Sparse matrix and zero pivots

Specific Domains Numerics
1

I have a large sparse matrix and I need to find a position of zero pivots, so my matrix is singular. Standard QR factorization for dense matrices without permutations gives the result that I need, the pivots are on the main diagonal of the matrix R. Because I have a sparse matrix I use SPQR, but then I have permutations of columns and rows and I lose the pivot position. Is there a smart way to find pivots, without converting matrix from sparse to dense?

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See SPQR: allow user-selected ordering by dpo · Pull Request #35599 · JuliaLang/julia · GitHub. In the next version of Julia, it will be possible to disable pivoting in the sparse QR.

Notice that zero pivots don’t imply singularity, e.g.

[0 1
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1 Like
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thank you, regarding the note, I agree with you :smiley: