[Octave-bug-tracker] [bug #53719] eigs delivers wron result in case of complex valued general eigenvalue problem

[Marco Caliari]

Follow-up Comment #3, bug #53719 (project octave):

The matrix B is not Hermitian positive definite, as required in the
documentation, and this is the main problem here. Looking for small
eigenvalues does not require explicit inversion of B by cholesky, and
therefore this problem is not detected. Matlab succeeds when asking 5
eigenvalues, but returns an error with 4 (ill-conditioned problem). I believe
that Matlab uses eig when asking 5 eigenvalues. This is reasonable: since the
default choice is to double the number of eigenvalues for the Krylov space,
when the Krylov space has the same dimension of the problem, we should use
eig. This is possible by replacing


if (rows (a) - k < 3)


with


if (2 * k >= rows (a))


in eigs.m. It seems that ARPACK does not detect problems in convergence and
therefore Octave silently returns wrong eigenvalues (when asking 4
eigenvalues). I will implement the example in fortran, to be 100% sure it is a
not-detected-problem in ARPACK.

For the crash, there is a problem in eigs-base:make_cholb. For the sparse
versions, when the factorization fails, it seems that fact.P () is not
available. The test should be as in the full case


if (info != 0)
  return false;
else


fact.P() (which is the second output of chol) is probably set later, I don't
know. I attach a diff (not yet a changeset): I had to change a lot of tests,
otherwise call_eig was used. Morever, I fixed some conditions in eigs.m.

To summarize:

1) the diff fixes the problem by calling eig (which is reasonable for this
example)
2) the diff fixes in general the crash when B is not SPD, but maybe a bug in
sparse_chol is now hidden (is it correct that fact.P() does not exist when
info != 0?)
3) the diff does not detect that the original problem is ill-conditioned (this
is probably a defect in ARPACK, I will check).


(file #43992)
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Additional Item Attachment:

File name: eigs.diff                      Size:9 KB


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