diff --git a/.gitignore b/.gitignore index a4f9074e1..c7f7d6abe 100644 --- a/.gitignore +++ b/.gitignore @@ -8,6 +8,8 @@ *.i *.out *.h5 +# kinetic-profile inputs are tracked despite the blanket *.h5 (output) ignore +!examples/**/*kinetic*.h5 .vscode *.DS_Store *.pdf @@ -26,3 +28,9 @@ pestotv regression-harness/*.sqlite regression-harness/*.sqlite-shm regression-harness/*.sqlite-wal +scratch/ +.claude/worktrees/ +.claude/agent-memory/ + +# Local profiling scratch (one-off study scripts, not part of the package) +profiling/ diff --git a/Project.toml b/Project.toml index fd2c512d4..f1067858e 100644 --- a/Project.toml +++ b/Project.toml @@ -7,6 +7,7 @@ version = "0.1.0" [deps] AdaptiveArrayPools = "4f381ef7-9af0-4cbe-99d4-cf36d7b0f233" Contour = "d38c429a-6771-53c6-b99e-75d170b6e991" +DelaunayTriangulation = "927a84f5-c5f4-47a5-9785-b46e178433df" DelimitedFiles = "8bb1440f-4735-579b-a4ab-409b98df4dab" DiffEqCallbacks = "459566f4-90b8-5000-8ac3-15dfb0a30def" Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4" @@ -36,6 +37,7 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" [compat] AdaptiveArrayPools = "0.3.5" Contour = "0.6.3" +DelaunayTriangulation = "1.6.6" DelimitedFiles = "1.9.1" DiffEqCallbacks = "4.9.0" Documenter = "1.14.1" diff --git a/docs/make.jl b/docs/make.jl index 892920ab2..cbe4f29ed 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -35,7 +35,7 @@ makedocs(; "KineticForces" => "kinetic_forces.md", "Forcing Terms" => "forcing_terms.md", "Perturbed Equilibrium" => "perturbed_equilibrium.md", - "Inner Layer" => "inner_layer.md", + "Tearing" => "inner_layer.md", "Analysis" => "analysis.md", "Utilities" => "utilities.md" ], diff --git a/docs/src/inner_layer.md b/docs/src/inner_layer.md index cc80f52ea..387c06553 100644 --- a/docs/src/inner_layer.md +++ b/docs/src/inner_layer.md @@ -1,9 +1,10 @@ -# Inner Layer Module +# Tearing Module -The InnerLayer module provides abstract scaffolding for resistive inner-layer -models used in matched asymptotic expansions for resistive MHD stability -analysis. It currently includes the GGJ (Glasser–Greene–Johnson) shooting -method for computing the inner-layer response. +The `Tearing` module groups the resistive tearing-mode analysis stack: +`InnerLayer` (per-surface inner-layer matching data Δ(Q) for the GGJ and +SLAYER models), `Dispersion` (physics-agnostic complex-plane scan and +contour-intersection root extraction), and `Runner` (user-facing TOML +configuration, profile loading, and HDF5 output). ## InnerLayer @@ -16,3 +17,21 @@ Modules = [GeneralizedPerturbedEquilibrium.InnerLayer] ```@autodocs Modules = [GeneralizedPerturbedEquilibrium.InnerLayer.GGJ] ``` + +## SLAYER + +```@autodocs +Modules = [GeneralizedPerturbedEquilibrium.InnerLayer.SLAYER] +``` + +## Dispersion + +```@autodocs +Modules = [GeneralizedPerturbedEquilibrium.Dispersion] +``` + +## Runner + +```@autodocs +Modules = [GeneralizedPerturbedEquilibrium.Runner] +``` 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/examples/DIIID-like_SLAYER_example/gpec.toml b/examples/DIIID-like_SLAYER_example/gpec.toml new file mode 100644 index 000000000..776d60e12 --- /dev/null +++ b/examples/DIIID-like_SLAYER_example/gpec.toml @@ -0,0 +1,97 @@ +# DIII-D-like SLAYER tearing-mode growth-rate example. +# Reuses the equilibrium and H-mode kinetic profiles of the sibling +# DIIID-like_ideal_example (geqdsk referenced by relative path; not +# duplicated). Runs equilibrium + ForceFreeStates + SLAYER and skips +# PerturbedEquilibrium (ForceFreeStates.force_termination = true). + +[Equilibrium] +eq_filename = "../DIIID-like_ideal_example/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 = "log_asymptotic" # Radial grid packing type +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 +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] +force_termination = true # Run FFS + SLAYER, skip PerturbedEquilibrium +local_stability_flag = true # Perform local stability analysis (Mercier and ballooning) across the ψ profile +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 + +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 +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) +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 = 1 # serial/bit-deterministic BVP — keeps the regression Δ' (and hence γ) reproducible +populate_dense_xi = false # No PerturbedEquilibrium here; the dense EL pass has no consumer (auto-disabled under force_termination anyway). SLAYER needs only delta_prime_matrix from the parallel BVP. +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 + +[SLAYER] +# SLAYER tearing-mode growth-rate analysis on the DIII-D-like H-mode equilibrium. +# Runs in the force_termination path (PE skipped). Kinetic profiles (incl. the +# χ⊥/χ_φ heat/momentum diffusivities) are read from the standardized HDF5 +# kinetic file shared with the kinetic/NTV physics. Per-surface (uncoupled) +# analysis: the headline is the unstable 2/1; the validity gate drops surfaces +# with no real root (e.g. the 5/1, whose Δ' BVP yields a huge uncancellable Δ'). +enabled = true +inner_model = "slayer_fitzpatrick" +scan_mode = "amr" +coupling_mode = "uncoupled" +dc_type = "none" +mu_i = 2.0 +zeff = 1.0 +chi_perp = 1.0 # fallback only; the kinetic file supplies χ⊥(ψ) +chi_tor = 1.0 # fallback only; the kinetic file supplies χ_φ(ψ) +pole_threshold_adaptive = true # SLAYER |Δ| spans many orders; adapt to 10·median(|Δ|) +filter_above_poles = true +filter_outside_re = true +polish_roots = true # refine each root to the true zero; enables the validity gate +store_scan = false # per-surface scans omitted from HDF5 (uncoupled has one per surface) +# Standardized kinetic-profile file (GPEC HDF5 kinetic schema), shared with the +# sibling ideal example; carries n_e, T_e, T_i, omega_E, chi_e (χ⊥), chi_phi (χ_φ). +profile_file = "../DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode_kinetic.h5" + +[SLAYER.scan_grid] +Q_re_range = [-2.0, 2.0] +Q_im_range = [-0.5, 3.0] +nre = 41 +nim = 31 diff --git a/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk b/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk index 41a07c2de..fa39228fe 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 0.000000000E+00 - 0.174381757E+01-0.531557994E-02 0.348275840E+00 0.440248810E-01 0.202434754E+01 - 0.120003950E+07 0.348275840E+00 0.000000000E+00 0.174381757E+01 0.000000000E+00 --0.531557994E-02 0.000000000E+00 0.440248810E-01 0.000000000E+00 0.000000000E+00 - 0.349233675E+01 0.349158883E+01 0.349083281E+01 0.349007487E+01 0.348931623E+01 - 0.348855710E+01 0.348779750E+01 0.348703742E+01 0.348627710E+01 0.348551631E+01 - 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0.102635734E+00 0.100081146E+00 0.974739641E-01 0.948141813E-01 0.921277553E-01 - 0.896753073E-01 0.872890800E-01 0.849690884E-01 0.822592005E-01 0.794706345E-01 - 0.766679868E-01 0.738512725E-01 0.710204914E-01 0.681756288E-01 0.653166920E-01 - 0.624436885E-01 0.595355742E-01 0.566500984E-01 0.537951440E-01 0.509707145E-01 - 0.481703654E-01 0.453761220E-01 0.425869226E-01 0.398027636E-01 0.370236486E-01 - 0.342495814E-01 0.314805545E-01 0.287172031E-01 0.259717070E-01 0.232386272E-01 - 0.205179583E-01 0.178097058E-01 0.151138650E-01 0.124304388E-01 0.975942705E-02 - 0.709339092E-02 0.444506062E-02 0.183252699E-02-0.744209508E-03-0.328548648E-02 --0.580122275E-02-0.829486176E-02-0.107664047E-01-0.132158510E-01-0.156431999E-01 --0.180484541E-01-0.204316098E-01-0.227876697E-01-0.251117367E-01-0.274085030E-01 --0.296779703E-01-0.319201387E-01-0.341350064E-01-0.363225788E-01-0.384828486E-01 --0.406085886E-01-0.426998623E-01-0.447580256E-01-0.467830785E-01-0.487750247E-01 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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 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0.102543190E+00 0.104362227E+00 0.106093884E+00 0.107696749E+00 0.109167889E+00 - 0.110507295E+00 0.111714967E+00 0.112790905E+00 0.113735110E+00 0.114547580E+00 - 0.115228318E+00 0.115858220E+00 0.116405480E+00 0.116804220E+00 0.117054433E+00 - 0.117156118E+00 0.117109284E+00 0.116913922E+00 0.116570041E+00 0.116077632E+00 - 0.115436703E+00 0.114750579E+00 0.113867216E+00 0.112867482E+00 0.111751392E+00 - 0.110518947E+00 0.109170139E+00 0.107704967E+00 0.106123433E+00 0.104425542E+00 - 0.102611288E+00 0.100825191E+00 0.989301205E-01 0.969824567E-01 0.949821845E-01 - 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 --0.459495410E-01-0.477390550E-01-0.494954586E-01-0.512187518E-01-0.529140458E-01 --0.545888357E-01-0.562294163E-01-0.578357093E-01-0.594077073E-01-0.609454177E-01 --0.624488369E-01-0.639179647E-01-0.653528050E-01-0.667533502E-01-0.681346804E-01 --0.694924295E-01-0.708194524E-01-0.721169040E-01-0.733847767E-01-0.746230707E-01 --0.758317932E-01-0.770109370E-01-0.781605020E-01-0.792804882E-01-0.803931430E-01 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0.587542653E-01 0.611969903E-01 0.636221021E-01 0.660367534E-01 0.684409365E-01 - 0.708346590E-01 0.732179135E-01 0.755907074E-01 0.779398829E-01 0.802293345E-01 - 0.824688002E-01 0.846922994E-01 0.868530646E-01 0.889403224E-01 0.909540802E-01 - 0.928943455E-01 0.947559178E-01 0.965356901E-01 0.982479304E-01 0.999063551E-01 - 0.101451889E+00 0.102865696E+00 0.104147770E+00 0.105298117E+00 0.106316723E+00 - 0.107203595E+00 0.108006813E+00 0.108733453E+00 0.109369487E+00 0.109930940E+00 - 0.110349990E+00 0.110620521E+00 0.110742524E+00 0.110716000E+00 0.110540956E+00 - 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 --0.899551529E-02-0.111554367E-01-0.133026503E-01-0.154403728E-01-0.175587535E-01 --0.196498353E-01-0.217136182E-01-0.237501021E-01-0.257592872E-01-0.277411733E-01 --0.297003575E-01-0.316424407E-01-0.335664637E-01-0.354747511E-01-0.373534523E-01 --0.391990468E-01-0.410115309E-01-0.427909046E-01-0.445371717E-01-0.462503321E-01 --0.479415134E-01-0.496124327E-01-0.512620434E-01-0.528870150E-01-0.544779561E-01 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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 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0.961477235E-01 0.968580022E-01 0.974776745E-01 0.980314761E-01 0.984911546E-01 - 0.988023132E-01 0.989733487E-01 0.990399122E-01 0.990043879E-01 0.988667905E-01 - 0.986271128E-01 0.982709527E-01 0.978221744E-01 0.972862989E-01 0.966633335E-01 - 0.959558710E-01 0.951727033E-01 0.942731798E-01 0.932428241E-01 0.921415836E-01 - 0.909699351E-01 0.897278786E-01 0.884154215E-01 0.870325491E-01 0.855792761E-01 - 0.840705484E-01 0.825283006E-01 0.809249431E-01 0.792503804E-01 0.775344446E-01 - 0.757771581E-01 0.739784986E-01 0.721384883E-01 0.702571049E-01 0.683343709E-01 - 0.663889870E-01 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 --0.510717072E-01-0.525332466E-01-0.539737828E-01-0.553933196E-01-0.567918569E-01 --0.581693910E-01-0.595259219E-01-0.608614534E-01-0.621829107E-01-0.634795576E-01 --0.647462234E-01-0.659898072E-01-0.672146156E-01-0.684206635E-01-0.696079284E-01 --0.707753748E-01-0.719253495E-01-0.730607733E-01-0.741816387E-01-0.752879530E-01 --0.763800219E-01-0.774519220E-01-0.785008967E-01-0.795338079E-01-0.805556998E-01 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--0.144138888E+00-0.145687312E+00-0.147267073E+00-0.148878172E+00-0.150520608E+00 --0.152194679E+00-0.153906912E+00-0.155659780E+00-0.157442421E+00-0.159251109E+00 --0.161091253E+00-0.162962854E+00-0.164865941E+00-0.166800484E+00-0.168766499E+00 --0.170764014E+00-0.172799274E+00-0.174874589E+00-0.176978543E+00-0.179108173E+00 --0.181264281E+00-0.183446839E+00-0.185655892E+00-0.187891394E+00-0.190153375E+00 --0.192436352E+00-0.194745630E+00-0.197083667E+00-0.199443892E+00-0.201821387E+00 --0.204216152E+00-0.206628188E+00-0.209059730E+00-0.211511046E+00-0.213973165E+00 --0.216447830E+00-0.218935177E+00-0.221435845E+00-0.223949909E+00-0.226477340E+00 --0.229017541E+00-0.231555596E+00-0.234096095E+00-0.236642703E+00 0.317211002E-01 - 0.339882299E-01 0.362483896E-01 0.385015793E-01 0.407451317E-01 0.429861322E-01 - 0.452268720E-01 0.474525243E-01 0.496546887E-01 0.518333688E-01 0.539885648E-01 - 0.561202765E-01 0.582285002E-01 0.603132360E-01 0.623705983E-01 0.643896013E-01 - 0.663696378E-01 0.683107078E-01 0.702128187E-01 0.720629990E-01 0.738530606E-01 - 0.755932927E-01 0.772824064E-01 0.788975060E-01 0.804385915E-01 0.819056630E-01 - 0.832932368E-01 0.846429169E-01 0.858886614E-01 0.870437995E-01 0.881083310E-01 - 0.890822560E-01 0.899655670E-01 0.907582790E-01 0.914603844E-01 0.920718759E-01 - 0.926065519E-01 0.930557624E-01 0.933874622E-01 0.936170891E-01 0.937446281E-01 - 0.937700942E-01 0.936934724E-01 0.935161412E-01 0.932508931E-01 0.928985626E-01 - 0.924591348E-01 0.919326171E-01 0.913190171E-01 0.906108469E-01 0.897977427E-01 - 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 --0.200367272E-01-0.218351074E-01-0.236154255E-01-0.253776722E-01-0.271218624E-01 --0.288479943E-01-0.305566043E-01-0.322460569E-01-0.339142084E-01-0.355610549E-01 --0.371865965E-01-0.387908369E-01-0.403737724E-01-0.419354029E-01-0.434757322E-01 --0.449947529E-01-0.464941114E-01-0.479725413E-01-0.494299680E-01-0.508663952E-01 --0.522818193E-01-0.536762439E-01-0.550496653E-01-0.564020872E-01-0.577335060E-01 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--0.121680103E+00-0.122863874E+00-0.124066383E+00-0.125287637E+00-0.126527652E+00 --0.127790406E+00-0.129071966E+00-0.130379766E+00-0.131713822E+00-0.133074135E+00 --0.134460717E+00-0.135873541E+00-0.137312621E+00-0.138777971E+00-0.140269563E+00 --0.141795829E+00-0.143345505E+00-0.144926533E+00-0.146538883E+00-0.148182571E+00 --0.149857610E+00-0.151563972E+00-0.153301686E+00-0.155070737E+00-0.156873778E+00 --0.158708349E+00-0.160572380E+00-0.162467882E+00-0.164394855E+00-0.166353285E+00 --0.168343186E+00-0.170364559E+00-0.172417387E+00-0.174501687E+00-0.176620647E+00 --0.178769007E+00-0.180943832E+00-0.183145121E+00-0.185372889E+00-0.187627122E+00 --0.189907834E+00-0.192215011E+00-0.194548652E+00-0.196908757E+00-0.199288636E+00 --0.201691732E+00-0.204114467E+00-0.206557333E+00-0.209020317E+00-0.211503834E+00 --0.214003921E+00-0.216516539E+00-0.219041705E+00-0.221579418E+00-0.224129662E+00 --0.226692468E+00-0.229270488E+00-0.231864482E+00-0.234458923E+00-0.237057701E+00 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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 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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 --0.543070994E-01-0.555930175E-01-0.568630397E-01-0.581171624E-01-0.593553931E-01 --0.605855137E-01-0.618024766E-01-0.630029961E-01-0.641964227E-01-0.653757006E-01 --0.665408298E-01-0.676918253E-01-0.688314289E-01-0.699637458E-01-0.710885450E-01 --0.722058415E-01-0.733134300E-01-0.744117647E-01-0.755017400E-01-0.765833631E-01 --0.776566267E-01-0.787215307E-01-0.797813162E-01-0.808386803E-01-0.818936154E-01 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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 --0.273710098E-01-0.288972016E-01-0.304104090E-01-0.319108628E-01-0.333946310E-01 --0.348617211E-01-0.363160558E-01-0.377576500E-01-0.391848087E-01-0.405986905E-01 --0.419962816E-01-0.433781072E-01-0.447493270E-01-0.461060144E-01-0.474460013E-01 --0.487692766E-01-0.500807986E-01-0.513814501E-01-0.526726395E-01-0.539484434E-01 --0.552085228E-01-0.564571731E-01-0.576947331E-01-0.589211695E-01-0.601363406E-01 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0.356897712E-01 0.376096219E-01 0.395074897E-01 0.413775295E-01 0.432221107E-01 - 0.450403541E-01 0.468273945E-01 0.485829897E-01 0.503042117E-01 0.519870482E-01 - 0.536315739E-01 0.552297756E-01 0.567811355E-01 0.582877323E-01 0.597478040E-01 - 0.611560270E-01 0.625124648E-01 0.638146698E-01 0.650581643E-01 0.662402064E-01 - 0.673549548E-01 0.684105009E-01 0.694040731E-01 0.703333542E-01 0.711949021E-01 - 0.719887167E-01 0.727030337E-01 0.733468458E-01 0.739261955E-01 0.744348988E-01 - 0.748824552E-01 0.752436444E-01 0.755288377E-01 0.757415518E-01 0.758829638E-01 - 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 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--0.108821414E+00-0.110124834E+00-0.111441374E+00-0.112774007E+00-0.114121996E+00 --0.115486473E+00-0.116868645E+00-0.118269414E+00-0.119688801E+00-0.121128246E+00 --0.122588500E+00-0.124070778E+00-0.125572324E+00-0.127096027E+00-0.128641799E+00 --0.130210131E+00-0.131802514E+00-0.133419156E+00-0.135060444E+00-0.136727482E+00 --0.138421327E+00-0.140142068E+00-0.141887113E+00-0.143660232E+00-0.145460591E+00 --0.147288591E+00-0.149145067E+00-0.151029974E+00-0.152943879E+00-0.154886901E+00 --0.156859890E+00-0.158862367E+00-0.160893217E+00-0.162954688E+00-0.165045753E+00 --0.167166591E+00-0.169317141E+00-0.171497509E+00-0.173707411E+00-0.175946608E+00 --0.178214595E+00-0.180512249E+00-0.182838470E+00-0.185193896E+00-0.187577859E+00 --0.189989522E+00-0.192428693E+00-0.194895163E+00-0.197387651E+00-0.199904814E+00 --0.202445894E+00-0.205014765E+00-0.207606778E+00-0.210222855E+00-0.212862298E+00 --0.215523675E+00-0.218207166E+00-0.220908731E+00-0.223628268E+00-0.226366818E+00 --0.229122713E+00-0.231895968E+00-0.234686568E+00-0.237494528E+00-0.240319833E+00 --0.243161157E+00-0.246008471E+00-0.248860106E+00-0.251716942E+00 0.168612171E-01 - 0.188582782E-01 0.208441783E-01 0.228169970E-01 0.247791503E-01 0.267337598E-01 - 0.286663882E-01 0.305770338E-01 0.324657001E-01 0.343340859E-01 0.361831337E-01 - 0.380122438E-01 0.398086607E-01 0.415763855E-01 0.433133207E-01 0.450185910E-01 - 0.466903411E-01 0.483255684E-01 0.499215685E-01 0.514782406E-01 0.529908538E-01 - 0.544576943E-01 0.558796190E-01 0.572539866E-01 0.585765690E-01 0.598466955E-01 - 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 --0.570067875E-01-0.582225546E-01-0.594326966E-01-0.606365390E-01-0.618336909E-01 --0.630258173E-01-0.642132759E-01-0.653955936E-01-0.665736347E-01-0.677492619E-01 --0.689211041E-01-0.700896382E-01-0.712563545E-01-0.724207312E-01-0.735828951E-01 --0.747450963E-01-0.759066418E-01-0.770677328E-01-0.782300308E-01-0.793941617E-01 --0.805593878E-01-0.817268267E-01-0.828972310E-01-0.840705633E-01-0.852472559E-01 --0.864289403E-01-0.876154080E-01-0.888072103E-01-0.900056362E-01-0.912108049E-01 --0.924224332E-01-0.936420336E-01-0.948700458E-01-0.961065069E-01-0.973527580E-01 --0.986094028E-01-0.998764634E-01-0.101154409E+00-0.102444589E+00-0.103747003E+00 --0.105062187E+00-0.106391720E+00-0.107735574E+00-0.109093964E+00-0.110467993E+00 --0.111858070E+00-0.113264628E+00-0.114688583E+00-0.116130106E+00-0.117590189E+00 --0.119069539E+00-0.120568842E+00-0.122088470E+00-0.123628721E+00-0.125190765E+00 --0.126774698E+00-0.128381133E+00-0.130010575E+00-0.131663457E+00-0.133340612E+00 --0.135042801E+00-0.136770070E+00-0.138523132E+00-0.140302271E+00-0.142107978E+00 --0.143940702E+00-0.145800740E+00-0.147688210E+00-0.149603680E+00-0.151547566E+00 --0.153520033E+00-0.155521348E+00-0.157551780E+00-0.159611523E+00-0.161700562E+00 --0.163819194E+00-0.165967301E+00-0.168144926E+00-0.170352235E+00-0.172589093E+00 --0.174855337E+00-0.177150950E+00-0.179475829E+00-0.181829900E+00-0.184212953E+00 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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 --0.323380195E-01-0.336931013E-01-0.350396037E-01-0.363775603E-01-0.377073437E-01 --0.390285589E-01-0.403417498E-01-0.416468196E-01-0.429435149E-01-0.442327112E-01 --0.455146879E-01-0.467892177E-01-0.480564833E-01-0.493170209E-01-0.505706891E-01 --0.518183745E-01-0.530603155E-01-0.542963482E-01-0.555265620E-01-0.567520708E-01 --0.579730272E-01-0.591890514E-01-0.604013205E-01-0.616101399E-01-0.628156736E-01 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0.414649583E-01 0.429860279E-01 0.444695204E-01 0.459143259E-01 0.473191328E-01 - 0.486803800E-01 0.499985181E-01 0.512730628E-01 0.524988435E-01 0.536755174E-01 - 0.548044071E-01 0.558816940E-01 0.569060780E-01 0.578782037E-01 0.587948337E-01 - 0.596561693E-01 0.604614131E-01 0.612094067E-01 0.618994609E-01 0.625301376E-01 - 0.631027818E-01 0.636170208E-01 0.640692487E-01 0.644627810E-01 0.647976696E-01 - 0.650706440E-01 0.652841926E-01 0.654398873E-01 0.655371174E-01 0.655742884E-01 - 0.655540824E-01 0.654756799E-01 0.653411150E-01 0.651516318E-01 0.649063364E-01 - 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 --0.591449533E-02-0.735654868E-02-0.879465882E-02-0.102278683E-01-0.116561381E-01 --0.130792838E-01-0.144969756E-01-0.159090292E-01-0.173147582E-01-0.187148768E-01 --0.201092567E-01-0.214964598E-01-0.228773728E-01-0.242513660E-01-0.256189182E-01 --0.269793980E-01-0.283335075E-01-0.296803825E-01-0.310205985E-01-0.323544182E-01 --0.336809829E-01-0.350010432E-01-0.363145992E-01-0.376217328E-01-0.389220454E-01 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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 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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 --0.361448377E-01-0.374265090E-01-0.387056395E-01-0.399823301E-01-0.412561931E-01 --0.425287038E-01-0.437994152E-01-0.450679995E-01-0.463358574E-01-0.476023294E-01 --0.488678627E-01-0.501330942E-01-0.513977930E-01-0.526625365E-01-0.539277680E-01 --0.551936738E-01-0.564604662E-01-0.577290803E-01-0.589989275E-01-0.602708906E-01 --0.615453310E-01-0.628225207E-01-0.641030893E-01-0.653873086E-01-0.666755065E-01 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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 --0.114928512E-01-0.128010167E-01-0.141073121E-01-0.154124312E-01-0.167162661E-01 --0.180180445E-01-0.193182416E-01-0.206164960E-01-0.219133422E-01-0.232076216E-01 --0.245007984E-01-0.257920530E-01-0.270812251E-01-0.283690970E-01-0.296546929E-01 --0.309390109E-01-0.322216675E-01-0.335033461E-01-0.347834863E-01-0.360622704E-01 --0.373403542E-01-0.386177488E-01-0.398948938E-01-0.411710367E-01-0.424471684E-01 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0.170921963E-01 0.187244322E-01 0.203332771E-01 0.219201632E-01 0.234810226E-01 - 0.250156354E-01 0.265240073E-01 0.280044898E-01 0.294555165E-01 0.308763534E-01 - 0.322664976E-01 0.336233564E-01 0.349460579E-01 0.362349451E-01 0.374877825E-01 - 0.387037173E-01 0.398811474E-01 0.410197563E-01 0.421195552E-01 0.431779623E-01 - 0.441950075E-01 0.451700576E-01 0.461015515E-01 0.469892919E-01 0.478322282E-01 - 0.486304313E-01 0.493840650E-01 0.500904061E-01 0.507504232E-01 0.513646640E-01 - 0.519321635E-01 0.524514690E-01 0.529247113E-01 0.533502996E-01 0.537282191E-01 - 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 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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 --0.398294292E-01-0.411267802E-01-0.424271189E-01-0.437311977E-01-0.450392552E-01 --0.463513359E-01-0.476677567E-01-0.489885546E-01-0.503145084E-01-0.516454503E-01 --0.529821552E-01-0.543246828E-01-0.556725897E-01-0.570270754E-01-0.583887696E-01 --0.597579107E-01-0.611340441E-01-0.625180155E-01-0.639102459E-01-0.653110370E-01 --0.667205900E-01-0.681397244E-01-0.695682839E-01-0.710068792E-01-0.724561363E-01 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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 --0.155871501E-01-0.168383587E-01-0.180919431E-01-0.193482954E-01-0.206074100E-01 --0.218691770E-01-0.231337585E-01-0.244009141E-01-0.256713238E-01-0.269444101E-01 --0.282207038E-01-0.295003373E-01-0.307831801E-01-0.320695229E-01-0.333595350E-01 --0.346532166E-01-0.359509289E-01-0.372527540E-01-0.385588370E-01-0.398699008E-01 --0.411853381E-01-0.425057039E-01-0.438316315E-01-0.451630168E-01-0.464999042E-01 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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 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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 --0.442637205E-01-0.456558093E-01-0.470568798E-01-0.484671779E-01-0.498869084E-01 --0.513164178E-01-0.527559184E-01-0.542058498E-01-0.556664132E-01-0.571376346E-01 --0.586205423E-01-0.601147972E-01-0.616210252E-01-0.631395504E-01-0.646703839E-01 --0.662144050E-01-0.677717403E-01-0.693424940E-01-0.709274188E-01-0.725265369E-01 --0.741403922E-01-0.757694021E-01-0.774136633E-01-0.790739655E-01-0.807501525E-01 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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 --0.191489309E-01-0.204192102E-01-0.216960143E-01-0.229801107E-01-0.242717229E-01 --0.255705919E-01-0.268763583E-01-0.281900819E-01-0.295114256E-01-0.308409426E-01 --0.321783088E-01-0.335238166E-01-0.348780043E-01-0.362407193E-01-0.376121812E-01 --0.389928035E-01-0.403825678E-01-0.417817235E-01-0.431908034E-01-0.446095318E-01 --0.460386574E-01-0.474783629E-01-0.489285402E-01-0.503898002E-01-0.518623628E-01 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0.275315624E-01 0.286147129E-01 0.296676867E-01 0.306904539E-01 0.316811949E-01 - 0.326399617E-01 0.335677974E-01 0.344625600E-01 0.353246070E-01 0.361535363E-01 - 0.369487032E-01 0.377101488E-01 0.384387448E-01 0.391327403E-01 0.397923961E-01 - 0.404177867E-01 0.410086513E-01 0.415655822E-01 0.420880355E-01 0.425759703E-01 - 0.430296399E-01 0.434490144E-01 0.438346751E-01 0.441860482E-01 0.445035324E-01 - 0.447877608E-01 0.450386144E-01 0.452565737E-01 0.454415604E-01 0.455941260E-01 - 0.457146429E-01 0.458033867E-01 0.458603166E-01 0.458862521E-01 0.458816849E-01 - 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 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0.313653587E-02 0.462668482E-02 0.609972235E-02 0.755284959E-02 0.898610335E-02 - 0.103992065E-01 0.117913662E-01 0.131622888E-01 0.145105505E-01 0.158360153E-01 - 0.171377603E-01 0.184155963E-01 0.196685269E-01 0.208959132E-01 0.220970660E-01 - 0.232715607E-01 0.244193971E-01 0.255391914E-01 0.266304836E-01 0.276931077E-01 - 0.287268851E-01 0.297307726E-01 0.307044704E-01 0.316481218E-01 0.325604044E-01 - 0.334419049E-01 0.342926979E-01 0.351105444E-01 0.358965807E-01 0.366508141E-01 - 0.373729244E-01 0.380622745E-01 0.387192406E-01 0.393437147E-01 0.399347171E-01 - 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 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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 --0.230236985E-01-0.243828297E-01-0.257538445E-01-0.271360334E-01-0.285301954E-01 --0.299363025E-01-0.313541517E-01-0.327847674E-01-0.342278332E-01-0.356833041E-01 --0.371513925E-01-0.386327729E-01-0.401273482E-01-0.416352637E-01-0.431569517E-01 --0.446926095E-01-0.462424457E-01-0.478065982E-01-0.493856445E-01-0.509795956E-01 --0.525885187E-01-0.542129204E-01-0.558530688E-01-0.575091466E-01-0.591815710E-01 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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 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0.104090367E-01 0.117117837E-01 0.129933944E-01 0.142537327E-01 0.154921133E-01 - 0.167077165E-01 0.179007687E-01 0.190704893E-01 0.202163458E-01 0.213377792E-01 - 0.224347338E-01 0.235064533E-01 0.245528035E-01 0.255737342E-01 0.265684277E-01 - 0.275364798E-01 0.284782294E-01 0.293929074E-01 0.302803181E-01 0.311404299E-01 - 0.319729298E-01 0.327777229E-01 0.335544720E-01 0.343034938E-01 0.350241847E-01 - 0.357166827E-01 0.363811404E-01 0.370174497E-01 0.376252420E-01 0.382045172E-01 - 0.387559123E-01 0.392789468E-01 0.397738777E-01 0.402407944E-01 0.406799912E-01 - 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 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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 --0.279465988E-01-0.294593740E-01-0.309871472E-01-0.325313173E-01-0.340915173E-01 --0.356678963E-01-0.372605361E-01-0.388699919E-01-0.404962599E-01-0.421394221E-01 --0.437999666E-01-0.454777852E-01-0.471735671E-01-0.488870479E-01-0.506185293E-01 --0.523686670E-01-0.541373864E-01-0.559249818E-01-0.577315390E-01-0.595577359E-01 --0.614034384E-01-0.632688329E-01-0.651547089E-01-0.670610815E-01-0.689879209E-01 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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 --0.176338560E-02-0.302677299E-02-0.430479599E-02-0.559781073E-02-0.690584490E-02 --0.822871551E-02-0.956666283E-02-0.109197628E-01-0.122879846E-01-0.136716515E-01 --0.150705911E-01-0.164849814E-01-0.179151036E-01-0.193609968E-01-0.208226237E-01 --0.223002080E-01-0.237940233E-01-0.253040772E-01-0.268303715E-01-0.283732973E-01 --0.299328845E-01-0.315091461E-01-0.331027322E-01-0.347135700E-01-0.363416262E-01 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0.169500057E-01 0.180869102E-01 0.192023329E-01 0.202960633E-01 0.213677287E-01 - 0.224171039E-01 0.234439317E-01 0.244478285E-01 0.254287329E-01 0.263862982E-01 - 0.273202881E-01 0.282307118E-01 0.291175526E-01 0.299799833E-01 0.308187753E-01 - 0.316332094E-01 0.324234106E-01 0.331894122E-01 0.339308642E-01 0.346476808E-01 - 0.353402831E-01 0.360084251E-01 0.366519317E-01 0.372711234E-01 0.378658660E-01 - 0.384364985E-01 0.389825255E-01 0.395043492E-01 0.400021002E-01 0.404758751E-01 - 0.409252569E-01 0.413509645E-01 0.417528562E-01 0.421310030E-01 0.424855873E-01 - 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 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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 --0.529159512E-02-0.670968089E-02-0.814542174E-02-0.959968287E-02-0.110721886E-01 --0.125632947E-01-0.140728503E-01-0.156010184E-01-0.171479080E-01-0.187138356E-01 --0.202984642E-01-0.219023973E-01-0.235256497E-01-0.251682252E-01-0.268301349E-01 --0.285117794E-01-0.302132480E-01-0.319346599E-01-0.336762331E-01-0.354380831E-01 --0.372202620E-01-0.390230790E-01-0.408468172E-01-0.426915362E-01-0.445573926E-01 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0.447814167E-01 0.443736911E-01 0.439413004E-01 0.434849821E-01 - 0.430062301E-01 0.425045192E-01 0.419802479E-01 0.414336883E-01 0.408653021E-01 - 0.402751639E-01 0.396633632E-01 0.390297323E-01 0.383753553E-01 0.377000272E-01 - 0.370036177E-01 0.362864956E-01 0.355492271E-01 0.347914882E-01 0.340134166E-01 - 0.332153663E-01 0.323972777E-01 0.315596163E-01 0.307021029E-01 0.298253652E-01 - 0.289287418E-01 0.280127805E-01 0.270777941E-01 0.261237528E-01 0.251503140E-01 - 0.241580904E-01 0.231468491E-01 0.221165232E-01 0.210675821E-01 0.200000666E-01 - 0.189134516E-01 0.178077836E-01 0.166840311E-01 0.155414399E-01 0.143799335E-01 - 0.132000567E-01 0.120014679E-01 0.107842209E-01 0.954831112E-02 0.829372834E-02 - 0.702040456E-02 0.572867459E-02 0.441805599E-02 0.308864005E-02 0.174042280E-02 - 0.373620831E-03-0.101232319E-02-0.241707056E-02-0.384080899E-02-0.528362067E-02 --0.674546883E-02-0.822679326E-02-0.972718839E-02-0.112468684E-01-0.127861490E-01 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0.217425846E-02 0.349967461E-02 0.481014047E-02 0.610548537E-02 0.738542527E-02 - 0.864916854E-02 0.989691168E-02 0.111282645E-01 0.123427482E-01 0.135401627E-01 - 0.147201456E-01 0.158829652E-01 0.170278344E-01 0.181543492E-01 0.192628335E-01 - 0.203527827E-01 0.214242954E-01 0.224767383E-01 0.235101841E-01 0.245245118E-01 - 0.255195163E-01 0.264952835E-01 0.274512619E-01 0.283873789E-01 0.293037631E-01 - 0.302009918E-01 0.310778748E-01 0.319345780E-01 0.327719301E-01 0.335887484E-01 - 0.343856439E-01 0.351627506E-01 0.359194018E-01 0.366565324E-01 0.373732112E-01 - 0.380702764E-01 0.387475304E-01 0.394045077E-01 0.400419384E-01 0.406594090E-01 - 0.412572958E-01 0.418354906E-01 0.423943400E-01 0.429336242E-01 0.434534475E-01 - 0.439541861E-01 0.444351435E-01 0.448958650E-01 0.453361757E-01 0.457548648E-01 - 0.461520515E-01 0.465271622E-01 0.468794256E-01 0.472086780E-01 0.475136563E-01 - 0.477941968E-01 0.480501838E-01 0.482799262E-01 0.484835282E-01 0.486604981E-01 - 0.488105640E-01 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0.995811913E-02 0.866627507E-02 0.735494774E-02 - 0.602411106E-02 0.467339251E-02 0.330317672E-02 0.191300584E-02 0.502923795E-03 --0.926553563E-03-0.237614941E-02-0.384586956E-02-0.533557963E-02-0.684527447E-02 --0.837501884E-02-0.992526207E-02-0.114956815E-01-0.130865192E-01-0.146981422E-01 --0.163300876E-01-0.179826599E-01-0.196563601E-01-0.213507842E-01-0.230663978E-01 --0.248033255E-01-0.265614521E-01-0.283409320E-01-0.301421285E-01-0.319650955E-01 --0.338099524E-01-0.356767438E-01-0.375659540E-01-0.394773185E-01-0.414112918E-01 --0.433679633E-01-0.453476459E-01-0.473502800E-01-0.493761338E-01-0.514254682E-01 --0.534985624E-01-0.555954576E-01-0.577164665E-01-0.598617084E-01-0.620315634E-01 --0.642260239E-01-0.664453506E-01-0.686900988E-01-0.709602088E-01-0.732558519E-01 --0.755776241E-01-0.779255182E-01-0.802996755E-01-0.827007741E-01-0.851289108E-01 --0.875842050E-01-0.900669396E-01-0.925776213E-01-0.951164663E-01-0.976837724E-01 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0.326828137E-01 0.317620523E-01 0.308205076E-01 0.298578423E-01 - 0.288744215E-01 0.278705209E-01 0.268456452E-01 0.258001313E-01 0.247339755E-01 - 0.236472897E-01 0.225400310E-01 0.214122590E-01 0.202639960E-01 0.190951750E-01 - 0.179058369E-01 0.166961309E-01 0.154659403E-01 0.142151937E-01 0.129441163E-01 - 0.116523951E-01 0.103402389E-01 0.900762249E-02 0.765443360E-02 0.628054421E-02 - 0.488625886E-02 0.347119011E-02 0.203550374E-02 0.579104817E-03-0.897992519E-03 --0.239605154E-02-0.391497230E-02-0.545488345E-02-0.701581547E-02-0.859773159E-02 --0.102009168E-01-0.118254591E-01-0.134713473E-01-0.151384724E-01-0.168272909E-01 --0.185378287E-01-0.202700086E-01-0.220239647E-01-0.237999875E-01-0.255981702E-01 --0.274186060E-01-0.292613823E-01-0.311266314E-01-0.330145694E-01-0.349252634E-01 --0.368588679E-01-0.388156176E-01-0.407956876E-01-0.427991226E-01-0.448260643E-01 --0.468770266E-01-0.489517339E-01-0.510505773E-01-0.531736650E-01-0.553215742E-01 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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 --0.548333637E-01-0.571105257E-01-0.594137646E-01-0.617434755E-01-0.640997142E-01 --0.664824694E-01-0.688923150E-01-0.713294074E-01-0.737938285E-01-0.762859583E-01 --0.788059086E-01-0.813539177E-01-0.839303732E-01-0.865355209E-01-0.891695172E-01 --0.918326601E-01-0.945253000E-01-0.972476974E-01-0.100000054E+00-0.102782957E+00 --0.105596490E+00-0.108441055E+00-0.111316711E+00-0.114224210E+00-0.117163919E+00 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0.328127444E-01 0.317285024E-01 0.306211449E-01 0.294904672E-01 - 0.283364318E-01 0.271595381E-01 0.259595364E-01 0.247362293E-01 0.234900303E-01 - 0.222209860E-01 0.209285747E-01 0.196130034E-01 0.182747524E-01 0.169131681E-01 - 0.155283334E-01 0.141208554E-01 0.126902172E-01 0.112362634E-01 0.975908805E-02 - 0.825904217E-02 0.673576212E-02 0.518921996E-02 0.361958216E-02 0.202654744E-02 - 0.410290959E-03-0.122938305E-02-0.289248861E-02-0.457907142E-02-0.628911611E-02 --0.802279450E-02-0.978017226E-02-0.115610706E-01-0.133657921E-01-0.151946321E-01 --0.170471743E-01-0.189239699E-01-0.208248626E-01-0.227498543E-01-0.246992819E-01 --0.266732797E-01-0.286717881E-01-0.306948982E-01-0.327428840E-01-0.348157249E-01 --0.369136706E-01-0.390368477E-01-0.411854126E-01-0.433593690E-01-0.455589332E-01 --0.477843173E-01-0.500358306E-01-0.523133315E-01-0.546171702E-01-0.569474809E-01 --0.593045577E-01-0.616883002E-01-0.640991032E-01-0.665373430E-01-0.690030083E-01 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0.379544050E-01 0.388434380E-01 0.397171192E-01 0.405762978E-01 0.414205231E-01 - 0.422499552E-01 0.430650525E-01 0.438654311E-01 0.446515232E-01 0.454222821E-01 - 0.461770818E-01 0.469162427E-01 0.476376712E-01 0.483405367E-01 0.490246601E-01 - 0.496872887E-01 0.503276922E-01 0.509451665E-01 0.515369140E-01 0.521027856E-01 - 0.526420288E-01 0.531526133E-01 0.536350906E-01 0.540886857E-01 0.545129701E-01 - 0.549080111E-01 0.552738681E-01 0.556104966E-01 0.559178889E-01 0.561965629E-01 - 0.564464740E-01 0.566679277E-01 0.568617210E-01 0.570271425E-01 0.571649112E-01 - 0.572750382E-01 0.573583245E-01 0.574138202E-01 0.574419610E-01 0.574430339E-01 - 0.574170500E-01 0.573644936E-01 0.572848208E-01 0.571779422E-01 0.570438989E-01 - 0.568833314E-01 0.566954836E-01 0.564801134E-01 0.562376045E-01 0.559673160E-01 - 0.556692854E-01 0.553433485E-01 0.549890585E-01 0.546065457E-01 0.541960001E-01 - 0.537555963E-01 0.532866269E-01 0.527895503E-01 0.522634499E-01 0.517076105E-01 - 0.511228479E-01 0.505079925E-01 0.498650819E-01 0.491950065E-01 0.484972224E-01 - 0.477705523E-01 0.470148772E-01 0.462342203E-01 0.454284437E-01 0.445948839E-01 - 0.437355042E-01 0.428526141E-01 0.419436321E-01 0.410118513E-01 0.400558338E-01 - 0.390753783E-01 0.380705632E-01 0.370415561E-01 0.359885022E-01 0.349111073E-01 - 0.338096768E-01 0.326843262E-01 0.315349586E-01 0.303617045E-01 0.291643683E-01 - 0.279430579E-01 0.266978182E-01 0.254286993E-01 0.241356734E-01 0.228188056E-01 - 0.214779023E-01 0.201133378E-01 0.187249240E-01 0.173125118E-01 0.158762392E-01 - 0.144159989E-01 0.129319457E-01 0.114240991E-01 0.989222154E-02 0.833644904E-02 - 0.675666519E-02 0.515290629E-02 0.352511695E-02 0.187317631E-02 0.197390866E-03 --0.150269258E-02-0.322695100E-02-0.497544929E-02-0.674828747E-02-0.854537822E-02 --0.103668608E-01-0.122129368E-01-0.140835484E-01-0.159786567E-01-0.178985558E-01 --0.198432729E-01-0.218127649E-01-0.238074008E-01-0.258270819E-01-0.278718155E-01 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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 --0.692820176E-01-0.718885586E-01-0.745237842E-01-0.771881565E-01-0.798817053E-01 --0.826048255E-01-0.853574947E-01-0.881399587E-01-0.909529850E-01-0.937965512E-01 --0.966706723E-01-0.995757058E-01-0.102512285E+00-0.105480418E+00-0.108480513E+00 --0.111512825E+00-0.114577778E+00-0.117675595E+00-0.120806806E+00-0.123971678E+00 --0.127170697E+00-0.130404100E+00-0.133672148E+00-0.136975840E+00-0.140315175E+00 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0.320336558E-01 0.307386201E-01 0.294180345E-01 0.280720890E-01 - 0.267005693E-01 0.253034849E-01 0.238810796E-01 0.224330910E-01 0.209595412E-01 - 0.194611214E-01 0.179370809E-01 0.163876079E-01 0.148127293E-01 0.132124862E-01 - 0.115867974E-01 0.993568916E-02 0.825935975E-02 0.655745668E-02 0.483009638E-02 - 0.307746790E-02 0.129914156E-02-0.504776312E-03-0.233400101E-02-0.418897998E-02 --0.606957637E-02-0.797582697E-02-0.990781374E-02-0.118656056E-01-0.138493124E-01 --0.158589073E-01-0.178943723E-01-0.199560523E-01-0.220437031E-01-0.241576154E-01 --0.262979679E-01-0.284645464E-01-0.306575522E-01-0.328773819E-01-0.351236686E-01 --0.373968296E-01-0.396970399E-01-0.420241356E-01-0.443785153E-01-0.467600822E-01 --0.491692387E-01-0.516058728E-01-0.540702417E-01-0.565625466E-01-0.590828955E-01 --0.616314933E-01-0.642084852E-01-0.668141097E-01-0.694484487E-01-0.721117631E-01 --0.748043433E-01-0.775261745E-01-0.802777335E-01-0.830590874E-01-0.858705044E-01 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0.532391965E-01 0.524394996E-01 0.516050793E-01 0.507382601E-01 - 0.498378612E-01 0.489042215E-01 0.479372032E-01 0.469395332E-01 0.459128171E-01 - 0.448574573E-01 0.437732637E-01 0.426616631E-01 0.415236615E-01 0.403583348E-01 - 0.391674191E-01 0.379502997E-01 0.367064700E-01 0.354365334E-01 0.341399647E-01 - 0.328169726E-01 0.314679518E-01 0.300924294E-01 0.286904443E-01 0.272625834E-01 - 0.258085635E-01 0.243283678E-01 0.228220206E-01 0.212894119E-01 0.197308622E-01 - 0.181462429E-01 0.165354423E-01 0.148985153E-01 0.132357534E-01 0.115468130E-01 - 0.983167347E-02 0.809062086E-02 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 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0.642862096E-01 0.640547201E-01 0.637956262E-01 0.635087490E-01 - 0.631941184E-01 0.628508702E-01 0.624783859E-01 0.620768331E-01 0.616461672E-01 - 0.611850917E-01 0.606950149E-01 0.601741970E-01 0.596212931E-01 0.590361990E-01 - 0.584191158E-01 0.577695295E-01 0.570859239E-01 0.563680790E-01 0.556149818E-01 - 0.548261181E-01 0.540010482E-01 0.531392880E-01 0.522411130E-01 0.513072610E-01 - 0.503380410E-01 0.493358597E-01 0.482987911E-01 0.472264774E-01 0.461235866E-01 - 0.449917689E-01 0.438303836E-01 0.426403508E-01 0.414242521E-01 0.401804075E-01 - 0.389090218E-01 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 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0.867243391E-02 0.100276377E-01 0.113730645E-01 0.127088977E-01 0.140351690E-01 - 0.153511297E-01 0.166569445E-01 0.179526415E-01 0.192377660E-01 0.205126144E-01 - 0.217767525E-01 0.230300296E-01 0.242726747E-01 0.255046058E-01 0.267251972E-01 - 0.279348362E-01 0.291337445E-01 0.303213913E-01 0.314979069E-01 0.326633081E-01 - 0.338174477E-01 0.349604823E-01 0.360924788E-01 0.372130945E-01 0.383227095E-01 - 0.394213647E-01 0.405088551E-01 0.415854938E-01 0.426515080E-01 0.437066257E-01 - 0.447507612E-01 0.457839482E-01 0.468049049E-01 0.478123613E-01 0.488058738E-01 - 0.497820452E-01 0.507401451E-01 0.516761541E-01 0.525888652E-01 0.534765385E-01 - 0.543362312E-01 0.551678501E-01 0.559700392E-01 0.567424670E-01 0.574853159E-01 - 0.581985749E-01 0.588829294E-01 0.595386811E-01 0.601662286E-01 0.607656538E-01 - 0.613374189E-01 0.618814118E-01 0.623981766E-01 0.628878325E-01 0.633506104E-01 - 0.637871251E-01 0.641972944E-01 0.645812824E-01 0.649393350E-01 0.652716681E-01 - 0.655782893E-01 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0.281973165E-01 0.266195163E-01 0.250143763E-01 - 0.233819168E-01 0.217218474E-01 0.200345051E-01 0.183198992E-01 0.165779442E-01 - 0.148086073E-01 0.130119855E-01 0.111880740E-01 0.933688506E-02 0.745849591E-02 - 0.555268349E-02 0.361983781E-02 0.165958772E-02-0.328103226E-03-0.234282436E-02 --0.438492978E-02-0.645461399E-02-0.855158269E-02-0.106757646E-01-0.128274653E-01 --0.150067005E-01-0.172135215E-01-0.194477122E-01-0.217096992E-01-0.239993036E-01 --0.263165329E-01-0.286617465E-01-0.310347527E-01-0.334357284E-01-0.358648412E-01 --0.383220054E-01-0.408074483E-01-0.433211960E-01-0.458634384E-01-0.484342054E-01 --0.510336608E-01-0.536619872E-01-0.563191622E-01-0.590054616E-01-0.617210045E-01 --0.644658878E-01-0.672403499E-01-0.700444505E-01-0.728785098E-01-0.757425800E-01 --0.786369368E-01-0.815617219E-01-0.845172927E-01-0.875035822E-01-0.905210301E-01 --0.935698599E-01-0.966501981E-01-0.997623131E-01-0.102906674E+00-0.106083304E+00 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0.551816151E-01 0.541801453E-01 0.531381592E-01 0.520564541E-01 - 0.509337075E-01 0.497741252E-01 0.485768132E-01 0.473395362E-01 0.460719690E-01 - 0.447729416E-01 0.434421971E-01 0.420798138E-01 0.406898446E-01 0.392724052E-01 - 0.378260463E-01 0.363511741E-01 0.348478667E-01 0.333165824E-01 0.317570195E-01 - 0.301692542E-01 0.285532512E-01 0.269094203E-01 0.252374150E-01 0.235374290E-01 - 0.218096524E-01 0.200535990E-01 0.182697643E-01 0.164582003E-01 0.146185961E-01 - 0.127512421E-01 0.108560631E-01 0.893306080E-02 0.698218727E-02 0.500358129E-02 - 0.299733318E-02 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 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0.693545043E-01 0.689758211E-01 0.685666651E-01 0.681272522E-01 - 0.676575601E-01 0.671562329E-01 0.666233003E-01 0.660582334E-01 0.654633641E-01 - 0.648353249E-01 0.641733557E-01 0.634774491E-01 0.627479255E-01 0.619817451E-01 - 0.611792319E-01 0.603408776E-01 0.594654642E-01 0.585502684E-01 0.575957038E-01 - 0.566004477E-01 0.555631667E-01 0.544834770E-01 0.533582754E-01 0.521928519E-01 - 0.509877391E-01 0.497380309E-01 0.484463051E-01 0.471222997E-01 0.457649119E-01 - 0.443739779E-01 0.429479964E-01 0.414940752E-01 0.400113910E-01 0.384997986E-01 - 0.369591378E-01 0.353897549E-01 0.337916464E-01 0.321647674E-01 0.305090062E-01 - 0.288246460E-01 0.271116290E-01 0.253701117E-01 0.236000698E-01 0.218014345E-01 - 0.199742801E-01 0.181187689E-01 0.162349530E-01 0.143227838E-01 0.123822084E-01 - 0.104133692E-01 0.841627270E-02 0.639086124E-02 0.433723908E-02 0.225539971E-02 - 0.145302067E-03-0.199293299E-02-0.415950455E-02-0.635422301E-02-0.857718848E-02 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0.135677252E-01 0.115565788E-01 0.951591786E-02 - 0.744626625E-02 0.534769194E-02 0.322028692E-02 0.106428284E-02-0.111995009E-02 --0.333248288E-02-0.557278935E-02-0.784076937E-02-0.101362951E-01-0.124592418E-01 --0.148092033E-01-0.171860512E-01-0.195897128E-01-0.220200680E-01-0.244766939E-01 --0.269594658E-01-0.294683874E-01-0.320031978E-01-0.345636830E-01-0.371498913E-01 --0.397614241E-01-0.423981473E-01-0.450601690E-01-0.477471836E-01-0.504590273E-01 --0.531956553E-01-0.559569485E-01-0.587428324E-01-0.615531467E-01-0.643878207E-01 --0.672467500E-01-0.701298863E-01-0.730371699E-01-0.759685189E-01-0.789238960E-01 --0.819031745E-01-0.849064291E-01-0.879335254E-01-0.909845904E-01-0.940594971E-01 --0.971582010E-01-0.100280747E+00-0.103427291E+00-0.106597595E+00-0.109791905E+00 --0.113010243E+00-0.116252430E+00-0.119518898E+00-0.122809581E+00-0.126124188E+00 --0.129463375E+00-0.132827133E+00-0.136215255E+00-0.139628008E+00-0.143065795E+00 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0.360594504E-01 0.349016301E-01 0.337111726E-01 0.324882716E-01 - 0.312334318E-01 0.299467370E-01 0.286281295E-01 0.272778422E-01 0.258962512E-01 - 0.244833920E-01 0.230394546E-01 0.215644743E-01 0.200586952E-01 0.185222030E-01 - 0.169555899E-01 0.153589323E-01 0.137319332E-01 0.120751616E-01 0.103887385E-01 - 0.867284369E-02 0.692773191E-02 0.515334634E-02 0.334993191E-02 0.151803368E-02 --0.342705665E-03-0.223188614E-02-0.414903648E-02-0.609427597E-02-0.806759018E-02 --0.100685768E-01-0.120969545E-01-0.141527411E-01-0.162357539E-01-0.183458067E-01 --0.204826426E-01-0.226461645E-01-0.248362925E-01-0.270527657E-01-0.292954426E-01 --0.315642282E-01-0.338590071E-01-0.361794457E-01-0.385256149E-01-0.408972465E-01 --0.432942249E-01-0.457164980E-01-0.481639020E-01-0.506363586E-01-0.531337187E-01 --0.556558520E-01-0.582028218E-01-0.607743450E-01-0.633704290E-01-0.659909323E-01 --0.686358288E-01-0.713051334E-01-0.739987567E-01-0.767165497E-01-0.794585273E-01 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0.262693558E-01 0.272326376E-01 0.281837974E-01 0.291223675E-01 0.300482642E-01 - 0.309613980E-01 0.318611152E-01 0.327475034E-01 0.336202495E-01 0.344787985E-01 - 0.353228338E-01 0.361524597E-01 0.369668938E-01 0.377659425E-01 0.385493077E-01 - 0.393168405E-01 0.400674567E-01 0.408012383E-01 0.415178090E-01 0.422160439E-01 - 0.428963192E-01 0.435575359E-01 0.441992022E-01 0.448202379E-01 0.454196520E-01 - 0.459974706E-01 0.465526134E-01 0.470830575E-01 0.475901216E-01 0.480714403E-01 - 0.485261604E-01 0.489544347E-01 0.493553653E-01 0.497277491E-01 0.500723347E-01 - 0.503873341E-01 0.506728478E-01 0.509275831E-01 0.511514395E-01 0.513443425E-01 - 0.515068360E-01 0.516380891E-01 0.517371893E-01 0.518043898E-01 0.518396944E-01 - 0.518426672E-01 0.518127903E-01 0.517497435E-01 0.516535640E-01 0.515234359E-01 - 0.513592176E-01 0.511608981E-01 0.509279482E-01 0.506591797E-01 0.503566563E-01 - 0.500205159E-01 0.496449918E-01 0.492334254E-01 0.487891696E-01 0.483095907E-01 - 0.477928370E-01 0.472389944E-01 0.466491468E-01 0.460252799E-01 0.453651920E-01 - 0.446714982E-01 0.439432971E-01 0.431791991E-01 0.423818007E-01 0.415510722E-01 - 0.406870283E-01 0.397894569E-01 0.388591327E-01 0.378959440E-01 0.368998647E-01 - 0.358709171E-01 0.348094776E-01 0.337157547E-01 0.325897038E-01 0.314314589E-01 - 0.302414428E-01 0.290195122E-01 0.277659446E-01 0.264809672E-01 0.251646545E-01 - 0.238170847E-01 0.224387404E-01 0.210292954E-01 0.195893552E-01 0.181190316E-01 - 0.166184567E-01 0.150876036E-01 0.135267787E-01 0.119360304E-01 0.103157554E-01 - 0.866610929E-02 0.698721688E-02 0.527911354E-02 0.354205002E-02 0.177637930E-02 --0.180249444E-04-0.184086710E-02-0.369175780E-02-0.557077117E-02-0.747754751E-02 --0.941230264E-02-0.113745667E-01-0.133640431E-01-0.153808733E-01-0.174248815E-01 --0.194956623E-01-0.215930957E-01-0.237171724E-01-0.258675590E-01-0.280442573E-01 --0.302470960E-01-0.324758478E-01-0.347305164E-01-0.370108373E-01-0.393165909E-01 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0.753944553E-02 0.865011383E-02 0.975165423E-02 0.108438451E-01 0.119265094E-01 - 0.129994890E-01 0.140626626E-01 0.151156969E-01 0.161584932E-01 0.171908308E-01 - 0.182124991E-01 0.192233808E-01 0.202231146E-01 0.212116390E-01 0.221886467E-01 - 0.231541339E-01 0.241075382E-01 0.250488259E-01 0.259779170E-01 0.268941689E-01 - 0.277975872E-01 0.286882296E-01 0.295652039E-01 0.304285791E-01 0.312781222E-01 - 0.321134627E-01 0.329342633E-01 0.337405577E-01 0.345314518E-01 0.353070684E-01 - 0.360669382E-01 0.368104987E-01 0.375375934E-01 0.382476822E-01 0.389407575E-01 - 0.396159701E-01 0.402726717E-01 0.409109592E-01 0.415299423E-01 0.421290956E-01 - 0.427083783E-01 0.432663597E-01 0.438030176E-01 0.443183482E-01 0.448100381E-01 - 0.452780537E-01 0.457212888E-01 0.461396612E-01 0.465319492E-01 0.468974523E-01 - 0.472360849E-01 0.475458726E-01 0.478268825E-01 0.480803549E-01 0.483041853E-01 - 0.484975278E-01 0.486610830E-01 0.487944968E-01 0.488962270E-01 0.489658490E-01 - 0.490031317E-01 0.490100347E-01 0.489843823E-01 0.489253551E-01 0.488327108E-01 - 0.487070791E-01 0.485488288E-01 0.483567379E-01 0.481302068E-01 0.478690714E-01 - 0.475754179E-01 0.472461581E-01 0.468824655E-01 0.464855582E-01 0.460543446E-01 - 0.455868170E-01 0.450844727E-01 0.445486270E-01 0.439782143E-01 0.433748923E-01 - 0.427356847E-01 0.420637503E-01 0.413584597E-01 0.406194255E-01 0.398479737E-01 - 0.390433930E-01 0.382059403E-01 0.373358019E-01 0.364331491E-01 0.354978368E-01 - 0.345298871E-01 0.335299820E-01 0.324980244E-01 0.314338505E-01 0.303379241E-01 - 0.292103216E-01 0.280510802E-01 0.268604383E-01 0.256386027E-01 0.243853703E-01 - 0.231014118E-01 0.217865035E-01 0.204408541E-01 0.190647468E-01 0.176585019E-01 - 0.162219089E-01 0.147550460E-01 0.132585531E-01 0.117324265E-01 0.101766670E-01 - 0.859142467E-02 0.697713904E-02 0.533352327E-02 0.366119016E-02 0.196032203E-02 - 0.230643360E-03-0.152720709E-02-0.331342523E-02-0.512766931E-02-0.696982769E-02 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0.421562307E-01 0.426067710E-01 0.430346318E-01 0.434384570E-01 0.438182205E-01 - 0.441728048E-01 0.445008092E-01 0.448023416E-01 0.450775698E-01 0.453244634E-01 - 0.455426760E-01 0.457326733E-01 0.458938032E-01 0.460251644E-01 0.461258106E-01 - 0.461953580E-01 0.462348275E-01 0.462438129E-01 0.462204032E-01 0.461644307E-01 - 0.460767373E-01 0.459564999E-01 0.458037220E-01 0.456179157E-01 0.453990102E-01 - 0.451477841E-01 0.448638983E-01 0.445461981E-01 0.441952422E-01 0.438107699E-01 - 0.433931202E-01 0.429416969E-01 0.424573645E-01 0.419403948E-01 0.413894765E-01 - 0.408059768E-01 0.401891246E-01 0.395393968E-01 0.388568528E-01 0.381417722E-01 - 0.373941883E-01 0.366138965E-01 0.358012132E-01 0.349564999E-01 0.340792723E-01 - 0.331702083E-01 0.322293639E-01 0.312566124E-01 0.302521307E-01 0.292160530E-01 - 0.281485151E-01 0.270497315E-01 0.259197820E-01 0.247585978E-01 0.235665683E-01 - 0.223439373E-01 0.210905652E-01 0.198066775E-01 0.184924491E-01 0.171480738E-01 - 0.157736633E-01 0.143692214E-01 0.129349893E-01 0.114714019E-01 0.997822452E-02 - 0.845568907E-02 0.690418901E-02 0.532366056E-02 0.371435517E-02 0.207644165E-02 - 0.409861066E-03-0.128485833E-02-0.300781988E-02-0.475878222E-02-0.653747749E-02 --0.834399369E-02-0.101779420E-01-0.120393084E-01-0.139278304E-01-0.158433635E-01 --0.177857708E-01-0.197548810E-01-0.217507742E-01-0.237730071E-01-0.258213039E-01 --0.278959014E-01-0.299963579E-01-0.321226157E-01-0.342746116E-01-0.364520214E-01 --0.386550277E-01-0.408833176E-01-0.431365184E-01-0.454148464E-01-0.477181748E-01 --0.500461571E-01-0.523988046E-01-0.547760166E-01-0.571777113E-01-0.596037023E-01 --0.620540269E-01-0.645285398E-01-0.670271292E-01-0.695497841E-01-0.720964447E-01 --0.746669546E-01-0.772614330E-01-0.798796490E-01-0.825216994E-01-0.851875246E-01 --0.878770947E-01-0.905904621E-01-0.933275819E-01-0.960885584E-01-0.988732427E-01 --0.101681836E+00-0.104514308E+00-0.107370742E+00-0.110251270E+00-0.113155916E+00 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0.300249103E-01 0.307570733E-01 0.314734168E-01 0.321735218E-01 0.328572504E-01 - 0.335242860E-01 0.341739766E-01 0.348063298E-01 0.354207605E-01 0.360167623E-01 - 0.365941972E-01 0.371522978E-01 0.376909487E-01 0.382094048E-01 0.387073010E-01 - 0.391843282E-01 0.396401696E-01 0.400735885E-01 0.404845476E-01 0.408726297E-01 - 0.412368514E-01 0.415770411E-01 0.418922752E-01 0.421825685E-01 0.424465127E-01 - 0.426839031E-01 0.428947061E-01 0.430780984E-01 0.432333574E-01 0.433603302E-01 - 0.434575267E-01 0.435260832E-01 0.435651690E-01 0.435740128E-01 0.435519256E-01 - 0.434986055E-01 0.434150696E-01 0.433002301E-01 0.431538075E-01 0.429754816E-01 - 0.427654795E-01 0.425238311E-01 0.422496833E-01 0.419430137E-01 0.416046269E-01 - 0.412340090E-01 0.408308655E-01 0.403955653E-01 0.399278365E-01 0.394276232E-01 - 0.388949290E-01 0.383299813E-01 0.377328582E-01 0.371033736E-01 0.364415906E-01 - 0.357476920E-01 0.350219868E-01 0.342643075E-01 0.334746651E-01 0.326534249E-01 - 0.318003073E-01 0.309157800E-01 0.299998112E-01 0.290523060E-01 0.280737709E-01 - 0.270640496E-01 0.260232426E-01 0.249516647E-01 0.238491818E-01 0.227160100E-01 - 0.215526167E-01 0.203584675E-01 0.191340595E-01 0.178797320E-01 0.165952351E-01 - 0.152808493E-01 0.139368270E-01 0.125632575E-01 0.111601790E-01 0.972775836E-02 - 0.826622918E-02 0.677567301E-02 0.525631243E-02 0.370813860E-02 0.213158783E-02 - 0.526558084E-03-0.110679551E-02-0.276804972E-02-0.445737597E-02-0.617445167E-02 --0.791912433E-02-0.969131663E-02-0.114907641E-01-0.133172954E-01-0.151709383E-01 --0.170513652E-01-0.189584624E-01-0.208921600E-01-0.228521712E-01-0.248383339E-01 --0.268506333E-01-0.288889967E-01-0.309530962E-01-0.330427252E-01-0.351580270E-01 --0.372985974E-01-0.394643955E-01-0.416552350E-01-0.438710488E-01-0.461118445E-01 --0.483772606E-01-0.506672598E-01-0.529819056E-01-0.553208888E-01-0.576840565E-01 --0.600714423E-01-0.624829419E-01-0.649184659E-01-0.673779249E-01-0.698612630E-01 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0.387625098E-01 0.383723192E-01 0.379505232E-01 0.374969766E-01 - 0.370120667E-01 0.364954397E-01 0.359472483E-01 0.353674106E-01 0.347560756E-01 - 0.341133028E-01 0.334389918E-01 0.327330828E-01 0.319959335E-01 0.312276557E-01 - 0.304279551E-01 0.295971595E-01 0.287354104E-01 0.278426912E-01 0.269191563E-01 - 0.259647425E-01 0.249796882E-01 0.239640027E-01 0.229178444E-01 0.218414366E-01 - 0.207347255E-01 0.195978004E-01 0.184309073E-01 0.172341745E-01 0.160074625E-01 - 0.147512881E-01 0.134654967E-01 0.121502774E-01 0.108058983E-01 0.943238381E-02 - 0.802985858E-02 0.659850286E-02 0.513839815E-02 0.364973443E-02 0.213263161E-02 - 0.587267801E-03-0.986276078E-03-0.258769747E-02-0.421690242E-02-0.587393157E-02 --0.755853392E-02-0.927038770E-02-0.110095479E-01-0.127758551E-01-0.145688634E-01 --0.163888540E-01-0.182355978E-01-0.201085545E-01-0.220078956E-01-0.239334535E-01 --0.258849934E-01-0.278624892E-01-0.298656616E-01-0.318944342E-01-0.339486338E-01 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0.383043848E-01 0.384187438E-01 0.385064073E-01 0.385671854E-01 0.386001728E-01 - 0.386056304E-01 0.385828093E-01 0.385314003E-01 0.384513177E-01 0.383420847E-01 - 0.382036418E-01 0.380355604E-01 0.378377549E-01 0.376097411E-01 0.373521820E-01 - 0.370642841E-01 0.367456675E-01 0.363967828E-01 0.360172428E-01 0.356070288E-01 - 0.351660326E-01 0.346944369E-01 0.341919512E-01 0.336585343E-01 0.330943577E-01 - 0.324992985E-01 0.318734460E-01 0.312166605E-01 0.305290576E-01 0.298109800E-01 - 0.290618129E-01 0.282821544E-01 0.274720546E-01 0.266314223E-01 0.257602036E-01 - 0.248586088E-01 0.239267759E-01 0.229647011E-01 0.219724923E-01 0.209503379E-01 - 0.198981706E-01 0.188161638E-01 0.177044664E-01 0.165632386E-01 0.153922038E-01 - 0.141920159E-01 0.129625127E-01 0.117037492E-01 0.104159731E-01 0.909930468E-02 - 0.775376521E-02 0.637971144E-02 0.497702463E-02 0.354581955E-02 0.208657025E-02 - 0.599064981E-03-0.916554010E-03-0.245975354E-02-0.403092057E-02-0.562966755E-02 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0.311315395E-01 0.315972082E-01 0.320437327E-01 0.324702300E-01 0.328764059E-01 - 0.332620628E-01 0.336267203E-01 0.339701585E-01 0.342917293E-01 0.345912166E-01 - 0.348681137E-01 0.351218581E-01 0.353523083E-01 0.355589613E-01 0.357415564E-01 - 0.358992703E-01 0.360320620E-01 0.361395217E-01 0.362210833E-01 0.362766050E-01 - 0.363056362E-01 0.363074914E-01 0.362825505E-01 0.362299643E-01 0.361495130E-01 - 0.360411443E-01 0.359042659E-01 0.357390083E-01 0.355446897E-01 0.353217423E-01 - 0.350695550E-01 0.347878337E-01 0.344765745E-01 0.341359302E-01 0.337654315E-01 - 0.333652683E-01 0.329349935E-01 0.324749500E-01 0.319848247E-01 0.314645134E-01 - 0.309140738E-01 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 --0.546972677E-01-0.569273233E-01-0.591809526E-01-0.614581220E-01-0.637588575E-01 --0.660829395E-01-0.684301108E-01-0.708006322E-01-0.731943324E-01-0.756108612E-01 --0.780504569E-01-0.805129558E-01-0.829982758E-01-0.855064914E-01-0.880373865E-01 --0.905910656E-01-0.931675360E-01-0.957667381E-01-0.983886197E-01-0.101033255E+00 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0.196220204E-01 0.203405228E-01 0.210440680E-01 0.217323862E-01 0.224054344E-01 - 0.230626687E-01 0.237040464E-01 0.243295599E-01 