Preconditioned LOBPCG solver for large non-periodic problems (v0.4.0) - #8
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New opt-in solver = lobpcg (input files and API): LOBPCG with a tensor-product kinetic preconditioner - the kinetic operator is approximated by the Kronecker sum of the per-dimension 1D stencil operators, whose shifted inverse is applied exactly through small per-dimension eigenbasis transforms, so no factorization of the full operator and no 3D fill-in. Measured on the 3D harmonic oscillator (solver time): 9.7x faster than Arpack shift-invert at 51^3 (13.8 s vs 133.8 s), 3.8x at 35^3, with eigenvalue agreement at 1e-12; end-to-end 3.7x at 51^3. Accuracy safeguards, since correctness outranks speed: - every iterative solve is verified after the fact: the kept eigenpairs' relative residuals are computed against the actual Hamiltonian, near-zero eigenvectors count as infinitely loose (a silently collapsed block can never pass), and lobpcg results that fail verification are re-solved with Arpack shift-invert - lobpcg breakdowns (its internal factorizations can fail) retry with a fresh random block, then fall back to Arpack - never worse than the previous solver in either accuracy or robustness - complex Hermitian (periodic) problems are rejected with a clear error; arpack remains the default everywhere Adds IterativeSolvers as a dependency; version 0.4.0.
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## main #8 +/- ##
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+ Coverage 97.02% 97.20% +0.18%
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Files 32 33 +1
Lines 1645 1752 +107
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+ Hits 1596 1703 +107
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Benchmark Results (Julia v1)Time benchmarks
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…r accuracy claim Codecov flagged src/preconditioner.jl and src/solve.jl at ~87% patch coverage on PR #8: the uncovered lines were the lobpcg retry/fallback and residual-escalation branches, which had only been exercised by chance (RNG-dependent) rather than deliberately, so coverage varied by platform/session. - Expose lobpcg_maxiter and krylov_maxiter as tunable keywords on solveWrapper and use them to deterministically force the three failure modes these safety nets exist for, using genuine solver behavior rather than mocks: * IterativeSolvers.lobpcg refuses to run (throws) when the matrix is smaller than 3x the block size - reliably fails both retry attempts, forcing the arpack fallback * lobpcg_maxiter = 1 produces an under-converged (not thrown) result - caught by the residual verifier, re-solved with arpack * krylov_maxiter = 1 similarly under-converges KrylovKit's solver, exercising the generic (non-escalating) residual warning for solvers with no further fallback - Add test_KineticPreconditioner, verifying the preconditioner against an independently-derived dense reference (not calling any of its own internals) across 1D/2D/3D and a periodic dimension, through all four ldiv! dispatches While building that reference, discovered that the preconditioner's Kronecker-sum kinetic operator is only an EXACT match to the true production operator for 1D and 2D (buildLaplace_2d's Laplacian is separable - dividing by 2^(dimension-1) recovers the Kronecker sum bit-for-bit); buildLaplace_3d uses a more elaborate, non-separable stencil, so for 3D the preconditioner is a heuristic approximation. This does not affect correctness - every result is independently residual-verified regardless of preconditioner quality - but the docstring previously implied a close approximation to the true operator in all cases, which was wrong for 3D. Corrected the wording and added a regression assertion for the 1D/2D exactness. Local coverage of both flagged files is now 0 uncovered lines.
…input validation gaps - solveWrapper: re-check the residual after the lobpcg->arpack escalation solve, instead of returning it unconditionally - the rescue itself can land above tolerance for ill-conditioned Hamiltonians and was previously returned without any warning. - setupSystem: reject solver=lobpcg for reciprocal (periodic k-point) runs as soon as reciprocal is known, before any output file is touched - previously this only threw deep in solve(), after main.jl had already deleted a pre-existing eigenvalues.dat. - api.jl: extend the n_eigenvalues+5 < grid size guard to :lobpcg and :krylov, not just :arpack - lobpcg transparently falls back to arpack and was raising an opaque BoundsError instead of a clear ArgumentError. - preconditioner.jl: correct the docstring's claim that the preconditioner is exact for all 2D problems - it is only exact for the 5-point stencil, not the package's default (9); broaden the regression test accordingly. - test_3Dsmoke: seed the RNG and assert no fallback/escalation warning fires in the lobpcg-vs-arpack degenerate-cluster check, so the test actually proves lobpcg converged rather than merely that the pipeline's answer is correct (measured a 1/20-7/20 unseeded fallback rate that the old assertions couldn't distinguish from genuine convergence).
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Pushed a follow-up commit after a deeper self-review pass:
Full suite (1000 tests) passes. Heads-up for whoever merges this and #9: both branches independently add |
# Conflicts: # Project.toml
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Adds
solver = lobpcg(input files and API, opt-in —arpackstays default): LOBPCG with a tensor-product kinetic preconditioner built from per-dimension 1D stencil operators, applied exactly via small per-dimension eigenbasis transforms — no full-operator factorization, so no 3D fill-in.Solver time (3D harmonic oscillator)
Accuracy safeguards
Adds IterativeSolvers to deps. Version 0.4.0.