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<center><b><big><big>CppAD Speed: Sparse Jacobian</big></big></b></center>
<br/>
<b><big><a name="Specifications" id="Specifications">Specifications</a></big></b>
<br/>
See <a href="link_sparse_jacobian.xml" target="_top"><span style='white-space: nowrap'>link_sparse_jacobian</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;
# include &lt;cppad/speed/sparse_jac_fun.hpp&gt;

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

namespace {
	using CppAD::vector;
	typedef vector&lt; std::set&lt;size_t&gt; &gt;  SetVector;
	typedef vector&lt;bool&gt;                BoolVector;

	void calc_sparsity(SetVector&amp; sparsity_set, CppAD::<a href="funconstruct.xml" target="_top">ADFun</a>&lt;double&gt;&amp; f)
	{	size_t n = f.Domain();
		SetVector r_set(n);
		for(size_t j = 0; j &lt; n; j++)
			r_set[j].insert(j);
		sparsity_set = f.ForSparseJac(n, r_set);
	}
	void calc_sparsity(BoolVector&amp; sparsity_bool, CppAD::<a href="funconstruct.xml" target="_top">ADFun</a>&lt;double&gt;&amp; f)
	{	size_t n = f.Domain();
		BoolVector r_bool(n * n);
		size_t i, j;
		for(i = 0; i &lt; n; i++)
		{	for(j = 0; j &lt; n; j++)
				r_bool[ i * n + j] = false;
			r_bool[ i * n + i] = true;
		}
		sparsity_bool = f.ForSparseJac(n, r_bool);
	}

}

bool link_sparse_jacobian(
	size_t                           size     , 
	size_t                           repeat   , 
	size_t                           m        ,
	const CppAD::vector&lt;size_t&gt;&amp;     row      ,
	const CppAD::vector&lt;size_t&gt;&amp;     col      ,
	      CppAD::vector&lt;double&gt;&amp;     x        ,
	      CppAD::vector&lt;double&gt;&amp;     jacobian ,
	      size_t&amp;                    n_sweep  )
{
	if( global_atomic )
		return false;
# ifndef CPPAD_COLPACK_SPEED
	if( global_colpack )
		return false;
# endif
	// -----------------------------------------------------
	// setup
	typedef vector&lt; std::set&lt;size_t&gt; &gt;  SetVector;
	typedef CppAD::vector&lt;double&gt;       DblVector;
	typedef CppAD::<a href="ad.xml" target="_top">AD</a>&lt;double&gt;           ADScalar;
	typedef CppAD::vector&lt;ADScalar&gt;     ADVector;

	size_t i, j, k;
	size_t order = 0;         // derivative order corresponding to function 
	size_t K     = row.size();// number of row and column indices 
	size_t n     = size;      // number of independent variables
	ADVector   a_x(n);        // AD domain space vector
	ADVector   a_y(m);        // AD range space vector y = g(x)
	DblVector  jac(K);        // non-zeros in Jacobian
	CppAD::<a href="funconstruct.xml" target="_top">ADFun</a>&lt;double&gt; f;   // AD function object

	// declare sparsity pattern
	SetVector  set_sparsity(m);
	BoolVector bool_sparsity(m * n);

	// initialize all entries as zero
	for(i = 0; i &lt; m; i++)
	{	for(j = 0; j &lt; n; j++)
			jacobian[ i * n + j ] = 0.;
	}
	// ------------------------------------------------------
	if( ! global_onetape ) while(repeat--)
	{	// choose a value for x 
		CppAD::uniform_01(n, x);
		for(k = 0; k &lt; n; k++)
			a_x[k] = x[k];

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

		// AD computation of f (x) 
		CppAD::sparse_jac_fun&lt;ADScalar&gt;(m, n, a_x, row, col, order, a_y);

		// create function object f : X -&gt; Y
		f.Dependent(a_x, a_y);

		if( global_optimize )
			f.optimize();

		// calculate the Jacobian sparsity pattern for this function
		if( global_boolsparsity )
			calc_sparsity(bool_sparsity, f);
		else
			calc_sparsity(set_sparsity, f);

		// structure that holds some of the work done by SparseJacobian
		CppAD::sparse_jacobian_work work;
# ifdef CPPAD_COLPACK_SPEED
		if( global_colpack )
			work.color_method = &quot;colpack&quot;;
# endif
		// calculate the Jacobian at this x
		// (use forward mode because m &gt; n ?)
		if( global_boolsparsity) n_sweep = f.SparseJacobianForward(
				x, bool_sparsity, row, col, jac, work
		);
		else n_sweep = f.SparseJacobianForward(
				x, set_sparsity, row, col, jac, work
		);
		for(k = 0; k &lt; K; k++)
			jacobian[ row[k] * n + col[k] ] = jac[k];
	}
	else
	{	// choose a value for x 
		CppAD::uniform_01(n, x);
		for(k = 0; k &lt; n; k++)
			a_x[k] = x[k];

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

		// AD computation of f (x) 
		CppAD::sparse_jac_fun&lt;ADScalar&gt;(m, n, a_x, row, col, order, a_y);

		// create function object f : X -&gt; Y
		f.Dependent(a_x, a_y);

		if( global_optimize )
			f.optimize();

		// calculate the Jacobian sparsity pattern for this function
		if( global_boolsparsity )
			calc_sparsity(bool_sparsity, f);
		else
			calc_sparsity(set_sparsity, f);

		// structure that holds some of the work done by SparseJacobian
		CppAD::sparse_jacobian_work work;
# ifdef CPPAD_COLPACK_SPEED
		if( global_colpack )
			work.color_method = &quot;colpack&quot;;
# endif

		while(repeat--)
		{	// choose a value for x 
			CppAD::uniform_01(n, x);

			// calculate the Jacobian at this x
			// (use forward mode because m &gt; n ?)
			if( global_boolsparsity ) n_sweep = f.SparseJacobianForward(
					x, bool_sparsity, row, col, jac, work
			);
			else n_sweep = f.SparseJacobianForward(
					x, set_sparsity, row, col, jac, work
			);
			for(k = 0; k &lt; K; k++)
				jacobian[ row[k] * n + col[k] ] = jac[k];
		}
	}
	return true;
}
</pre></font></code>


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

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