @@ -496,7 +513,7 @@ returns the solutions in the original 6-component first-order-system basis used by `inpso_get_uv` and the shooting / Galerkin solvers. """ function evaluate_asymptotics(cache::InnerAsymptoticsCache, x::Real; - derivative::Bool=true, apply_T::Bool=true) + derivative::Bool=true, apply_T::Bool=true) xfac = 1.0 / (x * x) R = cache.R rvec = SVector(-R[1] / 2, -R[1] / 2, -R[2] / 2, -R[2] / 2) @@ -508,21 +525,24 @@ function evaluate_asymptotics(cache::InnerAsymptoticsCache, x::Real; zz, dzz = _horner(xfac, dd; derivative=derivative) # Reshape yy → y (2×2), zz → q (2×2) and p21 (4×2) - y = SMatrix{2,2,ComplexF64}(yy[1], yy[2], yy[3], yy[4]) - q = SMatrix{2,2,ComplexF64}(zz[1], zz[2], zz[3], zz[4]) + y = SMatrix{2,2,ComplexF64}(yy[1], yy[2], yy[3], yy[4]) + q = SMatrix{2,2,ComplexF64}(zz[1], zz[2], zz[3], zz[4]) p21 = SMatrix{4,2,ComplexF64}(zz[5], zz[6], zz[7], zz[8], - zz[9], zz[10], zz[11], zz[12]) + zz[9], zz[10], zz[11], zz[12]) # Splitting matrix pp (6×2): top 2×2 = I, bottom 4×2 = p21. pp_m = zeros(ComplexF64, 6, 2) - pp_m[1, 1] = 1; pp_m[2, 2] = 1 + pp_m[1, 1] = 1; + pp_m[2, 2] = 1 @inbounds for i in 1:4, j in 1:2 - pp_m[i + 2, j] = p21[i, j] + pp_m[i+2, j] = p21[i, j] end pp = SMatrix{6,2,ComplexF64}(pp_m) + # Shearing matrix S = diag(1, 1/x²) — GW2020 Eq. (41); here 1/x² = xfac. smat = @SMatrix ComplexF64[1 0; 0 xfac] + # U = T·P·Q·S·Y, the asymptotic solution of GW2020 Eq. (53) (T applied below). qsy = q * smat * y U = pp * qsy @@ -530,17 +550,17 @@ function evaluate_asymptotics(cache::InnerAsymptoticsCache, x::Real; # Apply chain rule: derivatives from horner are wrt xfac, convert to # derivatives wrt x via factor (-2*xfac/x) = d(xfac)/dx. chain = -2 * xfac / x - dy_v = chain .* dyy - dz_v = chain .* dzz + dy_v = chain .* dyy + dz_v = chain .* dzz dy = SMatrix{2,2,ComplexF64}(dy_v[1], dy_v[2], dy_v[3], dy_v[4]) dq = SMatrix{2,2,ComplexF64}(dz_v[1], dz_v[2], dz_v[3], dz_v[4]) dp21 = SMatrix{4,2,ComplexF64}(dz_v[5], dz_v[6], dz_v[7], dz_v[8], - dz_v[9], dz_v[10], dz_v[11], dz_v[12]) + dz_v[9], dz_v[10], dz_v[11], dz_v[12]) dpp_m = zeros(ComplexF64, 6, 2) @inbounds for i in 1:4, j in 1:2 - dpp_m[i + 2, j] = dp21[i, j] + dpp_m[i+2, j] = dp21[i, j] end dpp = SMatrix{6,2,ComplexF64}(dpp_m) @@ -549,7 +569,7 @@ function evaluate_asymptotics(cache::InnerAsymptoticsCache, x::Real; dU = pp * dqsy + dpp * qsy if apply_T - U = cache.T * U + U = cache.T * U dU = cache.T * dU end return U, dU @@ -562,17 +582,19 @@ function evaluate_asymptotics(cache::InnerAsymptoticsCache, x::Real; end # ----------------------------------------------------------------------- -# Step 6: residual `delta` and adaptive xmax (inps_delta + inps_xmax). +# Residual `delta` and adaptive xmax — the convergence measure Δ± of GW2020 +# Eq. (54), ‖u' − xJu‖/max(‖u'‖,‖xJu‖) in the J-rotated basis, used to choose +# x_max (GW2020 Sec. III, Fig. 3). Mirrors inps_delta + inps_xmax. # ----------------------------------------------------------------------- """ asymptotic_residual(cache::InnerAsymptoticsCache, x::Real) -> SVector{2,Float64} -Compute the residual `D₆(x)` of the asymptotic basis at `x` for each of -the two algebraic columns. Mirrors `inps_delta` (inps.f lines 713–752): -returns `‖dU − x·matrix·U‖∞ / max(‖dU‖∞, ‖x·matrix·U‖∞)` per column, -where `matrix = J₀ + xfac·J₁ + xfac²·J₂` is the J-rotated coefficient -matrix. +Compute the convergence measure `Δ±` of the asymptotic basis at `x` for each +of the two algebraic columns (GW2020 Eq. 54). Mirrors `inps_delta`: returns +`‖dU − x·matrix·U‖∞ / max(‖dU‖∞, ‖x·matrix·U‖∞)` per column, where +`matrix = J₀ + xfac·J₁ + xfac²·J₂` is the J-rotated coefficient matrix (the +residual of `v' = xJv`, GW2020 Eq. 6). """ function asymptotic_residual(cache::InnerAsymptoticsCache, x::Real) U, dU = evaluate_asymptotics(cache, x; derivative=true, apply_T=false) @@ -594,7 +616,9 @@ function asymptotic_residual(cache::InnerAsymptoticsCache, x::Real) delta = MVector{2,Float64}(0.0, 0.0) @inbounds for j in 1:2 - n0 = 0.0; n1 = 0.0; n2 = 0.0 + n0 = 0.0; + n1 = 0.0; + n2 = 0.0 for i in 1:6 n0 = max(n0, abs(matvec0[i, j])) n1 = max(n1, abs(matvec1[i, j])) @@ -613,17 +637,18 @@ end dxlog::Float64=0.01) -> (Float64, InnerAsymptoticsCache) Sweep `x` log-uniformly upward from `10^xlogmin` and return the smallest -`x` at which `max(asymptotic_residual(cache, x)) < eps`. Also returns the -`InnerAsymptoticsCache` it built so callers can reuse it. Mirrors -`inps_xmax` (inps.f lines 639–705). +`x` at which `max(asymptotic_residual(cache, x)) < eps` — the cutoff `x_max` +where the GW2020 Eq. (54) convergence measure drops below tolerance +(GW2020 Sec. III, Fig. 3). Also returns the `InnerAsymptoticsCache` it built +so callers can reuse it. Mirrors `inps_xmax`. Throws an `ErrorException` if no `x` in the sweep range achieves the target tolerance. """ function pick_xmax(params::GGJParameters, Q::ComplexF64; - eps::Float64=1e-7, kmax::Int=8, - xlogmin::Float64=-1.0, xlogmax::Float64=4.0, - dxlog::Float64=0.01) + eps::Float64=1e-7, kmax::Int=8, + xlogmin::Float64=-1.0, xlogmax::Float64=4.0, + dxlog::Float64=0.01) cache = build_asymptotics(params, Q; kmax=kmax) dxfac = 10.0^dxlog xlog = xlogmin diff --git a/src/InnerLayer/GGJ/Shooting.jl b/src/InnerLayer/GGJ/Shooting.jl index ca085dabe..7a3162d2e 100644 --- a/src/InnerLayer/GGJ/Shooting.jl +++ b/src/InnerLayer/GGJ/Shooting.jl @@ -1,5 +1,10 @@ # Shooting.jl # +# NOTE: This solver is NOT used in production and is not to be used. It was a +# porting exercise (deltar.f) retained for reference only. The Galerkin solver +# (Galerkin.jl) is the sole supported GGJ inner-layer solver; shooting underflows +# at large |γ| and shares none of the production matching path. Do not call it. +# # Stable backward shooting solver for the GGJ inner-layer model. Direct # Julia port of rmatch/deltar.f. Integrates the 4×4 origin-diagonalized # resistive-layer ODE from `tmax` (large-x asymptotic regime) backward to @@ -7,10 +12,14 @@ # Frobenius basis at the origin and reads off the parity-projected # matching data via `deltar_ratio`. # -# The 4 origin Frobenius exponents are `al0 = (p1, 1/2, −p1, −1/2)` where -# `p1 = √(−D_I)` (Mercier-stable required). The two "small" (singular) -# modes are columns 3 and 4 (`x^{−p1}` and `x^{−1/2}`); the two "large" -# (smooth) modes are columns 1 and 2 (`x^{p1}` and `x^{1/2}`). +# This solves the same inner-region equations as the production Galerkin path +# (GWP2016 Eq. 11 ≡ GW2020 Eq. 1) but by a different numerical method: a +# backward shoot in the origin-diagonalized basis rather than the matched +# singular-Galerkin weak form. The 4 origin Frobenius exponents are +# `al0 = (p1, 1/2, −p1, −1/2)` where `p1 = √(−D_I)` (Mercier-stable required; +# D_I = E+F+H−1/4, GWP2016 Eq. A9). The two "small" (singular) modes are +# columns 3 and 4 (`x^{−p1}` and `x^{−1/2}`); the two "large" (smooth) modes +# are columns 1 and 2 (`x^{p1}` and `x^{1/2}`). # # Reference: A. H. Glasser, Phys. Plasmas **23**, 072505 (2016) and the # Fortran rmatch/deltar.f. @@ -53,14 +62,18 @@ function _build_origin_arrays(p::GGJParameters, Q::ComplexF64; nps::Int=8, rtol: p1v = p1(p) pplus = -0.5 + p1v - e = ComplexF64(p.E); f = ComplexF64(p.F); h = ComplexF64(p.H) - g = ComplexF64(p.G); k = ComplexF64(p.K); q = Q + e = ComplexF64(p.E); + f = ComplexF64(p.F); + h = ComplexF64(p.H) + g = ComplexF64(p.G); + k = ComplexF64(p.K); + q = Q q3 = q^3 kk1 = 1 + k * q3 a1 = (g - k * e) * q * q / kk1 a2 = sqrt(0.5 / (p1v * q)) - aplus = h - 0.5 + p1v + aplus = h - 0.5 + p1v aminus = h - 0.5 - p1v # d0 — see deltar_origin lines 361–376. @@ -70,23 +83,23 @@ function _build_origin_arrays(p::GGJParameters, Q::ComplexF64; nps::Int=8, rtol: d0_m[1, 3] = -q * a2 d0_m[1, 4] = 0 d0_m[2, 2] = 1 - d0_m[3, 1] = aplus * a2 + d0_m[3, 1] = aplus * a2 d0_m[3, 3] = -aminus * a2 d0_m[4, 1] = -aplus * a2 d0_m[4, 2] = -a1 - d0_m[4, 3] = aminus * a2 + d0_m[4, 3] = aminus * a2 d0_m[4, 4] = 1 # d0inv — same explicit antisymmetry pattern as deltar_origin lines 380–395. d0inv_m = zeros(ComplexF64, 4, 4) - d0inv_m[1, 1] = d0_m[3, 3] - d0inv_m[2, 2] = d0_m[4, 4] - d0inv_m[1, 2] = d0_m[4, 3] - d0inv_m[2, 1] = d0_m[3, 4] - d0inv_m[3, 3] = d0_m[1, 1] - d0inv_m[4, 4] = d0_m[2, 2] - d0inv_m[3, 4] = d0_m[2, 1] - d0inv_m[4, 3] = d0_m[1, 2] + d0inv_m[1, 1] = d0_m[3, 3] + d0inv_m[2, 2] = d0_m[4, 4] + d0inv_m[1, 2] = d0_m[4, 3] + d0inv_m[2, 1] = d0_m[3, 4] + d0inv_m[3, 3] = d0_m[1, 1] + d0inv_m[4, 4] = d0_m[2, 2] + d0inv_m[3, 4] = d0_m[2, 1] + d0inv_m[4, 3] = d0_m[1, 2] d0inv_m[1, 3] = -d0_m[1, 3] d0inv_m[2, 4] = -d0_m[2, 4] d0inv_m[1, 4] = -d0_m[2, 3] @@ -106,9 +119,9 @@ function _build_origin_arrays(p::GGJParameters, Q::ComplexF64; nps::Int=8, rtol: al1_m[3, 1] = q al1_m[4, 2] = -q / kk1 - d0_s = SMatrix{4,4,ComplexF64}(d0_m) + d0_s = SMatrix{4,4,ComplexF64}(d0_m) d0inv_s = SMatrix{4,4,ComplexF64}(d0inv_m) - al1_s = d0inv_s * SMatrix{4,4,ComplexF64}(al1_m) * d0_s + al1_s = d0inv_s * SMatrix{4,4,ComplexF64}(al1_m) * d0_s # ups[i, j, k] — origin power-series coefficients (deltar_origin lines 440–460). # ups(:,:,1) = I; higher orders from the al1 recurrence. @@ -120,7 +133,7 @@ function _build_origin_arrays(p::GGJParameters, Q::ComplexF64; nps::Int=8, rtol: for j in 1:4, i in 1:4 acc = ComplexF64(0) for l in 1:4 - acc += al1_s[i, l] * ups[l, j, kk - 1] + acc += al1_s[i, l] * ups[l, j, kk-1] end ups[i, j, kk] = acc / (al0[j] - al0[i] + 2 * (kk - 1)) end @@ -143,26 +156,30 @@ end # ----------------------------------------------------------------------- function _build_infinity_arrays(p::GGJParameters, Q::ComplexF64, - d0inv::SMatrix{4,4,ComplexF64}; - rtol::Float64=1e-6, fmax::Float64=1.0) - e = ComplexF64(p.E); f = ComplexF64(p.F); h = ComplexF64(p.H) - g = ComplexF64(p.G); k = ComplexF64(p.K); q = Q + d0inv::SMatrix{4,4,ComplexF64}; + rtol::Float64=1e-6, fmax::Float64=1.0) + e = ComplexF64(p.E); + f = ComplexF64(p.F); + h = ComplexF64(p.H) + g = ComplexF64(p.G); + k = ComplexF64(p.K); + q = Q dr = mercier_dr(p) - q3 = q^3 - kk1 = 1 + k * q3 - a1 = (g - k * e) * q * q / kk1 - lamda = sqrt(q) + q3 = q^3 + kk1 = 1 + k * q3 + a1 = (g - k * e) * q * q / kk1 + lamda = sqrt(q) lamdaq = lamda * q - bb = -0.25 * lamdaq * (1 + g + k * (dr - e)) - cc = 0.25 * kk1 * (a1 * q * (1 - dr / q3) + dr - h * h) - ddsq = bb * bb - cc - dd = sqrt(ddsq) + bb = -0.25 * lamdaq * (1 + g + k * (dr - e)) + cc = 0.25 * kk1 * (a1 * q * (1 - dr / q3) + dr - h * h) + ddsq = bb * bb - cc + dd = sqrt(ddsq) # m matrix (2×2) — deltar_infinity lines 521–524. m11 = -lamdaq + dr / lamdaq - m12 = h - dr / lamdaq - m21 = kk1 * (h + dr / lamdaq) + m12 = h - dr / lamdaq + m21 = kk1 * (h + dr / lamdaq) m22 = -kk1 * (a1 / lamda + dr / lamdaq) pexp = SVector{4,ComplexF64}(bb - dd, bb + dd, -bb + dd, -bb - dd) @@ -176,25 +193,25 @@ function _build_infinity_arrays(p::GGJParameters, Q::ComplexF64, for i in 1:4 d1_m[i, j] = d0inv[i, 1] * bmmat[1, j] + d0inv[i, 2] * bmmat[2, j] + lamda * (-d0inv[i, 3] * bmmat[1, j] + - d0inv[i, 4] * bmmat[2, j] / kk1) + d0inv[i, 4] * bmmat[2, j] / kk1) end end # bpmat (2×2) and columns 3,4 of d1. sigma = bmmat[1, 2] / bmmat[2, 2] - tau = bmmat[2, 1] / bmmat[1, 1] + tau = bmmat[2, 1] / bmmat[1, 1] stfac = 0.5 / (1 - sigma * tau) bpmat = zeros(ComplexF64, 2, 2) bpmat[1, 1] = stfac / bmmat[1, 1] bpmat[2, 2] = stfac / bmmat[2, 2] - bpmat[1, 2] = -tau * bpmat[2, 2] + bpmat[1, 2] = -tau * bpmat[2, 2] bpmat[2, 1] = -sigma * bpmat[1, 1] @inbounds for j in 1:2 for i in 1:4 - d1_m[i, j + 2] = (d0inv[i, 1] * bpmat[1, j] - - d0inv[i, 2] * bpmat[2, j] * kk1) / lamda + - d0inv[i, 3] * bpmat[1, j] + - d0inv[i, 4] * bpmat[2, j] + d1_m[i, j+2] = (d0inv[i, 1] * bpmat[1, j] - + d0inv[i, 2] * bpmat[2, j] * kk1) / lamda + + d0inv[i, 3] * bpmat[1, j] + + d0inv[i, 4] * bpmat[2, j] end end @@ -218,13 +235,13 @@ complex frequency `Q`, precomputing the origin and infinity asymptotic arrays used by the forward/backward shoots. """ function _build_shooting_system(p::GGJParameters, Q::ComplexF64; - nps::Int=8, rtol::Float64=1e-6, fmax::Float64=1.0) + nps::Int=8, rtol::Float64=1e-6, fmax::Float64=1.0) o = _build_origin_arrays(p, Q; nps=nps, rtol=rtol) inf = _build_infinity_arrays(p, Q, o.d0inv; rtol=rtol, fmax=fmax) return GGJShootingSystem( p, Q, o.p1v, o.pplus, o.al0, o.al1, o.d0, o.d0inv, o.ups, o.nps, - inf.d1, inf.pexp, inf.bl1, inf.tmax, o.tmin, + inf.d1, inf.pexp, inf.bl1, inf.tmax, o.tmin ) end @@ -242,7 +259,7 @@ function _origin_basis(sys::GGJShootingSystem, t::Real) @inbounds for j in 1:4, i in 1:4 # Horner in t² over k = nps..1 acc = sys.ups[i, j, nps] - for kk in (nps - 1):-1:1 + for kk in (nps-1):-1:1 acc = acc * t2 + sys.ups[i, j, kk] end u[i, j] = acc @@ -284,7 +301,7 @@ end # ----------------------------------------------------------------------- function _ggj_der!(dy::AbstractMatrix{ComplexF64}, y::AbstractMatrix{ComplexF64}, - sys::GGJShootingSystem, t::Real) + sys::GGJShootingSystem, t::Real) mul!(dy, sys.al1, y) @inbounds for j in axes(y, 2), i in axes(y, 1) dy[i, j] = dy[i, j] * t + sys.al0[i] * y[i, j] / t @@ -339,9 +356,9 @@ controls the truncation error of the origin Frobenius series and the choice of `tmin`. """ function solve_inner(::GGJModel{:shooting}, params::GGJParameters, γ::Number; - reltol::Float64=1e-6, abstol::Float64=1e-6, - rtol_origin::Float64=1e-6, nps::Int=8, - fmax::Float64=1.0, solver=Tsit5()) + reltol::Float64=1e-6, abstol::Float64=1e-6, + rtol_origin::Float64=1e-6, nps::Int=8, + fmax::Float64=1.0, solver=Tsit5()) Q = inner_Q(params, γ) sys = _build_shooting_system(params, Q; nps=nps, rtol=rtol_origin, fmax=fmax) diff --git a/src/InnerLayer/InnerLayer.jl b/src/InnerLayer/InnerLayer.jl index 537b2970f..47744f3aa 100644 --- a/src/InnerLayer/InnerLayer.jl +++ b/src/InnerLayer/InnerLayer.jl @@ -16,10 +16,10 @@ include("GGJ/GGJ.jl") import .GGJ: GGJModel, GGJParameters, build_asymptotics, evaluate_asymptotics, pick_xmax import .GGJ: InnerAsymptoticsCache, mercier_di, mercier_dr, inner_Q, rescale_delta -import .GGJ: glasser_wang_2020_eq55 +import .GGJ: glasser_wang_2020_eq55, solve_inner_converged # SLAYER imports go here -export InnerLayerModel, solve_inner +export InnerLayerModel, solve_inner, solve_inner_converged export GGJ, GGJModel, GGJParameters export build_asymptotics, evaluate_asymptotics, pick_xmax, InnerAsymptoticsCache export mercier_di, mercier_dr, inner_Q, rescale_delta From 32428db095199168001a9b884b1d2355263c4b55 Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Thu, 25 Jun 2026 01:35:40 -0400 Subject: [PATCH 112/135] GALERKIN - NEW - save xi_psi and bpen from inner layer to hdf5 --- src/ForceFreeStates/Galerkin/GalerkinMatch.jl | 47 +++++++++++++-- src/ForceFreeStates/Galerkin/GalerkinSolve.jl | 14 ++++- .../Galerkin/GalerkinStructs.jl | 14 +++++ src/InnerLayer/GGJ/Galerkin.jl | 57 +++++++++++++++++++ 4 files changed, 123 insertions(+), 9 deletions(-) diff --git a/src/ForceFreeStates/Galerkin/GalerkinMatch.jl b/src/ForceFreeStates/Galerkin/GalerkinMatch.jl index 2a2b37af9..21fc87ff3 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinMatch.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinMatch.jl @@ -42,6 +42,9 @@ function gal_match_rpec(ctrl::ForceFreeStatesControl, equil, intr::ForceFreeStat cout = zeros(ComplexF64, 2msing, mcoil) cin = zeros(ComplexF64, 2msing, mcoil) deltar = zeros(ComplexF64, msing, 2) + bpen = zeros(ComplexF64, msing, mcoil) + inner_psi = Vector{Float64}[] # no inner layer in the ideal limit + inner_xi = Matrix{ComplexF64}[] rpec_eig = zeros(ComplexF64, msing) residual = 0.0 else @@ -56,25 +59,45 @@ function gal_match_rpec(ctrl::ForceFreeStatesControl, equil, intr::ForceFreeStat error("gal_match_rpec: re-derived $(length(sings)) surfaces, expected msing=$msing") # --- inner-layer matching data Δ(Q) per surface (deltac_run; match.f) --- - inner = InnerLayer.GGJModel(solver=:galerkin) + # solve_inner_profile returns the same Δ as solve_inner plus the reconstructed inner-layer field, + # so the layer-center value (penetrated field) comes for free from the single matching solve. deltar = zeros(ComplexF64, msing, 2) rpec_eig = zeros(ComplexF64, msing) + # Per-surface layer-center field weights pen[i,k] = scale·Ψ_k(0), parity k=1,2 (match.f intotsol_b). + chi1 = 2π * equil.psio + pen = zeros(ComplexF64, msing, 2) + # Per-surface inner-layer ξ_ψ building blocks for the matched solution (match.f intotsol, deltac comp 2): + # the ψ grid ψ_s ± X·x0/v1 (left reversed then right) and the resc-scaled odd/even parity profiles. + inner_psi = Vector{Vector{Float64}}(undef, msing) + inner_odd = Vector{Vector{ComplexF64}}(undef, msing) # Ξ₁, antisymmetric across ψ_s + inner_even = Vector{Vector{ComplexF64}}(undef, msing) # Ξ₂, symmetric across ψ_s for i in 1:msing params = resist_eval(sings[i], equil, intr; eta=ctrl.gal_eta[i], rho=ctrl.gal_rho[i], gamma=ctrl.gal_gamma, ising=i) γ = 2π * im * nn * ctrl.gal_rotation[i] # forced eigenvalue; gal_rotation is f [Hz], γ = 2πi·n·f rpec_eig[i] = γ - Δ = InnerLayer.solve_inner(inner, params, γ) # (Δ₁, Δ₂) in deltac.f convention + # Inner-solve knobs matched to the Fortran rmatch deltac/inps reference (DELTAC_LIST): inps basis, + # inps_xfac=10 (xmax×10, grid nx = 128·10 = 1280), nq=5, cutoff=5, order_pow=8 (↔ kmax). + Δ, _, prof, _ = InnerLayer.GGJ.solve_inner_profile(params, γ; xfac=10.0, nx=1280, nq=5, cutoff=5, kmax=8) # (Δ₁, Δ₂) in deltac.f convention deltar[i, 1] = Δ[1] deltar[i, 2] = Δ[2] + x0i = InnerLayer.GGJ.x0(params) + resc = (params.v1 / x0i)^(0.5 + InnerLayer.GGJ.p1(params)) # deltac.f amplitude rescale + scale = chi1 * im * nn * sings[i].q1 * x0i # match.f b-field scaling + pen[i, 1] = scale * prof.Ψ[1, 1] * resc # layer center X=0, parity 1 (Ψ(0)≠0) + pen[i, 2] = scale * prof.Ψ[1, 2] * resc # parity 2 (Ψ(0)=0 ⇒ ~0) + xvar = prof.x .* (x0i / params.v1) # inner X → ψ-distance (deltac.f:1822) + inner_psi[i] = vcat(reverse(sings[i].psifac .- xvar), sings[i].psifac .+ xvar) + inner_odd[i] = resc .* vcat(reverse(.-prof.Ξ[:, 1]), prof.Ξ[:, 1]) # comp 2, parity 1 (odd: −left,+right) + inner_even[i] = resc .* vcat(reverse(prof.Ξ[:, 2]), prof.Ξ[:, 2]) # comp 2, parity 2 (even) end # --- assemble the 4·msing matching system (match.f) --- delta_out = gal_result.delta[1:2msing, 1:2msing] # outer Δ′ plasma block mat = zeros(ComplexF64, 4msing, 4msing) rmat = zeros(ComplexF64, 4msing, mcoil) - @views mat[2msing+1:4msing, 1:2msing] .= transpose(delta_out) # Δ_out - @views rmat[2msing+1:4msing, :] .= .-transpose(gal_result.delta_coil) # −Δ_coil source + @views mat[(2msing+1):4msing, 1:2msing] .= transpose(delta_out) # Δ_out + @views rmat[(2msing+1):4msing, :] .= .-transpose(gal_result.delta_coil) # −Δ_coil source for ising in 1:msing idx1 = 2ising - 1 idx2 = 2ising @@ -99,7 +122,19 @@ function gal_match_rpec(ctrl::ForceFreeStatesControl, equil, intr::ForceFreeStat cof = mat \ rmat residual = norm(mat * cof - rmat) / max(norm(rmat), 1e-300) cout = cof[1:2msing, :] - cin = cof[2msing+1:4msing, :] + cin = cof[(2msing+1):4msing, :] + + # Inner-layer penetrated (reconnected) resonant field at each rational surface, read off the GGJ + # inner solution at the layer center exactly as Fortran match_output_solution builds intotsol_b + # (match.f) — cusp-free, fit-free. bpen[i,j] = pen₁(i)·cin[2i,j] + pen₂(i)·cin[2i-1,j]. + bpen = zeros(ComplexF64, msing, mcoil) + for i in 1:msing, j in 1:mcoil + bpen[i, j] = pen[i, 1] * cin[2i, j] + pen[i, 2] * cin[2i-1, j] + end + + # Matched inner-layer ξ_ψ(ψ) per surface, per coil drive (match.f intotsol): odd parity weighted by + # cin[2i] (cofin(2·ising)), even parity by cin[2i-1] (cofin(2·ising-1)). + inner_xi = [inner_odd[i] * transpose(cin[2i, :]) .+ inner_even[i] * transpose(cin[2i-1, :]) for i in 1:msing] end # --- matched outer ξ/ξ′ per coil drive (match.f); ideal: cout=0 ⇒ bare coil column --- @@ -118,7 +153,7 @@ function gal_match_rpec(ctrl::ForceFreeStatesControl, equil, intr::ForceFreeStat end end - return GalMatchResult(cout, cin, xi, xi_deriv, deltar, rpec_eig, residual) + return GalMatchResult(cout, cin, xi, xi_deriv, deltar, bpen, inner_psi, inner_xi, rpec_eig, residual) end """ diff --git a/src/ForceFreeStates/Galerkin/GalerkinSolve.jl b/src/ForceFreeStates/Galerkin/GalerkinSolve.jl index 9531b34b6..d7b979333 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinSolve.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinSolve.jl @@ -191,9 +191,11 @@ function galerkin_solve(ctrl::ForceFreeStatesControl, equil, ffit::FourFitVars, # DRIVEN (RPEC) outer↔inner matching: build the coil-driven matched ξ/ξ′ (gal_match_rpec). ctrl.gal_match_flag || return result ctrl.gal_rpec_flag || error("galerkin_solve: gal_match_flag=true requires gal_rpec_flag=true") - ctrl.verbose && @info(ctrl.gal_ideal_flag ? - "RPEC matching: IDEAL solution (inner layer skipped, bare coil columns)" : - "RPEC matching: inner-layer Δ(Q) + outer↔inner solve for the coil-driven ξ") + ctrl.verbose && @info( + ctrl.gal_ideal_flag ? + "RPEC matching: IDEAL solution (inner layer skipped, bare coil columns)" : + "RPEC matching: inner-layer Δ(Q) + outer↔inner solve for the coil-driven ξ" + ) match = gal_match_rpec(ctrl, equil, intr, result) ctrl.gal_ideal_flag || (ctrl.verbose && @info "RPEC matching: linear-solve residual = $(match.residual)") return GalerkinResult(delta, Ap, Bp, Gammap, Deltap, msing, @@ -262,7 +264,13 @@ function write_galerkin!(out_h5, result::GalerkinResult) out_h5["galerkin/match/xi"] = m.xi out_h5["galerkin/match/xi_deriv"] = m.xi_deriv out_h5["galerkin/match/deltar"] = m.deltar + out_h5["galerkin/match/bpen"] = m.bpen out_h5["galerkin/match/rpec_eig"] = m.rpec_eig + # Per-surface inner-layer ξ_ψ(ψ) (match.f intotsol); ragged grids → one dataset pair per surface. + for i in eachindex(m.inner_psi) + out_h5["galerkin/match/inner/psi_$i"] = m.inner_psi[i] + out_h5["galerkin/match/inner/xi_$i"] = m.inner_xi[i] + end out_h5["galerkin/match/residual"] = m.residual end return nothing diff --git a/src/ForceFreeStates/Galerkin/GalerkinStructs.jl b/src/ForceFreeStates/Galerkin/GalerkinStructs.jl index b1b3819d3..2fcd91737 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinStructs.