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## [Octave-bug-tracker] [bug #53700] eigs test failure related to ARPACK ge

 From: Dan Sebald Subject: [Octave-bug-tracker] [bug #53700] eigs test failure related to ARPACK generating real NaN rather than complex NaN+1i*NaN Date: Mon, 23 Apr 2018 04:10:11 -0400 (EDT) User-agent: Mozilla/5.0 (X11; Ubuntu; Linux x86_64; rv:55.0) Gecko/20100101 Firefox/55.0

```Follow-up Comment #25, bug #53700 (project octave):

Oh, so the reason for the less robust system for NEV=10 is that the Krylov
subspace dimensionality is not even near the cardinality of the largest
eigenvalue group, which is 97 in this case.  I.e., 97 eigenvalues of 1.0.
That's what the algorithm is struggling with.  On the other hand, had we
chosen a system for which there were more variation in the eigenvalues, e.g.,
1.0 1.0 3.0 3.0 3.5 2-2j 2+2j, etc., and used a Krylov subspace of 10 then
we'd get good convergence.

Going the other direction, increasing NEV to 50 (or is it p=50?) makes the
Krylov subspace nearer to the size of the largest eigenvalue group in this
case.

Thanks for the explanation.

Would there be any other type of more assured test?  Say, if instead of
looking for "sm" eigenvalues, we looked for "lm".  The largest eigenvalues
have a group cardinality of 1 or 2 and therefore those few really large
eigenvalues should converge nicely on all systems, compilers and linear
algebra libraries with a choice of NEV=10.  I'm seeing

octave:32> d = eigs (A, 10, "lm", opts);
octave:33> d
d =

50006.00000
2887.60700
-2885.60700
1.00000
NaN
NaN
NaN
NaN
NaN
NaN

But that too ends up being not complex, so I don't know if that gets us
anywhere different.

How about choosing an odd number for NEV?  Will that force there to be a
conjugate pair somehow?

octave:34> d = eigs (A, 9, "lm", opts);
octave:35> d
d =

50006.00000 +     0.00000i
2887.60700 +     0.00000i
-2885.60700 +     0.00000i
1.00000 -     0.00000i
1.00000 +     0.00000i
NaN +         NaNi
NaN +         NaNi
NaN +         NaNi
NaN +         NaNi

What do others see for such tests?  Is it just as arbitrary?

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