// $Id: ipopt_solve.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.
-------------------------------------------------------------------------- */
/*
Testing ipopt::solve
*/
# ifdef CPPAD_IPOPT_TEST

# include <cppad/ipopt/solve.hpp>

namespace {
	using CppAD::AD;

	class FG_eval {
	public:
		typedef CPPAD_TESTVECTOR( AD<double> ) ADvector;
		void operator()(ADvector& fg, const ADvector& x)
		{	assert( fg.size() == 3 );
			assert( x.size()  == 4 );

			// Fortran style indexing
			AD<double> x1 = x[0];
			AD<double> x2 = x[1];
			AD<double> x3 = x[2];
			AD<double> x4 = x[3];
			// f(x)
			fg[0] = x1 * x4 * (x1 + x2 + x3) + x3;
			// g_1 (x)
			fg[1] = x1 * x2 * x3 * x4;
			// g_2 (x)
			fg[2] = x1 * x1 + x2 * x2 + x3 * x3 + x4 * x4;
			//
			return;
		}
	};
}

bool ipopt_solve(void)
{	bool ok = true;
	size_t i, j;
	typedef CPPAD_TESTVECTOR( double ) Dvector;

	// number of independent variables (domain dimension for f and g)
	size_t nx = 4;
	// number of constraints (range dimension for g)
	size_t ng = 2;
	// initial value of the independent variables
	Dvector xi(nx);
	xi[0] = 1.0;
	xi[1] = 5.0;
	xi[2] = 5.0;
	xi[3] = 1.0;
	// lower and upper limits for x
	Dvector xl(nx), xu(nx);
	for(j = 0; j < nx; j++)
	{	xl[j] = 1.0;
		xu[j] = 5.0;
	}
	// lower and upper limits for g
	Dvector gl(ng), gu(ng);
	gl[0] = 25.0;     gu[0] = 1.0e19;
	gl[1] = 40.0;     gu[1] = 40.0;

	// object that computes objective and constraints
	FG_eval fg_eval;

	// options
	std::string base_options;
	// turn off any printing
	base_options += "Integer print_level  0\n";
	base_options += "String  sb         yes\n";
	// maximum number of iterations
	base_options += "Integer max_iter     10\n";
	// approximate accuracy in first order necessary conditions;
	// see Mathematical Programming, Volume 106, Number 1,
	// Pages 25-57, Equation (6)
	base_options += "Numeric tol          1e-6\n";
	// derivative testing
	base_options += "String  derivative_test            second-order\n";
	// maximum amount of random pertubation; e.g.,
	// when evaluation finite diff
	base_options += "Numeric point_perturbation_radius  0.\n";

	// place to return solution
	CppAD::ipopt::solve_result<Dvector> solution;

	// solution values and tolerances
	double check_x[]  = { 1.000000, 4.743000, 3.82115, 1.379408 };
	double check_zl[] = { 1.087871, 0.,       0.,      0.       };
	double check_zu[] = { 0.,       0.,       0.,      0.       };
	double rel_tol    = 1e-6;  // relative tolerance
	double abs_tol    = 1e-6;  // absolute tolerance

	for(i = 0; i < 3; i++)
	{	std::string options( base_options );
		if( i == 1 )
			options += "Sparse true forward\n";
		if( i == 2 )
			options += "Sparse true reverse\n";

		// solve the problem
		CppAD::ipopt::solve<Dvector, FG_eval>(
			options, xi, xl, xu, gl, gu, fg_eval, solution
		);
		ok &= solution.status==CppAD::ipopt::solve_result<Dvector>::success;
		//
		// Check some of the solution values
		for(j = 0; j < nx; j++)
		{	ok &= CppAD::NearEqual(
				check_x[j],  solution.x[j],   rel_tol, abs_tol
			);
			ok &= CppAD::NearEqual(
				check_zl[j], solution.zl[j], rel_tol, abs_tol
			);
			ok &= CppAD::NearEqual(
				check_zu[j], solution.zu[j], rel_tol, abs_tol
			);
		}
	}

	return ok;
}

# endif