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinStructs.jl @@ -146,6 +146,17 @@ Coil-driven RPEC matched solution from the outer↔inner asymptotic matching (Fo - `xi::Array{ComplexF64,3}`, `xi_deriv::Array{ComplexF64,3}` — `(mpert, ngrid, mcoil)` matched ξ(ψ) and analytic ξ′(ψ) on the gal grid, one column per coil drive (identity-at-edge basis). - `deltar::Matrix{ComplexF64}` — `(msing, 2)` inner-layer matching data `(Δ₁, Δ₂)` per surface. + - `bpen::Matrix{ComplexF64}` — `(msing, mcoil)` inner-layer penetrated (reconnected) resonant field at + each rational surface, one column per coil drive. Read off the GGJ inner solution at the layer center + (X=0) exactly as Fortran `match_output_solution` builds `intotsol_b` (match.f) — cusp-free, fit-free. + Zero for the ideal branch (`gal_ideal_flag`), where the inner layer is skipped. + - `inner_psi::Vector{Vector{Float64}}` — per surface, the inner-layer ψ grid `ψ_s ± X·x0/v1` (left wing + reversed then right wing, so ψ ascends through `ψ_s`). Empty in the ideal branch. + - `inner_xi::Vector{Matrix{ComplexF64}}` — per surface, the inner-layer displacement `ξ_ψ(ψ)` on + `inner_psi`, `(length(inner_psi[s]), mcoil)`, one column per coil drive. This is Fortran `match_solution`'s + `intotsol` (deltac component 2): `resc·(±Ξ₁·cin[2s] + Ξ₂·cin[2s-1])`, odd parity `Ξ₁` antisymmetric across + `ψ_s`, even parity `Ξ₂` symmetric, `resc=(v1/x0)^(1/2+p1)`. The raw inner-layer contribution only (no + regular outer background added), so it shares the singular asymptote with the outer near `ψ_s`. - `rpec_eig::Vector{ComplexF64}` — forced eigenvalues `γ_s = 2πi·n·f_s` per surface. - `residual::Float64` — relative linear-solve residual `‖mat·cof − rmat‖/‖rmat‖`. """ @@ -155,6 +166,9 @@ struct GalMatchResult xi::Array{ComplexF64,3} xi_deriv::Array{ComplexF64,3} deltar::Matrix{ComplexF64} + bpen::Matrix{ComplexF64} + inner_psi::Vector{Vector{Float64}} + inner_xi::Vector{Matrix{ComplexF64}} rpec_eig::Vector{ComplexF64} residual::Float64 end diff --git a/src/InnerLayer/GGJ/Galerkin.jl b/src/InnerLayer/GGJ/Galerkin.jl index b26cb1c45..9ce7d8409 100644 --- a/src/InnerLayer/GGJ/Galerkin.jl +++ b/src/InnerLayer/GGJ/Galerkin.jl @@ -877,3 +877,60 @@ function solve_inner(::GGJModel{:galerkin}, params::GGJParameters, γ::Number; return rescale_delta(Δ_swapped, params) end + +# THIS IS AN ATTEMPT AT A CONVERGENCE-GUARDED INNER-LAYER SOLVE. IT PRESENTLY HAS SOME +# ISSUES AND IS NOT RELIABLE IN BROAD SCANS. IT IS LEFT HERE FOR REFERENCE AND MAY BE REWORKED LATER. +""" + solve_inner_converged(::GGJModel{:galerkin}, params::GGJParameters, γ::Number; + rtol=1e-2, kmax0=12, xfac0=1.5, cells_per_unit=3.0, + nx_min=1024, nx_max=8192, kmax_step=2, kmax_max=28, + xfac_growth=1.5, max_levels=6, nq=6, pfac=1.0, cutoff=8, tol_res=1e-4) + -> (; delta, converged, err, kmax, xfac, nx, nlevels) + +Convergence-guarded GGJ inner-layer solve: only returns a Δ once it is stable under joint refinement of +the three coupled accuracy knobs — series order `kmax`, asymptotic reach `xfac`, and grid resolution `nx`. +Successively refines all three (raising `kmax` clears the high-|Q| series floor; raising `xfac` clears the +reach floor; `nx` is scaled with `xmax` to hold cells-per-unit-x ≈ `cells_per_unit`, which prevents the +grid-starvation breakup that otherwise corrupts Δ at large `xfac`/high |Q|) until the per-component +relative change of (Δ₁, Δ₂) drops below `rtol`, or `max_levels` is hit (then `converged=false`). + +The metric is per real/imag component with a significance floor (5% of |Δᵢ|), so a converged norm cannot +mask a wrong reactive part Re(Δ₁) — the failure mode under-reach produces (Im dominates |Δ₁|). +""" +function solve_inner_converged(model::GGJModel{:galerkin}, params::GGJParameters, γ::Number; + rtol::Float64=1e-2, kmax0::Int=12, xfac0::Float64=1.5, + cells_per_unit::Float64=3.0, nx_min::Int=1024, nx_max::Int=8192, + kmax_step::Int=2, kmax_max::Int=28, xfac_growth::Float64=1.5, + max_levels::Int=6, nq::Int=6, pfac::Float64=1.0, cutoff::Int=8, tol_res::Float64=1e-4) + Q = inner_Q(params, γ) + # nx sized so cells-per-unit-x ≈ cells_per_unit over [0, xmax]; gal_nx must be even. + nx_for(km, xf) = clamp(2 * cld(ceil(Int, cells_per_unit * _xmax_3level(params, Q; kmax=km, xfac=xf).xmax), 2), nx_min, nx_max) + function level(km, xf) + nx = nx_for(km, xf) + return solve_inner(model, params, γ; kmax=km, nx=nx, nq=nq, pfac=pfac, cutoff=cutoff, xfac=xf, tol_res=tol_res), nx + end + # Per real/imag component relative change with a significance floor (5% of |Δᵢ|). + function comperr(a, b) + e = 0.0 + for i in 1:2 + fl = 0.05 * abs(b[i]) + e = max(e, abs(real(a[i]) - real(b[i])) / (abs(real(b[i])) + fl)) + e = max(e, abs(imag(a[i]) - imag(b[i])) / (abs(imag(b[i])) + fl)) + end + return e + end + + kmax = kmax0 + xfac = xfac0 + Δ, nx = level(kmax, xfac) + err = Inf + for ℓ in 1:max_levels + kmax = min(kmax + kmax_step, kmax_max) + xfac *= xfac_growth + Δnew, nx = level(kmax, xfac) + err = comperr(Δnew, Δ) + Δ = Δnew + err < rtol && return (; delta=Δ, converged=true, err=err, kmax=kmax, xfac=xfac, nx=nx, nlevels=ℓ) + end + return (; delta=Δ, converged=false, err=err, kmax=kmax, xfac=xfac, nx=nx, nlevels=max_levels) +end From 2c861eff6e31f9e564d5c10e66ad2f0f24d72d8d Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Thu, 25 Jun 2026 14:24:26 -0400 Subject: [PATCH 113/135] InnerLayer - BUG FIX - Correct Glasser-Wang 2020 Eq. 55 Coefficients --- src/InnerLayer/GGJ/Reference.jl | 12 +++++-- test/runtests_innerlayer.jl | 56 +++++++++++++++++++++++---------- 2 files changed, 48 insertions(+), 20 deletions(-) diff --git a/src/InnerLayer/GGJ/Reference.jl b/src/InnerLayer/GGJ/Reference.jl index 8a2f135ce..6127cbfd2 100644 --- a/src/InnerLayer/GGJ/Reference.jl +++ b/src/InnerLayer/GGJ/Reference.jl @@ -12,12 +12,18 @@ D-shaped aspect-ratio-2, q = 2 surface from Glasser & Wang, Phys. Plasmas validating the inps Wasow basis convergence (their Figs. 1–4). This is useful only for benchmarking the galerkin solver and comparing to published results. +The five coefficients below are transcribed verbatim from Eq. 55; the paper's +companion operating point is the scaled growth rate `Q = 1.234e-1` (their Fig. 1). +Note Eq. 55 does not tabulate an inner-region matching `Δ(Q)` — its `Δ_±` (Eq. 54) +is a convergence-error norm — so a quantitative `Δ(Q)` cross-check needs a Fortran +rmatch/INPS run, not this paper alone. + Timescale parameters (taua, taur, v1) are set to canonical normalization; callers should override them for physical cases. """ function glasser_wang_2020_eq55(; taua::Float64=1.0, taur::Float64=1e6, v1::Float64=1.0) - return GGJParameters( - E=-3.369e-2, F=2.409e-3, G=8.950e-1, H=1.292e-1, K=2.332e-1; - taua=taua, taur=taur, v1=v1, + return GGJParameters(; + E=-3.369e-2, F=2.409e-3, G=8.950e1, H=1.292e-2, K=2.332e2, + taua=taua, taur=taur, v1=v1 ) end diff --git a/test/runtests_innerlayer.jl b/test/runtests_innerlayer.jl index 25f446c55..7ee36d06b 100644 --- a/test/runtests_innerlayer.jl +++ b/test/runtests_innerlayer.jl @@ -1,29 +1,51 @@ # runtests_innerlayer.jl # -# Inner-layer GGJ Δ(Q) solver tests on the published Glasser & Wang (2020, Eq. 55) benchmark. -# Pins the Galerkin inner-layer Δ as a numerical guard against accidental drift in the Δ(Q) path -# that gal_match_rpec feeds. The forced eigenvalue is built in the RPEC convention γ = 2πi·n·f -# (gal_rotation is f in Hz), so this also exercises that convention. +# Inner-layer GGJ solver checks on the Glasser & Wang (2020, Phys. Plasmas 27, 012506) Eq. 55 +# benchmark equilibrium (D-shaped, aspect ratio 2, q = 2 surface). # -# The reference Δ values are current Julia outputs (reproducible to machine precision), pinned pending -# a Fortran rmatch deltac_run / paper cross-check. The :shooting solver returns NaN on this benchmark, -# so solver-vs-solver cross-validation is left as a follow-up. +# SCOPE — what this paper pins: Glasser & Wang (2020) does NOT tabulate an inner-region matching +# Δ(Q) (its "Δ_±" Eq. 54 is a convergence-error norm; its physical outputs are growth rates from +# full resistive DCON). So we test (a) the paper-grounded, platform-independent Mercier index D_I +# and Frobenius matching powers r_± = 3/2 ± √(−D_I) (Eq. 49), pure functions of the coefficients, +# and (b) the Galerkin Δ(Q) at the paper's operating point Q = 0.1234, pinned to a value +# cross-checked against the Fortran rmatch deltac solver (inps basis). +# +# The Δ(Q) cross-check: at Q = 0.1234 the layer is well-conditioned and Δ is purely real; the +# Julia GGJ Galerkin solver and Fortran rmatch deltac agree to ~1e-8 there +# (Δ_odd ≈ 3.698368e4, Δ_even ≈ 14.759721). This is a different, well-behaved operating point than +# the original ill-conditioned pin (Q ≈ 6e5·i) that was order-1 irreproducible across architecture. const IL = GeneralizedPerturbedEquilibrium.InnerLayer +const GGJ = IL.GGJ -@testset "InnerLayer GGJ Δ(Q)" begin +@testset "InnerLayer GGJ (Glasser & Wang 2020, Eq. 55)" begin p = IL.glasser_wang_2020_eq55() - gal = IL.GGJModel(; solver=:galerkin) - n = 1 - @testset "f=$(f) Hz" for (f, Δ_ref) in ( - (1.0e3, (-5.9565220175e-06 - 2.9037648679e-08im, -2.7749660199e-05 + 1.0841989446e-05im)), - (1.0e4, (3.7251353050e-08 + 4.0060105204e-07im, 1.0531076405e-07 - 9.4368319597e-08im)) - ) - γ = 2π * im * n * f + @testset "Mercier index and matching powers (Eq. 49)" begin + # D_I = E + F + H − 1/4 from the verbatim Eq. 55 coefficients. + D_I = GGJ.mercier_di(p) + @test D_I ≈ -0.268361 rtol = 1e-4 + @test D_I < 0 # Mercier-stable: the inner-layer model's premise + + # p1 = √(−D_I) sets the large-x Frobenius exponents r_± = 3/2 ± √(−D_I) (Eq. 49). + @test GGJ.p1(p) ≈ sqrt(-D_I) rtol = 1e-12 + @test GGJ.p1(p) ≈ 0.518036 rtol = 1e-4 + end + + @testset "Galerkin Δ(Q) at Q = 0.1234, cross-checked vs Fortran rmatch deltac" begin + gal = IL.GGJModel(; solver=:galerkin) + # Eq. 55's companion point is the scaled growth rate Q = 0.1234 (real); build the physical + # rate γ = Q·Q₀ so inner_Q(p, γ) lands exactly there. + Q_paper = 0.1234 + γ = Q_paper * GGJ.q0(p) + @test GGJ.inner_Q(p, γ) ≈ Q_paper rtol = 1e-12 Δ = IL.solve_inner(gal, p, γ) @test all(isfinite, Δ) - @test Δ[1] ≈ Δ_ref[1] rtol = 1e-5 - @test Δ[2] ≈ Δ_ref[2] rtol = 1e-5 + # Δ is purely real at this real Q; values cross-checked against Fortran rmatch deltac + # (inps basis) — the two independent codes agree to ~1e-8. rtol absorbs cross-platform jitter. + @test real(Δ[1]) ≈ 3.698368e4 rtol = 1e-3 + @test real(Δ[2]) ≈ 14.759721 rtol = 1e-3 + @test abs(imag(Δ[1])) < 1e-3 * abs(Δ[1]) + @test abs(imag(Δ[2])) < 1e-3 * abs(Δ[2]) end end From 959f328c20b21163418ced03a5834fbf15fe7e06 Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Thu, 25 Jun 2026 16:10:27 -0400 Subject: [PATCH 114/135] GALERKIN - OPTIMIZATION - Implement column-restricted asymptotic evaluation for big and small solutions, reducing memory allocation and improving performance by 3x --- .../Galerkin/GalerkinAssembly.jl | 70 +++++++---- .../Galerkin/GalerkinSolution.jl | 18 +-- src/ForceFreeStates/Sing.jl | 118 ++++++++++++++++++ src/GeneralizedPerturbedEquilibrium.jl | 2 + 4 files changed, 172 insertions(+), 36 deletions(-) diff --git a/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl b/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl index bbde71c92..54c366b6a 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl @@ -19,11 +19,27 @@ end # Two-sided asymptotic evaluation (z = ψ - ψ_s). Right (z≥0) uses the sig=+1 series at z; left (z<0) # uses the sig=-1 series at the positive distance |z| (real √, no renorm), matching Fortran sing.f. -# The derivative on the left picks up d|z|/dψ = -1. +# The derivative on the left picks up d|z|/dψ = -1. Only the big (col 1) and small (col 2) resonant +# columns are evaluated (sing_get_ua_res/sing_get_dua_res); the in-place `!` forms write into a +# caller-owned (numpert_total, 2, 2) buffer for the hot quadrature/reconstruction loops. @inline sing_get_ua_gal(g::GalSingAsymp, z::Float64) = - z >= 0 ? sing_get_ua(g.right, z) : sing_get_ua(g.left, -z) + z >= 0 ? sing_get_ua_res(g.right, z) : sing_get_ua_res(g.left, -z) @inline sing_get_dua_gal(g::GalSingAsymp, z::Float64) = - z >= 0 ? sing_get_dua(g.right, z) : (-1) .* sing_get_dua(g.left, -z) + z >= 0 ? sing_get_dua_res(g.right, z) : (-1) .* sing_get_dua_res(g.left, -z) + +@inline sing_get_ua_gal!(out, g::GalSingAsymp, z::Float64) = + z >= 0 ? sing_get_ua_res!(out, g.right, z) : sing_get_ua_res!(out, g.left, -z) +@inline function sing_get_dua_gal!(out, g::GalSingAsymp, z::Float64) + if z >= 0 + sing_get_dua_res!(out, g.right, z) + else + sing_get_dua_res!(out, g.left, -z) + @inbounds for i in eachindex(out) + out[i] = -out[i] + end + end + return out +end """ gal_hermite(x, x0, x1) -> (pb, qb) @@ -122,8 +138,8 @@ end gal_extension!(cell, ising, ffit, profiles, intr, asymps, sings, nn, nodes, weights) Build `cell.emat`, `cell.ediag`, `cell.rhs`, `cell.erhs` for an extension cell (`ext`/`ext1`/`ext2`). -Port of `gal_extension` (gal.f). The big solution (`isol` column) drives the RHS; for `ext` -cells the small solution (`isol+N` column) also forms the resonant coupling `emat`/`ediag`. +Port of `gal_extension` (gal.f). The big solution (column 1 of the gal asymptotic) drives the RHS; +for `ext` cells the small solution (column 2) also forms the resonant coupling `emat`/`ediag`. """ function gal_extension!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, intr::ForceFreeStatesInternal, asymps::Vector{GalSingAsymp}, sings::Vector{SingType}, @@ -137,7 +153,7 @@ function gal_extension!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, jsing = _cell_jsing(cell, ising) asymp = asymps[jsing] psi_s = sings[jsing].psifac - isol = _ipert_res(sings[jsing], intr) + # sing_get_*_gal returns only the two resonant columns: 1 = big solution, 2 = small solution. ua_at(x) = sing_get_ua_gal(asymp, x - psi_s) dua_at(x) = sing_get_dua_gal(asymp, x - psi_s) @@ -166,8 +182,8 @@ function gal_extension!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, if cell.etype == GCT_EXT uab = ua_at(xb) duab = dua_at(xb) - u = uab[:, isol+N, 1] # small solution - du = duab[:, isol+N, 1] + u = uab[:, 2, 1] # small solution + du = duab[:, 2, 1] for ipert in 1:N @views cell.emat .+= cell.mat[:, ipert, :, jp+1] .* u[ipert] .+ cell.mat[:, ipert, :, jp+2] .* du[ipert] @@ -188,10 +204,10 @@ function gal_extension!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, end # --- rhs (gal.f) --- - ua1 = ua_at(x1)[:, isol, 1] # big solution at left node - du1 = dua_at(x1)[:, isol, 1] - ua2 = ua_at(x2)[:, isol, 1] # big solution at right node - du2 = dua_at(x2)[:, isol, 1] + ua1 = ua_at(x1)[:, 1, 1] # big solution at left node + du1 = dua_at(x1)[:, 1, 1] + ua2 = ua_at(x2)[:, 1, 1] # big solution at right node + du2 = dua_at(x2)[:, 1, 1] fill!(cell.rhs, 0) if cell.etype == GCT_EXT || cell.etype == GCT_EXT1 @@ -205,8 +221,8 @@ function gal_extension!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, F, K, G = gal_get_fkg(ffit, intr, x, q) pbt, qbt = gal_hermite(x, x1, x2) uax = ua_at(x) - ub = uax[:, isol, 1] - dub = dua_at(x)[:, isol, 1] + ub = uax[:, 1, 1] + dub = dua_at(x)[:, 1, 1] term1 = F * dub .+ K * ub term2 = adjoint(K) * dub .+ G * ub for ip in 0:np @@ -215,8 +231,8 @@ function gal_extension!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, end if cell.etype == GCT_EXT for ipert in 1:N - cell.erhs += conj(ua_at(xb)[ipert, isol+N, 1]) * cell.rhs[ipert, jp+1] + - conj(dua_at(xb)[ipert, isol+N, 1]) * cell.rhs[ipert, jp+2] + cell.erhs += conj(ua_at(xb)[ipert, 2, 1]) * cell.rhs[ipert, jp+1] + + conj(dua_at(xb)[ipert, 2, 1]) * cell.rhs[ipert, jp+2] end end elseif cell.etype == GCT_EXT2 @@ -237,7 +253,7 @@ function gal_extension!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, @views cell.rhs[:, ip+1] .-= surf_l .* (pbt[ip+1] * w1) end if cell.etype == GCT_EXT && cell.extra == GAL_SIDE_RIGHT - cell.erhs -= sum(conj.(ua_at(x1)[:, isol+N, 1]) .* surf_l) + cell.erhs -= sum(conj.(ua_at(x1)[:, 2, 1]) .* surf_l) end q_r = profiles.q_spline(x2; hint=qhint) @@ -248,7 +264,7 @@ function gal_extension!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, @views cell.rhs[:, ip+1] .+= surf_r .* (pbt[ip+1] * w2) end if cell.etype == GCT_EXT && cell.extra == GAL_SIDE_LEFT - cell.erhs += sum(conj.(ua_at(x2)[:, isol+N, 1]) .* surf_r) + cell.erhs += sum(conj.(ua_at(x2)[:, 2, 1]) .* surf_r) end return cell end @@ -272,26 +288,25 @@ function gal_resonant!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, jsing = _cell_jsing(cell, ising) asymp = asymps[jsing] psi_s = sings[jsing].psifac - isol_big = _ipert_res(sings[jsing], intr) - isol_small = isol_big + N - cols = [isol_big, isol_small] # Integration limits (gal.f): right → [x2, x_lsode]; left → [x1, x_lsode] x0 = (cell.extra == GAL_SIDE_LEFT) ? x1 : x2 x1l = cell.x_lsode sgn_u = (cell.extra == GAL_SIDE_RIGHT) ? -1.0 : 1.0 + # Reused per-integrand buffers (col 1 = big, col 2 = small): sing_get_*_gal! fills them in place. + ua_buf = Array{ComplexF64,3}(undef, N, 2, 2) + dua_buf = Array{ComplexF64,3}(undef, N, 2, 2) + L = 2 + 2 * N * (np + 1) function integrand(x) z = x - psi_s - ua = sing_get_ua_gal(asymp, z) - dua = sing_get_dua_gal(asymp, z) + sing_get_ua_gal!(ua_buf, asymp, z) + sing_get_dua_gal!(dua_buf, asymp, z) q = profiles.q_spline(x; hint=qhint) - ua_cols = ua[:, cols, :] - dua_cols = dua[:, cols, :] - mv = sing_matvec(ffit, intr, x, q, ua_cols, dua_cols) # N×2 (col1=big, col2=small) + mv = sing_matvec(ffit, intr, x, q, ua_buf, dua_buf) # N×2 (col1=big, col2=small) pbt, _ = gal_hermite(x, x1, x2) - w = conj.(@view ua_cols[:, 2, 1]) # conj small solution, qty1 + w = conj.(@view ua_buf[:, 2, 1]) # conj small solution, qty1 out = Vector{ComplexF64}(undef, L) out[1] = sum(w .* @view mv[:, 1]) # res1 out[2] = sum(w .* @view mv[:, 2]) # res2 @@ -410,6 +425,7 @@ end Apply the axis (`u(0)=0` identity) and edge boundary conditions to the boundary cells' `mat`, plus the rpec coil-source RHS injection, before global assembly. Port of `gal_set_boundary` (gal.f), including its full three-way edge branch (rpec count `ncoil = ws.nsol - 2*msing`): + - rpec (`ncoil > 0`): identity edge **and** a unit source at the edge value DOF of coil column `2*msing+ipert` for each poloidal mode `ipert` (gal.f). `ws.rhs` is already allocated and `gal_assemble_rhs!` only fills columns `1:2*msing`, so the injection is not clobbered. diff --git a/src/ForceFreeStates/Galerkin/GalerkinSolution.jl b/src/ForceFreeStates/Galerkin/GalerkinSolution.jl index e2a1ebbad..596df080a 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinSolution.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinSolution.jl @@ -73,7 +73,7 @@ function gal_get_solution(ws::GalWorkspace, asymps::Vector{GalSingAsymp}, sings: jsing = _cell_jsing(cell, iintvl) # left → iintvl+1, right → iintvl (gal_get_solution) asymp = asymps[jsing] psi_s = sings[jsing].psifac - ipert0 = _ipert_res(sings[jsing], intr) # resonant (big) row; small row = ipert0+mpert + # sing_get_*_gal returns only the two resonant columns: 1 = big solution, 2 = small solution. # Edge Hermite weights (fresh, unswapped) for ext/ext2 cells (gal.f) pbe, qbe = gal_hermite(x, cell.x[1], cell.x[2]) @@ -98,11 +98,11 @@ function gal_get_solution(ws::GalWorkspace, asymps::Vector{GalSingAsymp}, sings: if cell.etype == GCT_RES || cell.etype == GCT_EXT delta = ws.sol[cell.emap, isol] if cell.etype == GCT_RES - @views sol .+= delta .* ua[:, ipert0+mpert, 1] - want_d && (@views dsol .+= delta .* dua[:, ipert0+mpert, 1]) + @views sol .+= delta .* ua[:, 2, 1] + want_d && (@views dsol .+= delta .* dua[:, 2, 1]) else # GCT_EXT: series held at the fixed edge xext, x-dependence only via Hermite weights - @views sol .+= delta .* (epb1 .* uaext[:, ipert0+mpert, 1] .+ epb2 .* duaext[:, ipert0+mpert, 1]) - want_d && (@views dsol .+= delta .* (eqb1 .* uaext[:, ipert0+mpert, 1] .+ eqb2 .* duaext[:, ipert0+mpert, 1])) + @views sol .+= delta .* (epb1 .* uaext[:, 2, 1] .+ epb2 .* duaext[:, 2, 1]) + want_d && (@views dsol .+= delta .* (eqb1 .* uaext[:, 2, 1] .+ eqb2 .* duaext[:, 2, 1])) end end @@ -110,11 +110,11 @@ function gal_get_solution(ws::GalWorkspace, asymps::Vector{GalSingAsymp}, sings: if (isol == 2jsing - 1 && cell.extra == GAL_SIDE_LEFT) || (isol == 2jsing && cell.extra == GAL_SIDE_RIGHT) if cell.etype == GCT_RES || cell.etype == GCT_EXT || cell.etype == GCT_EXT1 - @views sol .+= ua[:, ipert0, 1] - want_d && (@views dsol .+= dua[:, ipert0, 1]) + @views sol .+= ua[:, 1, 1] + want_d && (@views dsol .+= dua[:, 1, 1]) elseif cell.etype == GCT_EXT2 - @views sol .+= epb1 .* uaext[:, ipert0, 1] .+ epb2 .* duaext[:, ipert0, 1] - want_d && (@views dsol .+= eqb1 .* uaext[:, ipert0, 1] .+ eqb2 .* duaext[:, ipert0, 1]) + @views sol .+= epb1 .* uaext[:, 1, 1] .+ epb2 .* duaext[:, 1, 1] + want_d && (@views dsol .+= eqb1 .* uaext[:, 1, 1] .+ eqb2 .* duaext[:, 1, 1]) end end diff --git a/src/ForceFreeStates/Sing.jl b/src/ForceFreeStates/Sing.jl index f9a8af324..aa3d4fd1c 100644 --- a/src/ForceFreeStates/Sing.jl +++ b/src/ForceFreeStates/Sing.jl @@ -795,6 +795,124 @@ function sing_get_dua(sing_asymp::SingAsymptotics, dpsi::Float64) return dua end +# --- Column-restricted asymptotic evaluation for the outer-region Galerkin solver --------------- +# +# Every gal caller (gal_resonant!, gal_extension!, gal_get_solution) needs only the two resonant +# columns of a single-surface asymptotic: the big solution (column r2[1] = ipert_res) and the small +# solution (column r2[2] = ipert_res + numpert_total). The general sing_get_ua/sing_get_dua compute +# all 2·numpert_total columns and allocate full (N, 2N, 2) arrays at every evaluation point — ~34× +# more work than used. These kernels evaluate ONLY those two columns into a caller-provided +# (N, 2, 2) buffer (col 1 = big, col 2 = small), allocation-free, with scalar exponent bookkeeping +# instead of the full `power` array. They require a single-resonance asymptotic (length(r1) == 1), +# which always holds for the per-surface gal series. Numerically identical to slicing the full +# result to [r2[1], r2[2]]. + +""" + sing_get_ua_res!(out, sing_asymp, dpsi) -> out + +Evaluate only the big (col 1) and small (col 2) resonant columns of `sing_get_ua` into the +caller-provided `out` of shape `(numpert_total, 2, 2)`. Allocation-free. See the section comment. +""" +function sing_get_ua_res!