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<p class="MsoNormal"><span style="font-size:11.0pt;mso-fareast-language:EN-US">Thank you Hong. I will look into it.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;mso-fareast-language:EN-US">Best,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;mso-fareast-language:EN-US">Karthik.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;mso-fareast-language:EN-US"><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">Zhang, Hong <hzhang@mcs.anl.gov><br>
<b>Date: </b>Thursday, 20 April 2023 at 16:47<br>
<b>To: </b>Matthew Knepley <knepley@gmail.com>, Chockalingam, Karthikeyan (STFC,DL,HC) <karthikeyan.chockalingam@stfc.ac.uk><br>
<b>Cc: </b>petsc-users@mcs.anl.gov <petsc-users@mcs.anl.gov><br>
<b>Subject: </b>Re: [petsc-users] question about MatSetLocalToGlobalMapping<o:p></o:p></span></p>
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<p class="MsoNormal" style="background:white"><span class="contentpasted2"><span style="font-size:11.0pt;color:black;background:white">Karthik,</span></span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black">We built a KKT matrix in TaoSNESJacobian_PDIPM() (see petsc/src/tao/constrained/impls/ipm/pdipm.c) which assembles several small matrices into a large KKT matrix in mpiaij
format. You could take the same approach to insert P and P^T into your K.<o:p></o:p></span></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black">FYI, I attached our paper.<o:p></o:p></span></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black">Hong<o:p></o:p></span></p>
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<p class="MsoNormal"><b><span style="font-size:11.0pt;color:black">From:</span></b><span style="font-size:11.0pt;color:black"> petsc-users <petsc-users-bounces@mcs.anl.gov> on behalf of Matthew Knepley <knepley@gmail.com><br>
<b>Sent:</b> Thursday, April 20, 2023 5:37 AM<br>
<b>To:</b> Karthikeyan Chockalingam - STFC UKRI <karthikeyan.chockalingam@stfc.ac.uk><br>
<b>Cc:</b> petsc-users@mcs.anl.gov <petsc-users@mcs.anl.gov><br>
<b>Subject:</b> Re: [petsc-users] question about MatSetLocalToGlobalMapping</span><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">On Thu, Apr 20, 2023 at 6:13 AM Karthikeyan Chockalingam - STFC UKRI 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="xmsonormal">Hello,<o:p></o:p></p>
<p class="xmsonormal"> <o:p></o:p></p>
<p class="xmsonormal">I created a new thread, thought would it be more appropriate (and is a continuation of my previous post). I want to construct the below K matrix (which is composed of submatrices)
<o:p></o:p></p>
<p class="xmsonormal"> <o:p></o:p></p>
<p class="xmsonormal"><span style="color:black">K = [A P^T</span><o:p></o:p></p>
<p class="xmsonormal"><span style="color:black"> P 0]</span><o:p></o:p></p>
<p class="xmsonormal"><span style="color:black"> </span><o:p></o:p></p>
<p class="xmsonormal"><span style="color:black">Where K is of type MatMPIAIJ. I first constructed the top left [A] using MatSetValues().</span><o:p></o:p></p>
<p class="xmsonormal"><span style="color:black"> </span><o:p></o:p></p>
<p class="xmsonormal"><span style="color:black">Now, I would like to construct the bottom left [p] and top right [p^T]
</span>using MatSetValuesLocal().<o:p></o:p></p>
<p class="xmsonormal"> <o:p></o:p></p>
<p class="xmsonormal">To use MatSetValuesLocal(), I first have to create a local-to-global mapping using ISLocalToGlobalMappingCreate. I have created two mapping row_mapping and column_mapping.<o:p></o:p></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">I do not understand why they are not the same map. Maybe I was unclear before. It looks like you have two fields, say phi and lambda, where lambda is a Lagrange multiplier imposing some constraint. Then you
get a saddle point like this. You can imagine matrices<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"> (phi, phi) --> A<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> (phi, lambda) --> P^T<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> (lambda, phi) --> P<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">So you make a L2G map for the phi field and the lambda field. Oh, you are calling them row and col map, but they are my phi and lambda<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">maps. I do not like the row and col names since in P they reverse.<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="xmsonormal"><span style="color:black">Q1) At what point should I declare