0.249385070E-01 0.255309306E-01 - 0.261064526E-01 0.266649723E-01 0.272058602E-01 0.277290996E-01 0.282345805E-01 - 0.287216380E-01 0.291901175E-01 0.296397917E-01 0.300700981E-01 0.304809678E-01 - 0.308720320E-01 0.312427450E-01 0.315930918E-01 0.319223329E-01 0.322303958E-01 - 0.325167030E-01 0.327810869E-01 0.330231711E-01 0.332423002E-01 0.334385075E-01 - 0.336111449E-01 0.337597467E-01 0.338841788E-01 0.339840613E-01 0.340591371E-01 - 0.341086052E-01 0.341324881E-01 0.341307223E-01 0.341023393E-01 0.340473242E-01 - 0.339655988E-01 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 --0.234041139E-01-0.252082497E-01-0.270378198E-01-0.288928542E-01-0.307730269E-01 --0.326783136E-01-0.346085690E-01-0.365634561E-01-0.385430604E-01-0.405474268E-01 --0.425760783E-01-0.446288139E-01-0.467059463E-01-0.488069803E-01-0.509318747E-01 --0.530805364E-01-0.552528352E-01-0.574486293E-01-0.596679375E-01-0.619104840E-01 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0.310778413E-01 0.308324359E-01 0.305596218E-01 0.302587021E-01 - 0.299297888E-01 0.295729935E-01 0.291879401E-01 0.287744515E-01 0.283325072E-01 - 0.278620254E-01 0.273629986E-01 0.268354416E-01 0.262788590E-01 0.256936103E-01 - 0.250794794E-01 0.244365167E-01 0.237647016E-01 0.230639186E-01 0.223342646E-01 - 0.215758234E-01 0.207883716E-01 0.199721549E-01 0.191272013E-01 0.182531774E-01 - 0.173505209E-01 0.164194144E-01 0.154595664E-01 0.144711342E-01 0.134541793E-01 - 0.124087781E-01 0.113348933E-01 0.102329692E-01 0.910268072E-02 0.794402324E-02 - 0.675752154E-02 0.554328179E-02 0.430092355E-02 0.303088431E-02 0.173330505E-02 - 0.407984015E-03-0.944673782E-03-0.232456159E-02-0.373184169E-02-0.516619440E-02 --0.662737759E-02-0.811557658E-02-0.963036809E-02-0.111717563E-01-0.127397208E-01 --0.143339476E-01-0.159544554E-01-0.176009424E-01-0.192733593E-01-0.209716782E-01 --0.226957519E-01-0.244451910E-01-0.262200069E-01-0.280201789E-01-0.298453867E-01 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0.293862727E-01 0.295610297E-01 0.297135729E-01 0.298433602E-01 0.299503207E-01 - 0.300342105E-01 0.300943144E-01 0.301305614E-01 0.301428083E-01 0.301304832E-01 - 0.300934296E-01 0.300314184E-01 0.299443174E-01 0.298313592E-01 0.296929125E-01 - 0.295284148E-01 0.293376204E-01 0.291205402E-01 0.288768113E-01 0.286059976E-01 - 0.283082519E-01 0.279834922E-01 0.276314076E-01 0.272516422E-01 0.268443488E-01 - 0.264093913E-01 0.259467233E-01 0.254559088E-01 0.249372199E-01 0.243905634E-01 - 0.238157287E-01 0.232126210E-01 0.225813966E-01 0.219217744E-01 0.212340578E-01 - 0.205179267E-01 0.197735019E-01 0.190008860E-01 0.181999616E-01 0.173706412E-01 - 0.165131092E-01 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 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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 --0.486775301E-01-0.506859906E-01-0.527176298E-01-0.547720864E-01-0.568497218E-01 --0.589499772E-01-0.610726811E-01-0.632180572E-01-0.653857738E-01-0.675757974E-01 --0.697880089E-01-0.720222592E-01-0.742783919E-01-0.765564144E-01-0.788562372E-01 --0.811777487E-01-0.835208073E-01-0.858853161E-01-0.882713124E-01-0.906787068E-01 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0.112298662E-01 0.119473487E-01 0.126501406E-01 0.133378813E-01 0.140106035E-01 - 0.146681219E-01 0.153100751E-01 0.159366000E-01 0.165474787E-01 0.171422940E-01 - 0.177210569E-01 0.182836782E-01 0.188298449E-01 0.193593949E-01 0.198722389E-01 - 0.203680489E-01 0.208467804E-01 0.213081390E-01 0.217519328E-01 0.221779440E-01 - 0.225859918E-01 0.229758862E-01 0.233473536E-01 0.237003099E-01 0.240343008E-01 - 0.243493449E-01 0.246449504E-01 0.249209832E-01 0.251772013E-01 0.254133157E-01 - 0.256292801E-01 0.258245058E-01 0.259988941E-01 0.261524450E-01 0.262845755E-01 - 0.263948794E-01 0.264833868E-01 0.265498850E-01 0.265938286E-01 0.266151838E-01 - 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 --0.208378118E-01-0.224335548E-01-0.240540951E-01-0.256998166E-01-0.273701567E-01 --0.290649440E-01-0.307844449E-01-0.325281993E-01-0.342961997E-01-0.360883102E-01 --0.379045531E-01-0.397443958E-01-0.416080579E-01-0.434952639E-01-0.454058573E-01 --0.473397374E-01-0.492967367E-01-0.512767136E-01-0.532796234E-01-0.553053096E-01 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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 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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 --0.436312966E-01-0.454437435E-01-0.472789966E-01-0.491368137E-01-0.510168001E-01 --0.529193096E-01-0.548438132E-01-0.567901097E-01-0.587583221E-01-0.607482046E-01 --0.627596825E-01-0.647925064E-01-0.668464452E-01-0.689216778E-01-0.710177720E-01 --0.731346682E-01-0.752723292E-01-0.774307027E-01-0.796092972E-01-0.818083510E-01 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--0.254916728E+00-0.258567363E+00-0.262258410E+00-0.265988141E+00-0.269760489E+00 --0.273577482E+00-0.277439117E+00-0.515849590E-01-0.503069349E-01-0.490329228E-01 --0.477632917E-01-0.464989170E-01-0.452395603E-01-0.439852178E-01-0.427368432E-01 --0.414935797E-01-0.402566493E-01-0.390262604E-01-0.378020704E-01-0.365842953E-01 --0.353738256E-01-0.341706946E-01-0.329749882E-01-0.317869075E-01-0.306071006E-01 --0.294353887E-01-0.282722339E-01-0.271178279E-01-0.259723738E-01-0.248362981E-01 --0.237096138E-01-0.225927290E-01-0.214857049E-01-0.203891154E-01-0.193028077E-01 --0.182269067E-01-0.171622448E-01-0.161086153E-01-0.150663489E-01-0.140353562E-01 --0.130163310E-01-0.120094083E-01-0.110145537E-01-0.100320242E-01-0.906186737E-02 --0.810472202E-02-0.716034416E-02-0.622898992E-02-0.531115476E-02-0.440655882E-02 --0.351542118E-02-0.263825734E-02-0.177498837E-02-0.925614033E-03-0.905386914E-04 - 0.730202533E-03 0.153648457E-02 0.232814625E-02 0.310507789E-02 0.386713608E-02 - 0.461423909E-02 0.534619996E-02 0.606297283E-02 0.676446455E-02 0.745036872E-02 - 0.812075473E-02 0.877547730E-02 0.941451639E-02 0.100376299E-01 0.106446948E-01 - 0.112356469E-01 0.118104555E-01 0.123689333E-01 0.129109519E-01 0.134365447E-01 - 0.139454072E-01 0.144374790E-01 0.149128111E-01 0.153711298E-01 0.158123039E-01 - 0.162363127E-01 0.166429412E-01 0.170321222E-01 0.174037237E-01 0.177575853E-01 - 0.180935953E-01 0.184115786E-01 0.187114794E-01 0.189930722E-01 0.192562323E-01 - 0.195008423E-01 0.197266191E-01 0.199335515E-01 0.201214142E-01 0.202900358E-01 - 0.204393063E-01 0.205689333E-01 0.206788760E-01 0.207688957E-01 0.208387841E-01 - 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 --0.187557265E-01-0.201701485E-01-0.216087997E-01-0.230716746E-01-0.245585740E-01 --0.260697659E-01-0.276048090E-01-0.291634910E-01-0.307459608E-01-0.323520340E-01 --0.339815505E-01-0.356344171E-01-0.373104662E-01-0.390095711E-01-0.407317914E-01 --0.424767211E-01-0.442443751E-01-0.460346267E-01-0.478471816E-01-0.496820398E-01 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--0.199399605E+00-0.202474251E+00-0.205573127E+00-0.208697706E+00-0.211846769E+00 --0.215022281E+00-0.218224972E+00-0.221454158E+00-0.224712014E+00-0.227998167E+00 --0.231314108E+00-0.234660476E+00-0.238035977E+00-0.241448477E+00-0.244894207E+00 --0.248372436E+00-0.251883179E+00-0.255426466E+00-0.259002268E+00-0.262629181E+00 --0.266288102E+00-0.269981563E+00-0.273719698E+00-0.277502447E+00-0.508996993E-01 --0.496241115E-01-0.483522750E-01-0.470841825E-01-0.458220989E-01-0.445657074E-01 --0.433146916E-01-0.420690887E-01-0.408291854E-01-0.395963304E-01-0.383703858E-01 --0.371508114E-01-0.359378867E-01-0.347327515E-01-0.335353166E-01-0.323456228E-01 --0.311640725E-01-0.299910586E-01-0.288265795E-01-0.276711024E-01-0.265248381E-01 --0.253878683E-01-0.242605116E-01-0.231432281E-01-0.220360942E-01-0.209393222E-01 --0.198533740E-01-0.187781807E-01-0.177141838E-01-0.166617017E-01-0.156207336E-01 --0.145913754E-01-0.135742659E-01-0.125694405E-01-0.115769003E-01-0.105971107E-01 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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 --0.607318769E-03-0.161159458E-02-0.264049927E-02-0.369431428E-02-0.477299513E-02 --0.587647827E-02-0.700471969E-02-0.815766584E-02-0.933538657E-02-0.105376821E-01 --0.117645739E-01-0.130159939E-01-0.142920045E-01-0.155923562E-01-0.169170890E-01 --0.182661228E-01-0.196393561E-01-0.210366715E-01-0.224581007E-01-0.239034388E-01 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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 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0.103087127E-01 0.108163767E-01 0.113070477E-01 0.117805060E-01 0.122366939E-01 - 0.126754502E-01 0.130969258E-01 0.135010593E-01 0.138875516E-01 0.142565239E-01 - 0.146078384E-01 0.149414260E-01 0.152572170E-01 0.155551722E-01 0.158351175E-01 - 0.160970874E-01 0.163409375E-01 0.165665671E-01 0.167738944E-01 0.169628263E-01 - 0.171332564E-01 0.172850750E-01 0.174182300E-01 0.175325442E-01 0.176279154E-01 - 0.177042354E-01 0.177614018E-01 0.177992601E-01 0.178177264E-01 0.178166442E-01 - 0.177958254E-01 0.177552197E-01 0.176946782E-01 0.176139735E-01 0.175131187E-01 - 0.173918828E-01 0.172500052E-01 0.170875657E-01 0.169044044E-01 0.167000834E-01 - 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 --0.391746871E-01-0.408169776E-01-0.424816348E-01-0.441683717E-01-0.458769463E-01 --0.476074256E-01-0.493597202E-01-0.511336140E-01-0.529287942E-01-0.547452867E-01 --0.565830097E-01-0.584416054E-01-0.603210442E-01-0.622211173E-01-0.641417056E-01 --0.660828128E-01-0.680440739E-01-0.700251386E-01-0.720261410E-01-0.740469471E-01 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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 --0.167826768E-01-0.180423129E-01-0.193254873E-01-0.206319448E-01-0.219619405E-01 --0.233151074E-01-0.246914122E-01-0.260908417E-01-0.275133476E-01-0.289589036E-01 --0.304271970E-01-0.319182575E-01-0.334321037E-01-0.349685326E-01-0.365274549E-01 --0.381087810E-01-0.397123247E-01-0.413380452E-01-0.429857522E-01-0.446553752E-01 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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 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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 --0.612014309E-01-0.630476028E-01-0.649138391E-01-0.667997077E-01-0.687051564E-01 --0.706297830E-01-0.725737065E-01-0.745365769E-01-0.765181035E-01-0.785183758E-01 --0.805370212E-01-0.825738758E-01-0.846286193E-01-0.867013186E-01-0.887916237E-01 --0.908992216E-01-0.930240527E-01-0.951660052E-01-0.973246247E-01-0.994998515E-01 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0.692521874E-02 0.746716745E-02 0.799079984E-02 0.849598460E-02 0.898278877E-02 - 0.945118256E-02 0.990129821E-02 0.103328684E-01 0.107461233E-01 0.111410981E-01 - 0.115176458E-01 0.118758772E-01 0.122157969E-01 0.125374319E-01 0.128407814E-01 - 0.131258182E-01 0.133926235E-01 0.136411646E-01 0.138714388E-01 0.140835037E-01 - 0.142773204E-01 0.144528598E-01 0.146101546E-01 0.147491843E-01 0.148699125E-01 - 0.149723394E-01 0.150564322E-01 0.151221687E-01 0.151695563E-01 0.151984356E-01 - 0.152088292E-01 0.152007807E-01 0.151741011E-01 0.151287448E-01 0.150646493E-01 - 0.149817988E-01 0.148801478E-01 0.147595294E-01 0.146199819E-01 0.144612379E-01 - 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 --0.349401459E-01-0.364359468E-01-0.379535705E-01-0.394928753E-01-0.410538130E-01 --0.426363721E-01-0.442403816E-01-0.458655506E-01-0.475120023E-01-0.491795763E-01 --0.508679338E-01-0.525771976E-01-0.543071032E-01-0.560574085E-01-0.578281507E-01 --0.596191138E-01-0.614300780E-01-0.632608458E-01-0.651113987E-01-0.669814125E-01 --0.688707158E-01-0.707792938E-01-0.727067888E-01-0.746530741E-01-0.766179860E-01 --0.786011741E-01-0.806025937E-01-0.826219767E-01-0.846591666E-01-0.867138803E-01 --0.887859315E-01-0.908751041E-01-0.929812416E-01-0.951041058E-01-0.972433314E-01 --0.993989110E-01-0.101570614E+00-0.103758089E+00-0.105961278E+00-0.108179763E+00 --0.110413440E+00-0.112662084E+00-0.114925638E+00-0.117203847E+00-0.119496405E+00 --0.121802919E+00-0.124123633E+00-0.126458168E+00-0.128806263E+00-0.131168127E+00 --0.133542880E+00-0.135931209E+00-0.138332576E+00-0.140746847E+00-0.143173516E+00 --0.145612955E+00-0.148065120E+00-0.150529817E+00-0.153006852E+00-0.155496165E+00 --0.157997817E+00-0.160511658E+00-0.163037732E+00-0.165575817E+00-0.168126255E+00 --0.170688748E+00-0.173263922E+00-0.175850973E+00-0.178450406E+00-0.181062385E+00 --0.183686733E+00-0.186323851E+00-0.188973173E+00-0.191635862E+00-0.194311559E+00 --0.196999893E+00-0.199702203E+00-0.202418014E+00-0.205146849E+00-0.207890287E+00 --0.210647807E+00-0.213419393E+00-0.216205850E+00-0.219007120E+00-0.221823543E+00 --0.224655941E+00-0.227503374E+00-0.230366781E+00-0.233247027E+00-0.236143902E+00 --0.239057422E+00-0.241984069E+00-0.244930938E+00-0.247902408E+00-0.250890434E+00 --0.253895015E+00-0.256916165E+00-0.259953856E+00-0.263008147E+00-0.266071826E+00 --0.269162387E+00-0.272280067E+00-0.275424808E+00-0.448534973E-01-0.435741656E-01 --0.423019007E-01-0.410359316E-01-0.397755839E-01-0.385223068E-01-0.372772478E-01 --0.360401683E-01-0.348107181E-01-0.335894413E-01-0.323773064E-01-0.311741624E-01 --0.299801305E-01-0.287962779E-01-0.276224371E-01-0.264593586E-01-0.253069606E-01 --0.241659302E-01-0.230365731E-01-0.219190549E-01-0.208137818E-01-0.197211578E-01 --0.186416302E-01-0.175754186E-01-0.165226869E-01-0.154841933E-01-0.144598214E-01 --0.134500973E-01-0.124552716E-01-0.114759477E-01-0.105119618E-01-0.956392288E-02 --0.863185711E-02-0.771614304E-02-0.681710057E-02-0.593476137E-02-0.506946957E-02 --0.422147848E-02-0.339096831E-02-0.257814047E-02-0.178294559E-02-0.100568403E-02 --0.246821728E-03 0.493854866E-03 0.121642335E-02 0.192036747E-02 0.260583824E-02 - 0.327273225E-02 0.392080192E-02 0.455027726E-02 0.516084582E-02 0.575253833E-02 - 0.632551406E-02 0.687954715E-02 0.741473073E-02 0.793098565E-02 0.842835847E-02 - 0.890693907E-02 0.936663244E-02 0.980756059E-02 0.102296397E-01 0.106329843E-01 - 0.110176308E-01 0.113835903E-01 0.117309224E-01 0.120596234E-01 0.123696877E-01 - 0.126612987E-01 0.129344650E-01 0.131891016E-01 0.134253018E-01 0.136430860E-01 - 0.138425231E-01 0.140236160E-01 0.141863627E-01 0.143308491E-01 0.144570228E-01 - 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 --0.145871360E-01-0.157174356E-01-0.168700237E-01-0.180449020E-01-0.192422625E-01 --0.204617754E-01-0.217036009E-01-0.229676869E-01-0.242540576E-01-0.255625620E-01 --0.268932376E-01-0.282460544E-01-0.296209268E-01-0.310177431E-01-0.324365422E-01 --0.338772163E-01-0.353396684E-01-0.368238539E-01-0.383297130E-01-0.398570970E-01 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--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 --0.438046493E-01-0.425228402E-01-0.412471108E-01-0.399774574E-01-0.387142003E-01 --0.374589562E-01-0.362119339E-01-0.349732712E-01-0.337437056E-01-0.325217247E-01 --0.313091539E-01-0.301056784E-01-0.289115123E-01-0.277279746E-01-0.265549459E-01 --0.253927354E-01-0.242418777E-01-0.231028385E-01-0.219756328E-01-0.208608769E-01 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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 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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 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0.506852055E-02 0.567056565E-02 0.625190232E-02 0.681253383E-02 0.735215377E-02 - 0.787119102E-02 0.836970285E-02 0.884734932E-02 0.930424221E-02 0.974091142E-02 - 0.101571176E-01 0.105528971E-01 0.109284744E-01 0.112838643E-01 0.116193267E-01 - 0.119347721E-01 0.122305341E-01 0.125066740E-01 0.127630951E-01 0.130002527E-01 - 0.132181449E-01 0.134167532E-01 0.135962889E-01 0.137569336E-01 0.138986669E-01 - 0.140217105E-01 0.141260875E-01 0.142118661E-01 0.142792715E-01 0.143282823E-01 - 0.143589573E-01 0.143713588E-01 0.143656377E-01 0.143417791E-01 0.142998248E-01 - 0.142398514E-01 0.141617963E-01 0.140657993E-01 0.139518837E-01 0.138198817E-01 - 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 --0.306057427E-01-0.319756791E-01-0.333669111E-01-0.347794518E-01-0.362131074E-01 --0.376681425E-01-0.391441695E-01-0.406411886E-01-0.421591774E-01-0.436980501E-01 --0.452577360E-01-0.468380861E-01-0.484390073E-01-0.500604212E-01-0.517022014E-01 --0.533642098E-01-0.550464876E-01-0.567485876E-01-0.584705286E-01-0.602121949E-01 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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 --0.118966019E-01-0.129207196E-01-0.139658079E-01-0.150319105E-01-0.161190815E-01 --0.172272846E-01-0.183567069E-01-0.195072368E-01-0.206789207E-01-0.218717996E-01 --0.230859257E-01-0.243212376E-01-0.255777314E-01-0.268554818E-01-0.281544998E-01 --0.294747017E-01-0.308160223E-01-0.321785957E-01-0.335622728E-01-0.349670425E-01 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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 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--0.117807463E+00-0.120011881E+00-0.122227453E+00-0.124454260E+00-0.126691550E+00 --0.128939092E+00-0.131196514E+00-0.133463532E+00-0.135739684E+00-0.138024777E+00 --0.140318215E+00-0.142619848E+00-0.144929260E+00-0.147246584E+00-0.149570793E+00 --0.151901647E+00-0.154239818E+00-0.156583965E+00-0.158933789E+00-0.161289588E+00 --0.163651064E+00-0.166017979E+00-0.168389782E+00-0.170766726E+00-0.173148423E+00 --0.175534517E+00-0.177925020E+00-0.180320188E+00-0.182718784E+00-0.185121834E+00 --0.187529400E+00-0.189940199E+00-0.192355603E+00-0.194775194E+00-0.197197676E+00 --0.199624777E+00-0.202055782E+00-0.204490662E+00-0.206929237E+00-0.209372222E+00 --0.211819336E+00-0.214270785E+00-0.216726512E+00-0.219186425E+00-0.221651182E+00 --0.224120378E+00-0.226594269E+00-0.229073286E+00-0.231557146E+00-0.234045938E+00 --0.236539960E+00-0.239039153E+00-0.241543591E+00-0.244054988E+00-0.246571898E+00 --0.249093324E+00-0.251619250E+00-0.254149675E+00-0.256684631E+00-0.259224057E+00 --0.261768043E+00-0.264323533E+00-0.266870826E+00-0.269424349E+00-0.271985829E+00 --0.378044099E-01-0.365002602E-01-0.352021270E-01-0.339099690E-01-0.326244794E-01 --0.313482285E-01-0.300812460E-01-0.288235284E-01-0.275750607E-01-0.263364911E-01 --0.251079537E-01-0.238894466E-01-0.226814393E-01-0.214858763E-01-0.203027036E-01 --0.191320796E-01-0.179749783E-01-0.168313626E-01-0.157018732E-01-0.145876296E-01 --0.134886988E-01-0.124057354E-01-0.113390321E-01-0.102893086E-01-0.925711449E-02 --0.824267417E-02-0.724700047E-02-0.626986474E-02-0.531239854E-02-0.437475694E-02 --0.345726451E-02-0.256017060E-02-0.168436940E-02-0.829635363E-03 0.347032642E-05 - 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 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--0.842035860E-01-0.861729458E-01-0.881588534E-01-0.901608169E-01-0.921787694E-01 --0.942122489E-01-0.962612852E-01-0.983251408E-01-0.100403480E+00-0.102496579E+00 --0.104603410E+00-0.106723748E+00-0.108857498E+00-0.111004069E+00-0.113163494E+00 --0.115335032E+00-0.117518134E+00-0.119712844E+00-0.121918477E+00-0.124135166E+00 --0.126361817E+00-0.128598258E+00-0.130844504E+00-0.133099526E+00-0.135363325E+00 --0.137635708E+00-0.139915690E+00-0.142203704E+00-0.144498661E+00-0.146800041E+00 --0.149108291E+00-0.151422411E+00-0.153742760E+00-0.156068161E+00-0.158398688E+00 --0.160734549E+00-0.163074479E+00-0.165418461E+00-0.167766809E+00-0.170118794E+00 --0.172474101E+00-0.174833059E+00-0.177195489E+00-0.179559872E+00-0.181927279E+00 --0.184297934E+00-0.186671048E+00-0.189046547E+00-0.191424459E+00-0.193804294E+00 --0.196186930E+00-0.198571816E+00-0.200959086E+00-0.203347996E+00-0.205740005E+00 --0.208133996E+00-0.210530221E+00-0.212929159E+00-0.215330288E+00-0.217734590E+00 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0.448401319E-02 0.518999156E-02 0.587124517E-02 0.652845670E-02 0.716107292E-02 - 0.776935788E-02 0.835291855E-02 0.891228952E-02 0.944705401E-02 0.995747093E-02 - 0.104437657E-01 0.109056523E-01 0.113433497E-01 0.117574809E-01 0.121479938E-01 - 0.125147523E-01 0.128582306E-01 0.131784948E-01 0.134764966E-01 0.137515906E-01 - 0.140044531E-01 0.142353382E-01 0.144444453E-01 0.146321272E-01 0.147984326E-01 - 0.149439741E-01 0.150689781E-01 0.151734911E-01 0.152577292E-01 0.153222857E-01 - 0.153673925E-01 0.153930001E-01 0.153995175E-01 0.153871858E-01 0.153560415E-01 - 0.153065501E-01 0.152388755E-01 0.151529936E-01 0.150490869E-01 0.149275865E-01 - 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 --0.259132329E-01-0.271752644E-01-0.284577794E-01-0.297609027E-01-0.310846306E-01 --0.324289501E-01-0.337937996E-01-0.351792686E-01-0.365853384E-01-0.380118862E-01 --0.394589715E-01-0.409265645E-01-0.424145609E-01-0.439229794E-01-0.454516411E-01 --0.470005944E-01-0.485697538E-01-0.501591228E-01-0.517684184E-01-0.533976406E-01 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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 --0.850062538E-02-0.944027863E-02-0.103992019E-01-0.113775777E-01-0.123754079E-01 --0.133928219E-01-0.144298971E-01-0.154867545E-01-0.165634099E-01-0.176599044E-01 --0.187764484E-01-0.199129488E-01-0.210695751E-01-0.222463645E-01-0.234433301E-01 --0.246605966E-01-0.258980934E-01-0.271559954E-01-0.284341797E-01-0.297327526E-01 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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 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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 --0.420119949E-01-0.435039625E-01-0.450161099E-01-0.465482660E-01-0.481004082E-01 --0.496725962E-01-0.512646362E-01-0.528764389E-01-0.545081124E-01-0.561594740E-01 --0.578304380E-01-0.595209934E-01-0.612310171E-01-0.629603416E-01-0.647087097E-01 --0.664761737E-01-0.682625026E-01-0.700675547E-01-0.718912184E-01-0.737332851E-01 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0.470217830E-02 0.557710743E-02 0.642456207E-02 0.724458508E-02 0.803264696E-02 - 0.879503042E-02 0.952943973E-02 0.102324765E-01 0.109069236E-01 0.115517918E-01 - 0.121677341E-01 0.127539979E-01 0.133104147E-01 0.138371354E-01 0.143309217E-01 - 0.147937397E-01 0.152286515E-01 0.156346131E-01 0.160117000E-01 0.163608249E-01 - 0.166819990E-01 0.169728845E-01 0.172368437E-01 0.174744148E-01 0.176873207E-01 - 0.178738125E-01 0.180329811E-01 0.181668326E-01 0.182759296E-01 0.183614343E-01 - 0.184237715E-01 0.184644442E-01 0.184818618E-01 0.184766725E-01 0.184495952E-01 - 0.184019711E-01 0.183339361E-01 0.182457343E-01 0.181383546E-01 0.180130731E-01 - 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 --0.206745118E-01-0.218444150E-01-0.230334643E-01-0.242422745E-01-0.254707672E-01 --0.267189201E-01-0.279868990E-01-0.292746462E-01-0.305819977E-01-0.319093429E-01 --0.332567170E-01-0.346240886E-01-0.360114984E-01-0.374189503E-01-0.388460159E-01 --0.402933471E-01-0.417607538E-01-0.432481989E-01-0.447557345E-01-0.462832600E-01 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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 --0.423913170E-02-0.511594396E-02-0.601024926E-02-0.692189718E-02-0.785091799E-02 --0.879727490E-02-0.976210553E-02-0.107448418E-01-0.117451670E-01-0.127630811E-01 --0.137996124E-01-0.148549778E-01-0.159290433E-01-0.170217175E-01-0.181331541E-01 --0.192633029E-01-0.204129182E-01-0.215815213E-01-0.227690954E-01-0.239756405E-01 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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 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0.174458586E-01 0.180044528E-01 0.185237490E-01 0.190087091E-01 0.194593519E-01 - 0.198756754E-01 0.202576816E-01 0.206109472E-01 0.209346190E-01 0.212123469E-01 - 0.214571469E-01 0.216709822E-01 0.218585823E-01 0.220145192E-01 0.221308656E-01 - 0.222165287E-01 0.222750269E-01 0.223063603E-01 0.223105289E-01 0.222889185E-01 - 0.222490225E-01 0.221870579E-01 0.220960211E-01 0.219801106E-01 0.218420178E-01 - 0.216809288E-01 0.215006210E-01 0.213016365E-01 0.210839752E-01 0.208476353E-01 - 0.205926318E-01 0.203183368E-01 0.200245269E-01 0.197172835E-01 0.193937272E-01 - 0.190510191E-01 0.186944082E-01 0.183238983E-01 0.179394875E-01 0.175411776E-01 - 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 --0.349459015E-01-0.363427289E-01-0.377592295E-01-0.391953960E-01-0.406512767E-01 --0.421270803E-01-0.436227471E-01-0.451381393E-01-0.466732793E-01-0.482284799E-01 --0.498035997E-01-0.513985492E-01-0.530133285E-01-0.546479300E-01-0.563022941E-01 --0.579764955E-01-0.596706122E-01-0.613840558E-01-0.631167069E-01-0.648693144E-01 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0.489740726E-02 0.601375010E-02 0.710576959E-02 0.817346573E-02 0.921683852E-02 - 0.102353524E-01 0.112142451E-01 0.121578733E-01 0.130662378E-01 0.139393387E-01 - 0.147771761E-01 0.155797489E-01 0.163470581E-01 0.170791037E-01 0.177805908E-01 - 0.184525810E-01 0.190779828E-01 0.196602345E-01 0.201993361E-01 0.206952114E-01 - 0.211514719E-01 0.215734169E-01 0.219610427E-01 0.223143492E-01 0.226312913E-01 - 0.229138136E-01 0.231627990E-01 0.233761445E-01 0.235577300E-01 0.237014163E-01 - 0.238072034E-01 0.238751471E-01 0.239118375E-01 0.239213649E-01 0.239037257E-01 - 0.238589216E-01 0.237884298E-01 0.236957390E-01 0.235809796E-01 0.234441534E-01 - 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 --0.147663672E-01-0.158583876E-01-0.169700943E-01-0.180995483E-01-0.192469563E-01 --0.204123165E-01-0.215956308E-01-0.227970518E-01-0.240173656E-01-0.252566654E-01 --0.265149511E-01-0.277922507E-01-0.290889349E-01-0.304050110E-01-0.317404754E-01 --0.330949202E-01-0.344689637E-01-0.358626731E-01-0.372760519E-01-0.387091003E-01 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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 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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 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0.215452258E-01 0.223723147E-01 0.231668353E-01 0.239310190E-01 0.246599391E-01 - 0.253602602E-01 0.260067768E-01 0.265971553E-01 0.271313917E-01 0.276094880E-01 - 0.280314460E-01 0.283972621E-01 0.287458431E-01 0.290517472E-01 0.293118376E-01 - 0.295049157E-01 0.296643972E-01 0.297783483E-01 0.298467688E-01 0.298696589E-01 - 0.298470184E-01 0.297788456E-01 0.296758711E-01 0.295563471E-01 0.294189565E-01 - 0.292400885E-01 0.290299132E-01 0.287919454E-01 0.285310205E-01 0.282471403E-01 - 0.279403049E-01 0.276105125E-01 0.272577666E-01 0.268860813E-01 0.264986455E-01 - 0.260925479E-01 0.256592091E-01 0.252075624E-01 0.247445889E-01 0.242702849E-01 - 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 --0.273298081E-01-0.286384467E-01-0.299667548E-01-0.313131288E-01-0.326783508E-01 --0.340630710E-01-0.354672968E-01-0.368910208E-01-0.383342467E-01-0.397969745E-01 --0.412792116E-01-0.427810699E-01-0.443025976E-01-0.458434634E-01-0.474038571E-01 --0.489845723E-01-0.505856164E-01-0.522069819E-01-0.538486764E-01-0.555106923E-01 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0.385288103E-02 0.526568526E-02 0.667837076E-02 0.807681493E-02 0.944808498E-02 - 0.107921828E-01 0.121091064E-01 0.133988569E-01 0.146614332E-01 0.158968363E-01 - 0.171050671E-01 0.182753466E-01 0.194140878E-01 0.205047764E-01 0.215461440E-01 - 0.225381926E-01 0.234809183E-01 0.243743248E-01 0.252184086E-01 0.260131732E-01 - 0.267586149E-01 0.274820216E-01 0.281742364E-01 0.288103111E-01 0.293902438E-01 - 0.299140383E-01 0.303816926E-01 0.307932049E-01 0.311485790E-01 0.314478129E-01 - 0.316909067E-01 0.319150724E-01 0.320656002E-01 0.321705937E-01 0.322300605E-01 - 0.322439931E-01 0.322123952E-01 0.321352705E-01 0.320126116E-01 0.318444222E-01 - 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 --0.811322685E-02-0.914633926E-02-0.101956110E-01-0.112610413E-01-0.123426300E-01 --0.134403780E-01-0.145542854E-01-0.156843513E-01-0.168305766E-01-0.179951079E-01 --0.191739257E-01-0.203704312E-01-0.215851478E-01-0.228180736E-01-0.240692068E-01 --0.253385510E-01-0.266261026E-01-0.279318653E-01-0.292558353E-01-0.305997469E-01 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--0.148677468E+00-0.151066095E+00-0.153454751E+00-0.155843481E+00-0.158232257E+00 --0.160621077E+00-0.163009942E+00-0.165398866E+00-0.167775452E+00-0.170178100E+00 --0.172562733E+00-0.174929395E+00-0.177278042E+00-0.179608703E+00-0.181921363E+00 --0.184216037E+00-0.186492711E+00-0.188751400E+00-0.190992460E+00-0.193237543E+00 --0.195449591E+00-0.197628587E+00-0.199774534E+00-0.201887429E+00-0.203967288E+00 --0.206014082E+00-0.208027840E+00-0.210013613E+00-0.212023556E+00-0.214026883E+00 --0.215994403E+00-0.217926115E+00-0.219822019E+00-0.221682116E+00-0.223506406E+00 --0.225294873E+00-0.227047548E+00-0.228781909E+00-0.230495289E+00-0.232196882E+00 --0.233873531E+00-0.235525250E+00-0.237152010E+00-0.238753825E+00-0.240330696E+00 --0.241882607E+00-0.243409589E+00-0.244922712E+00-0.246446446E+00-0.247957587E+00 --0.249456108E+00-0.250941992E+00-0.252415240E+00-0.253875881E+00-0.255323857E+00 --0.256759226E+00-0.258181989E+00-0.259593666E+00-0.260983944E+00-0.262367785E+00 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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 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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 --0.418890305E-01-0.434222668E-01-0.449789800E-01-0.465567335E-01-0.481461734E-01 --0.497526079E-01-0.513806306E-01-0.530328974E-01-0.547054857E-01-0.563984029E-01 --0.581116416E-01-0.598452054E-01-0.615990944E-01-0.633733049E-01-0.651682317E-01 --0.669840276E-01-0.688200742E-01-0.706763789E-01-0.725529343E-01-0.744497404E-01 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a/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode_kinetic.gpeckf b/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode_kinetic.gpeckf new file mode 100644 index 000000000..aec26a951 --- /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 1.000000e+05 +1.949000e-03 4.499240e+19 5.494810e+19 4.978366e+03 2.498558e+03 9.965297e+04 +3.899000e-03 4.498020e+19 5.489310e+19 4.958428e+03 2.496873e+03 9.930683e+04 +5.848000e-03 4.496540e+19 5.483680e+19 4.939117e+03 2.495082e+03 9.896196e+04 +7.797000e-03 4.494860e+19 5.477970e+19 4.920222e+03 2.493218e+03 9.861816e+04 +9.747000e-03 4.493000e+19 5.472190e+19 4.901643e+03 2.491298e+03 9.827526e+04 +1.169600e-02 4.491010e+19 5.466380e+19 4.883321e+03 2.489332e+03 9.793362e+04 +1.364500e-02 4.488890e+19 5.460520e+19 4.865219e+03 2.487326e+03 9.759304e+04 +1.559500e-02 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a/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode_kinetic.h5 b/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode_kinetic.h5 new file mode 100644 index 000000000..2f084f080 Binary files /dev/null and b/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode_kinetic.h5 differ diff --git a/examples/DIIID-like_ideal_example/gpec.toml b/examples/DIIID-like_ideal_example/gpec.toml index 6f2ecb634..db73bb377 100644 --- a/examples/DIIID-like_ideal_example/gpec.toml +++ b/examples/DIIID-like_ideal_example/gpec.toml @@ -7,11 +7,14 @@ 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 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 +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 (sin²: packs core+edge). Robust δW/Δ' vs log_asymptotic. +psilow = 1e-4 # Lower 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 newq0 = 0 # Override for on-axis safety factor (0 = use input value) etol = 1e-10 # Error tolerance for equilibrium solver @@ -77,3 +80,24 @@ 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) + +[KineticForces] +kinetic_file = "TkMkr_D3Dlike_Hmode_kinetic.h5" # GPEC HDF5 kinetic schema (psi,n_i,n_e,T_i,T_e,omega_E,+chi_e,chi_phi). Legacy .gpeckf/.kin still readable. +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-2 # Outer psi quadrature tolerances (relaxed from 1e-3: +rtol_psi = 1e-2 # NTV torque integrand has sharp resonant peaks at rational + # surfaces; tight tol over-refines. Proper fix = panel the + # psi-integral at rationals (deferred follow-up). +write_outputs_to_HDF5 = true +verbose = true diff --git a/examples/Solovev_ideal_example/gpec.toml b/examples/Solovev_ideal_example/gpec.toml index 9a74f1d35..0c478d10e 100644 --- a/examples/Solovev_ideal_example/gpec.toml +++ b/examples/Solovev_ideal_example/gpec.toml @@ -44,6 +44,11 @@ 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) +# Note: SLAYER tearing analysis is not run on the Solovev analytic equilibrium +# — its Δ' / inner-layer dispersion does not yield meaningful tearing roots. +# The SLAYER example and regression case use the DIII-D-like geqdsk instead +# (see examples/DIIID-like_SLAYER_example). + [ForceFreeStates] local_stability_flag = true # Perform local stability analysis (Mercier and ballooning) across the ψ profile mat_flag = true # Construct coefficient matrices for diagnostic purposes diff --git a/regression-harness/cases/diiid_n1.toml b/regression-harness/cases/diiid_n1.toml index 1a69b7279..6693b5601 100644 --- a/regression-harness/cases/diiid_n1.toml +++ b/regression-harness/cases/diiid_n1.toml @@ -347,6 +347,19 @@ 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" diff --git a/regression-harness/cases/diiid_slayer_n1.toml b/regression-harness/cases/diiid_slayer_n1.toml new file mode 100644 index 000000000..13167efe5 --- /dev/null +++ b/regression-harness/cases/diiid_slayer_n1.toml @@ -0,0 +1,162 @@ +[case] +name = "diiid_slayer_n1" +description = "DIII-D-like H-mode equilibrium, n=1, SLAYER tearing-mode analysis (uncoupled per-surface, AMR, validity-gated)" +example_dir = "examples/DIIID-like_SLAYER_example" + +# --------------------------------------------------------------------- +# Per-surface SLAYER layer parameters (geometry + dimensionless) +# --------------------------------------------------------------------- +[quantities.slayer_ising] +h5path = "slayer/per_surface/ising" +type = "real_vector" +extract = "all_real" +label = "SLAYER surface indices" +noise_threshold = 0 +order = 10 + +[quantities.slayer_m] +h5path = "slayer/per_surface/m" +type = "real_vector" +extract = "all_real" +label = "SLAYER poloidal m" +noise_threshold = 0 +order = 11 + +[quantities.slayer_n] +h5path = "slayer/per_surface/n" +type = "real_vector" +extract = "all_real" +label = "SLAYER toroidal n" +noise_threshold = 0 +order = 12 + +[quantities.slayer_rs] +h5path = "slayer/per_surface/rs" +type = "real_vector" +extract = "all_real" +label = "SLAYER minor radius rs" +noise_threshold = 1e-10 +order = 13 + +[quantities.slayer_sval_r] +h5path = "slayer/per_surface/sval_r" +type = "real_vector" +extract = "all_real" +label = "SLAYER r-based shear" +noise_threshold = 1e-10 +order = 14 + +[quantities.slayer_lu] +h5path = "slayer/per_surface/lu" +type = "real_vector" +extract = "all_real" +label = "SLAYER Lundquist S" +noise_threshold = 1e-8 +order = 15 + +[quantities.slayer_D_norm] +h5path = "slayer/per_surface/D_norm" +type = "real_vector" +extract = "all_real" +label = "SLAYER D_norm" +noise_threshold = 1e-10 +order = 16 + +[quantities.slayer_P_perp] +h5path = "slayer/per_surface/P_perp" +type = "real_vector" +extract = "all_real" +label = "SLAYER P_perp" +noise_threshold = 1e-8 +order = 17 + +[quantities.slayer_tauk] +h5path = "slayer/per_surface/tauk" +type = "real_vector" +extract = "all_real" +label = "SLAYER tauk" +noise_threshold = 1e-12 +order = 18 + +[quantities.slayer_iota_e] +h5path = "slayer/per_surface/iota_e" +type = "real_vector" +extract = "all_real" +label = "SLAYER iota_e" +noise_threshold = 1e-12 +order = 19 + +# --------------------------------------------------------------------- +# Tearing eigenvalue (coupled mode → length 1). The headline deliverable: +# a real, nonzero growth rate on a realistic equilibrium. Root-extraction +# is sensitive to the AMR cell topology and ODE solver, so the Q/ω/γ +# thresholds are absolute and modestly loose; re-pin intentionally if a +# solver/AMR change shifts the root inventory. +# Growth-rate / frequency / root outputs. Pinned for the inner three rational +# surfaces only (2/1, 3/1, 4/1) via `first_3`: the Δ'/γ contour search is +# numerically unreliable on the outermost surfaces (e.g. 5/1, 6/1, 7/1 near the +# edge), so those are deliberately not golden-tracked. +# --------------------------------------------------------------------- +[quantities.slayer_Q_re] +h5path = "slayer/roots/Q_root_real" +type = "real_vector" +extract = "first_3" +label = "SLAYER Re(Q_root) [2/1,3/1,4/1]" +noise_threshold = 1e-4 +order = 30 + +[quantities.slayer_Q_im] +h5path = "slayer/roots/Q_root_imag" +type = "real_vector" +extract = "first_3" +label = "SLAYER Im(Q_root) [2/1,3/1,4/1]" +noise_threshold = 1e-4 +order = 31 + +[quantities.slayer_omega_Hz] +h5path = "slayer/roots/omega_Hz" +type = "real_vector" +extract = "first_3" +label = "SLAYER ω_Hz [2/1,3/1,4/1]" +noise_threshold = 1.0 +order = 32 + +[quantities.slayer_gamma_Hz] +h5path = "slayer/roots/gamma_Hz" +type = "real_vector" +extract = "first_3" +label = "SLAYER γ_Hz [2/1,3/1,4/1]" +noise_threshold = 1e-1 +order = 33 + +# no_root flag (1 = extraction failed). Pinned for the inner three surfaces; +# this case guards that the 2/1, 3/1, 4/1 keep finding a real root. +[quantities.slayer_no_root] +h5path = "slayer/roots/no_root" +type = "real_vector" +extract = "first_3" +label = "SLAYER no_root flags [2/1,3/1,4/1]" +noise_threshold = 0 +order = 34 + +# --------------------------------------------------------------------- +# Settings (catches accidental config drift) +# --------------------------------------------------------------------- +[quantities.slayer_enabled] +h5path = "slayer/enabled" +type = "int_scalar" +extract = "value" +label = "SLAYER enabled flag" +noise_threshold = 0 +order = 90 + +# --------------------------------------------------------------------- +# Runtime +# --------------------------------------------------------------------- +[quantities.runtime] +h5path = "" +type = "runtime" +extract = "value" +label = "Runtime (s)" +noise_threshold = 0.0 +order = 999 diff --git a/regression-harness/src/extractor.jl b/regression-harness/src/extractor.jl index c251ed1ad..bd7fc400b 100644 --- a/regression-harness/src/extractor.jl +++ b/regression-harness/src/extractor.jl @@ -70,12 +70,23 @@ function apply_extraction(spec::QuantitySpec, raw)::ExtractedQuantity elseif spec.extract == "all_real" arr = Float64.(real.(raw)) - json_str = JSON.json(arr) + # allownan: SLAYER γ/Q_root are NaN when no dispersion root is found — + # a legitimate state to record so a future root appearing flags a diff. + json_str = JSON.json(arr; allownan=true) + return ExtractedQuantity(name, label, nothing, nothing, json_str, "json_array", threshold) + + elseif startswith(spec.extract, "first_") + # "first_N": real values of the leading N vector elements only. Used to + # golden-pin the inner (trustworthy) rational surfaces while ignoring + # edge surfaces where the Δ'/γ contour search is numerically unreliable. + nkeep = parse(Int, spec.extract[(length("first_")+1):end]) + arr = Float64.(real.(raw))[1:min(nkeep, length(raw))] + json_str = JSON.json(arr; allownan=true) return ExtractedQuantity(name, label, nothing, nothing, json_str, "json_array", threshold) elseif spec.extract == "all_complex" pairs = [[real(x), imag(x)] for x in raw] - json_str = JSON.json(pairs) + json_str = JSON.json(pairs; allownan=true) return ExtractedQuantity(name, label, nothing, nothing, json_str, "json_array", threshold) elseif spec.extract == "diagonal_complex" @@ -85,7 +96,7 @@ function apply_extraction(spec::QuantitySpec, raw)::ExtractedQuantity error("diagonal_complex requires a square 2-D matrix; got size $(size(raw))") diag_vec = [raw[i, i] for i in 1:size(raw, 1)] pairs = [[real(x), imag(x)] for x in diag_vec] - json_str = JSON.json(pairs) + json_str = JSON.json(pairs; allownan=true) return ExtractedQuantity(name, label, nothing, nothing, json_str, "json_array", threshold) elseif spec.extract == "checksum" @@ -98,9 +109,14 @@ function apply_extraction(spec::QuantitySpec, raw)::ExtractedQuantity end end -"""Compute absolute difference between two JSON-parsed elements (scalars, pairs, or nested arrays).""" +""" +Compute absolute difference between two JSON-parsed elements (scalars, pairs, or nested arrays). +""" function _json_element_diff(a, b)::Float64 if a isa Number && b isa Number + # Two NaN values denote the same "no result" state (e.g. SLAYER + # Q_root when no dispersion root is found) — treat as identical. + (isnan(Float64(a)) && isnan(Float64(b))) && return 0.0 return abs(Float64(a) - Float64(b)) elseif a isa Vector && b isa Vector return sqrt(sum(_json_element_diff(ai, bi)^2 for (ai, bi) in zip(a, b))) @@ -109,9 +125,14 @@ function _json_element_diff(a, b)::Float64 end end -"""Compute absolute value/magnitude of a JSON-parsed element.""" +""" +Compute absolute value/magnitude of a JSON-parsed element. +""" function _json_element_abs(x)::Float64 if x isa Number + # NaN denotes a "no result" state (e.g. SLAYER Q_root with no root); + # treat as 0 magnitude so it doesn't poison a vector's reference norm. + isnan(Float64(x)) && return 0.0 return abs(Float64(x)) elseif x isa Vector return sqrt(sum(_json_element_abs(xi)^2 for xi in x)) @@ -162,8 +183,8 @@ function compare_values(q1::NamedTuple, q2::NamedTuple) if t1 === nothing || t2 === nothing return (NaN, NaN, "N/A") end - arr1 = JSON.parse(t1) - arr2 = JSON.parse(t2) + arr1 = JSON.parse(t1; allownan=true) + arr2 = JSON.parse(t2; allownan=true) if length(arr1) != length(arr2) return (NaN, NaN, "CHANGED (length)") end diff --git a/regression-harness/src/reporter.jl b/regression-harness/src/reporter.jl index e86fc498f..c0c57758f 100644 --- a/regression-harness/src/reporter.jl +++ b/regression-harness/src/reporter.jl @@ -14,7 +14,7 @@ function _short_err(msg)::String lines = filter(!isempty, strip.(split(s, '\n'))) isempty(lines) && return "(empty)" pick = something(findfirst(l -> startswith(l, "ERROR:") || occursin("Error", l), lines), - length(lines)) + length(lines)) line = lines[pick] return length(line) > 200 ? line[1:200] * "..." : line end @@ -36,7 +36,7 @@ function format_value(q::NamedTuple)::String elseif q.value_type == "json_array" t = q.value_text t === nothing && return "N/A" - arr = JSON.parse(t) + arr = JSON.parse(t; allownan=true) return "[$(length(arr)) elem]" elseif q.value_type == "checksum" t = q.value_text @@ -66,7 +66,9 @@ function format_diff(abs_diff::Float64, rel_diff::Float64, status::String, value return @sprintf("%.3e (%.2f%%)", abs_diff, rel_diff * 100) end -"""Helper: print a row of padded columns.""" +""" +Helper: print a row of padded columns. +""" function _print_row(cols::Vector{String}, widths::Vector{Int}) parts = [rpad(cols[i], widths[i]) for i in eachindex(cols)] println(join(parts, " ")) @@ -76,7 +78,7 @@ end Print a two-ref comparison report for a single case. """ function report_two_ref_comparison(db::SQLite.DB, case_spec::CaseSpec, - ref1::ResolvedRef, ref2::ResolvedRef) + ref1::ResolvedRef, ref2::ResolvedRef) info1 = get_run_info(db, ref1.commit_hash, case_spec.name) info2 = get_run_info(db, ref2.commit_hash, case_spec.name) @@ -103,7 +105,9 @@ function report_two_ref_comparison(db::SQLite.DB, case_spec::CaseSpec, # Pre-compute all rows: (label, v1, v2, diff, status) header = ["Quantity", ref1.name, ref2.name, "Diff", "Status"] rows = Vector{Vector{String}}() - n_ok = 0; n_changed = 0; n_missing = 0 + n_ok = 0 + n_changed = 0 + n_missing = 0 # Helper: pick the value-cell text for one ref/quantity, accounting for # whole-ref failure (which should render as "FAILED" rather than "N/A"). @@ -114,7 +118,7 @@ function report_two_ref_comparison(db::SQLite.DB, case_spec::CaseSpec, runtime_cell = (failed::Bool, qs::Dict, qname::String) -> begin failed && return "FAILED" (haskey(qs, qname) && qs[qname].value_real !== nothing) ? - @sprintf("%.1fs", qs[qname].value_real) : "N/A" + @sprintf("%.1fs", qs[qname].value_real) : "N/A" end for spec in case_spec.quantities @@ -145,15 +149,20 @@ function report_two_ref_comparison(db::SQLite.DB, case_spec::CaseSpec, continue end - q1 = q1_all[qname]; q2 = q2_all[qname] + q1 = q1_all[qname] + q2 = q2_all[qname] abs_diff, rel_diff, status = compare_values(q1, q2) st = status == "CHANGED" ? "** CHANGED **" : status push!(rows, [spec.label, format_value(q1), format_value(q2), - format_diff(abs_diff, rel_diff, status, q1.value_type), st]) + format_diff(abs_diff, rel_diff, status, q1.value_type), st]) - if status == "OK"; n_ok += 1 - elseif contains(status, "CHANGED"); n_changed += 1 - else; n_missing += 1; end + if status == "OK" + n_ok += 1 + elseif contains(status, "CHANGED") + n_changed += 1 + else + n_missing += 1 + end end # Derive column widths from header + all row content @@ -202,13 +211,15 @@ Print a multi-ref tracking report for a single case. One row per quantity, one column per ref. """ function report_multi_ref(db::SQLite.DB, case_spec::CaseSpec, - refs::Vector{ResolvedRef}) + refs::Vector{ResolvedRef}) run_infos = [get_run_info(db, ref.commit_hash, case_spec.name) for ref in refs] failed_mask = [info === nothing || !info.success for info in run_infos] - all_qs = [begin - info = run_infos[i] - (info !== nothing && info.success) ? get_quantities(db, refs[i].commit_hash, case_spec.name) : Dict{String,NamedTuple}() - end for i in eachindex(refs)] + all_qs = [ + begin + info = run_infos[i] + (info !== nothing && info.success) ? get_quantities(db, refs[i].commit_hash, case_spec.name) : Dict{String,NamedTuple}() + end for i in eachindex(refs) + ] show_diff = length(refs) >= 2 ref_names = [ref.name for ref in refs] @@ -223,7 +234,9 @@ function report_multi_ref(db::SQLite.DB, case_spec::CaseSpec, # Pre-compute rows rows = Vector{Vector{String}}() - n_ok = 0; n_changed = 0; n_missing = 0 + n_ok = 0 + n_changed = 0 + n_missing = 0 for spec in case_spec.quantities qname = spec.name @@ -274,9 +287,13 @@ function report_multi_ref(db::SQLite.DB, case_spec::CaseSpec, st = status == "CHANGED" ? "** CHANGED **" : status push!(row, format_diff(abs_diff, rel_diff, status, q_prev.value_type)) push!(row, st) - if status == "OK"; n_ok += 1 - elseif contains(status, "CHANGED"); n_changed += 1 - else; n_missing += 1; end + if status == "OK" + n_ok += 1 + elseif contains(status, "CHANGED") + n_changed += 1 + else + n_missing += 1 + end elseif last_failed || prev_failed push!(row, "") push!(row, "FAILED") diff --git a/src/Equilibrium/DirectEquilibrium.jl b/src/Equilibrium/DirectEquilibrium.jl index 8d3d08a4e..d214b05c1 100644 --- a/src/Equilibrium/DirectEquilibrium.jl +++ b/src/Equilibrium/DirectEquilibrium.jl @@ -380,7 +380,7 @@ function direct_refine(rfac::Float64, eta::Float64, psi0::Float64, params::Field end return find_zero((f, fp), rfac, Roots.Newton(); - atol=1e-12*abs(psi0), rtol=1e-12, maxevals=50) + atol=1e-12 * abs(psi0), rtol=1e-12, maxevals=50) end """ @@ -456,7 +456,7 @@ The middle-region spacing is driven by profile curvature (P, F, dV/dψ, q) via s """ function make_optimal_mpsi(psilow, psihigh, A, sq_in; tau=0.005, psi_split_core=0.03, psi_split_edge=0.98) - dlog = (13.0 * tau / A)^(1/4) + dlog = (13.0 * tau / A)^(1 / 4) N_edge = ceil(Int, log((1.0 - psi_split_edge) / (1.0 - psihigh)) / dlog) + 1 h_mid = _estimate_mid_spacing(sq_in, psi_split_core, psi_split_edge, tau) N_mid = ceil(Int, (psi_split_edge - psi_split_core) / h_mid) @@ -582,7 +582,7 @@ robustness. @. ff_x_nodes = @view(y_out[:, 5]) / y_out[end, 5] ff_fs_nodes = acquire!(pool, Float64, size(y_out, 1), 4) - @. ff_fs_nodes[:, 1] = @view(y_out[:, 3]) ^ 2 + @. ff_fs_nodes[:, 1] = @view(y_out[:, 3])^2 @. ff_fs_nodes[:, 2] = @view(y_out[:, 1]) / (2π) - ff_x_nodes @. ff_fs_nodes[:, 3] = bfield.f * (@view(y_out[:, 4]) - ff_x_nodes * y_out[end, 4]) @. ff_fs_nodes[:, 4] = @view(y_out[:, 2]) / y_out[end, 2] - ff_x_nodes diff --git a/src/Equilibrium/Equilibrium.jl b/src/Equilibrium/Equilibrium.jl index 13e478e29..461345194 100644 --- a/src/Equilibrium/Equilibrium.jl +++ b/src/Equilibrium/Equilibrium.jl @@ -26,7 +26,8 @@ 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 export compute_sqrt_jac_delpsi, compute_sqrtamat, rootarea_to_area_weight, area_to_rootarea_weight diff --git a/src/Equilibrium/KineticProfiles.jl b/src/Equilibrium/KineticProfiles.jl index a465409f7..413cd1503 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/src/ForceFreeStates/ForceFreeStates.jl b/src/ForceFreeStates/ForceFreeStates.jl index cc144731f..d740a16ae 100644 --- a/src/ForceFreeStates/ForceFreeStates.jl +++ b/src/ForceFreeStates/ForceFreeStates.jl @@ -24,6 +24,7 @@ include("ForceFreeStatesStructs.jl") include("Ballooning.jl") include("EulerLagrange.jl") include("Sing.jl") +include("ResistEval.jl") include("Fourfit.jl") include("FixedKineticMatrices.jl") include("Kinetic.jl") diff --git a/src/ForceFreeStates/ForceFreeStatesStructs.jl b/src/ForceFreeStates/ForceFreeStatesStructs.jl index 337eb158b..fc47219c6 100644 --- a/src/ForceFreeStates/ForceFreeStatesStructs.jl +++ b/src/ForceFreeStates/ForceFreeStatesStructs.jl @@ -31,6 +31,7 @@ A mutable struct holding data related to the singular surfaces in the equilibriu ua_right::Array{ComplexF64,3} = Array{ComplexF64}(undef, 0, 0, 0) # asymptotic basis at right inner-layer boundary psi_ua_left::Float64 = 0.0 # ψ where ua_left was evaluated (left inner-layer boundary) psi_ua_right::Float64 = 0.0 # ψ where ua_right was evaluated (right inner-layer boundary) + restype::Any = nothing # ResistGeometry from ResistEval.jl (populated by resist_eval_all!); typed `Any` to avoid a cross-file type reference end """ @@ -193,6 +194,23 @@ A mutable struct holding internal state variables for stability calculations. raw 2msing×2msing BVP solution to produce the PEST3-compatible tearing parameter. """ delta_prime_matrix::Matrix{ComplexF64} = Matrix{ComplexF64}(undef, 0, 0) + + """ + Raw 2msing × 2msing outer-region matching matrix `D'` from the STRIDE global + BVP, in the side-major ordering `[L_s1, R_s1, L_s2, R_s2, …, L_sm, R_sm]` + (left vs right of each singular surface, interleaved surface-by-surface). + This is the Pletzer–Dewar 1991 outer-region matrix before parity rotation, + and is stored byte-compatibly with the Fortran `rdcon/gal.f::gal_write_delta` + convention (top 2msing×2msing block of `delta_gw.dat`). The PEST3 Δ' matrix + stored in `delta_prime_matrix` is the odd-parity tearing projection of this + raw matrix; the even-parity A' and off-parity B', Γ' blocks are recovered + via `pest3_decompose(dp_raw)` — needed for the full det(D' − D(γ)) = 0 + eigenvalue problem with Glasser stabilization. + + Empty unless `ctrl.use_parallel` is true. No ½ prefactor is applied (matches + Fortran rdcon; Pletzer–Dewar paper multiplies by ½). + """ + delta_prime_raw::Matrix{ComplexF64} = Matrix{ComplexF64}(undef, 0, 0) end """ @@ -242,7 +260,7 @@ A mutable struct containing control parameters for stability analysis, set by th - `force_termination::Bool` - Terminate after force-free states (skip perturbed equilibrium calculations) - `use_riccati::Bool` - Use the dual Riccati reformulation S = U₁·U₂⁻¹ instead of the standard U₁/U₂ ODE. Reduces stiffness for faster integration. See Glasser (2018) Phys. Plasmas 25, 032507. - `use_parallel::Bool` - Parallel fundamental matrix (propagator) integration using `Threads.@threads`. Each chunk is integrated independently from identity IC and assembled serially. Requires `singfac_min != 0`. Uses the same chunk bounds as the standard path but sub-divides chunks for load balancing. Crossings use the Riccati-style algorithm (no Gaussian reduction). - - `parallel_threads::Int` - Cap on the number of threads the parallel BVP uses. **Default `2`** parallelises the FM chunks across two threads (the BVP has ~10 chunks; 2 threads is enough to amortize them — speedup saturates here, raising to 4 adds scheduling overhead). Set `parallel_threads = 1` to run the FM chunks SERIALLY (no `Threads.@threads`), which is bit-deterministic and immune to the thread-schedule sensitivity that historically caused intermittent BVP divergences on numerically delicate equilibria like DIII-D 147131 (see CONVENTIONS.md §7). Empirical reliability sweep (5 trials × {1,2,4} on DIII-D 147131 βₚ≈0.07): 15/15 bit-identical Δ′ at every setting; pt=2 ≈ pt=4 ≈ 20 % faster than serial. If a parallel run diverges, drop to `parallel_threads = 1` rather than switching `use_parallel = false` — the latter is silently wrong. Capped at `Threads.nthreads()`. + - `parallel_threads::Int` - Cap on the number of threads the parallel BVP uses. **Default `2`** parallelises the FM chunks across two threads (the BVP has ~10 chunks; 2 threads is enough to amortize them — speedup saturates here, raising to 4 adds scheduling overhead). Set `parallel_threads = 1` to run the FM chunks SERIALLY (no `Threads.@threads`), which is bit-deterministic and immune to the thread-schedule sensitivity that can cause intermittent BVP divergence on numerically delicate equilibria. The parallel path produces bit-identical Δ′ across thread counts; `parallel_threads = 2` is about 20% faster than serial and saturates the speedup. If a parallel run diverges, drop to `parallel_threads = 1` rather than switching `use_parallel = false` — the latter is silently wrong. Capped at `Threads.nthreads()`. - `populate_dense_xi::Bool` - When `use_parallel = true`, append a serial Euler-Lagrange pass at the end of the propagator BVP and let it replace the `odet` returned to the main pipeline. This populates `u_store` / `ud_store` densely in the axis (EL) basis — the only convention the PerturbedEquilibrium / FieldReconstruction downstream code consumes correctly. Without it the parallel path stores only chunk-endpoint Riccati S matrices and zeros for `ud_store` (see Riccati.jl docstring caveats), and HDF5 `integration/xi_psi`/`dxi_psi`/`xi_s` are unusable. Δ' (`singular/delta_prime_matrix`) is computed from the parallel BVP and is bit-identical between `populate_dense_xi=true` and `false`. Energies (`vacuum/ep`/`ev`/`et`) are computed by `free_run!` from `odet`, so with `populate_dense_xi=true` they match what a pure serial run (`use_parallel=false`) would produce; with `populate_dense_xi=false` they use the parallel-pass Riccati `odet.u` instead (differs by the ~0.12 % Riccati-vs-axis algorithmic gap on DIIID-class cases). **Default `false`** to avoid paying the dense-pass cost on Δ'/vacuum/ideal-stability-only runs; **PerturbedEquilibrium-using configs must set `populate_dense_xi = true` explicitly** when `use_parallel = true` (otherwise PE silently reads Riccati-basis garbage). Auto-disabled when `force_termination = true` regardless of the user setting, since the dense pass has no downstream consumer in that case. Approximate cost when enabled: one extra serial EL integration (~1× the parallel BVP wall-clock for typical N). - `extended_precision_bvp::Bool` - When `true` (default), promote the Δ' BVP linear system to `Complex{Double64}` (~31 digits) for the LU solve and PEST3 combination. Guards against catastrophic cancellation in the PEST3 four-term combination (dp_raw entries can be 10⁴–10⁵× larger than the result; the imaginary part of off-diagonal Δ' is particularly sensitive). Disabling (`false`) saves ~1.5–2× the BVP solve time but on DIIID-class equilibria the imaginary Δ' components can drift by factors of 2–5×; only disable for performance experiments on cases where Float64 has been validated against Double64. """ diff --git a/src/ForceFreeStates/ResistEval.jl b/src/ForceFreeStates/ResistEval.jl new file mode 100644 index 000000000..8bfc5a03f --- /dev/null +++ b/src/ForceFreeStates/ResistEval.jl @@ -0,0 +1,214 @@ +# ResistEval.jl +# +# Per-singular-surface Glasser-Greene-Johnson geometric coefficients (E, F, +# G, H, K, M) and the two flux-surface averages (⟨B²/|∇ψ|²⟩, ⟨B²⟩) that +# downstream callers need to turn geometry into τ_A / τ_R with kinetic +# profiles. +# +# Port of Fortran RDCON `resist_eval` (geometric part only). +# Unlike the Fortran, this routine produces *only* the pure-equilibrium +# quantities; kinetic timescales (τ_A, τ_R) are built on top in the +# downstream `build_ggj_inputs` helper using the same KineticProfiles that +# feed SLAYER, rather than Fortran's hardcoded `ne=1e14, te=3e3` +# parameter defaults. +# +# The 6 theta-integrands match the Fortran layout: +# 1: B² / |∇ψ|² +# 2: 1 / |∇ψ|² +# 3: 1 / B² +# 4: 1 / (B² · |∇ψ|²) +# 5: B² +# 6: |∇ψ|² / B² +# All weighted by `jac / v1` (jacobian / dV/dψ) before integration. +# +# A seventh integrand, B, is added (beyond the Fortran set) so that ⟨B⟩ is +# available for the Lin-Liu & Miller 1995 trapped-fraction formula used by +# the shared NeoclassicalResistivity closure. B_max, B_min, and the flux- +# surface-averaged major radius R_major are accumulated alongside by +# running extrema over the θ-loop. + +""" + ResistGeometry + +Per-singular-surface Glasser-Greene-Johnson geometric coefficients and +supporting flux-surface averages. + +| field | meaning | +|-------------|------------------------------------------------------| +| `E`, `F` | Glasser interchange parameters (enter `D_I = E+F+H-¼`) | +| `G` | Coupling coefficient (curvature × pressure gradient) | +| `H` | Pfirsch-Schlüter coefficient | +| `K` | Glasser parameter | +| `M` | Mass factor | +| `avg_bsq_over_dpsisq` | ⟨B²/|∇ψ|²⟩ — needed for τ_R | +| `avg_bsq` | ⟨B²⟩ — needed for τ_R | +| `avg_B` | ⟨B⟩ — needed for Lin-Liu-Miller f_t | +| `B_max`, `B_min` | θ-extrema of B on the surface [T] | +| `f_trap` | Lin-Liu & Miller 1995 trapped-particle fraction | +| `R_major` | flux-surface-averaged major radius ⟨R⟩ [m] | +| `eps_local` | (R_max − R_min)/2 / R_major — local inverse aspect ratio | +| `p_local` | Plasma pressure at this surface [Pa] | +| `p1_local` | dp/dψ at this surface | +| `v1_local` | dV/dψ at this surface | + +`H` here is identical to the `H` reported by `mercier_scan!