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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>Using ColPack: Example and Test</title>
<meta http-equiv='Content-Type' content='text/html' charset='utf-8'/>
<meta name="description" id="description" content="Using ColPack: Example and Test"/>
<meta name="keywords" id="keywords" content=" using colpack: example and test colpack spare "/>
<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='_colpack.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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</select>
</td>
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<td>
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<option>Install-&gt;</option>
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</td>
<td>
<select onchange='choose_down2(this)'>
<option>cmake-&gt;</option>
<option>adolc_prefix</option>
<option>colpack_prefix</option>
<option>eigen_prefix</option>
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<td>
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<option>colpack_prefix-&gt;</option>
<option>colpack.cpp</option>
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</select>
</td>
<td>colpack.cpp</td>
<td>Headings</td>
</tr></table><br/>



<center><b><big><big>Using ColPack: Example and Test</big></big></b></center>
<code><font color="blue"><pre style='display:inline'> 

# include &lt;cppad/cppad.hpp&gt;
bool colpack(void)
{	bool ok = true;
	using CppAD::AD;
	using CppAD::NearEqual;
	typedef <a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(AD&lt;double&gt;) a_vector;
	typedef <a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(double)     d_vector;
	typedef CppAD::vector&lt;size_t&gt;        i_vector;
	size_t i, j, k, ell;
	double eps = 10. * CppAD::numeric_limits&lt;double&gt;::epsilon();

	// domain space vector
	size_t n = 4;
	a_vector  a_x(n);
	for(j = 0; j &lt; n; j++)
		a_x[j] = <a href="ad.xml" target="_top">AD</a>&lt;double&gt; (0);

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

	size_t m = 3;
	a_vector  a_y(m);
	a_y[0] = a_x[0] + a_x[1];
	a_y[1] = a_x[2] + a_x[3];
	a_y[2] = a_x[0] + a_x[1] + a_x[2] + a_x[3] * a_x[3] / 2.;

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

	// new value for the independent variable vector
	d_vector x(n);
	for(j = 0; j &lt; n; j++)
		x[j] = double(j);

	/*
	      [ 1 1 0 0  ]
	jac = [ 0 0 1 1  ]
	      [ 1 1 1 x_3]
	*/
	d_vector check(m * n);
	check[0] = 1.; check[1] = 1.; check[2]  = 0.; check[3]  = 0.;
	check[4] = 0.; check[5] = 0.; check[6]  = 1.; check[7]  = 1.;
	check[8] = 1.; check[9] = 1.; check[10] = 1.; check[11] = x[3];

	// Normally one would use f.ForSparseJac or f.RevSparseJac to compute 
	// sparsity pattern, but for this example we extract it from check.
	std::vector&lt; std::set&lt;size_t&gt; &gt;  p(m);

	// using row and column indices to compute non-zero in rows 1 and 2
	i_vector row, col;
	for(i = 0; i &lt; m; i++)
	{	for(j = 0; j &lt; n; j++)
		{	ell = i * n + j;
			if( check[ell] != 0. )
			{	row.push_back(i);
				col.push_back(j);
				p[i].insert(j);
			}
		}
	} 
	size_t K = row.size();
	d_vector jac(K);

	// empty work structure
	CppAD::sparse_jacobian_work work;
	ok &amp;= work.color_method == &quot;cppad&quot;;

	// choose to use ColPack
	work.color_method = &quot;colpack&quot;;

	// forward mode
	size_t n_sweep = f.SparseJacobianForward(x, p, row, col, jac, work);
	for(k = 0; k &lt; K; k++)
	{	ell = row[k] * n + col[k];
		ok &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(check[ell], jac[k], eps, eps);
	}
	ok &amp;= n_sweep == 4;

	// reverse mode
	work.clear();
	work.color_method = &quot;colpack&quot;;
	n_sweep = f.SparseJacobianReverse(x, p, row, col, jac, work);
	for(k = 0; k &lt; K; k++)
	{	ell = row[k] * n + col[k];
		ok &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(check[ell], jac[k], eps, eps);
	}
	ok &amp;= n_sweep == 2;

	return ok;
}
</pre>

</font></code>


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

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