<?xml version="1.0" encoding="iso-8859-1" ?> 
<?xml-stylesheet type="text/css" href="hsl_ma97.css"?> 
<?xml-stylesheet type="text/xsl" href="pmathml.xsl"?> 
<!--http://www.w3.org/Math/XSL/pmathml.xsl--> 
<html  
xmlns="http://www.w3.org/1999/xhtml"  
><head>
   <title>HSL_MA97 &#x2014; Sparse symmetric system using OpenMP</title> 
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1" /> 
<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)" /> 
<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)" /> 
<!-- html,pmathml,xhtml,mozilla --> 
<meta name="src" content="hsl_ma97.tex" /> 
<meta name="date" content="2013-04-10 15:02:00" /> 
<link rel="stylesheet" type="text/css" href="hsl_ma97.css" /> 
<link rel="stylesheet" href="/css/hsl.css" type="text/css" /><link rel="stylesheet" href="/css/catalog.css" type="text/css" /></head><body 
>
   <div id="body"> 
<div id="header">  
<div class="w100"> 
<div class="stfc-logo"> 
<a accesskey="1" tabindex="2" href="http://www.stfc.ac.uk"> 
<img alt="STFC Home Page" src="/images/stfc-logo.jpg"/> </a> 
<a class="hide_tab" accesskey="S" tabindex="1" href="#pgContent">Skip navigation</a> 
</div> 
<div class="clear"></div> 
</div> 
<div class="w100">  
<div class="RCUK"> 
<a href="http://www.rcuk.ac.uk/Publications/policy/framework" target="_blank" title="RCUK website - opens in a new window">Excellence with Impact - part of Research Councils UK</a> 
</div> 
<div class="header-links"> 
<a href="index.html">HSL Home</a> : <a href="/contact.html">Contact HSL</a> 
</div> 
<div class="clear"></div> 
</div> 
</div> 
  <div id="menu"> 
<ul> 
<li> 
<a href="http://www.stfc.ac.uk">STFC home</a> 
<span class="mTags"><br /> 
The Science and Technology Facilities Council 
</span> 
</li> 
<li> 
<a href="/index.html">HSL home</a> 
<span class="mTags"><br /> 
About the HSL Mathematical Software Library 
</span> 
</li> 
<li> 
<a href="/catalogue/">HSL 2013</a> 
<span class="mTags"><br /> 
Our current release 
</span> 
</li> 
<li> 
<a href="/archive/index.html"> 
HSL archive</a> 
<span class="mTags"><br /> 
Older packages available at no cost 
</span> 
</li> 
<li> 
<a href="/catalogue/"> 
Academic access</a> 
<span class="mTags"><br /> 
Free access for teaching and research 
</span> 
</li> 
<li> 
<a href="http://www.stfc.ac.uk/CSE/26555.aspx"> 
The Numerical Analysis Group</a> 
<span class="mTags"><br /> 
About the research group behind HSL 
</span> 
</li> 
<!--<li> 
<a href="http://galahad.rl.ac.uk/">GALAHAD</a> 
<span class="mTags"><br /> 
Our optimization software library 
</span> 
</li>--> 
<li> 
<a href="/contact.html">Contact us</a> 
<span class="mTags"><br /> 
Our contact details 
</span> 
</li> 
</ul> 
</div> 
 <div id="bodytext"> 
<a name="pgContent"></a> 
 <div> 
<form action="http://www.hsl.rl.ac.uk/search.html" id="cse-search-box"> 
<div> 
<input type="hidden" name="cx" value="011781803477211733479:s9roibysody" /> 
<input type="hidden" name="cof" value="FORID:11" /> 
<input type="hidden" name="ie" value="UTF-8" /> 
<input type="text" name="q" size="31" /> 
<input type="submit" name="sa" value="Search" /> 
</div> 
 
