[petsc-users] [SLEPc] non-deterministic behaviour in GHEP with Krylov-Schur

[Matthew Knepley]

On Tue, Mar 8, 2016 at 6:13 AM, Denis Davydov <davydden at gmail.com> wrote:

>
> > On 8 Mar 2016, at 12:38, Jose E. Roman <jroman at dsic.upv.es> wrote:
> >
> > As you can see, the eigenvector for the first eigenvalue (which is
> simple) is the same in both runs. The rest are multiple eigenvalues, so the
> corresponding eigenvectors are not uniquely determined simply by
> normalization. This means that, for instance, any linear combination of
> v1,v2,v3 is an eigenvector corresponding to 4.71385. Parallel
>
> There is no questions about this.
>
> > computation implies slightly different numerical error in different
> runs, and that is why you are getting different eigenvectors. But in terms
> of linear algebra, both runs are
> > correct.
>
> Frankly, i don’t see a reason for that.
> Assuming that the partition of degrees-of-freedom is the same and the
> number of MPI cores is the same,
> the result should be deterministic on the same machine.
>

This is not true. If you have reductions, the order of operations is not
prescribed by the standard, and can change. I believe
there is an MPI implementation for climate that allows no reordering, so
you get "bit-level reproducibility". However, that
seems to me to defeat the whole purpose of efficient numerics. We should
only care about things to the given tolerance,
and since you have a multiple eigenvalue to that tolerance you should not
care which basis vectors are chosen.

  Thanks,

     Matt


> Unless some random number seed is changing and thus influence which
> eigenvectors are obtained for the degenerate eigenvalue...
>
>
> Regards,
> Denis
>
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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