[petsc-users] [SLEPc] Best method to compute all eigenvalues of a MatShell

[Sreeram R Venkat]

Apologies, I accidentally hit "reply" instead of "reply-all."

Thank you for the reference. Actually, I just tested that N ~ 1e4 case
where I had saved the dense matrix to a python-readable format. Using
scipy.linalg.eigvalsh, I got the eigenvalues in ~1.5 minutes. They agree
with the ones I got from SLEPc as well. I believe the scipy routine just
calls LAPACK in the backend, so I assume I would get similar results if I
used the LAPACK solver in SLEPc.

The MatShell object I am working with requires me to operate on multiple
processes to fit all the data, so to use the LAPACK solver in SLEPc, I
believe I would have to read/write the dense matrix as well.

So at the cost of storing the dense matrix, I think the dense eigensolver
seems to be the way to go. I will need to store at least one large dense
matrix of this size for my application, so that should not be the limiting
factor.

Sreeram

On Mon, May 13, 2024 at 1:54 PM Jose E. Roman <jroman at dsic.upv.es> wrote:

> Please respond to the list.
>
> The mpd parameter means "maximum projected dimension". You can think of
> the projected problem as the "sequential" part of the computation, that is
> not parallelized ("small" dense eigenproblem). When you run with MPI,
> everything will scale reasonably well except that part, so it is better to
> keep it small, specially when you request many eigenvalues. A value
> mpd=2000 might be too large, it may be better to reduce it to 500, say. The
> paper https://urldefense.us/v3/__https://doi.org/10.1016/j.cpc.2010.09.007__;!!G_uCfscf7eWS!elC1IPQR-J0CwJ8mp-zPPEXvkzawO1RCvusBFlcaG2xfHHzqRFzOQqHgXXqpFf1EBfhJx3LzgTYotr_Jwv1_o0wyag$  includes a discussion on
> the ncv and mpd paramters, mostly in terms of memory usage.
>
> Jose
>
> > El 13 may 2024, a las 20:33, Sreeram R Venkat <srvenkat at utexas.edu>
> escribió:
> >
> > Thank you for the suggestions. I will try out LAPACK/ELPA and the n/2
> method. For the latter, how should I choose the MPD? In the examples I
> could find online, it looked like they were using something like mpd ~
> nev/10.
> >
> > Sreeram
> >
>
>
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