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

# include &lt;cppad/cppad.hpp&gt;
namespace { // ---------------------------------------------------------
bool reverse()
{	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 <a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(size_t)       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);

	// Jacobian of y without sparsity pattern
	d_vector jac(m * n);
	jac = f.SparseJacobian(x);
	/*
	      [ 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];
	for(ell = 0; ell &lt; size_t(check.size()); ell++)
		ok &amp;=  <a href="nearequal.xml" target="_top">NearEqual</a>(check[ell], jac[ell], eps, eps );

	// using packed boolean sparsity patterns
	CppAD::vectorBool s_b(m * m), p_b(m * n);
	for(i = 0; i &lt; m; i++)
	{	for(ell = 0; ell &lt; m; ell++)
			s_b[i * m + ell] = false;
		s_b[i * m + i] = true;
	}
	p_b   = f.RevSparseJac(m, s_b);
	jac   = f.SparseJacobian(x, p_b);
	for(ell = 0; ell &lt; size_t(check.size()); ell++)
		ok &amp;=  <a href="nearequal.xml" target="_top">NearEqual</a>(check[ell], jac[ell], eps, eps );

	// using vector of sets sparsity patterns
	std::vector&lt; std::set&lt;size_t&gt; &gt; s_s(m),  p_s(m);
	for(i = 0; i &lt; m; i++)
		s_s[i].insert(i);
	p_s   = f.RevSparseJac(m, s_s);
	jac   = f.SparseJacobian(x, p_s);
	for(ell = 0; ell &lt; size_t(check.size()); ell++)
		ok &amp;=  <a href="nearequal.xml" target="_top">NearEqual</a>(check[ell], jac[ell], eps, eps );

	// using row and column indices to compute non-zero in rows 1 and 2
	// (skip row 0). 
	size_t K = 6;
	i_vector row(K), col(K);
	jac.resize(K);
	k = 0;
	for(j = 0; j &lt; n; j++)
	{	for(i = 1; i &lt; m; i++)
		{	ell = i * n + j;
			if( p_b[ell] )
			{	ok &amp;= check[ell] != 0.;
				row[k] = i;
				col[k] = j;
				k++;
			}
		}
	} 
	ok &amp;= k == K;

	// empty work structure
	CppAD::sparse_jacobian_work work;

	// could use p_b 
	size_t n_sweep = f.SparseJacobianReverse(x, p_s, 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;

	// now recompute at a different x value (using work from previous call)
	check[11] = x[3] = 10.;
	n_sweep = f.SparseJacobianReverse(x, p_s, 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;
}

bool forward()
{	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 <a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(size_t)       i_vector;
	size_t i, j, k, ell;
	double eps = 10. * CppAD::numeric_limits&lt;double&gt;::epsilon();

	// domain space vector
	size_t n = 3;
	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 = 4;
	a_vector  a_y(m);
	a_y[0] = a_x[0] + a_x[2];
	a_y[1] = a_x[0] + a_x[2];
	a_y[2] = a_x[1] + a_x[2];
	a_y[3] = a_x[1] + a_x[2] * a_x[2] / 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);

	// Jacobian of y without sparsity pattern
	d_vector jac(m * n);
	jac = f.SparseJacobian(x);
	/*
	      [ 1 0 1   ]
	jac = [ 1 0 1   ]
	      [ 0 1 1   ]
	      [ 0 1 x_2 ]
	*/
	d_vector check(m * n);
	check[0] = 1.; check[1]  = 0.; check[2]  = 1.; 
	check[3] = 1.; check[4]  = 0.; check[5]  = 1.;
	check[6] = 0.; check[7]  = 1.; check[8]  = 1.; 
	check[9] = 0.; check[10] = 1.; check[11] = x[2];
	for(ell = 0; ell &lt; size_t(check.size()); ell++)
		ok &amp;=  <a href="nearequal.xml" target="_top">NearEqual</a>(check[ell], jac[ell], eps, eps );

	// test using packed boolean vectors for sparsity pattern
	CppAD::vectorBool r_b(n * n), p_b(m * n);
	for(j = 0; j &lt; n; j++)
	{	for(ell = 0; ell &lt; n; ell++)
			r_b[j * n + ell] = false;
		r_b[j * n + j] = true;
	}
	p_b = f.ForSparseJac(n, r_b);
	jac = f.SparseJacobian(x, p_b);
	for(ell = 0; ell &lt; size_t(check.size()); ell++)
		ok &amp;=  <a href="nearequal.xml" target="_top">NearEqual</a>(check[ell], jac[ell], eps, eps );

	// test using vector of sets for sparsity pattern
	std::vector&lt; std::set&lt;size_t&gt; &gt; r_s(n), p_s(m);
	for(j = 0; j &lt; n; j++)
		r_s[j].insert(j);
	p_s = f.ForSparseJac(n, r_s);
	jac = f.SparseJacobian(x, p_s);
	for(ell = 0; ell &lt; size_t(check.size()); ell++)
		ok &amp;=  <a href="nearequal.xml" target="_top">NearEqual</a>(check[ell], jac[ell], eps, eps );

	// using row and column indices to compute non-zero elements excluding
	// row 0 and column 0. 
	size_t K = 5;
	i_vector row(K), col(K);
	jac.resize(K);
	k = 0;
	for(i = 1; i &lt; m; i++)
	{	for(j = 1; j &lt; n; j++)
		{	ell = i * n + j;
			if( p_b[ell] )
			{	ok &amp;= check[ell] != 0.;
				row[k] = i;
				col[k] = j;
				k++;
			}
		}
	} 
	ok &amp;= k == K;

	// empty work structure
	CppAD::sparse_jacobian_work work;

	// could use p_s 
	size_t n_sweep = f.SparseJacobianForward(x, p_b, 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;

	// now recompute at a different x value (using work from previous call)
	check[11] = x[2] = 10.;
	n_sweep = f.SparseJacobianForward(x, p_s, 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;
}
} // End empty namespace 

bool sparse_jacobian(void)
{	bool ok = true;
	ok &amp;= forward();
	ok &amp;= reverse();

	return ok;
}
</pre>

</font></code>


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

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