[Octave-bug-tracker] [bug #60738] logm returning incorrect result with some real non-symmetric matrices

[anonymous]

Follow-up Comment #4, bug #60738 (project octave):

I'm not sure either. The tolerance should be the error in the Schur
factorization which should be around the machine precision of each eigenvalue.
I think it would be safe to base it on the absolute value of the largest
eigenvalue. I'm open to other suggestions.

As the consequence of having a tolerance that is too lax is a few results will
contain small complex values that are unlikely to change the final result by
much and it should be obvious to the user that they come from numerical error
whereas if the tolerance is too tight the complex values that need to be
present will be removed and the answer will be wrong in a non-obvious way
(this bug has been present for years and I'm the first person to notice it).

I gave it the tight tolerance below because it worked for a large number of
random matrices. The error I typically see for complex components of real
eigenvalues from the Schur factorization is normally very small.

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