` and stored +in `locstab/h` — the GGJ routine recomputes it for convenience. + +`avg_B`, `B_max`, `B_min`, `f_trap`, `R_major`, and `eps_local` are used +by `NeoclassicalResistivity.eta_neoclassical` to form the Sauter/Redl +F_33 correction to Spitzer resistivity. See Sauter, Angioni & Lin-Liu +1999, Phys. Plasmas 6, 2834 and Lin-Liu & Miller 1995, Phys. Plasmas 2, +1666. +""" +struct ResistGeometry + E::Float64 + F::Float64 + G::Float64 + H::Float64 + K::Float64 + M::Float64 + avg_bsq_over_dpsisq::Float64 + avg_bsq::Float64 + avg_B::Float64 + B_max::Float64 + B_min::Float64 + f_trap::Float64 + R_major::Float64 + eps_local::Float64 + p_local::Float64 + p1_local::Float64 + v1_local::Float64 +end + +""" + resist_geometry(equil, psifac, q1; gamma=5/3) -> ResistGeometry + +Port of Fortran RDCON `resist_eval` restricted to the +pure-equilibrium geometric coefficients. Integrates the 6 theta integrands +at the given flux surface and combines them into E, F, G, H, K, M via the +standard GGJ formulas. + +# Arguments + + - `equil::PlasmaEquilibrium` — the fully-solved equilibrium + - `psifac` — normalized flux coordinate of the singular surface + - `q1` — dq/dψ at this surface (from `SingType.q1`) + +# Keyword arguments + + - `gamma` — adiabatic index (default 5/3) + +!!! note "Contract" + `psifac` must be a genuine interior rational surface (`0 < ψ < 1`) with + nonzero `q1`, `p1 = dp/dψ`, and `p`. The GGJ combination divides by these + and by `|∇ψ|²` (which → 0 at the axis), so calling on the magnetic axis, + a flat-pressure surface, or a zero-shear surface yields `Inf`/`NaN`. This + matches the Fortran `resist_eval`, which is only ever invoked on interior + rationals. +""" +function resist_geometry(equil::Equilibrium.PlasmaEquilibrium, + psifac::Real, q1::Real; gamma::Real=5/3) + profiles = equil.profiles + twopi = 2π + chi1 = twopi * equil.psio + psi_f = Float64(psifac) + + # Surface-profile quantities (evaluate via the existing splines) + twopif = profiles.F_spline(psi_f) + p = profiles.P_spline(psi_f) + p1 = profiles.P_deriv(psi_f) + v1 = profiles.dVdpsi_spline(psi_f) + v2 = profiles.dVdpsi_deriv(psi_f) + q = profiles.q_spline(psi_f) + + # Build the 6 GGJ θ-integrands plus a 7th (B) for the neoclassical + # resistivity f_t calculation, and accumulate running extrema of + # (B, R) for Lin-Liu-Miller f_t and the local ε. + ntheta = length(equil.rzphi_ys) + ff = zeros(Float64, ntheta, 7) + B_max = -Inf + B_min = Inf + R_max = -Inf + R_min = Inf + for itheta in 1:ntheta + theta = equil.rzphi_ys[itheta] + f1 = equil.rzphi_rsquared((psi_f, theta)) + f2 = equil.rzphi_offset((psi_f, theta)) + jac = equil.rzphi_jac((psi_f, theta)) + fy1 = FastInterpolations.deriv_view(equil.rzphi_rsquared, (0, 1))((psi_f, theta)) + fy2 = FastInterpolations.deriv_view(equil.rzphi_offset, (0, 1))((psi_f, theta)) + fy3 = FastInterpolations.deriv_view(equil.rzphi_nu, (0, 1))((psi_f, theta)) + + rfac = sqrt(f1) + eta = twopi * (theta + f2) + r = equil.ro + rfac * cos(eta) + + v21 = fy1 / (2 * rfac * jac) + v22 = (1 + fy2) * twopi * rfac / jac + v23 = fy3 * r / jac + v33 = twopi * r / jac + bsq = chi1^2 * (v21^2 + v22^2 + (v23 + q*v33)^2) + dpsisq = (twopi * r)^2 * (v21^2 + v22^2) + + B_here = sqrt(bsq) + B_max = max(B_max, B_here) + B_min = min(B_min, B_here) + R_max = max(R_max, r) + R_min = min(R_min, r) + + 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 + ff[itheta, 7] = B_here + @views ff[itheta, :] .*= jac / v1 + end + + # Integrate each column around θ using the same periodic cubic-spline + # integrator Mercier.jl uses + itp = cubic_interp(equil.rzphi_ys, Series(ff); bc=PeriodicBC()) + avg = FastInterpolations.integrate(itp) + avg_B = avg[7] + R_major = 0.5 * (R_max + R_min) + eps_local = R_major > 0 ? 0.5 * (R_max - R_min) / R_major : 0.0 + f_trap = Utilities.NeoclassicalResistivity.trapped_fraction(avg_B, avg[5], B_min, B_max) + + # GGJ coefficients (Fortran RDCON resist_eval) + E_coef = p1 * v1 / (q1 * chi1^2)^2 * avg[1] * + (twopif * q1 * chi1 / avg[5] - v2) + F_coef = (p1 * v1 / (q1 * chi1^2))^2 * + (avg[1] * avg[3] + (twopif / chi1)^2 * + (avg[1] * avg[4] - avg[2]^2)) + H_coef = twopif * p1 * v1 / (q1 * chi1^3) * (avg[2] - avg[1] / avg[5]) + M_coef = avg[1] * + (avg[6] + (twopif / chi1)^2 * (avg[3] - 1.0 / avg[5])) + G_coef = avg[5] / (M_coef * gamma * p) + K_coef = (q1 * chi1^2 / (p1 * v1))^2 * + avg[5] / (M_coef * avg[1]) + + return ResistGeometry( + E_coef, F_coef, G_coef, H_coef, K_coef, M_coef, + avg[1], avg[5], + avg_B, B_max, B_min, f_trap, R_major, eps_local, + p, p1, v1, + ) +end + +""" + resist_eval_all!(intr::ForceFreeStatesInternal, equil; gamma=5/3) + +Populate `sing.restype` for every `SingType` in `intr.sing` using +`resist_geometry`. No-op for surfaces whose `restype` has already been +filled. +""" +function resist_eval_all!(intr::ForceFreeStatesInternal, + equil::Equilibrium.PlasmaEquilibrium; + gamma::Real=5/3) + for sing in intr.sing + sing.restype === nothing || continue + sing.restype = resist_geometry(equil, sing.psifac, sing.q1; gamma=gamma) + end + return intr +end diff --git a/src/ForceFreeStates/Riccati.jl b/src/ForceFreeStates/Riccati.jl index 715c6421d..1be78f7f2 100644 --- a/src/ForceFreeStates/Riccati.jl +++ b/src/ForceFreeStates/Riccati.jl @@ -334,8 +334,15 @@ function compute_delta_prime_matrix!( @info "Δ' BVP: nMat=$nMat, rank(M)=$(rank(M)), cond(M)=$(@sprintf("%.2e", cond(M)))" end - intr.delta_prime_matrix = _solve_bvp_and_combine_pest3( + deltap, dp_raw_persisted = _solve_bvp_and_combine_pest3( M, msing, N, nMat, use_S_axis, ipert_all, col_edge, ctrl, debug) + + # Persist both the PEST3 tearing projection (msing × msing) and the raw 2msing × 2msing + # D' matrix (side-major ordering, byte-compatible with Fortran rdcon/gal.f::gal_write_delta). + # The raw matrix is consumed by `pest3_decompose` to recover (A', B', Γ', Δ') for the full + # det(D' − D(γ)) = 0 eigenvalue problem; see ForceFreeStatesStructs.jl docstring. + intr.delta_prime_matrix = deltap + intr.delta_prime_raw = dp_raw_persisted end # Column index helpers for the BVP matrix. j is the 1-based singular-surface index, @@ -727,7 +734,9 @@ function _solve_bvp_and_combine_pest3(M::Matrix{ComplexF64}, msing::Int, N::Int, deltap = ComplexF64.(deltap_ext) debug && _log_bvp_pest3(dp_raw, deltap, s2, msing, Tc) - return deltap + # Return the PEST3-combined matrix AND the raw 2msing×2msing D' matrix (ComplexF64 + # for compatibility with downstream pest3_decompose / HDF5 writer). + return deltap, ComplexF64.(dp_raw) end # Logging helpers for `compute_delta_prime_matrix!`. Called only when debug=true. @@ -836,6 +845,69 @@ function _log_bvp_pest3(dp_raw, deltap, s2, msing, Tc) @info "Δ' BVP: deltap diagonal = $([@sprintf("%.4f%+.4fi", real(deltap[i,i]), imag(deltap[i,i])) for i in 1:msing])" end +""" + pest3_decompose(dp_raw::AbstractMatrix) -> (A', B', Γ', Δ') + +Rotate the raw 2m×2m outer-region matching matrix `dp_raw` (side-major +ordering `[L_s1, R_s1, L_s2, R_s2, …]`) into the Pletzer–Dewar 1991 parity +blocks. Given rows and columns paired by surface (odd index = left, even +index = right), the Fortran RDCON parity combination is + +``` +A'(i,j) = RR + RL + LR + LL (even-i, even-j) — interchange↔interchange +B'(i,j) = RR − RL + LR − LL (even-i, odd-j) — interchange↔tearing +Γ'(i,j) = RR + RL − LR − LL (odd-i, even-j) — tearing↔interchange +Δ'(i,j) = RR − RL − LR + LL (odd-i, odd-j) — tearing↔tearing +``` + +where `RR = dp_raw[2i, 2j]`, `RL = dp_raw[2i, 2j−1]`, +`LR = dp_raw[2i−1, 2j]`, `LL = dp_raw[2i−1, 2j−1]`. Each block is m×m. + +Matches Fortran exactly — no ½ prefactor (Pletzer–Dewar multiply by ½, but +the Fortran RDCON code leaves it commented out and our Julia port follows +Fortran to keep the benchmark bit-identical; the prefactor cancels in +`det(D' − D(γ)) = 0`). + +The Δ' block returned here equals `intr.delta_prime_matrix` (the m×m PEST3 +tearing projection computed inside `compute_delta_prime_matrix!`). + +# Arguments + + - `dp_raw` — 2m×2m complex matrix (typically `intr.delta_prime_raw`). + +# Returns + +Named tuple `(A=A', B=B', Γ=Gp, Δ=Dp)` of four m×m complex matrices. In the +full `det(D' − D(γ)) = 0` eigenvalue problem, these fill the 2m×2m outer +matrix as `D' = [[A' B'] [Γ' Δ']]` with the interchange channel (Glasser +stabilization) in the upper-left block and the tearing channel in the +lower-right. +""" +function pest3_decompose(dp_raw::AbstractMatrix) + s2 = size(dp_raw, 1) + size(dp_raw, 2) == s2 || + throw(ArgumentError("pest3_decompose: dp_raw must be square, got $(size(dp_raw))")) + iseven(s2) || + throw(ArgumentError("pest3_decompose: dp_raw side must be 2m for integer m, got $s2")) + m = s2 ÷ 2 + Tc = eltype(dp_raw) + Ap = zeros(Tc, m, m) + Bp = zeros(Tc, m, m) + Gp = zeros(Tc, m, m) + Dp = zeros(Tc, m, m) + for i in 1:m, j in 1:m + LL = dp_raw[2i-1, 2j-1] + LR = dp_raw[2i-1, 2j] + RL = dp_raw[2i, 2j-1] + RR = dp_raw[2i, 2j] + Ap[i, j] = RR + RL + LR + LL + Bp[i, j] = RR - RL + LR - LL + Gp[i, j] = RR + RL - LR - LL + Dp[i, j] = RR - RL - LR + LL + end + return (A=Ap, B=Bp, Γ=Gp, Δ=Dp) +end + """ riccati_der!(du, u, params, psieval) @@ -1641,7 +1713,7 @@ function _log_parallel_start(ctrl::ForceFreeStatesControl, odet::OdeState, end # Integrate each chunk's FM propagator from identity IC. Serial when bvp_threads == 1 -# (bit-deterministic; ~20% slower than 2-thread on DIII-D 147131 but immune to thread- +# (bit-deterministic; ~20% slower than 2-thread but immune to thread- # schedule sensitivity). Parallel uses :static scheduler so Threads.threadid() returns a # stable index into odet_proxies. If a parallel run ever diverges on a delicate equilibrium, # drop to parallel_threads = 1 rather than use_parallel = false — the latter is silently wrong. diff --git a/src/GeneralizedPerturbedEquilibrium.jl b/src/GeneralizedPerturbedEquilibrium.jl index 004c3841b..854c7c959 100755 --- a/src/GeneralizedPerturbedEquilibrium.jl +++ b/src/GeneralizedPerturbedEquilibrium.jl @@ -28,9 +28,15 @@ include("ForceFreeStates/ForceFreeStates.jl") import .ForceFreeStates as ForceFreeStates export ForceFreeStates -include("InnerLayer/InnerLayer.jl") -import .InnerLayer as InnerLayer -export InnerLayer +include("Tearing/Tearing.jl") +import .Tearing as Tearing +export Tearing +# Backward-compat top-level aliases so callers can still reach these +# directly; the canonical nested path is `Tearing.{InnerLayer,Dispersion,Runner}`. +import .Tearing.InnerLayer as InnerLayer +import .Tearing.Dispersion as Dispersion +import .Tearing.Runner as Runner +export InnerLayer, Dispersion, Runner include("ForcingTerms/ForcingTerms.jl") import .ForcingTerms as ForcingTerms @@ -52,7 +58,7 @@ include("Rerun.jl") # 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_find!, resist_eval_all!, resist_geometry, ResistGeometry 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! @@ -298,6 +304,14 @@ function main_from_inputs( end end + # Populate Glasser-Greene-Johnson geometric coefficients (E, F, G, H, + # K, M) for each surviving singular surface. Needed by the Julia GGJ + # inner-layer analysis; kinetic timescales (τ_A, τ_R) are layered on + # top by `build_ggj_inputs` using the same kinetic profiles as SLAYER. + if intr.msing > 0 + ForceFreeStates.resist_eval_all!(intr, equil) + end + # Determine poloidal mode numbers if ctrl.delta_mlow < 0 || ctrl.delta_mhigh < 0 error("Negative delta_mlow or delta_mhigh not allowed") @@ -454,10 +468,47 @@ function main_from_inputs( @info "Force-Free States completed in $(@sprintf("%.3f", time() - ffs_start)) s" - # Early exit if user only requested force-free states + # SLAYER tearing-mode analysis stage. Needs only equil + intr, so it runs in + # both the force_termination=true path and the full pipeline. `pe_file` is the + # HDF5 file PE wrote (to append into), or `nothing` if PE did not run. + function _run_slayer_stage(pe_file::Union{String,Nothing}) + ("SLAYER" in keys(inputs)) || return nothing + # SLAYER is a post-processing diagnostic. A failure here must not + # discard the equilibrium / stability / PE results already computed, + # so the whole stage is guarded: on error we log loudly and return + # `nothing` for the `slayer` field rather than propagating. + try + slayer_ctrl = Runner.slayer_control_from_toml(inputs["SLAYER"]) + slayer_ctrl.enabled || return nothing + @info "\n SLAYER\n$_SECTION" + slayer_start = time() + result = Runner.run_slayer(equil, intr, slayer_ctrl; + dir_path=intr.dir_path) + @info "SLAYER completed in $(@sprintf("%.3f", time() - slayer_start)) s" + h5_filename = pe_file === nothing ? ctrl.HDF5_filename : pe_file + h5_path = joinpath(intr.dir_path, h5_filename) + # Append the slayer/ group; create the file if no prior stage wrote + # it (e.g. write_outputs_to_HDF5 disabled) rather than failing on "r+". + HDF5.h5open(h5_path, isfile(h5_path) ? "r+" : "w") do f + Runner.write_slayer_hdf5!(f, result) + end + @info "SLAYER results written to $h5_filename" + return result + catch err + @error "SLAYER stage failed; continuing without tearing results. " * + "Equilibrium / stability / PE outputs are unaffected." exception = + (err, catch_backtrace()) + return nothing + end + end + + # Early exit if user only requested force-free states (SLAYER still runs). if ctrl.force_termination + slayer_result = _run_slayer_stage(nothing) @info "\n$_BANNER\n GPEC completed successfully in $(@sprintf("%.3f", time() - total_start)) s\n$_BANNER" - return + return (ctrl=ctrl, equil=equil, intr=intr, ffit=ffit, odet=odet, + vac_data=ctrl.vac_flag ? vac_data : nothing, + slayer=slayer_result) end # ---------------------------------------------------------------- @@ -556,6 +607,18 @@ function main_from_inputs( @info "KineticForces completed in $(@sprintf("%.3f", time() - kf_start)) s" end + # ---------------------------------------------------------------- + # SLAYER tearing-mode analysis (after PE so it appends to the PE output + # file; falls back to the ForceFreeStates file when PE did not run). + # ---------------------------------------------------------------- + pe_file = if "PerturbedEquilibrium" in keys(inputs) + pe_out = get(inputs["PerturbedEquilibrium"], "output_filename", "") + isempty(pe_out) ? ctrl.HDF5_filename : pe_out + else + ctrl.HDF5_filename + end + slayer_result = _run_slayer_stage(pe_file) + # ---------------------------------------------------------------- # Done # ---------------------------------------------------------------- @@ -563,7 +626,9 @@ function main_from_inputs( # TODO: Do not allow perturbed equilibrium calculations if zero crossings are found - return (ctrl=ctrl, equil=equil, intr=intr, ffit=ffit, odet=odet, vac_data=ctrl.vac_flag ? vac_data : nothing) + return (ctrl=ctrl, equil=equil, intr=intr, ffit=ffit, odet=odet, + vac_data=ctrl.vac_flag ? vac_data : nothing, + slayer=slayer_result) end @@ -727,6 +792,26 @@ function write_outputs_to_HDF5( end out_h5["singular/m"] = m_matrix out_h5["singular/n"] = n_matrix + + # Glasser-Greene-Johnson geometric coefficients + surface averages + # (populated by ForceFreeStates.resist_eval_all! after sing_find!). + # Both kinetic-free (E, F, G, H, K, M) and geometry-only + # (avg_bsq_over_dpsisq, avg_bsq) quantities are written so + # downstream consumers (Tearing.InnerLayer.GGJ.build_ggj_inputs) + # can reconstruct τ_A / τ_R from any kinetic-profile source. + if all(s -> s.restype !== nothing, intr.sing) + out_h5["singular/E"] = [s.restype.E for s in intr.sing] + out_h5["singular/F"] = [s.restype.F for s in intr.sing] + out_h5["singular/G"] = [s.restype.G for s in intr.sing] + out_h5["singular/H"] = [s.restype.H for s in intr.sing] + out_h5["singular/K"] = [s.restype.K for s in intr.sing] + out_h5["singular/M"] = [s.restype.M for s in intr.sing] + out_h5["singular/avg_bsq_over_dpsisq"] = [s.restype.avg_bsq_over_dpsisq for s in intr.sing] + out_h5["singular/avg_bsq"] = [s.restype.avg_bsq for s in intr.sing] + out_h5["singular/p_local"] = [s.restype.p_local for s in intr.sing] + out_h5["singular/p1_local"] = [s.restype.p1_local for s in intr.sing] + out_h5["singular/v1_local"] = [s.restype.v1_local for s in intr.sing] + end end # Per-surface ca-based Δ' (`sing.delta_prime`) is a stub; only the BVP matrix is emitted (see SingType.delta_prime docstring). @@ -737,6 +822,15 @@ function write_outputs_to_HDF5( out_h5["singular/delta_prime_matrix"] = intr.delta_prime_matrix end + # Write raw 2msing×2msing outer-region D' matrix in side-major ordering + # [L_s1, R_s1, L_s2, R_s2, …]. Byte-compatible with Fortran + # rdcon/gal.f::gal_write_delta top 2msing×2msing block of delta_gw.dat. + # Needed for the full det(D' − D(γ)) = 0 eigenvalue problem via + # pest3_decompose to recover (A', B', Γ', Δ'). + if intr.msing > 0 && !isempty(intr.delta_prime_raw) + out_h5["singular/delta_prime_raw"] = intr.delta_prime_raw + end + # Write kinetic singular surface data (det(F̄) near-zeros) and the cond(F̄) scan # used to find them. Populated only when kinetic crossings were searched for. out_h5["singular/kinetic/kmsing"] = intr.kmsing diff --git a/src/InnerLayer/InnerLayerInterface.jl b/src/InnerLayer/InnerLayerInterface.jl deleted file mode 100644 index 3c6e90109..000000000 --- a/src/InnerLayer/InnerLayerInterface.jl +++ /dev/null @@ -1,29 +0,0 @@ -# InnerLayerInterface.jl -# -# Abstract interface for resistive inner-layer models. Concrete models -# (e.g. GGJ, SLAYER, kinetic) live in submodules and specialize `solve_inner`. - -""" - InnerLayerModel - -Abstract supertype for resistive inner-layer models. Each concrete model is a -small, parameter-free type tag (often parameterized by a solver-choice symbol) -that selects a `solve_inner` method. - -Implementations live in submodules of `InnerLayer`, e.g. `InnerLayer.GGJ`. -""" -abstract type InnerLayerModel end - -""" - solve_inner(model::InnerLayerModel, params, γ::ComplexF64; kwargs...) -> SVector{2,ComplexF64} - -Compute the parity-projected matching data `(Δ_odd, Δ_even)` for the given -inner-layer `model`, physical parameters `params`, and complex growth rate -`γ`. Concrete models specialize this function. - -The two returned components correspond to the homogeneous odd / even parity -solutions of the half-domain inner-layer problem (parity boundary conditions -imposed at the rational surface, X = 0). They are the Δ_{j,±}(γ) of -Glasser, Wang & Park, Phys. Plasmas **23**, 112506 (2016), Eqs. (34)–(35). -""" -function solve_inner end diff --git a/src/InnerLayer/SLAYER/Slayer.jl b/src/InnerLayer/SLAYER/Slayer.jl deleted file mode 100644 index 5a7f87290..000000000 --- a/src/InnerLayer/SLAYER/Slayer.jl +++ /dev/null @@ -1,4 +0,0 @@ -# Slayer.jl -# -# Placeholder for the SLAYER (Slab Layer) drift-MHD two-fluid inner layer model. -# Implementation pending. diff --git a/src/KineticForces/Torque.jl b/src/KineticForces/Torque.jl index 35d55a00f..fef1ad043 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 diff --git a/src/Tearing/Dispersion/BruteForceScan.jl b/src/Tearing/Dispersion/BruteForceScan.jl new file mode 100644 index 000000000..6e7b8aead --- /dev/null +++ b/src/Tearing/Dispersion/BruteForceScan.jl @@ -0,0 +1,89 @@ +# BruteForceScan.jl +# +# Brute-force evaluation of a complex-Q-callable residual (`SurfaceCoupling`, +# `MultiSurfaceCoupling`, or any user-supplied function) on a regular 2D +# Q-plane grid. The output `ScanResult` is then consumed by +# `find_growth_rates` (`GrowthRateExtraction.jl`) to extract growth-rate +# eigenvalues from the Re(Δ)=0 ∩ Im(Δ)=0 contour intersections. +# +# Resolution and box are entirely user-controlled. Threading is enabled by +# default; pass `threaded=false` for deterministic single-threaded +# evaluation (e.g. when the residual is itself non-thread-safe). + +""" + ScanResult + +Output of a brute-force or AMR Q-plane scan. + +| field | meaning | +|------------|---------------------------------------------------| +| `Q` | Complex Q values (`Matrix` for grid, `Vector` for AMR) | +| `Δ` | Residual values, same shape as `Q` | +| `re_axis` | Real-axis grid (only for regular-grid `ScanResult`) | +| `im_axis` | Imaginary-axis grid (only for regular-grid `ScanResult`) | +""" +struct ScanResult + Q::Matrix{ComplexF64} + Δ::Matrix{ComplexF64} + re_axis::Vector{Float64} + im_axis::Vector{Float64} +end + +""" + brute_force_scan(f, Q_re_range, Q_im_range; nre, nim, + threaded::Bool=true) -> ScanResult + +Evaluate the Q-callable residual `f` on a regular `nre × nim` grid spanning +the rectangle `Q_re_range × Q_im_range` in the complex Q plane. `f` must +accept a single `Complex` argument and return a `Complex` value (typically a +`SurfaceCoupling` or `MultiSurfaceCoupling`, but any callable works). + +Use `find_growth_rates(scan, tauk; ...)` to extract growth-rate eigenvalues +from the result. + +# Arguments + + - `f` -- Q-callable residual (e.g. `SurfaceCoupling`, `MultiSurfaceCoupling`) + - `Q_re_range` -- `(re_min, re_max)` tuple + - `Q_im_range` -- `(im_min, im_max)` tuple + +# Keyword arguments + + - `nre`, `nim` -- grid resolution along each axis + - `threaded` -- distribute Q evaluations across `Threads.@threads` +""" +function brute_force_scan(f, Q_re_range::NTuple{2,<:Real}, + Q_im_range::NTuple{2,<:Real}; + nre::Integer, nim::Integer, + threaded::Bool=true) + nre >= 2 || throw(ArgumentError("brute_force_scan: nre must be ≥ 2")) + nim >= 2 || throw(ArgumentError("brute_force_scan: nim must be ≥ 2")) + re_axis = collect(range(Float64(Q_re_range[1]); stop=Float64(Q_re_range[2]), + length=nre)) + im_axis = collect(range(Float64(Q_im_range[1]); stop=Float64(Q_im_range[2]), + length=nim)) + Q = ComplexF64[(qr + qi*im) for qr in re_axis, qi in im_axis] + Δ = Matrix{ComplexF64}(undef, nre, nim) + if threaded + # Pin BLAS to one thread for the parallel region — `f(Q)` calls `det()`, + # and concurrent multithreaded-BLAS calls give non-reproducible + # reductions that can flip the extracted root run-to-run. The residual + # matrices are tiny, so single-threaded BLAS costs nothing here. + _blas0 = BLAS.get_num_threads() + BLAS.set_num_threads(1) + try + Threads.@threads for j in 1:nim + for i in 1:nre + Δ[i, j] = f(Q[i, j]) + end + end + finally + BLAS.set_num_threads(_blas0) + end + else + for j in 1:nim, i in 1:nre + Δ[i, j] = f(Q[i, j]) + end + end + return ScanResult(Q, Δ, re_axis, im_axis) +end diff --git a/src/Tearing/Dispersion/ContourSearchAMR.jl b/src/Tearing/Dispersion/ContourSearchAMR.jl new file mode 100644 index 000000000..3533a1773 --- /dev/null +++ b/src/Tearing/Dispersion/ContourSearchAMR.jl @@ -0,0 +1,634 @@ +# ContourSearchAMR.jl +# +# Cell-based adaptive mesh refinement scanner of the complex Q plane. +# +# Each `AMRCell` is an axis-aligned rectangle holding its 4 corner Q values +# and the corresponding Δ values evaluated by the user-supplied residual +# `f(Q)`. After `passes` refinement steps, every cell that brackets a zero +# in `Re(Δ)` or `Im(Δ)` has been subdivided into 4 quadrant children +# carrying 5 freshly evaluated midpoint Δ values. +# +# All evaluations of `f(Q)` are deduplicated through a `Dict{ComplexF64, +# ComplexF64}` hash cache so that adjacent cells sharing a corner (and +# adjacent refinement levels sharing an edge midpoint) cost only one +# evaluation. +# +# Output: `AMRResult` holds the final list of `AMRCell`s (preserving the +# axis-aligned-rectangle structure that downstream marching-squares contour +# extraction in `GrowthRateExtraction.jl` exploits) plus the flat +# (Q::Vector, Δ::Vector) of all unique evaluations. + +# Corner ordering: 1 = BL, 2 = BR, 3 = TL, 4 = TR. + +""" + AMRCell + +A single axis-aligned-rectangle cell of an AMR scan. The four corner Q +values (`q_bl`, `q_br`, `q_tl`, `q_tr`) and corresponding residual values +(`d_bl`, `d_br`, `d_tl`, `d_tr`) are sufficient for marching-squares +contour extraction. +""" +struct AMRCell + q_bl::ComplexF64 + q_br::ComplexF64 + q_tl::ComplexF64 + q_tr::ComplexF64 + d_bl::ComplexF64 + d_br::ComplexF64 + d_tl::ComplexF64 + d_tr::ComplexF64 +end + +""" + AMRResult + +Output of `amr_scan`. + +| field | meaning | +|:----------- |:-------------------------------------------------------- | +| `cells` | Final list of `AMRCell` after all refinement passes | +| `Q` | Flat `Vector{ComplexF64}` of every unique residual eval | +| `Δ` | Corresponding `Vector{ComplexF64}` of residual values | +| `truncated` | `true` if `max_cells` was hit and remaining refinement | +| | passes were skipped (`max_cells_action=:warn_truncate`). | +| | A `true` result is NOT fully converged — distinguish it | +| | from a converged scan in convergence studies. | +""" +struct AMRResult + cells::Vector{AMRCell} + Q::Vector{ComplexF64} + Δ::Vector{ComplexF64} + truncated::Bool +end + +# Back-compat constructor: a scan that ran to completion is not truncated. +AMRResult(cells::Vector{AMRCell}, Q::Vector{ComplexF64}, Δ::Vector{ComplexF64}) = + AMRResult(cells, Q, Δ, false) + +# Hash-cached residual evaluator. Returns the cached Δ value if `q` is +# already known, otherwise evaluates `f(q)`, stores it, and returns it. +@inline function _cached_eval!(cache::Dict{ComplexF64,ComplexF64}, + f, q::ComplexF64) + haskey(cache, q) && return cache[q] + Δ = ComplexF64(f(q)) + cache[q] = Δ + return Δ +end + +# Parallel-friendly bulk filler: given a list of Q values, evaluates the +# residual at each one that isn't already in `cache` and stores the result. +# When `parallel=true` AND more than one Julia thread is available, the +# evaluations run via `@threads`; the cache is populated serially afterward +# to avoid Dict data races. Per-call evaluations of `f` are assumed to be +# thread-safe (true for `mc_fort(Q)` which constructs its own local state). +function _bulk_eval_into_cache!(cache::Dict{ComplexF64,ComplexF64}, f, + qs::AbstractVector{ComplexF64}; + parallel::Bool) + # First pass: partition `qs` into already-cached vs new. Keep uniqueness. + seen = Set{ComplexF64}() + new_qs = Vector{ComplexF64}() + for q in qs + if !haskey(cache, q) && !(q in seen) + push!(new_qs, q) + push!(seen, q) + end + end + isempty(new_qs) && return + new_vals = Vector{ComplexF64}(undef, length(new_qs)) + if parallel && Threads.nthreads() > 1 + # Pin BLAS to one thread for the Julia-level parallel region. The + # residual `f(Q)` calls `det()` (LAPACK); concurrent multithreaded-BLAS + # calls from several Julia threads give non-reproducible reductions that + # perturb `f` at the ULP level — enough to flip the extracted root + # between near-degenerate solutions run-to-run. The residual matrices are + # tiny (≤ a few ×msing), so single-threaded BLAS costs nothing here. + _blas0 = BLAS.get_num_threads() + BLAS.set_num_threads(1) + try + Threads.@threads for k in eachindex(new_qs) + new_vals[k] = ComplexF64(f(new_qs[k])) + end + finally + BLAS.set_num_threads(_blas0) + end + else + @inbounds for k in eachindex(new_qs) + new_vals[k] = ComplexF64(f(new_qs[k])) + end + end + @inbounds for k in eachindex(new_qs) + cache[new_qs[k]] = new_vals[k] + end + return +end + +# Sign-crossing test: does `vals` straddle zero? Used in both Re and Im +# directions on a cell's 4 corners (mirrors check_cell_crossing_sub). +@inline function _crosses_zero(vals) + # A non-finite corner (NaN/Inf) marks a divergence — typically a pole, where + # the inner-layer solver returns a NaN sentinel. Flag such cells as active so + # they are refined / pre-screened rather than silently dropped: a NaN corner + # makes both the product test below and the `abs >= threshold` pole check + # evaluate to false, which would hide the pole region entirely. + any(!isfinite, vals) && return true + return minimum(vals) * maximum(vals) <= 0 +end + +# Subdivide a parent cell into 4 quadrants, evaluating Δ at the 5 +# midpoints (BM, TM, LM, RM, MM) via the hash cache. +function _subdivide_cell(parent::AMRCell, + cache::Dict{ComplexF64,ComplexF64}, f) + q_bm = 0.5 * (parent.q_bl + parent.q_br) + q_tm = 0.5 * (parent.q_tl + parent.q_tr) + q_lm = 0.5 * (parent.q_bl + parent.q_tl) + q_rm = 0.5 * (parent.q_br + parent.q_tr) + q_mm = 0.25 * (parent.q_bl + parent.q_br + parent.q_tl + parent.q_tr) + + d_bm = _cached_eval!(cache, f, q_bm) + d_tm = _cached_eval!(cache, f, q_tm) + d_lm = _cached_eval!(cache, f, q_lm) + d_rm = _cached_eval!(cache, f, q_rm) + d_mm = _cached_eval!(cache, f, q_mm) + + return ( + AMRCell(parent.q_bl, q_bm, q_lm, q_mm, # bottom-left quadrant + parent.d_bl, d_bm, d_lm, d_mm), + AMRCell(q_bm, parent.q_br, q_mm, q_rm, # bottom-right quadrant + d_bm, parent.d_br, d_mm, d_rm), + AMRCell(q_lm, q_mm, parent.q_tl, q_tm, # top-left quadrant + d_lm, d_mm, parent.d_tl, d_tm), + AMRCell(q_mm, q_rm, q_tm, parent.q_tr, # top-right quadrant + d_mm, d_rm, d_tm, parent.d_tr) + ) +end + +""" + amr_scan(f, Q_re_range, Q_im_range; + nre0, nim0, passes, + max_cells=10_000_000, + max_cells_action=:error, + snapshot_callback=nothing, + parallel=Threads.nthreads() > 1) -> AMRResult + +Adaptively refine a Q-plane scan of the residual `f(Q)`. An initial +`nre0 × nim0` axis-aligned grid of cells is built over `Q_re_range × Q_im_range` and `passes` rounds of refinement are applied. Each pass: + + 1. flags any cell whose 4 corner residuals straddle zero in `Re(Δ)` or + `Im(Δ)`; + 2. subdivides each flagged cell into 4 quadrant children, evaluating `f` + at 5 new midpoints; + 3. unflagged cells are kept unchanged. + +All evaluations of `f` are deduplicated through a `Dict{ComplexF64, ComplexF64}` hash cache so that adjacent cells share a single evaluation +per corner. The returned `AMRResult` carries both the final cell list (for +marching-squares contour extraction) and the flat list of all unique Q/Δ +evaluations. + +# Keyword arguments + + - `nre0`, `nim0` -- initial coarse-grid cell counts along each axis + - `passes` -- number of refinement passes + - `max_cells` -- safety cap on total cells; behavior on hit is set + by `max_cells_action` + - `max_cells_action` -- `:error` (raises) or `:warn_truncate` (logs a + warning and returns the partial result). The latter is useful for + convergence-vs-resolution studies where we deliberately push max_cells + and want graceful degradation. Default `:error` preserves the prior + safety-rail behaviour. + - `snapshot_callback` -- if not `nothing`, a function called after each + pass (and once for the initial grid, pass=0) with arguments + `(pass::Int, cells::Vector{AMRCell}, cache::Dict{ComplexF64,ComplexF64})`. + The callback receives live references — copy if you need persistence. + Used by convergence studies to extract intermediate γ at each pass count. + - `parallel` -- evaluate `f` in parallel via `Threads.@threads` within + each phase (initial grid + each refinement pass). Defaults to `true` + when more than one Julia thread is available. Per-call evaluations of + `f` must be thread-safe. The result is deterministic regardless of thread + count: cache updates and cell-list construction stay serial, AND BLAS is + pinned to one thread during the parallel region so the `det()`-based + residual does not pick up non-reproducible multithreaded-LAPACK reductions + (which otherwise flip the extracted root between near-degenerate solutions). +""" +function amr_scan(f, Q_re_range::NTuple{2,<:Real}, + Q_im_range::NTuple{2,<:Real}; + nre0::Integer, nim0::Integer, passes::Integer, + max_cells::Integer=10_000_000, + max_cells_action::Symbol=:error, + snapshot_callback::Union{Nothing,Function}=nothing, + parallel::Bool=Threads.nthreads() > 1) + nre0 >= 1 || throw(ArgumentError("amr_scan: nre0 must be ≥ 1")) + nim0 >= 1 || throw(ArgumentError("amr_scan: nim0 must be ≥ 1")) + passes >= 0 || throw(ArgumentError("amr_scan: passes must be ≥ 0")) + max_cells_action in (:error, :warn_truncate) || + throw(ArgumentError("amr_scan: max_cells_action must be :error or " * + ":warn_truncate, got :$max_cells_action")) + + re_lo, re_hi = Float64.(Q_re_range) + im_lo, im_hi = Float64.(Q_im_range) + re_step = (re_hi - re_lo) / nre0 + im_step = (im_hi - im_lo) / nim0 + + cache = Dict{ComplexF64,ComplexF64}() + + # ---- 1. coarse initial grid (nre0 × nim0 cells, (nre0+1)·(nim0+1) corners) + # Collect every corner Q, evaluate in parallel, then build the cells using + # cache lookups (no further evaluation happens in the build step). + ncorners_x = nre0 + 1 + ncorners_y = nim0 + 1 + corners = Vector{ComplexF64}(undef, ncorners_x * ncorners_y) + @inbounds for j in 0:nim0, i in 0:nre0 + corners[j*ncorners_x+i+1] = + ComplexF64(re_lo + i * re_step, im_lo + j * im_step) + end + _bulk_eval_into_cache!(cache, f, corners; parallel=parallel) + + cells = Vector{AMRCell}(undef, nre0 * nim0) + @inbounds for j in 0:nim0-1, i in 0:nre0-1 + # Read corner Q values from the same `corners` array used to populate + # the cache. Recomputing them with `x + re_step` here would differ in + # the last floating-point bit from the cache keys, causing spurious + # KeyErrors on lookup. + q_bl = corners[j*ncorners_x+i+1] + q_br = corners[j*ncorners_x+(i+1)+1] + q_tl = corners[(j+1)*ncorners_x+i+1] + q_tr = corners[(j+1)*ncorners_x+(i+1)+1] + cells[j*nre0+i+1] = AMRCell(q_bl, q_br, q_tl, q_tr, + cache[q_bl], cache[q_br], + cache[q_tl], cache[q_tr]) + end + + # Snapshot the initial grid (pass 0) before any refinement. + snapshot_callback === nothing || snapshot_callback(0, cells, cache) + + # ---- 2. refinement passes + truncated = false # set true when max_cells is hit and action == :warn_truncate + for pass_idx in 1:passes + truncated && break + # Phase A: identify flagged parent cells and collect the midpoints we + # need to evaluate. The 5 midpoints per parent (BM, TM, LM, RM, MM) + # mirror _subdivide_cell's coordinates exactly. + flagged_idx = Int[] + new_qs = Vector{ComplexF64}() + sizehint!(new_qs, length(cells)) + for (idx, cell) in enumerate(cells) + re_corners = (real(cell.d_bl), real(cell.d_br), + real(cell.d_tl), real(cell.d_tr)) + im_corners = (imag(cell.d_bl), imag(cell.d_br), + imag(cell.d_tl), imag(cell.d_tr)) + if _crosses_zero(re_corners) || _crosses_zero(im_corners) + push!(flagged_idx, idx) + push!(new_qs, 0.5 * (cell.q_bl + cell.q_br)) + push!(new_qs, 0.5 * (cell.q_tl + cell.q_tr)) + push!(new_qs, 0.5 * (cell.q_bl + cell.q_tl)) + push!(new_qs, 0.5 * (cell.q_br + cell.q_tr)) + push!(new_qs, 0.25 * (cell.q_bl + cell.q_br + + cell.q_tl + cell.q_tr)) + end + end + + # Phase B: evaluate all new midpoints in parallel, fill the cache. + _bulk_eval_into_cache!(cache, f, new_qs; parallel=parallel) + + # Phase C: build the refined cell list using cache lookups. + new_cells = Vector{AMRCell}() + sizehint!(new_cells, length(cells) + 3 * length(flagged_idx)) + flagged_set = Set(flagged_idx) + skip_remaining = false # true once max_cells is hit (warn_truncate path) + for (idx, cell) in enumerate(cells) + if idx in flagged_set && !skip_remaining + q_bm = 0.5 * (cell.q_bl + cell.q_br) + q_tm = 0.5 * (cell.q_tl + cell.q_tr) + q_lm = 0.5 * (cell.q_bl + cell.q_tl) + q_rm = 0.5 * (cell.q_br + cell.q_tr) + q_mm = 0.25 * (cell.q_bl + cell.q_br + + cell.q_tl + cell.q_tr) + d_bm = cache[q_bm] + d_tm = cache[q_tm] + d_lm = cache[q_lm] + d_rm = cache[q_rm] + d_mm = cache[q_mm] + push!(new_cells, + AMRCell(cell.q_bl, q_bm, q_lm, q_mm, + cell.d_bl, d_bm, d_lm, d_mm), + AMRCell(q_bm, cell.q_br, q_mm, q_rm, + d_bm, cell.d_br, d_mm, d_rm), + AMRCell(q_lm, q_mm, cell.q_tl, q_tm, + d_lm, d_mm, cell.d_tl, d_tm), + AMRCell(q_mm, q_rm, q_tm, cell.q_tr, + d_mm, d_rm, d_tm, cell.d_tr)) + else + push!(new_cells, cell) + end + if length(new_cells) > max_cells + if max_cells_action === :error + error( + "amr_scan: exceeded max_cells=$max_cells " * + "(currently $(length(new_cells))). Reduce " * + "`passes` or raise `max_cells`, or pass " * + "max_cells_action=:warn_truncate to truncate gracefully." + ) + else # :warn_truncate (validated at function entry) + @warn "amr_scan: max_cells=$max_cells reached at pass=$pass_idx cell=$idx/$(length(cells)); truncating refinement here and skipping remaining passes" + skip_remaining = true + truncated = true + end + end + end + cells = new_cells + # Snapshot after this pass. + snapshot_callback === nothing || snapshot_callback(pass_idx, cells, cache) + end + + # ---- 3. flatten the cache into output Q/Δ vectors + n = length(cache) + Q = Vector{ComplexF64}(undef, n) + Δ = Vector{ComplexF64}(undef, n) + for (k, (q, d)) in enumerate(cache) + Q[k] = q + Δ[k] = d + end + + return AMRResult(cells, Q, Δ, truncated) +end + +# ============================================================================= +# Multi-box AMR scan with pre-screen +# ============================================================================= +# +# Motivation. A single wide AMR box (e.g. ω ∈ [-100, +100] kHz, γ ∈ [-25, +25]) +# spends most of its evaluations on regions that contain neither roots nor +# poles. Splitting the same area into several smaller boxes and pre-screening +# each on a coarse 25×25 grid lets us skip refinement on inactive boxes +# entirely, while keeping full AMR sensitivity on the active ones. +# +# A box is flagged ACTIVE if any cell of its pre-screen grid satisfies AT LEAST +# ONE of: +# - sign change in Re(Δ) across the cell's 4 corners (zero-isoline of Re(Δ) +# crosses the cell — root candidate); +# - sign change in Im(Δ) across the cell's 4 corners (zero-isoline of Im(Δ) +# crosses the cell — root candidate); +# - any corner with |Δ| ≥ `pole_magnitude_threshold` (likely pole inside or +# near the box; sign-only criteria miss poles unless their fringe sign +# change happens to land inside the pre-screen resolution). +# +# The pole-magnitude criterion is essential: a tight pole tucked inside one +# pre-screen cell can leave all four corners with the same large-magnitude sign +# (because Re(Δ) and Im(Δ) flip together as you orbit the pole, and at the +# corners we may sample the same lobe), so the sign-change tests would miss it. + +""" + BoxActivity + +Why a box was retained or skipped by `multi_box_amr_scan`. `NoActivity` means +the pre-screen grid showed no zero-isoline crossings and no large-`|Δ|` +corners; the box is excluded from refinement. The other variants record which +criterion fired first. +""" +@enum BoxActivity NoActivity ReZeroCrossing ImZeroCrossing PoleMagnitude + +# Pre-screen activity check: scan the pre-built cells and return the first +# satisfied criterion (or NoActivity if none fire). Designed for early exit so +# fully-quiet boxes cost just enough cell scans to confirm. +function _check_box_activity(cells::AbstractVector{AMRCell}, + pole_magnitude_threshold::Real) + @inbounds for cell in cells + re_corners = (real(cell.d_bl), real(cell.d_br), + real(cell.d_tl), real(cell.d_tr)) + im_corners = (imag(cell.d_bl), imag(cell.d_br), + imag(cell.d_tl), imag(cell.d_tr)) + _crosses_zero(re_corners) && return ReZeroCrossing + _crosses_zero(im_corners) && return ImZeroCrossing + if max(abs(cell.d_bl), abs(cell.d_br), + abs(cell.d_tl), abs(cell.d_tr)) >= pole_magnitude_threshold + return PoleMagnitude + end + end + return NoActivity +end + +""" + MultiBoxAMRResult + +Output of `multi_box_amr_scan`. Per-box `AMRResult`s plus the aggregated +cells/Q/Δ across all *active* boxes. Pre-screen-inactive boxes have `nothing` +for their `AMRResult` and contribute nothing to the aggregated arrays. + +| field | meaning | +|:----------------- |:------------------------------------------------------ | +| `box_results` | per-box `AMRResult`, or `nothing` if box was skipped | +| `box_activity` | per-box `BoxActivity` enum | +| `cells` | concatenated `AMRCell`s from all active boxes | +| `Q` | union of all unique `Q` evaluations (active + skipped) | +| `Δ` | corresponding `Δ` values | +| `prescreen_evals` | total `f(Q)` evaluations spent on pre-screening | + +The aggregated `(cells, Q, Δ)` are suitable for direct consumption by +`find_growth_rates`. Pre-screen evaluations are still included in `Q`/`Δ` even +for skipped boxes, so any downstream pole-magnitude diagnostic that uses the +flat residual list sees the full sample. +""" +struct MultiBoxAMRResult + box_results::Vector{Union{Nothing,AMRResult}} + box_activity::Vector{BoxActivity} + cells::Vector{AMRCell} + Q::Vector{ComplexF64} + Δ::Vector{ComplexF64} + prescreen_evals::Int +end + +""" + multi_box_amr_scan(f, boxes; + pole_magnitude_threshold, + prescreen_nre=25, prescreen_nim=25, + nre0=25, nim0=25, passes=4, + max_cells=10_000_000, + max_cells_action=:error, + parallel=Threads.nthreads() > 1) -> MultiBoxAMRResult + +Run `amr_scan` over multiple Q-plane boxes with a coarse pre-screen step that +skips inactive boxes entirely. The typical use case is the three-stripe ω-axis +scan for SLAYER coupled tearing dispersion: + + ω ∈ [-75, -25], γ ∈ [-25, +25] (left stripe) + ω ∈ [-25, +25], γ ∈ [-25, +25] (centre stripe) + ω ∈ [+25, +75], γ ∈ [-25, +25] (right stripe) + +A single 150×50 box is wasteful when the dispersion is concentrated near a +narrow ω band; splitting into stripes and pre-screening lets the AMR effort +land on the active stripe. + +# Pre-screen logic + +Each box is sampled on a `prescreen_nre × prescreen_nim` corner grid (default +25×25, matching the typical AMR initial-grid resolution). A box is ACTIVE if +ANY pre-screen cell satisfies at least one criterion: + + 1. sign change of `Re(Δ)` across the cell's 4 corners (zero-isoline of + `Re(Δ)` crosses the cell — root candidate); + 2. sign change of `Im(Δ)` across the cell's 4 corners (zero-isoline of + `Im(Δ)` crosses the cell — root candidate); + 3. any corner with `|Δ| ≥ pole_magnitude_threshold` (likely pole — the + sign-only criteria miss poles whose fringe doesn't straddle a corner). + +Active boxes get the full `amr_scan` treatment. Inactive boxes are dropped +(their `AMRResult` is `nothing`). + +# Arguments + + - `f`: residual function `Q::ComplexF64 → Δ::ComplexF64`. Must be thread-safe + if `parallel=true`. + - `boxes`: vector of `(Q_re_range, Q_im_range)` tuples, one per box. Boxes + may overlap or share boundaries; the aggregator deduplicates Q values. + +# Required keyword + + - `pole_magnitude_threshold`: activity threshold for `|Δ|`. A natural choice + is `≈ |mean(Δ)|` from a baseline (or the same value used for adaptive + pole_threshold in `find_growth_rates`). + +# Optional keywords + + - `prescreen_nre`, `prescreen_nim` (default 25 each): pre-screen grid + resolution. Coarser misses small features; finer wastes evaluations on + inactive boxes. + - `nre0, nim0, passes, max_cells, max_cells_action, parallel`: forwarded to + each per-box `amr_scan` call. Defaults match `amr_scan`. + +# Returns + +A `MultiBoxAMRResult`. The aggregated `(cells, Q, Δ)` can be wrapped in an +`AMRResult` (helper `as_amr_result` below) for direct use with +`find_growth_rates`. + +# Notes / TODO + + - Each per-box `amr_scan` rebuilds its own cache, so the 25×25 pre-screen + corners get re-evaluated by the AMR initial pass on active boxes + (≈ 676 wasted evals per active box). A future refactor could thread a + shared cache through `amr_scan`. For now the cost is small relative to + the AMR refinement evals. + - Boxes that share a boundary line (e.g. the three ω-stripe layout above) + duplicate ≈ `prescreen_nim+1` corner evaluations per shared edge. Also + small. + +# Example + +```julia +boxes = [((-75.0, -25.0), (-25.0, 25.0)), + ((-25.0, 25.0), (-25.0, 25.0)), + ((25.0, 75.0), (-25.0, 25.0))] +result = multi_box_amr_scan(f_residual, boxes; + pole_magnitude_threshold=1e-3, + prescreen_nre=25, prescreen_nim=25, + nre0=25, nim0=25, passes=4) +amr = AMRResult(result.cells, result.Q, result.Δ) +roots = find_growth_rates(amr, tauk; pole_threshold=1e-3) +``` +""" +function multi_box_amr_scan(f, + boxes::AbstractVector; + pole_magnitude_threshold::Real, + prescreen_nre::Integer=25, prescreen_nim::Integer=25, + nre0::Integer=25, nim0::Integer=25, passes::Integer=4, + max_cells::Integer=10_000_000, + max_cells_action::Symbol=:error, + parallel::Bool=Threads.nthreads() > 1) + prescreen_nre >= 1 || throw(ArgumentError("multi_box_amr_scan: prescreen_nre must be ≥ 1")) + prescreen_nim >= 1 || throw(ArgumentError("multi_box_amr_scan: prescreen_nim must be ≥ 1")) + pole_magnitude_threshold >= 0 || + throw(ArgumentError("multi_box_amr_scan: pole_magnitude_threshold must be ≥ 0")) + + n_boxes = length(boxes) + box_results = Vector{Union{Nothing,AMRResult}}(undef, n_boxes) + box_activity = Vector{BoxActivity}(undef, n_boxes) + prescreen_evals_total = 0 + + # Aggregator: dedupe Q/Δ across all per-box caches and the pre-screen samples. + # Using a Dict keyed by Q gives O(1) dedup and lets us merge results in any + # order. We also collect cells (from active boxes only) for downstream + # marching-squares extraction. + qd_aggregate = Dict{ComplexF64,ComplexF64}() + cells_aggregate = AMRCell[] + + for (b_idx, box) in enumerate(boxes) + Q_re_range, Q_im_range = box + re_lo, re_hi = Float64.(Q_re_range) + im_lo, im_hi = Float64.(Q_im_range) + re_step = (re_hi - re_lo) / prescreen_nre + im_step = (im_hi - im_lo) / prescreen_nim + ncorners_x = prescreen_nre + 1 + ncorners_y = prescreen_nim + 1 + + # Pre-screen corners for THIS box. Local cache so we can both drive the + # activity check and feed into the aggregate without polluting an + # eventual per-box AMR cache. + box_cache = Dict{ComplexF64,ComplexF64}() + corners = Vector{ComplexF64}(undef, ncorners_x * ncorners_y) + @inbounds for j in 0:prescreen_nim, i in 0:prescreen_nre + corners[j*ncorners_x+i+1] = + ComplexF64(re_lo + i * re_step, im_lo + j * im_step) + end + _bulk_eval_into_cache!(box_cache, f, corners; parallel=parallel) + prescreen_evals_total += length(box_cache) + + # Build pre-screen cells + ps_cells = Vector{AMRCell}(undef, prescreen_nre * prescreen_nim) + @inbounds for j in 0:prescreen_nim-1, i in 0:prescreen_nre-1 + q_bl = corners[j*ncorners_x+i+1] + q_br = corners[j*ncorners_x+(i+1)+1] + q_tl = corners[(j+1)*ncorners_x+i+1] + q_tr = corners[(j+1)*ncorners_x+(i+1)+1] + ps_cells[j*prescreen_nre+i+1] = + AMRCell(q_bl, q_br, q_tl, q_tr, + box_cache[q_bl], box_cache[q_br], + box_cache[q_tl], box_cache[q_tr]) + end + + # Activity check + activity = _check_box_activity(ps_cells, pole_magnitude_threshold) + box_activity[b_idx] = activity + + # Merge pre-screen evals into aggregate (for both active and skipped + # boxes — diagnostics see all samples). + for (q, d) in box_cache + qd_aggregate[q] = d + end + + if activity == NoActivity + box_results[b_idx] = nothing + else + res = amr_scan(f, Q_re_range, Q_im_range; + nre0=nre0, nim0=nim0, passes=passes, + max_cells=max_cells, + max_cells_action=max_cells_action, + parallel=parallel) + box_results[b_idx] = res + append!(cells_aggregate, res.cells) + for k in eachindex(res.Q) + qd_aggregate[res.Q[k]] = res.Δ[k] + end + end + end + + # Flatten aggregator + n = length(qd_aggregate) + Q_all = Vector{ComplexF64}(undef, n) + Δ_all = Vector{ComplexF64}(undef, n) + for (k, (q, d)) in enumerate(qd_aggregate) + Q_all[k] = q + Δ_all[k] = d + end + + return MultiBoxAMRResult(box_results, box_activity, cells_aggregate, + Q_all, Δ_all, prescreen_evals_total) +end + +""" + as_amr_result(mbres::MultiBoxAMRResult) -> AMRResult + +Wrap the aggregated cells/Q/Δ from a multi-box scan as a plain `AMRResult` so +it can be passed directly to `find_growth_rates(::AMRResult, tauk; ...)`. +""" +as_amr_result(mbres::MultiBoxAMRResult) = + AMRResult(mbres.cells, mbres.Q, mbres.Δ, + any(r -> r !== nothing && r.truncated, mbres.box_results)) diff --git a/src/Tearing/Dispersion/Coupled.jl b/src/Tearing/Dispersion/Coupled.jl new file mode 100644 index 000000000..4029943b9 --- /dev/null +++ b/src/Tearing/Dispersion/Coupled.jl @@ -0,0 +1,110 @@ +# Coupled.jl +# +# Multi-surface coupled tearing dispersion residual `det(M(Q))` (the +# coupled, tearing-only reduction of the full Pletzer-Dewar matching in +# `CoupledFullMatch.jl`). Shares the per-surface `SurfaceCoupling` +# Q-callable interface so a brute-force or AMR scan can evaluate either +# residual identically. +# +# Construction: +# +# mc = multi_surface_coupling(surfaces, dp_matrix; ref_idx=1, msing_max=...) +# +# Evaluation: +# +# det = mc(Q::ComplexF64) +# +# At each evaluation, for k = 1 .. msing_max, the inner-layer Δ is computed +# at a Q rescaled by `tauk_ref / tauk_k`, then subtracted (with the dc +# offset) from the diagonal of an `msing_max × msing_max` upper-left +# submatrix of `dp_matrix`. The off-diagonal Δ' couplings are passed +# through unchanged. + +""" + MultiSurfaceCoupling{V<:AbstractVector{<:SurfaceCoupling}} + +Multi-surface dispersion data: a vector of `SurfaceCoupling`, the full Δ' +matrix, the index of the reference surface (whose `tauk` defines the Q +normalization), and the truncation `msing_max` (number of surfaces actually +participating in the determinant). Calling `mc(Q)` returns `det(M(Q))` where + +``` +M[k,k] = dp_matrix[k,k] - scale_k · Δ_inner_k(Q · tauk_ref / tauk_k) - dc_k +M[i,j] = dp_matrix[i,j] for i ≠ j (off-diagonal Δ' couplings) +``` + +A root of `mc` in the complex `Q` plane is a coupled tearing eigenvalue. +""" +struct MultiSurfaceCoupling{V<:AbstractVector{<:SurfaceCoupling}} + surfaces::V + dp_matrix::Matrix{ComplexF64} + ref_idx::Int + msing_max::Int +end + +""" + multi_surface_coupling(surfaces, dp_matrix; + ref_idx=1, + msing_max=min(3, length(surfaces))) + -> MultiSurfaceCoupling + +Construct a multi-surface coupling from a vector of `SurfaceCoupling` and +the full outer-region Δ' matrix. `dp_matrix` must be square with side +length `length(surfaces)` (it is the same matrix returned by +`PerturbedEquilibrium.SingularCoupling`'s Δ' boundary-value problem). + +# Keyword arguments + + - `ref_idx` -- index of the reference surface whose `tauk` defines the + Q normalization. Defaults to `1`. + - `msing_max` -- number of surfaces from the front of `surfaces` to + include in the determinant. Defaults to `min(3, length(surfaces))`: + Δ' off-diagonal couplings beyond the third surface tend to be erratic + in practice, so the determinant is conservatively truncated to the + upper-left `msing_max × msing_max` submatrix of `dp_matrix`. Set + explicitly (up to `length(surfaces)`) to override. +""" +function multi_surface_coupling(surfaces::AbstractVector{<:SurfaceCoupling}, + dp_matrix::AbstractMatrix; + ref_idx::Integer=1, + msing_max::Integer=min(3, length(surfaces))) + n = length(surfaces) + size(dp_matrix) == (n, n) || + throw(ArgumentError("multi_surface_coupling: dp_matrix size " * + "$(size(dp_matrix)) ≠ ($n, $n)")) + 1 <= ref_idx <= n || + throw(ArgumentError("multi_surface_coupling: ref_idx=$ref_idx out " * + "of range 1:$n")) + 1 <= msing_max <= n || + throw(ArgumentError("multi_surface_coupling: msing_max=$msing_max " * + "out of range 1:$n")) + return MultiSurfaceCoupling(surfaces, + Matrix{ComplexF64}(dp_matrix), + Int(ref_idx), Int(msing_max)) +end + +function (mc::MultiSurfaceCoupling)(Q::Number) + n = mc.msing_max + Qc = ComplexF64(Q) + ref_tauk = mc.surfaces[mc.ref_idx].tauk + + M = mc.dp_matrix[1:n, 1:n] + @inbounds for k in 1:n + sc = mc.surfaces[k] + Q_k = Qc * (ref_tauk / sc.tauk) + # m×m scalar coupling: use only the tearing channel. The + # interchange (Glasser-stabilization) channel is carried in the + # full 4m×4m dispersion in `CoupledFullMatch.jl`; this reduced + # form is equivalent for pressureless SLAYER surfaces + # (Δ_interchange=0) and approximate for GGJ surfaces (drops + # Glasser stabilization). + Δ_k = solve_inner(sc.model, sc.params, Q_k).tearing * sc.scale + # The inner-layer solver returns NaN when the Riccati integration fails + # (clustered near poles). Propagate it as the residual so the scan flags + # this Q-cell via its isfinite checks, rather than feeding NaN into the + # LU factorization where it silently contaminates the whole determinant. + isfinite(Δ_k) || return ComplexF64(NaN, NaN) + M[k, k] -= Δ_k + sc.dc + end + return det(M) +end diff --git a/src/Tearing/Dispersion/CoupledFullMatch.jl b/src/Tearing/Dispersion/CoupledFullMatch.jl new file mode 100644 index 000000000..8bf5fb97c --- /dev/null +++ b/src/Tearing/Dispersion/CoupledFullMatch.jl @@ -0,0 +1,214 @@ +# CoupledFullMatch.jl +# +# Full Pletzer-Dewar 4m × 4m tearing+interchange dispersion matrix, with +# the m inner-layer resonances decoupled via the matching-identity rows +# +# C^j_L = d^j_+ − d^j_- +# C^j_R = -(d^j_+ + d^j_-) +# +# (see Wang-Glasser-Brennan-Liu-Park 2020, Phys. Plasmas **27**, 122503, +# Eq. (11a)-(11d) and Glasser-Wang-Park 2016, Phys. Plasmas **23**, 112506, +# Eq. (36)-(40); original matching construction Pletzer & Dewar 1991, +# J. Plasma Phys. **45**, 427). +# +# Why 4m × 4m and not 2m × 2m? +# +# The outer-region matching matrix D' (Julia `intr.delta_prime_raw`) is +# expressed in the side-major basis `[L_s1, R_s1, L_s2, R_s2, …]` of +# large-solution driving amplitudes. The inner-layer Galerkin solver +# (`solve_inner(GGJModel, …)`) returns Δ_tearing and Δ_interchange in +# the even/odd parity (+/−) basis instead. The naive relation +# `det(D' − diag(Δ_+, Δ_-)) = 0` cannot be written directly because +# the two quantities live in different bases. The fix is to introduce +# both sets of amplitudes (`C^j_{L,R}` for outer, `d^j_±` for inner) as +# explicit unknowns and use the ±1 matching identity as two extra rows +# per surface, yielding the 4m × 4m linear system. A naive 2m × 2m +# `det(D' − diag(Δ_+, Δ_-))` form cannot work here: it subtracts the +# inner Δ (parity ± basis) from the outer D' (side-major L/R basis), two +# quantities living in different bases, producing a determinant with +# structurally-wrong magnitude and topology. This module reproduces the +# full Pletzer-Dewar result. +# +# Per surface `k` (1-indexed), the 4 block indices are +# +# idx1 = 2k − 1 (row/col for C^k_L) +# idx2 = 2k (row/col for C^k_R) +# idx3 = idx1 + 2m (row/col for d^k_+) +# idx4 = idx2 + 2m (row/col for d^k_-) +# +# The global 4m × 4m matrix has: +# +# - lower-left 2m × 2m block = transpose(dp_raw) +# - upper-left 2m × 2m block: per-surface 2 × 2 identity +# - upper-right 2m × 2m block: per-surface 2 × 2 matching identity +# - lower-right 2m × 2m block: per-surface 2 × 2 inner Δ block +# +# See the per-surface fill table in the body of `(::MultiSurfaceCouplingFull)`. + +""" + MultiSurfaceCouplingFull{V<:AbstractVector{<:SurfaceCoupling}} + +Full 4m × 4m tearing+interchange Pletzer-Dewar dispersion matrix +(Wang et al. 2020, Phys. Plasmas **27**, 122503). + +Given the raw 2m × 2m outer-region matrix `dp_raw` (side-major ordering +`[L_s1, R_s1, L_s2, R_s2, …]`, from `intr.delta_prime_raw`) and a vector +of `SurfaceCoupling` (each containing the inner-layer model and +parameters), calling `mc(Q)` assembles the 4m × 4m Pletzer-Dewar +matching matrix and returns `det(mat)`. + +This is the correct Pletzer-Dewar dispersion relation for +tearing+interchange coupling. A naive 2m × 2m `det(D' − D(γ))` form is +not equivalent: it subtracts the inner Δ (parity ± basis) from the outer +D' (side-major L/R basis), mixing two different bases. The 4m × 4m +matching system introduced here keeps the bases separate via the explicit +`C^j_{L,R}` / `d^j_±` unknowns. For pure-tearing (pressureless SLAYER) +studies use the reduced m × m `MultiSurfaceCoupling` instead. + +# Fields + + - `surfaces::V` — per-surface `SurfaceCoupling`. + - `dp_raw::Matrix{ComplexF64}` — 2m × 2m outer-region matrix (side-major). + - `ref_idx::Int` — reference surface for Q rescaling (1-based). + - `msing_max::Int` — number of surfaces to include (truncates). + - `rotation::Vector{Float64}` — per-surface rotation frequencies (s⁻¹). + - `ntor::Int` — toroidal mode number `n` (default 1). +""" +struct MultiSurfaceCouplingFull{V<:AbstractVector{<:SurfaceCoupling},K<:NamedTuple} + surfaces::V + dp_raw::Matrix{ComplexF64} + ref_idx::Int + msing_max::Int + rotation::Vector{Float64} + ntor::Int + inner_kwargs::K # kwargs forwarded to solve_inner; e.g. (pfac=0.1, nx=128, nq=5) +end + +""" + multi_surface_coupling_full(surfaces, dp_raw; + ref_idx=1, + msing_max=length(surfaces), + rotation=zeros(length(surfaces)), + ntor=1) -> MultiSurfaceCouplingFull + +Construct the 4m × 4m dispersion matrix driver. `dp_raw` must be the +2m × 2m matrix in side-major ordering (the `intr.delta_prime_raw` +field populated by `ForceFreeStates.compute_delta_prime_matrix!