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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>CppAD Speed: Second Derivative of a Polynomial</title>
<meta http-equiv='Content-Type' content='text/html' charset='utf-8'/>
<meta name="description" id="description" content="CppAD Speed: Second Derivative of a Polynomial"/>
<meta name="keywords" id="keywords" content=" cppad speed: second derivative of a polynomial link_poly speed specifications implementation "/>
<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='_cppad_poly.cpp_xml.js'>
</script>
</head>
<body>
<table><tr>
<td>
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</td>
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<option>cppad_ode.cpp</option>
<option>cppad_poly.cpp</option>
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<td>cppad_poly.cpp</td>
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<option>Specifications</option>
<option>Implementation</option>
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</td>
</tr></table><br/>



<center><b><big><big>CppAD Speed: Second Derivative of a Polynomial</big></big></b></center>
<br/>
<b><big><a name="Specifications" id="Specifications">Specifications</a></big></b>
<br/>
See <a href="link_poly.xml" target="_top"><span style='white-space: nowrap'>link_poly</span></a>
.

<br/>
<br/>
<b><big><a name="Implementation" id="Implementation">Implementation</a></big></b>


<code><font color='blue'><pre style='display:inline'> 
# include &lt;cppad/cppad.hpp&gt;
# include &lt;cppad/speed/uniform_01.hpp&gt;

// Note that CppAD uses global_memory at the main program level
extern bool
	global_onetape, global_atomic, global_optimize;

bool link_poly(
	size_t                     size     , 
	size_t                     repeat   , 
	CppAD::vector&lt;double&gt;     &amp;a        ,  // coefficients of polynomial
	CppAD::vector&lt;double&gt;     &amp;z        ,  // polynomial argument value
	CppAD::vector&lt;double&gt;     &amp;ddp      )  // second derivative w.r.t z  
{
	// speed test global option values
	if( global_atomic )
		return false;

	// -----------------------------------------------------
	// setup
	typedef CppAD::<a href="ad.xml" target="_top">AD</a>&lt;double&gt;     ADScalar; 
	typedef CppAD::vector&lt;ADScalar&gt; ADVector; 

	size_t i;      // temporary index
	size_t m = 1;  // number of dependent variables
	size_t n = 1;  // number of independent variables
	ADVector Z(n); // AD domain space vector
	ADVector P(m); // AD range space vector

	// choose the polynomial coefficients
	CppAD::uniform_01(size, a);

	// AD copy of the polynomial coefficients
	ADVector A(size);
	for(i = 0; i &lt; size; i++)
		A[i] = a[i];

	// forward mode first and second differentials
	CppAD::vector&lt;double&gt; p(1), dp(1), dz(1), ddz(1);
	dz[0]  = 1.;
	ddz[0] = 0.;

	// AD function object
	CppAD::<a href="funconstruct.xml" target="_top">ADFun</a>&lt;double&gt; f;

	// --------------------------------------------------------------------
	if( ! global_onetape ) while(repeat--)
	{
		// choose an argument value
		CppAD::uniform_01(1, z);
		Z[0] = z[0];

		// declare independent variables
		<a href="independent.xml" target="_top">Independent</a>(Z);

		// AD computation of the function value 
		P[0] = CppAD::Poly(0, A, Z[0]);

		// create function object f : A -&gt; detA
		f.Dependent(Z, P);

		if( global_optimize )
			f.optimize();

		// pre-allocate memory for three forward mode calculations
		f.capacity_order(3);

		// evaluate the polynomial 
		p = f.<a href="forward.xml" target="_top">Forward</a>(0, z);

		// evaluate first order Taylor coefficient
		dp = f.<a href="forward.xml" target="_top">Forward</a>(1, dz);

		// second derivative is twice second order Taylor coef
		ddp     = f.<a href="forward.xml" target="_top">Forward</a>(2, ddz);
		ddp[0] *= 2.;
	}
	else
	{
		// choose an argument value
		CppAD::uniform_01(1, z);
		Z[0] = z[0];

		// declare independent variables
		<a href="independent.xml" target="_top">Independent</a>(Z);

		// AD computation of the function value 
		P[0] = CppAD::Poly(0, A, Z[0]);

		// create function object f : A -&gt; detA
		f.Dependent(Z, P);

		if( global_optimize )
			f.optimize();

		while(repeat--)
		{	// sufficient memory is allocated by second repetition

			// get the next argument value
			CppAD::uniform_01(1, z);

			// evaluate the polynomial at the new argument value
			p = f.<a href="forward.xml" target="_top">Forward</a>(0, z);

			// evaluate first order Taylor coefficient
			dp = f.<a href="forward.xml" target="_top">Forward</a>(1, dz);

			// second derivative is twice second order Taylor coef
			ddp     = f.<a href="forward.xml" target="_top">Forward</a>(2, ddz);
			ddp[0] *= 2.;
		}
	}
	return true;
}
</pre></font></code>


<hr/>Input File: speed/cppad/poly.cpp

</body>
</html>