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On Mon, May 13, 2024 at 1: 40 PM Sreeram R Venkat <srvenkat@ 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,
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<div dir="ltr"><div dir="ltr">On Mon, May 13, 2024 at 1:40 PM Sreeram R Venkat <<a href="mailto:srvenkat@utexas.edu">srvenkat@utexas.edu</a>> wrote:<br></div><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div class="msg-6360357948739967649">
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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
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<div dir="ltr"><div dir="ltr" class="gmail_signature"><div dir="ltr"><div style="color:rgb(34,34,34)">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.</div><div style="color:rgb(34,34,34)"><br></div><div style="color:rgb(34,34,34)">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?</div></div></div></div></div></blockquote><div><br></div><div>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).</div><div><br></div><div> Thanks,</div><div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div class="msg-6360357948739967649"><div dir="ltr"><div dir="ltr" class="gmail_signature"><div dir="ltr"><div style="color:rgb(34,34,34)">I do need the full spectrum here since I am trying to analyze how the spectral decay changes for different problem configurations.</div><div style="color:rgb(34,34,34)"><br></div><div style="color:rgb(34,34,34)">Thanks for your help,</div><div style="color:rgb(34,34,34)">Sreeram</div></div></div></div>
</div></blockquote></div><br clear="all"><div><br></div><span class="gmail_signature_prefix">-- </span><br><div dir="ltr" class="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div>What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>-- Norbert Wiener</div><div><br></div><div><a href="https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!cLlaAsyk3G1fWIZGlTet7-bB1VMxzmbrmnjxP0IPtxxAA-mYn4vGvI9tzI2x7GXRMPqOjNBQZZrrDie62V3N$" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br></div></div></div></div></div></div></div></div>