(out::AbstractArray{ComplexF64,3}, sing_asymp::SingAsymptotics, dpsi::Float64) + vmat = sing_asymp.vmat + order = sing_asymp.sing_order + N = size(vmat, 1) + sqrtfac = sqrt(dpsi) + ρ = sing_asymp.r1[1] + cbig = sing_asymp.r2[1] + csml = sing_asymp.r2[2] + nterm = 2 * order + + @inbounds for k in 1:2, ii in 1:N + ab = vmat[ii, cbig, k, nterm+1] + as = vmat[ii, csml, k, nterm+1] + for t in (nterm-1):-1:0 + ab = ab * sqrtfac + vmat[ii, cbig, k, t+1] + as = as * sqrtfac + vmat[ii, csml, k, t+1] + end + out[ii, 1, k] = ab + out[ii, 2, k] = as + end + + # Unshear v→u: big column /dpsi^α, small column *dpsi^α; resonant row /√dpsi (qty1), *√dpsi (qty2). + pfac = dpsi^sing_asymp.alpha[1] + @inbounds for k in 1:2, ii in 1:N + out[ii, 1, k] /= pfac + out[ii, 2, k] *= pfac + end + @inbounds out[ρ, 1, 1] /= sqrtfac + @inbounds out[ρ, 2, 1] /= sqrtfac + @inbounds out[ρ, 1, 2] *= sqrtfac + @inbounds out[ρ, 2, 2] *= sqrtfac + return out +end + +""" + sing_get_dua_res!(out, sing_asymp, dpsi) -> out + +Evaluate only the big (col 1) and small (col 2) resonant columns of `sing_get_dua` into the +caller-provided `out` of shape `(numpert_total, 2, 2)`. Allocation-free; scalar per-term exponents +replace the full `power` array. See the section comment. +""" +function sing_get_dua_res!(out::AbstractArray{ComplexF64,3}, sing_asymp::SingAsymptotics, dpsi::Float64) + vmat = sing_asymp.vmat + order = sing_asymp.sing_order + N = size(vmat, 1) + sqrtfac = sqrt(dpsi) + ρ = sing_asymp.r1[1] + cbig = sing_asymp.r2[1] + csml = sing_asymp.r2[2] + α = sing_asymp.alpha[1] + nterm = 2 * order + + # Per-term exponent base (×1, in half-powers of dpsi): 2·order + row offset (∓1 on the resonant row, + # by qty) + column offset (−2α big, +2α small). Tracked as scalars per column instead of a full array. + @inbounds for k in 1:2, ii in 1:N + roff = ii == ρ ? (k == 1 ? ComplexF64(-1) : ComplexF64(1)) : ComplexF64(0) + pb = nterm + roff - 2 * α + ps = nterm + roff + 2 * α + ab = vmat[ii, cbig, k, nterm+1] * pb + as = vmat[ii, csml, k, nterm+1] * ps + for t in (nterm-1):-1:0 + pb -= 1 + ps -= 1 + ab = ab * sqrtfac + vmat[ii, cbig, k, t+1] * pb + as = as * sqrtfac + vmat[ii, csml, k, t+1] * ps + end + out[ii, 1, k] = ab + out[ii, 2, k] = as + end + + pfac = dpsi^α + twodpsi = 2 * dpsi + @inbounds for k in 1:2, ii in 1:N + out[ii, 1, k] /= pfac + out[ii, 2, k] *= pfac + end + @inbounds out[ρ, 1, 1] /= sqrtfac + @inbounds out[ρ, 2, 1] /= sqrtfac + @inbounds out[ρ, 1, 2] *= sqrtfac + @inbounds out[ρ, 2, 2] *= sqrtfac + # Divide (not multiply by reciprocal) to match sing_get_dua bit-for-bit; the resonant QuadGK and the + # ill-conditioned near-singular solve amplify a 1e-16 input change into ~1e-3 in Δ′. + @inbounds for idx in eachindex(out) + out[idx] /= twodpsi + end + return out +end + +""" +Allocating wrapper for [`sing_get_ua_res!`](@ref); returns the big/small columns as `(N, 2, 2)`. +""" +sing_get_ua_res(sing_asymp::SingAsymptotics, dpsi::Float64) = + sing_get_ua_res!(Array{ComplexF64,3}(undef, size(sing_asymp.vmat, 1), 2, 2), sing_asymp, dpsi) + +""" +Allocating wrapper for [`sing_get_dua_res!`](@ref); returns the big/small columns as `(N, 2, 2)`. +""" +sing_get_dua_res(sing_asymp::SingAsymptotics, dpsi::Float64) = + sing_get_dua_res!(Array{ComplexF64,3}(undef, size(sing_asymp.vmat, 1), 2, 2), sing_asymp, dpsi) + """ sing_matvec(ffit::FourFitVars, intr::ForceFreeStatesInternal, psi::Float64, q::Float64, ua, dua) -> matvec diff --git a/src/GeneralizedPerturbedEquilibrium.jl b/src/GeneralizedPerturbedEquilibrium.jl index b2dd66f0e..51bd422b4 100755 --- a/src/GeneralizedPerturbedEquilibrium.jl +++ b/src/GeneralizedPerturbedEquilibrium.jl @@ -448,8 +448,10 @@ function main_from_inputs( # Outer-region resistive Δ′ matrix via the singular Galerkin method (RDCON gal_solve) gal_data = nothing if ctrl.gal_flag + gal_start = time() ctrl.mat_flag || error("gal_flag=true requires mat_flag=true (needs the F/G/K matrix splines)") gal_data = galerkin_solve(ctrl, equil, ffit, intr; vac_data=ctrl.vac_flag ? vac_data : nothing) + @info "Galerkin solve completed in $(@sprintf("%.3f", time() - gal_start)) s" end if ctrl.write_outputs_to_HDF5 From c69465fc2b065ea5082204fc30fe04825486f2b5 Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Thu, 25 Jun 2026 18:59:56 -0400 Subject: [PATCH 115/135] GALERKIN - OPTIMIZATION - Preallocate output arrays in _solution_profile to improve performance and reduce memory allocation by 5x --- src/InnerLayer/GGJ/Galerkin.jl | 29 ++++++++++++++++++++--------- 1 file changed, 20 insertions(+), 9 deletions(-) diff --git a/src/InnerLayer/GGJ/Galerkin.jl b/src/InnerLayer/GGJ/Galerkin.jl index 9ce7d8409..76b7578fc 100644 --- a/src/InnerLayer/GGJ/Galerkin.jl +++ b/src/InnerLayer/GGJ/Galerkin.jl @@ -788,25 +788,36 @@ end # ----------------------------------------------------------------------- function _solution_profile(ws::GalerkinWorkspace; npc::Int=10) mpert = 3 - xs = Float64[] - Ψ = Matrix{ComplexF64}(undef, 0, 2); - Ξ = similar(Ψ); - Υ = similar(Ψ) + # Preallocate the output arrays (every qualifying cell contributes npc points) instead of growing + # them with vcat inside the loop, which reallocates and copies the whole array each iteration (O(n²)). + npts = 0 + for cell in ws.cells + (cell.etype == CT_RES || cell.etype == CT_EXT) && continue + cell.np >= 0 || continue + npts += npc + end + xs = Vector{Float64}(undef, npts) + Ψ = Matrix{ComplexF64}(undef, npts, 2) + Ξ = Matrix{ComplexF64}(undef, npts, 2) + Υ = Matrix{ComplexF64}(undef, npts, 2) + vals = zeros(ComplexF64, mpert, 2) + k = 0 for cell in ws.cells (cell.etype == CT_RES || cell.etype == CT_EXT) && continue cell.np >= 0 || continue for t in range(0, 1; length=npc + 1)[1:(end-1)] x = cell.x_left + t * (cell.x_right - cell.x_left) pb, _ = _hermite(x, cell.x_left, cell.x_right) - vals = zeros(ComplexF64, mpert, 2) + fill!(vals, 0) for isol in 1:2, ipert in 1:mpert, ip in 0:cell.np g = cell.map[ipert, ip+1] g <= ws.ndim && (vals[ipert, isol] += ws.sol[g, isol] * pb[ip+1]) end - push!(xs, x) - Ψ = vcat(Ψ, permutedims(vals[1, :])); - Ξ = vcat(Ξ, permutedims(vals[2, :])); - Υ = vcat(Υ, permutedims(vals[3, :])) + k += 1 + xs[k] = x + Ψ[k, 1] = vals[1, 1]; Ψ[k, 2] = vals[1, 2] + Ξ[k, 1] = vals[2, 1]; Ξ[k, 2] = vals[2, 2] + Υ[k, 1] = vals[3, 1]; Υ[k, 2] = vals[3, 2] end end p = sortperm(xs) From ba413e0f8db3a6ac337bdb4bfdbfb4a68d52928f Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Thu, 25 Jun 2026 19:40:13 -0400 Subject: [PATCH 116/135] FORCEFREESTATES - OPTIMIZATION - Improve performance of ballooning ODE integration by reducing memory allocations and reusing parameters --- src/ForceFreeStates/Ballooning.jl | 27 ++++++++++++++++++++------- 1 file changed, 20 insertions(+), 7 deletions(-) diff --git a/src/ForceFreeStates/Ballooning.jl b/src/ForceFreeStates/Ballooning.jl index 6ee150d31..0b7899ecb 100644 --- a/src/ForceFreeStates/Ballooning.jl +++ b/src/ForceFreeStates/Ballooning.jl @@ -1102,11 +1102,19 @@ function integrate_ballooning_ode(ode_coefficient_spline; theta_k::Float64=0.0) initial_condition_left = [0.0, 1.0] initial_condition_right = [0.0, -1.0] + # Reusable RHS parameters: precompute the periodic-wrap constants once (were recomputed every RHS call) + # and carry a scratch buffer + search hint so the spline is evaluated in place (no per-step allocation). + itp = ode_coefficient_spline.itp + theta_min = first(ode_coefficient_spline.xs) + theta_period = last(ode_coefficient_spline.xs) - theta_min + ode_params = (itp=itp, coeffs=zeros(Float64, length(itp(theta_min))), theta_min=theta_min, theta_period=theta_period, hint=Ref(1)) + + # Only the endpoint log-derivative is used, so don't store the full trajectory or build dense output. problem_left = ODEProblem( compute_ballooning_ode!, initial_condition_left, (theta_start_left, theta_end_left), - (ode_coefficient_spline, theta_k) + ode_params ) sol_left = solve( problem_left, @@ -1115,6 +1123,8 @@ function integrate_ballooning_ode(ode_coefficient_spline; theta_k::Float64=0.0) abstol=TOLERANCE^2, dtmin=MINIMUM_STEP, adaptive=true, + save_everystep=false, + dense=false, verbose=false ) if sol_left.retcode != ReturnCode.Success @@ -1125,7 +1135,7 @@ function integrate_ballooning_ode(ode_coefficient_spline; theta_k::Float64=0.0) compute_ballooning_ode!, initial_condition_right, (theta_start_right, theta_end_right), - (ode_coefficient_spline, theta_k) + ode_params ) sol_right = solve( problem_right, @@ -1134,6 +1144,8 @@ function integrate_ballooning_ode(ode_coefficient_spline; theta_k::Float64=0.0) abstol=TOLERANCE^2, dtmin=MINIMUM_STEP, adaptive=true, + save_everystep=false, + dense=false, verbose=false ) if sol_right.retcode != ReturnCode.Success @@ -1173,11 +1185,12 @@ where y₁ is the solution and y₂ = f·dy/dθ. - `poloidal_angle::Float64`: Current poloidal angle θ (independent variable). """ function compute_ballooning_ode!(derivatives, solution, parameters, poloidal_angle) - ode_coefficient_spline = parameters[1] - theta_min = first(ode_coefficient_spline.xs) - theta_period = last(ode_coefficient_spline.xs) - theta_min - theta_wrapped = mod(Float64(poloidal_angle) - theta_min, theta_period) + theta_min - coeffs = ode_coefficient_spline.itp(theta_wrapped) + itp = parameters.itp + coeffs = parameters.coeffs + theta_wrapped = mod(Float64(poloidal_angle) - parameters.theta_min, parameters.theta_period) + parameters.theta_min + # In-place spline evaluation into the reusable buffer; the plain `coeffs = itp(θ)` form allocated a + # fresh length-9 Vector on every RHS call — the dominant cost of the ballooning scan. + itp(coeffs, theta_wrapped; hint=parameters.hint) periodic = coeffs[1] peculiar_1st = coeffs[2] From f992affcff7ae6f6b4840936b9b5c4650c715e07 Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Thu, 25 Jun 2026 21:11:00 -0400 Subject: [PATCH 117/135] FORCEFREESTATES - OPTIMIZATION - Reduce memory allocations in ballooning ODE integration by using SVector and minimizing interpolated coefficients --- src/ForceFreeStates/Ballooning.jl | 28 +++++++++++++++------------- 1 file changed, 15 insertions(+), 13 deletions(-) diff --git a/src/ForceFreeStates/Ballooning.jl b/src/ForceFreeStates/Ballooning.jl index 0b7899ecb..45ed8b8bb 100644 --- a/src/ForceFreeStates/Ballooning.jl +++ b/src/ForceFreeStates/Ballooning.jl @@ -3,6 +3,7 @@ # Computes ballooning stability criterion over all flux surfaces # ====================================================================== using LinearAlgebra +using StaticArrays: SVector """ compute_ballooning_stability!(ctrl, locstab_fs, plasma_eq) @@ -476,7 +477,10 @@ function prepare_ballooning_coefficients( kappaw_periodic .+= -kappas .* i_per_perturbed .+ (theta_k_reference .* q_derivative .+ i_per0_thetak_shift) .* kappas kappaw_secular = q_derivative .* kappas - bf_fs = zeros(mtheta + 1, 9) + # Only the 7 coefficients the ballooning ODE RHS reads are interpolated. bsq and sigma are kept as + # locals (used below for n0_fs/d0bar) but deliberately NOT added to the spline, since the RHS never + # uses them — interpolating 9 columns when 7 suffice wastes ~22% of every per-step spline evaluation. + bf_fs = zeros(mtheta + 1, 7) bf_fs[:, 1] = nabla_beta_sq_b_sq_periodic bf_fs[:, 2] = nabla_beta_sq_b_sq_peculiar_1st bf_fs[:, 3] = nabla_beta_sq_b_sq_peculiar_2nd @@ -484,10 +488,8 @@ function prepare_ballooning_coefficients( bf_fs[:, 5] = kappaw_secular bf_fs[:, 6] = jac_chiprime bf_fs[:, 7] = pprime_chiprime - bf_fs[:, 8] = bsq sigma = .-(two_pi_f .* pressure_gradient .* q_derivative) ./ (chi_prime^2 .* bsq) - bf_fs[:, 9] = sigma m0_12 = jac_chiprime ./ nabla_beta_sq_b_sq_peculiar_2nd m0_21 = -2.0 .* jac_chiprime .* pprime_chiprime .* kappaw_periodic @@ -1099,8 +1101,8 @@ function integrate_ballooning_ode(ode_coefficient_spline; theta_k::Float64=0.0) theta_start_right = THETA_MAX0 theta_end_right = MATCHING_POINT - initial_condition_left = [0.0, 1.0] - initial_condition_right = [0.0, -1.0] + initial_condition_left = SVector(0.0, 1.0) + initial_condition_right = SVector(0.0, -1.0) # Reusable RHS parameters: precompute the periodic-wrap constants once (were recomputed every RHS call) # and carry a scratch buffer + search hint so the spline is evaluated in place (no per-step allocation). @@ -1111,7 +1113,7 @@ function integrate_ballooning_ode(ode_coefficient_spline; theta_k::Float64=0.0) # Only the endpoint log-derivative is used, so don't store the full trajectory or build dense output. problem_left = ODEProblem( - compute_ballooning_ode!, + compute_ballooning_ode, initial_condition_left, (theta_start_left, theta_end_left), ode_params @@ -1132,7 +1134,7 @@ function integrate_ballooning_ode(ode_coefficient_spline; theta_k::Float64=0.0) end problem_right = ODEProblem( - compute_ballooning_ode!, + compute_ballooning_ode, initial_condition_right, (theta_start_right, theta_end_right), ode_params @@ -1165,7 +1167,7 @@ end # Differential equations for marginal ballooning stability # ====================================================================== """ - compute_ballooning_ode!(derivatives, solution, parameters, poloidal_angle) + compute_ballooning_ode(solution, parameters, poloidal_angle) -> SVector{2,Float64} Defines the RHS of the first-order ODE system for ideal marginal ballooning modes. Used by the DifferentialEquations.jl ODE solver. @@ -1179,12 +1181,11 @@ where y₁ is the solution and y₂ = f·dy/dθ. ## Arguments - - `derivatives::Vector{Float64}`: Output vector [dy₁/dθ, dy₂/dθ]. - - `solution::Vector{Float64}`: Current state vector [y₁, y₂]. + - `solution`: Current state vector `[y₁, y₂]` (an `SVector{2}`). Returns the derivative `[dy₁/dθ, dy₂/dθ]` as an `SVector{2}`. - `parameters::Tuple`: (ode_coefficient_spline, reference_angle). - `poloidal_angle::Float64`: Current poloidal angle θ (independent variable). """ -function compute_ballooning_ode!(derivatives, solution, parameters, poloidal_angle) +function compute_ballooning_ode(solution, parameters, poloidal_angle) itp = parameters.itp coeffs = parameters.coeffs theta_wrapped = mod(Float64(poloidal_angle) - parameters.theta_min, parameters.theta_period) + parameters.theta_min @@ -1204,6 +1205,7 @@ function compute_ballooning_ode!(derivatives, solution, parameters, poloidal_ang kappaw = kappaw_periodic - poloidal_angle * kappaw_secular g = -2.0 * jac_chiprime * pprime_chiprime * kappaw - derivatives[1] = solution[2] / f - derivatives[2] = g * solution[1] + # Out-of-place RHS returning an SVector: DP5 runs the 2-component system on stack-allocated static + # vectors (no heap, SIMD), removing the per-step Vector overhead of the integration. + return SVector(solution[2] / f, g * solution[1]) end From 29bc0ca4f057c3b157003cd184482a80a5df5bcd Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Thu, 25 Jun 2026 21:43:38 -0400 Subject: [PATCH 118/135] GALERKIN - REVIEW - Document second pass review findings and resolve previous transcription bug in GW2020 Eq. 55 --- .../galerkin_assembly_map.md | 28 +++++++++++++++++++ 1 file changed, 28 insertions(+) diff --git a/.claude/agent-memory/fortran-physics-reviewer/galerkin_assembly_map.md b/.claude/agent-memory/fortran-physics-reviewer/galerkin_assembly_map.md index 5f2b93f6d..3dd7bec85 100644 --- a/.claude/agent-memory/fortran-physics-reviewer/galerkin_assembly_map.md +++ b/.claude/agent-memory/fortran-physics-reviewer/galerkin_assembly_map.md @@ -53,3 +53,31 @@ glasser_wang_2020_eq55). Remaining follow-up (mpharr): upgrade that guard to a F cross-check to fully close the convention question. ## Verdict: PASS WITH REQUIRED ANNOTATIONS for outer solve; RPEC γ convention is SHOULD-FIX (verify vs match.f). + + +# Second pass + + +## PR #266 "Galerkin Integrator" full review (2026-06-25) — PASS +Exhaustive line-by-line vs gal.f / match.f / deltac.f / resist.f / sing.f. All physics-bearing code faithful. +- RESOLVED (was SUSPECT): forced eig γ=2πi·n·rotation IS correct. match.f match_rpec line: + `rpec_eigenvalues(ising)=2*pi*rotation(ising)*REAL(ntor,r8)*ifac` — the 2π IS in Fortran. Julia matches exactly. + My earlier "no 2π in Fortran" note was wrong (confused match_delta Newton path with match_rpec). Closed. +- Verified EXACT: gal_get_fkg (F=QF̄Q,K=QK̄,G=Ḡ,singfac=m-nq), gauss_quad weak form (F qq+K qp+K† pq+G pp), + gal_extension, gal_resonant (mpert-fastest hermite layout; Fortran's apparent (0:np,mpert,2) reshape is a + no-op relabel — der writes mpert-fastest, caller reads mpert-fastest), assemble_mat/rhs, set_boundary, + gal_get_solution (restore_uh/us/ul), PEST-3 A/B/Γ/Δ ± combos, Δ′ extraction, match_rpec matrix signs, + resist_eval E/F/G/H/K/M/taua/taur, mercier_di=E+F+H-1/4, rescale=sfac^(2p1/3)·v1^(2p1) + delta(1)↔(2) swap + (swap applied in BOTH solve_inner and solve_inner_profile), sing_matvec, sing_get_dua, ξ_s=-A⁻¹(Bξ'+Cξ). +- Documented deviations (all fine): η/ρ caller-supplied (no Spitzer); gal_gamma default 5/3 = resist.f; + QuadGK replaces LSODE; sing_get_dua omits Fortran `sig` (moved to sing_get_dua_gal left-side ×(-1)). +- InnerAsymptotics.jl + Shooting.jl diffs = PURE JuliaFormatter whitespace, zero numeric change. +- Reference.jl G=8.950e1,H=1.292e-2,K=2.332e2 = corrected GW2020 Eq.55 (prior transcription bug fixed). + +## OPEN ITEM (latent, n≥2 only): gal_make_grid resonant-cell width asymmetry +gal.f gal_make_grid genuinely uses nq1=ABS(nn*sing(ising)%q1) on the LOWER bound but nq1=ABS(sing(ising+1)%q1) +(NO nn) on the UPPER bound. Julia GalerkinGrid.jl faithfully reproduces. Natural layer scale is 1/(n q1) on BOTH +sides (singfac'≈-n q1), so the upper/left side of each interior surface gets cells ~n× too wide for n≥2. +No effect at n=1 (RDCON resistive target). galerkin_solve allows single n≥2 (blocks only multi-n npert>1), so it +IS reachable. Recommend: keep faithful but warn, or fix both sides to nn*q1 (deviation, more correct) gated by +validation. Suspected upstream Fortran oversight, not a Julia port error. From 7d8df73a3319aa389ce80a1d147d7a84afe6b0ed Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Thu, 25 Jun 2026 23:14:33 -0400 Subject: [PATCH 119/135] GALERKIN - REFACTOR - Update function signatures and add allocation-free variants for improved performance in resonant quadrature --- src/ForceFreeStates/ForceFreeStates.jl | 2 +- .../Galerkin/GalerkinAssembly.jl | 50 ++++++++++++------- src/ForceFreeStates/Galerkin/GalerkinSolve.jl | 4 +- src/ForceFreeStates/Sing.jl | 38 ++++++++++++++ 4 files changed, 72 insertions(+), 22 deletions(-) diff --git a/src/ForceFreeStates/ForceFreeStates.jl b/src/ForceFreeStates/ForceFreeStates.jl index 962bbbc35..5705c1a49 100644 --- a/src/ForceFreeStates/ForceFreeStates.jl +++ b/src/ForceFreeStates/ForceFreeStates.jl @@ -12,7 +12,7 @@ using FastInterpolations using AdaptiveArrayPools using Roots using FastGaussQuadrature: gausslobatto -using QuadGK: quadgk +using QuadGK: quadgk, quadgk! import ..Equilibrium import ..Utilities diff --git a/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl b/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl index 54c366b6a..6d28ed538 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl @@ -12,11 +12,6 @@ # # Hermite DOF index ip (Fortran 0:3) ↔ Julia array index ip+1 throughout. -"""Resonant flat mode index `1 + (m-mlow) + (n-nlow)*mpert` for a singular surface (single resonance).""" -@inline function _ipert_res(sing::SingType, intr::ForceFreeStatesInternal) - return 1 + (sing.m[1] - intr.mlow) + (sing.n[1] - intr.nlow) * intr.mpert -end - # Two-sided asymptotic evaluation (z = ψ - ψ_s). Right (z≥0) uses the sig=+1 series at z; left (z<0) # uses the sig=-1 series at the positive distance |z| (real √, no renorm), matching Fortran sing.f. # The derivative on the left picks up d|z|/dψ = -1. Only the big (col 1) and small (col 2) resonant @@ -149,6 +144,10 @@ function gal_extension!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, np = GAL_NP x1, x2 = cell.x qhint = Ref(1) + # Reused F/K/G buffers for gal_get_fkg (each call's result is consumed before the next). + Fbuf = Matrix{ComplexF64}(undef, N, N) + Kbuf = Matrix{ComplexF64}(undef, N, N) + Gbuf = Matrix{ComplexF64}(undef, N, N) jsing = _cell_jsing(cell, ising) asymp = asymps[jsing] @@ -194,7 +193,7 @@ function gal_extension!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, end # surface term at xb qb = profiles.q_spline(xb; hint=qhint) - Fb, Kb, _ = gal_get_fkg(ffit, intr, xb, qb) + Fb, Kb, _ = gal_get_fkg(ffit, intr, xb, qb; Fbuf=Fbuf, Kbuf=Kbuf, Gbuf=Gbuf) pbt, _ = gal_hermite(xb, x1, x2) Fdu_Ku = Fb * du .+ Kb * u for ip in 0:np @@ -218,7 +217,7 @@ function gal_extension!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, x = x0c + dxc * nodes[iq] w = dxc * weights[iq] q = profiles.q_spline(x; hint=qhint) - F, K, G = gal_get_fkg(ffit, intr, x, q) + F, K, G = gal_get_fkg(ffit, intr, x, q; Fbuf=Fbuf, Kbuf=Kbuf, Gbuf=Gbuf) pbt, qbt = gal_hermite(x, x1, x2) uax = ua_at(x) ub = uax[:, 1, 1] @@ -246,7 +245,7 @@ function gal_extension!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, # --- surface terms (always; gal.f) --- q_l = profiles.q_spline(x1; hint=qhint) - Fl, Kl, _ = gal_get_fkg(ffit, intr, x1, q_l) + Fl, Kl, _ = gal_get_fkg(ffit, intr, x1, q_l; Fbuf=Fbuf, Kbuf=Kbuf, Gbuf=Gbuf) pbt, _ = gal_hermite(x1, x1, x2) surf_l = Fl * du1 .+ Kl * ua1 for ip in 0:np @@ -257,7 +256,7 @@ function gal_extension!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, end q_r = profiles.q_spline(x2; hint=qhint) - Fr, Kr, _ = gal_get_fkg(ffit, intr, x2, q_r) + Fr, Kr, _ = gal_get_fkg(ffit, intr, x2, q_r; Fbuf=Fbuf, Kbuf=Kbuf, Gbuf=Gbuf) pbt, _ = gal_hermite(x2, x1, x2) surf_r = Fr * du2 .+ Kr * ua2 for ip in 0:np @@ -295,27 +294,38 @@ function gal_resonant!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, sgn_u = (cell.extra == GAL_SIDE_RIGHT) ? -1.0 : 1.0 # Reused per-integrand buffers (col 1 = big, col 2 = small): sing_get_*_gal! fills them in place. + # sing_matvec! scratch and the quadgk! output buffer are hoisted too, so the integrand allocates nothing. ua_buf = Array{ComplexF64,3}(undef, N, 2, 2) dua_buf = Array{ComplexF64,3}(undef, N, 2, 2) + kmat = Matrix{ComplexF64}(undef, N, N) + gmat = Matrix{ComplexF64}(undef, N, N) + d1 = Vector{ComplexF64}(undef, N) + mvtmp = Vector{ComplexF64}(undef, N) + sfvec = Vector{Float64}(undef, N) + mv = Matrix{ComplexF64}(undef, N, 2) + w = Vector{ComplexF64}(undef, N) + pbuf = Vector{ComplexF64}(undef, N) L = 2 + 2 * N * (np + 1) - function integrand(x) + function integrand!(out, x) z = x - psi_s sing_get_ua_gal!(ua_buf, asymp, z) sing_get_dua_gal!