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

[Matthew Knepley]

On Mon, May 13, 2024 at 1:40 PM Sreeram R Venkat <srvenkat at utexas.edu>
wrote:

> I have a MatShell object that computes matrix-vector products of a dense
> symmetric matrix of size NxN. The MatShell does not actually form the dense
> matrix, so it is never in memory/storage. For my application, N ranges from
> 1e4 to 1e5. I want
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> I have a MatShell object that computes matrix-vector products of a dense
> symmetric matrix of size NxN. The MatShell does not actually form the dense
> matrix, so it is never in memory/storage. For my application, N ranges from
> 1e4 to 1e5.
>
> I want to compute the full spectrum of this matrix. For an example with N
> ~1e4, I was able to use SLEPc's Krylov-Schur solver to get the spectrum in
> about 3 hours running on 6 A100 GPUs. There, I had set the MPD to 2000.
> Before moving on to larger matrices, I wanted to check whether this is the
> best way to go about it. I saw on other posts that for computing full
> spectra of dense matrices, it is generally better to go with
> LAPACK/SCALAPACK. Is the same true for MatShells of dense matrices? The
> matrix-vector products with the shell themselves are really cheap, so I can
> form the dense matrix with MatComputeOperator() and store it to later
> compute with another solver if needed. If SLEPc is not a bad option, what
> is a good way to select MPD/NCV?
>

You can select LAPACK through SLEPc. I would definitely try it since it is
easy. For the complete spectrum, it is likely to be faster (modulo how fast
KS converges).

  Thanks,

    Matt


> I do need the full spectrum here since I am trying to analyze how the
> spectral decay changes for different problem configurations.
>
> Thanks for your help,
> Sreeram
>


-- 
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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