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?
See https://github.com/JuliaLang/julia/pull/35599. 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 1 1]
thank you, regarding the note, I agree with you