// $Id: sparse_hessian.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 sparse_hessian.cpp$$
$spell
	Cpp
	Hessian
$$

$section Sparse Hessian: Example and Test$$
$mindex Hessian spare$$


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

$end
*/
// BEGIN C++
# include <cppad/cppad.hpp>
bool sparse_hessian(void)
{	bool ok = true;
	using CppAD::AD;
	using CppAD::NearEqual;
	size_t i, j, k, ell;
	typedef CPPAD_TESTVECTOR(AD<double>)               a_vector;
	typedef CPPAD_TESTVECTOR(double)                     d_vector;
	typedef CPPAD_TESTVECTOR(size_t)                     i_vector;
	typedef CPPAD_TESTVECTOR(bool)                       b_vector;
	typedef CPPAD_TESTVECTOR(std::set<size_t>)         s_vector;
	double eps = 10. * CppAD::numeric_limits<double>::epsilon();

	// domain space vector
	size_t n = 12;  // must be greater than or equal 3; see n_sweep below
	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);

	// range space vector
	size_t m = 1;
	a_vector a_y(m);
	a_y[0] = a_x[0]*a_x[1];
	for(j = 0; j < n; j++)
		a_y[0] += a_x[j] * a_x[j] * a_x[j];

	// create f: x -> y and stop tape recording
	// (without executing zero order forward calculation)
	CppAD::ADFun<double> f;
	f.Dependent(a_x, a_y);

	// new value for the independent variable vector, and weighting vector
	d_vector w(m), x(n);
	for(j = 0; j < n; j++)
		x[j] = double(j);
	w[0] = 1.0;

	// vector used to check the value of the hessian
	d_vector check(n * n);
	for(ell = 0; ell < n * n; ell++)
		check[ell] = 0.0;
	ell        = 0 * n + 1;
	check[ell] = 1.0;
	ell        = 1 * n + 0;
	check[ell] = 1.0 ;
	for(j = 0; j < n; j++)
	{	ell = j * n + j;
		check[ell] = 6.0 * x[j];
	}

	// -------------------------------------------------------------------
	// second derivative of y[0] w.r.t x
	d_vector hes(n * n);
	hes = f.SparseHessian(x, w);
	for(ell = 0; ell < n * n; ell++)
		ok &=  NearEqual(w[0] * check[ell], hes[ell], eps, eps );

	// --------------------------------------------------------------------
	// example using vectors of bools to compute sparsity pattern for Hessian
	b_vector r_bool(n * n);
	for(i = 0; i < n; i++)
	{	for(j = 0; j < n; j++)
			r_bool[i * n + j] = false;
		r_bool[i * n + i] = true;
	}
	f.ForSparseJac(n, r_bool);
	//
	b_vector s_bool(m);
	for(i = 0; i < m; i++)
		s_bool[i] = w[i] != 0;
	b_vector p_bool = f.RevSparseHes(n, s_bool);

	hes = f.SparseHessian(x, w, p_bool);
	for(ell = 0; ell < n * n; ell++)
		ok &=  NearEqual(w[0] * check[ell], hes[ell], eps, eps );

	// --------------------------------------------------------------------
	// example using vectors of sets to compute sparsity pattern for Hessian
	s_vector r_set(n);
	for(i = 0; i < n; i++)
		r_set[i].insert(i);
	f.ForSparseJac(n, r_set);
	//
	s_vector s_set(m);
	for(i = 0; i < m; i++)
		if( w[i] != 0. )
			s_set[0].insert(i);
	s_vector p_set = f.RevSparseHes(n, s_set);

	// example passing sparsity pattern to SparseHessian
	hes = f.SparseHessian(x, w, p_set);
	for(ell = 0; ell < n * n; ell++)
		ok &=  NearEqual(w[0] * check[ell], hes[ell], eps, eps );

	// --------------------------------------------------------------------
	// use row and column indices to specify upper triangle of
	// non-zero elements of Hessian
	size_t K = n + 1;
	i_vector row(K), col(K);
	hes.resize(K);
	k = 0;
	for(j = 0; j < n; j++)
	{	// diagonal of Hessian
		row[k] = j;
		col[k] = j;
		k++;
	}
	// only off diagonal non-zero elemenet in upper triangle
	row[k] = 0;
	col[k] = 1;
	k++;
	ok &= k == K;
	CppAD::sparse_hessian_work work;

	// can use p_set or p_bool.
	size_t n_sweep = f.SparseHessian(x, w, p_set, row, col, hes, work);
	for(k = 0; k < K; k++)
	{	ell = row[k] * n + col[k];
		ok &=  NearEqual(w[0] * check[ell], hes[k], eps, eps );
	}
	ok &= n_sweep == 2;

	// now recompute at a different x and w (using work from previous call
	w[0]       = 2.0;
	x[1]       = 0.5;
	ell        = 1 * n + 1;
	check[ell] = 6.0 * x[1];
	s_vector   not_used;
	n_sweep    = f.SparseHessian(x, w, not_used, row, col, hes, work);
	for(k = 0; k < K; k++)
	{	ell = row[k] * n + col[k];
		ok &=  NearEqual(w[0] * check[ell], hes[k], eps, eps );
	}
	ok &= n_sweep == 2;



	return ok;
}
// END C++
