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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 cosh Function: Example and Test</title>
<meta http-equiv='Content-Type' content='text/html' charset='utf-8'/>
<meta name="description" id="description" content="The AD cosh Function: Example and Test"/>
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body { color : black }
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<body>
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<center><b><big><big>The AD cosh Function: Example and Test</big></big></b></center>
<code><font color="blue"><pre style='display:inline'> 

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

bool Cosh(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);

	// 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::cosh(x[0]);

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

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

	return ok;
}

</pre>

</font></code>


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

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