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<?xml version='1.0'?>
<html xmlns='http://www.w3.org/1999/xhtml'
      xmlns:math='http://www.w3.org/1998/Math/MathML'
>
<head>
<title>Determinant Using Lu Factorization: Example and Test</title>
<meta http-equiv='Content-Type' content='text/html' charset='utf-8'/>
<meta name="description" id="description" content="Determinant Using Lu Factorization: Example and Test"/>
<meta name="keywords" id="keywords" content=" determinant using lu factorization: example test minors "/>
<style type='text/css'>
body { color : black }
body { background-color : white }
A:link { color : blue }
A:visited { color : purple }
A:active { color : purple }
</style>
<script type='text/javascript' language='JavaScript' src='_det_by_lu.cpp_xml.js'>
</script>
</head>
<body>
<table><tr>
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<td>Headings</td>
</tr></table><br/>



<center><b><big><big>Determinant Using Lu Factorization: Example and Test</big></big></b></center>
<code><font color="blue"><pre><tt>
<span style="font-weight: bold"><span style="color: #000080"># include</span></span> <span style="color: #FF0000">&lt;cppad/cppad.hpp&gt;</span>
<span style="font-weight: bold"><span style="color: #000080"># include</span></span> <span style="color: #FF0000">&lt;cppad/speed/det_by_lu.hpp&gt;</span>

<span style="color: #009900">bool</span> <span style="font-weight: bold"><span style="color: #000000">det_by_lu</span></span><span style="color: #990000">()</span>
<span style="color: #FF0000">{</span>     <span style="color: #009900">bool</span> ok <span style="color: #990000">=</span> <span style="font-weight: bold"><span style="color: #0000FF">true</span></span><span style="color: #990000">;</span>

     <span style="font-style: italic"><span style="color: #9A1900">// dimension of the matrix</span></span>
     <span style="color: #008080">size_t</span> n <span style="color: #990000">=</span> <span style="color: #993399">3</span><span style="color: #990000">;</span>

     <span style="font-style: italic"><span style="color: #9A1900">// construct the determinat object</span></span>
     CppAD<span style="color: #990000">::</span><span style="color: #008080">det_by_lu&lt;double&gt;</span> <span style="font-weight: bold"><span style="color: #000000">Det</span></span><span style="color: #990000">(</span>n<span style="color: #990000">);</span>

     <span style="color: #009900">double</span>  a<span style="color: #990000">[]</span> <span style="color: #990000">=</span> <span style="color: #FF0000">{</span>
          <span style="color: #993399">1</span><span style="color: #990000">.,</span> <span style="color: #993399">2</span><span style="color: #990000">.,</span> <span style="color: #993399">3</span><span style="color: #990000">.,</span>  <span style="font-style: italic"><span style="color: #9A1900">// a[0] a[1] a[2]</span></span>
          <span style="color: #993399">3</span><span style="color: #990000">.,</span> <span style="color: #993399">2</span><span style="color: #990000">.,</span> <span style="color: #993399">1</span><span style="color: #990000">.,</span>  <span style="font-style: italic"><span style="color: #9A1900">// a[3] a[4] a[5]</span></span>
          <span style="color: #993399">2</span><span style="color: #990000">.,</span> <span style="color: #993399">1</span><span style="color: #990000">.,</span> <span style="color: #993399">2</span><span style="color: #990000">.</span>   <span style="font-style: italic"><span style="color: #9A1900">// a[6] a[7] a[8]</span></span>
     <span style="color: #FF0000">}</span><span style="color: #990000">;</span>
     <span style="font-weight: bold"><span style="color: #000000">CPPAD_TESTVECTOR</span></span><span style="color: #990000">(</span><span style="color: #009900">double</span><span style="color: #990000">)</span> <span style="font-weight: bold"><span style="color: #000000">A</span></span><span style="color: #990000">(</span><span style="color: #993399">9</span><span style="color: #990000">);</span>
     <span style="color: #008080">size_t</span> i<span style="color: #990000">;</span>
     <span style="font-weight: bold"><span style="color: #0000FF">for</span></span><span style="color: #990000">(</span>i <span style="color: #990000">=</span> <span style="color: #993399">0</span><span style="color: #990000">;</span> i <span style="color: #990000">&lt;</span> <span style="color: #993399">9</span><span style="color: #990000">;</span> i<span style="color: #990000">++)</span>
          A<span style="color: #990000">[</span>i<span style="color: #990000">]</span> <span style="color: #990000">=</span> a<span style="color: #990000">[</span>i<span style="color: #990000">];</span>


     <span style="font-style: italic"><span style="color: #9A1900">// evaluate the determinant</span></span>
     <span style="color: #009900">double</span> det <span style="color: #990000">=</span> <span style="font-weight: bold"><span style="color: #000000">Det</span></span><span style="color: #990000">(</span>A<span style="color: #990000">);</span>

     <span style="color: #009900">double</span> check<span style="color: #990000">;</span>
     check <span style="color: #990000">=</span> a<span style="color: #990000">[</span><span style="color: #993399">0</span><span style="color: #990000">]*(</span>a<span style="color: #990000">[</span><span style="color: #993399">4</span><span style="color: #990000">]*</span>a<span style="color: #990000">[</span><span style="color: #993399">8</span><span style="color: #990000">]</span> <span style="color: #990000">-</span> a<span style="color: #990000">[</span><span style="color: #993399">5</span><span style="color: #990000">]*</span>a<span style="color: #990000">[</span><span style="color: #993399">7</span><span style="color: #990000">])</span>
           <span style="color: #990000">-</span> a<span style="color: #990000">[</span><span style="color: #993399">1</span><span style="color: #990000">]*(</span>a<span style="color: #990000">[</span><span style="color: #993399">3</span><span style="color: #990000">]*</span>a<span style="color: #990000">[</span><span style="color: #993399">8</span><span style="color: #990000">]</span> <span style="color: #990000">-</span> a<span style="color: #990000">[</span><span style="color: #993399">5</span><span style="color: #990000">]*</span>a<span style="color: #990000">[</span><span style="color: #993399">6</span><span style="color: #990000">])</span>
           <span style="color: #990000">+</span> a<span style="color: #990000">[</span><span style="color: #993399">2</span><span style="color: #990000">]*(</span>a<span style="color: #990000">[</span><span style="color: #993399">3</span><span style="color: #990000">]*</span>a<span style="color: #990000">[</span><span style="color: #993399">7</span><span style="color: #990000">]</span> <span style="color: #990000">-</span> a<span style="color: #990000">[</span><span style="color: #993399">4</span><span style="color: #990000">]*</span>a<span style="color: #990000">[</span><span style="color: #993399">6</span><span style="color: #990000">]);</span>

     ok <span style="color: #990000">=</span> CppAD<span style="color: #990000">::</span><span style="font-weight: bold"><span style="color: #000000">NearEqual</span></span><span style="color: #990000">(</span>det<span style="color: #990000">,</span> check<span style="color: #990000">,</span> <span style="color: #993399">1e-10</span><span style="color: #990000">,</span> <span style="color: #993399">1e-10</span><span style="color: #990000">);</span>

     <span style="font-weight: bold"><span style="color: #0000FF">return</span></span> ok<span style="color: #990000">;</span>
<span style="color: #FF0000">}</span>
</tt></pre>
</font></code>
<hr/>Input File: speed/example/det_by_lu.cpp

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