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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>Check Determinant of 3 by 3 matrix</title>
<meta http-equiv='Content-Type' content='text/html' charset='utf-8'/>
<meta name="description" id="description" content="Check Determinant of 3 by 3 matrix"/>
<meta name="keywords" id="keywords" content=" check determinant of 3 by matrix det_33 correct syntax purpose inclusion x d vector ok source code "/>
<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_33_xml.js'>
</script>
</head>
<body>
<table><tr>
<td>
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<option>speed_utility-&gt;</option>
<option>det_by_lu</option>
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<option>det_33</option>
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<option>Headings-&gt;</option>
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<option>Inclusion</option>
<option>x</option>
<option>d</option>
<option>Vector</option>
<option>ok</option>
<option>Source Code</option>
</select>
</td>
</tr></table><br/>



<center><b><big><big>Check Determinant of 3 by 3 matrix</big></big></b></center>
<br/>
<b><big><a name="Syntax" id="Syntax">Syntax</a></big></b>

<br/>

<code><font color="blue"><span style='white-space: nowrap'>#&#xA0;include&#xA0;&lt;cppad/speed/det_33.hpp&gt;<br/>
</span></font></code>

<code><i><font color="black"><span style='white-space: nowrap'>ok</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;=&#xA0;det_33(</span></font><i><font color="black"><span style='white-space: nowrap'>x</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>d</span></font></i><font color="blue"><span style='white-space: nowrap'>)</span></font></code>


<br/>
<br/>
<b><big><a name="Purpose" id="Purpose">Purpose</a></big></b>
<br/>
This routine can be used to check a method for computing
the determinant of a matrix.

<br/>
<br/>
<b><big><a name="Inclusion" id="Inclusion">Inclusion</a></big></b>
<br/>
The template function <code><font color="blue">det_33</font></code> is defined in the <code><font color="blue">CppAD</font></code>
namespace by including 
the file <code><font color="blue">cppad/speed/det_33.hpp</font></code> 
(relative to the CppAD distribution directory).
It is only intended for example and testing purposes, 
so it is not automatically included by
<a href="cppad.xml" target="_top"><span style='white-space: nowrap'>cppad.hpp</span></a>
.

<br/>
<br/>
<b><big><a name="x" id="x">x</a></big></b>
<br/>
The argument 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 has prototype

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;const&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>Vector</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;&amp;</span></font><i><font color="black"><span style='white-space: nowrap'>x</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
.
It contains the elements of the matrix 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='italic'>X</mi>
</mrow></math>

 in row major order; i.e.,

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow>
<msub><mi mathvariant='italic'>X</mi>
<mrow><mi mathvariant='italic'>i</mi>
<mo stretchy="false">,</mo>
<mi mathvariant='italic'>j</mi>
</mrow>
</msub>
<mo stretchy="false">=</mo>
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">[</mo>
<mi mathvariant='italic'>i</mi>
<mo stretchy="false">*</mo>
<mn>3</mn>
<mo stretchy="false">+</mo>
<mi mathvariant='italic'>j</mi>
<mo stretchy="false">]</mo>
</mrow></math>

<br/>
<b><big><a name="d" id="d">d</a></big></b>
<br/>
The argument 
<code><i><font color="black"><span style='white-space: nowrap'>d</span></font></i></code>
 has prototype

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;const&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>Vector</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;&amp;</span></font><i><font color="black"><span style='white-space: nowrap'>d</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
.
It is tested to see if 
<code><i><font color="black"><span style='white-space: nowrap'>d</span></font></i><font color="blue"><span style='white-space: nowrap'>[0]</span></font></code>
 it is equal to 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi>det</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='italic'>X</mi>
<mo stretchy="false">)</mo>
</mrow></math>

.

<br/>
<br/>
<b><big><a name="Vector" id="Vector">Vector</a></big></b>
<br/>
If 
<code><i><font color="black"><span style='white-space: nowrap'>y</span></font></i></code>
 is a 
<code><i><font color="black"><span style='white-space: nowrap'>Vector</span></font></i></code>
 object, 
it must support the syntax

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>y</span></font></i><font color="blue"><span style='white-space: nowrap'>[</span></font><i><font color="black"><span style='white-space: nowrap'>i</span></font></i><font color="blue"><span style='white-space: nowrap'>]<br/>
</span></font></code>
where 
<code><i><font color="black"><span style='white-space: nowrap'>i</span></font></i></code>
 has type <code><font color="blue">size_t</font></code> with value less than 9.
This must return a <code><font color="blue">double</font></code> value corresponding to the <code><i>i</i></code>-th
element of the vector 
<code><i><font color="black"><span style='white-space: nowrap'>y</span></font></i></code>
.
This is the only requirement of the type 
<code><i><font color="black"><span style='white-space: nowrap'>Vector</span></font></i></code>
.
(Note that only the first element of the vector 
<code><i><font color="black"><span style='white-space: nowrap'>d</span></font></i></code>
 is used.)

<br/>
<br/>
<b><big><a name="ok" id="ok">ok</a></big></b>
<br/>
The return value 
<code><i><font color="black"><span style='white-space: nowrap'>ok</span></font></i></code>
 has prototype

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;bool&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>ok</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
It is true, if the determinant 
<code><i><font color="black"><span style='white-space: nowrap'>d</span></font></i><font color="blue"><span style='white-space: nowrap'>[0]</span></font></code>
 
passes the test and false otherwise.



<br/>
<br/>
<b><big><a name="Source Code" id="Source Code">Source Code</a></big></b>
<br/>
The file 
<a href="det_33.hpp.xml" target="_top"><span style='white-space: nowrap'>det_33.hpp</span></a>

contains the source code for this template function.


<hr/>Input File: cppad/speed/det_33.hpp

</body>
</html>