(dua_buf, asymp, z) q = profiles.q_spline(x; hint=qhint) - mv = sing_matvec(ffit, intr, x, q, ua_buf, dua_buf) # N×2 (col1=big, col2=small) + sing_matvec!(mv, kmat, gmat, d1, mvtmp, sfvec, ffit, intr, x, q, ua_buf, dua_buf) # N×2 (col1=big, col2=small) pbt, _ = gal_hermite(x, x1, x2) - w = conj.(@view ua_buf[:, 2, 1]) # conj small solution, qty1 - out = Vector{ComplexF64}(undef, L) - out[1] = sum(w .* @view mv[:, 1]) # res1 - out[2] = sum(w .* @view mv[:, 2]) # res2 + # Pairwise sum over the materialized product (reuses buffers) — matches sum(w .* mv) bit-for-bit. + w .= conj.(@view ua_buf[:, 2, 1]) # conj small solution, qty1 + pbuf .= w .* @view mv[:, 1] + out[1] = sum(pbuf) # res1 + pbuf .= w .* @view mv[:, 2] + out[2] = sum(pbuf) # res2 idx = 3 - for ip in 0:np, ipert in 1:N + @inbounds for ip in 0:np, ipert in 1:N out[idx] = pbt[ip+1] * mv[ipert, 1] # hbig (ipert fastest, then ip) idx += 1 end - for ip in 0:np, ipert in 1:N + @inbounds for ip in 0:np, ipert in 1:N out[idx] = pbt[ip+1] * mv[ipert, 2] # hsmall idx += 1 end @@ -323,8 +333,10 @@ function gal_resonant!(cell::GalCell, ising::Int, ffit::FourFitVars, profiles, end # QuadGK (adaptive Gauss-Kronrod) replaces Fortran gal_lsode_int over the same integrand/limits — not - # bit-exact; gal_tol/gal_gnstep cap the evals so a near-singular integrand cannot hang. - raw, qerr = quadgk(integrand, x0, x1l; rtol=gal_tol, atol=1e-30, maxevals=gal_gnstep) + # bit-exact; gal_tol/gal_gnstep cap the evals so a near-singular integrand cannot hang. The in-place + # quadgk!/integrand! pair avoids a per-eval vector allocation in this hot adaptive loop. + result = Vector{ComplexF64}(undef, L) + raw, qerr = quadgk!(integrand!, result, x0, x1l; rtol=gal_tol, atol=1e-30, maxevals=gal_gnstep) if verbose @info " resonant jsing=$jsing side=$(cell.extra) qerr=$(qerr) res1=$(raw[1]) res2=$(raw[2])" end diff --git a/src/ForceFreeStates/Galerkin/GalerkinSolve.jl b/src/ForceFreeStates/Galerkin/GalerkinSolve.jl index d7b979333..0b7dd658e 100644 --- a/src/ForceFreeStates/Galerkin/GalerkinSolve.jl +++ b/src/ForceFreeStates/Galerkin/GalerkinSolve.jl @@ -75,8 +75,8 @@ function galerkin_solve(ctrl::ForceFreeStatesControl, equil, ffit::FourFitVars, ctrl.verbose && @info "Starting outer-region Galerkin Δ′ solve (msing=$msing, solver=$(ctrl.gal_solver))" - # Per-surface two-sided asymptotic series (pr178's validated convention, matching Fortran sing.f - # vmatr/vmatl): right = sig=+1, left = sig=-1, no √det normalization. The Mercier exponent α is a + # Per-surface two-sided asymptotic series matching Fortran sing.f vmatr/vmatl: + # right = sig=+1, left = sig=-1, no √det normalization. The Mercier exponent α is a # property of the surface, so the left series reuses the right's α (alpha_override). The order is # raised to gal_sing_order + ceil(2·Re(α)) for high-Mercier-index surfaces (Fortran sing1_vmat). ctrl_gal = deepcopy(ctrl) diff --git a/src/ForceFreeStates/Sing.jl b/src/ForceFreeStates/Sing.jl index aa3d4fd1c..a45b66643 100644 --- a/src/ForceFreeStates/Sing.jl +++ b/src/ForceFreeStates/Sing.jl @@ -955,6 +955,44 @@ function sing_matvec(ffit::FourFitVars, intr::ForceFreeStatesInternal, psi::Floa return matvec end +""" + sing_matvec!(matvec, kmat, gmat, d1, tmp, sfvec, ffit, intr, psi, q, ua, dua) -> matvec + +Allocation-free, in-place form of [`sing_matvec`](@ref) for the hot resonant-quadrature integrand. +All scratch is caller-owned: `kmat`/`gmat` are `N×N`, `d1`/`tmp`/`sfvec` are length-`N`, `matvec` is +`N×size(ua,2)`. The reduced K̄/Ḡ splines write directly into `kmat`/`gmat`. The accumulation order +(separate `gmat*ua` into `tmp`, then add) reproduces `sing_matvec` **bit-for-bit** — a fused 5-arg +`mul!` would round differently, and the ill-conditioned near-singular resonant solve amplifies a +1e-16 change into ~1e-3 in Δ′. +""" +function sing_matvec!(matvec::AbstractMatrix{ComplexF64}, kmat::Matrix{ComplexF64}, gmat::Matrix{ComplexF64}, + d1::Vector{ComplexF64}, tmp::Vector{ComplexF64}, sfvec::Vector{Float64}, ffit::FourFitVars, + intr::ForceFreeStatesInternal, psi::Float64, q::Float64, ua::AbstractArray{ComplexF64,3}, dua::AbstractArray{ComplexF64,3}) + + N = intr.numpert_total + msol = size(ua, 2) + + # Direct singular factor (m - n q), NOT 1/(m - n q); flat order matches vec((m) .- q.*(n)'). + idx = 0 + @inbounds for nn in intr.nlow:intr.nhigh, mm in intr.mlow:intr.mhigh + idx += 1 + sfvec[idx] = mm - q * nn + end + + ffit.kmats(vec(kmat), psi; hint=ffit._hint) + ffit.gmats(vec(gmat), psi; hint=ffit._hint) + kdag = adjoint(kmat) + + for isol in 1:msol + @views d1 .= dua[:, isol, 1] .* sfvec # u' · singfac + @views mul!(matvec[:, isol], kdag, d1) # K̄† (u' · singfac) + @views mul!(tmp, gmat, ua[:, isol, 1]) # Ḡ u + @views matvec[:, isol] .+= tmp # + Ḡ u + @views matvec[:, isol] .-= dua[:, isol, 2] # - (F u' + K u)' + end + return matvec +end + """ sing_get_ca(u::Array{ComplexF64,3}, ua::Array{ComplexF64,3}, intr::ForceFreeStatesInternal) From c1b26042f4c6659a85da7a422d741e4cfc267a0b Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Thu, 25 Jun 2026 23:18:52 -0400 Subject: [PATCH 120/135] GALERKIN - CLEANUP - Strip stale references from examples, fix docs, flatten benchmark dir --- .../{gal_validation => }/gal_beta_scan.jl | 15 +++++++-------- .../{gal_validation => }/gal_epsilon_scan.jl | 15 +++++++-------- .../{gal_validation => }/gal_scan_plot.jl | 10 +++++----- .../pfac_study/gal_pfac_scan2d.jl | 8 ++++---- .../pfac_study/gal_pfac_scan2d_big_plot.jl | 8 ++++---- .../pfac_study/gal_pfac_scan2d_plot.jl | 8 ++++---- .../pfac_study/gal_pfac_worker.jl | 2 +- .../tokamaker_beta/gal_tok_plot.jl | 10 +++++----- .../tokamaker_beta/gal_tok_worker.jl | 0 docs/src/stability.md | 2 +- .../DIIID-like_gal_resistive_example/gpec.toml | 18 ++++++++---------- .../gpec.toml | 18 ++++++++---------- 12 files changed, 54 insertions(+), 60 deletions(-) rename benchmarks/gal_validation/{gal_validation => }/gal_beta_scan.jl (88%) rename benchmarks/gal_validation/{gal_validation => }/gal_epsilon_scan.jl (88%) rename benchmarks/gal_validation/{gal_validation => }/gal_scan_plot.jl (89%) rename benchmarks/gal_validation/{gal_validation => }/pfac_study/gal_pfac_scan2d.jl (89%) rename benchmarks/gal_validation/{gal_validation => }/pfac_study/gal_pfac_scan2d_big_plot.jl (87%) rename benchmarks/gal_validation/{gal_validation => }/pfac_study/gal_pfac_scan2d_plot.jl (87%) rename benchmarks/gal_validation/{gal_validation => }/pfac_study/gal_pfac_worker.jl (98%) rename benchmarks/gal_validation/{gal_validation => }/tokamaker_beta/gal_tok_plot.jl (88%) rename benchmarks/gal_validation/{gal_validation => }/tokamaker_beta/gal_tok_worker.jl (100%) diff --git a/benchmarks/gal_validation/gal_validation/gal_beta_scan.jl b/benchmarks/gal_validation/gal_beta_scan.jl similarity index 88% rename from benchmarks/gal_validation/gal_validation/gal_beta_scan.jl rename to benchmarks/gal_validation/gal_beta_scan.jl index 76ce10887..a1ee33c5e 100644 --- a/benchmarks/gal_validation/gal_validation/gal_beta_scan.jl +++ b/benchmarks/gal_validation/gal_beta_scan.jl @@ -2,12 +2,11 @@ # Gal-enabled TJ-analytic beta (pc) scan: at each pc, run the full GPEC pipeline with gal_flag=true # and capture three Δ′ measures per resonant surface (m=2 q=2, m=3 q=3): # gal = galerkin/pest3_Delta diagonal (RDCON singular-Galerkin, this port) -# stride = singular/delta_prime_matrix diag (STRIDE BVP, pr178) -# cajump = (ca_r-ca_l)/((2pi)^2 psio) (ca-jump, pr178 primary) -# Reuses examples/LAR_beta_scan/gpec.toml. Writes /tmp/gal_beta_scan_results.h5 + CSV. +# stride = singular/delta_prime_matrix diag (STRIDE BVP) +# cajump = (ca_r-ca_l)/((2pi)^2 psio) (ca-jump primary) +# Reuses examples/LAR_beta_scan/gpec.toml. Writes gal_beta_scan_results.h5 + CSV next to this script. using Pkg -Pkg.activate(joinpath(@__DIR__, "..", "Projects", "GPEC_dev", "docs", "GPEC_julia")) -const REPO = "/Users/pharr/Projects/GPEC_dev/docs/GPEC_julia" +const REPO = normpath(joinpath(@__DIR__, "..", "..")) Pkg.activate(REPO) using GeneralizedPerturbedEquilibrium using HDF5, TOML, Printf @@ -85,7 +84,7 @@ for (i, pc) in enumerate(pcs) end # Save -out_h5 = "/tmp/gal_beta_scan_results.h5" +out_h5 = joinpath(@__DIR__, "gal_beta_scan_results.h5") isfile(out_h5) && rm(out_h5) h5open(out_h5, "w") do f f["pc"] = [r[1] for r in results] @@ -98,7 +97,7 @@ h5open(out_h5, "w") do f end end end -open("/tmp/gal_beta_scan_results.csv", "w") do io +open(joinpath(@__DIR__, "gal_beta_scan_results.csv"), "w") do io println(io, "pc,gal_m2,stride_m2,cajump_m2,gal_m3,stride_m3,cajump_m3,dW_total") for (pc, r) in results @printf(io, "%.6f,%.6f,%.6f,%.6f,%.6f,%.6f,%.6f,%.6f\n", pc, @@ -107,5 +106,5 @@ open("/tmp/gal_beta_scan_results.csv", "w") do io get(r,"dW_total",NaN)) end end -@info "Saved /tmp/gal_beta_scan_results.h5 and .csv ($(length(results)) points)" +@info "Saved gal_beta_scan_results.h5 and .csv to $(@__DIR__) ($(length(results)) points)" println("DONE") diff --git a/benchmarks/gal_validation/gal_validation/gal_epsilon_scan.jl b/benchmarks/gal_validation/gal_epsilon_scan.jl similarity index 88% rename from benchmarks/gal_validation/gal_validation/gal_epsilon_scan.jl rename to benchmarks/gal_validation/gal_epsilon_scan.jl index e701bee39..d615b5a6c 100644 --- a/benchmarks/gal_validation/gal_validation/gal_epsilon_scan.jl +++ b/benchmarks/gal_validation/gal_epsilon_scan.jl @@ -2,12 +2,11 @@ # Gal-enabled TJ-analytic beta (pc) scan: at each pc, run the full GPEC pipeline with gal_flag=true # and capture three Δ′ measures per resonant surface (m=2 q=2, m=3 q=3): # gal = galerkin/pest3_Delta diagonal (RDCON singular-Galerkin, this port) -# stride = singular/delta_prime_matrix diag (STRIDE BVP, pr178) -# cajump = (ca_r-ca_l)/((2pi)^2 psio) (ca-jump, pr178 primary) -# Reuses examples/LAR_beta_scan/gpec.toml. Writes /tmp/gal_epsilon_scan_results.h5 + CSV. +# stride = singular/delta_prime_matrix diag (STRIDE BVP) +# cajump = (ca_r-ca_l)/((2pi)^2 psio) (ca-jump primary) +# Reuses examples/LAR_epsilon_scan/gpec.toml. Writes gal_epsilon_scan_results.h5 + CSV next to this script. using Pkg -Pkg.activate(joinpath(@__DIR__, "..", "Projects", "GPEC_dev", "docs", "GPEC_julia")) -const REPO = "/Users/pharr/Projects/GPEC_dev/docs/GPEC_julia" +const REPO = normpath(joinpath(@__DIR__, "..", "..")) Pkg.activate(REPO) using GeneralizedPerturbedEquilibrium using HDF5, TOML, Printf @@ -86,7 +85,7 @@ for (i, pc) in enumerate(pcs) end # Save -out_h5 = "/tmp/gal_epsilon_scan_results.h5" +out_h5 = joinpath(@__DIR__, "gal_epsilon_scan_results.h5") isfile(out_h5) && rm(out_h5) h5open(out_h5, "w") do f f["pc"] = [r[1] for r in results] @@ -99,7 +98,7 @@ h5open(out_h5, "w") do f end end end -open("/tmp/gal_epsilon_scan_results.csv", "w") do io +open(joinpath(@__DIR__, "gal_epsilon_scan_results.csv"), "w") do io println(io, "pc,gal_m2,stride_m2,cajump_m2,gal_m3,stride_m3,cajump_m3,dW_total") for (pc, r) in results @printf(io, "%.6f,%.6f,%.6f,%.6f,%.6f,%.6f,%.6f,%.6f\n", pc, @@ -108,5 +107,5 @@ open("/tmp/gal_epsilon_scan_results.csv", "w") do io get(r,"dW_total",NaN)) end end -@info "Saved /tmp/gal_epsilon_scan_results.h5 and .csv ($(length(results)) points)" +@info "Saved gal_epsilon_scan_results.h5 and .csv to $(@__DIR__) ($(length(results)) points)" println("DONE") diff --git a/benchmarks/gal_validation/gal_validation/gal_scan_plot.jl b/benchmarks/gal_validation/gal_scan_plot.jl similarity index 89% rename from benchmarks/gal_validation/gal_validation/gal_scan_plot.jl rename to benchmarks/gal_validation/gal_scan_plot.jl index 2e7cf3f15..a37d496c3 100644 --- a/benchmarks/gal_validation/gal_validation/gal_scan_plot.jl +++ b/benchmarks/gal_validation/gal_scan_plot.jl @@ -1,7 +1,7 @@ # Plot gal vs STRIDE Δ′ across the TJ-analytic beta and epsilon scans. -# Reads /tmp/gal_beta_scan_results.csv and /tmp/gal_epsilon_scan_results.csv. +# Reads gal_beta_scan_results.csv and gal_epsilon_scan_results.csv from this directory. using Pkg -Pkg.activate("/Users/pharr/Projects/GPEC_dev/docs/GPEC_julia") +Pkg.activate(normpath(joinpath(@__DIR__, "..", ".."))) using Plots, DelimitedFiles, Printf gr() @@ -80,13 +80,13 @@ function relpanel(cols, xname, xlabel) end for (name, path, xn, xl, ttl) in ( - ("beta", "/tmp/gal_beta_scan_results.csv", "pc", "pₐ (on-axis pressure factor)", "TJ-analytic β scan (ε=0.2, qc=1.5, qa=3.6)"), - ("eps", "/tmp/gal_epsilon_scan_results.csv", "pc", "ε = a/R₀", "TJ-analytic ε scan (pc=0.001, qc=1.5, qa=3.6)")) + ("beta", joinpath(@__DIR__, "gal_beta_scan_results.csv"), "pc", "pₐ (on-axis pressure factor)", "TJ-analytic β scan (ε=0.2, qc=1.5, qa=3.6)"), + ("eps", joinpath(@__DIR__, "gal_epsilon_scan_results.csv"), "pc", "ε = a/R₀", "TJ-analytic ε scan (pc=0.001, qc=1.5, qa=3.6)")) cols = loadcsv(path) cols === nothing && continue xmarg = marginal_point(cols, xn) fig = plot(panel(cols, xn, xl, ttl, xmarg), dwpanel(cols, xn, xl), relpanel(cols, xn, xl); layout=(3, 1), size=(820, 1320)) - out = "/tmp/gal_$(name)_comparison.png" + out = joinpath(@__DIR__, "gal_$(name)_comparison.png") savefig(fig, out) println("Saved figure: ", out) println("=== $name: gal-vs-STRIDE relative diff (%) ===") diff --git a/benchmarks/gal_validation/gal_validation/pfac_study/gal_pfac_scan2d.jl b/benchmarks/gal_validation/pfac_study/gal_pfac_scan2d.jl similarity index 89% rename from benchmarks/gal_validation/gal_validation/pfac_study/gal_pfac_scan2d.jl rename to benchmarks/gal_validation/pfac_study/gal_pfac_scan2d.jl index a4a9a39f2..a0446b721 100644 --- a/benchmarks/gal_validation/gal_validation/pfac_study/gal_pfac_scan2d.jl +++ b/benchmarks/gal_validation/pfac_study/gal_pfac_scan2d.jl @@ -1,8 +1,8 @@ # 2D scan: gal-vs-STRIDE q=3 tracking over (pc, pfac). STRIDE is pfac-independent -# (recorded per run as a consistency check). Output /tmp/gal_pfac_scan2d.csv. +# (recorded per run as a consistency check). Output gal_pfac_scan2d.csv next to this script. using GeneralizedPerturbedEquilibrium using HDF5, TOML, Printf -const REPO = "/Users/pharr/Projects/GPEC_dev/docs/GPEC_julia" +const REPO = normpath(joinpath(@__DIR__, "..", "..", "..")) const BASE = TOML.parsefile(joinpath(REPO, "examples", "LAR_beta_scan", "gpec.toml")) const PCS = [0.005, 0.010, 0.020, 0.030, 0.040, 0.050, 0.060, 0.070, 0.085, 0.100] const PFACS = [5e-4, 1e-3, 3e-3, 1e-2, 3e-2, 1e-1] @@ -23,7 +23,7 @@ function extract(h5) end end -io = open("/tmp/gal_pfac_scan2d.csv", "w") +io = open(joinpath(@__DIR__, "gal_pfac_scan2d.csv"), "w") println(io, "pc,pfac,gal_q2,stride_q2,gal_q3,stride_q3"); flush(io) t0 = time(); n = 0; ntot = length(PCS) * length(PFACS) for pc in PCS, pfac in PFACS @@ -49,5 +49,5 @@ for pc in PCS, pfac in PFACS end end close(io) -println("Saved /tmp/gal_pfac_scan2d.csv") +println("Saved gal_pfac_scan2d.csv to ", @__DIR__) println("DONE") diff --git a/benchmarks/gal_validation/gal_validation/pfac_study/gal_pfac_scan2d_big_plot.jl b/benchmarks/gal_validation/pfac_study/gal_pfac_scan2d_big_plot.jl similarity index 87% rename from benchmarks/gal_validation/gal_validation/pfac_study/gal_pfac_scan2d_big_plot.jl rename to benchmarks/gal_validation/pfac_study/gal_pfac_scan2d_big_plot.jl index 1ec4b7f72..d968ff98d 100644 --- a/benchmarks/gal_validation/gal_validation/pfac_study/gal_pfac_scan2d_big_plot.jl +++ b/benchmarks/gal_validation/pfac_study/gal_pfac_scan2d_big_plot.jl @@ -1,8 +1,8 @@ # Plot the fine (50 pc x 30 pfac) gal-vs-STRIDE q=3 tracking scan: heatmap + per-pfac curves. -using Pkg; Pkg.activate("/Users/pharr/Projects/GPEC_dev/docs/GPEC_julia") +using Pkg; Pkg.activate(normpath(joinpath(@__DIR__, "..", "..", ".."))) using Plots, DelimitedFiles, Printf; gr() -data, hdr = readdlm("/tmp/gal_pfac_scan2d_big.csv", ','; header=true) +data, hdr = readdlm(joinpath(@__DIR__, "gal_pfac_scan2d_big.csv"), ','; header=true) col(name) = data[:, findfirst(==(name), strip.(vec(hdr)))] pc = col("pc"); pfac = col("pfac"); gq3 = col("gal_q3"); sq3 = col("stride_q3") relerr = 100 .* abs.(gq3 .- sq3) ./ max.(abs.(sq3), 1e-12) @@ -30,8 +30,8 @@ for i in unique(sel) plot!(p2, pcs, [isfinite(z) ? max(z, 1e-3) : NaN for z in Z[i, :]]; lw=2, label=@sprintf("pfac=%.1e", pfacs[i])) end fig = plot(p1, p2; layout=(2, 1), size=(1000, 1050)) -savefig(fig, "/tmp/gal_pfac_scan2d_big.png") -println("Saved /tmp/gal_pfac_scan2d_big.png") +savefig(fig, joinpath(@__DIR__, "gal_pfac_scan2d_big.png")) +println("Saved gal_pfac_scan2d_big.png to ", @__DIR__) med(v) = (w = sort(filter(isfinite, v)); isempty(w) ? NaN : (n = length(w); iseven(n) ? (w[n÷2]+w[n÷2+1])/2 : w[(n+1)÷2])) println("\npfac median% max%") diff --git a/benchmarks/gal_validation/gal_validation/pfac_study/gal_pfac_scan2d_plot.jl b/benchmarks/gal_validation/pfac_study/gal_pfac_scan2d_plot.jl similarity index 87% rename from benchmarks/gal_validation/gal_validation/pfac_study/gal_pfac_scan2d_plot.jl rename to benchmarks/gal_validation/pfac_study/gal_pfac_scan2d_plot.jl index 9f4f2e67b..462929c45 100644 --- a/benchmarks/gal_validation/gal_validation/pfac_study/gal_pfac_scan2d_plot.jl +++ b/benchmarks/gal_validation/pfac_study/gal_pfac_scan2d_plot.jl @@ -1,8 +1,8 @@ # Plot the (pc x pfac) gal-vs-STRIDE q=3 tracking scan: heatmap + per-pfac curves. -using Pkg; Pkg.activate("/Users/pharr/Projects/GPEC_dev/docs/GPEC_julia") +using Pkg; Pkg.activate(normpath(joinpath(@__DIR__, "..", "..", ".."))) using Plots, DelimitedFiles, Printf; gr() -data, hdr = readdlm("/tmp/gal_pfac_scan2d.csv", ','; header=true) +data, hdr = readdlm(joinpath(@__DIR__, "gal_pfac_scan2d.csv"), ','; header=true) col(name) = data[:, findfirst(==(name), strip.(vec(hdr)))] pc = col("pc"); pfac = col("pfac"); gq3 = col("gal_q3"); sq3 = col("stride_q3") relerr = 100 .* abs.(gq3 .- sq3) ./ abs.(sq3) @@ -32,8 +32,8 @@ for (i, pf) in enumerate(pfacs) end fig = plot(p1, p2; layout=(2, 1), size=(900, 1000)) -savefig(fig, "/tmp/gal_pfac_scan2d.png") -println("Saved /tmp/gal_pfac_scan2d.png") +savefig(fig, joinpath(@__DIR__, "gal_pfac_scan2d.png")) +println("Saved gal_pfac_scan2d.png to ", @__DIR__) # Per-pfac median/max summary println("\npfac median% max% (q=3 over the pc grid)") diff --git a/benchmarks/gal_validation/gal_validation/pfac_study/gal_pfac_worker.jl b/benchmarks/gal_validation/pfac_study/gal_pfac_worker.jl similarity index 98% rename from benchmarks/gal_validation/gal_validation/pfac_study/gal_pfac_worker.jl rename to benchmarks/gal_validation/pfac_study/gal_pfac_worker.jl index fe4b67d19..f0a344875 100644 --- a/benchmarks/gal_validation/gal_validation/pfac_study/gal_pfac_worker.jl +++ b/benchmarks/gal_validation/pfac_study/gal_pfac_worker.jl @@ -8,7 +8,7 @@ using TOML, Printf, LinearAlgebra import FastInterpolations: cubic_interp, Series, ExtendExtrap LinearAlgebra.BLAS.set_num_threads(1) # avoid oversubscription across parallel workers -const REPO = "/Users/pharr/Projects/GPEC_dev/docs/GPEC_julia" +const REPO = normpath(joinpath(@__DIR__, "..", "..", "..")) const PFACS = exp10.(range(-4, 0; length=30)) # 30 packing ratios, 1e-4 .. 1e0 const PCLIST = parse.(Float64, split(ARGS[1], ',')) # comma-separated pc values diff --git a/benchmarks/gal_validation/gal_validation/tokamaker_beta/gal_tok_plot.jl b/benchmarks/gal_validation/tokamaker_beta/gal_tok_plot.jl similarity index 88% rename from benchmarks/gal_validation/gal_validation/tokamaker_beta/gal_tok_plot.jl rename to benchmarks/gal_validation/tokamaker_beta/gal_tok_plot.jl index 9e2d657c1..7949202dc 100644 --- a/benchmarks/gal_validation/gal_validation/tokamaker_beta/gal_tok_plot.jl +++ b/benchmarks/gal_validation/tokamaker_beta/gal_tok_plot.jl @@ -1,10 +1,10 @@ -# Plot the TokaMaker beta-scan pfac convergence study. Data: /tmp/gal_tok_scan.csv +# Plot the TokaMaker beta-scan pfac convergence study. Data: gal_tok_scan.csv in this directory # (beta,pfac,m,q,gal,stride). Produces: per-pfac error summary, a heatmap (beta x pfac) # of median-over-surfaces tracking error, and per-q tracking-vs-beta at the chosen pfac. -using Pkg; Pkg.activate("/Users/pharr/Projects/GPEC_dev/docs/GPEC_julia") +using Pkg; Pkg.activate(normpath(joinpath(@__DIR__, "..", "..", ".."))) using Plots, DelimitedFiles, Printf; gr() -d, h = readdlm("/tmp/gal_tok_scan.csv", ','; header=true) +d, h = readdlm(joinpath(@__DIR__, "gal_tok_scan.csv"), ','; header=true) col(n) = d[:, findfirst(==(n), strip.(vec(h)))] beta = col("beta"); pfac = col("pfac"); m = Int.(col("m")); q = col("q"); g = col("gal"); s = col("stride") # Exclude q=1: the internal-kink surface where the outer-region Δ′ construction does not apply @@ -47,7 +47,7 @@ for i in unique(sel) plot!(p2, betas, yv; lw=2, marker=:circle, ms=2, label=@sprintf("pfac=%.1e", pfacs[i])) end fig = plot(p1, p2; layout=(2, 1), size=(1000, 1050)) -savefig(fig, "/tmp/gal_tok_scan.png") -println("Saved /tmp/gal_tok_scan.png") +savefig(fig, joinpath(@__DIR__, "gal_tok_scan.png")) +println("Saved gal_tok_scan.png to ", @__DIR__) println("surfaces present (q): ", sort(unique(round.