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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>Interpolation With Out Retaping: Example and Test</title>
<meta http-equiv='Content-Type' content='text/html' charset='utf-8'/>
<meta name="description" id="description" content="Interpolation With Out Retaping: Example and Test"/>
<meta name="keywords" id="keywords" content=" interpolation with out retaping: example and test interpolate tape retape see also "/>
<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='_interp_onetape.cpp_xml.js'>
</script>
</head>
<body>
<table><tr>
<td>
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</td>
<td><a href="tape_index.cpp.xml" target="_top">Prev</a>
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<center><b><big><big>Interpolation With Out Retaping: Example and Test</big></big></b></center>
<br/>
<b><big><a name="See Also" id="See Also">See Also</a></big></b>

<br/>
<a href="interp_retape.cpp.xml" target="_top"><span style='white-space: nowrap'>interp_retape.cpp</span></a>

<code><span style='white-space: nowrap'><br/>
<br/>
</span></code><code><font color="blue"><pre style='display:inline'> 
# include &lt;cppad/cppad.hpp&gt;
# include &lt;cassert&gt;
# include &lt;cmath&gt;

namespace {
	double ArgumentValue[] = {
		.0 ,
		.2 ,
		.4 ,
		.8 ,
		1.
	};
	double FunctionValue[] = {
		std::sin( ArgumentValue[0] ) ,
		std::sin( ArgumentValue[1] ) ,
		std::sin( ArgumentValue[2] ) ,
		std::sin( ArgumentValue[3] ) ,
		std::sin( ArgumentValue[4] )
	};
	size_t TableLength = 5;

	size_t Index(const double &amp;x)
	{	// determine the index j such that x is between
		// ArgumentValue[j] and ArgumentValue[j+1] 
		static size_t j = 0;
		while ( x &lt; ArgumentValue[j] &amp;&amp; j &gt; 0 )
			j--;
		while ( x &gt; ArgumentValue[j+1] &amp;&amp; j &lt; TableLength - 2)
			j++;
		// assert conditions that must be true given logic above
		assert( j &gt;= 0 &amp;&amp; j &lt; TableLength - 1 );
		return j;
	}

	double Argument(const double &amp;x)
	{	size_t j = Index(x);
		return ArgumentValue[j];
	}
	double Function(const double &amp;x)
	{	size_t j = Index(x);
		return FunctionValue[j];
	}

	double Slope(const double &amp;x)
	{	size_t j  = Index(x);
		double dx = ArgumentValue[j+1] - ArgumentValue[j];
		double dy = FunctionValue[j+1] - FunctionValue[j];
		return dy / dx;
	}
	CPPAD_DISCRETE_FUNCTION(double, Argument)
	CPPAD_DISCRETE_FUNCTION(double, Function)
	CPPAD_DISCRETE_FUNCTION(double, Slope)
}


bool interp_onetape(void)
{	bool ok = true;

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

	// domain space vector
	size_t n = 1;
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(AD&lt;double&gt;) X(n);
	X[0] = .4 * ArgumentValue[1] + .6 * ArgumentValue[2];

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

	// evaluate piecewise linear interpolant at X[0]
	<a href="ad.xml" target="_top">AD</a>&lt;double&gt; A = Argument(X[0]); 
	<a href="ad.xml" target="_top">AD</a>&lt;double&gt; F = Function(X[0]);
	<a href="ad.xml" target="_top">AD</a>&lt;double&gt; S = Slope(X[0]);
	<a href="ad.xml" target="_top">AD</a>&lt;double&gt; I = F + (X[0] - A) * S;

	// range space vector
	size_t m = 1;
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(AD&lt;double&gt;) Y(m);
	Y[0] = I;

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

	// vectors for arguments to the function object f
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(double) x(n);   // argument values
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(double) y(m);   // function values 
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(double) dx(n);  // differentials in x space
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(double) dy(m);  // differentials in y space

	// to check function value we use the fact that X[0] is between 
	// ArgumentValue[1] and ArgumentValue[2]
	x[0]          = Value(X[0]);
	double delta  = ArgumentValue[2] - ArgumentValue[1];
	double check  = FunctionValue[2] * (x[0] - ArgumentValue[1]) / delta
	              + FunctionValue[1] * (ArgumentValue[2] - x[0]) / delta; 
	ok  &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(Y[0], check, 1e-10, 1e-10);

	// evaluate f where x has different value
	x[0]   = .7 * ArgumentValue[2] + .3 * ArgumentValue[3];
	y      = f.<a href="forward.xml" target="_top">Forward</a>(0, x);

	// check function value 
	delta  = ArgumentValue[3] - ArgumentValue[2];
	check  = FunctionValue[3] * (x[0] - ArgumentValue[2]) / delta
	              + FunctionValue[2] * (ArgumentValue[3] - x[0]) / delta; 
	ok  &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(y[0], check, 1e-10, 1e-10);

	// evaluate partials w.r.t. x[0] 
	dx[0] = 1.;
	dy    = f.<a href="forward.xml" target="_top">Forward</a>(1, dx);

	// check that the derivative is the slope
	check = (FunctionValue[3] - FunctionValue[2])
	      / (ArgumentValue[3] - ArgumentValue[2]);
	ok   &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dy[0], check, 1e-10, 1e-10);

	return ok;
}

</pre>

</font></code>


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

</body>
</html>