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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>Forward Mode: Example and Test of Multiple Directions</title>
<meta http-equiv='Content-Type' content='text/html' charset='utf-8'/>
<meta name="description" id="description" content="Forward Mode: Example and Test of Multiple Directions"/>
<meta name="keywords" id="keywords" content=" forward mode: example and test of multiple directions orders order "/>
<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='_forward_dir.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>
<td><a href="forward_dir.xml" target="_top">Prev</a>
</td><td><a href="size_order.xml" target="_top">Next</a>
</td><td>
<select onchange='choose_across0(this)'>
<option>Index-&gt;</option>
<option>contents</option>
<option>reference</option>
<option>index</option>
<option>search</option>
<option>external</option>
</select>
</td>
<td>
<select onchange='choose_up0(this)'>
<option>Up-&gt;</option>
<option>CppAD</option>
<option>ADFun</option>
<option>FunEval</option>
<option>Forward</option>
<option>forward_dir</option>
<option>forward_dir.cpp</option>
</select>
</td>
<td>
<select onchange='choose_down3(this)'>
<option>FunEval-&gt;</option>
<option>Forward</option>
<option>Reverse</option>
<option>Sparse</option>
</select>
</td>
<td>
<select onchange='choose_down2(this)'>
<option>Forward-&gt;</option>
<option>forward_zero</option>
<option>forward_one</option>
<option>forward_two</option>
<option>forward_order</option>
<option>forward_dir</option>
<option>size_order</option>
<option>CompareChange</option>
<option>capacity_order</option>
<option>number_skip</option>
</select>
</td>
<td>
<select onchange='choose_down1(this)'>
<option>forward_dir-&gt;</option>
<option>forward_dir.cpp</option>
</select>
</td>
<td>forward_dir.cpp</td>
<td>Headings</td>
</tr></table><br/>



<center><b><big><big>Forward Mode: Example and Test of Multiple Directions</big></big></b></center>
<code><font color="blue"><pre style='display:inline'> 
# include &lt;limits&gt;
# include &lt;cppad/cppad.hpp&gt;
bool forward_dir(void)
{	bool ok = true;
	using CppAD::AD;
	using CppAD::NearEqual;
	double eps = 10. * std::numeric_limits&lt;double&gt;::epsilon();
	size_t j;

	// domain space vector
	size_t n = 3;
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(AD&lt;double&gt;) ax(n);
	ax[0] = 0.; 
	ax[1] = 1.;
	ax[2] = 2.;

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

	// range space vector
	size_t m = 1;
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(AD&lt;double&gt;) ay(m);
	ay[0] = ax[0] * ax[1] * ax[2];

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

	// initially, the variable values during taping are stored in f
	ok &amp;= f.size_order() == 1;

	// zero order Taylor coefficients
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(double) x0(n), y0;
	for(j = 0; j &lt; n; j++)
		x0[j] = double(j+1);
	y0          = f.<a href="forward.xml" target="_top">Forward</a>(0, x0);
	ok         &amp;= y0.size() == m;
	double y_0  = 1.*2.*3.; 
	ok         &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(y0[0], y_0, eps, eps);

	// first order Taylor coefficients
	size_t r = 2, ell;
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(double) x1(r*n), y1;
	for(ell = 0; ell &lt; r; ell++)
	{	for(j = 0; j &lt; n; j++)
			x1[ r * j + ell ] = double(j + 1 + ell);
	}
	y1  = f.<a href="forward.xml" target="_top">Forward</a>(1, r, x1);
	ok &amp;= y1.size() == r*m;
	
	// secondorder Taylor coefficients
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(double) x2(r*n), y2;
	for(ell = 0; ell &lt; r; ell++)
	{	for(j = 0; j &lt; n; j++)
			x2[ r * j + ell ] = 0.0;
	}
	y2  = f.<a href="forward.xml" target="_top">Forward</a>(2, r, x2);
	ok &amp;= y2.size() == r*m;
	// 
	// Y_0 (t)     = F[X_0(t)] 
	//             =  (1 + 1t)(2 + 2t)(3 + 3t) 
	double y_1_0   = 1.*2.*3. + 2.*1.*3. + 3.*1.*2.;
	double y_2_0   = 1.*2.*3. + 2.*1.*3. + 3.*1.*2.;
	// 
	// Y_1 (t)     = F[X_1(t)] 
	//             =  (1 + 2t)(2 + 3t)(3 + 4t) 
	double y_1_1   = 2.*2.*3. + 3.*1.*3. + 4.*1.*2.;
	double y_2_1   = 1.*3.*4. + 2.*2.*4. + 3.*2.*3.;
	//
	ok  &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(y1[0] , y_1_0, eps, eps);
	ok  &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(y1[1] , y_1_1, eps, eps);
	ok  &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(y2[0] , y_2_0, eps, eps);
	ok  &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(y2[1] , y_2_1, eps, eps);
	//
	// check number of orders 
	ok   &amp;= f.size_order() == 3;
	//
	// check number of directions 
	ok   &amp;= f.size_direction() == 2;
	//
	return ok;
}
</pre>

</font></code>


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

</body>
</html>