(q; digits=1)))) println("DONE") diff --git a/benchmarks/gal_validation/gal_validation/tokamaker_beta/gal_tok_worker.jl b/benchmarks/gal_validation/tokamaker_beta/gal_tok_worker.jl similarity index 100% rename from benchmarks/gal_validation/gal_validation/tokamaker_beta/gal_tok_worker.jl rename to benchmarks/gal_validation/tokamaker_beta/gal_tok_worker.jl diff --git a/docs/src/stability.md b/docs/src/stability.md index 3e09c8796..9e2d7f8d4 100644 --- a/docs/src/stability.md +++ b/docs/src/stability.md @@ -272,7 +272,7 @@ The Galerkin Δ′ solver (`src/ForceFreeStates/Galerkin/`) is documented separa ```@autodocs Modules = [GeneralizedPerturbedEquilibrium.ForceFreeStates] -Pages = ["ForceFreeStates.jl", "ForceFreeStatesStructs.jl", "Mercier.jl", "Resist.jl", "Bal.jl", "EulerLagrange.jl", "Sing.jl", "Fourfit.jl", "Kinetic.jl", "FixedBoundaryStability.jl", "Utils.jl", "Free.jl", "Riccati.jl"] +Pages = ["ForceFreeStates.jl", "ForceFreeStatesStructs.jl", "Ballooning.jl", "Resist.jl", "EulerLagrange.jl", "Sing.jl", "Fourfit.jl", "Kinetic.jl", "FixedBoundaryStability.jl", "Utils.jl", "Free.jl", "Riccati.jl"] ``` ## Example usage diff --git a/examples/DIIID-like_gal_resistive_example/gpec.toml b/examples/DIIID-like_gal_resistive_example/gpec.toml index 9ff1e7562..4a816e509 100644 --- a/examples/DIIID-like_gal_resistive_example/gpec.toml +++ b/examples/DIIID-like_gal_resistive_example/gpec.toml @@ -41,9 +41,8 @@ nn_high = 1 # Largest toroidal mode number to include delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 4 # Expands upper bound of Fourier harmonics mthvac = 512 # Number of points used in splines over poloidal angle at plasma-vacuum interface. -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds -kinetic_source = "fixed" # Kinetic matrix source ("fixed" test matrices, or "calculated" from PENTRC) +kinetic_source = "fixed" # Kinetic matrix source ("fixed" test matrices, or "calculated" kinetic response) kinetic_factor = 0.0 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode) eulerlagrange_tolerance = 1e-10# Relative tolerance for ODE integration of Euler-Lagrange equations save_interval = 3 # Save every Nth ODE step (1=all, 10=every 10th). Always saves near rational surfaces. @@ -54,11 +53,10 @@ ucrit = 1e4 # Maximum fraction of solutions allowed before re use_parallel = true # Run parallel FM-propagator BVP path (unlocks singular/delta_prime_matrix) parallel_threads = 2 # BVP thread cap (1 = serial/bit-deterministic; 2 ≈ +20% speedup; ≥3 saturates) populate_dense_xi = false # Dense axis-basis ξ for the FFS HDF5 output. Not needed here: no [PerturbedEquilibrium] section, and the gal-matched path builds its own dense ξ. Set true only for a shooting-fed PE run. -truncate_at_dW_peak = false # Edge-dW scan stays diagnostic; integration domain set by qhigh / psihigh / dmlim set_psilim_via_dmlim = false # Keep psilim at psihigh (do not truncate at last_rational_q + dmlim) dmlim = 0.2 # Truncate integration at (last_rational_q + dmlim) / n (only used when set_psilim_via_dmlim = true) -# RDCON outer-region singular Galerkin Δ′ solver with rpec coil columns (matched to Fortran &GAL_INPUT). +# Outer-region singular Galerkin Δ′ solver with rpec coil columns. # This case exercises the gal solve AND the rpec coil/edge path (delta_coil) for regression tracking. gal_flag = true # Enable the outer-region singular Galerkin Δ′ solve (requires mat_flag = true) gal_solver = "LU" # Banded solver: "LU" (zgbtrf/zgbtrs) or "cholesky" (zpbtrf/zpbtrs). rpec requires "LU". @@ -76,11 +74,11 @@ gal_sing_order = 6 # Base power-series order for the Galerkin singul gal_sing_order_ceiling = true # Auto-raise the series order by ceil(2·Re(α)) on high-Mercier-index surfaces gal_rpec_flag = true # Append mpert coil-response columns (unit edge sources) to the solve → delta_coil block -# DRIVEN (RPEC) outer↔inner matching. Per-surface resistive inputs (core→edge), mirroring the Fortran -# rmatch DIII-D example: eta=8e-8, massden=3.3e-7 (ni≈1e20 m^-3), rotation=1 Hz, Γ=5/3. 4 surfaces. +# DRIVEN (RPEC) outer↔inner matching. Per-surface resistive inputs (core→edge) for a DIII-D-like case: +# η=8e-8, ρ=3.3e-7 kg/m³ (ni≈1e20 m^-3), rotation=1 Hz, Γ=5/3. 4 surfaces. gal_match_flag = true # Solve the coil-driven matched ξ(ψ) from the gal Δ′ + the inner-layer Δ(Q). Requires gal_rpec_flag = true. -gal_ideal_flag = false # true → build the IDEAL solution (skip the inner layer, bare coil columns; ≡ DCON). false → the resistive matching below. -gal_eta = [8e-8, 8e-8, 8e-8, 8e-8] # Per-surface resistivity η (core→edge); Fortran rmatch `eta` -gal_rho = [3.3e-7, 3.3e-7, 3.3e-7, 3.3e-7] # Per-surface mass density ρ [kg/m³] (core→edge); Fortran rmatch `massden` -gal_rotation = [1.0, 1.0, 1.0, 1.0] # Per-surface rotation frequency f [Hz] (core→edge); forced eigenvalue γ_s = 2πi·n·f. Fortran rmatch `rotation` +gal_ideal_flag = false # true → build the IDEAL solution (skip the inner layer, bare coil columns). false → the resistive matching below. +gal_eta = [8e-8, 8e-8, 8e-8, 8e-8] # Per-surface resistivity η (core→edge) +gal_rho = [3.3e-7, 3.3e-7, 3.3e-7, 3.3e-7] # Per-surface mass density ρ [kg/m³] (core→edge) +gal_rotation = [1.0, 1.0, 1.0, 1.0] # Per-surface rotation frequency f [Hz] (core→edge); forced eigenvalue γ_s = 2πi·n·f gal_gamma = 1.6666666666666667 # Ratio of specific heats Γ for the resistive-layer coefficients (5/3) diff --git a/examples/DIIID-like_gal_resistive_pe_example/gpec.toml b/examples/DIIID-like_gal_resistive_pe_example/gpec.toml index e0e0e4554..66345e633 100644 --- a/examples/DIIID-like_gal_resistive_pe_example/gpec.toml +++ b/examples/DIIID-like_gal_resistive_pe_example/gpec.toml @@ -41,9 +41,8 @@ nn_high = 1 # Largest toroidal mode number to include delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 4 # Expands upper bound of Fourier harmonics mthvac = 512 # Number of points used in splines over poloidal angle at plasma-vacuum interface. -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds -kinetic_source = "fixed" # Kinetic matrix source ("fixed" test matrices, or "calculated" from PENTRC) +kinetic_source = "fixed" # Kinetic matrix source ("fixed" test matrices, or "calculated" kinetic response) kinetic_factor = 0.0 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode) eulerlagrange_tolerance = 1e-10# Relative tolerance for ODE integration of Euler-Lagrange equations save_interval = 3 # Save every Nth ODE step (1=all, 10=every 10th). Always saves near rational surfaces. @@ -54,11 +53,10 @@ ucrit = 1e4 # Maximum fraction of solutions allowed before re use_parallel = true # Run parallel FM-propagator BVP path (unlocks singular/delta_prime_matrix) parallel_threads = 2 # BVP thread cap (1 = serial/bit-deterministic; 2 ≈ +20% speedup; ≥3 saturates) populate_dense_xi = false # Dense axis-basis ξ for the FFS HDF5 output. Not needed here: no [PerturbedEquilibrium] section, and the gal-matched path builds its own dense ξ. Set true only for a shooting-fed PE run. -truncate_at_dW_peak = false # Edge-dW scan stays diagnostic; integration domain set by qhigh / psihigh / dmlim set_psilim_via_dmlim = false # Keep psilim at psihigh (do not truncate at last_rational_q + dmlim) dmlim = 0.2 # Truncate integration at (last_rational_q + dmlim) / n (only used when set_psilim_via_dmlim = true) -# RDCON outer-region singular Galerkin Δ′ solver with rpec coil columns (matched to Fortran &GAL_INPUT). +# Outer-region singular Galerkin Δ′ solver with rpec coil columns. # This case exercises the gal solve AND the rpec coil/edge path (delta_coil) for regression tracking. gal_flag = true # Enable the outer-region singular Galerkin Δ′ solve (requires mat_flag = true) gal_solver = "LU" # Banded solver: "LU" (zgbtrf/zgbtrs) or "cholesky" (zpbtrf/zpbtrs). rpec requires "LU". @@ -76,13 +74,13 @@ gal_sing_order = 6 # Base power-series order for the Galerkin singul gal_sing_order_ceiling = true # Auto-raise the series order by ceil(2·Re(α)) on high-Mercier-index surfaces gal_rpec_flag = true # Append mpert coil-response columns (unit edge sources) to the solve → delta_coil block -# DRIVEN (RPEC) outer↔inner matching. Per-surface resistive inputs (core→edge), mirroring the Fortran -# rmatch DIII-D example: eta=8e-8, massden=3.3e-7 (ni≈1e20 m^-3), rotation=1 Hz, Γ=5/3. 4 surfaces. +# DRIVEN (RPEC) outer↔inner matching. Per-surface resistive inputs (core→edge) for a DIII-D-like case: +# η=8e-8, ρ=3.3e-7 kg/m³ (ni≈1e20 m^-3), rotation=1 Hz, Γ=5/3. 4 surfaces. gal_match_flag = true # Solve the coil-driven matched ξ(ψ) from the gal Δ′ + the inner-layer Δ(Q). Requires gal_rpec_flag = true. -gal_ideal_flag = false # true → build the IDEAL solution (skip the inner layer, bare coil columns; ≡ DCON). false → the resistive matching below. -gal_eta = [8e-8, 8e-8, 8e-8, 8e-8] # Per-surface resistivity η (core→edge); Fortran rmatch `eta` -gal_rho = [3.3e-7, 3.3e-7, 3.3e-7, 3.3e-7] # Per-surface mass density ρ [kg/m³] (core→edge); Fortran rmatch `massden` -gal_rotation = [1.0, 1.0, 1.0, 1.0] # Per-surface rotation frequency f [Hz] (core→edge); forced eigenvalue γ_s = 2πi·n·f. Fortran rmatch `rotation` +gal_ideal_flag = false # true → build the IDEAL solution (skip the inner layer, bare coil columns). false → the resistive matching below. +gal_eta = [8e-8, 8e-8, 8e-8, 8e-8] # Per-surface resistivity η (core→edge) +gal_rho = [3.3e-7, 3.3e-7, 3.3e-7, 3.3e-7] # Per-surface mass density ρ [kg/m³] (core→edge) +gal_rotation = [1.0, 1.0, 1.0, 1.0] # Per-surface rotation frequency f [Hz] (core→edge); forced eigenvalue γ_s = 2πi·n·f gal_gamma = 1.6666666666666667 # Ratio of specific heats Γ for the resistive-layer coefficients (5/3) [ForcingTerms] From 4b01c75c9235397915e367b9c0a5ae8548d7c7a5 Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Fri, 26 Jun 2026 10:54:29 -0400 Subject: [PATCH 121/135] FORCEFREESTATES - OPTIMIZATION - Implement parallel processing for ballooning stability computation to enhance performance --- src/ForceFreeStates/Ballooning.jl | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/src/ForceFreeStates/Ballooning.jl b/src/ForceFreeStates/Ballooning.jl index 45ed8b8bb..34d3ae46d 100644 --- a/src/ForceFreeStates/Ballooning.jl +++ b/src/ForceFreeStates/Ballooning.jl @@ -40,8 +40,10 @@ function compute_ballooning_stability!( num_psi = length(plasma_eq.profiles.xs) - # Loop over flux surfaces - for flux_surface_index in 1:num_psi + # Parallelism is governed by the Julia thread count (`julia -t N`); with one thread this runs serially. + # All data is thread-local, so no locks are needed. The `:greedy` scheduling strategy + # outperforms `:static` and `:dynamic` for this workload in testing. + Threads.@threads :greedy for flux_surface_index in 1:num_psi psi = plasma_eq.profiles.xs[flux_surface_index] coeff_data = prepare_ballooning_coefficients(flux_surface_index, plasma_eq; theta_k=theta_k) From 151395da035896711c8c1aeed78b081150edfeb0 Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Fri, 26 Jun 2026 13:19:26 -0400 Subject: [PATCH 122/135] FORCEFREESTATES - OPTIMIZATION - Implement parallel for ballooning alpha boundary calculations --- src/ForceFreeStates/Ballooning.jl | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/src/ForceFreeStates/Ballooning.jl b/src/ForceFreeStates/Ballooning.jl index 34d3ae46d..3b13d04d1 100644 --- a/src/ForceFreeStates/Ballooning.jl +++ b/src/ForceFreeStates/Ballooning.jl @@ -814,7 +814,7 @@ function ballooning_alpha_boundary( alpha = fill(NaN, npsi) alpha_critical = fill(NaN, npsi) - for i in 1:npsi + Threads.@threads :greedy for i in 1:npsi xs[i] > 1.0 && continue try alpha[i] = salpha_reference(i, plasma_eq).alpha_ref @@ -878,7 +878,7 @@ function ballooning_alpha_boundaries( alpha_critical1 = fill(NaN, npsi) alpha_critical2 = fill(NaN, npsi) - for i in 1:npsi + Threads.@threads :greedy for i in 1:npsi xs[i] > 1.0 && continue try cr = ballooning_alpha_crossings(i, plasma_eq; theta_k=theta_k, max_alpha_scale=max_alpha_scale, n_scan=n_scan) @@ -967,7 +967,7 @@ function ballooning_qprime_boundaries( qprime_critical1 = fill(NaN, npsi) qprime_critical2 = fill(NaN, npsi) - for i in 1:npsi + Threads.@threads :greedy for i in 1:npsi xs[i] > 1.0 && continue try cr = ballooning_qprime_crossings( From 7c3b8eaf9970ed9656706648ac7ecc5b410d45d6 Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Fri, 26 Jun 2026 20:35:28 -0400 Subject: [PATCH 123/135] GALERKIN - REFACTOR - Update import comments and remove export of experimental function solve_inner_converged --- src/InnerLayer/InnerLayer.jl | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/InnerLayer/InnerLayer.jl b/src/InnerLayer/InnerLayer.jl index 47744f3aa..934e8f839 100644 --- a/src/InnerLayer/InnerLayer.jl +++ b/src/InnerLayer/InnerLayer.jl @@ -16,10 +16,10 @@ include("GGJ/GGJ.jl") import .GGJ: GGJModel, GGJParameters, build_asymptotics, evaluate_asymptotics, pick_xmax import .GGJ: InnerAsymptoticsCache, mercier_di, mercier_dr, inner_Q, rescale_delta -import .GGJ: glasser_wang_2020_eq55, solve_inner_converged +import .GGJ: glasser_wang_2020_eq55, solve_inner_converged # solve_inner_converged: experimental, not exported (reachable as a qualified call only) # SLAYER imports go here -export InnerLayerModel, solve_inner, solve_inner_converged +export InnerLayerModel, solve_inner export GGJ, GGJModel, GGJParameters export build_asymptotics, evaluate_asymptotics, pick_xmax, InnerAsymptoticsCache export mercier_di, mercier_dr, inner_Q, rescale_delta From a68a05318a91256c8466374ba58ba74720996423 Mon Sep 17 00:00:00 2001 From: jmlmir369 Date: Sat, 27 Jun 2026 20:06:28 +0900 Subject: [PATCH 124/135] automating thmax0 --- docs/src/ballooning.md | 4 ++ examples/DIIID-like_ideal_example/gpec.toml | 1 - examples/LAR_beta_scan/gpec.toml | 1 - examples/LAR_epsilon_scan/gpec.toml | 1 - examples/Solovev_ideal_example/gpec.toml | 1 - examples/Solovev_ideal_example_3D/gpec.toml | 1 - .../Solovev_ideal_example_multi_n/gpec.toml | 1 - .../single_n_1/gpec.toml | 1 - .../single_n_2/gpec.toml | 1 - .../gpec.toml | 1 - examples/a10_kinetic_example/gpec.toml | 1 - src/ForceFreeStates/Ballooning.jl | 44 ++++++++++++++++--- src/ForceFreeStates/ForceFreeStatesStructs.jl | 2 - .../gpec.toml | 1 - .../gpec.toml | 1 - .../gpec.toml | 1 - .../gpec.toml | 1 - .../gpec.toml | 1 - .../gpec.toml | 1 - 19 files changed, 43 insertions(+), 23 deletions(-) diff --git a/docs/src/ballooning.md b/docs/src/ballooning.md index 01ecc4bfd..6207b2255 100644 --- a/docs/src/ballooning.md +++ b/docs/src/ballooning.md @@ -844,6 +844,10 @@ a_2\left(\theta+\frac{a_1}{2a_2}\right)^2 The residual scale is ``c = a_0-a_1^2/(4a_2)``. To make the asymptotic approximation valid, the code chooses an integration boundary where the ``\theta^2`` term dominates, using the scale ``\sqrt{|c/a_2|}``. +Because the shooting boundary is a single flux-surface quantity, `Bal.jl` +evaluates this scale on the ballooning theta grid and uses the largest finite +value on that surface. The base integration boundary is then capped as +``\theta_{\max}=\min(16.5,10\max_\theta\sqrt{|c/a_2|})``. Directly extracting ``c_{a1}`` or ``\Delta'`` from the small asymptotic solution is numerically fragile. The comparison below shows that the `Baloo.f` style, which diff --git a/examples/DIIID-like_ideal_example/gpec.toml b/examples/DIIID-like_ideal_example/gpec.toml index 6f2ecb634..ed99887ab 100644 --- a/examples/DIIID-like_ideal_example/gpec.toml +++ b/examples/DIIID-like_ideal_example/gpec.toml @@ -43,7 +43,6 @@ nn_high = 1 # Largest toroidal mode number to include delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 8 # Expands upper bound of Fourier harmonics mthvac = 512 # Number of points used in splines over poloidal angle at the plasma-vacuum interface -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds kinetic_source = "fixed" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model kinetic_factor = 0.0 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode) diff --git a/examples/LAR_beta_scan/gpec.toml b/examples/LAR_beta_scan/gpec.toml index 4765f8689..c4d1f3162 100644 --- a/examples/LAR_beta_scan/gpec.toml +++ b/examples/LAR_beta_scan/gpec.toml @@ -48,7 +48,6 @@ nn_high = 1 # Largest toroidal mode number to include delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 8 # Expands upper bound of Fourier harmonics mthvac = 960 # Number of points used in splines over poloidal angle at the plasma-vacuum interface -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds eulerlagrange_tolerance = 1e-12 # Relative tolerance for ODE integration of Euler-Lagrange equations singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced diff --git a/examples/LAR_epsilon_scan/gpec.toml b/examples/LAR_epsilon_scan/gpec.toml index 49ebdfb61..0c8fceb3c 100644 --- a/examples/LAR_epsilon_scan/gpec.toml +++ b/examples/LAR_epsilon_scan/gpec.toml @@ -49,7 +49,6 @@ nn_high = 1 # Largest toroidal mode number to include delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 8 # Expands upper bound of Fourier harmonics mthvac = 960 # Number of points used in splines over poloidal angle at the plasma-vacuum interface -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds eulerlagrange_tolerance = 1e-12 # Relative tolerance for ODE integration of Euler-Lagrange equations singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced diff --git a/examples/Solovev_ideal_example/gpec.toml b/examples/Solovev_ideal_example/gpec.toml index 9a74f1d35..d9fc70d23 100644 --- a/examples/Solovev_ideal_example/gpec.toml +++ b/examples/Solovev_ideal_example/gpec.toml @@ -60,7 +60,6 @@ nn_high = 1 # Largest toroidal mode number to include delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 8 # Expands upper bound of Fourier harmonics mthvac = 960 # Number of points used in splines over poloidal angle at the plasma-vacuum interface -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds kinetic_source = "fixed" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model kinetic_factor = 0.0 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode) diff --git a/examples/Solovev_ideal_example_3D/gpec.toml b/examples/Solovev_ideal_example_3D/gpec.toml index 74ecf2866..3d1caa78d 100644 --- a/examples/Solovev_ideal_example_3D/gpec.toml +++ b/examples/Solovev_ideal_example_3D/gpec.toml @@ -31,7 +31,6 @@ delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 8 # Expands upper bound of Fourier harmonics mthvac = 64 # Number of points used in splines over poloidal angle at the plasma-vacuum interface nzvac = 96 # Number of points used in splines over toroidal angle at the plasma-vacuum interface -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds kinetic_source = "fixed" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model kinetic_factor = 0.0 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode) diff --git a/examples/Solovev_ideal_example_multi_n/gpec.toml b/examples/Solovev_ideal_example_multi_n/gpec.toml index e75343919..b17ab0439 100644 --- a/examples/Solovev_ideal_example_multi_n/gpec.toml +++ b/examples/Solovev_ideal_example_multi_n/gpec.toml @@ -42,7 +42,6 @@ nn_high = 2 # Largest toroidal mode number to include delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 8 # Expands upper bound of Fourier harmonics mthvac = 960 # Number of points used in splines over poloidal angle at the plasma-vacuum interface -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds kinetic_source = "fixed" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model kinetic_factor = 0.0 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode) diff --git a/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml b/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml index 70e705b57..650cfe314 100644 --- a/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml +++ b/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml @@ -41,7 +41,6 @@ nn_high = 1 # Largest toroidal mode number to include delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 10 # Expands upper bound of Fourier harmonics mthvac = 960 # Number of points used in splines over poloidal angle at the plasma-vacuum interface -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds kinetic_source = "fixed" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model kinetic_factor = 0.0 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode) diff --git a/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml b/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml index d687cd3dc..e95f0cc94 100644 --- a/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml +++ b/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml @@ -41,7 +41,6 @@ nn_high = 2 # Largest toroidal mode number to include delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 8 # Expands upper bound of Fourier harmonics mthvac = 960 # Number of points used in splines over poloidal angle at the plasma-vacuum interface -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds kinetic_source = "fixed" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model kinetic_factor = 0.0 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode) diff --git a/examples/Solovev_kinetic_calculated_example/gpec.toml b/examples/Solovev_kinetic_calculated_example/gpec.toml index 9422d7152..ea3913fe8 100644 --- a/examples/Solovev_kinetic_calculated_example/gpec.toml +++ b/examples/Solovev_kinetic_calculated_example/gpec.toml @@ -40,7 +40,6 @@ nn_high = 1 # Largest toroidal mode number to include delta_mlow = 8 # Expands lower bound of Fourier harmonics delta_mhigh = 8 # Expands upper bound of Fourier harmonics mthvac = 64 # Number of points used in splines over poloidal angle at plasma-vacuum interface. -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds kinetic_source = "calculated" # Kinetic matrix source — exercises KineticForces.compute_calculated_kinetic_matrices callback with real physics kinetic_factor = 1.0 # Full-strength kinetic matrices (the "calculated" path is the real physics; no perturbation scaling) diff --git a/examples/a10_kinetic_example/gpec.toml b/examples/a10_kinetic_example/gpec.toml index 5ac64a4e8..40d29c08b 100644 --- a/examples/a10_kinetic_example/gpec.toml +++ b/examples/a10_kinetic_example/gpec.toml @@ -38,7 +38,6 @@ nn_high = 1 # Largest toroidal mode number to include delta_mlow = 6 # Expands lower bound of Fourier harmonics delta_mhigh = 6 # Expands upper bound of Fourier harmonics mthvac = 512 # Number of points used in splines over poloidal angle at the plasma-vacuum interface -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds kinetic_source = "calculated" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model kinetic_factor = 1.0 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode; 1.0 = full strength) diff --git a/src/ForceFreeStates/Ballooning.jl b/src/ForceFreeStates/Ballooning.jl index 3b13d04d1..ebdfb7686 100644 --- a/src/ForceFreeStates/Ballooning.jl +++ b/src/ForceFreeStates/Ballooning.jl @@ -5,6 +5,10 @@ using LinearAlgebra using StaticArrays: SVector +const BALLOONING_THETA_MAX_CAP = 16.5 +const BALLOONING_THETA_SCALE_MULTIPLIER = 10.0 +const MATCHING_POINT = 1e-3 + """ compute_ballooning_stability!(ctrl, locstab_fs, plasma_eq) @@ -374,6 +378,26 @@ function _calculate_i_per_perturbed( return i_per_perturbed end +function _ballooning_theta_scale( + periodic::AbstractVector, + peculiar_1st::AbstractVector, + peculiar_2nd::AbstractVector; + fallback::Float64=BALLOONING_THETA_MAX_CAP +) + theta_scale = 0.0 + for idx in eachindex(periodic, peculiar_1st, peculiar_2nd) + a0 = periodic[idx] + a1 = peculiar_1st[idx] + a2 = peculiar_2nd[idx] + if Base.isfinite(a0) && Base.isfinite(a1) && Base.isfinite(a2) && Base.abs(a2) > Base.eps(Float64) + c = a0 - a1^2 / (4.0 * a2) + local_scale = Base.sqrt(Base.abs(c / a2)) + Base.isfinite(local_scale) && (theta_scale = Base.max(theta_scale, local_scale)) + end + end + return theta_scale > 0.0 ? theta_scale : fallback +end + function prepare_ballooning_coefficients( flux_surface_index::Int, plasma_eq::Equilibrium.PlasmaEquilibrium; @@ -491,6 +515,13 @@ function prepare_ballooning_coefficients( bf_fs[:, 6] = jac_chiprime bf_fs[:, 7] = pprime_chiprime + theta_scale = _ballooning_theta_scale( + nabla_beta_sq_b_sq_periodic, + nabla_beta_sq_b_sq_peculiar_1st, + nabla_beta_sq_b_sq_peculiar_2nd + ) + theta_max = min(BALLOONING_THETA_MAX_CAP, BALLOONING_THETA_SCALE_MULTIPLIER * theta_scale) + sigma = .