` on the +`use_parallel=true` path). `rotation[k]` is the per-surface rotation +frequency; it shifts the per-surface inner Q argument by +`i·ntor·rotation[k]`. Default zero rotation matches the static-equilibrium +case. + +# Keyword arguments + + - `ref_idx` — index of the reference surface whose `tauk` defines the + Q normalization (1 ≤ ref_idx ≤ m). Defaults to 1. + - `msing_max` — truncate to the leading `msing_max` surfaces; the + matching matrix becomes 4·msing_max × 4·msing_max, built from the + corresponding 2·msing_max × 2·msing_max submatrix of `dp_raw`. + Defaults to `length(surfaces)`. + - `rotation` — per-surface rotation frequencies in s⁻¹ (length m). + Defaults to all zero. + - `ntor` — toroidal mode number n. Defaults to 1. + - `inner_kwargs` — NamedTuple of kwargs forwarded to `solve_inner` at + every Q evaluation, e.g. `(pfac=0.1, xfac=10.0, nx=128, nq=5)` for + Galerkin grid tuning. Defaults to `NamedTuple()`. +""" +function multi_surface_coupling_full(surfaces::AbstractVector{<:SurfaceCoupling}, + dp_raw::AbstractMatrix; + ref_idx::Integer=1, + msing_max::Integer=length(surfaces), + rotation::AbstractVector{<:Real}=zeros(length(surfaces)), + ntor::Integer=1, + inner_kwargs::NamedTuple=NamedTuple()) + m = length(surfaces) + size(dp_raw) == (2m, 2m) || + throw(ArgumentError("multi_surface_coupling_full: dp_raw size " * + "$(size(dp_raw)) ≠ ($(2m), $(2m))")) + 1 <= ref_idx <= m || + throw(ArgumentError("multi_surface_coupling_full: ref_idx=$ref_idx " * + "out of range 1:$m")) + 1 <= msing_max <= m || + throw(ArgumentError("multi_surface_coupling_full: msing_max=$msing_max " * + "out of range 1:$m")) + length(rotation) == m || + throw(ArgumentError("multi_surface_coupling_full: rotation length " * + "$(length(rotation)) ≠ $m")) + return MultiSurfaceCouplingFull(surfaces, + Matrix{ComplexF64}(dp_raw), + Int(ref_idx), Int(msing_max), + Float64.(collect(rotation)), + Int(ntor), + inner_kwargs) +end + +# Assemble and return det(mat) where mat is the 4·msing_max × 4·msing_max +# Pletzer-Dewar matching matrix (Wang et al. 2020, Eq. 11; Glasser-Wang-Park +# 2016, Eqs. 36-40). +function (mc::MultiSurfaceCouplingFull)(Q::Number) + m = mc.msing_max + s2 = 2m + s4 = 4m + Qc = ComplexF64(Q) + ref_tauk = mc.surfaces[mc.ref_idx].tauk + + # Allocate the matching matrix and fill the lower-left 2m × 2m block + # with transpose(dp_raw[1:s2, 1:s2]). + mat = zeros(ComplexF64, s4, s4) + @views mat[s2+1:s4, 1:s2] .= transpose(mc.dp_raw[1:s2, 1:s2]) + + # Per-surface inner-layer assembly + @inbounds for k in 1:m + sc = mc.surfaces[k] + idx1 = 2k - 1 # C^k_L + idx2 = 2k # C^k_R + idx3 = idx1 + s2 # d^k_+ + idx4 = idx2 + s2 # d^k_- + + # Per-surface Q shift: guess_modify = Q + i·n·rotation[k]. + # Also apply ref_tauk / sc.tauk rescaling (we keep the SurfaceCoupling + # tauk normalization that SLAYER needs; GGJ has tauk=1 so it's a no-op). + Q_k = Qc * (ref_tauk / sc.tauk) + 1im * mc.ntor * mc.rotation[k] + resp = solve_inner(sc.model, sc.params, Q_k; mc.inner_kwargs...) + + # delta1 = interchange (parity −), delta2 = tearing (parity +); named + # fields expose the two channels directly. sc.scale converts inner-basis + # Δ to outer units (1.0 for GGJ since rescale_delta is applied inside + # solve_inner; S^(1/3) for SLAYER). + # + # NOTE: the fulldomain matching does NOT add any Δ_crit offset here — + # delta1, delta2 are the raw inner-layer outputs. The full 4m×4m + # Pletzer-Dewar residual includes the interchange channel, which + # provides Glasser (Mercier) stabilization natively; Δ_crit is a + # slab-layer proxy only relevant to SLAYER's tearing-only model. + delta1 = resp.interchange * sc.scale + delta2 = resp.tearing * sc.scale + # The inner-layer solver returns NaN when the Riccati integration fails + # (clustered near poles). Propagate it as the residual so the scan flags + # this Q-cell via its isfinite checks, rather than feeding NaN into the + # LU factorization where it silently contaminates the whole determinant. + (isfinite(delta1) && isfinite(delta2)) || return ComplexF64(NaN, NaN) + + # --- Upper-left 2×2 block: per-surface identity on C_{L,R} --- + mat[idx1, idx1] = 1 + mat[idx2, idx2] = 1 + + # --- Upper-right 2×2 block: matching identity --- + # C^k_L = d^k_+ − d^k_- ⇒ mat[idx1,idx3]=-1, mat[idx1,idx4]=+1 + # C^k_R = -(d^k_+ + d^k_-) ⇒ mat[idx2,idx3]=-1, mat[idx2,idx4]=-1 + mat[idx1, idx3] = -1 + mat[idx1, idx4] = 1 + mat[idx2, idx3] = -1 + mat[idx2, idx4] = -1 + + # --- Lower-right 2×2 block: inner Δ matching --- + # d^k_+ eqn: -Δ_int·d^k_+ + Δ_tear·d^k_- + (outer D' terms) = 0 + # d^k_- eqn: -Δ_int·d^k_+ - Δ_tear·d^k_- + (outer D' terms) = 0 + mat[idx3, idx3] = -delta1 + mat[idx3, idx4] = delta2 + mat[idx4, idx3] = -delta1 + mat[idx4, idx4] = -delta2 + end + + return det(mat) +end diff --git a/src/Tearing/Dispersion/Dispersion.jl b/src/Tearing/Dispersion/Dispersion.jl new file mode 100644 index 000000000..67731e5aa --- /dev/null +++ b/src/Tearing/Dispersion/Dispersion.jl @@ -0,0 +1,55 @@ +# Dispersion.jl +# +# Tearing-dispersion-relation solver shared between GGJ and SLAYER inner-layer +# models. Combines the outer-region Δ' from `PerturbedEquilibrium.SingularCoupling` +# with the inner-layer Δ(Q) from any `InnerLayerModel` to find growth-rate +# eigenvalues. +# +# Operating modes: +# - `SurfaceCoupling` -- per-surface residual r(Q) +# - `multi_surface_coupling` -- multi-surface determinant (Coupled.jl) +# - `brute_force_scan` -- regular 2D Q-plane scan +# - `find_growth_rates` -- contour-intersection root extraction (Re=0 ∩ Im=0) +# - `amr_scan` -- adaptive Q-plane refinement +# +# Roots are ISOLATED by 2D contour intersection on Nyquist-style Q-plane scans +# (`find_growth_rates`, Re=0 ∩ Im=0), then optionally POLISHED to the true zero +# of the residual by a bounded, neighbour-aware local solve (pass the residual +# callable to `find_growth_rates`). Polishing makes the extracted root +# resolution- and thread-independent; without it the reported root is the +# marching-squares estimate, sensitive to grid/rounding. This module provides +# both the residual building blocks and the scan/extraction machinery. +# +# The per-surface residual at one rational surface is +# +# r(Q) = Δ'_diag - scale · Δ_inner(Q) - Δ_crit +# +# where `scale` is the inner→outer-units conversion factor (S^(1/3) for SLAYER, +# 1 for GGJ since `rescale_delta` is applied internally) and `Δ_crit` is the +# `dc_tmp` chi-parallel offset (zero by default). + +module Dispersion + +using LinearAlgebra +using StaticArrays + +using ..InnerLayer +using ..InnerLayer: InnerLayerModel, solve_inner, GGJModel, GGJParameters, + SLAYERModel, SLAYERParameters + +include("SurfaceCoupling.jl") +include("Coupled.jl") +include("CoupledFullMatch.jl") +include("BruteForceScan.jl") +include("ContourSearchAMR.jl") +include("GrowthRateExtraction.jl") + +export SurfaceCoupling, surface_coupling +export MultiSurfaceCoupling, multi_surface_coupling +export MultiSurfaceCouplingFull, multi_surface_coupling_full +export ScanResult, brute_force_scan +export AMRCell, AMRResult, amr_scan +export BoxActivity, MultiBoxAMRResult, multi_box_amr_scan, as_amr_result +export GrowthRateResult, find_growth_rates + +end # module Dispersion diff --git a/src/Tearing/Dispersion/GrowthRateExtraction.jl b/src/Tearing/Dispersion/GrowthRateExtraction.jl new file mode 100644 index 000000000..42c2c9681 --- /dev/null +++ b/src/Tearing/Dispersion/GrowthRateExtraction.jl @@ -0,0 +1,992 @@ +# GrowthRateExtraction.jl +# +# Extracts tearing-mode growth rates by contour intersection (Re=0 ∩ Im=0) on a +# complex Q-plane scan: finds intersections of the Re(Δ)=0 and Im(Δ)=0 contours, +# classifies each intersection as a root or pole, and applies the "outside Re=0 +# contour, above pole" filter for spurious upper-branch roots. +# +# This PR (5/9) handles the regular-grid path via Contour.jl. PR 6 will add +# a scattered-data path (triangulation) for AMR scans. +# +# Algorithm summary: +# 1. Extract Re(Δ) = re_target and Im(Δ) = im_target contour polylines. +# 2. Find all segment-segment intersections of the two contour families. +# 3. For each intersection, find the closest Im=0 contour and classify as +# a pole if `max(|Re(Δ)|)` along the local arc exceeds `pole_threshold`. +# 4. For each non-pole intersection, find the closest Re=0 contour. If +# that contour is approximately closed, take a small +γ step along the +# Im=0 contour and test whether the step lands inside the Re=0 loop. +# Roots whose +γ step exits the loop AND that lie above the highest +# pole are filtered out (spurious upper branches). +# 5. Return the highest-γ surviving root in physical units. + +using Contour +using DelaunayTriangulation + +# --------------------------------------------------------------------- +# Public result struct + main entry point. +# --------------------------------------------------------------------- + +""" + GrowthRateResult + +Output of `find_growth_rates`. + +| field | meaning | +|:-------------------- |:----------------------------------------------------- | +| `Q_root` | Best (highest-γ surviving) root, normalized | +| `omega_Hz` | `Re(Q_root) / tauk` — physical rotation frequency | +| `gamma_Hz` | `Im(Q_root) / tauk` — physical growth rate | +| `Q_root_secondary` | Second-most-unstable root flagged for ambiguity, or | +| | `NaN+NaNim` if the primary root was unambiguous. | +| `omega_Hz_secondary` | physical ω of the secondary root, or 0 if none | +| `gamma_Hz_secondary` | physical γ of the secondary root, or 0 if none | +| `warning_flags` | `Vector{Symbol}` of warnings raised on `Q_root`: | +| | `:geom`, `:gap` (root accepted with caveat); | +| | `:spurious` when ≥1 contour near-miss was dropped by | +| | the validity gate (parked in `filtered_roots`); or | +| | `:no_root` when NO usable root was found (`Q_root` is | +| | `NaN`; `omega_Hz`/`gamma_Hz` fall back to 0 — check | +| | this flag to tell that apart from a true γ≈0 result). | +| | Empty if root is clean. | +| `valid_roots` | All non-pole intersections that survived pole filter | +| `poles` | Intersections classified as poles | +| `filtered_roots` | Intersections rejected by the above-pole/outside-Re | +| | filter or the new geom+gap recursion | +| `re_contours` | Extracted Re(Δ)=`re_target` polylines | +| `im_contours` | Extracted Im(Δ)=`im_target` polylines | +| `pole_threshold` | Threshold used for pole classification | +""" +struct GrowthRateResult + Q_root::ComplexF64 + omega_Hz::Float64 + gamma_Hz::Float64 + Q_root_secondary::ComplexF64 + omega_Hz_secondary::Float64 + gamma_Hz_secondary::Float64 + warning_flags::Vector{Symbol} + valid_roots::Vector{ComplexF64} + poles::Vector{ComplexF64} + filtered_roots::Vector{ComplexF64} + re_contours::Vector{Vector{ComplexF64}} + im_contours::Vector{Vector{ComplexF64}} + pole_threshold::Float64 +end + +""" + find_growth_rates(scan::ScanResult, tauk::Real; + re_target=0.0, im_target=0.0, + pole_threshold=10.0, + filter_above_poles=true, + filter_outside_re=true, + gap_kHz_threshold=1.0) -> GrowthRateResult + +Extract tearing growth-rate eigenvalues from a brute-force `ScanResult` by +contour-intersection analysis. `tauk` is the per-surface time normalization +used to convert `Q` back to physical (Hz) units (`SurfaceCoupling.tauk` for +single-surface scans; `mc.surfaces[mc.ref_idx].tauk` for coupled scans). + +# Keyword arguments + + - `re_target`, `im_target` -- contour levels (zero for vanilla dispersion + root-finding; nonzero values let the caller probe iso-residual contours) + - `pole_threshold` -- intersection is classified as a pole when + `max(|Re(Δ)|)` along the local arc of the nearest Im=0 contour exceeds + this value + - `filter_above_poles` -- discard roots whose γ exceeds the highest pole γ + - `filter_outside_re` -- restrict the above-pole rejection to roots whose + +γ step along the Im=0 contour exits the Re=0 contour loop. When `true`, + roots that are above a pole but geometrically inside the Re=0 contour + survive (matches the Python default). Note this gate fails when the + Re=0 contour is OPEN (e.g., exits the Q box edge), letting spurious + upper-branch roots through; the `:geom` and `:gap` flags below cover + that case. + - `gap_kHz_threshold` -- if the highest-γ root is unstable (γ > 0) AND its + γ exceeds the next root by more than this many kHz, it is flagged as + a `:gap` warning. Default 1.0 kHz. + - `residual` -- optional dispersion-residual callable `f(Q::Complex)`. When + supplied, each contour-intersection root is POLISHED to the true zero of + `f` by a bounded, neighbour-aware local solve (see `_polish_root`), making + the extracted root resolution- and thread-independent. `nothing` (default) + reports the raw marching-squares estimate, which is sensitive to grid and + floating-point rounding. + - `polish_maxit` -- max polish iterations per root (default 20). Each costs a + handful of `f` evaluations; failures fall back to the unpolished point. + - `validity_rtol` -- with `residual` supplied, a polished root is kept only if + `|residual| < validity_rtol · median(|Δ|)` (default 1e-3). Intersections + that don't polish to a true zero (contour near-misses, or surfaces whose + Δ' BVP failed → `|Δ'|` huge and uncancellable) are dropped from + `valid_roots`, parked in `filtered_roots`, and flagged `:spurious`. If every + candidate is spurious, the result carries `:no_root`. + +# Spurious-root recursion + +After the per-intersection pole / above-pole filters, the remaining roots +are sorted by descending γ. The selection loop walks down this list and at +each candidate evaluates two flags: + + - `:geom` — Re(Δ)=0 contour is locally a downward-concave "hill" at the + candidate (clean polyline-following quadratic fit). + - `:gap` — candidate is unstable AND its γ exceeds the next root's by + more than `gap_kHz_threshold` kHz. + +If BOTH fire, the candidate is discarded as spurious and the next-most- +unstable root is tried. If exactly ONE fires, the candidate is accepted as +primary with that warning recorded, and the next root is exposed as +`Q_root_secondary` so downstream tools can plot or reanalyse it. If +neither fires, the candidate is accepted cleanly. +""" +function find_growth_rates(scan::ScanResult, tauk::Real; + re_target::Real=0.0, im_target::Real=0.0, + pole_threshold::Real=10.0, + filter_above_poles::Bool=true, + filter_outside_re::Bool=true, + gap_kHz_threshold::Real=1.0, + residual=nothing, + polish_maxit::Integer=20, + validity_rtol::Real=1e-3) + return _extract_growth_rates(scan.re_axis, scan.im_axis, scan.Δ, + Float64(tauk); + re_target=Float64(re_target), + im_target=Float64(im_target), + pole_threshold=Float64(pole_threshold), + filter_above_poles=filter_above_poles, + filter_outside_re=filter_outside_re, + gap_kHz_threshold=Float64(gap_kHz_threshold), + residual=residual, + polish_maxit=Int(polish_maxit), + validity_scale=_residual_scale(scan.Δ), + validity_rtol=Float64(validity_rtol)) +end + +""" + find_growth_rates(amr::AMRResult, tauk::Real; + re_target=0.0, im_target=0.0, + pole_threshold=10.0, + filter_above_poles=true, + filter_outside_re=true) -> GrowthRateResult + +Extract tearing growth-rate eigenvalues from an AMR `AMRResult` via Delaunay +triangulation + marching triangles on the scattered evaluation points. The +pipeline after contour extraction (segment intersection, pole classification, +outside-Re filter, physical-Hz conversion) is identical to the brute-force +grid path — only the contour extractor changes. Hanging-node issues from the +quadtree's mixed refinement levels are resolved by the triangulation +respecting every evaluated point uniformly. +""" +function find_growth_rates(amr::AMRResult, tauk::Real; + re_target::Real=0.0, im_target::Real=0.0, + pole_threshold::Real=10.0, + filter_above_poles::Bool=true, + filter_outside_re::Bool=true, + gap_kHz_threshold::Real=1.0, + residual=nothing, + polish_maxit::Integer=20, + validity_rtol::Real=1e-3) + return _extract_growth_rates_amr(amr.Q, amr.Δ, Float64(tauk); + re_target=Float64(re_target), + im_target=Float64(im_target), + pole_threshold=Float64(pole_threshold), + filter_above_poles=filter_above_poles, + filter_outside_re=filter_outside_re, + gap_kHz_threshold=Float64(gap_kHz_threshold), + residual=residual, + polish_maxit=Int(polish_maxit), + validity_scale=_residual_scale(amr.Δ), + validity_rtol=Float64(validity_rtol)) +end + +# --------------------------------------------------------------------- +# Implementation. +# --------------------------------------------------------------------- + +# Bilinear interpolation of `values` on the regular grid `(re_axis, im_axis)` +# at point (qr, qi). Out-of-grid points are clamped to the boundary. +function _bilinear(re_axis::Vector{Float64}, im_axis::Vector{Float64}, + values::Matrix{Float64}, qr::Real, qi::Real) + nre = length(re_axis) + nim = length(im_axis) + i = clamp(searchsortedlast(re_axis, qr), 1, nre - 1) + j = clamp(searchsortedlast(im_axis, qi), 1, nim - 1) + tx = (qr - re_axis[i]) / (re_axis[i+1] - re_axis[i]) + ty = (qi - im_axis[j]) / (im_axis[j+1] - im_axis[j]) + tx = clamp(tx, 0.0, 1.0) + ty = clamp(ty, 0.0, 1.0) + return (1 - tx) * (1 - ty) * values[i, j] + tx * (1 - ty) * values[i+1, j] + + (1 - tx) * ty * values[i, j+1] + tx * ty * values[i+1, j+1] +end + +# Extract polylines for a single contour level on a regular grid. +# Returns Vector{Vector{ComplexF64}} (one polyline per closed/open curve). +function _extract_contours(re_axis::Vector{Float64}, im_axis::Vector{Float64}, + values::Matrix{Float64}, level::Float64) + polylines = Vector{Vector{ComplexF64}}() + for cl in lines(contour(re_axis, im_axis, values, level)) + xs, ys = coordinates(cl) + path = ComplexF64[xs[i] + ys[i] * im for i in eachindex(xs)] + length(path) >= 2 && push!(polylines, path) + end + return polylines +end + +# Segment-segment intersection on the complex plane. Returns the +# intersection point if segments [a,b] and [c,d] cross strictly (parameters +# in (0,1)), else nothing. Endpoint touches return the touch point. +function _segment_intersection(a::ComplexF64, b::ComplexF64, + c::ComplexF64, d::ComplexF64) + d1r, d1i = real(b - a), imag(b - a) + d2r, d2i = real(d - c), imag(d - c) + denom = d1r * d2i - d1i * d2r + abs(denom) < 1e-30 && return nothing # parallel or degenerate + diffr, diffi = real(c - a), imag(c - a) + t = (diffr * d2i - diffi * d2r) / denom + u = (diffr * d1i - diffi * d1r) / denom + if 0 <= t <= 1 && 0 <= u <= 1 + return a + t * (b - a) + end + return nothing +end + +# Find all intersections between two families of polylines. Returns +# Vector{ComplexF64}. +function _all_intersections(re_paths::Vector{Vector{ComplexF64}}, + im_paths::Vector{Vector{ComplexF64}}) + out = ComplexF64[] + for re_path in re_paths + for i in 1:length(re_path)-1 + a, b = re_path[i], re_path[i+1] + for im_path in im_paths + for j in 1:length(im_path)-1 + c, d = im_path[j], im_path[j+1] + pt = _segment_intersection(a, b, c, d) + pt !== nothing && push!(out, pt) + end + end + end + end + return out +end + +# Index of the closest vertex in a polyline to a point. +function _closest_vertex(path::Vector{ComplexF64}, pt::ComplexF64) + best_i = 0 + best_d = Inf + for i in eachindex(path) + d = abs(path[i] - pt) + if d < best_d + best_d = d + best_i = i + end + end + return best_i, best_d +end + +# Find the polyline (and vertex within it) whose vertex is closest to pt. +function _closest_polyline_vertex(paths::Vector{Vector{ComplexF64}}, + pt::ComplexF64) + best_path_idx = 0 + best_vert_idx = 0 + best_d = Inf + for (pi_, path) in enumerate(paths) + vi, d = _closest_vertex(path, pt) + if d < best_d + best_d = d + best_path_idx = pi_ + best_vert_idx = vi + end + end + return best_path_idx, best_vert_idx, best_d +end + +# Ray-casting point-in-polygon. `polygon` need not be closed (function +# closes it internally). +function _point_in_polygon(pt::ComplexF64, polygon::Vector{ComplexF64}) + n = length(polygon) + n < 3 && return false + inside = false + pr, pi_ = real(pt), imag(pt) + j = n + for i in 1:n + xi, yi = real(polygon[i]), imag(polygon[i]) + xj, yj = real(polygon[j]), imag(polygon[j]) + if ((yi > pi_) != (yj > pi_)) && + (pr < (xj - xi) * (pi_ - yi) / (yj - yi) + xi) + inside = !inside + end + j = i + end + return inside +end + +# --------------------------------------------------------------------- +# Shared analysis: intersections + pole classification + outside-Re filter. +# Both the regular-grid path (_extract_growth_rates) and the AMR +# triangulation path (_extract_growth_rates_amr) funnel through this. +# --------------------------------------------------------------------- +# Geometric "spurious upper-branch" detector — flags candidates where the +# Re(Δ)=0 contour is locally a downward-concave "hill" or "hump" (⌒) at the +# candidate location. Legitimate tearing roots sit at the bottom of upward- +# concave "wells" (∪); spurious upper-branch roots sit at the top of hills. +# +# Algorithm: +# 1. Find the closest Re=0 polyline + closest vertex on it. +# 2. Walk outward along that polyline, collecting consecutive vertices +# within `max_walk` Q-distance of the candidate. Walking the polyline +# (rather than averaging over a radius) avoids polluting the fit with +# vertices from disconnected nearby Re=0 fragments — important on +# AMR-triangulated meshes where the contour is fragmented. +# 3. Fit γ = a + b·Δω + c·(Δω)² to the collected vertices via least squares. +# Sign of `c` is the local concavity: +# c < 0 → contour is concave-DOWN (hill, ⌒) ← SPURIOUS pattern +# c > 0 → contour is concave-UP (well, ∪) ← legitimate pattern +# 4. Gate on fit quality: only flag when RMS_residual / γ_spread is below +# `quality_threshold`. Noisy fits (e.g. multiple overlapping contour +# fragments) leave the candidate unflagged — letting the gap criterion +# and downstream review handle ambiguous cases. +# +# Returns `true` when the candidate is on a CLEAN concave-down arc; else +# `false`. The orientation-invariance of the previous 3-point stencil +# version is preserved because we fit γ = f(ω) which has a sign-stable +# second derivative regardless of traversal direction. +function _is_geom_spurious(pt::ComplexF64, + re_paths::Vector{Vector{ComplexF64}}; + max_walk::Float64=0.5, + curvature_threshold::Float64=0.05, + quality_threshold::Float64=0.15) + re_idx, re_v_idx, _ = _closest_polyline_vertex(re_paths, pt) + re_idx == 0 && return false + re_path = re_paths[re_idx] + n_path = length(re_path) + n_path < 5 && return false + + # Walk outward from re_v_idx along the polyline, collecting vertices + # within max_walk Q-distance of pt. Stop in each direction at the first + # vertex that exceeds the walk radius. + collected_idx = Int[re_v_idx] + @inbounds for k in (re_v_idx+1):n_path + if abs(re_path[k] - pt) < max_walk + push!(collected_idx, k) + else + break + end + end + @inbounds for k in (re_v_idx-1):-1:1 + if abs(re_path[k] - pt) < max_walk + push!(collected_idx, k) + else + break + end + end + n = length(collected_idx) + n < 5 && return false + + ω₀ = real(pt) + ωs = Vector{Float64}(undef, n) + γs = Vector{Float64}(undef, n) + @inbounds for (i, k) in enumerate(collected_idx) + ωs[i] = real(re_path[k]) - ω₀ + γs[i] = imag(re_path[k]) + end + ω_sp = maximum(ωs) - minimum(ωs) + γ_sp = maximum(γs) - minimum(γs) + (ω_sp < 1e-6 || γ_sp < 1e-12) && return false + + # Quadratic least-squares fit γ = a + b·ω + c·ω² via the normal equations + # MᵀM·coeffs = Mᵀγ, where M = [1 ω ω²]. Hand-rolled to avoid an allocation + # for the n×3 design matrix (we just need the 3×3 normal-equation matrix). + sx = 0.0 + sx2 = 0.0 + sx3 = 0.0 + sx4 = 0.0 + sy = 0.0 + sxy = 0.0 + sx2y = 0.0 + @inbounds for i in 1:n + ω = ωs[i] + γ = γs[i] + ω2 = ω * ω + sx += ω + sx2 += ω2 + sx3 += ω2 * ω + sx4 += ω2 * ω2 + sy += γ + sxy += ω * γ + sx2y += ω2 * γ + end + M = [Float64(n) sx sx2; + sx sx2 sx3; + sx2 sx3 sx4] + rhs = [sy, sxy, sx2y] + coeffs = M \ rhs + c = coeffs[3] + + # Fit-quality residual norm + rms_sq = 0.0 + @inbounds for i in 1:n + pred = coeffs[1] + coeffs[2] * ωs[i] + coeffs[3] * ωs[i]^2 + rms_sq += (γs[i] - pred)^2 + end + rms = sqrt(rms_sq / n) + rms_norm = rms / γ_sp + + # Spurious if concave-down AND fit is clean enough to trust + return c < -curvature_threshold && rms_norm < quality_threshold +end + +# γ-gap separation: the candidate at `idx` (in γ-descending order) is unstable +# AND clearly separated above the next-most-unstable candidate by more than +# `gap_kHz_threshold` kHz. Flags an outlier "lone peak" root. +function _is_gap_spurious(sorted_roots::Vector{ComplexF64}, idx::Int, + tauk::Float64, gap_kHz_threshold::Float64) + γ_idx = imag(sorted_roots[idx]) / tauk * 1e-3 # kHz + γ_idx > 0.0 || return false # only suspicious if unstable + idx >= length(sorted_roots) && return false # nothing below to compare + γ_next = imag(sorted_roots[idx+1]) / tauk * 1e-3 + return (γ_idx - γ_next) > gap_kHz_threshold +end + +# --------------------------------------------------------------------- +# Root polishing (isolate-then-polish). +# +# The contour scan only *locates* roots to the grid/cell resolution: the +# marching-squares intersection is a linear estimate of where Re(f)=0 and +# Im(f)=0 cross, so the residual there is small only relative to the scan's +# huge dynamic range, not zero. Its exact position is sensitive to ULP-level +# jitter in the sampled `f` values (BLAS/thread reduction order), which can +# shift the reported γ between near-degenerate estimates of the SAME root. +# +# `_polish_root` refines one contour intersection to the actual zero of `f` +# by bounded minimization of `|f(Q)|`, so the reported root becomes +# resolution- and thread-independent. It is a no-op-or-better layer: any +# failure (non-finite, no decrease, pole approach) falls back to the +# unpolished contour point. +# --------------------------------------------------------------------- + +# Median contour-segment length — a robust proxy for the local grid/cell +# resolution, used to cap how far a polish may move a root. +function _median_segment_length(re_paths::Vector{Vector{ComplexF64}}, + im_paths::Vector{Vector{ComplexF64}}) + lens = Float64[] + for paths in (re_paths, im_paths), p in paths + @inbounds for i in 1:length(p)-1 + push!(lens, abs(p[i+1] - p[i])) + end + end + isempty(lens) && return 0.0 + sort!(lens) + return lens[cld(length(lens), 2)] +end + +# Trust-region radius for polishing the intersection at `pts[idx]`. Capped by +# `nn_frac` × distance to the NEAREST other intersection (root OR pole), so a +# polished root can never migrate into a neighbour's basin — `nn_frac < 0.5` +# guarantees, by the triangle inequality, that the result stays strictly +# closer to its own contour point than to any other. Also capped at a few grid +# cells (`k_cell·h`) so refinement only corrects the discretization error. +function _polish_trust_radius(pts::Vector{ComplexF64}, idx::Int, h_grid::Real; + k_cell::Float64=3.0, nn_frac::Float64=0.45) + p0 = pts[idx] + d_nn = Inf + @inbounds for j in eachindex(pts) + j == idx && continue + d = abs(pts[j] - p0) + d < d_nn && (d_nn = d) + end + r_cell = k_cell * Float64(h_grid) + r = isfinite(d_nn) ? min(r_cell, nn_frac * d_nn) : r_cell + return r > 0 ? r : r_cell +end + +# Bounded Gauss-Newton minimization of |f(Q)| within a disk of radius `R` +# around `Q0`. Returns (Q_best, n_evals, improved). `improved == false` ⇒ +# Q0 is returned unchanged (hard fallback). Secant derivative + trust-region +# projection + |f|-decrease backtracking keep it strictly "improve-or-no-op": +# it cannot diverge, jump to another root, or be pulled into a pole. +function _polish_root(f, Q0::ComplexF64, R::Float64; maxit::Int=8, + tol_step::Float64=1e-12, tol_f::Float64=1e-8) + (R > 0) || return (Q0, 0, false) + f0 = ComplexF64(f(Q0)) + nev = 1 + isfinite(f0) || return (Q0, nev, false) + a0 = abs(f0) + a0 == 0 && return (Q0, nev, false) + + # Second point for the secant slope: a small real offset scaled to R. + Qk, fk = Q0, f0 + Qp = Q0 + complex(max(R * 1e-3, eps(Float64)), 0.0) + fp = ComplexF64(f(Qp)) + nev += 1 + Qbest, abest = Q0, a0 + + for _ in 1:maxit + df = (Qp == Qk) ? ComplexF64(0) : (fp - fk) / (Qp - Qk) + (isfinite(df) && abs(df) > 0) || break + step = -fk / df # zero of local linear model + Qt = Qk + step + if abs(Qt - Q0) > R # project into trust region + Qt = Q0 + R * (Qt - Q0) / abs(Qt - Q0) + end + ft = ComplexF64(f(Qt)) + nev += 1 + bt = 0 + while (!isfinite(ft) || abs(ft) >= abest) && bt < 3 # backtrack on no-decrease + Qt = Qk + 0.5 * (Qt - Qk) + (abs(Qt - Q0) <= R) || break + ft = ComplexF64(f(Qt)) + nev += 1 + bt += 1 + end + if isfinite(ft) && abs(ft) < abest + Qp, fp = Qk, fk + Qk, fk = Qt, ft + Qbest, abest = Qt, abs(ft) + (abs(step) < tol_step * (abs(Qk) + tol_step) || abest < tol_f * a0) && break + else + break # no further decrease → stop + end + end + return (abest < a0 ? Qbest : Q0, nev, abest < a0) +end + +# Median |Δ| over the finite scan values — the "typical residual magnitude" +# reference for the validity gate. A genuine root drives the polished |residual| +# orders of magnitude below this; a near-miss stays near it. +function _residual_scale(Δ) + a = Float64[] + for z in Δ + az = abs(z) + (isfinite(az) && az < 1e30) && push!(a, az) + end + isempty(a) && return 0.0 + sort!(a) + n = length(a) + return isodd(n) ? a[(n+1)÷2] : 0.5 * (a[n÷2] + a[n÷2+1]) +end + +function _run_analysis(re_paths::Vector{Vector{ComplexF64}}, + im_paths::Vector{Vector{ComplexF64}}, + im_re_vals::Vector{Vector{Float64}}, + tauk::Float64; + pole_threshold::Float64, + filter_above_poles::Bool, + filter_outside_re::Bool, + gap_kHz_threshold::Float64=1.0, + residual=nothing, + polish_maxit::Int=20, + validity_scale::Float64=0.0, + validity_rtol::Float64=1e-3) + raw_intersections = _all_intersections(re_paths, im_paths) + + poles = ComplexF64[] + candidates = Tuple{ComplexF64,Bool}[] # (pt, on_top_half_re_flag) + spurious_roots = ComplexF64[] # polished, but |residual| ≫ 0 + + # Isolate-then-polish: when a residual callable is supplied, refine each + # (non-pole) contour intersection to the true zero of `f`. Trust radii are + # capped by the spacing to neighbouring intersections so closely-spaced + # coupled roots stay coherently bound to their own contour crossing. + do_polish = residual !== nothing + h_grid = do_polish ? _median_segment_length(re_paths, im_paths) : 0.0 + # Validity gate: a genuine root drives |residual| ≈ 0; a spurious contour + # near-miss (e.g. a surface whose Δ' BVP failed → |Δ'| huge and + # uncancellable by the inner layer) leaves |residual| stuck near the typical + # scan magnitude. Only active when polishing AND a scale is supplied. + do_gate = do_polish && validity_scale > 0 + polish_evals = 0 + + for (i_pt, pt) in enumerate(raw_intersections) + # --- 1. classify as pole or root via local Re-magnitude on Im contour + best_im_path_idx, best_im_vert_idx, _ = + _closest_polyline_vertex(im_paths, pt) + is_pole = false + if best_im_path_idx > 0 + re_vals = im_re_vals[best_im_path_idx] + n = length(re_vals) + i_prev = max(1, best_im_vert_idx - 1) + i_next = min(n, best_im_vert_idx + 1) + local_max = max(abs(re_vals[i_prev]), + abs(re_vals[i_next]), + abs(re_vals[best_im_vert_idx])) + is_pole = local_max > pole_threshold + end + + if is_pole + push!(poles, pt) + continue + end + + # --- 1b. polish this (non-pole) intersection to the true zero of `f`, + # bounded to a neighbour-aware trust region (no-op on failure). + if do_polish + R = _polish_trust_radius(raw_intersections, i_pt, h_grid) + pt, nev, _ = _polish_root(residual, pt, R; maxit=polish_maxit) + polish_evals += nev + # --- 1c. validity gate: drop intersections that don't polish to a + # true zero (|residual| stays ≫ 0 relative to the scan scale). These + # are contour near-misses / failed-BVP surfaces, not real roots. + if do_gate + rmag = abs(ComplexF64(residual(pt))) + polish_evals += 1 + if !(rmag < validity_rtol * validity_scale) # NaN ⇒ spurious + push!(spurious_roots, pt) + continue + end + end + end + + # --- 2. "+γ step inside Re contour" flag for spurious-upper-branch filter + on_top_half_re = false + best_re_path_idx, _, _ = _closest_polyline_vertex(re_paths, pt) + if best_im_path_idx > 0 && best_re_path_idx > 0 + re_path = re_paths[best_re_path_idx] + xs = real.(re_path) + ys = imag.(re_path) + contour_extent = max(maximum(xs) - minimum(xs), + maximum(ys) - minimum(ys)) + closure_gap = abs(re_path[1] - re_path[end]) + + if contour_extent > 0 && closure_gap < 0.1 * contour_extent + # Re=0 contour is approximately closed → containment test applies + im_path = im_paths[best_im_path_idx] + n_im = length(im_path) + im_nearest = best_im_vert_idx + i_a = min(im_nearest + 1, n_im) + i_b = max(im_nearest - 1, 1) + gamma_a = imag(im_path[i_a]) + gamma_b = imag(im_path[i_b]) + gamma_here = imag(im_path[im_nearest]) + + tangent = if gamma_a >= gamma_b && gamma_a > gamma_here + im_path[i_a] - im_path[im_nearest] + elseif gamma_b > gamma_here + im_path[i_b] - im_path[im_nearest] + else + ComplexF64(0.0, 1.0) # fall back to straight up + end + + tlen = abs(tangent) + if tlen > 0 + step_size = 0.01 * contour_extent + step_pt = pt + (step_size / tlen) * tangent + inside = _point_in_polygon(step_pt, re_path) + on_top_half_re = !inside + end + end + end + + push!(candidates, (pt, on_top_half_re)) + end + + # --- 3. pole + closed-loop filter (legacy), then geom + gap recursion (new) + valid_roots = ComplexF64[c[1] for c in candidates] + filtered_roots = copy(spurious_roots) # gate-rejected near-misses kept here + Q_root = ComplexF64(NaN, NaN) + Q_root_2nd = ComplexF64(NaN, NaN) + warning_flags = Symbol[] + isempty(spurious_roots) || push!(warning_flags, :spurious) + + if !isempty(valid_roots) + order = sortperm(valid_roots; by=q -> -imag(q)) + sorted_pts = valid_roots[order] + sorted_top = Bool[c[2] for c in candidates][order] + + max_pole_gamma = isempty(poles) ? -Inf : maximum(imag, poles) + + chosen_idx = 0 + for k in 1:length(sorted_pts) + cand = sorted_pts[k] + top_re = sorted_top[k] + # Legacy filter: above-pole + closed-loop outside-Re + legacy_reject = filter_above_poles && imag(cand) > max_pole_gamma && + (!filter_outside_re || top_re) + if legacy_reject + push!(filtered_roots, cand) + continue + end + # New checks: 2 spurious-root flags — :geom and :gap. + # :geom — Re=0 contour is locally a downward-concave "hill" + # at the candidate (clean polyline-following fit) + # :gap — candidate is unstable AND >1 kHz above next root + # (isolated γ peak — spurious outlier signature) + # + # Policy: WARN, DO NOT DISCARD. The both-flags-fire criterion + # is too aggressive in the kink-approach regime where valid + # roots become sparse — a few-kHz γ separation between the + # dominant unstable root and the next-stable root can be + # genuine dispersion structure rather than a "lone peak" + # artifact, yet :gap fires regardless. So every candidate is + # accepted with whatever warnings apply, and downstream tools + # see the same valid_roots regardless of flag combination. + # filtered_roots is preserved for the legacy above-pole + + # outside-Re reject branch only. + geom_flag = _is_geom_spurious(cand, re_paths) + gap_flag = _is_gap_spurious(sorted_pts, k, tauk, + gap_kHz_threshold) + chosen_idx = k + geom_flag && push!(warning_flags, :geom) + gap_flag && push!(warning_flags, :gap) + break + end + + if chosen_idx > 0 + Q_root = sorted_pts[chosen_idx] + # When a warning fired, expose the next-down root as secondary so + # downstream tools can plot/reanalyse. (Indices > chosen_idx in + # sorted_pts are the next-most-unstable.) + if !isempty(warning_flags) && chosen_idx < length(sorted_pts) + Q_root_2nd = sorted_pts[chosen_idx+1] + end + end + end + + # No usable root: either the scan produced no zero-crossing intersections + # (`valid_roots` empty) or every candidate was rejected by the legacy + # above-pole filter (`chosen_idx == 0`). Flag this explicitly so callers + # can distinguish a genuine marginally-stable result (γ ≈ 0) from a failed + # extraction — both otherwise surface as `gamma_Hz == 0.0` below. + isnan(real(Q_root)) && push!(warning_flags, :no_root) + + omega_Hz = isnan(real(Q_root)) ? 0.0 : real(Q_root) / tauk + gamma_Hz = isnan(imag(Q_root)) ? 0.0 : imag(Q_root) / tauk + omega_Hz_2nd = isnan(real(Q_root_2nd)) ? 0.0 : real(Q_root_2nd) / tauk + gamma_Hz_2nd = isnan(imag(Q_root_2nd)) ? 0.0 : imag(Q_root_2nd) / tauk + + return GrowthRateResult(Q_root, omega_Hz, gamma_Hz, + Q_root_2nd, omega_Hz_2nd, gamma_Hz_2nd, + warning_flags, + valid_roots, poles, filtered_roots, + re_paths, im_paths, pole_threshold) +end + +# Regular-grid path: extract contours via Contour.jl, compute im_re_vals by +# bilinear interpolation on the grid, then run the shared analysis. +function _extract_growth_rates(re_axis::Vector{Float64}, + im_axis::Vector{Float64}, + Δ_grid::Matrix{ComplexF64}, + tauk::Float64; + re_target::Float64, + im_target::Float64, + pole_threshold::Float64, + filter_above_poles::Bool, + filter_outside_re::Bool, + gap_kHz_threshold::Float64=1.0, + residual=nothing, + polish_maxit::Int=20, + validity_scale::Float64=0.0, + validity_rtol::Float64=1e-3) + re_field = real.(Δ_grid) + im_field = imag.(Δ_grid) + + re_paths = _extract_contours(re_axis, im_axis, re_field, re_target) + im_paths = _extract_contours(re_axis, im_axis, im_field, im_target) + + im_re_vals = [Float64[_bilinear(re_axis, im_axis, re_field, + real(v), imag(v)) + for v in path] + for path in im_paths] + + return _run_analysis(re_paths, im_paths, im_re_vals, tauk; + pole_threshold=pole_threshold, + filter_above_poles=filter_above_poles, + filter_outside_re=filter_outside_re, + gap_kHz_threshold=gap_kHz_threshold, + residual=residual, + polish_maxit=polish_maxit, + validity_scale=validity_scale, + validity_rtol=validity_rtol) +end + +# --------------------------------------------------------------------- +# AMR path: Delaunay triangulation + marching triangles. Hanging nodes +# from the quadtree's mixed refinement levels become first-class vertices +# in the triangulation, so contour segments piece together without gaps. +# --------------------------------------------------------------------- + +# Emit a Re=0 and Im=0 segment (if any) from a single triangle. Returns +# `(re_seg, im_seg)` where each may be `nothing`. A segment is a +# `@NamedTuple{p1::ComplexF64, p2::ComplexF64, a1::Float64, a2::Float64}` +# where `a1`, `a2` carry the *complementary* field value at the endpoints +# (Re-value for Im=0 segments, Im-value for Re=0 segments). +function _march_triangle(p1::ComplexF64, p2::ComplexF64, p3::ComplexF64, + v1::ComplexF64, v2::ComplexF64, v3::ComplexF64, + re_target::Float64, im_target::Float64) + return (_march_single(p1, p2, p3, real(v1), real(v2), real(v3), + imag(v1), imag(v2), imag(v3), re_target), + _march_single(p1, p2, p3, imag(v1), imag(v2), imag(v3), + real(v1), real(v2), real(v3), im_target)) +end + +# Core marching step for one scalar field `f` with complementary field `g`. +# Produces the contour segment at level=L (if any) along with the value of +# `g` linearly interpolated at each endpoint. +@inline function _march_single(p1::ComplexF64, p2::ComplexF64, p3::ComplexF64, + f1::Float64, f2::Float64, f3::Float64, + g1::Float64, g2::Float64, g3::Float64, + L::Float64) + a1 = f1 >= L + a2 = f2 >= L + a3 = f3 >= L + count = Int(a1) + Int(a2) + Int(a3) + (count == 0 || count == 3) && return nothing + + # Identify the "odd" vertex and produce crossings on the two edges + # incident to it. + if a1 != a2 && a1 != a3 + pt_a, ga = _cross_edge(p1, p2, f1, f2, g1, g2, L) + pt_b, gb = _cross_edge(p1, p3, f1, f3, g1, g3, L) + elseif a2 != a1 && a2 != a3 + pt_a, ga = _cross_edge(p2, p1, f2, f1, g2, g1, L) + pt_b, gb = _cross_edge(p2, p3, f2, f3, g2, g3, L) + else + pt_a, ga = _cross_edge(p3, p1, f3, f1, g3, g1, L) + pt_b, gb = _cross_edge(p3, p2, f3, f2, g3, g2, L) + end + return (p1=pt_a, p2=pt_b, a1=ga, a2=gb) +end + +# Linear crossing on edge (pa, pb) for field `f` at level `L`, with +# complementary value `g` interpolated at the same parameter. +@inline function _cross_edge(pa::ComplexF64, pb::ComplexF64, + fa::Float64, fb::Float64, + ga::Float64, gb::Float64, L::Float64) + denom = fb - fa + t = denom == 0 ? 0.0 : (L - fa) / denom + t = clamp(t, 0.0, 1.0) + return (pa + t * (pb - pa), ga + t * (gb - ga)) +end + +# Chain segments into polylines by endpoint matching. Each segment endpoint +# is a `ComplexF64` that is shared bit-exactly with any adjacent triangle's +# crossing (both sides of a triangulation edge compute the same linear +# crossing from identical endpoint values). Returns +# `(paths::Vector{Vector{ComplexF64}}, aux::Vector{Vector{Float64}})`. +function _chain_segments(segs::Vector{<:NamedTuple}) + # Build an endpoint → list-of-segment-indices adjacency map. + adj = Dict{ComplexF64,Vector{Int}}() + for (i, s) in enumerate(segs) + push!(get!(adj, s.p1, Int[]), i) + push!(get!(adj, s.p2, Int[]), i) + end + + used = falses(length(segs)) + paths = Vector{Vector{ComplexF64}}() + aux_vals = Vector{Vector{Float64}}() + + # Walk a polyline starting from segment `start_seg` via endpoint + # `start_pt`; returns the path and aux values. + function _walk(start_seg::Int, start_pt::ComplexF64) + path = ComplexF64[start_pt] + aux = Float64[] + # Emit the aux value for start_pt on the first segment + s0 = segs[start_seg] + push!(aux, start_pt == s0.p1 ? s0.a1 : s0.a2) + + cur_seg = start_seg + cur_pt = start_pt + while true + used[cur_seg] = true + s = segs[cur_seg] + next_pt = cur_pt == s.p1 ? s.p2 : s.p1 + next_aux = cur_pt == s.p1 ? s.a2 : s.a1 + push!(path, next_pt) + push!(aux, next_aux) + + nbrs = adj[next_pt] + nxt = 0 + for j in nbrs + if !used[j] && j != cur_seg + nxt = j + break + end + end + nxt == 0 && break + cur_seg = nxt + cur_pt = next_pt + end + return path, aux + end + + # Open polylines first: start from any endpoint touched by exactly + # one still-unused segment. + for (pt, nbrs) in adj + count = 0 + start_seg = 0 + for j in nbrs + if !used[j] + count += 1 + start_seg = j + end + end + if count == 1 + path, aux = _walk(start_seg, pt) + length(path) >= 2 && (push!(paths, path); push!(aux_vals, aux)) + end + end + + # Remaining segments form closed loops. + for i in eachindex(segs) + used[i] && continue + path, aux = _walk(i, segs[i].p1) + length(path) >= 2 && (push!(paths, path); push!(aux_vals, aux)) + end + + return paths, aux_vals +end + +# AMR entry point: triangulate the scattered (Q, Δ) points, march triangles +# to extract Re=0 and Im=0 contour segments with complementary-field values +# at endpoints, chain into polylines, then run the shared analysis. +function _extract_growth_rates_amr(Q::Vector{ComplexF64}, + Δ::Vector{ComplexF64}, + tauk::Float64; + re_target::Float64, + im_target::Float64, + pole_threshold::Float64, + filter_above_poles::Bool, + filter_outside_re::Bool, + gap_kHz_threshold::Float64=1.0, + residual=nothing, + polish_maxit::Int=20, + validity_scale::Float64=0.0, + validity_rtol::Float64=1e-3) + length(Q) == length(Δ) || + throw(ArgumentError("_extract_growth_rates_amr: length(Q) ≠ length(Δ)")) + length(Q) >= 3 || + throw(ArgumentError("_extract_growth_rates_amr: need ≥ 3 points to triangulate")) + + pts = [(real(q), imag(q)) for q in Q] + tri = triangulate(pts) + + # Segment types (carry complementary-field value at each endpoint) + re_segs = NamedTuple{(:p1, :p2, :a1, :a2), + Tuple{ComplexF64,ComplexF64,Float64,Float64}}[] + im_segs = NamedTuple{(:p1, :p2, :a1, :a2), + Tuple{ComplexF64,ComplexF64,Float64,Float64}}[] + + for T in each_solid_triangle(tri) + i1, i2, i3 = T + p1 = Q[i1] + p2 = Q[i2] + p3 = Q[i3] + v1 = Δ[i1] + v2 = Δ[i2] + v3 = Δ[i3] + re_seg, im_seg = _march_triangle(p1, p2, p3, v1, v2, v3, + re_target, im_target) + re_seg !== nothing && push!(re_segs, re_seg) + im_seg !== nothing && push!(im_segs, im_seg) + end + + re_paths, _ = _chain_segments(re_segs) + im_paths, im_re_vals = _chain_segments(im_segs) + + return _run_analysis(re_paths, im_paths, im_re_vals, tauk; + pole_threshold=pole_threshold, + filter_above_poles=filter_above_poles, + filter_outside_re=filter_outside_re, + gap_kHz_threshold=gap_kHz_threshold, + residual=residual, + polish_maxit=polish_maxit, + validity_scale=validity_scale, + validity_rtol=validity_rtol) +end diff --git a/src/Tearing/Dispersion/SurfaceCoupling.jl b/src/Tearing/Dispersion/SurfaceCoupling.jl new file mode 100644 index 000000000..271162c1a --- /dev/null +++ b/src/Tearing/Dispersion/SurfaceCoupling.jl @@ -0,0 +1,103 @@ +# SurfaceCoupling.jl +# +# `SurfaceCoupling` packages everything the dispersion solver needs at one +# rational surface: the inner-layer model, its parameters, the outer Δ' +# diagonal element, the critical-Δ offset, the inner→outer-units scale +# factor, and the per-surface time normalization `tauk`. The struct is +# `Q`-callable and returns the complex residual +# +# r(Q) = Δ'_diag - scale · Δ_inner(Q) - Δ_crit +# +# `tauk` is unused for single-surface evaluation but is required by the +# multi-surface `MultiSurfaceCoupling` to rescale Q between each surface's +# normalization. +# +# Constructor convenience: `surface_coupling(model, params, dp_diag; dc=0.0)` +# auto-fills `scale` and `tauk` based on the model type — `scale = S^(1/3)` +# and `tauk = params.tauk` for SLAYER (de-normalizes the inner-layer Δ to +# outer units), `scale = 1` and `tauk = 1` for GGJ (Δ already in outer units +# after `rescale_delta`; no inter-surface Q rescaling). + +""" + SurfaceCoupling{M<:InnerLayerModel, P} + +Per-surface dispersion data: `(model, params, dp_diag, dc, scale, tauk)`. +Calling `sc(Q)` returns the complex residual + +``` +r(Q) = dp_diag - scale * solve_inner(model, params, Q).tearing - dc +``` + +A root of `sc` in the complex `Q` plane is a **tearing** eigenvalue at +this surface in the *uncoupled* approximation (only the tearing channel +of the inner-layer response appears — the interchange channel enters the +full 2m×2m dispersion via `MultiSurfaceCoupling`, not this scalar form). +Coupled multi-surface eigenvalues come from `MultiSurfaceCoupling` +evaluating the determinant of the modified Δ' matrix. +""" +struct SurfaceCoupling{M<:InnerLayerModel,P} + model::M + params::P + dp_diag::ComplexF64 + dc::Float64 + scale::Float64 + tauk::Float64 +end + +function (sc::SurfaceCoupling)(Q::Number) + Δ = solve_inner(sc.model, sc.params, ComplexF64(Q)).tearing + return sc.dp_diag - sc.scale * Δ - sc.dc +end + +""" + surface_coupling(model::SLAYERModel, params::SLAYERParameters, + dp_diag::Number; dc::Real=0.0) -> SurfaceCoupling + +SLAYER convenience constructor. `scale` is set to `params.lu^(1/3)` so that +the dimensionless Δ from `riccati_f` is mapped to outer ψ-units before +subtraction from the Δ' diagonal. `tauk` is taken from `params.tauk` for use +by `MultiSurfaceCoupling` Q rescaling. +""" +function surface_coupling(model::SLAYERModel, params::SLAYERParameters, + dp_diag::Number; dc::Real=0.0) + return SurfaceCoupling(model, params, ComplexF64(dp_diag), + Float64(dc), params.lu^(1 / 3), params.tauk) +end + +""" + surface_coupling(model::GGJModel, params::GGJParameters, + dp_diag::Number) -> SurfaceCoupling + +GGJ convenience constructor. `scale` is `1.0` because GGJ's `solve_inner` +applies its own `rescale_delta` (S^(2p₁/3)·v1^(2p₁)) internally, so the +returned Δ is already in outer units. `tauk` defaults to `1.0` (GGJ has no +direct analogue of SLAYER's per-surface time normalization, so multi-surface +Q rescaling is a no-op for GGJ surfaces unless overridden). + +**No `dc` kwarg**: GGJ's 4m×4m Pletzer-Dewar residual already includes the +interchange channel, which provides Glasser (Mercier) stabilization +natively. A Δ_crit proxy (χ_parallel-matching offset on the diagonal) is +meaningful only for tearing-only slab-layer approximations like SLAYER; +for GGJ it would double-count the interchange physics. The `SurfaceCoupling` +struct's `dc` field is hard-wired to 0 here. +""" +function surface_coupling(model::GGJModel, params::GGJParameters, + dp_diag::Number) + return SurfaceCoupling(model, params, ComplexF64(dp_diag), + 0.0, 1.0, 1.0) +end + +""" + surface_coupling(model::InnerLayerModel, params, dp_diag::Number; + dc::Real=0.0, scale::Real=1.0, tauk::Real=1.0) + -> SurfaceCoupling + +Generic fallback constructor. Use this when wiring a new inner-layer model +into the dispersion solver — pass the appropriate inner→outer-units `scale` +and per-surface `tauk` explicitly. +""" +function surface_coupling(model::InnerLayerModel, params, dp_diag::Number; + dc::Real=0.0, scale::Real=1.0, tauk::Real=1.0) + return SurfaceCoupling(model, params, ComplexF64(dp_diag), + Float64(dc), Float64(scale), Float64(tauk)) +end diff --git a/src/InnerLayer/GGJ/GGJ.jl b/src/Tearing/InnerLayer/GGJ/GGJ.jl similarity index 86% rename from src/InnerLayer/GGJ/GGJ.jl rename to src/Tearing/InnerLayer/GGJ/GGJ.jl index 1b8aacb23..773c5b64b 100644 --- a/src/InnerLayer/GGJ/GGJ.jl +++ b/src/Tearing/InnerLayer/GGJ/GGJ.jl @@ -17,13 +17,13 @@ module GGJ using LinearAlgebra using StaticArrays -import ..InnerLayerModel, ..solve_inner +import ..InnerLayerModel, ..InnerLayerResponse, ..solve_inner, ..InnerLayerParameters """ 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. @@ -37,11 +37,14 @@ include("InnerAsymptotics.jl") include("Reference.jl") include("Shooting.jl") include("Galerkin.jl") +include("LayerInputs.jl") export GGJModel, GGJParameters export mercier_di, mercier_dr, inner_Q, rescale_delta export build_asymptotics, evaluate_asymptotics, pick_xmax export InnerAsymptoticsCache export glasser_wang_2020_eq55 +export build_ggj_inputs +export NeoResistivityModel, SpitzerModel, SauterNeoModel, RedlNeoModel end # module GGJ diff --git a/src/InnerLayer/GGJ/GGJParameters.jl b/src/Tearing/InnerLayer/GGJ/GGJParameters.jl similarity index 77% rename from src/InnerLayer/GGJ/GGJParameters.jl rename to src/Tearing/InnerLayer/GGJ/GGJParameters.jl index c6986ea2a..8a27393c8 100644 --- a/src/InnerLayer/GGJ/GGJParameters.jl +++ b/src/Tearing/InnerLayer/GGJ/GGJParameters.jl @@ -2,8 +2,7 @@ # # Physical parameters for the Glasser–Greene–Johnson inner-layer model and # the derived scale factors that map between physical and inner-layer -# (Wasow-normalized) variables. Mirrors the Fortran `resist_type` defined -# in rmatch/deltar_mod and rmatch/deltac_mod. +# (Wasow-normalized) variables. """ GGJParameters @@ -12,16 +11,16 @@ 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. -Fields are the same as the Fortran `resist_type`: +Fields: -| 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 | @@ -30,7 +29,7 @@ Fields are the same as the Fortran `resist_type`: The complex growth rate `γ` is **not** stored here; it is passed as a separate argument to `solve_inner`. """ -Base.@kwdef struct GGJParameters +Base.@kwdef struct GGJParameters <: InnerLayerParameters E::Float64 F::Float64 G::Float64 @@ -46,15 +45,14 @@ 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`. """ 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`. """ mercier_dr(p::GGJParameters) = p.E + p.F + p.H * p.H @@ -81,14 +79,14 @@ 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 length scale `X₀ = S^(−1/3)`. """ 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 `Q₀ = X₀ / τ_A`. """ q0(p::GGJParameters) = x0(p) / p.taua @@ -96,7 +94,7 @@ 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 +basis. The argument `γ` may be real or complex; the result is always complex. """ inner_Q(p::GGJParameters, γ::Number) = ComplexF64(γ) / q0(p) @@ -105,8 +103,8 @@ 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)`. +matching data back to physical Δ at the rational surface. 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/Tearing/InnerLayer/GGJ/Galerkin.jl similarity index 71% rename from src/InnerLayer/GGJ/Galerkin.jl rename to src/Tearing/InnerLayer/GGJ/Galerkin.jl index 93f889018..f14173175 100644 --- a/src/InnerLayer/GGJ/Galerkin.jl +++ b/src/Tearing/InnerLayer/GGJ/Galerkin.jl @@ -1,11 +1,11 @@ # Galerkin.jl # # Hermite-cubic finite element (Galerkin) solver for the GGJ inner-layer -# model. Direct port of rmatch/deltac.f in the "resonant + noexp + inps" -# configuration. The half-domain problem (x ∈ [0, xmax]) is solved with -# parity boundary conditions at x = 0 and asymptotic matching at x = xmax. +# model, in the "resonant + noexp + inps" configuration. The half-domain +# problem (x ∈ [0, xmax]) is solved with parity boundary conditions at +# x = 0 and asymptotic matching at x = xmax. # -# Configuration assumed (matches deltac.f defaults when called with inps): +# Configuration assumed: # 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) @@ -18,23 +18,23 @@ using FastGaussQuadrature: gausslobatto using QuadGK: quadgk # ----------------------------------------------------------------------- -# Physical-variable helpers (replacements for inpso_get_ua/dua/uv). +# Physical-variable helpers. # ----------------------------------------------------------------------- """ 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. +(W, N, Θ) and (W', N', Θ') representation. Returns `(ua, dua)` each 3×2 complex, where columns are the two algebraic solutions and rows are (W, N, Θ). """ 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 @@ -44,70 +44,74 @@ 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. +`I·u'' − V·u' − U·u = 0` at coordinate `x`. All matrices are 3×3 complex. """ 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 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): + # Build U and V: pre-scaled from column-major reshape, then row 2 *=q², row 3 *=q. + # Pre-scaled U (column-major 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 = @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): + # Pre-scaled V (column-major reshape → Julia row-major): # V[1,:] = (0, 0, h) # V[2,:] = (-h/q², 0, 0) # V[3,:] = (h*k*q, 0, 0) 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 end # ----------------------------------------------------------------------- -# Hermite cubic basis functions — port of deltac_hermite. +# Hermite cubic basis functions. # Returns (pb[1:4], qb[1:4]) where pb = values, qb = derivatives, -# indexed 1:4 → Fortran 0:3. +# indexed 1:4 → physical 0:3. # ----------------------------------------------------------------------- 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. # ----------------------------------------------------------------------- function _pack(nx::Int, pfac::Float64, side::String) @@ -149,13 +153,13 @@ function _pack(nx::Int, pfac::Float64, side::String) end # ----------------------------------------------------------------------- -# Three-level xmax sweep — replaces inpso_xmax for inps mode. +# Three-level xmax sweep for inps mode. # 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 +183,8 @@ 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") @@ -227,13 +232,21 @@ struct GalerkinWorkspace ndim::Int nx::Int kl::Int - mat::Array{ComplexF64,3} # (ldab, ndim, 2) banded storage - rhs::Matrix{ComplexF64} # (ndim, 2) - sol::Matrix{ComplexF64} # (ndim, 2) + mat::Array{ComplexF64,3} # (ldab, ndim, 2) banded storage + rhs::Matrix{ComplexF64} # (ndim, 2) + sol::Matrix{ComplexF64} # (ndim, 2) + # Reusable scratch buffers, zeroed per-cell via `fill!`. Eliminates the + # per-cell `zeros(...)` that otherwise allocates thousands of MiB over a + # full dispersion scan. + cell_mat_buf::Array{ComplexF64,4} # (mpert=3, mpert, np+1=4, np+1=4) + cell_mat_ext_buf::Array{ComplexF64,4} # (3, 3, 4, 4) max over CT_EXT/EXT1/EXT2 + cell_rhs_ext_buf::Matrix{ComplexF64} # (3, 4) + ab_buf::Matrix{ComplexF64} # (ldab, ndim) scratch for banded LU + rhs_buf::Vector{ComplexF64} # (ndim,) scratch for banded solve 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 +268,10 @@ 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 +285,8 @@ 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 @@ -282,7 +298,7 @@ function _build_grid_and_workspace(nx::Int, xmax::Float64, dx1::Float64, dx2::Fl x_lsode = (et == CT_RES) ? xr : 0.0 - # Build map (matching deltac_make_map_hermite logic) + # Build local-to-global Hermite DOF map. if et == CT_RES # Will be set after the loop map_local = zeros(Int, mpert, 1) # map(:, 0:0) @@ -307,7 +323,7 @@ function _build_grid_and_workspace(nx::Int, xmax::Float64, dx1::Float64, dx2::Fl if et == CT_EXT # Extra asymptotic DOFs: emap = (imap, imap+1, imap+2). # With noexp, ndim = imap so only emap[1] is active; emap[2,3] > ndim - # and are skipped during assembly. This matches Fortran convention. + # and are skipped during assembly. emap_local = [imap, imap + 1, imap + 2] map_extra = [imap; imap + 1; imap + 2] # 3-element column map_local = hcat(map_local, map_extra) @@ -321,30 +337,39 @@ 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) # Bandwidth - kl = mpert * (np + 1) + 1 - 1 # resonant method with noexp; +1-1 kept for agreement with Fortran indexing + kl = mpert * (np + 1) + 1 - 1 # resonant method with noexp; +1-1 kept for indexing agreement ku = kl ldab = 2kl + ku + 1 mat = zeros(ComplexF64, ldab, ndim, 2) rhs = zeros(ComplexF64, ndim, 2) sol = zeros(ComplexF64, ndim, 2) - - return GalerkinWorkspace(cells, ndim, nx, kl, mat, rhs, sol) + # Preallocate per-cell scratch buffers sized to the max case (np+1=4). + # Smaller cells (e.g. CT_EXT with cell.np=1) use a (2×2) sub-slice and + # rely on fill!(buf, 0) to keep the remainder zero. + cell_mat_buf = zeros(ComplexF64, mpert, mpert, np + 1, np + 1) + cell_mat_ext_buf = zeros(ComplexF64, mpert, mpert, np + 1, np + 1) + cell_rhs_ext_buf = zeros(ComplexF64, mpert, np + 1) + ab_buf = zeros(ComplexF64, ldab, ndim) + rhs_buf = zeros(ComplexF64, ndim) + + return GalerkinWorkspace(cells, ndim, nx, kl, mat, rhs, sol, + cell_mat_buf, cell_mat_ext_buf, cell_rhs_ext_buf, + ab_buf, rhs_buf) end # ----------------------------------------------------------------------- # Local assembly: Gauss quadrature for "none" cells. -# Port of deltac_gauss_quad. # ----------------------------------------------------------------------- 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 +385,27 @@ 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. +# Extension assembly. # Handles ext, ext1, ext2 cell types. # ----------------------------------------------------------------------- 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 +488,15 @@ function _extension!