Sparse Jacobian: Example and Test
Keywords: sparse jacobian: example test Jacobian spare

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Sparse Jacobian: Example and Test
`

    # include <cppad/cppad.hpp>
    namespace { // ---------------------------------------------------------
    bool reverse()
    {	bool ok = true;
    	using CppAD::AD;
    	using CppAD::NearEqual;
    	typedef CPPAD_TESTVECTOR(AD<double>) a_vector;
    	typedef CPPAD_TESTVECTOR(double)       d_vector;
    	typedef CPPAD_TESTVECTOR(size_t)       i_vector;
    	size_t i, j, k, ell;
    	double eps = 10. * CppAD::numeric_limits<double>::epsilon();

    	// domain space vector
    	size_t n = 4;
    	a_vector  a_x(n);
    	for(j = 0; j < n; j++)
    		a_x[j] = AD<double> (0);

    	// declare independent variables and starting recording
    	CppAD::Independent(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 -> y and stop tape recording
    	CppAD::ADFun<double> f(a_x, a_y);

    	// new value for the independent variable vector
    	d_vector x(n);
    	for(j = 0; j < 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 < size_t(check.size()); ell++)
    		ok &=  NearEqual(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 < m; i++)
    	{	for(ell = 0; ell < 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 < size_t(check.size()); ell++)
    		ok &=  NearEqual(check[ell], jac[ell], eps, eps );

    	// using vector of sets sparsity patterns
    	std::vector< std::set<size_t> > s_s(m),  p_s(m);
    	for(i = 0; i < m; i++)
    		s_s[i].insert(i);
    	p_s   = f.RevSparseJac(m, s_s);
    	jac   = f.SparseJacobian(x, p_s);
    	for(ell = 0; ell < size_t(check.size()); ell++)
    		ok &=  NearEqual(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 < n; j++)
    	{	for(i = 1; i < m; i++)
    		{	ell = i * n + j;
    			if( p_b[ell] )
    			{	ok &= check[ell] != 0.;
    				row[k] = i;
    				col[k] = j;
    				k++;
    			}
    		}
    	}
    	ok &= 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 < K; k++)
    	{	ell = row[k] * n + col[k];
    		ok &= NearEqual(check[ell], jac[k], eps, eps);
    	}
    	ok &= n_sweep == 2;

    	// now recompute at a different x value (using work from previous call)
    	check[11] = x[3] = 10.;
    	std::vector< std::set<size_t> > not_used;
    	n_sweep = f.SparseJacobianReverse(x, not_used, row, col, jac, work);
    	for(k = 0; k < K; k++)
    	{	ell = row[k] * n + col[k];
    		ok &= NearEqual(check[ell], jac[k], eps, eps);
    	}
    	ok &= n_sweep == 2;

    	return ok;
    }

    bool forward()
    {	bool ok = true;
    	using CppAD::AD;
    	using CppAD::NearEqual;
    	typedef CPPAD_TESTVECTOR(AD<double>) a_vector;
    	typedef CPPAD_TESTVECTOR(double)       d_vector;
    	typedef CPPAD_TESTVECTOR(size_t)       i_vector;
    	size_t i, j, k, ell;
    	double eps = 10. * CppAD::numeric_limits<double>::epsilon();

    	// domain space vector
    	size_t n = 3;
    	a_vector  a_x(n);
    	for(j = 0; j < n; j++)
    		a_x[j] = AD<double> (0);

    	// declare independent variables and starting recording
    	CppAD::Independent(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 -> y and stop tape recording
    	CppAD::ADFun<double> f(a_x, a_y);

    	// new value for the independent variable vector
    	d_vector x(n);
    	for(j = 0; j < 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 < size_t(check.size()); ell++)
    		ok &=  NearEqual(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 < n; j++)
    	{	for(ell = 0; ell < 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 < size_t(check.size()); ell++)
    		ok &=  NearEqual(check[ell], jac[ell], eps, eps );

    	// test using vector of sets for sparsity pattern
    	std::vector< std::set<size_t> > r_s(n), p_s(m);
    	for(j = 0; j < n; j++)
    		r_s[j].insert(j);
    	p_s = f.ForSparseJac(n, r_s);
    	jac = f.SparseJacobian(x, p_s);
    	for(ell = 0; ell < size_t(check.size()); ell++)
    		ok &=  NearEqual(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 < m; i++)
    	{	for(j = 1; j < n; j++)
    		{	ell = i * n + j;
    			if( p_b[ell] )
    			{	ok &= check[ell] != 0.;
    				row[k] = i;
    				col[k] = j;
    				k++;
    			}
    		}
    	}
    	ok &= 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 < K; k++)
    	{    ell = row[k] * n + col[k];
    		ok &= NearEqual(check[ell], jac[k], eps, eps);
    	}
    	ok &= 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 < K; k++)
    	{    ell = row[k] * n + col[k];
    		ok &= NearEqual(check[ell], jac[k], eps, eps);
    	}
    	ok &= n_sweep == 2;

    	return ok;
    }
    } // End empty namespace

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

    	return ok;
    }

`

Input File: example/sparse_jacobian.cpp