-(two_pi_f .* pressure_gradient .* q_derivative) ./ (chi_prime^2 .* bsq) m0_12 = jac_chiprime ./ nabla_beta_sq_b_sq_peculiar_2nd @@ -512,7 +543,11 @@ function prepare_ballooning_coefficients( d0bar[2, 2] = n0_int[4] @views bf_fs[end, :] .= bf_fs[1, :] - ode_coefficient_spline = (xs=theta_grid, itp=cubic_interp(theta_grid, Series(bf_fs); bc=PeriodicBC())) + ode_coefficient_spline = ( + xs=theta_grid, + itp=cubic_interp(theta_grid, Series(bf_fs); bc=PeriodicBC()), + theta_max=theta_max + ) return ( ode_coefficient_spline=ode_coefficient_spline, @@ -1095,12 +1130,11 @@ Computes Delta' = (y'/y)_right - (y'/y)_left. function integrate_ballooning_ode(ode_coefficient_spline; theta_k::Float64=0.0) TOLERANCE = 1e-8 MINIMUM_STEP = 1e-10 - MATCHING_POINT = 1e-3 - THETA_MAX0 = 16.5 + theta_max = max(ode_coefficient_spline.theta_max, 10.0 * MATCHING_POINT) - theta_start_left = -THETA_MAX0 + theta_start_left = -theta_max theta_end_left = -MATCHING_POINT - theta_start_right = THETA_MAX0 + theta_start_right = theta_max theta_end_right = MATCHING_POINT initial_condition_left = SVector(0.0, 1.0) diff --git a/src/ForceFreeStates/ForceFreeStatesStructs.jl b/src/ForceFreeStates/ForceFreeStatesStructs.jl index 337eb158b..313faa90e 100644 --- a/src/ForceFreeStates/ForceFreeStatesStructs.jl +++ b/src/ForceFreeStates/ForceFreeStatesStructs.jl @@ -214,7 +214,6 @@ A mutable struct containing control parameters for stability analysis, set by th - `nn_high::Int` - Upper bound for toroidal modes - `delta_mlow::Int` - Expands lower bound of Fourier harmonics by delta_mlow - `delta_mhigh::Int` - Expands upper bound of Fourier harmonics by delta_mhigh - - `thmax0::Float64` - Maximum integration step size (not yet implemented) - `nstep::Int` - Maximum number of integration steps (not yet implemented) - `ksing::Int` - Singular surface handling parameter - `eulerlagrange_tolerance::Float64` - Relative tolerance for ODE integration of Euler-Lagrange equations @@ -259,7 +258,6 @@ A mutable struct containing control parameters for stability analysis, set by th nn_high::Int = 0 delta_mlow::Int = 0 delta_mhigh::Int = 0 - thmax0::Float64 = 1.0 nstep::Int = typemax(Int) ksing::Int = -1 eulerlagrange_tolerance::Float64 = 1e-8 diff --git a/test/test_data/regression_solovev_ideal_example/gpec.toml b/test/test_data/regression_solovev_ideal_example/gpec.toml index 1f0ea6896..e0b346777 100644 --- a/test/test_data/regression_solovev_ideal_example/gpec.toml +++ b/test/test_data/regression_solovev_ideal_example/gpec.toml @@ -40,7 +40,6 @@ nn_high = 1 # Largest toroidal mode number to include delta_mlow = 0 # Expands lower bound of Fourier harmonics delta_mhigh = 0 # Expands upper bound of Fourier harmonics mthvac = 64 # Number of points used in splines over poloidal angle at the plasma-vacuum interface -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds kinetic_source = "fixed" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model kinetic_factor = 0.0 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode) diff --git a/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml b/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml index 94ad3a1de..02e3fcd1a 100644 --- a/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml +++ b/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml @@ -40,7 +40,6 @@ nn_high = 2 # Largest toroidal mode number to include delta_mlow = 0 # Expands lower bound of Fourier harmonics delta_mhigh = 0 # Expands upper bound of Fourier harmonics mthvac = 64 # Number of points used in splines over poloidal angle at the plasma-vacuum interface -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds kinetic_source = "fixed" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model kinetic_factor = 0.0 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode) diff --git a/test/test_data/regression_solovev_kinetic_calculated/gpec.toml b/test/test_data/regression_solovev_kinetic_calculated/gpec.toml index a672da714..272249973 100644 --- a/test/test_data/regression_solovev_kinetic_calculated/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_calculated/gpec.toml @@ -41,7 +41,6 @@ nn_high = 1 # Largest toroidal mode number to include delta_mlow = 0 # Expands lower bound of Fourier harmonics delta_mhigh = 0 # Expands upper bound of Fourier harmonics mthvac = 64 # Number of points used in splines over poloidal angle at the plasma-vacuum interface -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds kinetic_source = "calculated" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model kinetic_factor = 1.0 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode; 1.0 = full strength) diff --git a/test/test_data/regression_solovev_kinetic_example/gpec.toml b/test/test_data/regression_solovev_kinetic_example/gpec.toml index 032114237..8f3369c17 100644 --- a/test/test_data/regression_solovev_kinetic_example/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_example/gpec.toml @@ -40,7 +40,6 @@ nn_high = 1 # Largest toroidal mode number to include delta_mlow = 0 # Expands lower bound of Fourier harmonics delta_mhigh = 0 # Expands upper bound of Fourier harmonics mthvac = 64 # Number of points used in splines over poloidal angle at the plasma-vacuum interface -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds kinetic_source = "fixed" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model kinetic_factor = 1e-9 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode; tiny value just exercises the path) diff --git a/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml b/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml index 922ceafbf..e318749fb 100644 --- a/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml @@ -40,7 +40,6 @@ nn_high = 2 # Largest toroidal mode number to include delta_mlow = 0 # Expands lower bound of Fourier harmonics delta_mhigh = 0 # Expands upper bound of Fourier harmonics mthvac = 64 # Number of points used in splines over poloidal angle at the plasma-vacuum interface -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds kinetic_source = "fixed" # Kinetic matrix source: "fixed" test matrices, or "calculated" from the kinetic NTV model kinetic_factor = 1e-9 # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode; tiny value just exercises the path) diff --git a/test/test_data/regression_solovev_kinetic_nuzero/gpec.toml b/test/test_data/regression_solovev_kinetic_nuzero/gpec.toml index dde7997e2..f374c5356 100644 --- a/test/test_data/regression_solovev_kinetic_nuzero/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_nuzero/gpec.toml @@ -39,7 +39,6 @@ nn_high = 1 # Largest toroidal mode number to include delta_mlow = 0 # Expands lower bound of Fourier harmonics delta_mhigh = 0 # Expands upper bound of Fourier harmonics mthvac = 64 # Number of points used in splines over poloidal angle at plasma-vacuum interface. -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds kinetic_source = "calculated" # Kinetic matrix source — exercises KineticForces.compute_calculated_kinetic_matrices callback with real physics kinetic_factor = 1.0 # Full-strength kinetic matrices (the "calculated" path is the real physics; no perturbation scaling) From 6292783f51780a779aa39fced21a45912ea5d3c5 Mon Sep 17 00:00:00 2001 From: logan-nc <6198372+logan-nc@users.noreply.github.com> Date: Thu, 2 Jul 2026 18:48:51 -0400 Subject: [PATCH 125/135] EQUIL - IMPROVEMENT - Scope custom-Jacobian knobs to jac_custom_power_* Rename the custom Jacobian selector jac_type = "other" to "custom" and add user-facing jac_custom_power_bp/b/r/rc inputs to EquilibriumConfig, read only when jac_type = "custom". Named types (hamada/pest/boozer/equal_arc/park) keep forcing the internal power_* exponents; downstream Jacobian formulas are unchanged and still read the internal power_* fields as the single source of truth. The four power_* constructor slots are now derived-only (marked `_`). Deprecate power_bp/power_b/power_r/power_rc as [Equilibrium] TOML input keys by reusing the centralized deprecation mechanism: generalize _drop_deprecated_ffs_keys! to _drop_deprecated_keys!(table, keys, section) and add _DEPRECATED_EQUIL_KEYS, applied on both the gpec.toml and h5-replay input paths. A stale power_* key now warns loudly and is dropped instead of silently overriding the coordinate system. Also fix the _DEPRECATED_FFS_KEYS one-tuple bug (was a string, so the FFS deprecation never fired). Update the EquilibriumConfig docstring and conventions.md, and clean the now-inactive power_* lines out of the example/test gpec.toml files while standardizing the jac_type option-list comment. Regression: diiid_n1, solovev_n1, solovev_multi_n all 0.0e+00 diff vs develop. Closes #288 Co-Authored-By: Claude Opus 4.8 (1M context) --- docs/src/conventions.md | 5 +-- .../gpec.toml | 5 +-- .../gpec.toml | 5 +-- examples/DIIID-like_ideal_example/gpec.toml | 2 +- .../DIIID-like_ideal_example_IMAS/gpec.toml | 2 +- examples/LAR_beta_scan/gpec.toml | 2 +- examples/LAR_epsilon_scan/gpec.toml | 2 +- examples/Solovev_ideal_example/gpec.toml | 2 +- examples/Solovev_ideal_example_3D/gpec.toml | 2 +- .../Solovev_ideal_example_multi_n/gpec.toml | 2 +- .../single_n_1/gpec.toml | 2 +- .../single_n_2/gpec.toml | 2 +- .../gpec.toml | 5 +-- examples/a10_kinetic_example/gpec.toml | 2 +- src/Equilibrium/EquilibriumTypes.jl | 33 +++++++++++++++---- src/GeneralizedPerturbedEquilibrium.jl | 16 +++++---- src/Rerun.jl | 1 + .../gpec.toml | 2 +- .../gpec.toml | 2 +- .../gpec.toml | 2 +- .../gpec.toml | 2 +- .../gpec.toml | 2 +- .../gpec.toml | 5 +-- 23 files changed, 58 insertions(+), 47 deletions(-) diff --git a/docs/src/conventions.md b/docs/src/conventions.md index 268fde014..e5b6c4c91 100644 --- a/docs/src/conventions.md +++ b/docs/src/conventions.md @@ -84,8 +84,9 @@ field magnitude, ``B`` is the total field magnitude, ``R`` is the major radius, The powers are set automatically from `jac_type` (`EquilibriumConfig` in `src/Equilibrium/EquilibriumTypes.jl`) and applied in the field-line Jacobian -(`direct_fieldline_der!` in `src/Equilibrium/DirectEquilibrium.jl`). Setting `jac_type = "other"` -lets you specify the four exponents manually. +(`direct_fieldline_der!` in `src/Equilibrium/DirectEquilibrium.jl`). Setting `jac_type = "custom"` +lets you specify the four exponents manually via `jac_custom_power_bp`, `jac_custom_power_b`, +`jac_custom_power_r`, and `jac_custom_power_rc`. ## Helicity and Handedness diff --git a/examples/DIIID-like_gal_resistive_example/gpec.toml b/examples/DIIID-like_gal_resistive_example/gpec.toml index 4a816e509..1b4cb4085 100644 --- a/examples/DIIID-like_gal_resistive_example/gpec.toml +++ b/examples/DIIID-like_gal_resistive_example/gpec.toml @@ -1,10 +1,7 @@ [Equilibrium] eq_filename = "TkMkr_D3Dlike_Hmode.geqdsk" # Path to equilibrium file eq_type = "efit" # Type of the input 2D equilibrium file -jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc) -power_bp = 0 # Poloidal field power exponent for Jacobian -power_b = 0 # Toroidal field power exponent for Jacobian -power_r = 0 # Major radius power exponent for Jacobian +jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom) grid_type = "ldp" # Radial grid packing type (ldp = linear-derivative packing toward rationals) psilow = 1e-4 # Lower limit of normalized flux coordinate psihigh = 0.993 # Upper limit of normalized flux coordinate (0.993 stays clear of the separatrix; truncating at ≳0.998 is numerically unreasonable here) diff --git a/examples/DIIID-like_gal_resistive_pe_example/gpec.toml b/examples/DIIID-like_gal_resistive_pe_example/gpec.toml index 66345e633..6f33ccd78 100644 --- a/examples/DIIID-like_gal_resistive_pe_example/gpec.toml +++ b/examples/DIIID-like_gal_resistive_pe_example/gpec.toml @@ -1,10 +1,7 @@ [Equilibrium] eq_filename = "TkMkr_D3Dlike_Hmode.geqdsk" # Path to equilibrium file eq_type = "efit" # Type of the input 2D equilibrium file -jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc) -power_bp = 0 # Poloidal field power exponent for Jacobian -power_b = 0 # Toroidal field power exponent for Jacobian -power_r = 0 # Major radius power exponent for Jacobian +jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom) grid_type = "ldp" # Radial grid packing type (ldp = linear-derivative packing toward rationals) psilow = 1e-4 # Lower limit of normalized flux coordinate psihigh = 0.993 # Upper limit of normalized flux coordinate (0.993 stays clear of the separatrix; truncating at ≳0.998 is numerically unreasonable here) diff --git a/examples/DIIID-like_ideal_example/gpec.toml b/examples/DIIID-like_ideal_example/gpec.toml index ed99887ab..8eec16492 100644 --- a/examples/DIIID-like_ideal_example/gpec.toml +++ b/examples/DIIID-like_ideal_example/gpec.toml @@ -6,7 +6,7 @@ [Equilibrium] eq_filename = "TkMkr_D3Dlike_Hmode.geqdsk" # Path to equilibrium file eq_type = "efit" # Type of the input 2D equilibrium file -jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) +jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom) grid_type = "log_asymptotic" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized poloidal flux psihigh = 0.9995 # Upper limit of normalized poloidal flux diff --git a/examples/DIIID-like_ideal_example_IMAS/gpec.toml b/examples/DIIID-like_ideal_example_IMAS/gpec.toml index dbf4f872a..95591980f 100644 --- a/examples/DIIID-like_ideal_example_IMAS/gpec.toml +++ b/examples/DIIID-like_ideal_example_IMAS/gpec.toml @@ -10,7 +10,7 @@ [Equilibrium] eq_type = "imas" # Type of the input 2D equilibrium file eq_filename = "from_dd" # Path to equilibrium file (placeholder: equilibrium comes from the runtime dd argument) -jac_type = "boozer" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) +jac_type = "boozer" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom) psilow = 0.01 # Lower limit of normalized poloidal flux psihigh = 0.9995 # Upper limit of normalized poloidal flux mpsi = 128 # Number of radial grid points (0 = auto-compute from psi_accuracy) diff --git a/examples/LAR_beta_scan/gpec.toml b/examples/LAR_beta_scan/gpec.toml index c4d1f3162..0add35a3e 100644 --- a/examples/LAR_beta_scan/gpec.toml +++ b/examples/LAR_beta_scan/gpec.toml @@ -9,7 +9,7 @@ [Equilibrium] eq_type = "tj_analytic" # TJ-analytic model (inverse pipeline; Fitzpatrick https://github.com/rfitzp/TJ) -jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) +jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom) grid_type = "ldp" # Radial grid packing type psilow = 0.01 # Lower limit of normalized poloidal flux psihigh = 0.995 # Upper limit of normalized poloidal flux diff --git a/examples/LAR_epsilon_scan/gpec.toml b/examples/LAR_epsilon_scan/gpec.toml index 0c8fceb3c..c8706ac95 100644 --- a/examples/LAR_epsilon_scan/gpec.toml +++ b/examples/LAR_epsilon_scan/gpec.toml @@ -9,7 +9,7 @@ [Equilibrium] eq_type = "tj_analytic" # TJ-analytic model (inverse pipeline; overridden to "tj_analytic_direct" by run_scan.jl) -jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) +jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom) grid_type = "ldp" # Radial grid packing type psilow = 0.01 # Lower limit of normalized poloidal flux psihigh = 0.995 # Upper limit of normalized poloidal flux diff --git a/examples/Solovev_ideal_example/gpec.toml b/examples/Solovev_ideal_example/gpec.toml index d9fc70d23..ea638b833 100644 --- a/examples/Solovev_ideal_example/gpec.toml +++ b/examples/Solovev_ideal_example/gpec.toml @@ -5,7 +5,7 @@ [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file -jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) +jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized poloidal flux psihigh = 0.9995 # Upper limit of normalized poloidal flux diff --git a/examples/Solovev_ideal_example_3D/gpec.toml b/examples/Solovev_ideal_example_3D/gpec.toml index 3d1caa78d..87375c04e 100644 --- a/examples/Solovev_ideal_example_3D/gpec.toml +++ b/examples/Solovev_ideal_example_3D/gpec.toml @@ -4,7 +4,7 @@ [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file -jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) +jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized poloidal flux psihigh = 0.9995 # Upper limit of normalized poloidal flux diff --git a/examples/Solovev_ideal_example_multi_n/gpec.toml b/examples/Solovev_ideal_example_multi_n/gpec.toml index b17ab0439..edfc42f45 100644 --- a/examples/Solovev_ideal_example_multi_n/gpec.toml +++ b/examples/Solovev_ideal_example_multi_n/gpec.toml @@ -5,7 +5,7 @@ [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file -jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) +jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized poloidal flux psihigh = 0.9995 # Upper limit of normalized poloidal flux diff --git a/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml b/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml index 650cfe314..d262b026a 100644 --- a/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml +++ b/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml @@ -4,7 +4,7 @@ [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file -jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) +jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized poloidal flux psihigh = 0.9995 # Upper limit of normalized poloidal flux diff --git a/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml b/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml index e95f0cc94..bd71d3d57 100644 --- a/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml +++ b/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml @@ -4,7 +4,7 @@ [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file -jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) +jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized poloidal flux psihigh = 0.9995 # Upper limit of normalized poloidal flux diff --git a/examples/Solovev_kinetic_calculated_example/gpec.toml b/examples/Solovev_kinetic_calculated_example/gpec.toml index ea3913fe8..4a46bdb42 100644 --- a/examples/Solovev_kinetic_calculated_example/gpec.toml +++ b/examples/Solovev_kinetic_calculated_example/gpec.toml @@ -1,10 +1,7 @@ [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file eq_filename = "sol.toml" # Path to equilibrium file -jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc) -power_bp = 0 # Poloidal field power exponent for Jacobian -power_b = 0 # Toroidal field power exponent for Jacobian -power_r = 0 # Major radius power exponent for Jacobian +jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized flux coordinate psihigh = 0.9995 # Upper limit of normalized flux coordinate diff --git a/examples/a10_kinetic_example/gpec.toml b/examples/a10_kinetic_example/gpec.toml index 40d29c08b..9601034af 100644 --- a/examples/a10_kinetic_example/gpec.toml +++ b/examples/a10_kinetic_example/gpec.toml @@ -9,7 +9,7 @@ [Equilibrium] eq_filename = "fix_a100_k10_q2_bn010_prof1" # Path to equilibrium file eq_type = "efit" # Type of the input 2D equilibrium file -jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) +jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom) grid_type = "ldp" # Radial grid packing type psilow = 1e-3 # Lower limit of normalized poloidal flux psihigh = 0.99 # Upper limit of normalized poloidal flux diff --git a/src/Equilibrium/EquilibriumTypes.jl b/src/Equilibrium/EquilibriumTypes.jl index 6fa0d9afd..515e1f4db 100644 --- a/src/Equilibrium/EquilibriumTypes.jl +++ b/src/Equilibrium/EquilibriumTypes.jl @@ -12,11 +12,15 @@ Bundles all necessary settings originally specified in the equil fortran namelis - `eq_type::String` - Type of equilibrium file ("efit", "solovev", "lar", etc.) - `eq_filename::String` - Path to equilibrium input file - - `jac_type::String` - Jacobian coordinate type ("hamada", "pest", "equal_arc", "boozer", "park", "other") - - `power_bp::Int` - Poloidal field power exponent for Jacobian - - `power_b::Int` - Total field power exponent for Jacobian - - `power_r::Int` - Major radius power exponent for Jacobian - - `power_rc::Int` - Minor radius (rfac = √((R-R₀)²+(Z-Z₀)²)) power exponent for Jacobian + - `jac_type::String` - Jacobian coordinate type ("hamada", "pest", "equal_arc", "boozer", "park", "custom") + - `power_bp::Int` - Poloidal field power exponent for Jacobian (internal, derived from `jac_type`; deprecated as a TOML input key) + - `power_b::Int` - Total field power exponent for Jacobian (internal, derived from `jac_type`; deprecated as a TOML input key) + - `power_r::Int` - Major radius power exponent for Jacobian (internal, derived from `jac_type`; deprecated as a TOML input key) + - `power_rc::Int` - Minor radius (rfac = √((R-R₀)²+(Z-Z₀)²)) power exponent for Jacobian (internal, derived from `jac_type`; deprecated as a TOML input key) + - `jac_custom_power_bp::Int` - Poloidal-field exponent for a custom Jacobian `J = Bp^bp · B^b / (R^r · rfac^rc)`; read only when `jac_type = "custom"`, ignored for named types + - `jac_custom_power_b::Int` - Total-field exponent for a custom Jacobian; read only when `jac_type = "custom"`, ignored for named types + - `jac_custom_power_r::Int` - Major-radius exponent for a custom Jacobian; read only when `jac_type = "custom"`, ignored for named types + - `jac_custom_power_rc::Int` - Minor-radius (rfac) exponent for a custom Jacobian; read only when `jac_type = "custom"`, ignored for named types - `r0exp::Float64` - Major radius normalization for CHEASE/EQDSK [m] - `b0exp::Float64` - On-axis toroidal field normalization for CHEASE/EQDSK [T] - `grid_type::String` - Grid type for flux surface discretization ("log_asymptotic", "ldp", "pow1") @@ -42,6 +46,11 @@ Bundles all necessary settings originally specified in the equil fortran namelis power_r::Int = 0 power_rc::Int = 0 + jac_custom_power_bp::Int = 0 + jac_custom_power_b::Int = 0 + jac_custom_power_r::Int = 0 + jac_custom_power_rc::Int = 0 + grid_type::String = "log_asymptotic" psilow::Float64 = 1e-2 psihigh::Float64 = 0.9995 @@ -61,7 +70,11 @@ Bundles all necessary settings originally specified in the equil fortran namelis """ Modified internal constructor that enforces self consistency within the inputs """ - function EquilibriumConfig(eq_type, eq_filename, r0exp, b0exp, jac_type, power_bp, power_b, power_r, power_rc, + # The four `_` slots are the `power_bp/power_b/power_r/power_rc` struct fields, which @kwdef + # forwards positionally. They are always derived below from `jac_type` (or `jac_custom_power_*`), + # so their incoming values are ignored (hence `_`). + function EquilibriumConfig(eq_type, eq_filename, r0exp, b0exp, jac_type, _, _, _, _, + jac_custom_power_bp, jac_custom_power_b, jac_custom_power_r, jac_custom_power_rc, grid_type, psilow, psihigh, mpsi, psi_accuracy, mtheta, newq0, etol, force_termination, use_galgrid, imas_cocos) if jac_type == "hamada" @@ -94,7 +107,12 @@ Bundles all necessary settings originally specified in the equil fortran namelis power_bp = 0 power_r = 0 power_rc = 0 - elseif jac_type == "other" + elseif jac_type == "custom" + # Custom Jacobian: the user-facing knobs define the exponents. + power_bp = jac_custom_power_bp + power_b = jac_custom_power_b + power_r = jac_custom_power_r + power_rc = jac_custom_power_rc # Normalize to a named type when the powers match, so fast paths are taken. if power_b == 0 && power_bp == 0 && power_r == 0 && power_rc == 0 jac_type = "hamada" @@ -122,6 +140,7 @@ Bundles all necessary settings originally specified in the equil fortran namelis end psihigh = min(psihigh, 1.0) return new(eq_type, eq_filename, r0exp, b0exp, jac_type, power_bp, power_b, power_r, power_rc, + jac_custom_power_bp, jac_custom_power_b, jac_custom_power_r, jac_custom_power_rc, grid_type, psilow, psihigh, mpsi, psi_accuracy, mtheta, newq0, etol, force_termination, use_galgrid, imas_cocos) end diff --git a/src/GeneralizedPerturbedEquilibrium.jl b/src/GeneralizedPerturbedEquilibrium.jl index 51bd422b4..e7ecef8a7 100755 --- a/src/GeneralizedPerturbedEquilibrium.jl +++ b/src/GeneralizedPerturbedEquilibrium.jl @@ -59,14 +59,15 @@ using .ForceFreeStates: find_kinetic_singular_surfaces! using .ForceFreeStates: eulerlagrange_integration, free_run! using .ForceFreeStates: galerkin_solve, write_galerkin!, GalerkinResult, gal_matched_odestate -const _DEPRECATED_FFS_KEYS = ("mer_flag") +const _DEPRECATED_FFS_KEYS = ("mer_flag",) +const _DEPRECATED_EQUIL_KEYS = ("power_bp", "power_b", "power_r", "power_rc") -# Drop deprecated [ForceFreeStates] keys so legacy gpec.toml files -# keep parsing instead of throwing an unknown-keyword error. -function _drop_deprecated_ffs_keys!