</form> 
<script type="text/javascript" src="http://www.google.com/cse/brand?form=cse-search-box&amp;lang=en"></script> 
</div> 
 <div class="download"> 
 <h2>Version 2.2.0</h2> 
 <p class="vdate">20th December 2012</p> <p class="doclink">User documentation</p> 
 <ul> 
 <li><a href="/specs/hsl_ma97.pdf">Fortran</a></li> 
  <li><a href="/specs/hsl_ma97_C.pdf">C</a></li> 

<li><a href="/specs/hsl_ma97_MATLAB.txt">MATLAB</a></li> 
 </ul> 
 <p><a href="/changes/ChangeLog.hsl_ma97">Recent Changes</a></p> 
 <p><a href="/download/HSL_MA97/2.2.0/">Code Download</a></p> 
 <ul> 
  
  
 <li>Single</li> 
 <li>Double</li> 
 <li>Single Complex</li> 
 <li>Double Complex</li> 

</ul> 
</div> 

   <h3 class="likesectionHead"><a 
 id="x1-1000"></a>HSL_MA97 Sparse symmetric system using OpenMP</h3>
<!--l. 26--><p class="noindent" ><span 
class="cmtt-10">HSL</span><span 
class="cmtt-10">_MA97 </span>uses a direct method to solve  large sparse symmetric linear systems of
equations <!--l. 27--><math 
 xmlns="http://www.w3.org/1998/Math/MathML" display="inline" ><mstyle mathvariant="bold"><mi 
>A</mi><mi 
>X</mi> <mo 
class="MathClass-rel">=</mo> <mi 
>B</mi></mstyle></math>.
This package optionally uses OpenMP and is designed to achieve bit-compatible
results regardless of the number of threads used. It computes the sparse
factorization
<!--tex4ht:inline--></p><!--l. 30--><math 
 xmlns="http://www.w3.org/1998/Math/MathML" display="block" >
                     <mstyle mathvariant="bold"><mi 
>A</mi> <mo 
class="MathClass-rel">=</mo> <mi 
>P</mi><mi 
>L</mi><mi 
>D</mi><msup><mrow 
><mrow ><mo 
class="MathClass-open">(</mo><mrow><mi 
>P</mi><mi 
>L</mi></mrow><mo 
class="MathClass-close">)</mo></mrow></mrow><mrow 
><mo 
class="MathClass-bin">&#x22C6;</mo></mrow></msup 
></mstyle><mspace width="2em" class="qquad"/><!--mstyle 
class="mbox"--><mtext  >&#x00A0;(Indefinite)</mtext><!--/mstyle-->
</math>
<!--l. 32--><p class="nopar" > or
<!--tex4ht:inline--></p><!--l. 34--><math 
 xmlns="http://www.w3.org/1998/Math/MathML" display="block" >
                     <mstyle mathvariant="bold"><mi 
>A</mi> <mo 
class="MathClass-rel">=</mo> <mi 
>P</mi><mi 
>L</mi><msup><mrow 
><mi 
>L</mi></mrow><mrow 
><mo 
class="MathClass-bin">&#x22C6;</mo></mrow></msup 
></mstyle><mspace width="2em" class="qquad"/><!--mstyle 
class="mbox"--><mtext  >&#x00A0;(Positive-definite)</mtext><!--/mstyle-->
</math>
<!--l. 36--><p class="nopar" > where <!--l. 37--><math 
 xmlns="http://www.w3.org/1998/Math/MathML" display="inline" ><mstyle mathvariant="bold"><msup><mrow 
><mi 
>L</mi></mrow><mrow 
><mo 
class="MathClass-bin">&#x22C6;</mo></mrow></msup 
></mstyle> <mo 
class="MathClass-rel">=</mo><msup><mrow 
> <mstyle mathvariant="bold"><mi 
>L</mi></mstyle></mrow><mrow 
><mi 
>T</mi></mrow></msup 
></math>
(real symmetric or complex symmetric) or
<!--l. 38--><math 
 xmlns="http://www.w3.org/1998/Math/MathML" display="inline" ><msup><mrow 
><mstyle mathvariant="bold"><mi 
>L</mi></mstyle></mrow><mrow 
><mo 
class="MathClass-bin">&#x22C6;</mo></mrow></msup 
> <mo 
class="MathClass-rel">=</mo><msup><mrow 
> <mstyle mathvariant="bold"><mi 
>L</mi></mstyle></mrow><mrow 
><mi 
>H</mi></mrow></msup 
></math> (complex Hermitian,
where <!--l. 38--><math 
 xmlns="http://www.w3.org/1998/Math/MathML" display="inline" ><msup><mrow 
><mstyle mathvariant="bold"><mi 
>L</mi></mstyle></mrow><mrow 
><mi 
>H</mi></mrow></msup 
></math> denotes the
conjugate transpose of <!--l. 39--><math 
 xmlns="http://www.w3.org/1998/Math/MathML" display="inline" ><mstyle mathvariant="bold"><mi 
>L</mi></mstyle></math>),

