exp: Padé denominator via GESVFactorization#240
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Benchmarks of the four candidate solve paths on identical per-cell matrices (n = 5..250, scales 0.3/4.0, best-of-N with preallocated caches, Julia 1.12, OpenBLAS single-threaded) showed LinearSolve's new GESVFactorization (v4.2) is the only variant at parity with the raw LAPACK.gesv! this code historically used in every cell: -1.8% to +2.3% end-to-end, versus up to +5% for the pinned LUFactorization and up to +4.5% for the default algorithm choice (whose safety fallback adds an O(n^2) backup copy per refactorization). GESVFactorization also reproduces the gesv! results bit-for-bit, keeps the same per-call allocation bytes, and restores the historical SingularException throw on a singular denominator (the default algorithm's QR fallback resolved it silently instead). Requires LinearSolve 4.2 for GESVFactorization. Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com> Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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ExpMethodHigham2005Base's cached Padé denominator solve from LinearSolve's default algorithm toGESVFactorization(SciML/LinearSolve.jl#1074, v4.2.0): one combinedgesv!per refactorization, restoring raw-LAPACK parity at small n (−1.8% vs the originalgesv!code at n=5, ties within noise at n=10–250; bit-identical accuracy and allocation bytes across all 12 benchmark cells). Also restores the historicalSingularExceptioncontract — the default algorithm's QR safety-fallback silently resolved singular denominators.Compat:
LinearSolve = "4.2"— unmergeable until LinearSolve 4.2.0 tags (#1074). Full EU basictests pass locally against the dev'd branch (22 testsets, 1 pre-existing broken).🤖 Generated with Claude Code