[Octave-bug-tracker] [bug #53499] Factorization of symmetric positive definite sparse matrix fails whereas Cholesky factorization works

[Marco Caliari]

Follow-up Comment #6, bug #53499 (project octave):

Your matrix does not appear to be exactly symmetric, while it is at machine
precision


octave:13> issymmetric (A)
ans = 0
octave:14> issymmetric (A, eps)
ans = 1


Thus, the code in SparseMatrix::fsolve chooses a general solver (umfpack). I
already notice that in #53140. It is a little bit off-topic, but I would agree
to mark a matrix Hermitian if it is Hermitian at machine precision. Since a
general solver is used, refinement iterations are performed (1 in current
stable) and it takes a bit (970 seconds vs. 350 of chol). The errors for me
are comparable (1e-15 vs. 4.5e-15). Since the patch coming from #53140 is not
in 4.2.2, it is possible that the original submitter sees something different
(in 4.2.1 I see "error: SparseMatrix::solve numeric factorization failed. But
this could be related with #53390, and I cannot reproduce with current
stable). To summarize:

1) backslash is slower because the matrix is not detected as exactly
symmetric
2) both backslash and chol work in current stable and give comparable errors
of about 10*eps

I would close the report as Works for me, unless I missed something in my
analysis. 

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