<!--l. 40--><math 
 xmlns="http://www.w3.org/1998/Math/MathML" display="inline" ><mstyle mathvariant="bold"><mi 
>P</mi></mstyle></math> is a permutation matrix,
<!--l. 40--><math 
 xmlns="http://www.w3.org/1998/Math/MathML" display="inline" ><mstyle mathvariant="bold"><mi 
>L</mi></mstyle></math> is lower triangular,
and <!--l. 41--><math 
 xmlns="http://www.w3.org/1998/Math/MathML" display="inline" ><mstyle mathvariant="bold"><mi 
>D</mi></mstyle></math> is block diagonal
with blocks of size <!--l. 41--><math 
 xmlns="http://www.w3.org/1998/Math/MathML" display="inline" ><mn>1</mn> <mo 
class="MathClass-bin">&#x00D7;</mo> <mn>1</mn></math>
and <!--l. 42--><math 
 xmlns="http://www.w3.org/1998/Math/MathML" display="inline" ><mn>2</mn> <mo 
class="MathClass-bin">&#x00D7;</mo> <mn>2</mn></math>.
</p><!--l. 47--><p class="indent" >   If <!--l. 47--><math 
 xmlns="http://www.w3.org/1998/Math/MathML" display="inline" ><mstyle mathvariant="bold"><mi 
>A</mi></mstyle></math>
is large, bit-compatible answers are not required, we recommend using <span 
class="cmtt-10">HSL</span><span 
class="cmtt-10">_MA86 </span>or
<span 
class="cmtt-10">HSL</span><span 
class="cmtt-10">_MA87 </span>instead for better efficiency.
</p><!--l. 53--><p class="indent" >   .
</p>
    </div> <!-- bodytext -->  <div class="clear"></div> 
 
<div class="footer"> 
<div class="rcuk-footer"> 
<a href="http://www.rcuk.ac.uk" > 
<img src="/images/rcuk-footer.gif" alt="Click to visit RCUK web site"/> 
 
</a> 
</div> 
 
<div class="footer-links"> 
 
<a href="/site_map.html" accesskey="3">SITE-MAP</a> :  
<a href="http://www.stfc.ac.uk/About/Accessibility.aspx" accesskey="0">ACCESSIBILITY</a> :  
<a href="http://www.stfc.ac.uk/privacy.aspx">PRIVACY POLICY</a> :  
<a href="http://www.stfc.ac.uk/access.aspx">ACCESS TO INFORMATION</a> :  
<a href="http://www.stfc.ac.uk/disclaimer.aspx" accesskey="5">TERMS OF USE</a> : 
<a accesskey="9" href="mailto:hsl@stfc.ac.uk?subject=Feedback From Website">WEBMASTER</a> 
 
<span class="hide">|<a accesskey="7" tabindex="7" href="http://www.stfc.ac.uk/About/pol/sfirst/contents.aspx">Complaints Procedure</a></span> 
<span class="hide">|<a accesskey="2" tabindex="8" href="http://www.stfc.ac.uk/PMC/News.aspx">News</a></span> 
</div> 
</div> 
 <div class="clear"></div> 
</div> <!-- body --> 
  
</body> 
</html> 



