<html xmlns:v="urn:schemas-microsoft-com:vml" 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=us-ascii">
<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;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0in;
font-size:11.0pt;
font-family:"Calibri",sans-serif;}
p.MsoListParagraph, li.MsoListParagraph, div.MsoListParagraph
{mso-style-priority:34;
margin-top:0in;
margin-right:0in;
margin-bottom:0in;
margin-left:.5in;
font-size:11.0pt;
font-family:"Calibri",sans-serif;}
span.EmailStyle17
{mso-style-type:personal-compose;
font-family:"Calibri",sans-serif;
color:windowtext;}
span.EmailStyle19
{mso-style-type:personal;
font-family:"Calibri",sans-serif;
color:windowtext;}
.MsoChpDefault
{mso-style-type:export-only;
font-family:"Calibri",sans-serif;}
@page WordSection1
{size:8.5in 11.0in;
margin:1.0in 1.0in 1.0in 1.0in;}
div.WordSection1
{page:WordSection1;}
/* List Definitions */
@list l0
{mso-list-id:1285191378;
mso-list-type:hybrid;
mso-list-template-ids:-1731586082 67698705 67698713 67698715 67698703 67698713 67698715 67698703 67698713 67698715;}
@list l0:level1
{mso-level-text:"%1\)";
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-.25in;}
@list l0:level2
{mso-level-number-format:alpha-lower;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-.25in;}
@list l0:level3
{mso-level-number-format:roman-lower;
mso-level-tab-stop:none;
mso-level-number-position:right;
text-indent:-9.0pt;}
@list l0:level4
{mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-.25in;}
@list l0:level5
{mso-level-number-format:alpha-lower;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-.25in;}
@list l0:level6
{mso-level-number-format:roman-lower;
mso-level-tab-stop:none;
mso-level-number-position:right;
text-indent:-9.0pt;}
@list l0:level7
{mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-.25in;}
@list l0:level8
{mso-level-number-format:alpha-lower;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-.25in;}
@list l0:level9
{mso-level-number-format:roman-lower;
mso-level-tab-stop:none;
mso-level-number-position:right;
text-indent:-9.0pt;}
ol
{margin-bottom:0in;}
ul
{margin-bottom:0in;}
--></style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]-->
</head>
<body lang="EN-US" link="#0563C1" vlink="#954F72" style="word-wrap:break-word">
<div class="WordSection1">
<p class="MsoNormal">I am using LSQR to minimize || L x – b ||_2, where L is a sparse rectangular matrix with 145,253,395 rows, 209,423,775 columns, and around 54 billion non zeros.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">The numbers reported below are for a run with 27 compute nodes, each compute node with 4 MPI ranks, so a total of 108 ranks.
<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Throughout the run, I assess the runtime taken by all dot products during the LSQR iterations, and I differentiate between dot products involving vectors of the size of the solution vector “x”, and dot products involving vectors of the
size of the rhs “b”. Here are the numbers I get (we have an implementation of LSQR that performs some extra vector dot products for our needs):<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">236 VecDotSol take 1.523 seconds<o:p></o:p></p>
<p class="MsoNormal">226 VecDotRhs take 326.008 seconds<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Regarding the partition of rows and columns among the 108 MPI ranks:<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Rows: min = 838,529 ; avg = 1.34494e+06 ; max = 2,437,206<o:p></o:p></p>
<p class="MsoNormal">Columns: min = 1,903,500 ; avg = 1.93911e+06 ; max = 1,946,270<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Regarding the partition of rows and columns among the 27 compute nodes:<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Rows: min = 3,575,584 ; avg = 5.37976e+06 ; max = 8,788,062<o:p></o:p></p>
<p class="MsoNormal">Columns: min = 7,637,500 ; avg = 7.75644e+06 ; max = 7,785,080<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Questions:<o:p></o:p></p>
<ol style="margin-top:0in" start="1" type="1">
<li class="MsoListParagraph" style="margin-left:0in;mso-list:l0 level1 lfo1">Why the average run times are so different between VecDotSol and VecDotRhs?<o:p></o:p></li><li class="MsoListParagraph" style="margin-left:0in;mso-list:l0 level1 lfo1">Could the much bigger unbalancing among the number of rows per rank (compared to the very well balanced distribution of columns per rank) be the cause?<o:p></o:p></li><li class="MsoListParagraph" style="margin-left:0in;mso-list:l0 level1 lfo1">Have you ever observed such situation?<o:p></o:p></li><li class="MsoListParagraph" style="margin-left:0in;mso-list:l0 level1 lfo1">Could it be because of a bad MPI configuration / parametrization with respect to the underlying network?<o:p></o:p></li><li class="MsoListParagraph" style="margin-left:0in;mso-list:l0 level1 lfo1">But, if yes, why the VecDotSol dot products are so much faster than VecDotRhs?<o:p></o:p></li></ol>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Thank you in advance,<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Ernesto. <o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<br>
<p class="msipfooter6d2e06ff" align="Center" style="margin:0"><span style="font-size:10.0pt;font-family:Calibri;color:#000000">Schlumberger-Private</span></p>
</div>
</body>
</html>