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<p class="MsoNormal"><span style="font-size:11.0pt">I have an implementation of the slepc MFN matrix exponential which is implicitly using ExpoKit. You have to supply a matrix into the Slepc MFN operator to set the problem up as far as I know.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">Tyler<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><b><span style="font-size:12.0pt;color:black">From:
</span></b><span style="font-size:12.0pt;color:black">Matthew Knepley <knepley@gmail.com><br>
<b>Date: </b>Monday, January 30, 2023 at 12:24 PM<br>
<b>To: </b>Guglielmo, Tyler Hardy <guglielmo2@llnl.gov><br>
<b>Cc: </b>Barry Smith <bsmith@petsc.dev>, petsc-users@mcs.anl.gov <petsc-users@mcs.anl.gov><br>
<b>Subject: </b>Re: [petsc-users] Kronecker Product<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">On Mon, Jan 30, 2023 at 3:08 PM Guglielmo, Tyler Hardy via petsc-users <<a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a>> wrote:<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">I would need the Kronecker product to be explicitly available to perform matrix exponentials. A and B are of order 5000, so not too large. I will
give storing them on all ranks a shot. Thanks for the tips!<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">Were you going to do exponentials by explicit factorization? For large matrices, I thought it was common to<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">use matrix-free methods (<a href="https://urldefense.us/v3/__https:/slepc.upv.es/documentation/current/docs/manualpages/MFN/index.html__;!!G2kpM7uM-TzIFchu!nSXMSWur4Lrpt0oF_bjtBae92VccTBcCHUQJRYWByuB4bZ5HHzFHhGtLjs7NrgHZUCE$">https://slepc.upv.es/documentation/current/docs/manualpages/MFN/index.html</a>)<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> Thanks,<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> Matt<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">Best,<o:p></o:p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">Tyler<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:12.0pt"><b><span style="font-size:12.0pt;color:black">From:
</span></b><span style="font-size:12.0pt;color:black">Barry Smith <<a href="mailto:bsmith@petsc.dev" target="_blank">bsmith@petsc.dev</a>><br>
<b>Date: </b>Monday, January 30, 2023 at 12:01 PM<br>
<b>To: </b>Guglielmo, Tyler Hardy <<a href="mailto:guglielmo2@llnl.gov" target="_blank">guglielmo2@llnl.gov</a>><br>
<b>Cc: </b><a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a> <<a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a>><br>
<b>Subject: </b>Re: [petsc-users] Kronecker Product</span><span style="font-size:11.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"> What is large? If A and B have dimensions of 1000, then the Kronecker product is of size 1,000,000. Do you want the Kronecker product to be explicitly
formed or just available as matrix vector products? If just explicitly available then I think you can just store sparse A (for example) completely on all ranks, 10,000 by 10,000 sparse matrix is small for sequential) while B is distributed.<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">Barry<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:12.0pt"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">On Jan 30, 2023, at 2:48 PM, Guglielmo, Tyler Hardy <<a href="mailto:guglielmo2@llnl.gov" target="_blank">guglielmo2@llnl.gov</a>> wrote:<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">Both matrices (A and B) would be approximately the same size and large. The use case (for me at least) is to create several large sparse matrices
which will be combined in various ways through Kronecker products. The combination happens at every time step in an evolution, so it really needs to be fast as well. I’m thinking mpi/petsc is probably not the most optimal way for dealing with this, and might
just have to work with single node multi-threading.<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">Best,<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">Tyler<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:12.0pt"><b><span style="font-size:12.0pt">From:<span class="m1070881843546206487apple-converted-space"> </span></span></b><span style="font-size:12.0pt">Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>><br>
<b>Date:<span class="m1070881843546206487apple-converted-space"> </span></b>Monday, January 30, 2023 at 11:31 AM<br>
<b>To:<span class="m1070881843546206487apple-converted-space"> </span></b>Guglielmo, Tyler Hardy <<a href="mailto:guglielmo2@llnl.gov" target="_blank">guglielmo2@llnl.gov</a>><br>
<b>Cc:<span class="m1070881843546206487apple-converted-space"> </span></b>Barry Smith <<a href="mailto:bsmith@petsc.dev" target="_blank">bsmith@petsc.dev</a>>,<span class="m1070881843546206487apple-converted-space"> </span><a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a><span class="m1070881843546206487apple-converted-space"> </span><<a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a>><br>
<b>Subject:<span class="m1070881843546206487apple-converted-space"> </span></b>Re: [petsc-users] Kronecker Product</span><span style="font-size:11.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">On Mon, Jan 30, 2023 at 2:24 PM Guglielmo, Tyler Hardy via petsc-users <<a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a>>
