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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>The AD atan2 Function: Example and Test</title>
<meta http-equiv='Content-Type' content='text/html' charset='utf-8'/>
<meta name="description" id="description" content="The AD atan2 Function: Example and Test"/>
<meta name="keywords" id="keywords" content=" the ad atan2 function: example and test Ad "/>
<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='_atan2.cpp_xml.js'>
</script>
</head>
<body>
<table><tr>
<td>
<a href="http://www.coin-or.org/CppAD/" target="_top"><img border="0" src="_image.gif"/></a>
</td>
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<option>MathOther-&gt;</option>
<option>abs</option>
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<option>atan2</option>
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<td>atan2.cpp</td>
<td>Headings</td>
</tr></table><br/>



<center><b><big><big>The AD atan2 Function: Example and Test</big></big></b></center>
<code><font color="blue"><pre style='display:inline'> 

# include &lt;cppad/cppad.hpp&gt;

bool Atan2(void)
{	bool ok = true;

	using CppAD::AD;
	using CppAD::NearEqual;

	// domain space vector
	size_t n  = 1;
	double x0 = 0.5;
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(AD&lt;double&gt;) x(n);
	x[0]      = x0;

	// declare independent variables and start tape recording
	CppAD::<a href="independent.xml" target="_top">Independent</a>(x);

	// a temporary value
	<a href="ad.xml" target="_top">AD</a>&lt;double&gt; sin_of_x0 = CppAD::sin(x[0]);
	<a href="ad.xml" target="_top">AD</a>&lt;double&gt; cos_of_x0 = CppAD::cos(x[0]);

	// range space vector 
	size_t m = 1;
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(AD&lt;double&gt;) y(m);
	y[0] = CppAD::atan2(sin_of_x0, cos_of_x0);

	// create f: x -&gt; y and stop tape recording
	CppAD::<a href="funconstruct.xml" target="_top">ADFun</a>&lt;double&gt; f(x, y); 

	// check value 
	ok &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(y[0] , x0,  1e-10 , 1e-10);

	// forward computation of first partial w.r.t. x[0]
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(double) dx(n);
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(double) dy(m);
	dx[0] = 1.;
	dy    = f.<a href="forward.xml" target="_top">Forward</a>(1, dx);
	ok   &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dy[0], 1., 1e-10, 1e-10);

	// reverse computation of derivative of y[0]
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(double)  w(m);
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(double) dw(n);
	w[0]  = 1.;
	dw    = f.<a href="reverse.xml" target="_top">Reverse</a>(1, w);
	ok   &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dw[0], 1., 1e-10, 1e-10);

	// use a VecAD&lt;Base&gt;::reference object with atan2
	CppAD::VecAD&lt;double&gt; v(2);
	<a href="ad.xml" target="_top">AD</a>&lt;double&gt; zero(0);
	<a href="ad.xml" target="_top">AD</a>&lt;double&gt; one(1);
	v[zero]           = sin_of_x0;
	v[one]            = cos_of_x0;
	<a href="ad.xml" target="_top">AD</a>&lt;double&gt; result = CppAD::atan2(v[zero], v[one]);
	ok               &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(result, x0, 1e-10, 1e-10);

	return ok;
}

</pre>

</font></code>


<hr/>Input File: example/atan2.cpp

</body>
</html>