// $Id: colpack_jac.cpp 3757 2015-11-30 12:03:07Z bradbell $
/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell

CppAD is distributed under multiple licenses. This distribution is under
the terms of the
                    GNU General Public License Version 3.

A copy of this license is included in the COPYING file of this distribution.
Please visit http://www.coin-or.org/CppAD/ for information on other licenses.
-------------------------------------------------------------------------- */

/*
$begin colpack_jac.cpp$$
$spell
	colpack_jac
	jacobian
$$

$section Using ColPack: Example and Test$$
$mindex colpack jacobian sparse$$


$code
$verbatim%example/colpack_jac.cpp%0%// BEGIN C++%// END C++%1%$$
$$

$end
*/
// BEGIN C++

# include <cppad/cppad.hpp>
bool colpack_jac(void)
{	bool ok = true;
	using CppAD::AD;
	using CppAD::NearEqual;
	typedef CPPAD_TESTVECTOR(AD<double>) a_vector;
	typedef CPPAD_TESTVECTOR(double)     d_vector;
	typedef CppAD::vector<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);

	/*
	      [ 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< std::set<size_t> >  p(m);

	// using row and column indices to compute non-zero in rows 1 and 2
	i_vector row, col;
	for(i = 0; i < m; i++)
	{	for(j = 0; j < 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 &= work.color_method == "cppad";

	// choose to use ColPack
	work.color_method = "colpack";

	// forward mode
	size_t n_sweep = f.SparseJacobianForward(x, p, 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 == 4;

	// reverse mode
	work.clear();
	work.color_method = "colpack";
	n_sweep = f.SparseJacobianReverse(x, p, 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 C++