wrote:<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">Thanks Barry,<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">I saw that function, but wasn’t sure how to apply it since the documentation says that S and T are dense matrices, but in my case all matrices involved
are sparse. Is there a way to work around the dense requirement?<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">We don't have parallel sparse-sparse. It would not be too hard to write, but it would be some work.<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">It is hard to understand the use case. Is one matrix much smaller? If not, and you inherit the distribution from A, it seems<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">like it might be very suboptimal, and otherwise you would have to redistribute on the fly and it would get very complicated.<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"> Thanks,<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"> Matt<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">Best,<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">Tyler<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:12.0pt"><b><span style="font-size:12.0pt">From:<span class="m1070881843546206487apple-converted-space"> </span></span></b><span style="font-size:12.0pt">Barry Smith <<a href="mailto:bsmith@petsc.dev" target="_blank">bsmith@petsc.dev</a>><br>
<b>Date:<span class="m1070881843546206487apple-converted-space"> </span></b>Monday, January 30, 2023 at 11:12 AM<br>
<b>To:<span class="m1070881843546206487apple-converted-space"> </span></b>Guglielmo, Tyler Hardy <<a href="mailto:guglielmo2@llnl.gov" target="_blank">guglielmo2@llnl.gov</a>><br>
<b>Cc:<span class="m1070881843546206487apple-converted-space"> </span></b><a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a><span class="m1070881843546206487apple-converted-space"> </span><<a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a>><br>
<b>Subject:<span class="m1070881843546206487apple-converted-space"> </span></b>Re: [petsc-users] Kronecker Product</span><span style="font-size:11.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"> Do you need the explicit sparse representation of the Kronecker product? Or do you want to apply it as an operator or solve systems with it? If
the latter you can use <a href="https://urldefense.us/v3/__https:/petsc.org/release/docs/manualpages/Mat/MatCreateKAIJ/*matcreatekaij__;Iw!!G2kpM7uM-TzIFchu!lSQ9WFlYi6PMdfs3WAfEq4ydgCLZtfDgyFy9PjdLNTisCsHtwmVuukcpIv1J0i1EtiQ$" target="_blank">https://petsc.org/release/docs/manualpages/Mat/MatCreateKAIJ/#matcreatekaij</a><o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"> Barry<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:12.0pt"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:12.0pt"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">On Jan 30, 2023, at 12:53 PM, Guglielmo, Tyler Hardy via petsc-users <<a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a>>
wrote:<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">Hi all,<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">I am wondering if there is any functionality for taking Kronecker products of large sparse matrices that are parallel? MatSeqAIJKron is as close
as I have found, but it seems like this does not work for parallel matrices. Any ideas here? <o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">An option could be to make A and B sequential, compute the Kronecker product, C, then scatter C into a parallel matrix? This seems like a horribly
inefficient procedure. I’m still fairly new to petsc, so thanks for patience :)!<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">Best,<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">Tyler<span class="m1070881843546206487m1068516836359424776apple-converted-space"> </span><o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">+++++++++++++++++++++++++++++<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">Tyler Guglielmo<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">Postdoctoral Researcher<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">Lawrence Livermore National Lab<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">Office: 925-423-6186<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">Cell: 210-480-8000<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">+++++++++++++++++++++++++++++<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">--<span class="m1070881843546206487apple-converted-space"> </span><o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">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<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"><a href="https://urldefense.us/v3/__http:/www.cse.buffalo.edu/*knepley/__;fg!!G2kpM7uM-TzIFchu!nK03nUENfNtHoOs8RWmJWJQYJH2IlC_lYQPNn7kV9FsBv2CQKR_VSqbLGRLFShVpKmY$" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">-- <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>
-- Norbert Wiener<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"><a href="https://urldefense.us/v3/__http:/www.cse.buffalo.edu/*knepley/__;fg!!G2kpM7uM-TzIFchu!nSXMSWur4Lrpt0oF_bjtBae92VccTBcCHUQJRYWByuB4bZ5HHzFHhGtLjs7NCuV_8ZE$" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><o:p></o:p></span></p>
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