(cell_mat::Array{ComplexF64,4}, cell_rhs::Matrix{ComplexF64} end # ----------------------------------------------------------------------- -# Resonant integral — replaces deltac_lsode_int with QuadGK. +# Resonant integral via QuadGK. # 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 +506,8 @@ 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 +515,9 @@ 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 @@ -503,69 +532,79 @@ 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 fill!(ws.mat, 0) fill!(ws.rhs, 0) - # Per-cell assembly + # Per-cell assembly — reuse the preallocated scratch buffers, zeroing + # only the sub-slice actually used by this cell's np_eff. + cell_mat = ws.cell_mat_buf + cell_mat_ext = ws.cell_mat_ext_buf + cell_rhs_ext = ws.cell_rhs_ext_buf for ix in 1:ws.nx cell = ws.cells[ix] # Gauss quadrature for Hermite contribution (all cell types) if cell.np >= 0 np_eff = cell.np - cell_mat = zeros(ComplexF64, mpert, mpert, np_eff + 1, np_eff + 1) + fill!(cell_mat, 0) _gauss_quad!(cell_mat, cell, quad_nodes, quad_weights, params, Q) # 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 # Extension terms if cell.etype in (CT_EXT, CT_EXT1, CT_EXT2) + # np_eff matches the semantic size: CT_EXT has cell.np=1 → ext slot + # at index cell.np+1=2 (using 0-based; +1 in Julia), so the array + # used by the current code is (3,3,cell.np+2,cell.np+2)=(3,3,3,3). + # For CT_EXT1/EXT2 it's (3,3,cell.np+1,cell.np+1)=(3,3,4,4). + # Either way npp = cell.etype == CT_EXT ? cell.np + 1 : cell.np. np_eff = cell.etype == CT_EXT ? cell.np + 1 : cell.np - cell_mat_ext = zeros(ComplexF64, mpert, mpert, np_eff + 1, np_eff + 1) - cell_rhs_ext = zeros(ComplexF64, mpert, np_eff + 1) - # For ext, we need to create a temporary cell_mat that includes the extra DOF - if cell.etype == CT_EXT - cell_mat_ext = zeros(ComplexF64, mpert, mpert, cell.np + 2, cell.np + 2) - cell_rhs_ext = zeros(ComplexF64, mpert, cell.np + 2) - else - cell_mat_ext = zeros(ComplexF64, mpert, mpert, cell.np + 1, cell.np + 1) - cell_rhs_ext = zeros(ComplexF64, mpert, cell.np + 1) - end + fill!(cell_mat_ext, 0) + fill!(cell_rhs_ext, 0) _extension!(cell_mat_ext, cell_rhs_ext, cell, quad_nodes, quad_weights, params, Q, cache) # Assemble ext contributions - npp = size(cell_mat_ext, 3) - 1 + npp = np_eff for ip in 0:npp, ipert in 1:mpert i = ip < size(cell.map, 2) ? cell.map[ipert, ip+1] : cell.emap[1] # For the extra DOF, only ipert=1 is meaningful (noexp) 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] @@ -611,44 +650,58 @@ 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). - # 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. + # Apply parity BCs for each solution. + # isol=1 → "odd mode" = PHYSICS TEARING channel + # (W'(0)=0 → W even across x=0; N(0)=0, Θ(0)=0 → N,Θ odd). + # Even W ⇒ sheet-current reconnecting mode. This is the Δ_+ + # of Glasser-Wang-Park 2016. + # isol=2 → "even mode" = PHYSICS INTERCHANGE channel + # (W(0)=0 → W odd; N'(0)=0, Θ'(0)=0 → N,Θ even). Non-reconnecting; + # carries Glasser stabilization. This is GWP Δ_−. + # The raw ordering out of this loop is therefore (tearing, interchange). + # Downstream code receives an `InnerLayerResponse` whose fields are named + # by physics channel, not by parity label, eliminating the ambiguity. 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 + 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 + ws.mat[offset+i-jj, jj, isol] = 0 end end - # Odd parity (isol=1): W'(0)=0, N(0)=0, Θ(0)=0 + # isol=1 (tearing, "odd"): 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 + # isol=2 (interchange, "even"): 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 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 @@ -659,14 +712,19 @@ function _assemble_and_solve!(ws::GalerkinWorkspace, end end - # Solve for each parity using LAPACK banded LU (gbtrf! + gbtrs!) - n = ws.ndim; kl = ws.kl; ku = kl + # Solve for each parity using LAPACK banded LU (gbtrf! + gbtrs!). + # Reuse the preallocated `ab_buf` / `rhs_buf` instead of `copy`, which + # avoided two (ldab × ndim) ComplexF64 allocations per call (≈7 MiB at + # ndim=3000). + n = ws.ndim + kl = ws.kl + ku = kl for isol in 1:2 - ab = copy(ws.mat[:, :, isol]) - rhs_col = copy(ws.rhs[:, isol]) - ab, ipiv = LinearAlgebra.LAPACK.gbtrf!(kl, ku, n, ab) - LinearAlgebra.LAPACK.gbtrs!('N', kl, ku, n, ab, ipiv, rhs_col) - ws.sol[:, isol] .= rhs_col + copyto!(ws.ab_buf, @view(ws.mat[:, :, isol])) + copyto!(ws.rhs_buf, @view(ws.rhs[:, isol])) + _, ipiv = LinearAlgebra.LAPACK.gbtrf!(kl, ku, n, ws.ab_buf) + LinearAlgebra.LAPACK.gbtrs!('N', kl, ku, n, ws.ab_buf, ipiv, ws.rhs_buf) + ws.sol[:, isol] .= ws.rhs_buf end end @@ -678,18 +736,22 @@ end 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) - -> SVector{2,ComplexF64} + -> InnerLayerResponse 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, in the "resonant + noexp + inps" configuration. + +Returns an `InnerLayerResponse(tearing, interchange)` with rescaling +applied. `tearing` comes from `isol=1` (W even, N/Θ odd — "odd mode"; +reconnecting channel, GWP Δ_+); `interchange` comes from `isol=2` +(W odd, N/Θ even — "even mode"; Glasser stabilization channel, GWP Δ_−). -Returns `(Δ₁, Δ₂)` with rescaling applied. The ordering matches deltac.f's -output convention (swapped relative to deltar.f). +The two parity channels are returned in named fields, avoiding the +ambiguity between parity-by-W and parity-by-N,Θ conventions. """ 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 @@ -698,18 +760,20 @@ 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 delta from the resonant cell's emap DOF. isol=1 = tearing, + # isol=2 = interchange (see BC block above for the parity derivation). res_cell = ws.cells[ws.nx] 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) - Δ_swapped = SVector{2,ComplexF64}(Δ_raw[2], Δ_raw[1]) + # Rescaling is linear & diagonal; apply to the (tearing, interchange) + # pair directly, no parity swap. + Δ_rescaled = rescale_delta(Δ_raw, params) - return rescale_delta(Δ_swapped, params) + return InnerLayerResponse(Δ_rescaled[1], Δ_rescaled[2]) end diff --git a/src/InnerLayer/GGJ/InnerAsymptotics.jl b/src/Tearing/InnerLayer/GGJ/InnerAsymptotics.jl similarity index 73% rename from src/InnerLayer/GGJ/InnerAsymptotics.jl rename to src/Tearing/InnerLayer/GGJ/InnerAsymptotics.jl index 4f4de84a9..436bfa1af 100644 --- a/src/InnerLayer/GGJ/InnerAsymptotics.jl +++ b/src/Tearing/InnerLayer/GGJ/InnerAsymptotics.jl @@ -1,7 +1,6 @@ # InnerAsymptotics.jl # # 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: @@ -15,9 +14,6 @@ # 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) -# -# This file ports `inps_tjmat`, `inps_lyap_solve`, `inps_split`, `inps_coefs`, -# `inps_horner`, `inps_ua`, `inps_delta`, and `inps_xmax` from the Fortran. using LinearAlgebra using StaticArrays @@ -79,7 +75,6 @@ end # ----------------------------------------------------------------------- # Step 1: build T, Tinv, A_0..A_2, J_0..J_2. -# Mirrors inps_tjmat (inps.f lines 145–233). # ----------------------------------------------------------------------- function _build_tjmat(p::GGJParameters, Q::ComplexF64) @@ -92,27 +87,27 @@ function _build_tjmat(p::GGJParameters, Q::ComplexF64) q2 = q * q λ = 1 / sqrt(q) - # T (Eq. 7) — Fortran constructs this with column-major RESHAPE; the - # listing below is row-major Julia order matching that layout. + # T (Eq. 7) — built by column-major reshape; the listing below is + # row-major Julia order matching that layout. T = @SMatrix ComplexF64[ - 1 0 h*q q2/λ h*q -q2/λ - 0 0 0 -1/λ 0 1/λ - 0 0 -1/λ 0 1/λ 0 - 0 1 -h/λ -q2 h/λ -q2 - 0 0 0 1 0 1 - 0 0 1 0 1 0 + 1 0 h*q q2/λ h*q -q2/λ + 0 0 0 -1/λ 0 1/λ + 0 0 -1/λ 0 1/λ 0 + 0 1 -h/λ -q2 h/λ -q2 + 0 0 0 1 0 1 + 0 0 1 0 1 0 ] Tinv = @SMatrix ComplexF64[ - 1 q2 0 0 0 -h*q - 0 0 -h 1 q2 0 - 0 0 -λ/2 0 0 1/2 - 0 -λ/2 0 0 1/2 0 - 0 0 λ/2 0 0 1/2 - 0 λ/2 0 0 1/2 0 + 1 q2 0 0 0 -h*q + 0 0 -h 1 q2 0 + 0 0 -λ/2 0 0 1/2 + 0 -λ/2 0 0 1/2 0 + 0 0 λ/2 0 0 1/2 + 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 — physical-system coefficient matrices. Build mutable then freeze. A0 = zeros(ComplexF64, 6, 6) A1 = zeros(ComplexF64, 6, 6) A2 = zeros(ComplexF64, 6, 6) @@ -158,7 +153,6 @@ end # ----------------------------------------------------------------------- # Step 2: closed-form Lyapunov solve for the splitting transformation. -# Mirrors inps_lyap_solve (inps.f lines 241–270). # # 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 +166,10 @@ 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 +178,22 @@ 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 @@ -206,7 +202,7 @@ function _lyap_solve(K::SMatrix{6,6,ComplexF64}, λ::ComplexF64) end # ----------------------------------------------------------------------- -# Step 3: split recurrence (inps_split lines 278–361). +# Step 3: split recurrence. # Builds B_k, P_k, K6_k for k = 0..kmax+2. # ----------------------------------------------------------------------- @@ -221,21 +217,21 @@ 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 +242,12 @@ function _split_recurrence(J::NTuple{3,SMatrix{6,6,ComplexF64}}, λ::ComplexF64, end # ----------------------------------------------------------------------- -# Step 4: coefs recurrence (inps_coefs lines 369–496). +# Step 4: coefs recurrence. # Builds K2_k, Q_k, C_k for k = 0..kmax+2 and D_k, E_k, Y_k, Z_k. # ----------------------------------------------------------------------- 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 +263,54 @@ 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] + # Q_k = [[0, 0], [-K2[1,1], -K2[1,2]]] (column-major reshape gives this layout) + 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. 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]) + 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. 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 +319,16 @@ 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 @@ -362,7 +359,7 @@ 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 @@ -371,7 +368,6 @@ build_asymptotics(params::GGJParameters, Q::Number; kmax::Int=8) = # ----------------------------------------------------------------------- # Horner evaluator with optional fractional-power prefactor. -# Mirrors inps_horner (inps.f lines 587–631). # # 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 +377,15 @@ 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 +405,9 @@ 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 +418,9 @@ 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 @@ -435,19 +431,19 @@ function _horner(x::Real, c::AbstractMatrix{ComplexF64}; end # Pack the cache's Y, Qmat, and the [r2, r1] block of P into the row-major -# Fortran-reshape order used by inps_horner. Returned matrices are +# reshape order used by `_horner`. Returned matrices are # n_components × (kmax+1). 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] - # Fortran column-major reshape of (2,2) → 4 entries: + Yk = cache.Y[k+1] + # 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 +452,28 @@ 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] - # 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] + Qk = cache.Qmat[k+1] + Pk = cache.P[k+1] + # dd[1:4] from Q (column-major reshape of 2×2 block) + 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). +# Step 5: evaluator. # ----------------------------------------------------------------------- """ @@ -491,12 +487,12 @@ asymptotic solutions of the GGJ system, and (if `derivative=true`) the 6×2 matrix `dU` of their derivatives `dU/dx`. If `apply_T=false`, the result is left in the J-rotated coordinate basis -(used by `inps_delta` for residual checks). The default `apply_T=true` +(used by `asymptotic_residual` for residual checks). The default `apply_T=true` returns the solutions in the original 6-component first-order-system -basis used by `inpso_get_uv` and the shooting / Galerkin solvers. +basis used by `_physical_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) @@ -508,16 +504,17 @@ 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) @@ -530,26 +527,26 @@ 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) - dsmat = @SMatrix ComplexF64[0 0; 0 (-2 * xfac / x)] + dsmat = @SMatrix ComplexF64[0 0; 0 (-2*xfac/x)] dqsy = q * smat * dy + q * dsmat * y + dq * smat * y dU = pp * dqsy + dpp * qsy if apply_T - U = cache.T * U + U = cache.T * U dU = cache.T * dU end return U, dU @@ -562,14 +559,14 @@ function evaluate_asymptotics(cache::InnerAsymptoticsCache, x::Real; end # ----------------------------------------------------------------------- -# Step 6: residual `delta` and adaptive xmax (inps_delta + inps_xmax). +# Step 6: residual `delta` and adaptive 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): +the two algebraic columns: 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. @@ -586,15 +583,17 @@ function asymptotic_residual(cache::InnerAsymptoticsCache, x::Real) M = M + xfac * xfac * cache.J[3] end - # Match the Fortran convention: matvec(:,:,1) = dU; matvec(:,:,2) = -x*M*U; - # matvec(:,:,0) = sum. delta(j) = ||matvec(:,j,0)||∞ / max(||matvec(:,j,1)||∞, ||matvec(:,j,2)||∞). + # matvec(:,:,1) = dU; matvec(:,:,2) = -x*M*U; matvec(:,:,0) = sum. + # delta(j) = ||matvec(:,j,0)||∞ / max(||matvec(:,j,1)||∞, ||matvec(:,j,2)||∞). matvec1 = dU matvec2 = -x * (M * U) matvec0 = matvec1 + matvec2 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])) @@ -614,16 +613,15 @@ end 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). +`InnerAsymptoticsCache` it built so callers can reuse it. 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/Tearing/InnerLayer/GGJ/LayerInputs.jl b/src/Tearing/InnerLayer/GGJ/LayerInputs.jl new file mode 100644 index 000000000..eb9f7be0f --- /dev/null +++ b/src/Tearing/InnerLayer/GGJ/LayerInputs.jl @@ -0,0 +1,134 @@ +# LayerInputs.jl (GGJ) +# +# Build per-surface `GGJParameters` from a solved `PlasmaEquilibrium`, the +# `SingType` rational-surface list (each carrying a populated +# `restype::ResistGeometry` from `ForceFreeStates.resist_eval_all!`), and a +# `KineticProfiles` object — the same three ingredients `build_slayer_inputs` +# consumes. Produces the (E, F, G, H, K, τ_A, τ_R) tuple that GGJ's +# `solve_inner` needs, with τ_A / τ_R built from kinetic profiles using the +# same Spitzer resistivity and mass-density formulas SLAYER uses. +# +# Deliberately does *not* use any hardcoded `ne`/`te` defaults. The kinetic +# content enters through `profiles` alone; this keeps GGJ and SLAYER using +# bit-identical plasma inputs when both are driven by the same +# `KineticProfiles`. + +using ...Utilities: KineticProfiles +using ....Utilities.PhysicalConstants: MU_0, M_E, M_P, E_CHG, EPS_0 +using ....Utilities.NeoclassicalResistivity +using ....Utilities.NeoclassicalResistivity: NeoResistivityModel, SpitzerModel, + SauterNeoModel, RedlNeoModel, + coulomb_log_e, eta_spitzer, nu_star_e, eta_neoclassical +using ....ForceFreeStates: ResistGeometry + +""" + build_ggj_inputs(equil, sings, profiles; mu_i=2.0, zeff=1.0, + v1_scale=1.0, + resistivity_model::NeoResistivityModel=SpitzerModel(), + lnLambda_form::Symbol=:nrl) -> Vector{GGJParameters} + +Construct a `GGJParameters` for each rational surface in `sings`. Each +surface's geometric coefficients (E, F, G, H, K, M) come from the +`sing.restype::ResistGeometry` populated by `resist_eval_all!`. Kinetic +timescales are derived from the `KineticProfiles` at `sing.psifac`: + +``` +ρ(ψ) = μ_i · m_p · n_e(ψ) +η(ψ) = eta_neoclassical(model, n_e, T_e, Z_eff, f_t, ν*_e) [Ω·m] +τ_A = √(ρ · M · μ_0) / |2π · n · q' · χ₁ / V'| [Alfvén time] +τ_R = (⟨B²/|∇ψ|²⟩ / ⟨B²⟩) · μ_0 / η [resistive diffusion] +``` + +The mode number `n` is taken from `sings[k].n[1]` (first resonant mode at +the surface). `χ₁ = 2π · psio`. The `v1_scale` kwarg is an optional +multiplicative factor on `V'` in the τ_A denominator (a `v1 / volume` +normalization option); default `1.0` means use the raw `V'`. + +# Resistivity model + +`resistivity_model` selects the η closure: + + - `SpitzerModel()` (default) — Sauter 1999 Eq. 18a (Zeff-aware Spitzer), + with the NRL Coulomb log. + - `SauterNeoModel()` — multiplies by Sauter 1999 F_33 using f_t and ν*_e + from the surface's `ResistGeometry`. Produces the physically-correct + trapped-particle-corrected η for H-mode tearing stability. + - `RedlNeoModel()` — Redl 2021 F_33 (improved high-ν* fit). + +`lnLambda_form` selects `:nrl` (default), `:sauter`, or `:wesson`. + +Throws if any surface's `restype` is still `nothing` — call +`ForceFreeStates.resist_eval_all!(intr, equil)` first. +""" +function build_ggj_inputs(equil, sings, profiles::KineticProfiles; + mu_i::Real=2.0, zeff::Real=1.0, + v1_scale::Real=1.0, + resistivity_model::NeoResistivityModel=SpitzerModel(), + lnLambda_form::Symbol=:nrl) + psio = equil.psio + chi1 = 2π * psio + + out = Vector{GGJParameters}(undef, length(sings)) + for (k, sing) in enumerate(sings) + rg = sing.restype + rg === nothing && + throw( + ArgumentError( + "build_ggj_inputs: surface $k has " * + "restype = nothing. Call " * + "ForceFreeStates.resist_eval_all!(intr, equil) " * + "after sing_find! to populate it." + ) + ) + rg isa ResistGeometry || + throw(ArgumentError("build_ggj_inputs: surface $k has " * + "restype of unexpected type $(typeof(rg)).")) + + # Kinetic profiles at this surface + prof = profiles(sing.psifac) + n_e = prof.n_e # [m⁻³] + t_e = prof.T_e # [eV] + + # Shared Coulomb log and resistivity closure (identical to SLAYER + # when the same resistivity_model is selected). + lnLamb = coulomb_log_e(n_e, t_e; form=lnLambda_form) + if resistivity_model isa SpitzerModel + eta_use = eta_spitzer(n_e, t_e, zeff; lnLamb=lnLamb) + else + nuestar = nu_star_e(n_e, t_e, rg.R_major, rg.eps_local, + sing.q, zeff; lnLamb=lnLamb) + eta_use = eta_neoclassical(resistivity_model, n_e, t_e, zeff, + rg.f_trap, nuestar; lnLamb=lnLamb) + end + rho = mu_i * M_P * n_e + + # Alfvén time at the rational surface + n_tor = Int(sing.n[1]) + v1 = rg.v1_local * v1_scale + taua = sqrt(rho * rg.M * MU_0) / + abs(2π * n_tor * sing.q1 * chi1 / v1) + + # Resistive diffusion time + taur = (rg.avg_bsq_over_dpsisq / rg.avg_bsq) * MU_0 / eta_use + + # dV/dψ normalized by total plasma volume (`v1 = v1/volume`). This is + # the `v1` consumed by `rescale_delta` as v1^(2p1); NOT the raw V' + # used in τ_A above. + equil.params.volume === nothing && + throw( + ArgumentError( + "build_ggj_inputs: equil.params.volume " * + "is nothing. Ensure the equilibrium " * + "solver populated the total plasma " * + "volume before building GGJ inputs." + ) + ) + v1_norm = rg.v1_local / equil.params.volume + + out[k] = GGJParameters(; + E=rg.E, F=rg.F, G=rg.G, H=rg.H, K=rg.K, M=rg.M, + taua=taua, taur=taur, v1=v1_norm, ising=k + ) + end + return out +end diff --git a/src/InnerLayer/GGJ/Reference.jl b/src/Tearing/InnerLayer/GGJ/Reference.jl similarity index 80% rename from src/InnerLayer/GGJ/Reference.jl rename to src/Tearing/InnerLayer/GGJ/Reference.jl index 8a2f135ce..422ac3e0a 100644 --- a/src/InnerLayer/GGJ/Reference.jl +++ b/src/Tearing/InnerLayer/GGJ/Reference.jl @@ -1,8 +1,7 @@ # Reference.jl # # Hard-coded benchmark parameter sets for cross-validation of the GGJ -# inner-layer solvers. Values are taken from published papers and the -# corresponding Fortran RMATCH test cases. +# inner-layer solvers. Values are taken from published papers. """ glasser_wang_2020_eq55() -> GGJParameters @@ -16,8 +15,8 @@ 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=8.950e-1, H=1.292e-1, K=2.332e-1, + taua=taua, taur=taur, v1=v1 ) end diff --git a/src/InnerLayer/GGJ/Shooting.jl b/src/Tearing/InnerLayer/GGJ/Shooting.jl similarity index 71% rename from src/InnerLayer/GGJ/Shooting.jl rename to src/Tearing/InnerLayer/GGJ/Shooting.jl index ca085dabe..3086d5d7a 100644 --- a/src/InnerLayer/GGJ/Shooting.jl +++ b/src/Tearing/InnerLayer/GGJ/Shooting.jl @@ -1,19 +1,17 @@ # Shooting.jl # -# 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 -# a small `tmin` (origin Frobenius regime), then projects onto the local -# Frobenius basis at the origin and reads off the parity-projected -# matching data via `deltar_ratio`. +# Stable backward shooting solver for the GGJ inner-layer model. Integrates +# the 4×4 origin-diagonalized resistive-layer ODE from `tmax` (large-x +# asymptotic regime) backward to a small `tmin` (origin Frobenius regime), +# then projects onto the local Frobenius basis at the origin and reads off +# the parity-projected matching data. # # 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}`). # -# Reference: A. H. Glasser, Phys. Plasmas **23**, 072505 (2016) and the -# Fortran rmatch/deltar.f. +# Reference: A. H. Glasser, Phys. Plasmas **23**, 072505 (2016). using LinearAlgebra using SpecialFunctions: gamma @@ -22,8 +20,8 @@ using OrdinaryDiffEq """ GGJShootingSystem -Precomputed origin- and infinity-side arrays for the deltar.f-style -backward shoot. Construct via [`_build_shooting_system`](@ref). +Precomputed origin- and infinity-side arrays for the backward shoot. +Construct via [`_build_shooting_system`](@ref). """ struct GGJShootingSystem params::GGJParameters @@ -46,47 +44,51 @@ struct GGJShootingSystem end # ----------------------------------------------------------------------- -# Origin arrays — port of deltar_origin (deltar.f lines 333–482). +# Origin arrays for the origin-diagonalized Frobenius basis. # ----------------------------------------------------------------------- function _build_origin_arrays(p::GGJParameters, Q::ComplexF64; nps::Int=8, rtol::Float64=1e-6) 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. + # d0 — diagonalizing matrix at the origin. d0_m = zeros(ComplexF64, 4, 4) d0_m[1, 1] = q * a2 d0_m[1, 2] = 1 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 — explicit antisymmetry pattern of the origin diagonalizer inverse. 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] @@ -106,11 +108,11 @@ 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[i, j, k] — origin power-series coefficients. # ups(:,:,1) = I; higher orders from the al1 recurrence. ups = zeros(ComplexF64, 4, 4, nps) @inbounds for i in 1:4 @@ -120,13 +122,13 @@ 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 end - # tmin from the truncation-error bound on the origin series (line 470). + # tmin from the truncation-error bound on the origin series. unmax = 0.0 @inbounds for j in 1:4, i in 1:4 unmax = max(unmax, abs(ups[i, j, nps])) @@ -138,31 +140,35 @@ function _build_origin_arrays(p::GGJParameters, Q::ComplexF64; nps::Int=8, rtol: end # ----------------------------------------------------------------------- -# Infinity arrays — port of deltar_infinity (deltar.f lines 490–666). +# Infinity arrays — large-t asymptotic basis. # With nxps = 1 the higher-order vps recurrence is dead code; vps[:,:,1] = I. # ----------------------------------------------------------------------- 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. + # m matrix (2×2) — large-t asymptotic coupling. 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) @@ -176,32 +182,32 @@ 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 d1 = SMatrix{4,4,ComplexF64}(d1_m) bl1 = SVector{4,ComplexF64}(-lamda, -lamda, lamda, lamda) - # tmax (deltar_infinity lines 644–650, ntmax = 1 default). + # tmax (ntmax = 1 default). p1v = sqrt(-mercier_di(p)) tmax_inner = sqrt((max(0.5, p1v)^2 - log(rtol)) / abs(lamda)) tmax_outer = 6.0 / abs(q) @@ -218,18 +224,18 @@ 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 # ----------------------------------------------------------------------- -# Origin Frobenius basis evaluator — port of deltar_upsfit (lines 233–267). +# Origin Frobenius basis evaluator. # Returns the 4×4 matrix `u(t)` whose columns are the 4 fundamental # origin solutions evaluated at `t`. Solving `u * c0 = y` then projects a # 4-component integrated state onto the origin basis. @@ -242,7 +248,7 @@ 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 @@ -257,8 +263,8 @@ function _origin_basis(sys::GGJShootingSystem, t::Real) end # ----------------------------------------------------------------------- -# Initial condition at tmax — see deltar_run lines 121–126. -# With nxps = 1 in deltar.f, vps[:,:,1] = I, so the asymptotic-basis +# Initial condition at tmax. +# With nxps = 1, vps[:,:,1] = I, so the asymptotic-basis # evaluator returns a diagonal v. The IC is then # y(tmax) = d1 * v(:, 1:2) # which extracts the first two columns of d1 scaled by the algebraic-mode @@ -279,12 +285,12 @@ function _initial_condition(sys::GGJShootingSystem) end # ----------------------------------------------------------------------- -# ODE right-hand side — port of deltar_der (lines 185–224). +# ODE right-hand side. # dy/dt = al1 * y * t + diag(al0) * y / t # ----------------------------------------------------------------------- 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 @@ -293,7 +299,7 @@ function _ggj_der!(dy::AbstractMatrix{ComplexF64}, y::AbstractMatrix{ComplexF64} end # ----------------------------------------------------------------------- -# Parity-projected matching ratio — port of deltar_ratio (lines 674–716). +# Parity-projected matching ratio. # c0 is a 4×2 complex matrix whose rows are the four origin-mode # coefficients of the two integrated solutions (modes 1: x^{p1}, # 2: x^{1/2}, 3: x^{−p1}, 4: x^{−1/2}). @@ -324,24 +330,27 @@ end 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()) -> SVector{2,ComplexF64} + fmax::Float64=1.0, solver=Tsit5()) -> InnerLayerResponse Solve the GGJ inner-layer matching problem by stable backward shooting in -the origin-diagonalized 4×4 basis. Direct port of the rmatch `deltar.f` -algorithm. +the origin-diagonalized 4×4 basis. -Returns the parity-projected matching data `(Δ₁, Δ₂)` (already rescaled -back to physical units via `rescale_delta`). Index ordering matches the -Fortran `deltar` output. +Returns an `InnerLayerResponse(tearing, interchange)` with rescaling +applied. `_delta_from_c0` returns a `(Δ₁, Δ₂)` pair where `Δ₁` is the +**interchange** (anti-symmetric / W-odd) channel and `Δ₂` is the +**tearing** (symmetric / W-even) channel. We therefore map +`Δ₂ → tearing` and `Δ₁ → interchange` into the named fields, matching the +physics channel labels used by the Galerkin solver and by the +`InnerLayerResponse` docstring. Tolerances `reltol`/`abstol` are the integrator tolerances; `rtol_origin` 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) @@ -357,7 +366,9 @@ function solve_inner(::GGJModel{:shooting}, params::GGJParameters, γ::Number; c0 = Matrix(u) \ Matrix(y_end) Δ_raw = _delta_from_c0(c0, sys) - return rescale_delta(Δ_raw, params) + Δ_rescaled = rescale_delta(Δ_raw, params) + # Δ_rescaled ≡ (Δ₁, Δ₂) = (interchange, tearing). + return InnerLayerResponse(Δ_rescaled[2], Δ_rescaled[1]) end solve_inner(::GGJModel{:shooting}, params::GGJParameters, γ::Real; kwargs...) = diff --git a/src/InnerLayer/InnerLayer.jl b/src/Tearing/InnerLayer/InnerLayer.jl similarity index 54% rename from src/InnerLayer/InnerLayer.jl rename to src/Tearing/InnerLayer/InnerLayer.jl index 537b2970f..1d9430ab9 100644 --- a/src/InnerLayer/InnerLayer.jl +++ b/src/Tearing/InnerLayer/InnerLayer.jl @@ -10,22 +10,28 @@ module InnerLayer using LinearAlgebra using StaticArrays +using ..Utilities + include("InnerLayerInterface.jl") include("GGJ/GGJ.jl") -# include("SLAYER/Slayer.jl") --- SLAYER code goes here +include("SLAYER/SLAYER.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 -# SLAYER imports go here +import .GGJ: glasser_wang_2020_eq55, build_ggj_inputs + +import .SLAYER: SLAYERModel, SLAYERParameters, slayer_parameters, r_based_shear +import .SLAYER: riccati_del_s, slayer_layer_thickness, LayerWidths +import .SLAYER: surface_minor_radius, surface_da_dpsi, build_slayer_inputs -export InnerLayerModel, solve_inner +export InnerLayerModel, InnerLayerParameters, InnerLayerResponse, solve_inner export GGJ, GGJModel, GGJParameters export build_asymptotics, evaluate_asymptotics, pick_xmax, InnerAsymptoticsCache export mercier_di, mercier_dr, inner_Q, rescale_delta -export glasser_wang_2020_eq55 - -# SLAYER exports go here +export glasser_wang_2020_eq55, build_ggj_inputs +export SLAYER, SLAYERModel, SLAYERParameters, slayer_parameters, r_based_shear +export riccati_del_s, slayer_layer_thickness, LayerWidths +export surface_minor_radius, surface_da_dpsi, build_slayer_inputs end # module InnerLayer diff --git a/src/Tearing/InnerLayer/InnerLayerInterface.jl b/src/Tearing/InnerLayer/InnerLayerInterface.jl new file mode 100644 index 000000000..e67cd1414 --- /dev/null +++ b/src/Tearing/InnerLayer/InnerLayerInterface.jl @@ -0,0 +1,77 @@ +# InnerLayerInterface.jl +# +# Abstract interface for resistive inner-layer models. Concrete models +# (e.g. GGJ, SLAYER, kinetic) live in submodules and specialize `solve_inner`. + +""" + InnerLayerModel + +Abstract supertype for resistive inner-layer models. Each concrete model is a +small, parameter-free type tag (often parameterized by a solver-choice symbol) +that selects a `solve_inner` method. + +Implementations live in submodules of `InnerLayer`, e.g. `InnerLayer.GGJ`. +""" +abstract type InnerLayerModel end + +""" + InnerLayerParameters + +Abstract supertype for the per-surface physical-parameter structs consumed by +the inner-layer models (`SLAYERParameters`, `GGJParameters`). Lets the +dispersion runner and HDF5 output dispatch generically over a vector of +single-model parameters. +""" +abstract type InnerLayerParameters end + +""" + InnerLayerResponse + +Parity-projected inner-layer matching data at one rational surface. The two +components correspond to the homogeneous parity solutions of the half-domain +inner-layer problem (parity boundary conditions imposed at X = 0). They are +the `Δ_{j,±}(γ)` of Glasser, Wang & Park, Phys. Plasmas **23**, 112506 +(2016), Eqs. (34)–(35). + +# Fields + + - `tearing` — the **odd-parity** matching coefficient (GWP Δ_+, the + "odd mode"). Corresponds to a flux perturbation W that is EVEN in x and + a velocity/temperature perturbation that is ODD — i.e., the + reconnecting mode with a current sheet at the rational surface. This is + the tearing drive that appears as Δ' in the classical constant-ψ + tearing equation. Must be populated by every resistive inner-layer model. + + - `interchange` — the **even-parity** matching coefficient (GWP Δ_−, the + "even mode"). Corresponds to W odd, N and Θ even — i.e., the + non-reconnecting interchange/ballooning channel. Its dissipative piece + in toroidal geometry is the Glasser, Greene & Johnson stabilization + term that opposes tearing growth (Glasser, Greene & Johnson 1975; + Lütjens-Bondeson-Roy 1993). Pressureless inner-layer models (e.g. + SLAYER's Fitzpatrick Riccati) set this identically zero. + +The naming follows the physics channel rather than a mathematical parity +label because `odd/even` carries different meanings across the literature +depending on whether you label by the parity of W (GWP paper convention) +or the parity of (N, Θ). Using `tearing` and `interchange` avoids ambiguity. +""" +struct InnerLayerResponse + tearing::ComplexF64 + interchange::ComplexF64 +end + +InnerLayerResponse(; tearing::Number=0, interchange::Number=0) = + InnerLayerResponse(ComplexF64(tearing), ComplexF64(interchange)) + +""" + solve_inner(model::InnerLayerModel, params, γ::Number; kwargs...) -> InnerLayerResponse + +Compute the parity-projected matching data `(Δ_tearing, Δ_interchange)` for +the given inner-layer `model`, physical parameters `params`, and complex +growth rate `γ`. Concrete models specialize this function. + +See `InnerLayerResponse` for the physics-oriented field definitions. +Pressureless models (SLAYER) populate only `tearing` and leave +`interchange` at zero; two-fluid / finite-β models (GGJ) populate both. +""" +function solve_inner end diff --git a/src/Tearing/InnerLayer/SLAYER/LayerInputs.jl b/src/Tearing/InnerLayer/SLAYER/LayerInputs.jl new file mode 100644 index 000000000..96177903d --- /dev/null +++ b/src/Tearing/InnerLayer/SLAYER/LayerInputs.jl @@ -0,0 +1,311 @@ +# LayerInputs.jl +# +# Build per-surface `SLAYERParameters` from an in-memory `PlasmaEquilibrium`, +# the `SingType` rational-surface data produced by `ForceFreeStates`, and a +# `KineticProfiles` object. Everything needed is already held in memory, so +# the layer inputs are assembled directly without an intermediate file +# round-trip. +# +# Geometry extraction: +# - Minor radius at the outboard midplane (θ = 0) via +# `equil.rzphi_rsquared((ψ, 0.0))`. +# - `da/dψ` via central finite difference on the same bicubic. +# - r-based magnetic shear via `r_based_shear(rs, q, q1, da/dψ)` (defined +# in LayerParameters.jl). + +using ..Utilities: KineticProfiles +using ...Utilities.NeoclassicalResistivity: NeoResistivityModel, SpitzerModel, + coulomb_log_e, nu_star_e +using FastInterpolations: DerivOp + +""" + surface_minor_radius(equil, psi; theta=0.0) -> Float64 + +Minor radius at normalized flux `psi` and poloidal angle `theta`, +computed from `equil.rzphi_rsquared` as `√((R − R₀)² + (Z − Z₀)²)`. +`theta = 0.0` (outboard midplane) is the default; pass `θ = π` to measure +the inboard side if you want an average. +""" +function surface_minor_radius(equil, psi::Real; theta::Real=0.0) + r_sq = equil.rzphi_rsquared((Float64(psi), Float64(theta))) + return sqrt(r_sq) +end + +""" + surface_da_dpsi(equil, psi; theta=0.0, h=1e-5) -> Float64 + +Central finite-difference approximation of `d(minor radius)/dψ` at `psi`. +Falls back to one-sided differences near the flux-coordinate boundaries +(0 or 1). +""" +function surface_da_dpsi(equil, psi::Real; theta::Real=0.0, h::Real=1e-5) + psi_f = Float64(psi) + # Clamp to safe sampling range within (0, 1) + eps_edge = 10 * h + lo = psi_f - h + hi = psi_f + h + if lo < eps_edge + # one-sided forward + a0 = surface_minor_radius(equil, max(psi_f, eps_edge); theta=theta) + a1 = surface_minor_radius(equil, max(psi_f, eps_edge) + h; theta=theta) + return (a1 - a0) / h + elseif hi > 1.0 - eps_edge + # one-sided backward + a0 = surface_minor_radius(equil, min(psi_f, 1.0 - eps_edge) - h; theta=theta) + a1 = surface_minor_radius(equil, min(psi_f, 1.0 - eps_edge); theta=theta) + return (a1 - a0) / h + else + a_plus = surface_minor_radius(equil, psi_f + h; theta=theta) + a_minus = surface_minor_radius(equil, psi_f - h; theta=theta) + return (a_plus - a_minus) / (2h) + end +end + +""" + build_slayer_inputs(equil, sings, profiles; …) -> Vector{SLAYERParameters} + +Build a `SLAYERParameters` for each rational surface in `sings`, pulling +geometry (minor radius, r-based shear, q, dq/dψ, R₀) from the in-memory +`equil::PlasmaEquilibrium` and kinetic data (n_e, T_e, T_i, ω, ω\\_\\*e, +ω\\_\\*i) from `profiles::KineticProfiles`. + +Layer inputs are assembled directly from the in-memory equilibrium and +profiles, without an intermediate file round-trip. + +# Arguments + + - `equil` -- `PlasmaEquilibrium` + - `sings` -- `Vector{SingType}` (one per resonant surface) + - `profiles` -- `KineticProfiles` valid across all `sings` ψ values + +# Keyword arguments + + - `bt` -- toroidal field [T]. Scalar, callable of `psi`, or + `nothing` (default). When `nothing`, the physical `B_T = F(ψ) / (2π·R₀)` + is computed per surface from the equilibrium's F-spline. Note: + `equil.config.b0exp` is a *normalization* (often just `1.0`), not the + physical field, so passing it as a scalar is almost always wrong. + + - `mu_i` -- ion mass in proton-mass units (default `2.0` for D). + - `zeff` -- effective charge (default `1.0`). + - `chi_perp` -- perpendicular heat diffusivity [m²/s]. Scalar or a + callable of `psi` (default `1.0`). + - `chi_tor` -- toroidal heat diffusivity [m²/s]. Scalar or a callable + of `psi` (default `1.0`). + - `dr_val` -- resistive interchange index `D_R = E + F + H²` + (Glasser-Greene-Johnson 1975) feeding the critical-Δ formulas + (`:lar`, `:rfitzp`, `:toroidal`). When `nothing` (default), Julia + derives it per-surface from the equilibrium as + `dr_val_k = D_R(ψ_k) = E_k + F_k + H_k²`, + consistent with Connor-Hastie-Helander 2015 (PPCF 57 065001) Eq. 59 + which uses `(−D_R)` in the χ_‖-matching critical-Δ. Pass a scalar / + vector / callable to override. + + **NOTE**: the χ_‖-matching critical-Δ requires the resistive + interchange index `D_R = E + F + H²` (Glasser-Greene-Johnson 1975), + NOT the Mercier index `D_I = E + F + H − 1/4`. The two differ by + `(H − 1/2)²`, which is non-trivial on shaped equilibria (~factor 3 on + DIII-D); this code uses the physically correct `D_R`. + - `dgeo_val` -- Connor 2015 (PPCF 57 065001) Eq. 59 geometric factor + used by `dc_type=:toroidal`. When `nothing` (default), an error is + raised if `dc_type=:toroidal` is also requested — the auto-derived + formula additionally needs ⟨|∇ψ|²⟩ FSA which `ResistGeometry` + doesn't currently expose. Pass a scalar / vector / callable to use + a prescribed value. (For `dc_type=:rfitzp` and `:lar`, dgeo_val is + not consulted.) + - `dc_type` -- `:none` (default), `:lar`, `:rfitzp`, or `:toroidal`. + - `theta` -- poloidal angle at which to measure minor radius (default + `0.0`, outboard midplane). + - `resistivity_model` -- `SauterNeoModel()` (default), `RedlNeoModel()`, + `SpitzerModel()`, or `SpitzerHarmModel()` (legacy Fitzpatrick σ_∥). + Sets the η entering τ_R = μ₀r_s²/η. With a neoclassical model, `f_trap` + and ν*_e are taken from the surface's `ResistGeometry` if populated + (via `ForceFreeStates.resist_eval_all!`), otherwise fall back to the + ε-only Lin-Liu-Miller form and `rs/R_0` aspect ratio. + - `lnLambda_form` -- Coulomb-log form passed through to `slayer_parameters` + (default `:nrl`; `:wesson` + `SpitzerHarmModel()` reproduces legacy + SLAYER exactly). +""" +function build_slayer_inputs(equil, sings, profiles::KineticProfiles; + bt=nothing, + R0=nothing, + rs_method::Symbol=:midplane, + mu_i::Real=2.0, + zeff::Real=1.0, + z_i::Real=1.0, + chi_perp=1.0, + chi_tor=1.0, + dr_val=nothing, + dgeo_val=nothing, + dc_type::Symbol=:none, + theta::Real=0.0, + compute_omega_star::Bool=true, + resistivity_model::NeoResistivityModel=SauterNeoModel(), + lnLambda_form::Symbol=:nrl) + R0_use = R0 === nothing ? equil.ro : Float64(R0) + _eval(x, ψ) = x isa Real ? Float64(x) : Float64(x(ψ)) + + # Compute physical B_T = F(ψ) / (2π·R₀) per surface from the F spline + # when `bt` is not explicitly supplied. + _bt_at(ψ) = + if bt === nothing + Float64(equil.profiles.F_spline(ψ)) / (2π * R0_use) + elseif bt isa Real + Float64(bt) + else + Float64(bt(ψ)) + end + + # Minor-radius extractor: `:midplane` = outboard-midplane chord + # (original behavior); `:fsa` = θ-mean of √rzphi_rsquared, the + # flux-surface-averaged minor radius. + _rs_at(ψ) = + if rs_method === :fsa + integrand(θ) = sqrt(equil.rzphi_rsquared((Float64(ψ), Float64(θ)))) + N = 128 + s = 0.0 + @inbounds for k in 1:N + s += integrand((k - 0.5) / N) + end + s / N + else + surface_minor_radius(equil, ψ; theta=theta) + end + _da_dpsi_at(ψ) = + if rs_method === :fsa + # central finite difference on _rs_at + h = 1e-5 + lo = ψ - h + hi = ψ + h + eps_edge = 10h + if lo < eps_edge + (_rs_at(max(ψ, eps_edge) + h) - _rs_at(max(ψ, eps_edge))) / h + elseif hi > 1.0 - eps_edge + (_rs_at(min(ψ, 1.0 - eps_edge)) - _rs_at(min(ψ, 1.0 - eps_edge) - h)) / h + else + (_rs_at(ψ + h) - _rs_at(ψ - h)) / (2h) + end + else + surface_da_dpsi(equil, ψ; theta=theta) + end + + # Per-surface ω_*e, ω_*i (diamagnetic frequencies) from spline + # derivatives. When `compute_omega_star=true` we override any ω_*e/ω_*i + # carried in `profiles`. Main-ion density is + # taken equal to the electron density (quasi-neutrality, matching the + # staging step). + chi1 = 2π * equil.psio + _omega_star_at(ψ) = begin + n_e = Float64(profiles.n_e(ψ)) + dn_e = Float64(profiles.n_e(ψ; deriv=DerivOp(1))) + T_e = Float64(profiles.T_e(ψ)) + dT_e = Float64(profiles.T_e(ψ; deriv=DerivOp(1))) + T_i = Float64(profiles.T_i(ψ)) + dT_i = Float64(profiles.T_i(ψ; deriv=DerivOp(1))) + ω_star_e = (2π / chi1) * (T_e * dn_e / n_e + dT_e) + ω_star_i = -(2π / (Float64(z_i) * chi1)) * (T_i * dn_e / n_e + dT_i) + return (ω_star_e, ω_star_i) + end + + out = Vector{SLAYERParameters}(undef, length(sings)) + for (k, sing) in enumerate(sings) + psi = sing.psifac + q = sing.q + q1 = sing.q1 + + rs = _rs_at(psi) + da_dpsi = _da_dpsi_at(psi) + sval_r = r_based_shear(rs, q, q1, da_dpsi) + + prof = profiles(psi) + # Override ω_*e, ω_*i with spline-derivative values when requested. + ω_e_use, ω_i_use = if compute_omega_star + _omega_star_at(psi) + else + (prof.omega_e, prof.omega_i) + end + + # Resonant (m, n): take the first element of the mode-number vectors. + # Parallel-FM `sing.m`/`sing.n` hold exactly one entry each; ideal + # DCON may hold multiple — we pick the first and document the choice. + m_res = sing.m[1] + n_res = sing.n[1] + + # Pull geometric trapped-fraction inputs from ResistGeometry when + # available (populated by ForceFreeStates.resist_eval_all!); else + # fall back to nothing and let slayer_parameters compute them from + # aspect ratio + Lin-Liu-Miller ε-only form. + rg = sing.restype + f_trap_kw = rg === nothing ? nothing : rg.f_trap + R_major_eff = rg === nothing ? nothing : rg.R_major + nu_e_star_kw = if rg === nothing || + resistivity_model isa Union{SpitzerModel,SpitzerHarmModel} + nothing + else + lnL = coulomb_log_e(prof.n_e, prof.T_e; form=lnLambda_form) + nu_star_e(prof.n_e, prof.T_e, rg.R_major, rg.eps_local, + q, zeff; lnLamb=lnL) + end + + # dr_val: per-surface resistive interchange index D_R = E + F + H² + # (Glasser-Greene-Johnson 1975). Used by `_solve_dc_tmp` to compute + # the χ_‖-matching critical-Δ via Connor-Hastie-Helander 2015 Eq. 59, + # which has `(−D_R)` as a multiplier. NOT the Mercier index + # D_I = E + F + H − 1/4 (see this function's docstring); we use the + # physically correct D_R here. + dr_val_k = if dr_val === nothing + rg === nothing && + throw( + ArgumentError( + "build_slayer_inputs: dr_val=nothing " * + "requires `sing.restype` populated by " * + "ForceFreeStates.resist_eval_all!. " * + "Surface k=$k has restype=nothing." + ) + ) + rg.E + rg.F + rg.H^2 + else + _eval(dr_val, psi) + end + + # dgeo_val: only used by dc_type=:toroidal (the Connor-Hastie- + # Helander 2015 formula). Auto-derivation requires ⟨|∇ψ|²⟩ FSA + # which the current `ResistGeometry` doesn't expose; for now we + # require an explicit value if the toroidal dc_type is selected. + dgeo_val_k = if dgeo_val === nothing + dc_type === :toroidal && + throw( + ArgumentError( + "build_slayer_inputs: dc_type=:toroidal " * + "needs `dgeo_val` (Connor 2015 PPCF 57 " * + "065001 Eq. 59 geometric factor). " * + "Auto-derivation from equilibrium not " * + "yet implemented; pass a scalar / vector " * + "/ callable explicitly." + ) + ) + 0.0 + else + _eval(dgeo_val, psi) + end + + out[k] = slayer_parameters(; + n_e=prof.n_e, t_e=prof.T_e, t_i=prof.T_i, + omega=prof.omega, omega_e=ω_e_use, omega_i=ω_i_use, + qval=q, sval_r=sval_r, bt=_bt_at(psi), + rs=rs, R0=R0_use, mu_i=mu_i, zeff=zeff, + chi_perp=_eval(chi_perp, psi), + chi_tor=_eval(chi_tor, psi), + m=m_res, n=n_res, + dr_val=dr_val_k, + dgeo_val=dgeo_val_k, + dc_type=dc_type, ising=k, + resistivity_model=resistivity_model, + f_trap=f_trap_kw, + nu_e_star=nu_e_star_kw, + R_major_eff=R_major_eff, + lnLambda_form=lnLambda_form + ) + end + return out +end diff --git a/src/Tearing/InnerLayer/SLAYER/LayerParameters.jl b/src/Tearing/InnerLayer/SLAYER/LayerParameters.jl new file mode 100644 index 000000000..57ee30763 --- /dev/null +++ b/src/Tearing/InnerLayer/SLAYER/LayerParameters.jl @@ -0,0 +1,363 @@ +# LayerParameters.jl +# +# `SLAYERParameters` carries the dimensionless layer-physics parameters +# that the Fitzpatrick layer Riccati ODE consumes for one rational surface, +# plus the dimensional conversion factors needed to translate normalized +# frequencies and Δ values back to physical units. +# +# The constructor builds the per-surface state from dimensional equilibrium +# and kinetic-profile inputs. The Fitzpatrick two-fluid layer uses +# P_perp/P_tor/D_norm rather than the older magnetic/electron Prandtl +# (pr/pe) and ρ_s-based (ds) parametrization. Q is not stored — it is +# passed directly to `solve_inner`. + +""" + SLAYERParameters + +Dimensionless layer-physics parameters at one rational surface for the +Fitzpatrick two-fluid drift-MHD SLAYER inner-layer model (Fitzpatrick +2023; Park et al. 2022), plus dimensional auxiliaries required for +de-normalization. The parametrization uses `P_perp`, `P_tor`, and +`D_norm` (not the older `pr`/`pe`/`ds` set). + +| field | meaning | +|:---------- |:----------------------------------------------------------------- | +| `ising` | Singular-surface index (traceability only) | +| `m`, `n` | Poloidal / toroidal mode numbers at this surface | +| `tau` | T_i / T_e | +| `lu` | Lundquist number S = τ_R / τ_H | +| `c_beta` | Compressibility √(β_local / (1 + β_local)) | +| `D_norm` | (d_β/r_s) · S^(1/3) · √(τ/(1+τ)) (Fitzpatrick normalized scale) | +| `P_perp` | Perpendicular Prandtl number τ_R / τ_⊥ | +| `P_tor` | Toroidal-direction Prandtl number τ_R / τ_‖tor | +| `Q_e` | Normalized electron diamagnetic: −tauk · ω_*e | +| `Q_i` | Normalized ion diamagnetic: −tauk · ω_*i | +| `iota_e` | Q_e / (Q_e − Q_i) | +| `tauk` | Q-conversion factor S^(1/3) · τ_H [s] — multiplies ω to get Q | +| `tau_r` | Resistive diffusion time [s] | +| `delta_n` | Δ-normalization factor S^(1/3) / r_s [m⁻¹] | +| `rs` | Minor radius at this surface [m] | +| `R0` | Major radius [m] | +| `bt` | Toroidal field [T] | +| `sval_r` | r-based magnetic shear r_s · (dq/dr) / q (Fitzpatrick convention) | +| `dr_val` | Radial width parameter at surface (input to dc_tmp) | +| `dgeo_val` | Geometric Δ (Shafranov shift factor) | +| `eta` | Parallel resistivity entering τ_R = μ₀r_s²/η [Ω·m] | +| `d_beta` | Beta-weighted ion length scale c_β · d_i [m] | +| `dc_tmp` | Critical-Δ offset from chi_parallel matching | +| `dc_type` | Selector for `dc_tmp` formula | + +The complex normalized growth rate `Q = ω + iγ` is **not** stored here; +it is passed as a separate argument to `solve_inner`. +""" +Base.@kwdef struct SLAYERParameters <: InnerLayerParameters + # Surface identity + ising::Int = 0 + m::Int = 0 + n::Int = 0 + + # Normalized layer parameters consumed by riccati_f + tau::Float64 + lu::Float64 + c_beta::Float64 + D_norm::Float64 + P_perp::Float64 + P_tor::Float64 + Q_e::Float64 + Q_i::Float64 + iota_e::Float64 + + # Conversion factors (Q ↔ ω in rad/s) + tauk::Float64 + tau_r::Float64 + delta_n::Float64 + + # Geometric / fluid auxiliaries + rs::Float64 + R0::Float64 + bt::Float64 + sval_r::Float64 + dr_val::Float64 = 0.0 + dgeo_val::Float64 = 0.0 + eta::Float64 + d_beta::Float64 + + # Critical-Δ offset + dc_tmp::Float64 = 0.0 + dc_type::Symbol = :none +end + +# Allowed dc_type values for the critical-Δ offset. `:none` is the default +# `dc_tmp = 0` branch. +const ALLOWED_DC_TYPES = (:none, :lar, :rfitzp, :toroidal) + +""" + r_based_shear(rs, q, dq_dpsi, da_dpsi) -> Float64 + +Convert a ψ-based shear to the r-based (Fitzpatrick) convention used +throughout SLAYER: + +``` +s_r = r_s · (dq/dr) / q = r_s · (dq/dψ) / (q · da/dψ) +``` + +`rs` is the minor radius at the surface, `q` the safety factor, +`dq_dpsi` the radial derivative of q with respect to ψ, and `da_dpsi` +the derivative of the surface minor radius with respect to ψ. The two +ψ derivatives must use the **same** ψ convention (i.e., both with +respect to ψ_norm or both with respect to physical ψ — the conversion +factor cancels in the ratio). + +Equivalent to the conversion `s_Fitz = s_psiN · r_s / (psi_N · da_dpsiN)`. +""" +function r_based_shear(rs::Real, q::Real, dq_dpsi::Real, da_dpsi::Real) + da_dpsi != 0 || throw(ArgumentError("r_based_shear: da/dψ must be non-zero")) + q != 0 || throw(ArgumentError("r_based_shear: q must be non-zero")) + return rs * dq_dpsi / (q * da_dpsi) +end + +# Internal: solve the Wd self-consistency loop for the chi_parallel-based +# critical Δ (Connor-Hastie-Helander 2015). Returns dc_tmp as a Float64. +function _solve_dc_tmp(; dc_type::Symbol, dr_val::Real, dgeo_val::Real, + chi_perp::Real, t_e::Real, zeff::Real, tau_ee::Real, + rs::Real, R0::Real, sval_r::Real, n_tor::Integer, + max_iter::Integer=100, tol::Real=1e-10) + dc_type in ALLOWED_DC_TYPES || + throw(ArgumentError("SLAYERParameters: unknown dc_type=$dc_type. " * + "Allowed: $(ALLOWED_DC_TYPES)")) + (dc_type === :none || dr_val == 0.0) && return 0.0 + + vte = sqrt(2.0 * t_e * E_CHG / M_E) + chi_par_smfp = (1.581 * tau_ee * vte^2) / (1.0 + 0.2535 * zeff) + + Wd = 0.1 + converged = false + for _ in 1:max_iter + chi_par_lmfp = (2.0 * R0 * vte) / (sqrt(π) * n_tor * sval_r * Wd) + chi_par = (chi_par_smfp * chi_par_lmfp) / + (chi_par_smfp + chi_par_lmfp) + Wd_new = sqrt(8.0) * (chi_perp / chi_par)^0.25 * + (1.0 / sqrt((rs / R0) * sval_r * n_tor)) + if abs(Wd_new - Wd) / max(abs(Wd), 1e-30) < tol + Wd = Wd_new + converged = true + break + end + Wd = Wd_new + end + converged || error("SLAYERParameters: Wd iteration failed to converge") + + chi_par_lmfp = (2.0 * R0 * vte) / (sqrt(π) * n_tor * sval_r * Wd) + chi_par = (chi_par_smfp * chi_par_lmfp) / (chi_par_smfp + chi_par_lmfp) + + if dc_type === :lar + return 0.5 * (-dr_val) * π^1.5 * + (chi_par / chi_perp)^0.25 * + sqrt((n_tor * sval_r) / (R0 * rs)) + elseif dc_type === :rfitzp + return -(sqrt(2.0) * π^1.5 * dr_val) / Wd + elseif dc_type === :toroidal + return 0.5 * (-dr_val) * π^1.5 * + (chi_par / chi_perp)^0.25 * dgeo_val + end + return 0.0 +end + +""" + slayer_parameters(; n_e, t_e, t_i, omega, omega_e, omega_i, + qval, sval_r, bt, rs, R0, mu_i, zeff, + chi_perp, chi_tor, + m, n, + dr_val=0.0, dgeo_val=0.0, + dc_type=:none, ising=0, + resistivity_model=SauterNeoModel(), + f_trap=nothing, nu_e_star=nothing, + R_major_eff=nothing, + lnLambda_form=:nrl) + -> SLAYERParameters + +Build a `SLAYERParameters` for one rational surface from dimensional +equilibrium and kinetic-profile inputs, in the Fitzpatrick two-fluid layer +parametrization (P_perp/P_tor/D_norm; the older magnetic/electron Prandtl +`pr`/`pe` and ρ_s-based `ds` parameters are not used). + +# Arguments + + - `n_e` -- electron density [m⁻³] + - `t_e` -- electron temperature [eV] + - `t_i` -- ion temperature [eV] + - `omega` -- toroidal rotation frequency at the surface [rad/s] + - `omega_e` -- electron diamagnetic frequency [rad/s] + - `omega_i` -- ion diamagnetic frequency [rad/s] + - `qval` -- safety factor q at the surface + - `sval_r` -- **r-based** magnetic shear r·(dq/dr)/q (Fitzpatrick). + Use `r_based_shear` to convert from ψ-based shear. + - `bt` -- toroidal field [T] + - `rs` -- minor radius at the surface [m] + - `R0` -- major radius [m] + - `mu_i` -- ion mass in proton-mass units (e.g. 2.0 for D) + - `zeff` -- effective charge + - `chi_perp`, `chi_tor` -- perpendicular / toroidal heat diffusivity [m²/s] + - `m`, `n` -- poloidal / toroidal mode numbers at the surface + - `dr_val`, `dgeo_val` -- inputs for the critical-Δ formula + - `dc_type` -- one of `:none`, `:lar`, `:rfitzp`, `:toroidal` + - `ising` -- singular-surface index for traceability + +# Resistivity kwargs + +The selected resistivity sets the resistive diffusion time +`τ_R = μ₀ r_s² / η` and hence the Lundquist number and every normalized +layer parameter derived from it. + + - `resistivity_model` -- `SauterNeoModel()` (default: Sauter 1999 F_33 + trapped-particle correction, the physically-appropriate choice for + H-mode tearing stability), `RedlNeoModel()` (improved high-ν* fit), + `SpitzerModel()` (Sauter 18a fit, no trapped-particle correction), or + `SpitzerHarmModel()` (Fitzpatrick Spitzer-Härm σ_∥ — the legacy SLAYER + closure; pair with `lnLambda_form=:wesson` to reproduce legacy τ_R + exactly). + - `f_trap` -- trapped-particle fraction at this surface. If not provided + with a neoclassical model, falls back to Lin-Liu-Miller ε-only form + with `ε = rs / (R_major_eff or R0)`. + - `nu_e_star` -- electron collisionality. If `nothing` with a neoclassical + model, computed from Sauter 1999 Eq. 18b using the same ε. + - `R_major_eff` -- ⟨R⟩ at the surface for the ν*_e formula (default `R0`). + - `lnLambda_form` -- `:nrl` (default), `:sauter`, or `:wesson` (legacy + form). + +# Sign convention for diamagnetic frequencies + +The diamagnetic normalization uses + +``` +Q_e = -tauk · ω_*e +Q_i = -tauk · ω_*i +``` + +For the standard plasma-physics input where ω_*e is tabulated negative and +ω_*i positive (electrons and ions drifting in opposite directions), this +produces `Q_e > 0, Q_i < 0`, matching the opposite-drift expectation of the +dispersion relation. +""" +function slayer_parameters(; + n_e::Real, t_e::Real, t_i::Real, + omega::Real, omega_e::Real, omega_i::Real, + qval::Real, sval_r::Real, bt::Real, + rs::Real, R0::Real, mu_i::Real, zeff::Real, + chi_perp::Real, chi_tor::Real, + m::Integer, n::Integer, + dr_val::Real=0.0, dgeo_val::Real=0.0, + dc_type::Symbol=:none, ising::Integer=0, + resistivity_model::NeoResistivityModel=SauterNeoModel(), + f_trap::Union{Real,Nothing}=nothing, + nu_e_star::Union{Real,Nothing}=nothing, + R_major_eff::Union{Real,Nothing}=nothing, + lnLambda_form::Symbol=:nrl) + + # Coulomb logarithm shared by the resistivity closure and τ_ee. + lnLamb = coulomb_log_e(n_e, t_e; form=lnLambda_form) + + # Parallel resistivity entering τ_R. The model selects the closure: + # SpitzerHarmModel — Fitzpatrick Spitzer-Härm σ_∥; with + # lnLambda_form=:wesson this is bit-identical to the legacy SLAYER η. + # SpitzerModel — Sauter 18a fit (legacy 1.65e-9 form under :wesson). + # SauterNeoModel / RedlNeoModel — F_33 trapped-particle correction + # using f_trap and ν*_e (from ResistGeometry or ε-only fallback). + if resistivity_model isa SpitzerModel && lnLambda_form === :wesson + # Preserve bit-identical legacy η diagnostic behaviour. + eta = 1.65e-9 * lnLamb / (t_e / 1e3)^1.5 + elseif resistivity_model isa Union{SpitzerModel,SpitzerHarmModel} + eta = eta_neoclassical(resistivity_model, n_e, t_e, zeff, + 0.0, 0.0; lnLamb=lnLamb) + else + R_eff = R_major_eff === nothing ? R0 : Float64(R_major_eff) + eps_here = clamp(rs / R_eff, 1e-6, 1.0 - 1e-6) + ft_here = f_trap === nothing ? trapped_fraction_eps(eps_here) : + Float64(f_trap) + nue_here = nu_e_star === nothing ? + nu_star_e(n_e, t_e, R_eff, eps_here, qval, zeff; + lnLamb=lnLamb) : + Float64(nu_e_star) + eta = eta_neoclassical(resistivity_model, n_e, t_e, zeff, + ft_here, nue_here; lnLamb=lnLamb) + end + + # Basic plasma quantities + tau = t_i / t_e + rho = mu_i * M_P * n_e + + # Electron-electron collision time (still needed by the χ_∥-matching + # critical-Δ regardless of the resistivity model). + tau_ee = tau_ee_spitzer_harm(n_e, t_e; lnLamb=lnLamb) + + # Characteristic field, Alfven speed, length scales, fundamental + # timescales. + rho_s = 1.02e-4 * sqrt(mu_i * t_e) / bt # ion Larmor [m] + d_i = sqrt((mu_i * M_P) / (n_e * E_CHG^2 * MU_0)) # ion skin depth [m] + + # Alfven time uses minor-radius shear directly (sval enters the + # b_l = (n/m) r_s sval bt / R0 expression and cancels through to + # tau_h = R0 sqrt(mu0 rho) / (n sval bt)). + tau_h = R0 * sqrt(MU_0 * rho) / (n * sval_r * bt) + # Resistive diffusion time τ_R = μ₀ r_s² / η (Fitzpatrick 2023), with + # the selected η closure — neoclassical by default — setting the + # Lundquist number. + tau_r = MU_0 * rs^2 / eta + + # Lundquist number and Q-conversion factor + lu = tau_r / tau_h + tauk = lu^(1.0 / 3.0) * tau_h # = Qconv + + # Normalized diamagnetic frequencies, Q = -tauk·ω; see docstring sign + # convention. + Q_e = -tauk * omega_e + Q_i = -tauk * omega_i + Q_e_minus_Q_i = Q_e - Q_i + # iota_e = Q_e/(Q_e - Q_i) is singular when the electron and ion + # diamagnetic frequencies are degenerate (ω_*e == ω_*i). The downstream + # Riccati coefficients divide by iota_e, so silently setting it to 0 (or + # Inf) produces NaN/Inf; surface the degeneracy as a clear error instead. + Q_e_minus_Q_i != 0 || + throw( + ArgumentError( + "slayer_parameters: Q_e == Q_i (degenerate " * + "electron/ion diamagnetic frequencies) makes " * + "iota_e = Q_e/(Q_e - Q_i) singular. Check the " * + "diamagnetic-frequency inputs ω_*e, ω_*i." + ) + ) + iota_e = Q_e / Q_e_minus_Q_i + + # Plasma beta and compressibility + lbeta = (5.0 / 3.0) * MU_0 * n_e * E_CHG * (t_e + t_i) / bt^2 + c_beta = sqrt(lbeta / (1.0 + lbeta)) + + # Effective Prandtl-like transport ratios + tau_perp = rs^2 / chi_perp + P_perp = tau_r / tau_perp + tau_tor = rs^2 / chi_tor + P_tor = tau_r / tau_tor + + # Normalized beta-related width and Δ-normalization + d_beta = c_beta * d_i + D_norm = (d_beta / rs) * lu^(1.0 / 3.0) * sqrt(tau / (1.0 + tau)) + delta_n = lu^(1.0 / 3.0) / rs + + # Critical-Δ offset from chi_parallel matching + dc_tmp = _solve_dc_tmp(; dc_type=dc_type, dr_val=dr_val, dgeo_val=dgeo_val, + chi_perp=chi_perp, t_e=t_e, zeff=zeff, + tau_ee=tau_ee, rs=rs, R0=R0, sval_r=sval_r, + n_tor=n) + + return SLAYERParameters(; + ising=ising, m=m, n=n, + tau=tau, lu=lu, c_beta=c_beta, D_norm=D_norm, + P_perp=P_perp, P_tor=P_tor, + Q_e=Q_e, Q_i=Q_i, iota_e=iota_e, + tauk=tauk, tau_r=tau_r, delta_n=delta_n, + rs=rs, R0=R0, bt=bt, sval_r=sval_r, + dr_val=dr_val, dgeo_val=dgeo_val, + eta=eta, d_beta=d_beta, + dc_tmp=dc_tmp, dc_type=dc_type + ) +end diff --git a/src/Tearing/InnerLayer/SLAYER/LayerThickness.jl b/src/Tearing/InnerLayer/SLAYER/LayerThickness.jl new file mode 100644 index 000000000..eb16a7639 --- /dev/null +++ b/src/Tearing/InnerLayer/SLAYER/LayerThickness.jl @@ -0,0 +1,171 @@ +# LayerThickness.jl +# +# Resistive inner-layer *width* (del_s) diagnostic for the SLAYER two-fluid +# drift-MHD slab layer (Fitzpatrick, Tearing Mode Dynamics in Tokamak +# Plasmas, IOP 2023; Park et al. 2022, Phys. Plasmas 29, 122505; Burgess +# et al. 2026). This is a distinct quantity from the matching index +# Δ = π/W' returned by the dispersion solver (Riccati.jl): it integrates a +# separate reduced Riccati ODE evaluated at the electron diamagnetic +# frequency Q_e and extracts a dimensionless width ratio delta_s/d_beta, +# which scales to a layer thickness in metres via the beta-weighted ion +# length d_beta. +# +# Q_i, c_beta, and the scanned Q are NOT referenced by this width +# formulation; the E/F coefficients depend only on Q_e, P_perp, P_tor, tau, +# and D_norm. + +using OrdinaryDiffEq + +# --------------------------------------------------------------------- +# Pre-computed q-independent constants for the del_s Riccati ODE. +# Normalisation block: +# Q_hat = (Q_e (1+tau)/tau) / D_norm^4 +# P_perp_hat = P_perp / D_norm^6 +# P_tor_hat = P_tor / D_norm^6 +# `one_plus = 1 + 1/tau`, `inv_c = 1/(1+1/tau)` recur in E, F and the +# boundary/extraction prefactor, so they are cached here too. +# --------------------------------------------------------------------- +struct _DelSConsts + Q_hat::Float64 # normalised electron diamagnetic frequency + Pperp_hat::Float64 # normalised perpendicular Prandtl number + Ptor_hat::Float64 # normalised toroidal Prandtl number + one_plus::Float64 # 1 + 1/tau + inv_c::Float64 # 1 / (1 + 1/tau) +end + +@inline function _build_dels_consts(p::SLAYERParameters) + one_plus = 1.0 + 1.0 / p.tau # (1+tau)/tau + D2 = p.D_norm * p.D_norm + D4 = D2 * D2 + D6 = D4 * D2 + return _DelSConsts( + (p.Q_e * one_plus) / D4, + p.P_perp / D6, + p.P_tor / D6, + one_plus, + 1.0 / one_plus + ) +end + +# Scalar ODE right-hand side dW/dq for the del_s Riccati. The E, F +# dispersion coefficients are q-dependent and complex (via the `im·Q_hat` +# terms); +# everything else is cached in `_DelSConsts`. +@inline function _dels_rhs(W::Number, c::_DelSConsts, q::Real) + q2 = q * q + q4 = q2 * q2 + E = -(c.Q_hat^2) * c.inv_c - + im * c.Q_hat * (c.Pperp_hat + c.Ptor_hat) * q2 + + c.Pperp_hat * c.Ptor_hat * q4 + F = c.Pperp_hat - im * c.Q_hat + c.one_plus * c.Ptor_hat * q2 + return W / q - (W * W) / q + (q * E) / F +end + +# Analytic Jacobian dF/dW: the q·E/F term is W-independent, leaving +# d/dW(W/q - W²/q) = 1/q - 2W/q. +@inline _dels_jac(W::Number, c::_DelSConsts, q::Real) = 1.0 / q - 2.0 * W / q + +""" + riccati_del_s(p::SLAYERParameters; + q_start=5*p.D_norm, q_min=1e-5, + reltol=1e-10, abstol=1e-10, maxiters=50_000, + solver=Rodas5P(autodiff=false)) -> ComplexF64 + +Solve the SLAYER `del_s` inner-layer Riccati ODE and return the +**dimensionless** layer-thickness ratio `δ_s / d_β` at one rational +surface (see file header for references). + +Integrates `dW/dq = W/q − W²/q + q·E/F` inward from `q_start = 5·D_norm` +to `q_min`, with asymptotic boundary value `W = −α·q_start² − 0.5`, +`α = √(P̂_⊥ / (1 + 1/τ))`. The result is +`−(π / √(1 + 1/τ)) · W′(q_min)`, evaluated from a single RHS call at the +inner endpoint. + +Returns `NaN + NaN·im` if the stiff integration does not converge (the +caller treats this as a missing diagnostic rather than a hard error). + +Multiply the result by `p.d_beta` to obtain the resistive layer +thickness in meters (see [`slayer_layer_thickness`](@ref)). +""" +function riccati_del_s(p::SLAYERParameters; + q_start::Real=5.0 * p.D_norm, + q_min::Real=1e-5, + reltol::Real=1e-10, + abstol::Real=1e-10, + maxiters::Integer=50_000, + solver=Rodas5P(; autodiff=false)) + if !