</span>MatSetLocalToGlobalMapping – is it just before I use MatSetValuesLocal()?<o:p></o:p></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">Okay, it is good you are asking this because my thinking was somewhat confused. I think the precise steps are:<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"> 1) Create the large saddle point matrix K<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"> 1a) We must call <a href="https://petsc.org/main/manualpages/Mat/MatSetLocalToGlobalMapping/">https://petsc.org/main/manualpages/Mat/MatSetLocalToGlobalMapping/</a> on it. In the simplest case, this just
maps<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> the local rows numbers [0, Nrows) to the global rows numbers [rowStart, rowStart + Nrows).<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"> 2) To form each piece:<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"> 2a) Extract that block using <a href="https://petsc.org/main/manualpages/Mat/MatGetLocalSubMatrix/">https://petsc.org/main/manualpages/Mat/MatGetLocalSubMatrix/</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"> This gives back a Mat object that you subsequently restore using <a href="https://petsc.org/main/manualpages/Mat/MatRestoreLocalSubMatrix/">https://petsc.org/main/manualpages/Mat/MatRestoreLocalSubMatrix/</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"> 2b) Insert values using <a href="https://petsc.org/main/manualpages/Mat/MatSetValuesLocal/">
https://petsc.org/main/manualpages/Mat/MatSetValuesLocal/</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"> The local indices used for insertion here are indices relative to the block itself, and the L2G map for this matrix<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> has been rewritten to insert into that block in the larger matrix. Thus this looks like just calling MatSetValuesLocal()<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> on the smaller matrix block, but inserts correctly into the larger matrix.<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">Therefore, the code you write code in 2) could work equally well making the large matrix from 1), or independent smaller matrix blocks.<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">Does this make sense?<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="xmsonormal">I will use MatSetLocalToGlobalMapping(K, row_mapping, column_mapping) to build
<span style="color:black">the bottom left [P].</span><o:p></o:p></p>
<p class="xmsonormal"><span style="color:black"> </span><o:p></o:p></p>
<p class="xmsonormal"><span style="color:black"> </span><o:p></o:p></p>
<p class="xmsonormal"><span style="color:black">Q2) Can now I reset the mapping as
</span>MatSetLocalToGlobalMapping(K, column_mapping, row_mapping) to build <span style="color:black">
the top right [P^T]? </span><o:p></o:p></p>
<p class="xmsonormal"><span style="color:black"> </span><o:p></o:p></p>
<p class="xmsonormal"> <o:p></o:p></p>
<p class="xmsonormal">Many thanks!<o:p></o:p></p>
<p class="xmsonormal"><span style="color:black"> </span><o:p></o:p></p>
<p class="xmsonormal"><span style="color:black">Kind regards,</span><o:p></o:p></p>
<p class="xmsonormal"><span style="color:black">Karthik.</span><o:p></o:p></p>
<p class="xmsonormal"><span style="color:black"> </span><o:p></o:p></p>
<p class="xmsonormal"><span style="color:black"> </span><o:p></o:p></p>
<p class="xmsonormal"><span style="color:black"> </span><o:p></o:p></p>
<p class="xmsonormal"><span style="color:black"> </span><o:p></o:p></p>
<p class="xmsonormal"><span style="color:black"> </span><o:p></o:p></p>
<p class="xmsonormal"> <o:p></o:p></p>
<p class="xmsonormal"> <o:p></o:p></p>
<p class="xmsonormal"><span style="font-size:10.0pt;color:#212121"> </span><o:p></o:p></p>
<p class="xmsonormal"> <o:p></o:p></p>
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<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 class="xgmailsignatureprefix"><span style="font-size:11.0pt">--
</span></span><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="http://www.cse.buffalo.edu/~knepley/" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><o:p></o:p></span></p>
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