[petsc-users] Slepc: Nonlinear eigenvalue problem

[Matthew Knepley]

On Tue, Oct 23, 2018 at 10:53 AM Manav Bhatia <bhatiamanav at gmail.com> wrote:

> Really interesting!
>
> So this is a limitation of the algorithm and not the implementation.
>
> The challenge is that the eigenvalue solution  in my workflow is a small
> component of a large computation done with real numbers in an optimization
> problem. I could do the whole thing with complex numbers, but would be
> wasting a lot of cpu cycles doing that.
>
> Do you know if there is anyway to link to both real and complex versions
> of the library or switch between them at runtime?
>

Unfortunately, that is a huge amount of work. One group has done it, but we
do not support it.

  Thanks,

    Matt


> -Manav
>
> Sent from my iPhone
>
> > On Oct 23, 2018, at 9:42 AM, Jose E. Roman <jroman at dsic.upv.es> wrote:
> >
> >
> >
> >> El 23 oct 2018, a las 16:10, Manav Bhatia <bhatiamanav at gmail.com>
> escribió:
> >>
> >> Thanks for the clarification.
> >>
> >> Does this also apply to the standard non-hermitian eigenvalue problem?
> Do I need to compile with complex numbers if I want to capture the complex
> eigenvalues? Or does it work with real number support?
> >
> > No, linear eigenproblems (EPS) can be solved with real scalars for
> complex eigenvalues, but nonlinear eigenproblems (NEP) cannot.
> >
> > Jose
> >
> >>
> >> Thanks
> >> Manav
> >>
> >> Sent from my iPhone
> >>
> >>> On Oct 23, 2018, at 3:43 AM, Jose E. Roman <jroman at dsic.upv.es> wrote:
> >>>
> >>> If eigenvalues are complex then NLEIGS also needs to work in complex
> arithmetic because it needs a region of the complex plane containing the
> wanted eigenvalues. It seems that complex arithmetic is the only change in
> your problem.
> >>>
> >>> Jose
> >>>
> >>>
> >>>> El 22 oct 2018, a las 22:01, Manav Bhatia <bhatiamanav at gmail.com>
> escribió:
> >>>>
> >>>> Thanks, Jose.
> >>>>
> >>>> How difficult would it be to add the support for the general case (if
> at all possible)?
> >>>>
> >>>> My eigenvalue problem is of the form shown in the attachment. Beta is
> the eigenvalue and X_s^\Delta is the eigenvector. While some of the
> matrices are known, others are defined only as matrix vector products.
> >>>>
> >>>> I am interested in eigenvalues with the largest real part. I expect
> to find complex eigenvalues, although for a small subset of cases these
> will be real.
> >>>>
> >>>> What is your recommendation for attacking this problem with the
> nonlinear eigenvalue support in Slepc?
> >>>>
> >>>> Would appreciate your guidance.
> >>>>
> >>>> Regards,
> >>>> Manav
> >>>>
> >>>> <PastedGraphic-1.pdf>
> >>>>
> >>>>
> >>>>> On Oct 22, 2018, at 2:40 PM, Jose E. Roman <jroman at dsic.upv.es>
> wrote:
> >>>>>
> >>>>>
> >>>>>
> >>>>>> El 22 oct 2018, a las 21:05, Manav Bhatia <bhatiamanav at gmail.com>
> escribió:
> >>>>>>
> >>>>>> Hi,
> >>>>>>
> >>>>>> I am exploring the nonlinear eigenvalue problem solver in Slepc.
> >>>>>>
> >>>>>> From the notes in "Sec 6.4: Retrieving the Solution”, it appears
> that if I expect to find complex eigenpairs then I must compile the library
> (and Petsc) with complex scalars. Is that correct?
> >>>>>>
> >>>>>> Is there a way to include support for complex eigenpairs in a
> library complied with real scalars?
> >>>>>>
> >>>>>> Regards,
> >>>>>> Manav
> >>>>>>
> >>>>>>
> >>>>>
> >>>>> Currently, the only combination that supports complex eigenpairs
> with real scalars is the split form for the nonlinear function with the
> NLEIGS solver.
> >>>>>
> >>>>> Jose
> >>>>
> >>>
> >
>


-- 
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

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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