<html xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<meta name="Generator" content="Microsoft Word 15 (filtered medium)">
<style><!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
@font-face
{font-family:Menlo;
panose-1:2 11 6 9 3 8 4 2 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0cm;
font-size:10.0pt;
font-family:"Calibri",sans-serif;}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:blue;
text-decoration:underline;}
span.gmailsignatureprefix
{mso-style-name:gmail_signature_prefix;}
span.EmailStyle19
{mso-style-type:personal-reply;
font-family:"Calibri",sans-serif;
color:windowtext;}
p.p1, li.p1, div.p1
{mso-style-name:p1;
margin:0cm;
background:white;
font-size:8.5pt;
font-family:Menlo;
color:black;}
.MsoChpDefault
{mso-style-type:export-only;
font-size:10.0pt;
mso-ligatures:none;}
@page WordSection1
{size:612.0pt 792.0pt;
margin:72.0pt 72.0pt 72.0pt 72.0pt;}
div.WordSection1
{page:WordSection1;}
--></style>
</head>
<body lang="EN-GB" link="blue" vlink="purple" style="word-wrap:break-word">
<div class="WordSection1">
<p class="p1"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;mso-fareast-language:EN-US">Thank you for your response. I spend some time understanding how<o:p></o:p></span></p>
<p class="p1">MatSetValuesLocal and ISLocalToGlobalMappingCreate <span style="font-size:11.0pt;font-family:"Calibri",sans-serif;mso-fareast-language:EN-US">
work.</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;mso-fareast-language:EN-US">Q1) Will the matrix K be of type
</span><span style="font-size:11.0pt">MATMPIAIJ or MATIS?</span><span style="font-size:11.0pt;mso-fareast-language:EN-US"><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;color:black">K = [A P^T</span><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;color:black"> P 0]</span><span style="font-size:11.0pt"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;mso-fareast-language:EN-US">Q2) Can I use both
</span><span style="font-size:11.0pt">MatSetValues() to MatSetValuesLocal() to populate K? Since I have already used MatSetValues() to construct A.<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;mso-fareast-language:EN-US">Q3) What are the advantages of using
</span><span style="font-size:11.0pt">MatSetValuesLocal()? Is it that I can construct P directly using local indies and map the entrees to the global index in K?<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">Q4) I probably don’t have to construct an independent P matrix?<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">Best regards,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">Karthik.<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;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"><o:p> </o:p></span></p>
<div style="border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0cm 0cm 0cm">
<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>Tuesday, 18 April 2023 at 11:08<br>
<b>To: </b>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] Setting up a matrix for Lagrange multiplier<o:p></o:p></span></p>
</div>
<div>
<div>
<p class="MsoNormal"><span style="font-size:11.0pt">On Tue, Apr 18, 2023 at 5:24 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>
</div>
<div>
<blockquote style="border:none;border-left:solid #CCCCCC 1.0pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-right:0cm">
<div>
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;color:black">Hello,</span><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;color:black"> </span><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;color:black">I'm solving a problem using the Lagrange multiplier, the matrix has the form</span><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;color:black"> </span><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;color:black">K = [A P^T</span><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;color:black"> P 0]</span><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"> <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">I am familiar with constructing K using MATMPIAIJ. However, I would like to know if had [A], can I augment it with [P], [P^T] and [0] of type MATMPIAIJ?
Likewise for vectors as well.<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"> <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">Can you please point me to the right resource, if it is a common operation in PETSc?<o:p></o:p></span></p>
</div>
</div>
</div>
</blockquote>
<div>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:11.0pt">You can do this at least 2 ways:<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:11.0pt"> 1) Assemble you submatrices directly into the larger matrix by constructing local-to-global maps for the emplacement. so that you do<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:11.0pt"> not change your assembly code, except to change MatSetValues() to MatSetValuesLocal(). This is usually preferable.<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:11.0pt"> 2) Use MATNEST and VecNEST to put pointers to submatrices and subvectors directly in.<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:11.0pt"> Thanks,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:11.0pt"> Matt<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:11.0pt"> <o:p></o:p></span></p>
</div>
<blockquote style="border:none;border-left:solid #CCCCCC 1.0pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-right:0cm">
<div>
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt">Many thanks.<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"> <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">Kind regards,<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">Karthik.<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"> <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"> <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"> <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"> <o:p></o:p></span></p>
</div>
</div>
</div>
</blockquote>
</div>
<p class="MsoNormal"><span style="font-size:11.0pt"><br clear="all">
<o:p></o:p></span></p>
<div>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
</div>
<p class="MsoNormal"><span class="gmailsignatureprefix"><span style="font-size:11.0pt">--
</span></span><span style="font-size:11.0pt"><o:p></o:p></span></p>
<div>
<div>
<div>
<div>
<div>
<div>
<div>
<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>
</div>
<div>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
</div>
<div>
<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>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</body>
</html>