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SparseWithDenseRowColMatrices: a square matrix A = S + U*V (a sparse bulk S plus a low-rank dense correction), solved by Sherman-Morrison-Woodbury over a PureKLU sparse LU, with an augmented bordered-system fallback when S is singular. Provides symbolic-reuse caching (factorize / refactor! / update_lowrank!), a cheap pattern-only appropriateness detector (recommend_lowrank_peel), and a LinearSolve.jl extension mirroring KLUFactorization. Tested against dense references on Julia 1.10/1.11/1.12 (219 tests). Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com> Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com> Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com> Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
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Initial import of SparseWithDenseRowColMatrices.jl.
What it is
A square matrix
A = S + U*V— a sparse bulkSplus a low-rank dense correction (dense rows and/or columns). Solved by Sherman–Morrison–Woodbury over a PureKLU.jl sparse LU, with an augmented bordered-system fallback whenSis singular.factorize/lu(Woodbury, auto-falls-back to augmented),\/ldiv!, adjoint/transpose.refactor!/lu!(newSvalues, same pattern — Newton), andupdate_lowrank!(fixedS, changing low-rank correction — the SMW reuse case; ~785× faster than re-factoring the assembled matrix, which fills on the dense rows).recommend_lowrank_peel(A) -> PeelRecommendation— cheap, pattern-only check of whether the method is worthwhile.SparseWithDenseRowColFactorization()+defaultalg, mirroringKLUFactorization(symbolic cached in theLinearCache, reused across solves; singularAreturnsReturnCode.Infeasible).Float64/Complex,BigFloat, andForwardDiff.Dual(autodiff through the solve), inherited from PureKLU.Canonical use cases: bordered / saddle-point / KKT systems and BVP boundary-condition rows — sparse bulk + a low-rank dense border. (A pure single-spike arrowhead is better served by a specialized O(n) solver; documented.)
Verification
219 tests passing on Julia 1.10/1.11/1.12 (correctness vs dense references; allocations; generic eltypes; LinearSolve caching; arrow/bordered). Built with a multi-agent design + adversarial review pass.
Dependency caveat
Depends on the unregistered SciML/PureKLU.jl. Resolved via
[sources]inProject.toml(Julia 1.11+) and a CI step thatPkg.develops it. The package cannot be registered in General until PureKLU is registered.🤖 Generated with Claude Code