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exp: Padé denominator solve via LinearSolve default algorithm (alias_A) #240

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Merged
ChrisRackauckas merged 1 commit into from
Jul 10, 2026
Merged

exp: Padé denominator solve via LinearSolve default algorithm (alias_A) #240

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19 changes: 9 additions & 10 deletions src/exp_baseexp.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -16,11 +16,12 @@ function alloc_mem(
U = Matrix{T}(undef, n, n)
V = Matrix{T}(undef, n, n)
temp = Matrix{T}(undef, n, n)
# Cached LinearSolve workspace for the Padé denominator solves, using
# LinearSolve's default algorithm choice (size-dependent: e.g. generic LU
# for tiny matrices, LAPACK/RecursiveFactorization above). The buffers are
# workspace-owned, so aliasing lets the factorization refactorize in place
# on every `solve!` instead of copying the n×n matrix.
# Cached LinearSolve workspace for the Padé denominator solves, using the
# default algorithm choice: it size-selects the fastest available LU
# (RecursiveFactorization when loaded — markedly faster than LAPACK at
# small/medium n). The buffers are workspace-owned, so aliasing lets the
# factorization overwrite Abuf in place on every `solve!` (no n×n copy),
# keeping each call allocation-free.
Abuf = Matrix{T}(undef, n, n)
Bbuf = Matrix{T}(undef, n, n)
linsolve = LinearSolve.init(
Expand All @@ -37,13 +38,11 @@ function _pade_linsolve!(
) where {T}
Abuf = linsolve.A
copyto!(Abuf, temp)
linsolve.A = Abuf # flag the refactorization; lu! overwrites Abuf
linsolve.A = Abuf # flag refactorization; alias_A lets it overwrite Abuf
copyto!(linsolve.b, X)
sol = LinearSolve.solve!(linsolve)
# The Pade denominator is nonsingular by construction for the branch norm
# bounds, so this only triggers if even the default algorithm's safety
# fallback failed; surface it like LAPACK.gesv! did rather than silently
# propagating garbage.
# exp! historically threw on a singular denominator (via LAPACK.gesv!);
# keep that contract rather than propagating a failed factorization.
if !LinearSolve.SciMLBase.successful_retcode(sol.retcode)
throw(LinearAlgebra.SingularException(0))
end
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