(q_start > q_min) + @debug "riccati_del_s: degenerate integration span" q_start q_min p.D_norm + return ComplexF64(NaN, NaN) + end + + c = _build_dels_consts(p) + + # Asymptotic boundary condition at large q. P_hat is + # the normalised P_perp, i.e. c.Pperp_hat; α and W₀ are real. + α = sqrt(c.Pperp_hat * c.inv_c) + W0 = ComplexF64(-α * q_start^2 - 0.5) + + f = ODEFunction{false}(_dels_rhs; jac=_dels_jac) + prob = ODEProblem(f, W0, (q_start, q_min), c) + sol = solve(prob, solver; + reltol=reltol, abstol=abstol, maxiters=maxiters, + save_everystep=false, dense=false) + + if sol.retcode != ReturnCode.Success + @debug "SLAYER riccati_del_s did not return Success" sol.retcode + return ComplexF64(NaN, NaN) + end + + W_end = sol.u[end] + dW_end = _dels_rhs(W_end, c, q_min) + return -(π / sqrt(c.one_plus)) * dW_end +end + +""" + LayerWidths + +Resistive inner-layer length scales at one rational surface, in meters. +The primary quantity is `delta_s_m`, the resistive layer thickness from +the SLAYER `del_s` Riccati solve; `d_beta` is the β-weighted ion scale it +is built from, retained as a drift-scale reference. + +# Fields + + - `ising`, `m`, `n` -- surface index and mode numbers (traceability) + - `dels_db` -- dimensionless `δ_s / d_β` from [`riccati_del_s`](@ref) + - `delta_s` -- complex layer thickness `δ_s = dels_db · d_β` [m] + - `delta_s_m` -- `|δ_s|`, the resistive layer thickness [m] (primary) + - `d_beta` -- β-weighted ion scale `c_β·d_i` [m] (drift reference) + +`delta_s_m` should sit within a few orders of magnitude of `d_beta` for a +well-posed surface (`dels_db` is O(1)); a large gap flags a normalisation +or input problem. +""" +struct LayerWidths + ising::Int + m::Int + n::Int + dels_db::ComplexF64 + delta_s::ComplexF64 + delta_s_m::Float64 + d_beta::Float64 +end + +""" + slayer_layer_thickness(p::SLAYERParameters; kwargs...) -> LayerWidths + +Compute the resistive inner-layer thickness in meters at one rational +surface. + +Runs [`riccati_del_s`](@ref) for the dimensionless `δ_s / d_β` and scales +by `p.d_beta` to obtain `δ_s` in meters. Keyword arguments are forwarded +to `riccati_del_s`. +""" +function slayer_layer_thickness(p::SLAYERParameters; kwargs...) + dels_db = riccati_del_s(p; kwargs...) + delta_s = dels_db * p.d_beta + return LayerWidths(p.ising, p.m, p.n, + dels_db, delta_s, abs(delta_s), + p.d_beta) +end diff --git a/src/Tearing/InnerLayer/SLAYER/Riccati.jl b/src/Tearing/InnerLayer/SLAYER/Riccati.jl new file mode 100644 index 000000000..87781259b --- /dev/null +++ b/src/Tearing/InnerLayer/SLAYER/Riccati.jl @@ -0,0 +1,267 @@ +# Riccati.jl +# +# Inner-layer Δ via the Fitzpatrick two-fluid drift-MHD layer Riccati ODE +# (Fitzpatrick, Tearing Mode Dynamics in Tokamak Plasmas, IOP 2023; Park +# et al. 2022, Phys. Plasmas 29, 122505; Burgess et al. 2026), for the +# pressureless tearing channel (no parallel flow, pe = 0). The A, B, C +# coefficients, the dW/dp Riccati equation, the large-p asymptotic boundary +# conditions, the regime test D² > ι_e P_⊥/P_tor^(2/3), the small-p +# Δ = π/W' extraction, and the analytic Jacobian all follow that layer +# formulation; the full C(p) form is retained in every regime (no low-D +# reduction). +# +# The complex normalized growth rate `Q = ω + iγ` is passed directly to +# `solve_inner` rather than carried on the parameter struct. All other +# inputs come from `SLAYERParameters` (see `LayerParameters.jl`). +# +# Returns the parity-projected matching data as an `InnerLayerResponse` +# with only the `tearing` channel populated so callers can treat SLAYER and +# GGJ interchangeably through the shared `InnerLayerModel` interface. +# SLAYER's inner-layer dispersion relation produces a single complex Δ +# (the tearing channel); the interchange channel is zero. + +using OrdinaryDiffEq + +# --------------------------------------------------------------------- +# Coefficient evaluation for the two-fluid layer A, B, C terms (Fitzpatrick 2023). +# +# All x-independent quantities are bundled in `_RiccatiConsts` and computed +# once per `solve_inner` call (see line ~200). The hot RHS / Jacobian +# evaluations then access only the bundled constants and `x`, avoiding the +# tens of thousands of redundant complex muls/adds the prior code did. +# --------------------------------------------------------------------- + +# Pre-computed x-independent constants for the Fitzpatrick Riccati ODE. +# Derived from `(p::SLAYERParameters, Q::ComplexF64)` once per solve. Used as +# the integrator `params` so `_riccati_f_rhs` and `_riccati_f_jac` only need +# the x-dependent algebra. +struct _RiccatiConsts + Q_plus_iQe::ComplexF64 # constant part of denom = Q + iQe + x² + A::ComplexF64 # Q·(Q + iQi) — fB constant term + B::ComplexF64 # (Q + iQi)·(P_perp + P_tor) — fB · x² coefficient + C::Float64 # P_perp · P_tor — fB · x⁴ coefficient + E::ComplexF64 # (Q + iQi) · D² + P_perp — fC · x² coefficient + G::Float64 # P_tor · D² / iota_e — fC · x⁴ coefficient +end + +@inline function _build_riccati_consts(p::SLAYERParameters, Q::ComplexF64) + Q_plus_iQe = Q + im * p.Q_e + Q_plus_iQi = Q + im * p.Q_i + D2 = p.D_norm * p.D_norm + return _RiccatiConsts( + Q_plus_iQe, + Q * Q_plus_iQi, # A + Q_plus_iQi * (p.P_perp + p.P_tor), # B + p.P_perp * p.P_tor, # C + p.P_perp + Q_plus_iQi * D2, # E + p.P_tor * D2 / p.iota_e # G + ) +end + +# Riccati RHS coefficients fA, fA', fB, fC at point x. Receives the +# pre-built `_RiccatiConsts` so each call costs only a handful of muls/adds +# plus one complex division (the fA = p²/denom). +@inline function _riccati_f_coeffs(c::_RiccatiConsts, x::Real) + p2 = x * x + p4 = p2 * p2 + denom = c.Q_plus_iQe + p2 + + fA = p2 / denom + # Use the numerator-subtracts-twice-p² form rather than the algebraic + # identity 1 − 2·fA. The two are mathematically equal, but the + # integrator's adaptive stepping near marginal stability compounds + # ULP-level differences in fA' over thousands of steps; this form keeps + # the result tighter than the identity, which drifts to ~3e-3 relative + # (within abs-tolerance, but tighter is better). + fA_prime = (denom - 2 * p2) / denom + + fB = c.A + c.B * p2 + c.C * p4 + fC = c.Q_plus_iQe + c.E * p2 + c.G * p4 + + return fA, fA_prime, fB, fC +end + +# Scalar ODE right-hand side dW/dp for OrdinaryDiffEq. +# +# This is a 1-equation ODE — modeling W(x) as a `ComplexF64` scalar (rather +# than a 1-element `Vector{ComplexF64}`) lets the integrator's stage updates +# stay on the stack with no per-step allocations. SDIRK + Rosenbrock + BDF +# methods in OrdinaryDiffEq all support scalar `u`. +@inline function _riccati_f_rhs(W::Number, consts::_RiccatiConsts, x::Real) + fA, fA_prime, fB, fC = _riccati_f_coeffs(consts, x) + return -(fA_prime / x) * W - W * W / x + (fB / (fA * fC)) * (x * x * x) +end + +# Analytic Jacobian of the Riccati RHS. The full RHS has +# both the explicit (fA'/p, fB·p³) terms and the W² term; for the +# Jacobian only the W-dependent pieces survive. Returns a scalar — the +# 1×1 Jacobian of the scalar ODE. +@inline function _riccati_f_jac(W::Number, consts::_RiccatiConsts, x::Real) + p2 = x * x + denom = consts.Q_plus_iQe + p2 + fA_prime = (denom - 2 * p2) / denom + return -(fA_prime / x) - 2 * W / x +end + +# --------------------------------------------------------------------- +# Boundary-condition selection (large-p asymptotics, Fitzpatrick 2023). +# Two regimes selected by D_norm² vs. +# iota_e·P_perp/P_tor^(2/3). +# --------------------------------------------------------------------- + +# Returns (p_start, W_at_p_start, branch) where `branch ∈ (:large_D, :small_D)`. +function _riccati_f_initial(p::SLAYERParameters, Q::ComplexF64; + p_floor::Real=6.0) + D2 = p.D_norm * p.D_norm + Pperp_over_Ptor23 = p.P_perp / p.P_tor^(2 / 3) + + if D2 > p.iota_e * Pperp_over_Ptor23 + # Large-D_norm branch. In ((P_tor·D²)/(iota_e·P_tor·P_perp))^(1/4) + # the P_tor factor cancels — written out for traceability. + p_start = max(((p.P_tor * D2) / (p.iota_e * p.P_tor * p.P_perp))^0.25, + p_floor) + + ak = -(Q + im * p.Q_e) + bk = (p.iota_e * p.P_perp * p.P_tor) / (p.P_tor * D2) + ck = bk * (1 + (Q + im * p.Q_i) * ((p.P_tor + p.P_perp) / + (p.P_tor * p.P_perp)) + - + (p.P_perp + (Q + im * p.Q_i) * D2) * + (p.iota_e / (p.P_tor * D2))) + sqrt_bk = sqrt(bk) + xk = (ck - sqrt_bk * (1 - sqrt_bk * ak)) / (2 * sqrt_bk) + + W_bound = xk - sqrt_bk * p_start + return p_start, W_bound, :large_D + else + # Small-D_norm branch. + p_start = max(1.0 / p.P_tor^(1 / 6), p_floor) + + ak = -(Q + im * p.Q_e) + bk = ComplexF64(p.P_tor) # promoted to ComplexF64 for sqrt below + ck = -im * (p.Q_e - p.Q_i) * (p.P_tor / p.P_perp) + (Q + im * p.Q_i) + sqrt_bk = sqrt(bk) + xk = (ak * bk - ck) / (2 * sqrt_bk) + + W_bound = -1.0 + xk * p_start - sqrt_bk * p_start^3 + return p_start, W_bound, :small_D + end +end + +# --------------------------------------------------------------------- +# solve_inner dispatch for SLAYERModel{:fitzpatrick}. +# --------------------------------------------------------------------- + +""" + solve_inner(::SLAYERModel{:fitzpatrick}, + p::SLAYERParameters, Q::Number; + pmin=1e-6, p_floor=6.0, + reltol=1e-10, abstol=1e-10, + maxiters=50_000, + solver=Rodas5P(autodiff=false)) -> InnerLayerResponse + +Solve the Fitzpatrick SLAYER inner-layer Riccati ODE for the complex +normalized growth rate `Q = ω + iγ`. Returns an `InnerLayerResponse` with +`tearing = Δ` and `interchange = 0`, so the result is interface-compatible +with `GGJModel.solve_inner` (which populates both channels); SLAYER's +pressureless layer produces only the tearing channel. + +# Algorithm + +Implements the Fitzpatrick two-fluid drift-MHD layer formulation +(Fitzpatrick 2023; Park et al. 2022) for the pressureless tearing channel +(no parallel flow, pe = 0). Integrates +`dW/dp = -(fA'/p)·W − W²/p + (fB/(fA·fC))·p³` from a large `p_start` +(selected by `_riccati_f_initial` according to whether +`D_norm² ≷ iota_e·P_perp/P_tor^(2/3)`) inward to `pmin`, then computes +`Δ = π / W'(pmin)` from a single RHS evaluation at the inner endpoint. + +# Solver + +Default `Rodas5P(autodiff=false)` (Rosenbrock, stiff-friendly). The +analytic Jacobian wired via the `ODEFunction(jac=...)` field accelerates +the Newton solves. AD is disabled because complex `Dual` propagation +through the chained denominators incurs allocations in this regime; +finite-difference fallback is fast enough for the 1-equation system. + +**Note on solver swaps:** sub-percent floating-point differences between +ODE solvers cascade through the outer AMR's cell-flagging decisions +(`ContourSearchAMR.jl::_crosses_zero`) and produce **structurally +different** AMR cell trees. Swapping the ODE solver has been observed to +change the classified root/pole inventory substantially even when the +most-unstable γ agrees to within ~1e-5 relative. So solver choice is not +just a per-call optimization — it affects the downstream root/pole +inventory. Future solver swaps need to be validated against the topology +fields (`n_valid_roots`, `n_poles`), not just γ. + +# Keyword arguments + + - `pmin` -- inner-layer cutoff (default 1e-6) + - `p_floor` -- floor on `p_start` (default 6.0) + - `reltol`,`abstol`,`maxiters` -- stiff-solver tolerance/iteration limits + - `solver` -- any OrdinaryDiffEq algorithm; pass `Tsit5()` for the + non-stiff path (rarely needed here) +""" +function solve_inner(::SLAYERModel{:fitzpatrick}, + p::SLAYERParameters, Q::Number; + pmin::Real=1e-6, + p_floor::Real=6.0, + reltol::Real=1e-10, + abstol::Real=1e-10, + maxiters::Integer=50_000, + solver=Rodas5P(; autodiff=false)) + # Convention bridge between our scan plane and the layer eigenvalue. + # We scan in the Park plane `Q = ω + iγ` (+γ on the +imag axis; Park + # et al. 2022). Fitzpatrick's normalized layer eigenvalue is + # `ĝ = (γ − iω)·τ_k` in the co-rotating frame (Fitzpatrick 2023: + # γ = Re(ĝ)/τ_k, ω = −Im(ĝ)/τ_k), so +γ sits on his +real axis. The two + # planes differ by a pure −90° rotation, `ĝ = −i·Q` — relabeling which + # axis is growth, no physics. + # + # The layer ODE coefficients are analytic in ĝ with Q_e, Q_i, D, P_⊥, + # P_φ all real, so Schwarz reflection gives `Δ̂_s(conj ĝ) = conj(Δ̂_s(ĝ))`. + # We feed `Q_c = i·conj(Q) = conj(−i·Q) = conj(ĝ)`, hence evaluate + # `conj(Δ̂_s(ĝ))`. Conjugation maps zeros to zeros, so the extracted + # growth-rate roots are identical to those of Δ̂_s(ĝ); it only reflects + # the off-root residual surface, fixing the integration-path orientation + # so |Δ| contours are consistent across the scan plane. + Q_c = im * conj(ComplexF64(Q)) + + # Boundary condition at p_start + p_start, W_bound, _ = _riccati_f_initial(p, Q_c; p_floor=p_floor) + + # Pre-compute x-independent constants ONCE; the integrator threads this + # through to every RHS / Jacobian call instead of recomputing per-step. + rhs_params = _build_riccati_consts(p, Q_c) + + # Scalar `u0`: the ODE state is a single `ComplexF64`, not a 1-element + # vector. OrdinaryDiffEq supports scalar problems via the out-of-place + # form (`ODEFunction{false}`). This eliminates the per-step heap- + # allocation of intermediate `dW` vectors that the in-place form + # incurred for every stage of every accepted/rejected step. + u0 = ComplexF64(W_bound) + f = ODEFunction{false}(_riccati_f_rhs; jac=_riccati_f_jac) + prob = ODEProblem(f, u0, (p_start, pmin), rhs_params) + sol = solve(prob, solver; + reltol=reltol, abstol=abstol, maxiters=maxiters, + save_everystep=false, dense=false) + + if sol.retcode != ReturnCode.Success + # Unconverged solve: return a NaN sentinel so the dispersion scan / AMR + # flags this Q-cell (via its isfinite checks) rather than ingesting a + # bogus finite Δ built from an unconverged W_end. @debug not @warn: in a + # dense Q-plane scan failures cluster near poles and would flood the log. + @debug "SLAYER Riccati integration did not return Success" sol.retcode + return InnerLayerResponse(ComplexF64(NaN, NaN), zero(ComplexF64)) + end + + # Δ = π / W'(pmin) — single RHS evaluation at the inner endpoint + W_end = sol.u[end] + dW_end = _riccati_f_rhs(W_end, rhs_params, pmin) + Δ::ComplexF64 = π / dW_end + + # Fitzpatrick / pressureless SLAYER has no interchange channel + # (the Δ_− / even-parity matching quantity is identically zero in + # the pressureless limit), so populate only the tearing field. + return InnerLayerResponse(Δ, zero(ComplexF64)) +end diff --git a/src/Tearing/InnerLayer/SLAYER/SLAYER.jl b/src/Tearing/InnerLayer/SLAYER/SLAYER.jl new file mode 100644 index 000000000..ece897c15 --- /dev/null +++ b/src/Tearing/InnerLayer/SLAYER/SLAYER.jl @@ -0,0 +1,62 @@ +# SLAYER.jl +# +# SLAYER (Slab Layer) two-fluid drift-MHD inner-layer model (Fitzpatrick, +# Tearing Mode Dynamics in Tokamak Plasmas, IOP 2023; Park et al. 2022, +# Phys. Plasmas 29, 122505; Burgess et al. 2026). The dispersion path uses +# the Fitzpatrick layer formulation — P_perp / P_tor transport, c_beta +# compressibility, D_norm normalized ion-skin scale, two-fluid drift +# coupling via Q_e, Q_i, iota_e (see `Riccati.jl`). +# +# A separate `del_s` layer-thickness diagnostic (`slayer_layer_thickness` in +# `LayerThickness.jl`) returns the resistive layer width in meters at each +# rational surface. +# +# Type-parameter `S` of `SLAYERModel{S}` selects the Riccati formulation +# used for the dispersion relation; only `:fitzpatrick` is implemented. +# +# `Q = ω + iγ` is passed directly to `solve_inner` rather than stored on +# the parameter struct. + +module SLAYER + +using LinearAlgebra +using StaticArrays + +import ..InnerLayerModel, ..InnerLayerResponse, ..solve_inner, ..InnerLayerParameters +using ...Utilities.PhysicalConstants +using ...Utilities.NeoclassicalResistivity +using ...Utilities.NeoclassicalResistivity: NeoResistivityModel, SpitzerModel, + SpitzerHarmModel, SauterNeoModel, RedlNeoModel, + coulomb_log_e, eta_spitzer, tau_ee_spitzer_harm, eta_spitzer_harm, + trapped_fraction_eps, nu_star_e, eta_neoclassical + +""" + SLAYERModel{S} <: InnerLayerModel + +SLAYER inner-layer model selector. The type parameter `S` selects the +Riccati formulation: + + - `:fitzpatrick` -- P_perp/P_tor Fitzpatrick formulation (default; + Fitzpatrick 2023 two-fluid drift-MHD layer) + +Future dispersion variants (e.g. `:standard`) may be added but are not +currently implemented. The `del_s` formulation is exposed separately as +the layer-thickness diagnostic [`slayer_layer_thickness`](@ref), not as +a dispersion `solve_inner` path. +""" +struct SLAYERModel{S} <: InnerLayerModel end + +SLAYERModel(; variant::Symbol=:fitzpatrick) = SLAYERModel{variant}() + +include("LayerParameters.jl") +include("Riccati.jl") +include("LayerThickness.jl") +include("LayerInputs.jl") + +export SLAYERModel, SLAYERParameters, slayer_parameters +export r_based_shear +export riccati_del_s, slayer_layer_thickness, LayerWidths +export surface_minor_radius, surface_da_dpsi, build_slayer_inputs +export NeoResistivityModel, SpitzerModel, SpitzerHarmModel, SauterNeoModel, RedlNeoModel + +end # module SLAYER diff --git a/src/Tearing/Runner/Control.jl b/src/Tearing/Runner/Control.jl new file mode 100644 index 000000000..17128a3d6 --- /dev/null +++ b/src/Tearing/Runner/Control.jl @@ -0,0 +1,268 @@ +# Control.jl +# +# `SLAYERControl` holds every user-facing knob that drives the SLAYER +# growth-rate analysis. Populated either directly via the `@kwdef` +# constructor or by parsing the `[SLAYER]` (and nested `[SLAYER.*]`) +# section(s) of a `gpec.toml`. + +""" + SLAYERControl + +Configuration for the SLAYER tearing-mode analysis. All fields are +user-facing: read from the `[SLAYER]` TOML section of a `gpec.toml` via +`slayer_control_from_toml`, or built directly via the `@kwdef` keyword +constructor. + +# Core toggles + + - `enabled` -- run the analysis at all (default `false`) + - `inner_model` -- `:slayer_fitzpatrick` (default), `:ggj_shooting`, or + `:ggj_galerkin` + - `scan_mode` -- `:amr` (default) or `:brute_force` + - `coupling_mode` -- `:uncoupled` (default, per-surface) or `:coupled` + (multi-surface determinant) + - `dc_type` -- critical-Δ offset selector, one of `:none`, `:lar`, + `:rfitzp`, `:toroidal` (χ_‖-matching critical-Δ formulas, + Connor-Hastie-Helander 2015) + - `msing_max` -- number of surfaces to include in the coupled + determinant (default 3; capped at `length(sings)` at runtime) + +# Physics knobs + + - `bt` -- toroidal field [T]. `nothing` → use `equil.config.b0exp` + - `mu_i` -- ion mass in proton-mass units (default 2.0 for D) + - `zeff` -- effective charge + - `chi_perp`, `chi_tor` -- fallback perpendicular / toroidal heat + diffusivity [m²/s], used only when the kinetic file carries no usable + `chi_e`/`chi_phi` profile (dataset absent or all-zero); otherwise the + file's χ⊥(ψ)/χ_φ(ψ) take precedence + - `dr_val`, `dgeo_val` -- critical-Δ formula inputs. `nothing` (default) + auto-derives them from the equilibrium: `dr_val` from the resistive + interchange index `D_R = E + F + H²` at each surface, `dgeo_val` from the + toroidal geometric factor (required only by `dc_type=:toroidal`). Supply a + scalar only to override the auto-derivation; an explicit `0.0` disables the + critical-Δ offset (Δ_crit ≡ 0) + - `theta_sample` -- poloidal angle at which to sample minor radius + (default 0.0, outboard midplane) + - `resistivity_model` -- η closure setting τ_R = μ₀r_s²/η: `:sauter` + (default, neoclassical F_33), `:redl`, `:spitzer` (Sauter 18a, no + trapped correction), or `:spitzer_harm` (legacy Fitzpatrick σ_∥) + - `lnLambda_form` -- Coulomb-log form: `:nrl` (default), `:sauter`, or + `:wesson` (legacy; pair with `:spitzer_harm` to reproduce old SLAYER) + +# Scan grid (used for both brute-force and AMR initial mesh) + + - `Q_re_range`, `Q_im_range` -- box in the normalized Q plane + - `nre`, `nim` -- grid resolution along each axis + +# AMR refinement + + - `amr_passes` -- max refinement levels + - `amr_max_cells` -- hard safety cap + +# Growth-rate-extraction filters + + - `pole_threshold` -- threshold for pole classification (default 10) + - `pole_threshold_adaptive` -- if true, pole_threshold is OVERRIDDEN per + scan with `10 × median(|Δ|)` over the scan grid. The median is robust + where `|mean(Δ)|` is not: it resists inflation from the near-pole + samples that dominate a mean, and avoids the phase-cancellation that + can shrink `|mean|`. Useful when |Δ| spans 8+ orders of magnitude + (e.g. SLAYER scans where the hardcoded 10.0 default is too restrictive + and classifies all intersections as poles). + - `filter_above_poles` -- discard roots above the highest pole γ + - `filter_outside_re` -- condition the above-pole filter on the +γ + step exiting the Re(Δ)=0 contour loop + +# Kinetic-profile source + +SLAYER reads kinetic profiles through the shared `Equilibrium.read_kinetic_file` +reader (the same standardized object used by the kinetic/NTV physics), so +there is one consistent interface for resistive and kinetic profiles. + + - `profile_file` -- path to a kinetic-profile file (relative to the run + dir), required when SLAYER is enabled. HDF5 (`.h5`) files use the GPEC + kinetic schema and may carry `chi_e` (χ⊥) and `chi_phi` (χ_φ); ASCII + tables are also accepted but carry no χ. When a χ dataset is absent or + all-zero, the scalar `chi_perp`/`chi_tor` fallbacks below are used (so a + file can keep the χ keys set to 0 to defer to the scalars). + - `profile_group` -- group within the HDF5 file (default `"/"`) + +# Output control + + - `store_scan` -- write the full Q/Δ scan grid to HDF5. `false` by + default to keep the output file small. +""" +@kwdef struct SLAYERControl + enabled::Bool = false + + inner_model::Symbol = :slayer_fitzpatrick + scan_mode::Symbol = :amr + coupling_mode::Symbol = :uncoupled + dc_type::Symbol = :none + msing_max::Int = 3 + + bt::Union{Float64,Nothing} = nothing + mu_i::Float64 = 2.0 + zeff::Float64 = 1.0 + chi_perp::Float64 = 1.0 + chi_tor::Float64 = 1.0 + dr_val::Union{Float64,Nothing} = nothing + dgeo_val::Union{Float64,Nothing} = nothing + theta_sample::Float64 = 0.0 + resistivity_model::Symbol = :sauter + lnLambda_form::Symbol = :nrl + + Q_re_range::Tuple{Float64,Float64} = (-10.0, 10.0) + Q_im_range::Tuple{Float64,Float64} = (-2.0, 5.0) + nre::Int = 41 + nim::Int = 31 + + amr_passes::Int = 4 + amr_max_cells::Int = 10_000_000 + + # Multi-box stripe layout. When non-empty, `scan_mode=:amr` dispatches to + # `multi_box_amr_scan` instead of single-box `amr_scan`. Each entry is a + # dimensionless Q-space rectangle as `(omega_lo, omega_hi, gamma_lo, + # gamma_hi)`. Activity criteria fire on Re(Δ) sign change, Im(Δ) sign + # change, OR |Δ| ≥ pre-screen pole threshold. A typical 25-kHz stripe + # layout for DIII-D-style equilibria (with kHz/Q given by the per-surface + # τ_k) is built externally by the driver, converted to Q-units, and + # passed in here. + boxes::Vector{NTuple{4,Float64}} = NTuple{4,Float64}[] + multi_box_prescreen_n::Int = 25 # pre-screen grid resolution per box + + pole_threshold::Float64 = 10.0 + pole_threshold_adaptive::Bool = false + filter_above_poles::Bool = true + filter_outside_re::Bool = true + gap_kHz_threshold::Float64 = 1.0 # forwarded to find_growth_rates + # Refine each contour-intersection root to the true zero of the dispersion + # residual (isolate-then-polish). Makes the extracted γ resolution- and + # thread-independent; adds ~a handful of residual evals per root. Set false + # to report the raw marching-squares estimate. Applies to the UNCOUPLED + # (per-surface scalar) path; the coupled determinant is ill-conditioned and + # uses raw contour extraction regardless. + polish_roots::Bool = true + # Validity gate (uncoupled + polish_roots only): drop a root whose polished + # |residual| is not below validity_rtol × median(|Δ|) — a contour near-miss + # / failed-Δ'-BVP surface, not a real root. Flagged `:spurious`. + validity_rtol::Float64 = 1e-3 + + profile_file::String = "" + profile_group::String = "/" + + store_scan::Bool = false +end + +const _VALID_INNER_MODELS = (:slayer_fitzpatrick, :ggj_shooting, :ggj_galerkin) +const _VALID_SCAN_MODES = (:amr, :brute_force) +const _VALID_COUPLING_MODES = (:uncoupled, :coupled) +const _VALID_DC_TYPES = (:none, :lar, :rfitzp, :toroidal) +const _VALID_RESISTIVITY_MODELS = (:sauter, :redl, :spitzer, :spitzer_harm) +const _VALID_LNLAMBDA_FORMS = (:nrl, :sauter, :wesson) + +function validate(ctrl::SLAYERControl) + ctrl.inner_model in _VALID_INNER_MODELS || + throw(ArgumentError("SLAYERControl: inner_model=$(ctrl.inner_model) " * + "not in $(_VALID_INNER_MODELS)")) + ctrl.scan_mode in _VALID_SCAN_MODES || + throw(ArgumentError("SLAYERControl: scan_mode=$(ctrl.scan_mode) " * + "not in $(_VALID_SCAN_MODES)")) + ctrl.coupling_mode in _VALID_COUPLING_MODES || + throw(ArgumentError("SLAYERControl: coupling_mode=$(ctrl.coupling_mode) " * + "not in $(_VALID_COUPLING_MODES)")) + ctrl.dc_type in _VALID_DC_TYPES || + throw(ArgumentError("SLAYERControl: dc_type=$(ctrl.dc_type) " * + "not in $(_VALID_DC_TYPES)")) + ctrl.resistivity_model in _VALID_RESISTIVITY_MODELS || + throw(ArgumentError("SLAYERControl: resistivity_model=$(ctrl.resistivity_model) " * + "not in $(_VALID_RESISTIVITY_MODELS)")) + ctrl.lnLambda_form in _VALID_LNLAMBDA_FORMS || + throw(ArgumentError("SLAYERControl: lnLambda_form=$(ctrl.lnLambda_form) " * + "not in $(_VALID_LNLAMBDA_FORMS)")) + ctrl.msing_max >= 1 || + throw(ArgumentError("SLAYERControl: msing_max=$(ctrl.msing_max) must be ≥ 1")) + ctrl.nre >= 2 && ctrl.nim >= 2 || + throw(ArgumentError("SLAYERControl: nre and nim must both be ≥ 2")) + ctrl.amr_passes >= 0 || + throw(ArgumentError("SLAYERControl: amr_passes must be ≥ 0")) + return ctrl +end + +# Helper: coerce range-like values to a 2-tuple of Float64 +_as_range(x::NTuple{2,<:Real}) = (Float64(x[1]), Float64(x[2])) +_as_range(x::AbstractVector) = begin + length(x) == 2 || throw(ArgumentError("range must be length 2, got length $(length(x))")) + (Float64(x[1]), Float64(x[2])) +end + +""" + slayer_control_from_toml(section::AbstractDict) -> SLAYERControl + +Parse a `[SLAYER]` TOML section into a `SLAYERControl`. Known nested +subsections (`[SLAYER.scan_grid]`, `[SLAYER.amr]`, +`[SLAYER.growth_rate_filter]`) are flattened into the top-level fields. +Unknown keys raise an error so typos don't silently produce defaults. +""" +function slayer_control_from_toml(section::AbstractDict) + # Flatten nested sections into the top-level key dictionary + flat = Dict{String,Any}() + for (k, v) in section + if k == "scan_grid" && v isa AbstractDict + # Promote scan_grid fields to top-level + haskey(v, "Q_re_range") && (flat["Q_re_range"] = v["Q_re_range"]) + haskey(v, "Q_im_range") && (flat["Q_im_range"] = v["Q_im_range"]) + haskey(v, "nre") && (flat["nre"] = v["nre"]) + haskey(v, "nim") && (flat["nim"] = v["nim"]) + elseif k == "amr" && v isa AbstractDict + haskey(v, "passes") && (flat["amr_passes"] = v["passes"]) + haskey(v, "max_cells") && (flat["amr_max_cells"] = v["max_cells"]) + elseif k == "growth_rate_filter" && v isa AbstractDict + haskey(v, "pole_threshold") && (flat["pole_threshold"] = v["pole_threshold"]) + haskey(v, "filter_above_poles") && (flat["filter_above_poles"] = v["filter_above_poles"]) + haskey(v, "filter_outside_re") && (flat["filter_outside_re"] = v["filter_outside_re"]) + else + flat[k] = v + end + end + + # Validate keys against the struct fields + field_names = Set(String.(fieldnames(SLAYERControl))) + unknown = [k for k in keys(flat) if !(k in field_names)] + isempty(unknown) || + throw(ArgumentError("slayer_control_from_toml: unknown keys " * + "$(unknown) in [SLAYER] section. Known: " * + "$(sort(collect(field_names))).")) + + # Coerce types where needed + kwargs = Dict{Symbol,Any}() + for (k, v) in flat + sym = Symbol(k) + if sym in (:inner_model, :scan_mode, :coupling_mode, :dc_type, + :resistivity_model, :lnLambda_form) + kwargs[sym] = v isa Symbol ? v : Symbol(String(v)) + elseif sym in (:Q_re_range, :Q_im_range) + kwargs[sym] = _as_range(v) + elseif sym in (:bt, :dr_val, :dgeo_val) + # Allow explicit nothing (auto-derive) or a number (override) + kwargs[sym] = v === nothing ? nothing : Float64(v) + elseif sym === :boxes + # `boxes` is a Vector{NTuple{4,Float64}}; from TOML this comes + # in as a list of 4-element arrays. Coerce each. + kwargs[sym] = NTuple{4,Float64}[ + let bb = collect(Float64, b) + length(bb) == 4 || + throw(ArgumentError("SLAYER.boxes entry must have 4 " * + "elements (omega_lo, omega_hi, " * + "gamma_lo, gamma_hi); got $b")) + (bb[1], bb[2], bb[3], bb[4]) + end + for b in v + ] + else + kwargs[sym] = v + end + end + return validate(SLAYERControl(; kwargs...)) +end diff --git a/src/Tearing/Runner/HDF5Output.jl b/src/Tearing/Runner/HDF5Output.jl new file mode 100644 index 000000000..107a3be1a --- /dev/null +++ b/src/Tearing/Runner/HDF5Output.jl @@ -0,0 +1,238 @@ +# HDF5Output.jl +# +# Write a `SLAYERResult` into an HDF5 group. Designed to be called by the +# existing `PerturbedEquilibrium.write_outputs_to_HDF5` path — the +# top-level GPEC runner wires that up; this file only defines the pure +# writer. +# +# Output layout (relative to the parent group the caller provides): +# +# slayer/ +# ├── settings/ -- control snapshot (strings, scalars) +# ├── per_surface/ -- struct-of-arrays for SLAYERParameters fields +# │ ├── psi, q, q1, ... +# │ └── ... +# ├── roots/ -- Q_root (real, imag), omega_Hz, gamma_Hz +# ├── diagnostics/ -- all_valid_roots, poles, filtered_roots +# │ (flat-plus-offsets ragged encoding) +# └── scan/ -- optional: full Q/Δ scan data + +using HDF5 + +""" + write_slayer_hdf5!(parent::Union{HDF5.File,HDF5.Group}, + result::SLAYERResult) + +Write `result` into a `slayer/` subgroup of `parent`. The subgroup is +created if missing and overwritten if it already exists (keeps the +output file reproducible across reruns). +""" +function write_slayer_hdf5!(parent::Union{HDF5.File,HDF5.Group}, + result::SLAYERResult) + if haskey(parent, "slayer") + delete_object(parent, "slayer") + end + g = create_group(parent, "slayer") + g["enabled"] = Int(result.enabled) + + result.enabled || return g # nothing else to write + + _write_settings!(g, result.control) + _write_per_surface!(g, result.params, result.dp_matrix) + _write_roots!(g, result) + _write_layer_widths!(g, result.layer_widths) + _write_diagnostics!(g, result) + if result.control.store_scan && !isempty(result.scan_data) + _write_scan_data!(g, result) + end + return g +end + +# ---------- settings snapshot ---------- +function _write_settings!(g, ctrl::SLAYERControl) + s = create_group(g, "settings") + s["inner_model"] = String(ctrl.inner_model) + s["scan_mode"] = String(ctrl.scan_mode) + s["coupling_mode"] = String(ctrl.coupling_mode) + s["dc_type"] = String(ctrl.dc_type) + s["msing_max"] = ctrl.msing_max + s["bt"] = ctrl.bt === nothing ? NaN : ctrl.bt + s["mu_i"] = ctrl.mu_i + s["zeff"] = ctrl.zeff + s["chi_perp"] = ctrl.chi_perp + s["chi_tor"] = ctrl.chi_tor + # NaN sentinel records the auto-derive (nothing) setting in a numeric dataset. + s["dr_val"] = ctrl.dr_val === nothing ? NaN : ctrl.dr_val + s["dgeo_val"] = ctrl.dgeo_val === nothing ? NaN : ctrl.dgeo_val + s["theta_sample"] = ctrl.theta_sample + s["resistivity_model"] = String(ctrl.resistivity_model) + s["lnLambda_form"] = String(ctrl.lnLambda_form) + s["Q_re_range"] = collect(ctrl.Q_re_range) + s["Q_im_range"] = collect(ctrl.Q_im_range) + s["nre"] = ctrl.nre + s["nim"] = ctrl.nim + s["amr_passes"] = ctrl.amr_passes + s["amr_max_cells"] = ctrl.amr_max_cells + # Multi-box stripe layout: flatten Vector{NTuple{4}} to an N×4 matrix + # (empty → 0×4) so a rerun can reconstruct the exact scan boxes. + s["boxes"] = isempty(ctrl.boxes) ? Matrix{Float64}(undef, 0, 4) : + permutedims(reduce(hcat, collect.(ctrl.boxes))) + s["multi_box_prescreen_n"] = ctrl.multi_box_prescreen_n + s["pole_threshold"] = ctrl.pole_threshold + s["pole_threshold_adaptive"] = Int(ctrl.pole_threshold_adaptive) + s["filter_above_poles"] = Int(ctrl.filter_above_poles) + s["filter_outside_re"] = Int(ctrl.filter_outside_re) + s["gap_kHz_threshold"] = ctrl.gap_kHz_threshold + s["polish_roots"] = Int(ctrl.polish_roots) + s["validity_rtol"] = ctrl.validity_rtol + s["profile_file"] = ctrl.profile_file + s["profile_group"] = ctrl.profile_group + s["store_scan"] = Int(ctrl.store_scan) + return nothing +end + +# ---------- per-surface layer parameters ---------- +function _write_per_surface!(g, params::AbstractVector{SLAYERParameters}, + dp_matrix::Matrix{ComplexF64}) + ps = create_group(g, "per_surface") + + # Scalar struct-of-arrays for all Float64 / Int fields + for fname in (:ising, :m, :n) + ps[String(fname)] = Int[getfield(p, fname) for p in params] + end + for fname in (:tau, :lu, :c_beta, :D_norm, :P_perp, :P_tor, + :Q_e, :Q_i, :iota_e, + :tauk, :tau_r, :delta_n, + :rs, :R0, :bt, :sval_r, :dr_val, :dgeo_val, + :eta, :d_beta, :dc_tmp) + ps[String(fname)] = Float64[getfield(p, fname) for p in params] + end + # Store dc_type per-surface as string array + ps["dc_type"] = String[String(p.dc_type) for p in params] + + # Full Δ' matrix, split real/imag + dp = create_group(ps, "dp_matrix") + dp["real"] = real.(dp_matrix) + dp["imag"] = imag.(dp_matrix) + return nothing +end + +# GGJ per-surface parameters carry the geometric coefficients (E,F,G,H,K,M) +# and resistive/Alfvén times rather than the SLAYER dimensionless set. +function _write_per_surface!(g, params::AbstractVector{GGJParameters}, + dp_matrix::Matrix{ComplexF64}) + ps = create_group(g, "per_surface") + ps["ising"] = Int[p.ising for p in params] + for fname in (:E, :F, :G, :H, :K, :M, :taua, :taur, :v1) + ps[String(fname)] = Float64[getfield(p, fname) for p in params] + end + dp = create_group(ps, "dp_matrix") + dp["real"] = real.(dp_matrix) + dp["imag"] = imag.(dp_matrix) + return nothing +end + +# ---------- eigenvalue roots ---------- +function _write_roots!(g, r::SLAYERResult) + roots = create_group(g, "roots") + roots["Q_root_real"] = real.(r.Q_root) + roots["Q_root_imag"] = imag.(r.Q_root) + roots["omega_Hz"] = r.omega_Hz + roots["gamma_Hz"] = r.gamma_Hz + # `no_root[k] == 1` flags entries where the extraction found NO usable + # root (Q_root is NaN; omega_Hz/gamma_Hz are 0 placeholders, not a true + # γ≈0 result). Aligned element-wise with Q_root/omega_Hz/gamma_Hz. + extractions = r.coupled_extraction !== nothing ? [r.coupled_extraction] : + r.per_surface_extraction + roots["no_root"] = Int[(:no_root in gr.warning_flags) ? 1 : 0 + for gr in extractions] + return nothing +end + +# ---------- resistive layer thickness (del_s Riccati) ---------- +function _write_layer_widths!(g, widths::Vector{LayerWidths}) + lw = create_group(g, "layer_widths") + for fname in (:ising, :m, :n) + lw[String(fname)] = Int[getfield(w, fname) for w in widths] + end + # Dimensionless del_s/d_beta and the complex layer thickness, split re/im. + lw["dels_db_real"] = Float64[real(w.dels_db) for w in widths] + lw["dels_db_imag"] = Float64[imag(w.dels_db) for w in widths] + lw["delta_s_real"] = Float64[real(w.delta_s) for w in widths] + lw["delta_s_imag"] = Float64[imag(w.delta_s) for w in widths] + # Physical thickness [m] and the β-weighted ion drift scale [m]. + lw["delta_s_m"] = Float64[w.delta_s_m for w in widths] + lw["d_beta"] = Float64[w.d_beta for w in widths] + return nothing +end + +# ---------- diagnostics: valid roots, poles, filtered roots ---------- +function _write_diagnostics!(g, r::SLAYERResult) + diag = create_group(g, "diagnostics") + # Uncoupled: one GrowthRateResult per surface. Coupled: one total. + extractions = if r.coupled_extraction !== nothing + [r.coupled_extraction] + else + r.per_surface_extraction + end + + _write_ragged_complex!(diag, "valid_roots", + [gr.valid_roots for gr in extractions]) + _write_ragged_complex!(diag, "poles", + [gr.poles for gr in extractions]) + _write_ragged_complex!(diag, "filtered_roots", + [gr.filtered_roots for gr in extractions]) + return nothing +end + +# Write a ragged vector-of-vectors of ComplexF64 as (flat_re, flat_im, +# offsets) — `offsets[k+1] - offsets[k]` is the length of row `k`. This +# avoids HDF5 VLEN types, which have patchy cross-language support. +function _write_ragged_complex!(parent, name::String, + data::Vector{Vector{ComplexF64}}) + g = create_group(parent, name) + flat_re = Float64[] + flat_im = Float64[] + offsets = Int[0] + for v in data + append!(flat_re, real.(v)) + append!(flat_im, imag.(v)) + push!(offsets, offsets[end] + length(v)) + end + g["flat_real"] = flat_re + g["flat_imag"] = flat_im + g["offsets"] = offsets + return nothing +end + +# ---------- full scan data (optional) ---------- +function _write_scan_data!(g, r::SLAYERResult) + sc = create_group(g, "scan") + for (k, data) in enumerate(r.scan_data) + sk = create_group(sc, "surface_$(k)") + _write_single_scan!(sk, data) + end + return nothing +end + +function _write_single_scan!(g, data::ScanResult) + g["kind"] = "brute_force" + g["Q_real"] = real.(data.Q) + g["Q_imag"] = imag.(data.Q) + g["Delta_real"] = real.(data.Δ) + g["Delta_imag"] = imag.(data.Δ) + g["re_axis"] = data.re_axis + g["im_axis"] = data.im_axis + return nothing +end + +function _write_single_scan!(g, data::AMRResult) + g["kind"] = "amr" + g["Q_real"] = real.(data.Q) + g["Q_imag"] = imag.(data.Q) + g["Delta_real"] = real.(data.Δ) + g["Delta_imag"] = imag.(data.Δ) + g["n_cells"] = length(data.cells) + g["truncated"] = Int(data.truncated) + return nothing +end diff --git a/src/Tearing/Runner/Result.jl b/src/Tearing/Runner/Result.jl new file mode 100644 index 000000000..f5a57e88c --- /dev/null +++ b/src/Tearing/Runner/Result.jl @@ -0,0 +1,59 @@ +# Result.jl +# +# `SLAYERResult` packages the output of a full SLAYER analysis run: +# per-surface layer parameters, the extracted tearing eigenvalues, and (if +# `control.store_scan`) the full Q-plane scan data for plotting. + +""" + SLAYERResult + +Output of `run_slayer`. Carries both summary eigenvalues (ω_Hz, γ_Hz) and +full diagnostic detail (valid roots, poles, filtered roots, contours) for +downstream inspection and HDF5 output. + +# Fields + + - `enabled` -- `true` only when the analysis actually ran + - `control` -- the `SLAYERControl` used (frozen snapshot) + - `params` -- `Vector{SLAYERParameters}`, one per surface + - `dp_matrix` -- outer-region Δ' matrix used in the analysis + - `Q_root` -- tearing eigenvalue(s) in normalized Q + * length `nsurfaces` in `:uncoupled` mode + * length `1` in `:coupled` mode (global eigenvalue normalized by + `params[1].tauk`) + - `omega_Hz`, `gamma_Hz` -- physical rotation frequency / growth rate + - `per_surface_extraction` -- `Vector{GrowthRateResult}` of length + `nsurfaces` in uncoupled mode (each includes polelines, pole list, + valid roots, filtered roots). Empty in coupled mode. + - `coupled_extraction` -- single `GrowthRateResult` in coupled mode. + `nothing` otherwise. + - `layer_widths` -- `Vector{LayerWidths}`, one per surface: the + resistive layer thickness (in meters) from the `del_s` Riccati solve + plus FKR / visco-resistive sanity scales. Empty when disabled. + - `scan_data` -- scan results (per-surface in uncoupled, single + entry in coupled). Empty unless `control.store_scan == true`. +""" +struct SLAYERResult + enabled::Bool + control::SLAYERControl + params::AbstractVector{<:InnerLayerParameters} + dp_matrix::Matrix{ComplexF64} + Q_root::Vector{ComplexF64} + omega_Hz::Vector{Float64} + gamma_Hz::Vector{Float64} + per_surface_extraction::Vector{GrowthRateResult} + coupled_extraction::Union{Nothing,GrowthRateResult} + layer_widths::Vector{LayerWidths} + scan_data::Vector{Union{ScanResult,AMRResult}} +end + +# Empty result (enabled=false path) +function empty_slayer_result(control::SLAYERControl) + return SLAYERResult(false, control, + SLAYERParameters[], + zeros(ComplexF64, 0, 0), + ComplexF64[], Float64[], Float64[], + GrowthRateResult[], nothing, + LayerWidths[], + Union{ScanResult,AMRResult}[]) +end diff --git a/src/Tearing/Runner/Runner.jl b/src/Tearing/Runner/Runner.jl new file mode 100644 index 000000000..7ff036e7c --- /dev/null +++ b/src/Tearing/Runner/Runner.jl @@ -0,0 +1,57 @@ +# Runner.jl +# +# Top-level orchestration module that ties together the building blocks +# from InnerLayer, Dispersion, and Utilities into the user-facing SLAYER +# tearing-mode analysis pipeline. +# +# gpec.toml [SLAYER] → SLAYERControl +# │ +# equilibrium + Δ' │ +# + profiles → build_slayer_inputs → SLAYERParameters[] +# │ +# ▼ +# SurfaceCoupling[] / MultiSurfaceCoupling +# │ +# ▼ +# brute_force_scan / amr_scan +# │ +# ▼ +# find_growth_rates +# │ +# ▼ +# SLAYERResult → HDF5 (`slayer/` group) + +module Runner + +using LinearAlgebra +using Statistics: mean, median +using HDF5 + +using FastInterpolations: cubic_interp +using ..Utilities +using ..Utilities: KineticProfiles +using ...Equilibrium: read_kinetic_file, KineticProfileData +using ..InnerLayer +using ..InnerLayer: InnerLayerParameters, InnerLayerResponse, solve_inner, + SLAYERModel, SLAYERParameters, build_slayer_inputs, + GGJModel, GGJParameters, build_ggj_inputs, + LayerWidths, slayer_layer_thickness +using ..Dispersion +using ..Dispersion: SurfaceCoupling, surface_coupling, + MultiSurfaceCoupling, multi_surface_coupling, + ScanResult, brute_force_scan, + AMRResult, amr_scan, + MultiBoxAMRResult, multi_box_amr_scan, as_amr_result, + GrowthRateResult, find_growth_rates + +include("Control.jl") +include("Result.jl") +include("run_slayer.jl") +include("HDF5Output.jl") + +export SLAYERControl, slayer_control_from_toml, validate +export SLAYERResult, empty_slayer_result +export run_slayer, run_slayer_from_inputs, ggj_inner_deltas +export write_slayer_hdf5! + +end # module Runner diff --git a/src/Tearing/Runner/run_slayer.jl b/src/Tearing/Runner/run_slayer.jl new file mode 100644 index 000000000..0e254e625 --- /dev/null +++ b/src/Tearing/Runner/run_slayer.jl @@ -0,0 +1,435 @@ +# Runner.jl +# +# Top-level orchestration for the SLAYER tearing-mode analysis. Given a +# fully-solved `PlasmaEquilibrium` + `ForceFreeStatesInternal` (which +# supplies the rational-surface list and the outer-region Δ' matrix) + a +# populated `SLAYERControl`, `run_slayer` loads kinetic profiles, builds +# per-surface SLAYER parameters, runs the requested scan mode, extracts +# growth rates by contour intersection, and returns a `SLAYERResult`. +# +# A secondary entry point `run_slayer_from_inputs` takes pre-built +# per-surface parameters + a Δ' matrix and bypasses the +# equilibrium-driven `build_slayer_inputs` step. This is what the test +# suite drives; it keeps the end-to-end code covered without requiring a +# full equilibrium solve in every test. + +# --------------------------------------------------------------------- +# Profile loading +# --------------------------------------------------------------------- +# Read kinetic profiles through the shared `Equilibrium.read_kinetic_file` +# reader and adapt them to the SLAYER inner layer. Returns the spline-based +# `KineticProfiles` plus χ⊥(ψ)/χ_φ(ψ) callables built from the file's +# `chi_e`/`chi_phi` (or `nothing` when the file carries no usable χ, in which +# case the caller falls back to the scalar `control.chi_perp`/`chi_tor`). +function _load_profiles(control::SLAYERControl, dir_path::AbstractString) + isempty(control.profile_file) && + error("run_slayer: [SLAYER] profile_file is empty — point it at a " * + "kinetic-profile file (HDF5 GPEC kinetic schema or ASCII table).") + path = isabspath(control.profile_file) ? control.profile_file : + joinpath(dir_path, control.profile_file) + data = read_kinetic_file(path; group=control.profile_group) + + for (name, v) in (("n_e", data.n_e), ("T_e", data.T_e), ("T_i", data.T_i)) + v === nothing && + error("run_slayer: kinetic file '$path' is missing required " * + "dataset '$name' for the SLAYER inner layer.") + end + # ω_*e/ω_*i are recomputed per-surface from equilibrium gradients + # (compute_omega_star), so the diamagnetic-frequency inputs here are + # placeholders; `omega` carries the ExB rotation when present. + npsi = length(data.psi) + omega = data.omega_E === nothing ? zeros(npsi) : data.omega_E + profiles = KineticProfiles(; psi=data.psi, n_e=data.n_e, T_e=data.T_e, + T_i=data.T_i, omega=omega, + omega_e=zeros(npsi), omega_i=zeros(npsi)) + + # χ⊥(ψ)/χ_φ(ψ) splines from the file. A χ array that is absent OR all-zero + # is treated as "not provided" — χ must be positive (χ=0 ⇒ τ_⊥→∞), and the + # all-zero sentinel lets a file keep the chi_e/chi_phi keys while deferring + # to the scalar control.chi_perp/chi_tor fallback. Build the spline only + # from a usable (present, not all-zero) array. + psi_xs = collect(Float64, data.psi) + _chi_spline(v) = (v === nothing || all(iszero, v)) ? nothing : + cubic_interp(psi_xs, collect(Float64, v)) + chi_perp = _chi_spline(data.chi_e) + chi_tor = _chi_spline(data.chi_phi) + return (profiles=profiles, chi_perp=chi_perp, chi_tor=chi_tor) +end + +# --------------------------------------------------------------------- +# Inner-layer model factory +# --------------------------------------------------------------------- +function _build_inner_model(name::Symbol) + if name === :slayer_fitzpatrick + return SLAYERModel(; variant=:fitzpatrick) + elseif name === :ggj_shooting + return GGJModel(; solver=:shooting) + elseif name === :ggj_galerkin + return GGJModel(; solver=:galerkin) + end + throw(ArgumentError("_build_inner_model: unknown model $name")) +end + +# Map the TOML resistivity_model symbol to a NeoResistivityModel instance. +function _build_resistivity_model(name::Symbol) + name === :sauter && return SauterNeoModel() + name === :redl && return RedlNeoModel() + name === :spitzer && return SpitzerModel() + name === :spitzer_harm && return SpitzerHarmModel() + throw(ArgumentError("_build_resistivity_model: unknown model $name")) +end + +# Human-readable surface label for warnings. SLAYER params carry (m, n); +# GGJ params carry only the singular-surface index `ising`. +_surface_label(p::SLAYERParameters) = "m=$(p.m), n=$(p.n)" +_surface_label(p::InnerLayerParameters) = "ising=$(getfield(p, :ising))" + +# Is this an unvalidated GGJ inner-layer model? Used to gate the γ-extraction +# future-work warning. +_is_ggj(::GGJModel) = true +_is_ggj(::Any) = false + +# --------------------------------------------------------------------- +# Scan dispatch +# --------------------------------------------------------------------- +function _run_scan(f, control::SLAYERControl) + if control.scan_mode === :brute_force + return brute_force_scan(f, control.Q_re_range, control.Q_im_range; + nre=control.nre, nim=control.nim) + elseif control.scan_mode === :amr + if !isempty(control.boxes) + # Multi-box stripe layout. Pole magnitude threshold for the + # activity check is derived from a coarse 16×6 sample of the + # union of all boxes, using 10 × median(|Δ|) (median is robust + # to near-pole sample inflation; see the adaptive threshold note + # below). + ω_lo = minimum(b[1] for b in control.boxes) + ω_hi = maximum(b[2] for b in control.boxes) + γ_lo = minimum(b[3] for b in control.boxes) + γ_hi = maximum(b[4] for b in control.boxes) + coarse_pts = ComplexF64[ComplexF64(ω, γ) + for ω in range(ω_lo, ω_hi; length=16) + for γ in range(γ_lo, γ_hi; length=6)] + coarse_Δ = ComplexF64[ComplexF64(f(q)) for q in coarse_pts] + finite = filter(z -> isfinite(z) && abs(z) < 1e30, coarse_Δ) + pole_thr = isempty(finite) ? 1e8 : 10.0 * median(abs.(finite)) + # Convert NTuple{4,Float64} → ((ω_lo,ω_hi),(γ_lo,γ_hi)) tuples + boxes_in = [((b[1], b[2]), (b[3], b[4])) for b in control.boxes] + return multi_box_amr_scan(f, boxes_in; + pole_magnitude_threshold=pole_thr, + prescreen_nre=control.multi_box_prescreen_n, + prescreen_nim=control.multi_box_prescreen_n, + nre0=control.nre, nim0=control.nim, + passes=control.amr_passes, + max_cells=control.amr_max_cells, + max_cells_action=:warn_truncate) |> + as_amr_result # downstream expects AMRResult + end + return amr_scan(f, control.Q_re_range, control.Q_im_range; + nre0=control.nre, nim0=control.nim, + passes=control.amr_passes, + max_cells=control.amr_max_cells) + end + throw(ArgumentError("_run_scan: unknown scan_mode=$(control.scan_mode)")) +end + +# --------------------------------------------------------------------- +# Surface-coupling builder — dispatches on model type to thread the +# correct `scale` and `tauk` through the Dispersion API. +# --------------------------------------------------------------------- +# SLAYER: scale = lu^(1/3), tauk from the surface, dc from the χ‖ proxy. +function _build_surface_coupling(model::SLAYERModel, params::SLAYERParameters, + dp_diag) + return surface_coupling(model, params, dp_diag; dc=params.dc_tmp) +end + +# GGJ: scale = 1.0 (rescale_delta applied inside solve_inner), tauk = 1.0, +# dc = 0 (the 4m×4m Pletzer-Dewar residual carries interchange stabilization +# natively). See the GGJ `surface_coupling` method. +function _build_surface_coupling(model::GGJModel, params::GGJParameters, + dp_diag) + return surface_coupling(model, params, dp_diag) +end + +# --------------------------------------------------------------------- +# Core analysis entry point that takes pre-built parameters. +# --------------------------------------------------------------------- +""" + run_slayer_from_inputs(params::Vector{SLAYERParameters}, + dp_matrix::AbstractMatrix, + control::SLAYERControl) -> SLAYERResult + +Run the SLAYER tearing analysis given pre-built per-surface +`SLAYERParameters` and the outer-region Δ' matrix. Bypasses the +equilibrium-driven `build_slayer_inputs` step — use this when the +parameters are already known (e.g. in unit tests or when rebuilding +from cached HDF5 output). +""" +function run_slayer_from_inputs(params::AbstractVector{<:InnerLayerParameters}, + dp_matrix::AbstractMatrix, + control::SLAYERControl) + validate(control) + control.enabled || return empty_slayer_result(control) + isempty(params) && return empty_slayer_result(control) + + n = length(params) + size(dp_matrix) == (n, n) || + throw(ArgumentError("run_slayer: dp_matrix size $(size(dp_matrix)) " * + "≠ ($n, $n)")) + dp = Matrix{ComplexF64}(dp_matrix) + + model = _build_inner_model(control.inner_model) + + # Guard: the inner-layer model and the parameter eltype must match, or + # `_build_surface_coupling` throws an opaque MethodError downstream. + expected_P = _is_ggj(model) ? GGJParameters : SLAYERParameters + all(p -> p isa expected_P, params) || + throw( + ArgumentError( + "run_slayer: inner_model=$(control.inner_model) requires " * + "$(expected_P) per-surface parameters, but got eltype " * + "$(eltype(params)). Build inputs with the matching builder " * + "(build_slayer_inputs for SLAYER, build_ggj_inputs for GGJ).") + ) + + # The coupled determinant uses the reduced m×m (tearing-only) form, which + # drops the interchange channel. For GGJ that channel carries the Glasser + # interchange stabilization, so coupled-GGJ results omit real physics. + if _is_ggj(model) && control.coupling_mode === :coupled + @warn( + "SLAYER: coupling_mode=:coupled with a GGJ inner model uses the " * + "reduced m×m tearing-only determinant, which DROPS the GGJ " * + "interchange (Glasser stabilization) channel — results are " * + "physically incomplete. Use the full Pletzer-Dewar matching " * + "(multi_surface_coupling_full) for coupled GGJ studies." + ) + end + + # GGJ growth-rate extraction by Re/Im contour matching is not yet + # reliable (the contours do not robustly intersect at a dispersion-relation + # zero). The scan still runs so the user can inspect/plot the contours and + # access both parity Δ channels via `ggj_inner_deltas`, but the reported γ + # is unvalidated and should be treated as future work. + if _is_ggj(model) + @warn( + "SLAYER: GGJ γ-extraction by Re/Im contour matching is " * + "FUTURE WORK — contours do not reliably intersect at a " * + "dispersion-relation root. The scan grid and parity Δ channels " * + "are provided for inspection; reported growth rates are " * + "unvalidated placeholders." + ) + end + + # Per-surface SurfaceCoupling objects + scs = [_build_surface_coupling(model, params[k], dp[k, k]) for k in 1:n] + + # Per-surface resistive layer thickness [m] via the del_s Riccati solve. + # Independent of the dispersion scan / coupling mode — a pure diagnostic. + # SLAYER-only: the del_s Riccati is defined on SLAYERParameters. GGJ + # surfaces carry no analogous layer-thickness diagnostic, so leave it empty. + layer_widths = eltype(params) <: SLAYERParameters ? + LayerWidths[slayer_layer_thickness(params[k]) for k in 1:n] : + LayerWidths[] + + Q_root = ComplexF64[] + omega_Hz = Float64[] + gamma_Hz = Float64[] + per_surface_extraction = GrowthRateResult[] + coupled_extraction = nothing + scan_data_list = Union{ScanResult,AMRResult}[] + + # Helper: compute the pole_threshold actually passed to find_growth_rates. + # When `control.pole_threshold_adaptive` is true, override with + # `10 × median(|Δ|)` over the scan's dispersion residual array. + # + # The median formulation is robust against pre-screen samples landing + # near a pole. A single near-pole sample inflates `|mean(Δ)|` by orders + # of magnitude (and `|mean|` further collapses on oscillating residuals + # whose phases cancel in the complex sum). 10 × median(|Δ|) reflects + # "10× the typical residual magnitude" with median robust to both + # pathologies. + function _pole_threshold_for(scan) + control.pole_threshold_adaptive || return control.pole_threshold + # ScanResult and AMRResult both carry `.