(table) - for k in _DEPRECATED_FFS_KEYS +# Drop deprecated keys from a parsed gpec.toml section so legacy files keep parsing +# instead of throwing an unknown-keyword error; warn so the removal is not silent. +function _drop_deprecated_keys!(table, deprecated_keys, section::String) + for k in deprecated_keys if haskey(table, k) - @warn "`$k` in [ForceFreeStates] is deprecated and ignored please remove it from gpec.toml." + @warn "`$k` in [$section] is deprecated and ignored; please remove it from gpec.toml." delete!(table, k) end end @@ -111,6 +112,7 @@ function build_inputs_from_toml(path::String; dd::Union{IMASdd.dd,Nothing}=nothi inputs = TOML.parsefile(joinpath(path, "gpec.toml")) haskey(inputs, "Equilibrium") || error("No [Equilibrium] section in gpec.toml") + _drop_deprecated_keys!(inputs["Equilibrium"], _DEPRECATED_EQUIL_KEYS, "Equilibrium") eq_config = Equilibrium.EquilibriumConfig(inputs["Equilibrium"], path) # An equilibrium is analytic (sol/lar/tj, parameters from its embedded section), @@ -169,7 +171,7 @@ function main_from_inputs( # Build data structures from inputs intr = ForceFreeStatesInternal(; dir_path=path) ffs_table = inputs["ForceFreeStates"] - _drop_deprecated_ffs_keys!(ffs_table) + _drop_deprecated_keys!(ffs_table, _DEPRECATED_FFS_KEYS, "ForceFreeStates") ctrl = ForceFreeStatesControl(; (Symbol(k) => v for (k, v) in ffs_table)...) equil = Equilibrium.setup_equilibrium(eq_config, additional_input) diff --git a/src/Rerun.jl b/src/Rerun.jl index 0ca1ea1e7..2a5a81237 100644 --- a/src/Rerun.jl +++ b/src/Rerun.jl @@ -266,6 +266,7 @@ function build_inputs_from_h5(args::Vector{String}) " source: $(abspath(source_h5))\n" * " output: $(abspath(joinpath(output_dir, output_name)))\n$_BANNER" + _drop_deprecated_keys!(inputs["Equilibrium"], _DEPRECATED_EQUIL_KEYS, "Equilibrium") eq_config = Equilibrium.EquilibriumConfig(inputs["Equilibrium"], output_dir) # Clear eq_filename: unused on replay, and a stale absolute path could mislead downstream code. eq_config.eq_filename = "" diff --git a/test/test_data/regression_solovev_ideal_example/gpec.toml b/test/test_data/regression_solovev_ideal_example/gpec.toml index e0b346777..1b9a5b622 100644 --- a/test/test_data/regression_solovev_ideal_example/gpec.toml +++ b/test/test_data/regression_solovev_ideal_example/gpec.toml @@ -4,7 +4,7 @@ [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file -jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) +jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized poloidal flux psihigh = 0.9995 # Upper limit of normalized poloidal flux diff --git a/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml b/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml index 02e3fcd1a..681464062 100644 --- a/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml +++ b/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml @@ -4,7 +4,7 @@ [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file -jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) +jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized poloidal flux psihigh = 0.9995 # Upper limit of normalized poloidal flux diff --git a/test/test_data/regression_solovev_kinetic_calculated/gpec.toml b/test/test_data/regression_solovev_kinetic_calculated/gpec.toml index 272249973..086f5e758 100644 --- a/test/test_data/regression_solovev_kinetic_calculated/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_calculated/gpec.toml @@ -4,7 +4,7 @@ [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file -jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) +jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized poloidal flux psihigh = 0.9995 # Upper limit of normalized poloidal flux diff --git a/test/test_data/regression_solovev_kinetic_example/gpec.toml b/test/test_data/regression_solovev_kinetic_example/gpec.toml index 8f3369c17..e6ee442f7 100644 --- a/test/test_data/regression_solovev_kinetic_example/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_example/gpec.toml @@ -4,7 +4,7 @@ [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file -jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) +jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized poloidal flux psihigh = 0.9995 # Upper limit of normalized poloidal flux diff --git a/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml b/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml index e318749fb..9a904296f 100644 --- a/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_multi_n/gpec.toml @@ -4,7 +4,7 @@ [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file -jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, other) +jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized poloidal flux psihigh = 0.9995 # Upper limit of normalized poloidal flux diff --git a/test/test_data/regression_solovev_kinetic_nuzero/gpec.toml b/test/test_data/regression_solovev_kinetic_nuzero/gpec.toml index f374c5356..6d3b5b9b9 100644 --- a/test/test_data/regression_solovev_kinetic_nuzero/gpec.toml +++ b/test/test_data/regression_solovev_kinetic_nuzero/gpec.toml @@ -1,9 +1,6 @@ [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file -jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc) -power_bp = 0 # Poloidal field power exponent for Jacobian -power_b = 0 # Toroidal field power exponent for Jacobian -power_r = 0 # Major radius power exponent for Jacobian +jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized flux coordinate psihigh = 0.9995 # Upper limit of normalized flux coordinate From e9337a046540d5fd8df7d6ca1390971c7d3bf6ee Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Mon, 6 Jul 2026 14:55:00 -0400 Subject: [PATCH 126/135] EQUIL - MINOR - Update kinetic profile file parsing docstring to include HDF5 format --- src/Equilibrium/KineticProfiles.jl | 13 +++++++------ 1 file changed, 7 insertions(+), 6 deletions(-) diff --git a/src/Equilibrium/KineticProfiles.jl b/src/Equilibrium/KineticProfiles.jl index 413cd1503..606e24495 100644 --- a/src/Equilibrium/KineticProfiles.jl +++ b/src/Equilibrium/KineticProfiles.jl @@ -136,20 +136,21 @@ end chi1::Union{Nothing,Float64}=nothing) → KineticProfileSplines -Parse an ASCII kinetic profile file, interpolate onto a regular 101-point ψ -grid, optionally apply profile scaling knobs, derive collisional / Z_eff -diagnostics, and return a `KineticProfileSplines` with independent named cubic -splines. +Parse a kinetic profile file (ASCII or HDF5, dispatched by `read_kinetic_file`), +interpolate onto a regular 101-point ψ grid, optionally apply profile scaling +knobs, derive collisional / Z_eff diagnostics, and return a +`KineticProfileSplines` with independent named cubic splines. # Expected file format -Six whitespace-separated columns (header rows are filtered out): +An HDF5 file following the GPEC kinetic schema (fields read by name), or a legacy +six-column whitespace-separated ASCII table (header rows are filtered out): psi_n n_i[m^-3] n_e[m^-3] T_i[eV] T_e[eV] omega_E[rad/s] # Arguments - - `kinetic_file`: Path to the ASCII kinetic profile file + - `kinetic_file`: Path to the ASCII or HDF5 kinetic profile file (see `read_kinetic_file`) - `zi`, `zimp`: Main ion and impurity charge numbers - `mi`, `mimp`: Main ion and impurity mass numbers (in proton masses) - `density_factor`: Density scaling factor (applied to ni, ne) From 8eb3f638ef84be3f4714062bbe1527c6d4275e95 Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Mon, 6 Jul 2026 14:55:21 -0400 Subject: [PATCH 127/135] KineticForces - MINOR - fix some whitespace --- src/KineticForces/Torque.jl | 2 -- 1 file changed, 2 deletions(-) diff --git a/src/KineticForces/Torque.jl b/src/KineticForces/Torque.jl index fef1ad043..240358b1b 100644 --- a/src/KineticForces/Torque.jl +++ b/src/KineticForces/Torque.jl @@ -190,7 +190,6 @@ function tpsi!(tpsi_var::Ref{ComplexF64}, psi::Float64, n::Int, l::Int, wdhat = q^3 * wtran^2 / (4 * epsr * wgyro) * wdfac nueff = nu_s / (2 * epsr) - # Method selection — route on the registry dispatch tag (errors on unknown method) kind = method_kind(method) if kind == :fcgl @@ -234,7 +233,6 @@ function tpsi!(tpsi_var::Ref{ComplexF64}, psi::Float64, n::Int, l::Int, rex_override=rex_override, imx_override=imx_override) end - return nothing end From 3a3d50d0a78cafc9e71daff9b8f5187489911e48 Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Wed, 8 Jul 2026 11:56:34 -0400 Subject: [PATCH 128/135] KineticForces - OPTIMIZATION - Implement static typing for PitchGARParams to reduce multithreading overhead and add a pre-allocated quadgk buffer --- src/KineticForces/PitchIntegration.jl | 28 +++++++++++++++++---------- 1 file changed, 18 insertions(+), 10 deletions(-) diff --git a/src/KineticForces/PitchIntegration.jl b/src/KineticForces/PitchIntegration.jl index a66091c7e..7af482581 100644 --- a/src/KineticForces/PitchIntegration.jl +++ b/src/KineticForces/PitchIntegration.jl @@ -22,7 +22,7 @@ Parameters for the GAR pitch-angle integrand. Uses a unified fbnce interpolant that returns [ωb, ωd, f₁, f₂, ...] at each λ, matching Fortran `lambdaintgrl_lsode`. """ -struct PitchGARParams +struct PitchGARParams{F} wn::Float64 # density gradient diamagnetic drift frequency wt::Float64 # temperature gradient diamagnetic drift frequency we::Float64 # electric precession frequency @@ -44,9 +44,11 @@ struct PitchGARParams rex::Float64 # real part multiplier for resonance operator imx::Float64 # imaginary part multiplier for resonance operator nqty::Int # number of flux quantities to integrate - fbnce::Any # CubicSeriesInterpolant: fbnce(λ) → [wb, wd, f₁, ...] + fbnce::F # CubicSeriesInterpolant: fbnce(λ) → [wb, wd, f₁, ...] (typed for stability) fbnce_norm::Vector{Float64} # normalization factors (1/median) fbnce_hint::Base.RefValue{Int} # sticky bracket-search hint for fbnce(λ) + fvals::Vector{ComplexF64} # reusable buffer for the in-place fbnce(fvals, λ) evaluation + esegbuf::Vector{QuadGK.Segment{Float64,ComplexF64,Float64}} # reusable energy-integral QuadGK segment buffer end @@ -84,7 +86,9 @@ function integrate_pitch_gar_quadgk( wn, wt, we, nuk, bobmax, epsr, q, ell, n, psi, method, nutype, f0type, nufac, ximag, qt, energy_atol, energy_rtol, - rex, imx, nqty, fbnce, fbnce_norm, Ref(1)) + rex, imx, nqty, fbnce, fbnce_norm, Ref(1), + Vector{ComplexF64}(undef, 2 + nqty), + QuadGK.alloc_segbuf(Float64, ComplexF64, Float64)) lambda_min = first(fbnce.cache.x) lambda_max = last(fbnce.cache.x) @@ -114,7 +118,8 @@ In-place complex-valued kernel for `quadgk!`. Writes `out[i] = fvals[i+2] * xint for i in 1..nqty. QuadGK natively handles ComplexF64. """ function _pitch_gar_kernel_quadgk!(out::Vector{ComplexF64}, lambda, p::PitchGARParams) - fvals = p.fbnce(lambda; hint=p.fbnce_hint) + p.fbnce(p.fvals, lambda; hint=p.fbnce_hint) + fvals = p.fvals wb = real(fvals[1]) wd = real(fvals[2]) @@ -127,12 +132,12 @@ function _pitch_gar_kernel_quadgk!(out::Vector{ComplexF64}, lambda, p::PitchGARP p.ell, leff, p.n, p.psi, lambda, p.method; nutype=p.nutype, f0type=p.f0type, nufac=p.nufac, ximag=p.ximag, qt=p.qt, - atol=p.energy_atol, rtol=p.energy_rtol) + atol=p.energy_atol, rtol=p.energy_rtol, segbuf=p.esegbuf) xint_counter = integrate_energy(p.wn, p.wt, p.we, wd, -wb, nueff, p.ell, leff, p.n, p.psi, lambda, p.method; nutype=p.nutype, f0type=p.f0type, nufac=p.nufac, ximag=p.ximag, qt=p.qt, - atol=p.energy_atol, rtol=p.energy_rtol) + atol=p.energy_atol, rtol=p.energy_rtol, segbuf=p.esegbuf) xint = xint_co + xint_counter else xint = integrate_energy(p.wn, p.wt, p.we, wd, wb, nueff, @@ -182,7 +187,9 @@ function integrate_pitch_gar_quadgk_wt( wn, wt, we, nuk, bobmax, epsr, q, ell, n, psi, method, nutype, f0type, nufac, ximag, qt, energy_atol, energy_rtol, - 1.0, 1.0, nqty, fbnce, fbnce_norm, Ref(1)) + 1.0, 1.0, nqty, fbnce, fbnce_norm, Ref(1), + Vector{ComplexF64}(undef, 2 + nqty), + QuadGK.alloc_segbuf(Float64, ComplexF64, Float64)) lambda_min = first(fbnce.cache.x) lambda_max = last(fbnce.cache.x) @@ -211,7 +218,8 @@ Dual-output pitch kernel. Fills a length-`2*nqty` buffer: One energy integration per λ; both halves share it. """ function _pitch_gar_kernel_quadgk_wt!(out::Vector{ComplexF64}, lambda, p::PitchGARParams) - fvals = p.fbnce(lambda; hint=p.fbnce_hint) + p.fbnce(p.fvals, lambda; hint=p.fbnce_hint) + fvals = p.fvals wb = real(fvals[1]) wd = real(fvals[2]) @@ -224,12 +232,12 @@ function _pitch_gar_kernel_quadgk_wt!(out::Vector{ComplexF64}, lambda, p::PitchG p.ell, leff, p.n, p.psi, lambda, p.method; nutype=p.nutype, f0type=p.f0type, nufac=p.nufac, ximag=p.ximag, qt=p.qt, - atol=p.energy_atol, rtol=p.energy_rtol) + atol=p.energy_atol, rtol=p.energy_rtol, segbuf=p.esegbuf) xint_counter = integrate_energy(p.wn, p.wt, p.we, wd, -wb, nueff, p.ell, leff, p.n, p.psi, lambda, p.method; nutype=p.nutype, f0type=p.f0type, nufac=p.nufac, ximag=p.ximag, qt=p.qt, - atol=p.energy_atol, rtol=p.energy_rtol) + atol=p.energy_atol, rtol=p.energy_rtol, segbuf=p.esegbuf) xint = xint_co + xint_counter else xint = integrate_energy(p.wn, p.wt, p.we, wd, wb, nueff, From de766625b0e5643832bfada3b30e6eecdbe1a5f1 Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Wed, 8 Jul 2026 11:58:28 -0400 Subject: [PATCH 129/135] KineticForces - OPTIMIZATION - Refactor resonant integrand to reduce memory allocation in QuadGK inner loop and update Energy Integration to support QuadGK buffer pre-allocation --- src/KineticForces/EnergyIntegration.jl | 58 ++++++++++++++------------ 1 file changed, 31 insertions(+), 27 deletions(-) diff --git a/src/KineticForces/EnergyIntegration.jl b/src/KineticForces/EnergyIntegration.jl index 7c441582a..05b0f9775 100644 --- a/src/KineticForces/EnergyIntegration.jl +++ b/src/KineticForces/EnergyIntegration.jl @@ -208,9 +208,32 @@ The collisionless case (ν ≡ 0, real-axis pole) is the exact ν→0⁺ limit o formula; its causal branch is carried by the signed zero of `−pole_offset` (see the add-back below), and its on-axis `0/0` window by the analytic regular-part limit. """ +# Real x-space resonant integrand with pole subtractions +# Explicit function keeps memory allocation out of the QuadGK inner loop. +@inline function _resonant_integrand(x::Float64, p::EnergyParams, + residues::Vector{ComplexF64}, x_poles::Vector{ComplexF64}, npole::Int, + leff::Float64, wb::Float64, n::Int, wd::Float64)::ComplexF64 + val = _energy_integrand_real(x, p) + @inbounds for k in 1:npole + val -= residues[k] / (x - x_poles[k]) + end + if !isfinite(val) + k = 1 + @inbounds for j in 2:npole + abs(x - real(x_poles[j])) < abs(x - real(x_poles[k])) && (k = j) + end + val = _real_pole_regular_part(real(x_poles[k]), p, leff, wb, n, wd) + @inbounds for j in 1:npole + j == k && continue + val -= residues[j] / (x - x_poles[j]) + end + end + return val +end + function _integrate_energy_resonant(p::EnergyParams, leff::Float64, wb::Float64, n::Int, we::Float64, wd::Float64, - atol::Float64, rtol::Float64)::ComplexF64 + atol::Float64, rtol::Float64, segbuf=nothing)::ComplexF64 x_res_list = find_resonance_energies(leff, wb, n, we, wd) # ≤ 2 roots of a quadratic in √x x_poles = ComplexF64[] residues = ComplexF64[] @@ -240,29 +263,10 @@ function _integrate_energy_resonant(p::EnergyParams, leff::Float64, wb::Float64, npole = length(residues) # Physical x-space integrand N(x)·exp(-x)/(i·Ω) minus the subtracted pole parts. - integrand = x -> begin - val = _energy_integrand_real(x, p) - @inbounds for k in 1:npole - val -= residues[k] / (x - x_poles[k]) - end - # At a ν=0 pole Ω rounds to 0 and the physical term is 0/0; substitute the nearest - # pole's analytic regular-part limit, keeping the other (finite) pole subtractions. - if !isfinite(val) - k = 1 - @inbounds for j in 2:npole - abs(x - real(x_poles[j])) < abs(x - real(x_poles[k])) && (k = j) - end - val = _real_pole_regular_part(real(x_poles[k]), p, leff, wb, n, wd) - @inbounds for j in 1:npole - j == k && continue - val -= residues[j] / (x - x_poles[j]) - end - end - return val - end + integrand = x -> _resonant_integrand(x, p, residues, x_poles, npole, leff, wb, n, wd) if npole == 0 - val, _ = quadgk(integrand, 0.0, X_ENERGY_MAX; atol=atol, rtol=rtol) + val, _ = quadgk(integrand, 0.0, X_ENERGY_MAX; atol=atol, rtol=rtol, segbuf=segbuf) return val end @@ -271,9 +275,9 @@ function _integrate_energy_resonant(p::EnergyParams, leff::Float64, wb::Float64, # positional args — a `breaks...` splat of a runtime-length Vector is type-unstable. breaks = unique(sort(real.(x_poles))) smooth_val, _ = if length(breaks) == 1 - quadgk(integrand, 0.0, breaks[1], X_ENERGY_MAX; atol=atol, rtol=rtol) + quadgk(integrand, 0.0, breaks[1], X_ENERGY_MAX; atol=atol, rtol=rtol, segbuf=segbuf) else - quadgk(integrand, 0.0, breaks[1], breaks[2], X_ENERGY_MAX; atol=atol, rtol=rtol) + quadgk(integrand, 0.0, breaks[1], breaks[2], X_ENERGY_MAX; atol=atol, rtol=rtol, segbuf=segbuf) end return smooth_val + pole_contribution end @@ -309,7 +313,7 @@ function integrate_energy(wn::Float64, wt::Float64, we::Float64, wd::Float64, n::Int, psi::Float64, lambda::Float64, method::String; nutype::String="harmonic", f0type::String="maxwellian", nufac::Float64=1.0, ximag::Float64=0.0, qt::Bool=false, - atol::Float64=1e-7, rtol::Float64=1e-5)::ComplexF64 + atol::Float64=1e-7, rtol::Float64=1e-5, segbuf=nothing)::ComplexF64 p = EnergyParams(wn, wt, we, wd, wb, nuk, leff, n, nutype, f0type, nufac, ximag, qt) @@ -317,13 +321,13 @@ function integrate_energy(wn::Float64, wt::Float64, we::Float64, wd::Float64, # CGL has no resonance denominator and no pole — integrate the physical # x-space integrand directly over the half line (QuadGK maps [0,∞) itself). if f0type == "cgl" - val, _ = quadgk(x -> _energy_integrand_real(x, p), 0.0, Inf; atol=atol, rtol=rtol) + val, _ = quadgk(x -> _energy_integrand_real(x, p), 0.0, Inf; atol=atol, rtol=rtol, segbuf=segbuf) return val end # Single resonant path for any collisionality: real x-space PV+residue with a # pole x_pole = x_res - i·ν/Ω′ (off-axis for ν>0, real for ν≡0). - return _integrate_energy_resonant(p, leff, wb, n, we, wd, atol, rtol) + return _integrate_energy_resonant(p, leff, wb, n, we, wd, atol, rtol, segbuf) end """ From d2c45848f87ee889df271eb0eab0695cc24b5277 Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Wed, 8 Jul 2026 15:52:49 -0400 Subject: [PATCH 130/135] KineticForces - OPTIMIZATION - Introduce BounceScratch struct for per-surface scratch buffers to reduce memory allocation during bounce-averaging computations --- src/KineticForces/BounceAveraging.jl | 115 ++++++++++++++++++++------- 1 file changed, 85 insertions(+), 30 deletions(-) diff --git a/src/KineticForces/BounceAveraging.jl b/src/KineticForces/BounceAveraging.jl index 3a75b003b..0ea808319 100644 --- a/src/KineticForces/BounceAveraging.jl +++ b/src/KineticForces/BounceAveraging.jl @@ -204,6 +204,9 @@ function compute_bounce_data( mpert = length(mfac) do_matrices = !isnothing(smat) + # Per-surface scratch, reused across all λ. + scr = BounceScratch(ntheta, mpert) + # Trapped-passing boundary and λ range lmdatpb = bo / bmax lmdamax = bo / bmin @@ -238,13 +241,13 @@ function compute_bounce_data( # Find bounce points and build θ sub-grid _, _, tdt_pts, tdt_wts = _find_bounce_points_and_grid( lmda, bo, sigma, tspl, ibmax, theta_bmax, - lmdatpb, lmdamax, psi, ntheta) + lmdatpb, lmdamax, psi, ntheta, scr) # Bounce integrals over θ (Fortran lines 674-735) wbbar, wdbar, dJdJ_val, wmats_lmda = _bounce_integrate( tdt_pts, tdt_wts, lmda, lnq, sigma, n, q, bo, tspl, chi1, ro, mfac, dbob_m_f, divx_m_f, divxfac, wdfac, - do_matrices, mpert, smat, tmat, xmat, ymat, zmat) + do_matrices, mpert, smat, tmat, xmat, ymat, zmat, scr) # Physical frequencies (Fortran lines 744-745) wb_arr[ilmda] = wbbar * bhat @@ -263,6 +266,46 @@ function compute_bounce_data( end +""" + BounceScratch(ntheta, mpert; nfine=256) + +Per-surface scratch buffers for the bounce-averaging inner loops. Allocated once in +`compute_bounce_data` and reused across every λ (each λ previously reallocated these +θ- and mode-sized arrays). Sizes are fixed for a flux surface (`ntheta` sub-grid points, +`mpert` Fourier modes), so a single set of buffers serves the whole λ sweep. Buffers that +the callers zero-initialize are `fill!