[ViralBShah]

factorize of a sparse indefinite Hermitian matrix threw ZeroPivotException when its LDLt needs pivoting. \ on the same matrix works, and so does dense factorize. cond(A, 1) threw too, because it goes through factorize.

Before

julia> A = sparse([0.0 1; 1 0]); b = [1.0, 2.0];

julia> A \ b
2-element Vector{Float64}:
 2.0
 1.0

julia> factorize(A) \ b
ERROR: ZeroPivotException: factorization encountered one or more zero pivots. Consider switching to a pivoted LU factorization.

julia> cond(A, 1)
ERROR: ZeroPivotException: factorization encountered one or more zero pivots. Consider switching to a pivoted LU factorization.

After

julia> typeof(factorize(A))
SparseArrays.UMFPACK.UmfpackLU{Float64, Int64}

julia> factorize(A) \ b
2-element Vector{Float64}:
 2.0
 1.0

julia> cond(A, 1)
1.0

The Hermitian method tries cholesky(A; check = false) first. If that fails, it called ldlt!(F, A), which throws when CHOLMOD's unpivoted LDLt meets a zero pivot. It now calls ldlt!(F, A; check = false), and when that also fails it returns lu(A), as the Hermitian \ does (cholmod.jl). So factorize now succeeds wherever \ does. A singular matrix still throws, now a SingularException from lu. The inferred return type of factorize(::Hermitian{T,SparseMatrixCSC{T,Int}}) widens from CHOLMOD.Factor{T,Int} to Union{CHOLMOD.Factor{T,Int}, UMFPACK.UmfpackLU{T,Int}} (UmfpackLU{Float64,Int} for Float32). factorize(::SparseMatrixCSC) already returned a seven-member union that includes both.

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 94.73%. Comparing base (e4a42b4) to head (ad29290).

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #1116   +/-   ##
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  Coverage   94.73%   94.73%           
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  Files          16       16           
  Lines       10325    10325           
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  Hits         9781     9781           
  Misses        544      544           

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