Δ` — abstract over both + Δ_arr = hasproperty(scan, :Δ) ? scan.Δ : nothing + Δ_arr === nothing && return control.pole_threshold + finite = filter(z -> isfinite(z) && abs(z) < 1e30, Δ_arr) + isempty(finite) && return control.pole_threshold + return 10.0 * median(abs.(finite)) + end + + if control.coupling_mode === :uncoupled + for (k, sc) in enumerate(scs) + scan = _run_scan(sc, control) + pthr = _pole_threshold_for(scan) + gr = find_growth_rates(scan, sc.tauk; + pole_threshold=pthr, + filter_above_poles=control.filter_above_poles, + filter_outside_re=control.filter_outside_re, + gap_kHz_threshold=control.gap_kHz_threshold, + residual=control.polish_roots ? sc : nothing, + validity_rtol=control.validity_rtol) + :no_root in gr.warning_flags && @warn( + "SLAYER: no usable growth-rate root found for surface " * + "$(_surface_label(params[k])); reported γ=0 is a " * + "placeholder, not a physical result — check scan grid / " * + "pole_threshold.") + push!(Q_root, gr.Q_root) + push!(omega_Hz, gr.omega_Hz) + push!(gamma_Hz, gr.gamma_Hz) + push!(per_surface_extraction, gr) + control.store_scan && push!(scan_data_list, scan) + end + + elseif control.coupling_mode === :coupled + m_use = min(control.msing_max, n) + mc = multi_surface_coupling(scs, dp; ref_idx=1, msing_max=m_use) + scan = _run_scan(mc, control) + pthr = _pole_threshold_for(scan) + ref_tauk = scs[1].tauk + # Coupled path: no root polishing / validity gate. The m×m coupled + # determinant det(D'−D(Q)) is ill-conditioned (its magnitude floors well + # above zero), so |det|-based polishing is a no-op and the residual-scale + # gate is unreliable. A σ_min-based coupled refinement is a dev follow-up; + # for now the coupled determinant uses the raw contour extraction (the + # BLAS pin in the scan still makes it thread-deterministic). + gr = find_growth_rates(scan, ref_tauk; + pole_threshold=pthr, + filter_above_poles=control.filter_above_poles, + filter_outside_re=control.filter_outside_re, + gap_kHz_threshold=control.gap_kHz_threshold) + :no_root in gr.warning_flags && @warn( + "SLAYER: no usable growth-rate root found for the coupled " * + "$(m_use)-surface determinant; reported γ=0 is a placeholder, " * + "not a physical result — check scan grid / pole_threshold.") + push!(Q_root, gr.Q_root) + push!(omega_Hz, gr.omega_Hz) + push!(gamma_Hz, gr.gamma_Hz) + coupled_extraction = gr + control.store_scan && push!(scan_data_list, scan) + end + + return SLAYERResult(true, control, params, dp, + Q_root, omega_Hz, gamma_Hz, + per_surface_extraction, coupled_extraction, + layer_widths, scan_data_list) +end + +# --------------------------------------------------------------------- +# GGJ parity-Δ diagnostic +# --------------------------------------------------------------------- +""" + ggj_inner_deltas(params::AbstractVector{GGJParameters}, Q::Number; + solver=:galerkin) -> Vector{NamedTuple} + +Evaluate both parity channels of the GGJ inner-layer matching data at the +complex normalized growth rate `Q` for each rational surface. Returns a +vector of `(ising, tearing, interchange)` named tuples, where `tearing` +(GWP Δ_+) is the reconnecting channel and `interchange` (GWP Δ_−) the +non-reconnecting Glasser-stabilization channel (see `InnerLayerResponse`). + +This is the supported GGJ diagnostic: both parity Δ's are physical and +directly accessible here. Contour-matching γ extraction from these (the +Re/Im scan intersection) is not yet validated — see the warning in +`run_slayer_from_inputs`. +""" +function ggj_inner_deltas(params::AbstractVector{GGJParameters}, Q::Number; + solver::Symbol=:galerkin) + model = GGJModel(; solver=solver) + out = Vector{NamedTuple{(:ising, :tearing, :interchange), + Tuple{Int,ComplexF64,ComplexF64}}}(undef, length(params)) + for (k, p) in enumerate(params) + r = solve_inner(model, p, ComplexF64(Q)) + out[k] = (ising=p.ising, tearing=r.tearing, interchange=r.interchange) + end + return out +end + +# --------------------------------------------------------------------- +# Full pipeline: equilibrium + ForceFreeStates → parameters → analysis +# --------------------------------------------------------------------- +""" + run_slayer(equil, ffs_intr, control; dir_path="./") -> SLAYERResult + +Orchestrate the full SLAYER analysis against a solved +`PlasmaEquilibrium` and `ForceFreeStatesInternal`. Kinetic profiles are +read from `control.profile_file` (relative to `dir_path`) through the shared +`Equilibrium.read_kinetic_file` reader; when the file carries `chi_e`/`chi_phi` +profiles they set χ⊥(ψ)/χ_φ(ψ), otherwise the scalar `control.chi_perp`/ +`chi_tor` fallbacks are used. Per-surface parameters are built via +`build_slayer_inputs`; the outer-region Δ' matrix is pulled from +`ffs_intr.delta_prime_matrix` (or, if empty, from the diagonal +`sing.delta_prime` entries). + +Returns an `enabled=false` `SLAYERResult` when `control.enabled` is +false. +""" +function run_slayer(equil, ffs_intr, control::SLAYERControl; + dir_path::AbstractString="./") + validate(control) + control.enabled || return empty_slayer_result(control) + isempty(ffs_intr.sing) && return empty_slayer_result(control) + + loaded = _load_profiles(control, dir_path) + profiles = loaded.profiles + + if control.inner_model in (:ggj_shooting, :ggj_galerkin) + # GGJ γ-extraction is future work; `run_slayer_from_inputs` emits the + # warning once the model is built (so direct callers see it too). + params = build_ggj_inputs(equil, ffs_intr.sing, profiles; + mu_i=control.mu_i, + zeff=control.zeff, + resistivity_model=_build_resistivity_model(control.resistivity_model), + lnLambda_form=control.lnLambda_form) + else + bt = control.bt === nothing ? equil.config.b0exp : control.bt + # χ⊥/χ_φ from the kinetic file when present, else the scalar fallbacks. + chi_perp = loaded.chi_perp === nothing ? control.chi_perp : loaded.chi_perp + chi_tor = loaded.chi_tor === nothing ? control.chi_tor : loaded.chi_tor + (loaded.chi_perp === nothing || loaded.chi_tor === nothing) && @warn( + "SLAYER: kinetic file has no usable chi_e/chi_phi profile(s) " * + "(dataset absent or all-zero); using the scalar " * + "control.chi_perp/chi_tor fallback for the missing one(s).") + params = build_slayer_inputs(equil, ffs_intr.sing, profiles; + bt=bt, + mu_i=control.mu_i, + zeff=control.zeff, + chi_perp=chi_perp, + chi_tor=chi_tor, + dr_val=control.dr_val, + dgeo_val=control.dgeo_val, + dc_type=control.dc_type, + theta=control.theta_sample, + resistivity_model=_build_resistivity_model(control.resistivity_model), + lnLambda_form=control.lnLambda_form) + end + + # Δ' matrix: prefer the full parallel-FM matrix; fall back to a + # diagonal built from each SingType's scalar delta_prime. + dp = if !isempty(ffs_intr.delta_prime_matrix) && + size(ffs_intr.delta_prime_matrix) == (length(params), length(params)) + Matrix{ComplexF64}(ffs_intr.delta_prime_matrix) + else + # The full Δ' matrix is unavailable (e.g. the parallel-FM stage that + # populates it was not run). The scalar-diagonal fallback uses + # `sing.delta_prime`, which is a coarse per-surface stub; surfaces + # with no entry default to Δ'=0, giving γ computed from zero drive. + n_missing = count(s -> isempty(s.delta_prime), ffs_intr.sing) + @warn( + "SLAYER: ffs_intr.delta_prime_matrix is empty or wrong-sized " * + "($(size(ffs_intr.delta_prime_matrix)) vs " * + "($(length(params)),$(length(params)))); falling back to the " * + "diagonal `sing.delta_prime` stub. Growth rates use a coarse " * + "per-surface Δ' and may be unreliable" * + (n_missing > 0 ? "; $n_missing surface(s) have NO Δ' entry and " * + "default to Δ'=0 (zero tearing drive)." : ".") + ) + M = zeros(ComplexF64, length(params), length(params)) + for (k, s) in enumerate(ffs_intr.sing) + M[k, k] = isempty(s.delta_prime) ? 0.0 + 0im : s.delta_prime[1] + end + M + end + + return run_slayer_from_inputs(params, dp, control) +end diff --git a/src/Tearing/Tearing.jl b/src/Tearing/Tearing.jl new file mode 100644 index 000000000..2e096846b --- /dev/null +++ b/src/Tearing/Tearing.jl @@ -0,0 +1,31 @@ +# Tearing.jl +# +# Umbrella module grouping the tearing-mode analysis stack into a single +# layered hierarchy: +# +# InnerLayer -- pure physics: Δ_inner(Q) for GGJ or SLAYER models +# Dispersion -- physics-agnostic scan + contour-intersection root +# extraction (consumes any InnerLayerModel) +# Runner -- user-facing orchestration: TOML config, profile +# loading, HDF5 output, workflow hooks +# +# Relative-import dot counts inside this umbrella are simplified by +# re-binding `Utilities` at the Tearing level: all submodules reach +# Utilities via `..Utilities` (or `...Utilities` from sub-sub-modules) +# regardless of their depth in the original layout. + +module Tearing + +using ..Utilities + +include("InnerLayer/InnerLayer.jl") +include("Dispersion/Dispersion.jl") +include("Runner/Runner.jl") + +import .InnerLayer as InnerLayer +import .Dispersion as Dispersion +import .Runner as Runner + +export InnerLayer, Dispersion, Runner + +end # module Tearing diff --git a/src/Utilities/KineticProfiles.jl b/src/Utilities/KineticProfiles.jl new file mode 100644 index 000000000..70f1a2974 --- /dev/null +++ b/src/Utilities/KineticProfiles.jl @@ -0,0 +1,81 @@ +# KineticProfiles.jl +# +# Radial kinetic-profile container shared across GPEC modules that need +# electron density, electron/ion temperatures, and the three frequencies +# (toroidal rotation + electron/ion diamagnetic) as functions of the +# normalized poloidal flux ψ. SLAYER is the first consumer; PENTRC and +# future resistive-MHD modules will share this object. + +using FastInterpolations + +""" + KineticProfiles + +Radial kinetic-profile container. All six profiles are 1D cubic splines of +the normalized poloidal flux ψ ∈ [0, 1]. + +| field | meaning | units | +|:--------- |:--------------------------------------- |:----- | +| `n_e` | electron density | m⁻³ | +| `T_e` | electron temperature | eV | +| `T_i` | ion temperature | eV | +| `omega` | toroidal rotation | rad/s | +| `omega_e` | electron diamagnetic frequency ω\\_\\*e | rad/s | +| `omega_i` | ion diamagnetic frequency ω\\_\\*i | rad/s | + +Construct via the keyword constructor `KineticProfiles(; psi, n_e, T_e, T_i, omega, omega_e, omega_i)` with matched-length vectors. The SLAYER +runner builds this object from a standardized kinetic-profile file via +`Equilibrium.read_kinetic_file`. + +Evaluate all profiles at a given ψ via the call operator: + +```julia +vals = kp(0.5) # NamedTuple(n_e=..., T_e=..., ..., omega_i=...) +``` +""" +struct KineticProfiles{S} + n_e::S + T_e::S + T_i::S + omega::S + omega_e::S + omega_i::S +end + +function KineticProfiles(; psi::AbstractVector{<:Real}, + n_e::AbstractVector{<:Real}, + T_e::AbstractVector{<:Real}, + T_i::AbstractVector{<:Real}, + omega::AbstractVector{<:Real}, + omega_e::AbstractVector{<:Real}, + omega_i::AbstractVector{<:Real}) + xs = collect(Float64.(psi)) + for (name, v) in (("n_e", n_e), ("T_e", T_e), ("T_i", T_i), + ("omega", omega), ("omega_e", omega_e), + ("omega_i", omega_i)) + length(v) == length(xs) || + throw(ArgumentError("KineticProfiles: length($name) = $(length(v)) " * + "≠ length(psi) = $(length(xs))")) + end + return KineticProfiles(cubic_interp(xs, Float64.(n_e)), + cubic_interp(xs, Float64.(T_e)), + cubic_interp(xs, Float64.(T_i)), + cubic_interp(xs, Float64.(omega)), + cubic_interp(xs, Float64.(omega_e)), + cubic_interp(xs, Float64.(omega_i))) +end + +""" + (kp::KineticProfiles)(psi::Real) -> NamedTuple + +Evaluate all profiles at `psi` and return them as a NamedTuple with fields +`(n_e, T_e, T_i, omega, omega_e, omega_i)`. +""" +(kp::KineticProfiles)(psi::Real) = ( + n_e=kp.n_e(psi), + T_e=kp.T_e(psi), + T_i=kp.T_i(psi), + omega=kp.omega(psi), + omega_e=kp.omega_e(psi), + omega_i=kp.omega_i(psi) +) diff --git a/src/Utilities/NeoclassicalResistivity.jl b/src/Utilities/NeoclassicalResistivity.jl new file mode 100644 index 000000000..de256090d --- /dev/null +++ b/src/Utilities/NeoclassicalResistivity.jl @@ -0,0 +1,339 @@ +# NeoclassicalResistivity.jl +# +# Shared neoclassical-resistivity utilities used by both the GGJ and +# SLAYER inner-layer models. All formulas follow Sauter, Angioni & Lin-Liu +# Phys. Plasmas 6, 2834 (1999) and its errata, with an optional Redl et al. +# Phys. Plasmas 28, 022502 (2021) variant that improves the fit at high +# collisionality. +# +# Two external references were cross-checked during implementation: +# - OpenFUSIONToolkit `TokaMaker/bootstrap.py` (Redl 2021 path) +# - OMFIT `omfit_classes/utils_fusion.py::nclass_conductivity-style +# block` around lines 1255-1319 (Sauter 1999 and `neo_2021` paths) +# +# Formula provenance: +# - eq 18a (Spitzer): Sauter et al. 1999, Eq. (18a) +# - eq 18b (nu*_e): Sauter et al. 1999, Eq. (18b) +# - eq 13 (F_33 Sauter): Sauter et al. 1999, Eqs. (13a)-(13b) +# - eq 17 (F_33 Redl): Redl et al. 2021, Eqs. (17)-(18) +# - f_t (Lin-Liu & Miller): Phys. Plasmas 2, 1666 (1995), Eq. (6) +# - NRL Coulomb log: NRL Plasma Formulary 2009 + +""" + NeoclassicalResistivity + +Spitzer + Sauter / Redl neoclassical resistivity closures, shared between +the GGJ and SLAYER inner-layer models so both see identical plasma-input +physics when the same `NeoResistivityModel` is selected. + +# Exports + +| symbol | role | +|:---------------------- |:------------------------------------------------------ | +| `NeoResistivityModel` | abstract tag | +| `SpitzerModel` | plain Spitzer (no trapped-particle correction) | +| `SpitzerHarmModel` | Fitzpatrick/TJ Spitzer-Härm σ_∥ (legacy SLAYER τ_R) | +| `SauterNeoModel` | Sauter 1999 F_33 neoclassical correction | +| `RedlNeoModel` | Redl 2021 F_33 neoclassical correction | +| `coulomb_log_e` | ln Λ_e (NRL or Sauter form) | +| `eta_spitzer` | Sauter 18a Spitzer resistivity [Ω·m] | +| `tau_ee_spitzer_harm` | electron-electron collision time τ_ee [s] | +| `eta_spitzer_harm` | Fitzpatrick/TJ Spitzer-Härm resistivity 1/σ_∥ [Ω·m] | +| `trapped_fraction` | Lin-Liu & Miller 1995 f_t from ⟨B⟩, ⟨B²⟩, B_min, B_max | +| `trapped_fraction_eps` | simple ε-only f_t fallback | +| `nu_star_e` | Sauter 18b electron collisionality | +| `eta_neoclassical` | dispatched: Spitzer(-Härm) or F_33 · Spitzer | +""" +module NeoclassicalResistivity + +using ..PhysicalConstants: EPS_0, M_E, E_CHG + +export NeoResistivityModel, SpitzerModel, SpitzerHarmModel, SauterNeoModel, RedlNeoModel +export coulomb_log_e, eta_spitzer, tau_ee_spitzer_harm, eta_spitzer_harm +export trapped_fraction, trapped_fraction_eps +export nu_star_e, eta_neoclassical + +""" +Abstract tag for a neoclassical-resistivity closure. +""" +abstract type NeoResistivityModel end + +""" +Plain Spitzer resistivity — no trapped-particle correction. +""" +struct SpitzerModel <: NeoResistivityModel end + +""" +Spitzer-Härm parallel resistivity 1/σ_∥ as used by Fitzpatrick's TJ +(LayerParameters.tex Eqs. 7-8) and legacy SLAYER for τ_R. No +trapped-particle correction. Pair with `lnLambda_form=:wesson` to +reproduce legacy SLAYER behaviour bit-identically. +""" +struct SpitzerHarmModel <: NeoResistivityModel end + +""" +Sauter, Angioni & Lin-Liu 1999 F_33 neoclassical correction (Eqs. 13a,b). +""" +struct SauterNeoModel <: NeoResistivityModel end + +""" +Redl et al. 2021 F_33 neoclassical correction (Eqs. 17-18). Improved +high-collisionality fit vs SauterNeoModel. +""" +struct RedlNeoModel <: NeoResistivityModel end + +# -------------------------------------------------------------------------- +# Coulomb logarithm +# -------------------------------------------------------------------------- + +""" + coulomb_log_e(n_e, T_e; form=:nrl) -> Float64 + +Electron Coulomb logarithm. `n_e` in m⁻³, `T_e` in eV. + +`form=:nrl` (default) uses the NRL Plasma Formulary 2009 expression, which +OpenFUSIONToolkit's `bootstrap.py` also selects as the "more accurate" +option. `form=:sauter` uses the simpler Sauter 1999 Eq. 18d form. +""" +function coulomb_log_e(n_e::Real, T_e::Real; form::Symbol=:nrl) + n_e > 0 || throw(ArgumentError("coulomb_log_e: n_e must be > 0 (got $n_e)")) + T_e > 0 || throw(ArgumentError("coulomb_log_e: T_e must be > 0 (got $T_e)")) + if form === :nrl + # NRL 2009, n_e in cm⁻³; matches utils_fusion.py:1262-1264 + return 23.5 - log(sqrt(n_e / 1e6) * T_e^(-1.25)) - + sqrt(1e-5 + (log(T_e) - 2)^2 / 16.0) + elseif form === :sauter + # Sauter 1999 Eq. 18d; matches utils_fusion.py:1255 + return 31.3 - log(sqrt(n_e) / T_e) + elseif form === :wesson + # Legacy Wesson form used by previous Julia code & SLAYER + return 24.0 + 3.0 * log(10.0) - 0.5 * log(n_e) + log(T_e) + else + throw(ArgumentError("coulomb_log_e: unknown form=$form " * + "(expected :nrl, :sauter, or :wesson)")) + end +end + +# -------------------------------------------------------------------------- +# Spitzer resistivity (Sauter 1999 Eq. 18a) +# -------------------------------------------------------------------------- + +# Sauter 1999 Eq. 18a line 2 — Spitzer conductivity Zeff correction +_N_Z(Z::Real) = 0.58 + 0.74 / (0.76 + Z) + +""" + eta_spitzer(n_e, T_e, Z_eff; lnLamb=nothing) -> Float64 + +Spitzer resistivity in Ω·m, using the Sauter 1999 Eq. 18a form + +``` +σ_Sp = 1.9012e4 · T_e^1.5 / (Z_eff · N(Z_eff) · lnΛ_e) +N(Z) = 0.58 + 0.74 / (0.76 + Z) +η_Sp = 1 / σ_Sp +``` + +`n_e` [m⁻³], `T_e` [eV]. `lnLamb` defaults to `coulomb_log_e(n_e, T_e)` (NRL). +""" +function eta_spitzer(n_e::Real, T_e::Real, Z_eff::Real; + lnLamb::Union{Real,Nothing}=nothing) + T_e > 0 || throw(ArgumentError("eta_spitzer: T_e must be > 0 (got $T_e)")) + Z_eff > 0 || throw(ArgumentError("eta_spitzer: Z_eff must be > 0 (got $Z_eff)")) + lnL = lnLamb === nothing ? coulomb_log_e(n_e, T_e) : Float64(lnLamb) + sigma_sp = 1.9012e4 * T_e^1.5 / (Z_eff * _N_Z(Z_eff) * lnL) + return 1.0 / sigma_sp +end + +# -------------------------------------------------------------------------- +# Spitzer-Härm parallel resistivity (Fitzpatrick TJ LayerParameters.tex Eqs. 7-8) +# -------------------------------------------------------------------------- + +""" + tau_ee_spitzer_harm(n_e, T_e; lnLamb=nothing) -> Float64 + +Electron-electron collision time per Fitzpatrick TJ LayerParameters.tex Eq. 7: + +``` +τ_ee = 6√2 π^1.5 ε₀² √m_e T_e^1.5 / (lnΛ e^2.5 n_e) +``` + +`n_e` [m⁻³], `T_e` [eV] (the `e^2.5` denominator absorbs the eV→J +conversion). `lnLamb` defaults to `coulomb_log_e(n_e, T_e)` (NRL). +""" +function tau_ee_spitzer_harm(n_e::Real, T_e::Real; + lnLamb::Union{Real,Nothing}=nothing) + n_e > 0 || throw(ArgumentError("tau_ee_spitzer_harm: n_e must be > 0")) + T_e > 0 || throw(ArgumentError("tau_ee_spitzer_harm: T_e must be > 0")) + lnL = lnLamb === nothing ? coulomb_log_e(n_e, T_e) : Float64(lnLamb) + return 6.0 * sqrt(2.0) * π^1.5 * EPS_0^2 * sqrt(M_E) * T_e^1.5 / + (lnL * E_CHG^2.5 * n_e) +end + +""" + eta_spitzer_harm(n_e, T_e, Z_eff; lnLamb=nothing) -> Float64 + +Spitzer-Härm parallel resistivity η_∥ = 1/σ_∥ in Ω·m, per Fitzpatrick TJ +LayerParameters.tex Eq. 8: + +``` +σ_∥ = (√2 + 13 Z_eff/4) / (Z_eff (√2 + Z_eff)) · n_e e² τ_ee / m_e +``` + +This is the resistivity entering the legacy SLAYER / TJ resistive +diffusion time τ_R = μ₀ r_s² σ_∥ (LayerParameters.tex Eq. 17). Agrees +with `eta_spitzer` to the fit accuracy of the two formulas (~1% at Z=1). +""" +function eta_spitzer_harm(n_e::Real, T_e::Real, Z_eff::Real; + lnLamb::Union{Real,Nothing}=nothing) + Z_eff > 0 || throw(ArgumentError("eta_spitzer_harm: Z_eff must be > 0")) + tau_ee = tau_ee_spitzer_harm(n_e, T_e; lnLamb=lnLamb) + sigma_par = (sqrt(2.0) + 13.0 * (Z_eff / 4.0)) / + (Z_eff * (sqrt(2.0) + Z_eff)) * + (n_e * E_CHG^2 * tau_ee) / M_E + return 1.0 / sigma_par +end + +# -------------------------------------------------------------------------- +# Trapped fraction +# -------------------------------------------------------------------------- + +""" + trapped_fraction(avg_B, avg_Bsq, B_min, B_max) -> Float64 + +Lin-Liu & Miller 1995, Phys. Plasmas **2**, 1666, Eq. (6): + +``` +f_t = 1 − ⟨B⟩² / ⟨B²⟩ · (1 − √(1 − h) · (1 + h/2)), h = B_min / B_max +``` + +Equivalent to the OMFIT `f_t` / `f_c` pair at full geometric accuracy (uses +both the average-B ratio and the min/max extremes). Arguments are +flux-surface averages computed from the θ-loop in the equilibrium. +""" +function trapped_fraction(avg_B::Real, avg_Bsq::Real, + B_min::Real, B_max::Real) + B_max > 0 || throw(ArgumentError("trapped_fraction: B_max must be > 0")) + avg_Bsq > 0 || throw(ArgumentError("trapped_fraction: avg_Bsq must be > 0")) + h = clamp(B_min / B_max, 0.0, 1.0) + factor = 1.0 - sqrt(1.0 - h) * (1.0 + 0.5 * h) + ft = 1.0 - (avg_B^2 / avg_Bsq) * factor + return clamp(ft, 0.0, 1.0) +end + +""" + trapped_fraction_eps(eps) -> Float64 + +Simple ε-only trapped-fraction approximation (OMFIT `f_t`): + +``` +f_c ≈ (1 − ε)² / (√(1 − ε²) · (1 + 1.46·√ε + 0.2·ε)) +f_t = 1 − f_c +``` + +Used as a fallback when the full (⟨B⟩, ⟨B²⟩, B_min, B_max) moments are +unavailable — e.g. when feeding SLAYER directly from minor-radius geometry +without having evaluated `ResistGeometry` first. +""" +function trapped_fraction_eps(eps::Real) + e = clamp(eps, 0.0, 1.0 - 1e-12) + fc = (1.0 - e)^2 / (sqrt(1.0 - e^2) * (1.0 + 1.46 * sqrt(e) + 0.2 * e)) + return clamp(1.0 - fc, 0.0, 1.0) +end + +# -------------------------------------------------------------------------- +# Electron collisionality (Sauter 1999 Eq. 18b) +# -------------------------------------------------------------------------- + +""" + nu_star_e(n_e, T_e, R_major, eps, q, Z_eff; lnLamb=nothing) -> Float64 + +Electron collisionality ν*_e per Sauter 1999 Eq. 18b: + +``` +ν*_e = 6.921e-18 · |q| · R · n_e · Z_eff · lnΛ_e / (T_e² · ε^1.5) +``` + +`n_e` [m⁻³], `T_e` [eV], `R_major` [m]. Matches OFT `bootstrap.py:640` and +OMFIT `utils_fusion.py:1278`. +""" +function nu_star_e(n_e::Real, T_e::Real, R_major::Real, + eps::Real, q::Real, Z_eff::Real; + lnLamb::Union{Real,Nothing}=nothing) + eps > 0 || throw(ArgumentError("nu_star_e: eps must be > 0")) + T_e > 0 || throw(ArgumentError("nu_star_e: T_e must be > 0")) + lnL = lnLamb === nothing ? coulomb_log_e(n_e, T_e) : Float64(lnLamb) + return 6.921e-18 * abs(q) * R_major * n_e * Z_eff * lnL / + (T_e^2 * eps^1.5) +end + +# -------------------------------------------------------------------------- +# Neoclassical resistivity (F_33 · η_Sp) +# -------------------------------------------------------------------------- + +# Sauter 1999 Eqs. 13a-13b +function _F33_sauter(f_t::Real, nu_star::Real, Z_eff::Real) + x = f_t / (1.0 + (0.55 - 0.1 * f_t) * sqrt(nu_star) + + 0.45 * (1.0 - f_t) * nu_star * Z_eff^(-1.5)) + return 1.0 - (1.0 + 0.36 / Z_eff) * x + + (0.59 / Z_eff) * x^2 - (0.23 / Z_eff) * x^3 +end + +# Redl 2021 Eqs. 17-18 +function _F33_redl(f_t::Real, nu_star::Real, Z_eff::Real) + dZm1 = sqrt(max(Z_eff - 1.0, 0.0)) + x = f_t / (1.0 + 0.25 * (1.0 - 0.7 * f_t) * sqrt(nu_star) * + (1.0 + 0.45 * dZm1) + + 0.61 * (1.0 - 0.41 * f_t) * nu_star / sqrt(Z_eff)) + return 1.0 - (1.0 + 0.21 / Z_eff) * x + + (0.54 / Z_eff) * x^2 - (0.33 / Z_eff) * x^3 +end + +""" + eta_neoclassical(model, n_e, T_e, Z_eff, f_t, nu_e_star; + lnLamb=nothing) -> Float64 + +Neoclassical resistivity η [Ω·m] under the chosen closure. + + - `SpitzerModel()` -- returns `eta_spitzer(n_e, T_e, Z_eff; lnLamb)` + unchanged; `f_t` and `nu_e_star` are ignored. + - `SpitzerHarmModel()` -- returns `eta_spitzer_harm(n_e, T_e, Z_eff; lnLamb)` + (Fitzpatrick/TJ legacy); `f_t` and `nu_e_star` are ignored. + - `SauterNeoModel()` -- Sauter 1999 Eq. 13: η = η_Sp / F_33(Sauter). + - `RedlNeoModel()` -- Redl 2021 Eq. 17: η = η_Sp / F_33(Redl). + +Note that σ_neo = σ_Sp · F_33, so η_neo = η_Sp / F_33. For a banana-regime +plasma with f_t ≈ 0.5 and ν*_e ≪ 1, F_33 ≈ 0.4–0.5, so η_neo is a factor +of ~2 larger than η_Sp — this is the standard H-mode tearing correction. +""" +function eta_neoclassical(::SpitzerModel, n_e::Real, T_e::Real, Z_eff::Real, + f_t::Real, nu_e_star::Real; + lnLamb::Union{Real,Nothing}=nothing) + return eta_spitzer(n_e, T_e, Z_eff; lnLamb=lnLamb) +end + +function eta_neoclassical(::SpitzerHarmModel, n_e::Real, T_e::Real, Z_eff::Real, + f_t::Real, nu_e_star::Real; + lnLamb::Union{Real,Nothing}=nothing) + return eta_spitzer_harm(n_e, T_e, Z_eff; lnLamb=lnLamb) +end + +function eta_neoclassical(::SauterNeoModel, n_e::Real, T_e::Real, Z_eff::Real, + f_t::Real, nu_e_star::Real; + lnLamb::Union{Real,Nothing}=nothing) + eta_sp = eta_spitzer(n_e, T_e, Z_eff; lnLamb=lnLamb) + F33 = _F33_sauter(clamp(f_t, 0.0, 1.0), max(nu_e_star, 0.0), Z_eff) + F33 > 0 || throw(DomainError(F33, "eta_neoclassical: F_33 non-positive — " * + "inputs outside Sauter fit range")) + return eta_sp / F33 +end + +function eta_neoclassical(::RedlNeoModel, n_e::Real, T_e::Real, Z_eff::Real, + f_t::Real, nu_e_star::Real; + lnLamb::Union{Real,Nothing}=nothing) + eta_sp = eta_spitzer(n_e, T_e, Z_eff; lnLamb=lnLamb) + F33 = _F33_redl(clamp(f_t, 0.0, 1.0), max(nu_e_star, 0.0), Z_eff) + F33 > 0 || throw(DomainError(F33, "eta_neoclassical: F_33 non-positive — " * + "inputs outside Redl fit range")) + return eta_sp / F33 +end + +end # module NeoclassicalResistivity diff --git a/src/Utilities/PhysicalConstants.jl b/src/Utilities/PhysicalConstants.jl new file mode 100644 index 000000000..a9668b611 --- /dev/null +++ b/src/Utilities/PhysicalConstants.jl @@ -0,0 +1,22 @@ +""" + PhysicalConstants + +Shared physical constants used across GPEC modules. Values match the +Fortran GPEC/SLAYER conventions (sglobal_mod) so numerical results can +be directly compared. + +All quantities in SI units. +""" +module PhysicalConstants + +# Match the Fortran GPEC/SLAYER sglobal_mod values exactly so cross-code numerical comparison is meaningful. +const MU_0 = 4.0e-7 * π # vacuum permeability [H/m] +const M_E = 9.1094e-31 # electron mass [kg] +const M_P = 1.6726e-27 # proton mass [kg] +const E_CHG = 1.6021917e-19 # elementary charge [C] +const K_B = 1.3807e-23 # Boltzmann constant [J/K] +const EPS_0 = 8.8542e-12 # vacuum permittivity [F/m] + +export MU_0, M_E, M_P, E_CHG, K_B, EPS_0 + +end # module PhysicalConstants diff --git a/src/Utilities/Utilities.jl b/src/Utilities/Utilities.jl index 7cd036f11..2687340f6 100644 --- a/src/Utilities/Utilities.jl +++ b/src/Utilities/Utilities.jl @@ -10,11 +10,17 @@ mathematical utilities. # Submodules - `FourierTransforms`: Efficient Fourier transforms with pre-computed basis functions + - `PhysicalConstants`: SI physical constants matching Fortran GPEC/SLAYER values + - `NeoclassicalResistivity`: Spitzer/Sauter/Redl resistivity closures shared by + the GGJ and SLAYER inner-layer models """ module Utilities include("FourierTransforms.jl") include("FourierCoefficients.jl") +include("PhysicalConstants.jl") +include("KineticProfiles.jl") +include("NeoclassicalResistivity.jl") include("GridUtilities.jl") using .FourierTransforms @@ -24,4 +30,17 @@ export fourier_transform!, fourier_inverse_transform! export FourierCoefficients, empty_FourierCoefficients, get_complex_coeff, get_complex_coeffs! +using .PhysicalConstants +export PhysicalConstants +export MU_0, M_E, M_P, E_CHG, K_B, EPS_0 + +export KineticProfiles + +using .NeoclassicalResistivity +export NeoclassicalResistivity +export NeoResistivityModel, SpitzerModel, SpitzerHarmModel, SauterNeoModel, RedlNeoModel +export coulomb_log_e, eta_spitzer, tau_ee_spitzer_harm, eta_spitzer_harm +export trapped_fraction, trapped_fraction_eps +export nu_star_e, eta_neoclassical + end # module Utilities diff --git a/test/runtests.jl b/test/runtests.jl index 8f891dfb9..8642e8d68 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -30,6 +30,18 @@ else include("./runtests_parallel_integration.jl") include("./runtests_sing.jl") include("./runtests_tj_analytic.jl") + include("./runtests_kinetic_profiles.jl") + include("./runtests_resist_eval.jl") + include("./runtests_slayer_params.jl") + include("./runtests_slayer_riccati.jl") + include("./runtests_slayer_inputs.jl") + include("./runtests_dispersion_residual.jl") + include("./runtests_dispersion_coupled.jl") + include("./runtests_dispersion_coupled_full.jl") + include("./runtests_dispersion_scan.jl") + include("./runtests_dispersion_amr.jl") + include("./runtests_dispersion_polish.jl") + include("./runtests_slayer_runner.jl") include("./runtests_kinetic.jl") include("./runtests_fullruns.jl") include("./runtests_coils.jl") diff --git a/test/runtests_dispersion_amr.jl b/test/runtests_dispersion_amr.jl new file mode 100644 index 000000000..014f3d019 --- /dev/null +++ b/test/runtests_dispersion_amr.jl @@ -0,0 +1,239 @@ +@testset "Dispersion AMR scan + triangulation extraction" begin + using GeneralizedPerturbedEquilibrium.InnerLayer + using GeneralizedPerturbedEquilibrium.InnerLayer: InnerLayerModel, solve_inner + using GeneralizedPerturbedEquilibrium.Dispersion + using StaticArrays + + @testset "amr_scan: basic structure and hash-caching" begin + eval_count = Ref(0) + function counting_f(Q) + eval_count[] += 1 + return ComplexF64(Q)^2 - 1 + end + + # Small 2×2 initial grid → 9 unique corners + amr = amr_scan(counting_f, (-1.0, 1.0), (-1.0, 1.0); + nre0=2, nim0=2, passes=0) + @test amr isa AMRResult + @test length(amr.cells) == 4 # 2×2 cells + # Dedup: 9 unique corners (3×3) + @test length(amr.Q) == 9 + @test length(amr.Δ) == 9 + @test eval_count[] == 9 # exactly one call per unique Q + end + + @testset "amr_scan: refinement concentrates cells near zero crossings" begin + f(Q) = ComplexF64(Q) - (0.3 + 0.4im) # single zero + amr0 = amr_scan(f, (-1.0, 1.0), (-1.0, 1.0); nre0=4, nim0=4, passes=0) + amr3 = amr_scan(f, (-1.0, 1.0), (-1.0, 1.0); nre0=4, nim0=4, passes=3) + @test length(amr3.cells) > length(amr0.cells) + @test length(amr3.Q) > length(amr0.Q) + # A 4×4 coarse grid is 16 cells; adding 3 refinement passes must + # leave the total bounded by exponential growth of only the cells + # bracketing the root (roughly linear in the path length). + @test length(amr3.cells) < 1000 # not exponential in passes + end + + @testset "amr_scan: argument validation" begin + @test_throws ArgumentError amr_scan(identity, (0.0, 1.0), (0.0, 1.0); + nre0=0, nim0=2, passes=1) + @test_throws ArgumentError amr_scan(identity, (0.0, 1.0), (0.0, 1.0); + nre0=2, nim0=0, passes=1) + @test_throws ArgumentError amr_scan(identity, (0.0, 1.0), (0.0, 1.0); + nre0=2, nim0=2, passes=-1) + end + + @testset "amr_scan: max_cells safety cap fires" begin + # A pathological f that forces every cell to subdivide every pass + f(Q) = 0.0 + 0.0im # identically zero → every cell crosses + @test_throws ErrorException amr_scan(f, (-1.0, 1.0), (-1.0, 1.0); + nre0=4, nim0=4, passes=10, + max_cells=100) + end + + @testset "find_growth_rates(AMR): single isolated root" begin + Q_root = 0.42 + 0.27im + f(Q) = ComplexF64(Q) - Q_root + amr = amr_scan(f, (-1.0, 1.5), (-0.5, 1.0); + nre0=8, nim0=6, passes=4) + result = find_growth_rates(amr, 1.0) + @test result isa GrowthRateResult + @test abs(result.Q_root - Q_root) < 1e-3 # AMR-resolution limited + @test isempty(result.poles) + @test length(result.valid_roots) == 1 + end + + @testset "find_growth_rates(AMR): higher-γ root selected" begin + Q1 = 0.3 + 0.5im # higher γ + Q2 = -0.4 + 0.1im + f(Q) = (ComplexF64(Q) - Q1) * (ComplexF64(Q) - Q2) + amr = amr_scan(f, (-1.0, 1.0), (-0.3, 0.8); + nre0=10, nim0=8, passes=4) + result = find_growth_rates(amr, 1.0) + @test length(result.valid_roots) == 2 + @test abs(result.Q_root - Q1) < 1e-2 + end + + @testset "find_growth_rates(AMR): pole detection" begin + Q_r = 0.4 + 0.2im + Q_p = -0.5 + 0.6im + f(Q) = (ComplexF64(Q) - Q_r) / (ComplexF64(Q) - Q_p) + amr = amr_scan(f, (-1.5, 1.5), (-0.5, 1.5); + nre0=10, nim0=8, passes=5) + result = find_growth_rates(amr, 1.0; pole_threshold=10.0) + @test length(result.poles) >= 1 + @test any(p -> abs(p - Q_p) < 0.05, result.poles) + @test abs(result.Q_root - Q_r) < 1e-3 + end + + @testset "find_growth_rates(AMR): tauk normalization" begin + Q_root = 1.0 + 2.0im + f(Q) = ComplexF64(Q) - Q_root + amr = amr_scan(f, (-2.0, 3.0), (-1.0, 4.0); + nre0=8, nim0=8, passes=4) + tauk = 5e-5 + result = find_growth_rates(amr, tauk) + @test result.omega_Hz ≈ real(result.Q_root) / tauk + @test result.gamma_Hz ≈ imag(result.Q_root) / tauk + end + + @testset "find_growth_rates(AMR): argument validation" begin + # Too few points to triangulate + GRE = GeneralizedPerturbedEquilibrium.Dispersion + @test_throws ArgumentError GRE._extract_growth_rates_amr( + ComplexF64[0.0+0im, 1.0+0im], ComplexF64[1.0+0im, 2.0+0im], 1.0; + re_target=0.0, im_target=0.0, pole_threshold=10.0, + filter_above_poles=true, filter_outside_re=true) + # Length mismatch + @test_throws ArgumentError GRE._extract_growth_rates_amr( + ComplexF64[0.0+0im, 1.0+0im, 1.0+1im], + ComplexF64[1.0+0im, 2.0+0im], 1.0; + re_target=0.0, im_target=0.0, pole_threshold=10.0, + filter_above_poles=true, filter_outside_re=true) + end + + @testset "AMR vs brute-force: same root to within AMR refinement precision" begin + # Sanity: the AMR and brute-force paths should find the same root + # (to roughly the AMR resolution — the AMR typically resolves + # better per-evaluation than a uniform grid). + Q_root = 0.5 + 0.3im + f(Q) = ComplexF64(Q) - Q_root + scan = brute_force_scan(f, (-1.0, 1.0), (-0.5, 1.0); + nre=80, nim=60, threaded=false) + amr = amr_scan(f, (-1.0, 1.0), (-0.5, 1.0); + nre0=8, nim0=6, passes=4) + r_grid = find_growth_rates(scan, 1.0) + r_amr = find_growth_rates(amr, 1.0) + @test abs(r_grid.Q_root - Q_root) < 1e-3 + @test abs(r_amr.Q_root - Q_root) < 1e-3 + @test abs(r_grid.Q_root - r_amr.Q_root) < 5e-3 + end + + @testset "API: SurfaceCoupling and MultiSurfaceCoupling through amr_scan" begin + struct LinModel <: InnerLayerModel + a::ComplexF64 + b::ComplexF64 + end + GeneralizedPerturbedEquilibrium.InnerLayer.solve_inner( + m::LinModel, params, Q::Number) = + InnerLayerResponse(m.a + m.b * ComplexF64(Q), zero(ComplexF64)) + + Q_pin = 0.7 - 0.3im + sc = surface_coupling(LinModel(0.0im, 1.0+0im), nothing, + Q_pin; scale=1.0, tauk=1.0) + amr = amr_scan(sc, (-0.5, 1.5), (-1.0, 0.5); + nre0=8, nim0=6, passes=4) + r = find_growth_rates(amr, sc.tauk) + @test abs(r.Q_root - Q_pin) < 1e-2 + + # Multi-surface coupled scan through AMR + Q_a, Q_b = 0.7 - 0.3im, -0.4 + 0.5im + sc1 = surface_coupling(LinModel(0.0im, 1.0+0im), nothing, + ComplexF64(0); scale=1.0, tauk=1.0) + sc2 = surface_coupling(LinModel(0.0im, 1.0+0im), nothing, + ComplexF64(0); scale=1.0, tauk=1.0) + dp = ComplexF64[Q_a 0.0; 0.0 Q_b] + mc = multi_surface_coupling([sc1, sc2], dp) + amr_c = amr_scan(mc, (-1.0, 1.5), (-1.0, 1.0); + nre0=10, nim0=8, passes=4) + r_c = find_growth_rates(amr_c, mc.surfaces[mc.ref_idx].tauk) + @test abs(r_c.Q_root - Q_b) < 1e-2 # higher-γ root + end + + # ========================================================================= + # multi_box_amr_scan + # ========================================================================= + using GeneralizedPerturbedEquilibrium.Dispersion: BoxActivity, NoActivity, + ReZeroCrossing, ImZeroCrossing, PoleMagnitude, MultiBoxAMRResult, + multi_box_amr_scan, as_amr_result + + @testset "multi_box_amr_scan: 3-box stripe with zero, pole, and inactive box" begin + # Synthetic residual: zero at Q=0 (centre stripe), pole at Q=-50 + # (left stripe), nothing in right stripe. Complex offset 1+1im keeps + # Im(f) above zero in the right stripe so its sign-change tests don't + # fire spuriously on rational-function residuals (Im=0 contour + # otherwise crosses the entire real axis). + f(Q) = (ComplexF64(Q) - 0.0) / (ComplexF64(Q) - (-50.0)) + (1.0 + 1.0im) + boxes = [((-75.0, -25.0), (-25.0, 25.0)), + ((-25.0, 25.0), (-25.0, 25.0)), + (( 25.0, 75.0), (-25.0, 25.0))] + result = multi_box_amr_scan(f, boxes; + pole_magnitude_threshold=10.0, + prescreen_nre=25, prescreen_nim=25, + nre0=25, nim0=25, passes=2, + max_cells=100_000, + max_cells_action=:warn_truncate, + parallel=false) + @test result isa MultiBoxAMRResult + @test length(result.box_results) == 3 + @test length(result.box_activity) == 3 + @test result.box_activity[1] != NoActivity # contains pole + @test result.box_activity[2] != NoActivity # contains zero + @test result.box_activity[3] == NoActivity # empty stripe + @test result.box_results[3] === nothing + @test result.box_results[1] !== nothing + @test result.box_results[2] !== nothing + # prescreen_evals is bounded by 3 boxes × 26×26 = 2028 (some shared + # boundary corners are deduplicated within each box's local cache, so + # the count is ≤ 2028). + @test result.prescreen_evals ≤ 3 * 26 * 26 + + # as_amr_result wraps cleanly + amr = as_amr_result(result) + @test amr isa AMRResult + @test length(amr.cells) == length(result.cells) + @test length(amr.Q) == length(result.Q) + end + + @testset "multi_box_amr_scan: pole-only path" begin + # Sharp pole at Q=-50+0i with complex offset that keeps Re(f),Im(f) one- + # signed across the prescreen grid except in the cell containing the + # pole. Confirms the |Δ| ≥ pole_magnitude_threshold criterion fires + # independent of sign-change tests. + g(Q) = 1000.0 / (ComplexF64(Q) - (-50.0))^2 + (5.0 + 5.0im) + boxes = [((-75.0, -25.0), (-25.0, 25.0)), + ((-25.0, 25.0), (-25.0, 25.0)), + (( 25.0, 75.0), (-25.0, 25.0))] + result = multi_box_amr_scan(g, boxes; + pole_magnitude_threshold=50.0, + prescreen_nre=25, prescreen_nim=25, + nre0=25, nim0=25, passes=1, + max_cells=100_000, + max_cells_action=:warn_truncate, + parallel=false) + @test result.box_activity[1] != NoActivity + @test result.box_activity[2] == NoActivity + @test result.box_activity[3] == NoActivity + end + + @testset "multi_box_amr_scan: argument validation" begin + f(Q) = ComplexF64(Q) + boxes = [((-1.0, 1.0), (-1.0, 1.0))] + @test_throws ArgumentError multi_box_amr_scan(f, boxes; + pole_magnitude_threshold=1.0, prescreen_nre=0) + @test_throws ArgumentError multi_box_amr_scan(f, boxes; + pole_magnitude_threshold=1.0, prescreen_nim=0) + @test_throws ArgumentError multi_box_amr_scan(f, boxes; + pole_magnitude_threshold=-1.0) + end +end diff --git a/test/runtests_dispersion_coupled.jl b/test/runtests_dispersion_coupled.jl new file mode 100644 index 000000000..5a65539ff --- /dev/null +++ b/test/runtests_dispersion_coupled.jl @@ -0,0 +1,260 @@ +@testset "Dispersion coupled determinant" begin + using GeneralizedPerturbedEquilibrium.InnerLayer + using GeneralizedPerturbedEquilibrium.InnerLayer: InnerLayerModel, solve_inner + using GeneralizedPerturbedEquilibrium.Dispersion + using LinearAlgebra + using StaticArrays + + # --------------------------------------------------------------- + # Synthetic linear inner-layer model with adjustable per-surface + # tauk for testing the Q rescaling logic. + # Δ_inner(Q) = a + b·Q + # --------------------------------------------------------------- + struct LinTestModel <: InnerLayerModel + a::ComplexF64 + b::ComplexF64 + end + GeneralizedPerturbedEquilibrium.InnerLayer.solve_inner( + m::LinTestModel, params, Q::Number) = + InnerLayerResponse(m.a + m.b * ComplexF64(Q), zero(ComplexF64)) + + function _slayer_ref() + return slayer_parameters( + n_e=5.0e19, t_e=1000.0, t_i=1000.0, + omega=0.0, omega_e=1.0e4, omega_i=5.0e3, + qval=2.0, sval_r=1.0, bt=2.0, + rs=0.5, R0=1.7, mu_i=2.0, zeff=1.0, + chi_perp=1.0, chi_tor=1.0, m=2, n=1) + end + + @testset "Constructor validation" begin + sc1 = surface_coupling(LinTestModel(0.0im, 1.0+0im), nothing, + 1.0+0im; scale=1.0, tauk=1.0) + sc2 = surface_coupling(LinTestModel(0.0im, 1.0+0im), nothing, + 2.0+0im; scale=1.0, tauk=1.0) + good_dp = ComplexF64[1.0 0.1; 0.1 2.0] + + mc = multi_surface_coupling([sc1, sc2], good_dp) + @test mc.ref_idx == 1 + @test mc.msing_max == 2 # min(3, 2) = 2 + @test size(mc.dp_matrix) == (2, 2) + + # 3-surface default also caps at 3 (min(3, 3) = 3) + sc3 = surface_coupling(LinTestModel(0.0im, 1.0+0im), nothing, + 3.0+0im; scale=1.0, tauk=1.0) + good_dp3 = ComplexF64[1.0 0.1 0.0; 0.1 2.0 0.0; 0.0 0.0 3.0] + mc3 = multi_surface_coupling([sc1, sc2, sc3], good_dp3) + @test mc3.msing_max == 3 + + # 4-surface case caps at 3 (the design default — Δ' beyond 3 surfaces + # tends to be erratic in practice) + sc4 = surface_coupling(LinTestModel(0.0im, 1.0+0im), nothing, + 4.0+0im; scale=1.0, tauk=1.0) + good_dp4 = ComplexF64[1.0 0.0 0.0 0.0; + 0.0 2.0 0.0 0.0; + 0.0 0.0 3.0 0.0; + 0.0 0.0 0.0 4.0] + mc4 = multi_surface_coupling([sc1, sc2, sc3, sc4], good_dp4) + @test mc4.msing_max == 3 # default capped at 3 + # Caller can opt in to all 4 + mc4_full = multi_surface_coupling([sc1, sc2, sc3, sc4], good_dp4; + msing_max=4) + @test mc4_full.msing_max == 4 + + # Mismatched dp size + @test_throws ArgumentError multi_surface_coupling( + [sc1, sc2], ComplexF64[1.0 0.0 0.0; 0.0 2.0 0.0; 0.0 0.0 3.0]) + @test_throws ArgumentError multi_surface_coupling( + [sc1, sc2], ComplexF64[1.0 0.0]) + + # Out-of-range ref_idx + @test_throws ArgumentError multi_surface_coupling([sc1, sc2], good_dp; + ref_idx=3) + @test_throws ArgumentError multi_surface_coupling([sc1, sc2], good_dp; + ref_idx=0) + + # Out-of-range msing_max + @test_throws ArgumentError multi_surface_coupling([sc1, sc2], good_dp; + msing_max=3) + @test_throws ArgumentError multi_surface_coupling([sc1, sc2], good_dp; + msing_max=0) + end + + @testset "Diagonal Δ' factorizes (det = ∏ per-surface residuals)" begin + # When dp_matrix is diagonal, no off-diagonal coupling exists and + # the coupled determinant should reduce exactly to the product of + # per-surface residuals. + sc1 = surface_coupling(LinTestModel(1.0+0im, 1.0+0im), nothing, + 5.0+0im; scale=1.0, tauk=1.0) + sc2 = surface_coupling(LinTestModel(2.0+0im, 1.0+0im), nothing, + 7.0+0im; scale=1.0, tauk=1.0) + sc3 = surface_coupling(LinTestModel(0.5+0im, 0.5+0im), nothing, + 3.0+0im; scale=1.0, tauk=1.0) + dp = ComplexF64[5.0 0.0 0.0; + 0.0 7.0 0.0; + 0.0 0.0 3.0] + mc = multi_surface_coupling([sc1, sc2, sc3], dp) + for Q in (0.5+0im, 2.0+0.3im, -1.0-0.5im, 4.5+1.0im) + @test mc(Q) ≈ sc1(Q) * sc2(Q) * sc3(Q) rtol = 1e-12 + end + end + + @testset "Diagonal Δ' roots = single-surface roots" begin + # With Δ_inner(Q) = b·Q and dp_diag = b·Q_root for each surface, + # the coupled determinant has its roots exactly at the union of + # single-surface roots. + Q1, Q2 = 0.5+0.0im, 2.0+0.0im + sc1 = surface_coupling(LinTestModel(0.0im, 1.0+0im), nothing, + Q1; scale=1.0, tauk=1.0) + sc2 = surface_coupling(LinTestModel(0.0im, 1.0+0im), nothing, + Q2; scale=1.0, tauk=1.0) + dp = ComplexF64[real(Q1) 0.0; 0.0 real(Q2)] + mc = multi_surface_coupling([sc1, sc2], dp) + @test abs(mc(Q1)) < 1e-12 + @test abs(mc(Q2)) < 1e-12 + @test abs(mc(0.0+0.0im)) > 0 + end + + @testset "Off-diagonal coupling shifts the roots away from the diagonal" begin + sc1 = surface_coupling(LinTestModel(0.0im, 1.0+0im), nothing, + 0.5+0im; scale=1.0, tauk=1.0) + sc2 = surface_coupling(LinTestModel(0.0im, 1.0+0im), nothing, + 2.0+0im; scale=1.0, tauk=1.0) + # Coupling-free baseline + dp_diag = ComplexF64[0.5 0.0; 0.0 2.0] + mc_diag = multi_surface_coupling([sc1, sc2], dp_diag) + # With off-diagonal coupling + dp_offd = ComplexF64[0.5 0.3; 0.3 2.0] + mc_offd = multi_surface_coupling([sc1, sc2], dp_offd) + + # Single-surface roots are no longer roots of the coupled det + Q1 = 0.5 + 0.0im + @test abs(mc_diag(Q1)) < 1e-12 # diagonal: still a root + @test abs(mc_offd(Q1)) > 0 # coupled: no longer a root + # The shift size matches the off-diagonal magnitude squared + # det = (0.5-Q)(2-Q) - 0.3² ⇒ at Q=0.5 the det = -0.09 + @test mc_offd(Q1) ≈ -0.09 rtol = 1e-12 + end + + @testset "msing_max truncation uses upper-left submatrix" begin + sc1 = surface_coupling(LinTestModel(0.0im, 1.0+0im), nothing, + 1.0+0im; scale=1.0, tauk=1.0) + sc2 = surface_coupling(LinTestModel(0.0im, 1.0+0im), nothing, + 2.0+0im; scale=1.0, tauk=1.0) + sc3 = surface_coupling(LinTestModel(0.0im, 1.0+0im), nothing, + 3.0+0im; scale=1.0, tauk=1.0) + dp = ComplexF64[1.0 0.0 0.0; + 0.0 2.0 0.0; + 0.0 0.0 3.0] + + # msing_max = 1 reduces to sc1(Q) alone + mc1 = multi_surface_coupling([sc1, sc2, sc3], dp; msing_max=1) + for Q in (0.0+0im, 1.0+0im, 2.0+0im) + @test mc1(Q) ≈ sc1(Q) + end + + # msing_max = 2 uses the upper-left 2×2 → sc1·sc2 + mc2 = multi_surface_coupling([sc1, sc2, sc3], dp; msing_max=2) + for Q in (0.0+0im, 0.5+0.5im) + @test mc2(Q) ≈ sc1(Q) * sc2(Q) + end + + # msing_max = 3 (default for ≥3 surfaces) uses the full 3×3 → sc1·sc2·sc3 + mc3 = multi_surface_coupling([sc1, sc2, sc3], dp) + @test mc3.msing_max == 3 # min(3, 3) = 3 + for Q in (0.5+0.5im, 1.5-0.5im) + @test mc3(Q) ≈ sc1(Q) * sc2(Q) * sc3(Q) + end + end + + @testset "Per-surface Q rescaling via tauk_ref / tauk_k" begin + # Each surface evaluates its inner Δ at Q_k = Q · (tauk_ref/tauk_k). + # With Δ(Q) = Q (b=1, a=0), the diagonal modification is + # M[k,k] = dp_diag_k - scale·Q·(tauk_ref/tauk_k) + # Verify against an explicit closed form with mismatched tauks. + sc1 = surface_coupling(LinTestModel(0.0im, 1.0+0im), nothing, + 0.0+0im; scale=1.0, tauk=2.0) # ref tauk + sc2 = surface_coupling(LinTestModel(0.0im, 1.0+0im), nothing, + 0.0+0im; scale=1.0, tauk=4.0) # half rate + dp = ComplexF64[0.0 0.0; 0.0 0.0] + mc = multi_surface_coupling([sc1, sc2], dp; ref_idx=1) + for Q in (1.0+0im, 0.5+0.3im) + # M[1,1] = 0 - Q · (2/2) = -Q + # M[2,2] = 0 - Q · (2/4) = -Q/2 + # det = M[1,1] · M[2,2] = Q·Q/2 = Q²/2 + @test mc(Q) ≈ Q^2 / 2 rtol = 1e-12 + end + + # Switch ref_idx to surface 2 + mc2 = multi_surface_coupling([sc1, sc2], dp; ref_idx=2) + for Q in (1.0+0im, 0.5+0.3im) + # M[1,1] = -Q · (4/2) = -2Q + # M[2,2] = -Q · (4/4) = -Q + # det = 2Q · Q = 2Q² + @test mc2(Q) ≈ 2 * Q^2 rtol = 1e-12 + end + end + + @testset "SLAYER self-consistency: known coupled root" begin + # Build a 2-surface SLAYER MultiSurfaceCoupling, evaluate at + # Q_pin, and back-fill dp_matrix so that det(M(Q_pin)) = 0 + # exactly. + p_a = _slayer_ref() + p_b = _slayer_ref() + m = SLAYERModel() + sc1 = surface_coupling(m, p_a, 0.0+0im) + sc2 = surface_coupling(m, p_b, 0.0+0im) + + Q_pin = 0.3 + 0.4im + ref_tauk = sc1.tauk + + # Compute the diagonal modifications at Q_pin + Δ1 = solve_inner(m, p_a, Q_pin * (ref_tauk/sc1.tauk)).tearing * sc1.scale + Δ2 = solve_inner(m, p_b, Q_pin * (ref_tauk/sc2.tauk)).tearing * sc2.scale + + # Build dp such that M(Q_pin) is exactly singular. + # Choose off-diagonal couplings, then set diagonals so M[k,k]=Δ_k + # makes the matrix singular by setting M[1,1]·M[2,2] = M[1,2]·M[2,1]. + c12, c21 = 0.05+0im, 0.05+0im + # Pick M[1,1] arbitrarily, solve for M[2,2]: + M11 = 0.7 + 0.0im + M22 = (c12 * c21) / M11 + dp = ComplexF64[M11+Δ1 c12; + c21 M22+Δ2] + + mc = multi_surface_coupling([sc1, sc2], dp) + # The constructed M(Q_pin) is exactly singular by construction + @test abs(mc(Q_pin)) < 1e-10 + + # Off-pin Q gives a non-trivial determinant + @test abs(mc(Q_pin + 0.05)) > 1e-3 + end + + @testset "GGJ surfaces flow through the coupled API" begin + p = glasser_wang_2020_eq55() + sc1 = surface_coupling(GGJModel(solver=:shooting), p, -1.0+0im) + sc2 = surface_coupling(GGJModel(solver=:shooting), p, -2.0+0im) + dp = ComplexF64[-1.0 0.1; 0.1 -2.0] + mc = multi_surface_coupling([sc1, sc2], dp) + @test mc isa MultiSurfaceCoupling + @test mc.surfaces[1].tauk == 1.0 # GGJ default + @test mc(1e-3 + 0.0im) isa ComplexF64 + end + + @testset "Broadcast over a 2D Q grid" begin + # Coupled residual must be broadcast-compatible for PR 5/6 scans. + sc1 = surface_coupling(LinTestModel(0.0im, 1.0+0im), nothing, + 0.0+0im; scale=1.0, tauk=1.0) + sc2 = surface_coupling(LinTestModel(0.0im, 1.0+0im), nothing, + 0.0+0im; scale=1.0, tauk=1.0) + dp = ComplexF64[0.0 0.0; 0.0 0.0] + mc = multi_surface_coupling([sc1, sc2], dp) + + Q_grid = [(qr + qi*im) for qr in -1.0:0.5:1.0, qi in -1.0:0.5:1.0] + det_grid = mc.(Q_grid) + @test size(det_grid) == size(Q_grid) + @test all(d -> d isa ComplexF64, det_grid) + # det = Q² with these params; one interior cross-check + @test det_grid[3, 3] ≈ Q_grid[3, 3]^2 + end +end diff --git a/test/runtests_dispersion_coupled_full.jl b/test/runtests_dispersion_coupled_full.jl new file mode 100644 index 000000000..d471650f8 --- /dev/null +++ b/test/runtests_dispersion_coupled_full.jl @@ -0,0 +1,270 @@ +@testset "Dispersion 4m×4m full Pletzer-Dewar coupled determinant (CoupledFullMatch)" begin + using GeneralizedPerturbedEquilibrium.InnerLayer + using GeneralizedPerturbedEquilibrium.InnerLayer: InnerLayerModel, InnerLayerResponse, solve_inner + using GeneralizedPerturbedEquilibrium.Dispersion + using LinearAlgebra + + # Synthetic inner-layer model with explicit (tearing, interchange) + # pair — lets us probe both channels independently. + struct _LinearInnerF <: InnerLayerModel + a_t::ComplexF64 + b_t::ComplexF64 # tearing: Δ_t(Q) = a_t + b_t·Q + a_i::ComplexF64 + b_i::ComplexF64 # interchange: Δ_i(Q) = a_i + b_i·Q + end + GeneralizedPerturbedEquilibrium.InnerLayer.solve_inner( + m::_LinearInnerF, params, Q::Number) = + InnerLayerResponse(m.a_t + m.b_t * ComplexF64(Q), + m.a_i + m.b_i * ComplexF64(Q)) + + @testset "Constructor validation" begin + sc1 = surface_coupling(_LinearInnerF(-1.0 + 0im, 0 + 0im, 0.1 + 0im, 0 + 0im), + nothing, 0 + 0im; scale=1.0, tauk=1.0) + sc2 = surface_coupling(_LinearInnerF(-0.5 + 0im, 0 + 0im, 0.2 + 0im, 0 + 0im), + nothing, 0 + 0im; scale=1.0, tauk=1.0) + dp_raw = ComplexF64[ + 1.0 0.1 0.2 0.05; + 0.1 1.2 0.05 0.2; + 0.2 0.05 -5.0 0.3; + 0.05 0.2 0.3 -4.0] + mc = multi_surface_coupling_full([sc1, sc2], dp_raw) + @test size(mc.dp_raw) == (4, 4) + @test mc.msing_max == 2 + @test mc.ref_idx == 1 + @test mc.rotation == [0.0, 0.0] + @test mc.ntor == 1 + + # Wrong outer dim + @test_throws ArgumentError multi_surface_coupling_full([sc1, sc2], + dp_raw[1:2, 1:2]) + @test_throws ArgumentError multi_surface_coupling_full([sc1, sc2], + dp_raw; ref_idx=0) + @test_throws ArgumentError multi_surface_coupling_full([sc1, sc2], + dp_raw; ref_idx=3) + @test_throws ArgumentError multi_surface_coupling_full([sc1, sc2], + dp_raw; msing_max=0) + @test_throws ArgumentError multi_surface_coupling_full([sc1, sc2], + dp_raw; msing_max=3) + # Wrong rotation length + @test_throws ArgumentError multi_surface_coupling_full([sc1, sc2], + dp_raw; rotation=[0.0]) + end + + @testset "1-surface 4×4 det matches hand computation" begin + # m=1 case: matrix is 4×4 and fully hand-verifiable. + dp_raw = ComplexF64[1.0 0.5; 0.3 2.0] + sc = surface_coupling(_LinearInnerF(0.7 + 0im, 0 + 0im, 0.2 + 0im, 0 + 0im), + nothing, 0 + 0im; scale=1.0, tauk=1.0, dc=0.0) + mc = multi_surface_coupling_full([sc], dp_raw) + # At Q=0.1 both Δ_t and Δ_i are constants (b=0), so inner Δs independent of Q. + det_jl = mc(0.1 + 0.0im) + # Hand-computed matrix (see the port comment block for the layout): + # mat[3:4, 1:2] = transpose(dp_raw) = [1 0.3; 0.5 2] + # mat[1,1]=1, mat[2,2]=1 + # mat[1,3]=-1, mat[1,4]=+1, mat[2,3]=-1, mat[2,4]=-1 + # delta1=interchange=0.2, delta2=tearing=0.7 + # mat[3,3]=-0.2, mat[3,4]=+0.7, mat[4,3]=-0.2, mat[4,4]=-0.7 + M_hand = ComplexF64[ + 1 0 -1 1; + 0 1 -1 -1; + 1 0.3 -0.2 0.7; + 0.5 2 -0.2 -0.7] + @test det_jl ≈ det(M_hand) + end + + @testset "Static (rotation=0) delta1, delta2 assembly" begin + # Replicate the Pletzer-Dewar match assembly by hand for msing=2 and + # synthetic inner values; confirm the module agrees. + dp_raw = ComplexF64[ + 10.0 0.1 0.2 0.3; + 0.1 11.0 0.4 0.5; + 0.2 0.4 -5.0 0.6; + 0.3 0.5 0.6 -4.0] + sc1 = surface_coupling(_LinearInnerF(0.2 + 0.1im, 0 + 0im, 0.7 - 0.05im, 0 + 0im), + nothing, 0 + 0im; scale=1.0, tauk=1.0, dc=0.0) + sc2 = surface_coupling(_LinearInnerF(-0.3 + 0.0im, 0 + 0im, 1.5 + 0.3im, 0 + 0im), + nothing, 0 + 0im; scale=1.0, tauk=1.0, dc=0.0) + mc = multi_surface_coupling_full([sc1, sc2], dp_raw) + det_jl = mc(0.0 + 0.0im) + + # Hand assembly + M = zeros(ComplexF64, 8, 8) + M[5:8, 1:4] = transpose(dp_raw) + # Surface 1: idx1..4 = 1,2,5,6 + M[1, 1] = 1 + M[2, 2] = 1 + M[1, 5] = -1 + M[1, 6] = 1 + M[2, 5] = -1 + M[2, 6] = -1 + d1_1 = 0.7 - 0.05im # interchange + d2_1 = 0.2 + 0.1im # tearing + M[5, 5] = -d1_1 + M[5, 6] = d2_1 + M[6, 5] = -d1_1 + M[6, 6] = -d2_1 + # Surface 2: idx1..4 = 3,4,7,8 + M[3, 3] = 1 + M[4, 4] = 1 + M[3, 7] = -1 + M[3, 8] = 1 + M[4, 7] = -1 + M[4, 8] = -1 + d1_2 = 1.5 + 0.3im + d2_2 = -0.3 + 0im + M[7, 7] = -d1_2 + M[7, 8] = d2_2 + M[8, 7] = -d1_2 + M[8, 8] = -d2_2 + + @test det_jl ≈ det(M) atol = 1e-12 * abs(det(M)) + end + + @testset "Rotation shift applies i·ntor·rotation to inner Q argument" begin + # Ensure the per-surface rotation enters the inner-layer argument. + # Use a linear Δ_t model so Q-dependence is tractable. + dp_raw = ComplexF64[1.0 0; 0 1.0] + # Δ_t(Q) = Q (pure linear), Δ_i(Q) = 0 + sc = surface_coupling(_LinearInnerF(0 + 0im, 1 + 0im, 0 + 0im, 0 + 0im), + nothing, 0 + 0im; scale=1.0, tauk=1.0, dc=0.0) + # Case A: rotation=0, Q=2+0im → inner sees 2+0im → Δ_t=2, Δ_i=0 + mc0 = multi_surface_coupling_full([sc], dp_raw; rotation=[0.0], ntor=1) + # Case B: rotation=3, Q=2+0im → inner sees 2 + 1j*1*3 = 2+3i → Δ_t=2+3i + mcR = multi_surface_coupling_full([sc], dp_raw; rotation=[3.0], ntor=1) + @test mc0(2.0 + 0.0im) ≠ mcR(2.0 + 0.0im) + + # Check by hand. Both with the same outer matrix: + function detAt(Δ_t, Δ_i) + M = ComplexF64[ + 1 0 -1 1; + 0 1 -1 -1; + 1 0 -Δ_i Δ_t; + 0 1 -Δ_i -Δ_t] + return det(M) + end + @test mc0(2.0 + 0.0im) ≈ detAt(2.0 + 0.0im, 0.0 + 0.0im) + @test mcR(2.0 + 0.0im) ≈ detAt(2.0 + 3.0im, 0.0 + 0.0im) + end + + @testset "SurfaceCoupling scale multiplies both inner channels" begin + # sc.scale should hit both delta1 and delta2 equally. + dp_raw = ComplexF64[1 0; 0 1] + sc_unit = surface_coupling(_LinearInnerF(0.3 + 0im, 0 + 0im, 0.7 + 0im, 0 + 0im), + nothing, 0 + 0im; scale=1.0, tauk=1.0, dc=0.0) + sc_x2 = surface_coupling(_LinearInnerF(0.3 + 0im, 0 + 0im, 0.7 + 0im, 0 + 0im), + nothing, 0 + 0im; scale=2.0, tauk=1.0, dc=0.0) + mc1 = multi_surface_coupling_full([sc_unit], dp_raw) + mc2 = multi_surface_coupling_full([sc_x2], dp_raw) + # Expected hand det for scale=1: d_int=0.7, d_tear=0.3 + # For scale=2: d_int=1.4, d_tear=0.6 + function detAt(Δt, Δi) + M = ComplexF64[1 0 -1 1; 0 1 -1 -1; 1 0 -Δi Δt; 0 1 -Δi -Δt] + return det(M) + end + @test mc1(0.5 + 0im) ≈ detAt(0.3, 0.7) + @test mc2(0.5 + 0im) ≈ detAt(0.6, 1.4) + end + + @testset "msing_max truncation" begin + dp_raw = ComplexF64[ + 1.0 0.1 0.2 0.3; + 0.1 1.2 0.4 0.5; + 0.2 0.4 -5.0 0.6; + 0.3 0.5 0.6 -4.0] + sc1 = surface_coupling(_LinearInnerF(0.5 + 0im, 0 + 0im, 0.2 + 0im, 0 + 0im), + nothing, 0 + 0im; scale=1.0, tauk=1.0) + sc2 = surface_coupling(_LinearInnerF(-0.3 + 0im, 0 + 0im, 1.0 + 0im, 0 + 0im), + nothing, 0 + 0im; scale=1.0, tauk=1.0) + + # With msing_max=1, only surface 1 participates; matrix becomes 4×4 + # using the upper-left 2×2 block of dp_raw. + mc1 = multi_surface_coupling_full([sc1, sc2], dp_raw; msing_max=1) + det1 = mc1(0 + 0im) + # Hand construct the 4×4 + sub_dp = dp_raw[1:2, 1:2] + M1 = zeros(ComplexF64, 4, 4) + M1[3:4, 1:2] = transpose(sub_dp) + M1[1, 1] = 1 + M1[2, 2] = 1 + M1[1, 3] = -1 + M1[1, 4] = 1 + M1[2, 3] = -1 + M1[2, 4] = -1 + M1[3, 3] = -0.2 + M1[3, 4] = 0.5 + M1[4, 3] = -0.2 + M1[4, 4] = -0.5 + @test det1 ≈ det(M1) + + # Full msing_max=2 case must differ + mcfull = multi_surface_coupling_full([sc1, sc2], dp_raw; msing_max=2) + @test mcfull(0 + 0im) ≠ det1 + end + + @testset "SLAYER-like (Δ_interchange=0) still gives correct det" begin + # When both surfaces are pure-tearing (Δ_interchange=0), the matrix + # is non-trivial but still well-defined; verify it's non-zero and + # finite (not NaN from singular inner block). + dp_raw = ComplexF64[1.0 0.1 0.2 0.3; 0.1 1.2 0.4 0.5; + 0.2 0.4 -5.0 0.6; 0.3 0.5 0.6 -4.0] + sc1 = surface_coupling(_LinearInnerF(-2 + 0im, 0 + 0im, 0 + 0im, 0 + 0im), + nothing, 0 + 0im; scale=1.0, tauk=1.0) + sc2 = surface_coupling(_LinearInnerF(-3 + 0im, 0 + 0im, 0 + 0im, 0 + 0im), + nothing, 0 + 0im; scale=1.0, tauk=1.0) + mc = multi_surface_coupling_full([sc1, sc2], dp_raw) + d = mc(0.1 + 0.2im) + @test isfinite(real(d)) + @test isfinite(imag(d)) + end + + @testset "inner_kwargs pass-through" begin + # Verify that inner_kwargs reaches solve_inner at each Q evaluation. + # Use a synthetic model with a tuning parameter to confirm plumbing. + struct _ProbeModel <: InnerLayerModel end + GeneralizedPerturbedEquilibrium.InnerLayer.solve_inner( + ::_ProbeModel, params, Q::Number; scale_factor::Float64=1.0) = + InnerLayerResponse(scale_factor * (1.0 + 0im), + scale_factor * (0.5 + 0im)) + + dp_raw = ComplexF64[1.0 0; 0 1.0] + sc = surface_coupling(_ProbeModel(), nothing, 0 + 0im; + scale=1.0, tauk=1.0, dc=0.0) + mc_native = multi_surface_coupling_full([sc], dp_raw) + mc_tuned = multi_surface_coupling_full([sc], dp_raw; + inner_kwargs=(scale_factor=0.5,)) + @test mc_native.inner_kwargs == NamedTuple() + @test mc_tuned.inner_kwargs == (scale_factor=0.5,) + + # Det should differ because inner Δ's are halved by the kwarg + det_native = mc_native(0.0 + 0.0im) + det_tuned = mc_tuned(0.0 + 0.0im) + @test det_native ≠ det_tuned + @test isfinite(real(det_native)) && isfinite(imag(det_native)) + @test isfinite(real(det_tuned)) && isfinite(imag(det_tuned)) + end + + @testset "Static GGJ-like scenario runs without error" begin + # Smoke test: larger m=3 case, both channels non-trivial, Q shifted + m = 3 + Random_dp = ComplexF64[ + 5.0 0.2 0.1 0.05 0.3 0.2; + 0.2 7.0 0.3 0.1 0.2 0.1; + 0.1 0.3 -3.0 0.4 0.1 0.05; + 0.05 0.1 0.4 -8.0 0.2 0.1; + 0.3 0.2 0.1 0.2 -2.5 0.3; + 0.2 0.1 0.05 0.1 0.3 -6.5] + # Non-trivial Q dependence: Δ_t(Q) = a + 0.5·Q, Δ_i(Q) = b + 0.2·Q + scs = [surface_coupling(_LinearInnerF(0.3 + 0.01k * im, 0.5 + 0im, + 0.7 + 0.02k * im, 0.2 + 0im), + nothing, 0 + 0im; scale=1.0, tauk=1.0) + for k in 1:m] + mc = multi_surface_coupling_full(scs, Random_dp) + @test size(mc.dp_raw) == (6, 6) + d0 = mc(0.0 + 0.0im) + d1 = mc(1.0 + 0.5im) + @test isfinite(real(d0)) && isfinite(imag(d0)) + @test isfinite(real(d1)) && isfinite(imag(d1)) + # Check that it's actually Q-dependent + @test d0 != d1 + end +end diff --git a/test/runtests_dispersion_polish.jl b/test/runtests_dispersion_polish.jl new file mode 100644 index 000000000..8bc4c9702 --- /dev/null +++ b/test/runtests_dispersion_polish.jl @@ -0,0 +1,184 @@ +@testset "Dispersion root polishing" begin + using GeneralizedPerturbedEquilibrium.Dispersion + using LinearAlgebra + D = GeneralizedPerturbedEquilibrium.Dispersion + + # ---------------------------------------------------------------- + # _polish_root: core local-solve behaviour on synthetic residuals + # ---------------------------------------------------------------- + @testset "_polish_root: recovers a known simple root, |f| → 0" begin + r = 0.42 + 0.27im + f(Q) = ComplexF64(Q) - r # zero exactly at r + Q0 = r + (0.013 - 0.009im) # off-root start + Qp, nev, improved = D._polish_root(f, Q0, 0.1) + @test improved + @test abs(Qp - r) < 1e-10 + @test abs(f(Qp)) < 1e-10 + @test nev <= 3 * 8 + 2 # bounded eval budget + end + + @testset "_polish_root: nonlinear residual converges" begin + r = -0.3 + 0.5im + f(Q) = (ComplexF64(Q) - r) * (1 + 0.4 * (ComplexF64(Q) - r)) # simple root at r + Qp, _, improved = D._polish_root(f, r + 0.02 - 0.015im, 0.15) + @test improved + @test abs(Qp - r) < 1e-7 + end + + @testset "_polish_root: no-op-or-better invariant (never worse)" begin + # The polish must never return a point with larger |f| than the start. + for r in (0.1 + 0.2im, -0.5 + 0.0im, 0.3 - 0.4im) + f(Q) = (ComplexF64(Q) - r) * (ComplexF64(Q) + 1.7) + for off in (0.01 + 0.0im, 0.05 + 0.0im, 0.0 + 0.08im, -0.03 + 0.02im) + Q0 = r + off + Qp, _, _ = D._polish_root(f, Q0, 0.2) + @test abs(f(Qp)) <= abs(f(Q0)) + 1e-12 + end + end + end + + @testset "_polish_root: trust region bounds the step (no jump to far root)" begin + f(Q) = ComplexF64(Q) - (10.0 + 0.0im) # only root is far outside R + Q0 = 0.0 + 0.0im + R = 0.1 + Qp, _, _ = D._polish_root(f, Q0, R) + @test abs(Qp - Q0) <= R + 1e-9 # never leaves the trust disk + @test abs(Qp - (10.0 + 0.0im)) > 5.0 # did NOT migrate to the far root + @test abs(f(Qp)) <= abs(f(Q0)) # still moved downhill within the disk + end + + @testset "_polish_root: non-finite residual falls back, no crash" begin + fnan(Q) = ComplexF64(NaN, NaN) + Qp, nev, improved = D._polish_root(fnan, 0.3 + 0.1im, 0.1) + @test !improved + @test Qp == 0.3 + 0.1im # hard fallback to the start + @test nev >= 1 + end + + @testset "_polish_root: zero radius is a no-op" begin + f(Q) = ComplexF64(Q) - (0.2 + 0.1im) + Qp, _, improved = D._polish_root(f, 0.25 + 0.05im, 0.0) + @test !improved + @test Qp == 0.25 + 0.05im + end + + @testset "_polish_root: deterministic (same input → same output)" begin + f(Q) = (ComplexF64(Q) - (0.5 + 0.3im)) * (ComplexF64(Q) - 2) + a = D._polish_root(f, 0.52 + 0.31im, 0.1) + b = D._polish_root(f, 0.52 + 0.31im, 0.1) + @test a[1] == b[1] + @test a[2] == b[2] + end + + @testset "_polish_root: BLAS-thread-independent for a det residual" begin + # det() routes through LAPACK; polishing must be invariant to BLAS threads + # (this is the property the parallel-scan BLAS pin + polish together give). + Qstar = 0.3 + 0.2im + fdet(Q) = det(ComplexF64[1 0 0; 0 1 0; 0 0 (ComplexF64(Q)-Qstar)]) + b0 = BLAS.get_num_threads() + try + BLAS.set_num_threads(1) + r1 = D._polish_root(fdet, 0.31 + 0.21im, 0.1) + BLAS.set_num_threads(4) + r4 = D._polish_root(fdet, 0.31 + 0.21im, 0.1) + @test isapprox(r1[1], r4[1]; atol=1e-10) + @test abs(fdet(r1[1])) < 1e-8 + finally + BLAS.set_num_threads(b0) + end + end + + # ---------------------------------------------------------------- + # _polish_trust_radius: neighbour-aware bound keeps roots coherent + # ---------------------------------------------------------------- + @testset "_polish_trust_radius: capped by nearest neighbour spacing" begin + # Two close intersections + one far: radius of #1 is bound by the close one + pts = ComplexF64[0+0im, 0.001+0im, 5+0im] + R1 = D._polish_trust_radius(pts, 1, 0.01) + @test R1 <= 0.45 * 0.001 + 1e-15 # < half the close-pair spacing + # Isolated pair: radius falls back to the grid-cell cap (k_cell·h) + R2 = D._polish_trust_radius(ComplexF64[0+0im, 5+0im], 1, 0.01) + @test R2 <= 3.0 * 0.01 + 1e-12 + @test R2 > 0 + end + + @testset "_polish_trust_radius + polish: close roots stay coherent (no swap/merge)" begin + r1 = 0.30 + 0.20im + r2 = r1 + 0.002 # second root 0.002 away + f(Q) = (ComplexF64(Q) - r1) * (ComplexF64(Q) - r2) + pts = ComplexF64[r1 + 0.0003, r2 - 0.0003] # coarse contour estimates + R1 = D._polish_trust_radius(pts, 1, 0.001) + R2 = D._polish_trust_radius(pts, 2, 0.001) + p1 = D._polish_root(f, pts[1], R1)[1] + p2 = D._polish_root(f, pts[2], R2)[1] + @test abs(p1 - r1) < abs(p1 - r2) # #1 refined toward its OWN root + @test abs(p2 - r2) < abs(p2 - r1) # #2 refined toward its OWN root + @test p1 != p2 # did not collapse to one point + end + + # ---------------------------------------------------------------- + # _median_segment_length: grid-resolution proxy + # ---------------------------------------------------------------- + @testset "_median_segment_length" begin + re_paths = [ComplexF64[0+0im, 0.1+0im, 0.3+0im]] # segment lengths 0.1, 0.2 + im_paths = [ComplexF64[0+0im, 0+0.1im]] # segment length 0.1 + @test D._median_segment_length(re_paths, im_paths) ≈ 0.1 # median of [0.1,0.2,0.1] + @test D._median_segment_length(Vector{Vector{ComplexF64}}(), + Vector{Vector{ComplexF64}}()) == 0.0 + end + + # ---------------------------------------------------------------- + # Integration: find_growth_rates with `residual` polishes the root + # ---------------------------------------------------------------- + @testset "find_growth_rates: polish recovers the true root from a coarse scan" begin + r = 0.42 + 0.27im + f(Q) = (ComplexF64(Q) - r) * (1 + 0.4 * (ComplexF64(Q) - r)) # nonlinear, root at r + scan = brute_force_scan(f, (0.0, 1.0), (0.0, 0.6); nre=15, nim=12, threaded=false) + gr_raw = find_growth_rates(scan, 1.0; residual=nothing) + gr_pol = find_growth_rates(scan, 1.0; residual=f) + @test !isnan(real(gr_raw.Q_root)) # coarse scan still isolates it + @test abs(f(gr_pol.Q_root)) <= abs(f(gr_raw.Q_root)) # polish never worsens |f| + @test abs(gr_pol.Q_root - r) < 1e-4 # and converges to the true root + # polishing must not invent or drop roots vs the raw pass + @test length(gr_pol.valid_roots) == length(gr_raw.valid_roots) + end + + @testset "find_growth_rates: residual=nothing is unchanged (backward compatible)" begin + r = 0.42 + 0.27im + f(Q) = ComplexF64(Q) - r + scan = brute_force_scan(f, (0.0, 1.0), (0.0, 0.6); nre=21, nim=15, threaded=false) + a = find_growth_rates(scan, 1.0) # default: no residual, no polish + b = find_growth_rates(scan, 1.0; residual=nothing) + @test a.Q_root == b.Q_root + end + + # ---------------------------------------------------------------- + # Validity gate: drop intersections that don't polish to a true zero + # ---------------------------------------------------------------- + @testset "find_growth_rates: validity gate keeps real roots, drops spurious" begin + r = 0.42 + 0.27im + f(Q) = (ComplexF64(Q) - r) * (1 + 0.4 * (ComplexF64(Q) - r)) # real root at r + scan = brute_force_scan(f, (0.0, 1.0), (0.0, 0.6); nre=15, nim=12, threaded=false) + + # Normal tolerance: the genuine root polishes to |f|≈0 ⇒ kept, not flagged + gr = find_growth_rates(scan, 1.0; residual=f, validity_rtol=1e-3) + @test !