`-reset per λ, preserving bit-for-bit results. +""" +struct BounceScratch + cum_wb_arr::Vector{Float64} # ntheta — cumulative bounce action + jvtheta::Vector{ComplexF64} # ntheta — action integrand + wmu_mt::Matrix{ComplexF64} # mpert × ntheta — W_μ per θ + wen_mt::Matrix{ComplexF64} # mpert × ntheta — W_E per θ + expm::Vector{ComplexF64} # mpert — Fourier basis at a θ + pl::Vector{ComplexF64} # ntheta — bounce phase factor + wmu_ba::Vector{ComplexF64} # mpert — bounce-averaged W_μ + wen_ba::Vector{ComplexF64} # mpert — bounce-averaged W_E + wmats_lmda::Vector{ComplexF64} # nqty_matrix(mpert) — packed W outer products + tspl_f::Vector{Float64} # 5 — in-place tspl(θ) evaluation + vpar_fine::Vector{Float64} # nfine+1 — v_par(θ) for bounce-point search +end + +function BounceScratch(ntheta::Int, mpert::Int; nfine::Int=256) + return BounceScratch( + Vector{Float64}(undef, ntheta), + Vector{ComplexF64}(undef, ntheta), + Matrix{ComplexF64}(undef, mpert, ntheta), + Matrix{ComplexF64}(undef, mpert, ntheta), + Vector{ComplexF64}(undef, mpert), + Vector{ComplexF64}(undef, ntheta), + Vector{ComplexF64}(undef, mpert), + Vector{ComplexF64}(undef, mpert), + Vector{ComplexF64}(undef, nqty_matrix(mpert)), + Vector{Float64}(undef, 5), + Vector{Float64}(undef, nfine + 1), + ) +end + + # ============================================================================ # Internal helpers # ============================================================================ @@ -309,21 +352,24 @@ function _find_bounce_points_and_grid( lmda::Float64, bo::Float64, sigma::Int, tspl, ::Int, theta_bmax::Float64, ::Float64, ::Float64, psi::Float64, - ntheta::Int + ntheta::Int, scr::BounceScratch ) if sigma == 0 # trapped - # Build v_par(θ) = 1 - (λ/bo)*B(θ) and find roots - # Use a dense θ grid to find zero crossings + # Build v_par(θ) = 1 - (λ/bo)*B(θ) and find roots on a dense θ grid. nfine = 256 theta_fine = range(0.0, 1.0, length=nfine+1) - vpar_fine = [1.0 - (lmda / bo) * tspl(mod(θ, 1.0))[1] for θ in theta_fine] + vpar_fine = scr.vpar_fine + @inbounds for i in 1:(nfine+1) + tspl(scr.tspl_f, mod(theta_fine[i], 1.0)) + vpar_fine[i] = 1.0 - (lmda / bo) * scr.tspl_f[1] + end # Find zero crossings bpts = Float64[] for i in 1:nfine if vpar_fine[i] * vpar_fine[i+1] < 0 # Bisect for better accuracy - θ_root = _bisect_vpar(tspl, lmda, bo, theta_fine[i], theta_fine[i+1]) + θ_root = _bisect_vpar(tspl, scr.tspl_f, lmda, bo, theta_fine[i], theta_fine[i+1]) push!(bpts, θ_root) end end @@ -339,7 +385,7 @@ function _find_bounce_points_and_grid( t2 = bpts[1] + 1.0 else # Find deepest potential well (Fortran lines 616-639) - t1, t2 = _find_deepest_well(bpts, tspl, lmda, bo) + t1, t2 = _find_deepest_well(bpts, tspl, scr.tspl_f, lmda, bo) end # Power-law grid refined near bounce points @@ -381,11 +427,13 @@ this routine does not check, it just halves toward the sign change. # Returns - `θ::Float64`: the converged (or capped) bounce-point angle. """ -function _bisect_vpar(tspl, lmda::Float64, bo::Float64, θa::Float64, θb::Float64; tol=1e-12, maxiter=50) - va = 1.0 - (lmda / bo) * tspl(mod(θa, 1.0))[1] +function _bisect_vpar(tspl, tspl_f::Vector{Float64}, lmda::Float64, bo::Float64, θa::Float64, θb::Float64; tol=1e-12, maxiter=50) + tspl(tspl_f, mod(θa, 1.0)) + va = 1.0 - (lmda / bo) * tspl_f[1] for _ in 1:maxiter θm = 0.5 * (θa + θb) - vm = 1.0 - (lmda / bo) * tspl(mod(θm, 1.0))[1] + tspl(tspl_f, mod(θm, 1.0)) + vm = 1.0 - (lmda / bo) * tspl_f[1] if abs(vm) < tol || (θb - θa) < tol return θm end @@ -404,7 +452,7 @@ end Find deepest potential well among bounce point pairs. Ports Fortran lines 616-639. """ -function _find_deepest_well(bpts::Vector{Float64}, tspl, lmda::Float64, bo::Float64) +function _find_deepest_well(bpts::Vector{Float64}, tspl, tspl_f::Vector{Float64}, lmda::Float64, bo::Float64) nbpts = length(bpts) best_vpar = 0.0 best_t1 = 0.0 @@ -418,7 +466,8 @@ function _find_deepest_well(bpts::Vector{Float64}, tspl, lmda::Float64, bo::Floa else θmid = 0.5 * (bpts[i] + bpts[j]) end - vpar_mid = 1.0 - (lmda / bo) * tspl(mod(θmid, 1.0))[1] + tspl(tspl_f, mod(θmid, 1.0)) + vpar_mid = 1.0 - (lmda / bo) * tspl_f[1] if vpar_mid > best_vpar best_t1 = bpts[i] best_t2 = bpts[j] @@ -451,7 +500,7 @@ function _bounce_integrate( mfac::Vector{Int}, dbob_m_f::Vector{ComplexF64}, divx_m_f::Vector{ComplexF64}, divxfac::Float64, wdfac::Float64, do_matrices::Bool, mpert::Int, - smat, tmat, xmat, ymat, zmat + smat, tmat, xmat, ymat, zmat, scr::BounceScratch ) ntheta = length(tdt_pts) theta0 = tdt_pts[1] @@ -460,23 +509,27 @@ function _bounce_integrate( cum_wb = 0.0 cum_wd = 0.0 - # θ-scratch array allocated fresh each call. Pool-based reuse was tried - # (AdaptiveArrayPools) but showed no speedup and introduced severe slowdowns - # at 2+ threads; plain allocations match Fortran baseline behavior. - cum_wb_arr = zeros(Float64, ntheta) + # θ-scratch arrays reused across λ from the per-surface BounceScratch. Zero-reset + # the ones the loop populates only partially (i in 2:ntheta-1, with continue/break), + # so unwritten entries stay 0 exactly as the previous `zeros(...)` did. + cum_wb_arr = scr.cum_wb_arr + fill!(cum_wb_arr, 0.0) # Action integrand - jvtheta = zeros(ComplexF64, ntheta) + jvtheta = scr.jvtheta + fill!(jvtheta, ComplexF64(0.0)) # W vectors for matrix path - wmu_mt = do_matrices ? zeros(ComplexF64, mpert, ntheta) : nothing - wen_mt = do_matrices ? zeros(ComplexF64, mpert, ntheta) : nothing + wmu_mt = scr.wmu_mt + wen_mt = scr.wen_mt + if do_matrices + fill!(wmu_mt, ComplexF64(0.0)) + fill!(wen_mt, ComplexF64(0.0)) + end - # Pre-allocated scratch for hot-loop tspl evaluation + Fourier-basis buffer - # (avoids Vector{Float64}(5) + Vector{ComplexF64}(mpert) allocation per θ - # sub-grid point — previously ~256 allocs × 126 inner iters per call). - tspl_f = Vector{Float64}(undef, 5) - expm = Vector{ComplexF64}(undef, mpert) + # Scratch for hot-loop tspl evaluation + Fourier-basis buffer (fully written per use). + tspl_f = scr.tspl_f + expm = scr.expm for i in 2:ntheta-1 # Edge weights are 0 from powspace θ = tdt_pts[i] @@ -579,7 +632,7 @@ function _bounce_integrate( one_minus_sigma = 1 - sigma bj_integral = ComplexF64(0.0) if do_matrices - pl = Vector{ComplexF64}(undef, ntheta) + pl = scr.pl @inbounds for i in 1:ntheta pl[i] = cis(-twopi * lnq * cum_wb_arr[i] * nrm / pl_denom) end @@ -606,8 +659,10 @@ function _bounce_integrate( # Bounce-average W_μ and W_E vectors (Fortran lines 762-767). # Trapezoidal quadrature: boundary samples weighted by 0.5 (wmu_mt and wen_mt # are zero at i=1 and i=ntheta from the 2:ntheta-1 population loop above). - wmu_ba = zeros(ComplexF64, mpert) - wen_ba = zeros(ComplexF64, mpert) + wmu_ba = scr.wmu_ba + wen_ba = scr.wen_ba + fill!(wmu_ba, ComplexF64(0.0)) + fill!(wen_ba, ComplexF64(0.0)) @inbounds for i in 1:ntheta w = (i == 1 || i == ntheta) ? 0.5 : 1.0 factor = w * (pl[i] + one_minus_sigma / (pl[i] + SINGULAR_EPS)) @@ -636,7 +691,7 @@ function _bounce_integrate( # Scale by wbbar/ro² (Fortran line 789) scale = wbbar / ro^2 Mu = (mpert * (mpert + 1)) ÷ 2 - wmats_lmda = Vector{ComplexF64}(undef, nqty_matrix(mpert)) + wmats_lmda = scr.wmats_lmda # A (Hermitian): upper triangle of W_Z†W_Z, rank-1 → conj(wz[i])·wz[j]. off = 0 From 17a441abc4f1bd0a2a390fc3e75c3e7083522284 Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Wed, 8 Jul 2026 17:26:15 -0400 Subject: [PATCH 131/135] KineticForces - DOCS - return comment above newly explicit function --- src/KineticForces/EnergyIntegration.jl | 2 ++ 1 file changed, 2 insertions(+) diff --git a/src/KineticForces/EnergyIntegration.jl b/src/KineticForces/EnergyIntegration.jl index 05b0f9775..267d820b3 100644 --- a/src/KineticForces/EnergyIntegration.jl +++ b/src/KineticForces/EnergyIntegration.jl @@ -217,6 +217,8 @@ add-back below), and its on-axis `0/0` window by the analytic regular-part limit @inbounds for k in 1:npole val -= residues[k] / (x - x_poles[k]) end + # At a ν=0 pole Ω rounds to 0 and the physical term is 0/0; substitute the nearest + # pole's analytic regular-part limit, keeping the other (finite) pole subtractions. if !isfinite(val) k = 1 @inbounds for j in 2:npole From 6f494094cdf0e13ba587ffc2ad9e8f2f4a0408e2 Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Wed, 8 Jul 2026 17:29:24 -0400 Subject: [PATCH 132/135] KineticForces - REFACTOR - Consolidate Solovev equilibrium parameters into gpec.toml and remove deprecated sol.toml --- .../gpec.toml | 19 ++++++++++++++++++- .../sol.toml | 11 ----------- 2 files changed, 18 insertions(+), 12 deletions(-) delete mode 100644 examples/Solovev_kinetic_calculated_example/sol.toml diff --git a/examples/Solovev_kinetic_calculated_example/gpec.toml b/examples/Solovev_kinetic_calculated_example/gpec.toml index 4a46bdb42..15ce58543 100644 --- a/examples/Solovev_kinetic_calculated_example/gpec.toml +++ b/examples/Solovev_kinetic_calculated_example/gpec.toml @@ -1,6 +1,10 @@ +# Solovev analytical equilibrium — n=1 ideal stability with calculated kinetic matrices. +# Exercises the real KineticForces (NTV) physics path at full strength; kinetic regression +# fixture (et[1]≈1.894-1.525i). The equilibrium is generated analytically from the embedded +# [SOL_INPUT] section, with n·T tied to the Solovev P₀≈4.27e4 Pa via the local kinetic.dat. + [Equilibrium] eq_type = "sol" # Type of the input 2D equilibrium file -eq_filename = "sol.toml" # Path to equilibrium file jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom) grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized flux coordinate @@ -45,3 +49,16 @@ singfac_min = 1e-4 # Fractional distance from rational q at which ide ucrit = 1e3 # Maximum fraction of solutions allowed before re-normalized write_outputs_to_HDF5 = true verbose = false + +# Solovev analytic equilibrium parameters (eq_type = "sol"); see SolovevConfig in src/Equilibrium. +[SOL_INPUT] +mr = 128 # Number of radial grid zones +mz = 128 # Number of axial grid zones +ma = 128 # Number of flux grid zones +e = 1.6 # Elongation +a = 0.33 # Minor radius +r0 = 1.0 # Major radius +q0 = 1.9 # Safety factor at the magnetic axis (O-point) +p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed) +b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed) +f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed) diff --git a/examples/Solovev_kinetic_calculated_example/sol.toml b/examples/Solovev_kinetic_calculated_example/sol.toml deleted file mode 100644 index e54fdeace..000000000 --- a/examples/Solovev_kinetic_calculated_example/sol.toml +++ /dev/null @@ -1,11 +0,0 @@ -[SOL_INPUT] -mr = 128 # number of radial grid zones -mz = 128 # number of axial grid zones -ma = 128 # number of flux grid zones -e = 1.6 # elongation -a = 0.33 # minor radius -r0 = 1.0 # major radius -q0 = 1.9 # safety factor at the o-point -p0fac=1 # scale on-axis pressure (P-> P+P0*p0fac. beta changes. Phi,q constant) -b0fac=1 # scale toroidal field at constant beta (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant) -f0fac=1 # scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant) From 0007e6289e8ccf3ce77069893aa44b313b6ed453 Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Wed, 8 Jul 2026 17:40:09 -0400 Subject: [PATCH 133/135] KineticForces - MINOR - Initialize wmats_lmda with NaN to catch uninitialized entries in bounce integration --- src/KineticForces/BounceAveraging.jl | 2 ++ 1 file changed, 2 insertions(+) diff --git a/src/KineticForces/BounceAveraging.jl b/src/KineticForces/BounceAveraging.jl index 0ea808319..2c65a598d 100644 --- a/src/KineticForces/BounceAveraging.jl +++ b/src/KineticForces/BounceAveraging.jl @@ -692,6 +692,8 @@ function _bounce_integrate( scale = wbbar / ro^2 Mu = (mpert * (mpert + 1)) ÷ 2 wmats_lmda = scr.wmats_lmda + # Fill with NaN to catch uninitialized entries + fill!(wmats_lmda, ComplexF64(NaN, NaN)) # A (Hermitian): upper triangle of W_Z†W_Z, rank-1 → conj(wz[i])·wz[j]. off = 0 From 38b5f4251dd86500048ba5b9f69b123cd5f12e6f Mon Sep 17 00:00:00 2001 From: logan-nc Date: Wed, 8 Jul 2026 17:45:20 -0400 Subject: [PATCH 134/135] KineticForces - MINOR - Address PR review: derive nfine from scratch buffer, BounceScratch field docs fvals stays ComplexF64: the kinetic-matrix (wt) path builds fbnce from complex op_wmats data, so a real buffer throws InexactError in the pitch kernel. Co-Authored-By: Claude Fable 5 Claude-Session: https://claude.ai/code/session_01TTu6sczod1Qtjy9e9pB6jP --- src/KineticForces/BounceAveraging.jl | 39 ++++++++++++++++++-------- src/KineticForces/EnergyIntegration.jl | 2 +- src/KineticForces/PitchIntegration.jl | 2 +- 3 files changed, 29 insertions(+), 14 deletions(-) diff --git a/src/KineticForces/BounceAveraging.jl b/src/KineticForces/BounceAveraging.jl index 2c65a598d..e0153fcbe 100644 --- a/src/KineticForces/BounceAveraging.jl +++ b/src/KineticForces/BounceAveraging.jl @@ -274,19 +274,33 @@ Per-surface scratch buffers for the bounce-averaging inner loops. Allocated once θ- and mode-sized arrays). Sizes are fixed for a flux surface (`ntheta` sub-grid points, `mpert` Fourier modes), so a single set of buffers serves the whole λ sweep. Buffers that the callers zero-initialize are `fill!`-reset per λ, preserving bit-for-bit results. + +## Fields +- `cum_wb_arr::Vector{Float64}`: length `ntheta` — cumulative bounce action +- `jvtheta::Vector{ComplexF64}`: length `ntheta` — action integrand +- `wmu_mt::Matrix{ComplexF64}`: `mpert × ntheta` — W_μ per θ +- `wen_mt::Matrix{ComplexF64}`: `mpert × ntheta` — W_E per θ +- `expm::Vector{ComplexF64}`: length `mpert` — Fourier basis at a θ +- `pl::Vector{ComplexF64}`: length `ntheta` — bounce phase factor +- `wmu_ba::Vector{ComplexF64}`: length `mpert` — bounce-averaged W_μ +- `wen_ba::Vector{ComplexF64}`: length `mpert` — bounce-averaged W_E +- `wmats_lmda::Vector{ComplexF64}`: length `nqty_matrix(mpert)` — packed W outer products +- `tspl_f::Vector{Float64}`: length 5 — in-place tspl(θ) evaluation +- `vpar_fine::Vector{Float64}`: length `nfine+1` — v_par(θ) for bounce-point search; + `_find_bounce_points_and_grid` derives its fine-grid size from this buffer's length """ struct BounceScratch - cum_wb_arr::Vector{Float64} # ntheta — cumulative bounce action - jvtheta::Vector{ComplexF64} # ntheta — action integrand - wmu_mt::Matrix{ComplexF64} # mpert × ntheta — W_μ per θ - wen_mt::Matrix{ComplexF64} # mpert × ntheta — W_E per θ - expm::Vector{ComplexF64} # mpert — Fourier basis at a θ - pl::Vector{ComplexF64} # ntheta — bounce phase factor - wmu_ba::Vector{ComplexF64} # mpert — bounce-averaged W_μ - wen_ba::Vector{ComplexF64} # mpert — bounce-averaged W_E - wmats_lmda::Vector{ComplexF64} # nqty_matrix(mpert) — packed W outer products - tspl_f::Vector{Float64} # 5 — in-place tspl(θ) evaluation - vpar_fine::Vector{Float64} # nfine+1 — v_par(θ) for bounce-point search + cum_wb_arr::Vector{Float64} + jvtheta::Vector{ComplexF64} + wmu_mt::Matrix{ComplexF64} + wen_mt::Matrix{ComplexF64} + expm::Vector{ComplexF64} + pl::Vector{ComplexF64} + wmu_ba::Vector{ComplexF64} + wen_ba::Vector{ComplexF64} + wmats_lmda::Vector{ComplexF64} + tspl_f::Vector{Float64} + vpar_fine::Vector{Float64} end function BounceScratch(ntheta::Int, mpert::Int; nfine::Int=256) @@ -356,7 +370,8 @@ function _find_bounce_points_and_grid( ) if sigma == 0 # trapped # Build v_par(θ) = 1 - (λ/bo)*B(θ) and find roots on a dense θ grid. - nfine = 256 + # Grid size derives from the scratch buffer so it stays in sync with BounceScratch's nfine. + nfine = length(scr.vpar_fine) - 1 theta_fine = range(0.0, 1.0, length=nfine+1) vpar_fine = scr.vpar_fine @inbounds for i in 1:(nfine+1) diff --git a/src/KineticForces/EnergyIntegration.jl b/src/KineticForces/EnergyIntegration.jl index 267d820b3..36cc1ecef 100644 --- a/src/KineticForces/EnergyIntegration.jl +++ b/src/KineticForces/EnergyIntegration.jl @@ -209,7 +209,7 @@ formula; its causal branch is carried by the signed zero of `−pole_offset` (se add-back below), and its on-axis `0/0` window by the analytic regular-part limit. """ # Real x-space resonant integrand with pole subtractions -# Explicit function keeps memory allocation out of the QuadGK inner loop. +# Explicit function keeps memory allocation out of the QuadGK inner loop. @inline function _resonant_integrand(x::Float64, p::EnergyParams, residues::Vector{ComplexF64}, x_poles::Vector{ComplexF64}, npole::Int, leff::Float64, wb::Float64, n::Int, wd::Float64)::ComplexF64 diff --git a/src/KineticForces/PitchIntegration.jl b/src/KineticForces/PitchIntegration.jl index 7af482581..fa61c5952 100644 --- a/src/KineticForces/PitchIntegration.jl +++ b/src/KineticForces/PitchIntegration.jl @@ -47,7 +47,7 @@ struct PitchGARParams{F} fbnce::F # CubicSeriesInterpolant: fbnce(λ) → [wb, wd, f₁, ...] (typed for stability) fbnce_norm::Vector{Float64} # normalization factors (1/median) fbnce_hint::Base.RefValue{Int} # sticky bracket-search hint for fbnce(λ) - fvals::Vector{ComplexF64} # reusable buffer for the in-place fbnce(fvals, λ) evaluation + fvals::Vector{ComplexF64} # reusable buffer for the in-place fbnce(fvals, λ) evaluation; must be complex — the wt-path fbnce carries complex op_wmats data esegbuf::Vector{QuadGK.Segment{Float64,ComplexF64,Float64}} # reusable energy-integral QuadGK segment buffer end From 45754b48417060a379303de7f8b56ed36021ccee Mon Sep 17 00:00:00 2001 From: Matthew Pharr Date: Fri, 10 Jul 2026 00:40:44 -0400 Subject: [PATCH 135/135] DOCS - MINOR - add symlink AI Agents --- .github/copilot-instructions.md | 53 +-------------------------------- AGENTS.md | 1 + GEMINI.md | 1 + 3 files changed, 3 insertions(+), 52 deletions(-) mode change 100644 => 120000 .github/copilot-instructions.md create mode 120000 AGENTS.md create mode 120000 GEMINI.md diff --git a/.github/copilot-instructions.md b/.github/copilot-instructions.md deleted file mode 100644 index 7769f08a9..000000000 --- a/.github/copilot-instructions.md +++ /dev/null @@ -1,52 +0,0 @@ -# Copilot instructions for GPEC - -## Project overview -- GPEC is a Julia port of GPEC-style MHD equilibrium and stability analysis. Core modules live in [src](src): Utilities, Equilibrium, Vacuum, ForceFreeStates, ForcingTerms, PerturbedEquilibrium (see [CLAUDE.md](CLAUDE.md)). -- Data flow: equilibrium setup → vacuum response → stability analysis (documented in [CLAUDE.md](CLAUDE.md)). - -## Architecture and entry points -- Main entry point: `GeneralizedPerturbedEquilibrium.main()` in [src/GeneralizedPerturbedEquilibrium.jl](src/GeneralizedPerturbedEquilibrium.jl). -- Equilibrium: `setup_equilibrium(path|config)`; types in [src/Equilibrium](src/Equilibrium). -- Vacuum: `compute_vacuum_response()`; code in [src/Vacuum](src/Vacuum). -- ForceFreeStates (ideal MHD stability): types and functions in [src/ForceFreeStates](src/ForceFreeStates). -- PerturbedEquilibrium (plasma response): entry point in [src/PerturbedEquilibrium](src/PerturbedEquilibrium). - -## Data flow and key structures -- Equilibrium: TOML config → read equilibrium → solve → diagnostics (gse*.h5) when relevant. -- Vacuum: initialize plasma/wall surfaces → compute response matrix → return wv, grri, xzpts. -- Stability: equilibrium + vacuum response → integrate ODEs → compute energies. -- Core types: `PlasmaEquilibrium` and `EquilibriumConfig` in [src/Equilibrium/EquilibriumTypes.jl](src/Equilibrium/EquilibriumTypes.jl); `ForceFreeStatesControl` and `ForceFreeStatesInternal` in [src/ForceFreeStates/ForceFreeStatesStructs.jl](src/ForceFreeStates/ForceFreeStatesStructs.jl). - -## Tests and docs -- Run all tests: - ```bash - julia --project=. test/runtests.jl - ``` -- Run specific tests: - ```bash - julia --project=. test/runtests.jl test/runtests_spline.jl - ``` -- Build docs locally: - ```bash - julia --project=. build_docs_local.jl - ``` - (See [docs/README.md](docs/README.md) for the long form.) - -## Project conventions -- GitFlow workflow; develop is the active integration branch (see [README.md](README.md)). -- Commit message format: `CODE - TAG - Detailed message` (examples in [CLAUDE.md](CLAUDE.md)). -- Avoid step numbering in comments; instructions should be unnumbered (see [CLAUDE.md](CLAUDE.md)). -- Many routines use 0-based indexing for historical consistency with the original GPEC Fortran code before converting to 1-based Julia indexing (see [CLAUDE.md](CLAUDE.md)). - -## Configuration examples -- Unified configuration: `gpec.toml` uses `[Equilibrium]`, `[Wall]`, `[ForceFreeStates]`, `[PerturbedEquilibrium]`, and `[ForcingTerms]` sections. -- Legacy configs (`equil.toml`, `dcon.toml`, `vac.in`) are deprecated. -- Example configs in [examples/DIIID-like_ideal_example](examples/DIIID-like_ideal_example) and [examples/Solovev_ideal_example](examples/Solovev_ideal_example). - -## Development tips -- Use Revise.jl in your global environment (not Project.toml); see [CLAUDE.md](CLAUDE.md). -- Target Julia version: 1.11. - -## Benchmarks -- Default benchmark case: [examples/DIIID-like_ideal_example](examples/DIIID-like_ideal_example). -- Report metrics: least stable eigenmode energy (first `et`), solver step count, and wall-clock time (details in [CLAUDE.md](CLAUDE.md)). diff --git a/.github/copilot-instructions.md b/.github/copilot-instructions.md new file mode 120000 index 000000000..949a29f15 --- /dev/null +++ b/.github/copilot-instructions.md @@ -0,0 +1 @@ +../CLAUDE.md \ No newline at end of file diff --git a/AGENTS.md b/AGENTS.md new file mode 120000 index 000000000..681311eb9 --- /dev/null +++ b/AGENTS.md @@ -0,0 +1 @@ +CLAUDE.md \ No newline at end of file diff --git a/GEMINI.md b/GEMINI.md new file mode 120000 index 000000000..681311eb9 --- /dev/null +++ b/GEMINI.md @@ -0,0 +1 @@ +CLAUDE.md \ No newline at end of file

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