/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 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 rev_hes_sparsity.cpp$$
$spell
	Hessian
	Cpp
$$

$section Reverse Mode Hessian Sparsity: Example and Test$$


$code
$srcfile%example/sparse/rev_hes_sparsity.cpp%0%// BEGIN C++%// END C++%1%$$
$$

$end
*/
// BEGIN C++
# include <cppad/cppad.hpp>

bool rev_hes_sparsity(void)
{	bool ok = true;
	using CppAD::AD;
	typedef CPPAD_TESTVECTOR(size_t)     SizeVector;
	typedef CppAD::sparse_rc<SizeVector> sparsity;
	//
	// domain space vector
	size_t n = 3;
	CPPAD_TESTVECTOR(AD<double>) ax(n);
	ax[0] = 0.;
	ax[1] = 1.;
	ax[2] = 2.;

	// declare independent variables and start recording
	CppAD::Independent(ax);

	// range space vector
	size_t m = 2;
	CPPAD_TESTVECTOR(AD<double>) ay(m);
	ay[0] = sin( ax[2] );
	ay[1] = ax[0] * ax[1];

	// create f: x -> y and stop tape recording
	CppAD::ADFun<double> f(ax, ay);

	// sparsity pattern for the identity matrix
	size_t nr     = n;
	size_t nc     = n;
	size_t nnz_in = n;
	sparsity pattern_in(nr, nc, nnz_in);
	for(size_t k = 0; k < nnz_in; k++)
	{	size_t r = k;
		size_t c = k;
		pattern_in.set(k, r, c);
	}
	// compute sparsity pattern for J(x) = F'(x)
	bool transpose       = false;
	bool dependency      = false;
	bool internal_bool   = false;
	sparsity pattern_out;
	f.for_jac_sparsity(
		pattern_in, transpose, dependency, internal_bool, pattern_out
	);
	//
	// compute sparsity pattern for H(x) = F_1''(x)
	CPPAD_TESTVECTOR(bool) select_range(m);
	select_range[0] = false;
	select_range[1] = true;
	f.rev_hes_sparsity(
		select_range, transpose, internal_bool, pattern_out
	);
	size_t nnz = pattern_out.nnz();
	ok        &= nnz == 2;
	ok        &= pattern_out.nr() == n;
	ok        &= pattern_out.nc() == n;
	{	// check results
		const SizeVector& row( pattern_out.row() );
		const SizeVector& col( pattern_out.col() );
		SizeVector row_major = pattern_out.row_major();
		//
		ok &= row[ row_major[0] ] ==  0  && col[ row_major[0] ] ==  1;
		ok &= row[ row_major[1] ] ==  1  && col[ row_major[1] ] ==  0;
	}
	//
	// compute sparsity pattern for H(x) = F_0''(x)
	select_range[0] = true;
	select_range[1] = false;
	f.rev_hes_sparsity(
		select_range, transpose, internal_bool, pattern_out
	);
	nnz = pattern_out.nnz();
	ok &= nnz == 1;
	ok &= pattern_out.nr() == n;
	ok &= pattern_out.nc() == n;
	{	// check results
		const SizeVector& row( pattern_out.row() );
		const SizeVector& col( pattern_out.col() );
		//
		ok &= row[0] ==  2  && col[0] ==  2;
	}
	return ok;
}
// END C++