(:spurious in gr.warning_flags) + @test !isnan(real(gr.Q_root)) + @test abs(gr.Q_root - r) < 1e-4 + + # Absurdly tight tolerance: even the true root's residual (~machine eps) + # exceeds validity_rtol·median(|Δ|) ⇒ every candidate dropped. Exercises + # the gate firing + the :spurious / :no_root / filtered_roots plumbing. + gr2 = find_growth_rates(scan, 1.0; residual=f, validity_rtol=1e-300) + @test :spurious in gr2.warning_flags + @test :no_root in gr2.warning_flags # all candidates were spurious + @test isnan(real(gr2.Q_root)) # ⇒ no root reported + @test length(gr2.filtered_roots) >= 1 # dropped candidate parked here + @test isempty(gr2.valid_roots) + + # Gate is inert without a residual (no polishing ⇒ nothing to test against) + gr3 = find_growth_rates(scan, 1.0; residual=nothing, validity_rtol=1e-300) + @test !(:spurious in gr3.warning_flags) + @test !isnan(real(gr3.Q_root)) + end +end diff --git a/test/runtests_dispersion_residual.jl b/test/runtests_dispersion_residual.jl new file mode 100644 index 000000000..d0235a0da --- /dev/null +++ b/test/runtests_dispersion_residual.jl @@ -0,0 +1,117 @@ +@testset "Dispersion residual (SurfaceCoupling)" begin + using GeneralizedPerturbedEquilibrium.InnerLayer + using GeneralizedPerturbedEquilibrium.InnerLayer: InnerLayerModel, solve_inner + using GeneralizedPerturbedEquilibrium.Dispersion + using StaticArrays + + # --------------------------------------------------------------- + # Synthetic linear inner-layer model used to verify the residual + # arithmetic without ODE noise: + # Δ_inner(Q) = a + b·Q + # r(Q) = dp_diag - scale·(a + b·Q) - dc + # --------------------------------------------------------------- + struct LinearTestModel <: InnerLayerModel + a::ComplexF64 + b::ComplexF64 + end + GeneralizedPerturbedEquilibrium.InnerLayer.solve_inner( + m::LinearTestModel, params, Q::Number) = + InnerLayerResponse(m.a + m.b * ComplexF64(Q), zero(ComplexF64)) + + function _slayer_ref() + return slayer_parameters( + n_e=5.0e19, t_e=1000.0, t_i=1000.0, + omega=0.0, omega_e=1.0e4, omega_i=5.0e3, + qval=2.0, sval_r=1.0, bt=2.0, + rs=0.5, R0=1.7, mu_i=2.0, zeff=1.0, + chi_perp=1.0, chi_tor=1.0, m=2, n=1) + end + + @testset "Constructor scale defaults" begin + # SLAYER: scale = lu^(1/3) so the dimensionless Δ from riccati_f + # is mapped to outer ψ-units (Fortran SLAYER growthrates routine) + p_sl = _slayer_ref() + sc_sl = surface_coupling(SLAYERModel(), p_sl, -1.0 + 0.0im) + @test sc_sl.scale ≈ p_sl.lu^(1/3) + @test sc_sl.dc == 0.0 + @test sc_sl.dp_diag == ComplexF64(-1.0) + + # GGJ: scale = 1 because rescale_delta is applied inside solve_inner + p_ggj = glasser_wang_2020_eq55() + sc_ggj = surface_coupling(GGJModel(solver=:shooting), p_ggj, + -1.0 + 0.0im) + @test sc_ggj.scale == 1.0 + + # Generic fallback honors explicit scale + dc kwargs + sc_lin = surface_coupling(LinearTestModel(0.0im, 1.0+0im), nothing, + 3.0 + 0.0im; dc=0.5, scale=2.0) + @test sc_lin.scale == 2.0 + @test sc_lin.dc == 0.5 + end + + @testset "Residual arithmetic on synthetic linear model" begin + # r(Q) = dp_diag - scale·(a + b·Q) - dc + a, b = 1.0 + 2.0im, -0.5 + 1.0im + scale = 3.0 + dc = 0.25 + Q_root = -0.7 + 0.3im + dp_diag = (a + b * Q_root) * scale + dc # construct a known root + + sc = surface_coupling(LinearTestModel(a, b), nothing, dp_diag; + dc=dc, scale=scale) + @test sc(Q_root) ≈ 0 atol = 1e-12 + + # Off-root residual matches the closed form + for Q in (0.0+0im, 1.5-0.5im, -0.2+1.2im) + expected = dp_diag - scale * (a + b * Q) - dc + @test sc(Q) ≈ expected + end + end + + @testset "SLAYER residual: self-consistent zero at known Q" begin + # Build dp_diag = scale · Δ(Q_pin) so the residual is exactly zero + # at Q_pin (residual evaluated through the same ODE that produced Δ). + p = _slayer_ref() + m = SLAYERModel() + Q_pin = 0.3 + 0.4im + Δ_pin = solve_inner(m, p, Q_pin).tearing + dp_diag = p.lu^(1/3) * Δ_pin + + sc = surface_coupling(m, p, dp_diag) + @test abs(sc(Q_pin)) < 1e-13 # self-consistent + + # Perturbing Q gives a non-trivial residual + @test abs(sc(Q_pin + 0.05)) > 1e-3 + @test sc(Q_pin + 0.05) isa ComplexF64 + end + + @testset "Interface compliance: GGJ ↔ SLAYER through abstract dispatch" begin + # Both inner-layer models flow through the same SurfaceCoupling + # API. Numerical agreement is *not* asserted (different physics) — + # only that both pipelines construct and evaluate. + p_sl = _slayer_ref() + sc_sl = surface_coupling(SLAYERModel(), p_sl, -100.0 + 0.0im) + @test sc_sl isa SurfaceCoupling{SLAYERModel{:fitzpatrick},SLAYERParameters} + @test sc_sl(0.0 + 0.5im) isa ComplexF64 + + p_ggj = glasser_wang_2020_eq55() + sc_ggj = surface_coupling(GGJModel(solver=:shooting), p_ggj, + -1.0 + 0.0im) + @test sc_ggj isa SurfaceCoupling{GGJModel{:shooting},GGJParameters} + @test sc_ggj(1e-3 + 0.0im) isa ComplexF64 + end + + @testset "Residual is callable on grids (broadcast)" begin + # Brute-force / AMR scans (PR 5/6) will broadcast `sc` over a 2D + # complex-Q grid; verify that broadcasting works element-wise. + a, b = 0.0+0im, 1.0+0im + sc = surface_coupling(LinearTestModel(a, b), nothing, 2.0+0im; + dc=0.0, scale=1.0) + Q_grid = [(qr + qi*im) for qr in -1.0:0.5:1.0, qi in -1.0:0.5:1.0] + Δ_grid = sc.(Q_grid) + @test size(Δ_grid) == size(Q_grid) + @test all(d -> d isa ComplexF64, Δ_grid) + # Closed-form check at one interior grid point + @test Δ_grid[3, 3] ≈ sc(Q_grid[3, 3]) + end +end diff --git a/test/runtests_dispersion_scan.jl b/test/runtests_dispersion_scan.jl new file mode 100644 index 000000000..f50b449fc --- /dev/null +++ b/test/runtests_dispersion_scan.jl @@ -0,0 +1,151 @@ +@testset "Dispersion brute-force scan + growth-rate extraction" begin + using GeneralizedPerturbedEquilibrium.InnerLayer + using GeneralizedPerturbedEquilibrium.InnerLayer: InnerLayerModel, solve_inner + using GeneralizedPerturbedEquilibrium.Dispersion + using StaticArrays + + @testset "brute_force_scan: regular grid evaluation" begin + f(Q) = ComplexF64(Q)^2 - 1 + scan = brute_force_scan(f, (-2.0, 2.0), (-1.0, 1.0); + nre=21, nim=11, threaded=false) + @test scan isa ScanResult + @test size(scan.Q) == (21, 11) + @test size(scan.Δ) == (21, 11) + @test length(scan.re_axis) == 21 + @test length(scan.im_axis) == 11 + @test scan.re_axis[1] == -2.0 + @test scan.re_axis[end] == 2.0 + @test scan.im_axis[1] == -1.0 + @test scan.im_axis[end] == 1.0 + # Spot-check a grid value + i, j = 11, 6 + @test scan.Q[i, j] ≈ scan.re_axis[i] + scan.im_axis[j]*im + @test scan.Δ[i, j] ≈ scan.Q[i, j]^2 - 1 + end + + @testset "brute_force_scan: threaded vs non-threaded agree" begin + f(Q) = sin(ComplexF64(Q)) + s_t = brute_force_scan(f, (-1.0, 1.0), (-0.5, 0.5); + nre=15, nim=10, threaded=true) + s_n = brute_force_scan(f, (-1.0, 1.0), (-0.5, 0.5); + nre=15, nim=10, threaded=false) + @test s_t.Δ == s_n.Δ + end + + @testset "brute_force_scan: argument validation" begin + @test_throws ArgumentError brute_force_scan(identity, (0.0, 1.0), + (0.0, 1.0); nre=1, nim=10) + @test_throws ArgumentError brute_force_scan(identity, (0.0, 1.0), + (0.0, 1.0); nre=10, nim=1) + end + + @testset "find_growth_rates: single isolated root" begin + # Δ(Q) = Q - Q_root → unique zero at Q_root + Q_root = 0.42 + 0.27im + f(Q) = ComplexF64(Q) - Q_root + scan = brute_force_scan(f, (-1.0, 1.5), (-0.5, 1.0); + nre=80, nim=60, threaded=false) + result = find_growth_rates(scan, 1.0) + @test result isa GrowthRateResult + @test isempty(result.poles) + @test length(result.valid_roots) == 1 + @test abs(result.Q_root - Q_root) < 1e-3 # grid-resolution limited + @test result.omega_Hz ≈ real(result.Q_root) + @test result.gamma_Hz ≈ imag(result.Q_root) + end + + @testset "find_growth_rates: multiple roots — picks highest γ" begin + # Two roots; the higher-γ one must be reported + Q1 = 0.3 + 0.5im # higher γ + Q2 = -0.4 + 0.1im # lower γ + f(Q) = (ComplexF64(Q) - Q1) * (ComplexF64(Q) - Q2) + scan = brute_force_scan(f, (-1.0, 1.0), (-0.3, 0.8); + nre=100, nim=80, threaded=false) + result = find_growth_rates(scan, 1.0) + @test length(result.valid_roots) == 2 + @test abs(result.Q_root - Q1) < 1e-3 # higher-γ root chosen + @test imag(result.Q_root) > imag(Q2) + end + + @testset "find_growth_rates: pole detection" begin + # Δ(Q) = (Q - Q_root)/(Q - Q_pole) → 1 zero, 1 pole + Q_r = 0.4 + 0.2im + Q_p = -0.5 + 0.6im # pole at higher γ + f(Q) = (ComplexF64(Q) - Q_r) / (ComplexF64(Q) - Q_p) + scan = brute_force_scan(f, (-1.5, 1.5), (-0.5, 1.5); + nre=120, nim=100, threaded=false) + result = find_growth_rates(scan, 1.0; pole_threshold=10.0) + # Pole correctly classified — but the root is at lower γ than the + # pole, so even with filter_above_poles=true the root must survive. + @test length(result.poles) >= 1 + @test any(p -> abs(p - Q_p) < 0.05, result.poles) + @test abs(result.Q_root - Q_r) < 1e-3 + end + + @testset "find_growth_rates: tauk normalization to physical Hz" begin + Q_root = 1.0 + 2.0im + f(Q) = ComplexF64(Q) - Q_root + scan = brute_force_scan(f, (-2.0, 3.0), (-1.0, 4.0); + nre=80, nim=80, threaded=false) + tauk = 5.0e-5 + result = find_growth_rates(scan, tauk) + @test result.omega_Hz ≈ real(result.Q_root) / tauk + @test result.gamma_Hz ≈ imag(result.Q_root) / tauk + # Check sensible orders of magnitude (Q_root ≈ 1+2im, tauk ≈ 5e-5) + @test result.omega_Hz ≈ 1 / tauk atol = 1 / tauk * 5e-3 + @test result.gamma_Hz ≈ 2 / tauk atol = 2 / tauk * 5e-3 + end + + @testset "find_growth_rates: empty result when no contour intersections" begin + # Δ(Q) = 1 + Q (only a single zero at Q=-1; if scanned over a box + # away from -1 there will be no Im(Δ)=0 contour intersecting Re=0). + f(Q) = 1.0 + ComplexF64(Q) + # Choose a box where Δ has no zeros — far above the real axis + scan = brute_force_scan(f, (1.0, 2.0), (1.0, 2.0); + nre=30, nim=30, threaded=false) + result = find_growth_rates(scan, 1.0) + # Either no valid roots, or a NaN Q_root + @test isempty(result.valid_roots) || isnan(real(result.Q_root)) + end + + @testset "API: SurfaceCoupling and MultiSurfaceCoupling are scannable" begin + # Synthetic linear inner-layer model — verifies the Dispersion API + # accepts the actual residual containers, not just plain functions. + struct LinModel <: InnerLayerModel + a::ComplexF64 + b::ComplexF64 + end + GeneralizedPerturbedEquilibrium.InnerLayer.solve_inner( + m::LinModel, params, Q::Number) = + InnerLayerResponse(m.a + m.b * ComplexF64(Q), zero(ComplexF64)) + + # Single-surface scan via SurfaceCoupling (Q_root by construction = 0.7-0.3im) + Q_pin = 0.7 - 0.3im + sc = surface_coupling(LinModel(0.0im, 1.0+0im), nothing, + Q_pin; scale=1.0, tauk=1.0) + scan = brute_force_scan(sc, (-0.5, 1.5), (-1.0, 0.5); + nre=80, nim=80, threaded=false) + res = find_growth_rates(scan, sc.tauk) + @test abs(res.Q_root - Q_pin) < 1e-3 + + # Coupled scan via MultiSurfaceCoupling — pair two surfaces with + # *different* Q_pin values so the resulting determinant has simple + # (non-degenerate) roots that contour intersection can localize. + # Note: MultiSurfaceCoupling builds M[k,k] = dp[k,k] - Δ_inner_k(Q), + # so to put a root at Q = Q_pin_k we need dp[k,k] = Q_pin_k (the + # full complex value, not just its real part). + Q_a, Q_b = 0.7 - 0.3im, -0.4 + 0.5im + sc1 = surface_coupling(LinModel(0.0im, 1.0+0im), nothing, + ComplexF64(0); scale=1.0, tauk=1.0) + sc2 = surface_coupling(LinModel(0.0im, 1.0+0im), nothing, + ComplexF64(0); scale=1.0, tauk=1.0) + dp = ComplexF64[Q_a 0.0; 0.0 Q_b] # diagonal Δ' + mc = multi_surface_coupling([sc1, sc2], dp) + scan_c = brute_force_scan(mc, (-1.0, 1.5), (-1.0, 1.0); + nre=120, nim=100, threaded=false) + res_c = find_growth_rates(scan_c, mc.surfaces[mc.ref_idx].tauk) + # With diagonal Δ', det = (Q_a - Q)·(Q_b - Q) → roots at Q_a, Q_b. + # The higher-γ root is Q_b (γ = 0.5). + @test abs(res_c.Q_root - Q_b) < 1e-2 + end +end diff --git a/test/runtests_kinetic.jl b/test/runtests_kinetic.jl index 41aaccf67..073617c52 100644 --- a/test/runtests_kinetic.jl +++ b/test/runtests_kinetic.jl @@ -371,4 +371,59 @@ @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 diff --git a/test/runtests_kinetic_profiles.jl b/test/runtests_kinetic_profiles.jl new file mode 100644 index 000000000..d7308b2d1 --- /dev/null +++ b/test/runtests_kinetic_profiles.jl @@ -0,0 +1,53 @@ +@testset "Utilities: KineticProfiles" begin + using GeneralizedPerturbedEquilibrium.Utilities + + # Canonical synthetic dataset on ψ ∈ [0, 1] + function _synthetic() + psi = collect(0.0:0.1:1.0) + return ( + psi, + Dict( + "n_e" => fill(5.0e19, length(psi)), + "T_e" => 1000.0 .* (1.0 .- 0.7 .* psi), + "T_i" => 1200.0 .* (1.0 .- 0.6 .* psi), + "omega" => 1.0e4 .* psi, + "omega_e" => fill(1.0e4, length(psi)), + "omega_i" => fill(5.0e3, length(psi)) + ) + ) + end + + @testset "kwarg constructor + evaluation" begin + psi, d = _synthetic() + kp = KineticProfiles(; psi=psi, n_e=d["n_e"], T_e=d["T_e"], + T_i=d["T_i"], omega=d["omega"], + omega_e=d["omega_e"], omega_i=d["omega_i"]) + # Exact recovery at a node + vals = kp(0.5) + @test vals.n_e ≈ 5.0e19 + @test vals.T_e ≈ 1000.0 * (1 - 0.7 * 0.5) + @test vals.T_i ≈ 1200.0 * (1 - 0.6 * 0.5) + @test vals.omega ≈ 1.0e4 * 0.5 + @test vals.omega_e ≈ 1.0e4 + @test vals.omega_i ≈ 5.0e3 + + # Smooth interpolation between nodes + vals2 = kp(0.25) + @test vals2.T_e ≈ 1000.0 * (1 - 0.7 * 0.25) rtol = 1e-6 + + # NamedTuple fields + @test keys(vals) == (:n_e, :T_e, :T_i, :omega, :omega_e, :omega_i) + end + + @testset "length mismatch raises" begin + psi = collect(0.0:0.1:1.0) + @test_throws ArgumentError KineticProfiles(; + psi=psi, + n_e=fill(1.0, length(psi) - 1), # wrong length + T_e=fill(1000.0, length(psi)), + T_i=fill(1000.0, length(psi)), + omega=fill(0.0, length(psi)), + omega_e=fill(0.0, length(psi)), + omega_i=fill(0.0, length(psi))) + end +end diff --git a/test/runtests_parallel_integration.jl b/test/runtests_parallel_integration.jl index 26afbbd6a..3bfd5ab85 100644 --- a/test/runtests_parallel_integration.jl +++ b/test/runtests_parallel_integration.jl @@ -309,27 +309,19 @@ 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- 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. 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. - # 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 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 @@ -532,28 +524,16 @@ 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]), +7.280089e+00; rtol=1e-2) # q=2 + @test isapprox(real(dpm[2, 2]), -5.211187e+00; rtol=1e-2) # q=3 + @test isapprox(real(dpm[3, 3]), -1.581737e+01; rtol=3e-2) # q=4 end end diff --git a/test/runtests_resist_eval.jl b/test/runtests_resist_eval.jl new file mode 100644 index 000000000..660c0cf0b --- /dev/null +++ b/test/runtests_resist_eval.jl @@ -0,0 +1,198 @@ +@testset "ResistEval: GGJ geometric coefficients + GGJ builder" begin + using GeneralizedPerturbedEquilibrium + using GeneralizedPerturbedEquilibrium.Equilibrium + using GeneralizedPerturbedEquilibrium.ForceFreeStates + using GeneralizedPerturbedEquilibrium.ForceFreeStates: SingType, ResistGeometry + using GeneralizedPerturbedEquilibrium.Utilities + using GeneralizedPerturbedEquilibrium.InnerLayer + using FastInterpolations + using TOML + + # Load the bundled Solovev example equilibrium once for all tests. + dir_path = joinpath(dirname(@__DIR__), "examples", "Solovev_ideal_example") + inputs = TOML.parsefile(joinpath(dir_path, "gpec.toml")) + eq_cfg = Equilibrium.EquilibriumConfig(inputs["Equilibrium"], dir_path) + sol_cfg = Equilibrium.SolovevConfig(inputs["SOL_INPUT"]) + equil = Equilibrium.setup_equilibrium(eq_cfg, sol_cfg) + + @testset "resist_geometry: returns finite values with expected signs" begin + # Pick a few interior surfaces; compute q1 from the equilibrium + dq = deriv_view(equil.profiles.q_spline, 1) + for psi in (0.2, 0.5, 0.8) + q1 = dq(psi) + rg = ForceFreeStates.resist_geometry(equil, psi, q1) + + @test rg isa ResistGeometry + for f in (rg.E, rg.F, rg.G, rg.H, rg.K, rg.M) + @test isfinite(f) + end + # Geometric averages are positive + @test rg.avg_bsq_over_dpsisq > 0 + @test rg.avg_bsq > 0 + # Mass factor M > 0 (denominator in G and K) + @test rg.M > 0 + # Pressure is positive on this Solovev equilibrium + @test rg.p_local > 0 + @test rg.v1_local > 0 + end + end + + @testset "resist_geometry vs ballooning D_I: D_I = E + F + H − ¼" begin + # Independent D_I reference from the ballooning coefficient system: + # det(d0bar) is the Mercier interchange D_I that the local-stability + # scan stores in locstab[:,1]. Build it on the radial grid, interpolate + # to a few surface ψ values, and check against the GGJ reconstruction. + xs = equil.profiles.xs + di_ref = Float64[ForceFreeStates.prepare_ballooning_coefficients(i, equil).di for i in eachindex(xs)] + di_spline = cubic_interp(xs, di_ref) + + dq = deriv_view(equil.profiles.q_spline, 1) + for psi in (0.3, 0.5, 0.7) + q1 = dq(psi) + rg = ForceFreeStates.resist_geometry(equil, psi, q1) + di_from_ggj = rg.E + rg.F + rg.H - 0.25 + + # det(d0bar) is D_I directly (no ψ factor at the coefficient level). + di_from_ballooning = di_spline(psi) + + # The ballooning det(d0bar) route is an INDEPENDENT D_I evaluation + # (not the surface-average θ-integrals that build E,F,H), so the two + # agree only to the few-percent level set by each route's separate + # discretization — looser than the old same-integral cross-check. + @test abs(di_from_ggj - di_from_ballooning) < 8e-2 * abs(di_from_ballooning) + end + end + + @testset "resist_eval_all!: populates restype on every surface" begin + # Build a couple of synthetic SingTypes, run the populator, verify + # restype goes from nothing to ResistGeometry on each. + dq = deriv_view(equil.profiles.q_spline, 1) + s1 = SingType(; psifac=0.3, rho=sqrt(0.3), m=[2], n=[1], + q=2.0, q1=dq(0.3), + grri=zeros(Float64, 0, 0), grre=zeros(Float64, 0, 0), + delta_prime=ComplexF64[], + delta_prime_col=zeros(ComplexF64, 0, 0), + ua_left=zeros(ComplexF64, 0, 0, 0), + ua_right=zeros(ComplexF64, 0, 0, 0), + psi_ua_left=0.0, psi_ua_right=0.0) + s2 = SingType(; psifac=0.7, rho=sqrt(0.7), m=[3], n=[1], + q=3.0, q1=dq(0.7), + grri=zeros(Float64, 0, 0), grre=zeros(Float64, 0, 0), + delta_prime=ComplexF64[], + delta_prime_col=zeros(ComplexF64, 0, 0), + ua_left=zeros(ComplexF64, 0, 0, 0), + ua_right=zeros(ComplexF64, 0, 0, 0), + psi_ua_left=0.0, psi_ua_right=0.0) + + @test s1.restype === nothing + @test s2.restype === nothing + + intr = ForceFreeStates.ForceFreeStatesInternal(; sing=[s1, s2], msing=2) + ForceFreeStates.resist_eval_all!(intr, equil) + + @test intr.sing[1].restype isa ResistGeometry + @test intr.sing[2].restype isa ResistGeometry + # Idempotent — second call shouldn't recompute (already non-nothing) + rg_first = intr.sing[1].restype + ForceFreeStates.resist_eval_all!(intr, equil) + @test intr.sing[1].restype === rg_first + end + + @testset "build_ggj_inputs: builds GGJParameters from sings + profiles" begin + # Synthetic profiles + psi_pts = collect(0.0:0.1:1.0) + profiles = KineticProfiles(; psi=psi_pts, + n_e=fill(5.0e19, length(psi_pts)), + T_e=1000.0 .* (1.0 .- 0.7 .* psi_pts), + T_i=1000.0 .* (1.0 .- 0.6 .* psi_pts), + omega=fill(0.0, length(psi_pts)), + omega_e=fill(1.0e4, length(psi_pts)), + omega_i=fill(5.0e3, length(psi_pts))) + + dq = deriv_view(equil.profiles.q_spline, 1) + s1 = SingType(; psifac=0.3, rho=sqrt(0.3), m=[2], n=[1], + q=2.0, q1=dq(0.3), + grri=zeros(Float64, 0, 0), grre=zeros(Float64, 0, 0), + delta_prime=ComplexF64[], + delta_prime_col=zeros(ComplexF64, 0, 0), + ua_left=zeros(ComplexF64, 0, 0, 0), + ua_right=zeros(ComplexF64, 0, 0, 0), + psi_ua_left=0.0, psi_ua_right=0.0) + intr = ForceFreeStates.ForceFreeStatesInternal(; sing=[s1], msing=1) + ForceFreeStates.resist_eval_all!(intr, equil) + + gs = build_ggj_inputs(equil, intr.sing, profiles; mu_i=2.0, zeff=1.0) + @test length(gs) == 1 + @test gs[1] isa GGJParameters + + # Geometric coefficients flow through unchanged from restype + rg = intr.sing[1].restype + @test gs[1].E ≈ rg.E + @test gs[1].F ≈ rg.F + @test gs[1].G ≈ rg.G + @test gs[1].H ≈ rg.H + @test gs[1].K ≈ rg.K + @test gs[1].M ≈ rg.M + + # Timescales are positive and physical + @test gs[1].taua > 0 + @test gs[1].taur > 0 + @test gs[1].taur > gs[1].taua # resistive ≫ Alfvén for any tokamak + @test gs[1].taur / gs[1].taua > 1e3 # Lundquist S well into resistive regime + + # ising traceability + @test gs[1].ising == 1 + end + + @testset "build_ggj_inputs: errors when restype not populated" begin + # Need ≥4 points for the cubic spline + psi_pts = collect(0.0:0.25:1.0) + n = length(psi_pts) + profiles = KineticProfiles(; psi=psi_pts, + n_e=fill(5.0e19, n), T_e=fill(1000.0, n), T_i=fill(1000.0, n), + omega=fill(0.0, n), omega_e=fill(1.0e4, n), omega_i=fill(5.0e3, n)) + + s_unpop = SingType(; psifac=0.5, rho=sqrt(0.5), m=[2], n=[1], + q=2.0, q1=1.0, + grri=zeros(Float64, 0, 0), grre=zeros(Float64, 0, 0), + delta_prime=ComplexF64[], + delta_prime_col=zeros(ComplexF64, 0, 0), + ua_left=zeros(ComplexF64, 0, 0, 0), + ua_right=zeros(ComplexF64, 0, 0, 0), + psi_ua_left=0.0, psi_ua_right=0.0) + @test s_unpop.restype === nothing + @test_throws ArgumentError build_ggj_inputs(equil, [s_unpop], profiles) + end + + @testset "GGJ solve_inner runs on built parameters" begin + psi_pts = collect(0.0:0.1:1.0) + profiles = KineticProfiles(; psi=psi_pts, + n_e=fill(5.0e19, length(psi_pts)), + T_e=1000.0 .* (1.0 .- 0.7 .* psi_pts), + T_i=fill(1000.0, length(psi_pts)), + omega=fill(0.0, length(psi_pts)), + omega_e=fill(0.0, length(psi_pts)), + omega_i=fill(0.0, length(psi_pts))) + + dq = deriv_view(equil.profiles.q_spline, 1) + s1 = SingType(; psifac=0.3, rho=sqrt(0.3), m=[2], n=[1], + q=2.0, q1=dq(0.3), + grri=zeros(Float64, 0, 0), grre=zeros(Float64, 0, 0), + delta_prime=ComplexF64[], + delta_prime_col=zeros(ComplexF64, 0, 0), + ua_left=zeros(ComplexF64, 0, 0, 0), + ua_right=zeros(ComplexF64, 0, 0, 0), + psi_ua_left=0.0, psi_ua_right=0.0) + intr = ForceFreeStates.ForceFreeStatesInternal(; sing=[s1], msing=1) + ForceFreeStates.resist_eval_all!(intr, equil) + gs = build_ggj_inputs(equil, intr.sing, profiles; mu_i=2.0) + + # Verify D_I < 0 so the GGJ shooting solver doesn't bail + @test mercier_di(gs[1]) < 0 + + Δ = solve_inner(GGJModel(; solver=:shooting), gs[1], 0.01 + 0.0im) + @test Δ isa InnerLayerResponse + @test isfinite(Δ.tearing) + @test isfinite(Δ.interchange) + end +end diff --git a/test/runtests_slayer_inputs.jl b/test/runtests_slayer_inputs.jl new file mode 100644 index 000000000..5e2c5a34f --- /dev/null +++ b/test/runtests_slayer_inputs.jl @@ -0,0 +1,159 @@ +@testset "SLAYER LayerInputs (build from equilibrium + profiles)" begin + using GeneralizedPerturbedEquilibrium + using GeneralizedPerturbedEquilibrium.Equilibrium + using GeneralizedPerturbedEquilibrium.Utilities + using GeneralizedPerturbedEquilibrium.InnerLayer + using GeneralizedPerturbedEquilibrium.ForceFreeStates: SingType + using TOML + + # Load the Solovev analytic equilibrium shipped with the examples. + # This exercise gets run once for all LayerInputs tests. + dir_path = joinpath(dirname(@__DIR__), "examples", "Solovev_ideal_example") + inputs = TOML.parsefile(joinpath(dir_path, "gpec.toml")) + eq_cfg = Equilibrium.EquilibriumConfig(inputs["Equilibrium"], dir_path) + sol_cfg = Equilibrium.SolovevConfig(inputs["SOL_INPUT"]) + equil = Equilibrium.setup_equilibrium(eq_cfg, sol_cfg) + + # Synthetic profiles (simple linear-in-ψ temperature decrease) + psi_pts = collect(0.0:0.1:1.0) + profiles = KineticProfiles(; psi=psi_pts, + n_e=fill(5.0e19, length(psi_pts)), + T_e=1000.0 .* (1.0 .- 0.7 .* psi_pts), + T_i=1000.0 .* (1.0 .- 0.6 .* psi_pts), + omega=fill(0.0, length(psi_pts)), + omega_e=fill(1.0e4, length(psi_pts)), + omega_i=fill(5.0e3, length(psi_pts))) + + # Helper to build a minimal SingType without touching unused fields + _mk_sing(; psi, q, q1, m, n, delta_prime=-10.0+0im) = SingType( + psifac=psi, rho=sqrt(psi), m=[m], n=[n], q=q, q1=q1, + grri=zeros(Float64, 0, 0), grre=zeros(Float64, 0, 0), + delta_prime=ComplexF64[delta_prime], + delta_prime_col=zeros(ComplexF64, 0, 0), + ua_left=zeros(ComplexF64, 0, 0, 0), + ua_right=zeros(ComplexF64, 0, 0, 0), + psi_ua_left=0.0, psi_ua_right=0.0) + + @testset "surface_minor_radius: continuity + outboard > 0" begin + # Minor radius grows monotonically with ψ (outboard midplane). + r1 = surface_minor_radius(equil, 0.1) + r2 = surface_minor_radius(equil, 0.5) + r3 = surface_minor_radius(equil, 0.9) + @test r1 < r2 < r3 + @test r1 > 0 + end + + @testset "surface_da_dpsi: FD agrees with numerical derivative" begin + # Reference via a tighter FD + for psi in (0.1, 0.4, 0.7) + h_ref = 1e-4 + r_p = surface_minor_radius(equil, psi + h_ref) + r_m = surface_minor_radius(equil, psi - h_ref) + ref = (r_p - r_m) / (2 * h_ref) + @test surface_da_dpsi(equil, psi) ≈ ref rtol = 1e-3 + end + end + + @testset "surface_da_dpsi: one-sided near boundaries" begin + # Near ψ=0 and ψ=1, the function falls back to one-sided FD and + # should still produce a finite positive number (minor radius is + # still increasing). + d_near_axis = surface_da_dpsi(equil, 1e-6) + d_near_edge = surface_da_dpsi(equil, 1.0 - 1e-6) + @test isfinite(d_near_axis) && d_near_axis > 0 + @test isfinite(d_near_edge) && d_near_edge > 0 + end + + @testset "build_slayer_inputs: returns correct per-surface data" begin + sings = [_mk_sing(psi=0.3, q=2.0, q1=1.5, m=2, n=1), + _mk_sing(psi=0.6, q=3.0, q1=2.5, m=3, n=1)] + # dr_val=0.0 bypasses the build_slayer_inputs requirement that sing.restype be + # pre-populated by ForceFreeStates.resist_eval_all! — the test sings here are + # minimal stubs without restype, so we supply dr_val explicitly. + # compute_omega_star=false makes Q_e/Q_i pass through directly from profiles.omega_e/i + # rather than being recomputed from n_e/T_e/T_i gradients — required for the Q_e == + # -tauk·omega_e(ψ) identity check below. + sl = build_slayer_inputs(equil, sings, profiles; bt=2.0, dr_val=0.0, + compute_omega_star=false) + + @test length(sl) == 2 + @test sl[1] isa SLAYERParameters + @test sl[2] isa SLAYERParameters + + # ising traceability + @test sl[1].ising == 1 + @test sl[2].ising == 2 + + # Mode numbers flow through + @test sl[1].m == 2 && sl[1].n == 1 + @test sl[2].m == 3 && sl[2].n == 1 + + # Global geometry + @test sl[1].R0 ≈ equil.ro + @test sl[1].bt == 2.0 + + # Minor radius and r-based shear recovered from the equilibrium + rs1 = surface_minor_radius(equil, 0.3) + da1 = surface_da_dpsi(equil, 0.3) + @test sl[1].rs ≈ rs1 + @test sl[1].sval_r ≈ rs1 * 1.5 / (2.0 * da1) + + # Lundquist number and Q_e scale with surface parameters + @test sl[1].lu != sl[2].lu + @test sl[1].tauk != sl[2].tauk + + # Q_e, Q_i follow the SLAYER layerinputs sign convention + @test sl[1].Q_e == -sl[1].tauk * profiles.omega_e(0.3) + @test sl[1].Q_i == -sl[1].tauk * profiles.omega_i(0.3) + end + + @testset "build_slayer_inputs: chi_perp/chi_tor as scalars and callables" begin + sings = [_mk_sing(psi=0.5, q=2.4, q1=1.2, m=2, n=1)] + + # Scalar (dr_val=0.0 bypasses the sing.restype requirement; see comment above) + sl_s = build_slayer_inputs(equil, sings, profiles; + bt=2.0, chi_perp=2.0, chi_tor=1.5, dr_val=0.0) + # Callable with matching value + chi_p(psi) = 2.0 + 0.0*psi + chi_t(psi) = 1.5 + 0.0*psi + sl_c = build_slayer_inputs(equil, sings, profiles; + bt=2.0, chi_perp=chi_p, chi_tor=chi_t, dr_val=0.0) + @test sl_s[1].P_perp ≈ sl_c[1].P_perp + @test sl_s[1].P_tor ≈ sl_c[1].P_tor + + # Callable with ψ-dependence changes the result + chi_p_var(psi) = 1.0 + 10.0 * psi # χ⊥(0.5) = 6.0 > 2.0 + sl_var = build_slayer_inputs(equil, sings, profiles; + bt=2.0, chi_perp=chi_p_var, chi_tor=1.5, dr_val=0.0) + # P_perp = τ_r · χ⊥ / r² grows with χ⊥, so the varying-χ case at + # ψ=0.5 (χ⊥=6) gives a *larger* P_perp than the scalar χ⊥=2. + @test sl_var[1].P_perp > sl_s[1].P_perp + @test sl_var[1].P_perp ≈ sl_s[1].P_perp * 6.0 / 2.0 rtol = 1e-10 + end + + @testset "build_slayer_inputs: dc_type propagates and dr_val activates offset" begin + sings = [_mk_sing(psi=0.5, q=2.4, q1=1.2, m=2, n=1)] + + # dc_type=:none and dr_val=0.0 → dc_tmp = 0 regardless of dr_val + sl_none = build_slayer_inputs(equil, sings, profiles; + bt=2.0, dc_type=:none, dr_val=0.0) + @test sl_none[1].dc_tmp == 0.0 + + # dc_type=:rfitzp with dr_val = 0 still gives zero + sl_rf0 = build_slayer_inputs(equil, sings, profiles; + bt=2.0, dc_type=:rfitzp, dr_val=0.0) + @test sl_rf0[1].dc_tmp == 0.0 + + # dc_type=:rfitzp with dr_val > 0 → nonzero negative offset + sl_rf = build_slayer_inputs(equil, sings, profiles; + bt=2.0, dc_type=:rfitzp, dr_val=0.01) + @test sl_rf[1].dc_tmp < 0 + @test isfinite(sl_rf[1].dc_tmp) + end + + @testset "build_slayer_inputs: empty sings returns empty vector" begin + sl = build_slayer_inputs(equil, SingType[], profiles; bt=2.0) + @test sl isa Vector{SLAYERParameters} + @test isempty(sl) + end +end diff --git a/test/runtests_slayer_params.jl b/test/runtests_slayer_params.jl new file mode 100644 index 000000000..330ba7297 --- /dev/null +++ b/test/runtests_slayer_params.jl @@ -0,0 +1,168 @@ +@testset "SLAYER LayerParameters" begin + using GeneralizedPerturbedEquilibrium.InnerLayer + using GeneralizedPerturbedEquilibrium.Utilities: MU_0, M_E, M_P, E_CHG, EPS_0 + using GeneralizedPerturbedEquilibrium.Utilities: SpitzerModel, SpitzerHarmModel, + SauterNeoModel + + # Reference inputs: a simple deuterium plasma case suitable for + # hand-checking the SLAYER params formulas. + function _ref_kwargs(; dr_val=0.0, dc_type=:none) + return ( + n_e=5.0e19, t_e=1000.0, t_i=1000.0, + omega=0.0, omega_e=1.0e4, omega_i=5.0e3, + qval=2.0, sval_r=1.0, bt=2.0, + rs=0.5, R0=1.7, mu_i=2.0, zeff=1.0, + chi_perp=1.0, chi_tor=1.0, + m=2, n=1, + dr_val=dr_val, dgeo_val=0.5, dc_type=dc_type, + ising=3 + ) + end + + @testset "Test 1: round-trip from dimensional inputs" begin + @info "Building SLAYERParameters from a reference deuterium case" + p = slayer_parameters(; _ref_kwargs()...) + + # Identity / passthrough + @test p.ising == 3 + @test p.m == 2 + @test p.n == 1 + @test p.rs == 0.5 + @test p.R0 == 1.7 + @test p.bt == 2.0 + @test p.sval_r == 1.0 + @test p.dc_tmp == 0.0 # dr_val == 0 ⇒ no offset + @test p.dc_type === :none + + # Trivially exact ratios + @test p.tau ≈ 1.0 + # Q_e = −tauk·1e4 = negative; Q_i = −tauk·5e3 = negative + # Q_e − Q_i = −tauk·5e3 = Q_i (since Q_e = 2·Q_i) ⇒ iota_e = Q_e/Q_i = 2 + @test p.iota_e ≈ 2.0 + + # Sign convention check (SLAYER layerinputs) + @test p.Q_e == -p.tauk * 1.0e4 + @test p.Q_i == -p.tauk * 5.0e3 # SLAYER params convention: Q_i = −tauk·ω*i + + # Default resistivity closure is neoclassical (Sauter F_33). The + # trapped-particle correction raises η above plain Spitzer at the + # same lnΛ: η_neo = η_Sp / F_33 with F_33 ∈ (0,1). + p_spitzer = slayer_parameters(; _ref_kwargs()..., + resistivity_model=SpitzerModel(), lnLambda_form=:nrl) + @test p.eta > p_spitzer.eta + @test 1.1 < p.eta / p_spitzer.eta < 4.0 # banana-regime F_33 ≈ 0.3–0.9 + + # Legacy Fitzpatrick/TJ path: the Spitzer-Härm σ_∥ closure agrees with + # the old Wesson 1.65e-9 form to ~2.3% (the two are independent Spitzer + # formulas), so this is a genuine cross-check, not a tautology. + lnLamb_wesson = 24.0 + 3.0 * log(10.0) - 0.5 * log(5.0e19) + log(1000.0) + eta_wesson = 1.65e-9 * lnLamb_wesson / (1000.0 / 1e3)^1.5 + p_legacy = slayer_parameters(; _ref_kwargs()..., + resistivity_model=SpitzerHarmModel(), lnLambda_form=:wesson) + @test p_legacy.eta ≈ eta_wesson rtol = 3e-2 + + # τ_R = μ₀ r_s² / η holds for whichever closure was selected. + @test p.tau_r ≈ MU_0 * p.rs^2 / p.eta rtol = 1e-12 + @test p_legacy.tau_r ≈ MU_0 * p_legacy.rs^2 / p_legacy.eta rtol = 1e-12 + + # Mass density and Alfvén time (independent of conductivity). + rho_expected = 2.0 * M_P * 5.0e19 + tau_h_expected = 1.7 * sqrt(MU_0 * rho_expected) / (1 * 1.0 * 2.0) + # tauk = S^(1/3) · τ_H = (τ_R/τ_H)^(1/3)·τ_H = τ_R^(1/3)·τ_H^(2/3) + @test p.tauk ≈ p.lu^(1 / 3) * tau_h_expected rtol = 1e-12 + @test p.tauk^3 / tau_h_expected^2 ≈ p.tau_r rtol = 1e-12 + + # Lundquist number is large positive + @test p.lu > 1e6 + @test p.lu < 1e9 + + # Compressibility is in (0,1) for finite β + @test 0.0 < p.c_beta < 1.0 + + # Prandtl-like ratios are positive and equal here (chi_perp=chi_tor=1) + @test p.P_perp ≈ p.P_tor + @test p.P_perp > 0 + + # D_norm = (d_β/r_s)·S^(1/3)·√(τ/(1+τ)) + D_norm_expected = (p.d_beta / p.rs) * p.lu^(1 / 3) * sqrt(p.tau / (1 + p.tau)) + @test p.D_norm ≈ D_norm_expected rtol = 1e-12 + + # delta_n = S^(1/3)/r_s + @test p.delta_n ≈ p.lu^(1 / 3) / p.rs rtol = 1e-12 + end + + @testset "Test 1b: dc_tmp formulas activate when dr_val ≠ 0" begin + # All four dc_type branches must produce finite, non-NaN values + # and respect the signs/structure of the formulas in + # the SLAYER params dc_tmp formulas. + p_none = slayer_parameters(; _ref_kwargs(; dr_val=0.01, dc_type=:none)...) + @test p_none.dc_tmp == 0.0 # :none ignores dr_val + + p_lar = slayer_parameters(; _ref_kwargs(; dr_val=0.01, dc_type=:lar)...) + p_rf = slayer_parameters(; _ref_kwargs(; dr_val=0.01, dc_type=:rfitzp)...) + p_tor = slayer_parameters(; _ref_kwargs(; dr_val=0.01, dc_type=:toroidal)...) + + @test isfinite(p_lar.dc_tmp) + @test isfinite(p_rf.dc_tmp) + @test isfinite(p_tor.dc_tmp) + # dr_val > 0 with the (-dr_val) prefactor ⇒ negative dc_tmp for + # :lar, :rfitzp, :toroidal branches. + @test p_lar.dc_tmp < 0 + @test p_rf.dc_tmp < 0 + @test p_tor.dc_tmp < 0 + + # Sign flips with sign of dr_val + p_lar_neg = slayer_parameters(; + _ref_kwargs(; dr_val=-0.01, dc_type=:lar)...) + @test sign(p_lar_neg.dc_tmp) == -sign(p_lar.dc_tmp) + + # Reject unknown dc_type + @test_throws ArgumentError slayer_parameters(; + _ref_kwargs(; dr_val=0.01, dc_type=:bogus)...) + end + + @testset "Test 1c: SLAYERParameters direct kwarg construction" begin + # The @kwdef constructor must accept all required fields and + # default the optional ones. + p = SLAYERParameters(; + tau=1.0, lu=1e7, c_beta=0.1, D_norm=2.0, + P_perp=10.0, P_tor=10.0, + Q_e=-1.0, Q_i=0.5, iota_e=2.0 / 3.0, + tauk=1e-4, tau_r=10.0, delta_n=400.0, + rs=0.5, R0=1.7, bt=2.0, sval_r=1.0, + eta=2.5e-8, d_beta=4e-3 + ) + @test p.tau == 1.0 + @test p.dc_tmp == 0.0 + @test p.dc_type === :none + @test p.dr_val == 0.0 + @test p.ising == 0 + end + + @testset "Test 2: r-based shear conversion" begin + # Direct application of r_s · (dq/dψ) / (q · da/dψ). + @test r_based_shear(0.5, 2.0, 4.0, 0.5) ≈ 2.0 + @test r_based_shear(1.0, 1.0, 1.0, 1.0) ≈ 1.0 + + # Synthetic Solovev-like flux surface: a(ψ) = a₀·√ψ and q(ψ) = + # q₀·(1 + α·ψ). Then dq/dψ = q₀·α, da/dψ = a₀/(2√ψ), + # and the analytic r-based shear is + # s_r(ψ) = a(ψ)·(dq/dr)/q(ψ) + # = a₀√ψ · (dq/dψ)·(dψ/dr) / q(ψ) + # = a₀√ψ · q₀α · (2√ψ/a₀) / (q₀(1+α ψ)) + # = 2αψ / (1+αψ). + a0, q0, alpha = 0.6, 1.2, 1.5 + for psi in (0.1, 0.4, 0.7, 0.95) + a = a0 * sqrt(psi) + q = q0 * (1 + alpha * psi) + dq_dpsi = q0 * alpha + da_dpsi = a0 / (2 * sqrt(psi)) + expected = 2 * alpha * psi / (1 + alpha * psi) + @test r_based_shear(a, q, dq_dpsi, da_dpsi) ≈ expected rtol = 1e-12 + end + + # Argument validation + @test_throws ArgumentError r_based_shear(0.5, 2.0, 1.0, 0.0) + @test_throws ArgumentError r_based_shear(0.5, 0.0, 1.0, 0.5) + end +end diff --git a/test/runtests_slayer_riccati.jl b/test/runtests_slayer_riccati.jl new file mode 100644 index 000000000..22f7fc549 --- /dev/null +++ b/test/runtests_slayer_riccati.jl @@ -0,0 +1,162 @@ +@testset "SLAYER Riccati Δ" begin + using GeneralizedPerturbedEquilibrium.InnerLayer + using StaticArrays + using Statistics: median + + # Reach into the SLAYER submodule to test the BC selector helper + # without exporting it (it's an internal of the Riccati port). + _SLAYER_MOD = GeneralizedPerturbedEquilibrium.InnerLayer.SLAYER + + # A reference deuterium case in the *large-D_norm* regime. + # T_e = T_i = 3 keV (vs 1 keV) lifts D_norm² above the iota_e·P_perp/P_tor^(2/3) threshold: + # D_norm² ∝ T_e² but threshold ∝ T_e^0.5, so D_norm² / threshold ∝ T_e^(3/2). At 3 keV the + # ratio is ~2.4 (vs ~0.5 at 1 keV), placing the fixture solidly on the large_D side of the + # branch boundary. All other inputs unchanged. + function _ref_params_large_D() + return slayer_parameters(; + n_e=5.0e19, t_e=3000.0, t_i=3000.0, + omega=0.0, omega_e=1.0e4, omega_i=5.0e3, + qval=2.0, sval_r=1.0, bt=2.0, + rs=0.5, R0=1.7, mu_i=2.0, zeff=1.0, + chi_perp=1.0, chi_tor=1.0, + m=2, n=1) + end + + # A directly-built parameter set in the *small-D_norm* regime + function _ref_params_small_D() + return SLAYERParameters(; + tau=1.0, lu=1.0e7, c_beta=0.05, D_norm=0.05, + P_perp=20.0, P_tor=10.0, + Q_e=-1.0, Q_i=0.5, iota_e=2.0 / 3.0, + tauk=1.0e-4, tau_r=10.0, delta_n=400.0, + rs=0.5, R0=1.7, bt=2.0, sval_r=1.0, + eta=2.5e-8, d_beta=2.0e-4) + end + + @testset "Interface compliance" begin + p = _ref_params_large_D() + Δ = solve_inner(SLAYERModel(), p, 0.5 + 0.2im) + @test Δ isa InnerLayerResponse + @test Δ.interchange == zero(ComplexF64) # pressureless SLAYER has no interchange channel + @test isfinite(real(Δ.tearing)) + @test isfinite(imag(Δ.tearing)) + end + + @testset "Boundary-condition branch selection" begin + p_large = _ref_params_large_D() + p_small = _ref_params_small_D() + + # Sanity-check the regime ordering used by _riccati_f_initial: + # Branch 1 (large_D) iff D_norm² > iota_e·P_perp/P_tor^(2/3). + threshold(p) = p.iota_e * p.P_perp / p.P_tor^(2 / 3) + @test p_large.D_norm^2 > threshold(p_large) + @test p_small.D_norm^2 < threshold(p_small) + + _, _, branch_large = _SLAYER_MOD._riccati_f_initial(p_large, 0.5 + 0.0im) + _, _, branch_small = _SLAYER_MOD._riccati_f_initial(p_small, 0.5 + 0.0im) + @test branch_large === :large_D + @test branch_small === :small_D + + # Both branches should yield finite Δ values + Δl = solve_inner(SLAYERModel(), p_large, 0.5 + 0.1im) + Δs = solve_inner(SLAYERModel(), p_small, 0.5 + 0.1im) + @test isfinite(Δl.tearing) && isfinite(Δs.tearing) + + # p_floor (=6 by default) is honored even when the branch + # formula would produce a smaller value. + p_start_default, _, _ = _SLAYER_MOD._riccati_f_initial(p_small, 0.5 + 0.0im) + @test p_start_default >= 6.0 + # …and bumping the floor up bumps p_start up. + p_start_high, _, _ = _SLAYER_MOD._riccati_f_initial(p_small, 0.5 + 0.0im; + p_floor=12.0) + @test p_start_high >= 12.0 + end + + @testset "Smoothness across Q sweep" begin + p = _ref_params_large_D() + m = SLAYERModel() + γ = 0.2 + + # Full diamagnetic-band sweep. Δ(ω) is continuous and bounded across + # the whole band, but in the large-D_norm regime it rotates rapidly + # through the complex plane near the upper edge (ω ≳ 0.7 here), so a + # 0.2-spaced grid under-resolves that turn — adjacent samples there are + # legitimately far apart. We therefore test scale-invariant invariants + # (no NaN, bounded |Δ|, no isolated discontinuity) rather than an + # absolute step size, which would only measure sampling resolution and + # drift with the resistivity model. + ωs_full = collect(range(-1.5; stop=1.5, length=16)) + Δ_full = [solve_inner(m, p, ω + γ * im).tearing for ω in ωs_full] + @test all(isfinite.(real.(Δ_full))) + @test all(isfinite.(imag.(Δ_full))) + # Bounded magnitude over the full band — no blow-up / pole crossing. + @test all(0.1 .< abs.(Δ_full) .< 10.0) + + # Discontinuity check on the smooth central window. A solver glitch + # would show up as one step far larger than the local median; a smooth + # curve keeps that ratio small regardless of overall scale. + ωs = collect(range(-1.5; stop=0.5, length=11)) + Δs = [solve_inner(m, p, ω + γ * im).tearing for ω in ωs] + diffs = abs.(diff(Δs)) + @test maximum(diffs) < 6.0 * median(diffs) + + # Δ is genuinely Q-dependent (not silently constant). + @test maximum(diffs) > 1e-6 + end + + @testset "Tolerance self-consistency" begin + p = _ref_params_large_D() + m = SLAYERModel() + Q = 0.5 + 0.2im + # The default reltol=1e-10 matches the Fortran SLAYER LSODE + # setting. Tightening to 1e-13 typically agrees to ~4 digits; + # the long inward integration span amplifies local tolerances + # by roughly 5 orders of magnitude, so 1e-3 relative is the + # realistic self-consistency threshold here. + Δ_default = solve_inner(m, p, Q).tearing + Δ_tight = solve_inner(m, p, Q; reltol=1e-13, abstol=1e-13).tearing + @test abs(Δ_default - Δ_tight) < 1e-3 * abs(Δ_tight) + end + + @testset "p_min reduction stability" begin + # Pulling p_min closer to 0 (from the default 1e-6 down to 1e-7) + # changes Δ only marginally — the solution has well-developed + # asymptotic structure deep in the inner layer. + p = _ref_params_large_D() + m = SLAYERModel() + Q = 0.5 + 0.2im + Δ_default = solve_inner(m, p, Q; pmin=1e-6).tearing + Δ_deeper = solve_inner(m, p, Q; pmin=1e-7).tearing + @test abs(Δ_default - Δ_deeper) < 0.05 * abs(Δ_default) + end + + @testset "Resistive layer thickness (del_s)" begin + p = _ref_params_large_D() + + # riccati_del_s returns the dimensionless δ_s/d_β; must be finite. + dels_db = riccati_del_s(p) + @test dels_db isa ComplexF64 + @test isfinite(dels_db) + + lw = slayer_layer_thickness(p) + @test lw isa LayerWidths + @test lw.ising == p.ising && lw.m == p.m && lw.n == p.n + + # Meters scaling and the magnitude field are self-consistent. + @test lw.dels_db == dels_db + @test lw.delta_s ≈ dels_db * p.d_beta + @test lw.delta_s_m ≈ abs(dels_db * p.d_beta) + @test lw.delta_s_m > 0 + + # Drift-scale reference is carried through unchanged. + @test lw.d_beta == p.d_beta + + # The Riccati width should sit within a few orders of magnitude of + # the β-weighted ion scale it is built from (dels_db is O(1)). + @test 1e-3 * p.d_beta < lw.delta_s_m < 1e3 * p.d_beta + + # Degenerate integration span (q_start ≤ q_min) returns a NaN + # sentinel rather than throwing. + @test isnan(riccati_del_s(p; q_start=1e-6, q_min=1e-5)) + end +end diff --git a/test/runtests_slayer_runner.jl b/test/runtests_slayer_runner.jl new file mode 100644 index 000000000..c3ab86806 --- /dev/null +++ b/test/runtests_slayer_runner.jl @@ -0,0 +1,236 @@ +@testset "Runner: Control + run_slayer + HDF5 output" begin + using GeneralizedPerturbedEquilibrium + using GeneralizedPerturbedEquilibrium.InnerLayer + using GeneralizedPerturbedEquilibrium.Dispersion + using GeneralizedPerturbedEquilibrium.Runner + using HDF5 + + # ------- Helper: build a synthetic SLAYERParameters with full control + function _mk_params(; rs=0.5, lu=1e7, tauk=1e-4, + Q_e=-1.0, Q_i=0.5, m=2, n=1, ising=1, + c_beta=0.1, D_norm=2.0) + return SLAYERParameters(; + tau=1.0, lu=lu, c_beta=c_beta, D_norm=D_norm, + P_perp=20.0, P_tor=10.0, + Q_e=Q_e, Q_i=Q_i, + iota_e=Q_e == Q_i ? 0.0 : Q_e / (Q_e - Q_i), + tauk=tauk, tau_r=1.0, delta_n=lu^(1 / 3) / rs, + rs=rs, R0=1.7, bt=2.0, sval_r=1.0, + eta=2.5e-8, d_beta=4e-3, + m=m, n=n, ising=ising + ) + end + + @testset "SLAYERControl defaults + validation" begin + c = SLAYERControl() + @test c.enabled == false + @test c.inner_model === :slayer_fitzpatrick + @test c.scan_mode === :amr + @test c.coupling_mode === :uncoupled + @test c.msing_max == 3 + + # Validation catches bad symbols + @test_throws ArgumentError Runner.validate( + SLAYERControl(; inner_model=:bogus)) + @test_throws ArgumentError Runner.validate( + SLAYERControl(; scan_mode=:bogus)) + @test_throws ArgumentError Runner.validate( + SLAYERControl(; coupling_mode=:bogus)) + @test_throws ArgumentError Runner.validate( + SLAYERControl(; dc_type=:bogus)) + @test_throws ArgumentError Runner.validate( + SLAYERControl(; msing_max=0)) + @test_throws ArgumentError Runner.validate( + SLAYERControl(; nre=1)) + end + + @testset "slayer_control_from_toml: nested sections flatten" begin + section = Dict{String,Any}( + "enabled" => true, + "inner_model" => "slayer_fitzpatrick", + "scan_mode" => "brute_force", + "coupling_mode" => "coupled", + "dc_type" => "rfitzp", + "msing_max" => 2, + "bt" => 1.8, + "mu_i" => 2.0, + "dr_val" => 0.01, + "scan_grid" => Dict{String,Any}( + "Q_re_range" => [-5.0, 5.0], + "Q_im_range" => [-1.0, 3.0], + "nre" => 50, + "nim" => 40), + "amr" => Dict{String,Any}( + "passes" => 3, + "max_cells" => 50_000), + "growth_rate_filter" => Dict{String,Any}( + "pole_threshold" => 1e5, + "filter_above_poles" => false), + "profile_file" => "profiles.h5" + ) + c = slayer_control_from_toml(section) + @test c.enabled + @test c.inner_model === :slayer_fitzpatrick + @test c.scan_mode === :brute_force + @test c.coupling_mode === :coupled + @test c.dc_type === :rfitzp + @test c.msing_max == 2 + @test c.bt === 1.8 + @test c.dr_val == 0.01 + @test c.Q_re_range == (-5.0, 5.0) + @test c.Q_im_range == (-1.0, 3.0) + @test c.nre == 50 + @test c.nim == 40 + @test c.amr_passes == 3 + @test c.amr_max_cells == 50_000 + @test c.pole_threshold == 1e5 + @test c.filter_above_poles == false + @test c.profile_file == "profiles.h5" + + # Unknown keys should raise + bad = merge(section, Dict{String,Any}("mistyped_key" => 42)) + @test_throws ArgumentError slayer_control_from_toml(bad) + end + + @testset "run_slayer_from_inputs: disabled path is a no-op" begin + c = SLAYERControl(; enabled=false) + params = [_mk_params()] + dp = ComplexF64[0.0 + 0im;;] # 1×1 matrix + r = run_slayer_from_inputs(params, dp, c) + @test r.enabled == false + @test isempty(r.Q_root) + @test isempty(r.params) + end + + @testset "run_slayer_from_inputs: validation catches size mismatch" begin + c = SLAYERControl(; enabled=true) + params = [_mk_params()] + bad_dp = ComplexF64[0.0 0.0; 0.0 0.0] + @test_throws ArgumentError run_slayer_from_inputs(params, bad_dp, c) + end + + @testset "run_slayer_from_inputs: coupled mode finds known root" begin + # Build a 2-surface problem with a known coupled root by construction. + p1 = _mk_params(; rs=0.5, lu=1.0e7, tauk=1.0e-4, Q_e=-1.0, Q_i=0.5, + m=2, ising=1) + p2 = _mk_params(; rs=0.6, lu=2.0e7, tauk=1.2e-4, Q_e=-0.8, Q_i=0.4, + m=3, ising=2) + params = [p1, p2] + + model = SLAYERModel() + # Pick a target Q and pin the diagonal Δ'_kk so det(M(Q_target)) = 0 + Q_target = 0.2 + 0.3im + # Compute what each surface sees at Q_target (with per-surface + # rescaling: surface 2 sees Q_target * tauk_1/tauk_2). + Q_1 = Q_target * (p1.tauk / p1.tauk) # = Q_target + Q_2 = Q_target * (p1.tauk / p2.tauk) + Δ1 = InnerLayer.solve_inner(model, p1, Q_1).tearing * p1.lu^(1 / 3) + Δ2 = InnerLayer.solve_inner(model, p2, Q_2).tearing * p2.lu^(1 / 3) + # Setting dp[k,k] = Δ_k at Q_target makes both diagonals of M vanish, + # which makes det(M) = 0 at Q_target. + dp = ComplexF64[Δ1 0.0; 0.0 Δ2] + + c = SLAYERControl(; enabled=true, + inner_model=:slayer_fitzpatrick, + scan_mode=:brute_force, + coupling_mode=:coupled, + Q_re_range=(-1.0, 1.0), + Q_im_range=(-0.5, 0.8), + nre=80, nim=80, + pole_threshold=1e5) # tuned for lu^(1/3) scale + r = run_slayer_from_inputs(params, dp, c) + @test r.enabled + @test length(r.Q_root) == 1 # single coupled eigenvalue + @test abs(r.Q_root[1] - Q_target) < 2e-2 # grid-resolution limited + @test r.coupled_extraction isa GrowthRateResult + @test isempty(r.per_surface_extraction) + end + + @testset "write_slayer_hdf5!: round-trip structure" begin + p1 = _mk_params(; rs=0.5, lu=1.0e7, tauk=1.0e-4, m=2, ising=1) + p2 = _mk_params(; rs=0.6, lu=2.0e7, tauk=1.2e-4, m=3, ising=2) + params = [p1, p2] + + # Diagonal dp, zero coupling → trivial root structure at Q_target=0 + Q_target = 0.0 + 0.0im + model = SLAYERModel() + Δ1 = InnerLayer.solve_inner(model, p1, Q_target).tearing * p1.lu^(1 / 3) + Δ2 = InnerLayer.solve_inner(model, p2, Q_target).tearing * p2.lu^(1 / 3) + dp = ComplexF64[Δ1 0.0; 0.0 Δ2] + + c = SLAYERControl(; enabled=true, + scan_mode=:brute_force, + coupling_mode=:coupled, + Q_re_range=(-0.5, 0.5), + Q_im_range=(-0.3, 0.3), + nre=40, nim=40, + pole_threshold=1e5, + store_scan=true) + r = run_slayer_from_inputs(params, dp, c) + + mktemp() do path, io + close(io) + h5open(path, "w") do f + write_slayer_hdf5!(f, r) + end + h5open(path, "r") do f + g = f["slayer"] + @test haskey(g, "enabled") && read(g["enabled"]) == 1 + @test haskey(g, "settings") + @test haskey(g, "per_surface") + @test haskey(g, "roots") + @test haskey(g, "diagnostics") + @test haskey(g, "scan") + + # Settings round-trip + @test read(g["settings/inner_model"]) == "slayer_fitzpatrick" + @test read(g["settings/scan_mode"]) == "brute_force" + @test read(g["settings/coupling_mode"]) == "coupled" + @test read(g["settings/nre"]) == 40 + + # Per-surface arrays have the right length + @test length(read(g["per_surface/ising"])) == 2 + @test read(g["per_surface/ising"]) == [1, 2] + @test read(g["per_surface/lu"])[1] ≈ 1.0e7 + @test read(g["per_surface/lu"])[2] ≈ 2.0e7 + + # Roots arrays + @test length(read(g["roots/Q_root_real"])) == 1 # coupled + @test length(read(g["roots/omega_Hz"])) == 1 + + # Layer-thickness diagnostic: one entry per surface, with + # the physical thickness [m] and the drift scale. + @test length(read(g["layer_widths/delta_s_m"])) == 2 + @test all(read(g["layer_widths/delta_s_m"]) .>= 0) + @test haskey(g["layer_widths"], "dels_db_real") + @test haskey(g["layer_widths"], "d_beta") + + # Ragged diagnostics use flat+offsets encoding + @test haskey(g["diagnostics/valid_roots"], "flat_real") + @test haskey(g["diagnostics/valid_roots"], "flat_imag") + @test haskey(g["diagnostics/valid_roots"], "offsets") + + # Scan group present (store_scan=true) + @test haskey(g, "scan/surface_1") + @test read(g["scan/surface_1/kind"]) == "brute_force" + end + end + end + + @testset "write_slayer_hdf5!: disabled result still emits enabled=0" begin + c = SLAYERControl(; enabled=false) + r = empty_slayer_result(c) + mktemp() do path, io + close(io) + h5open(path, "w") do f + write_slayer_hdf5!(f, r) + end + h5open(path, "r") do f + g = f["slayer"] + @test read(g["enabled"]) == 0 + @test !haskey(g, "settings") # no further groups + @test !haskey(g, "per_surface") + end + end + end +end