// $Id: multiple_solution.cpp 3785 2016-02-08 12:53:06Z 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.
-------------------------------------------------------------------------- */

# include <cppad_ipopt_nlp.hpp>

namespace { // Begin empty namespace
using namespace cppad_ipopt;

// ---------------------------------------------------------------------------
/*
f(x)    = x[1]; k=0, ell=0, I[0] = 0, J[0] = 1
g_0 (x) = x[0]; k=0, ell=1, I[0] = 1, J[0] = 0
g_1 (x) = x[1]; k=0, ell=2, I[0] = 2, J[0] = 1

minimize   f(x)
subject to -1 <= g_0(x)  <= 0
            0 <= g_1 (x) <= 1

The solution is x[1] = 0 and x[0] arbitrary.
*/

class FG_J_changes : public cppad_ipopt_fg_info
{
private:
	bool retape_;
public:
	// constructor
	FG_J_changes(bool retape_in)
	: retape_ (retape_in)
	{ }
	size_t number_functions(void)
	{	return 1; }
	size_t domain_size(size_t k)
	{	size_t q;
		switch(k)
		{	case 0:  q = 1;  break;
			default: assert(0);
		}
		return q;
	}
	size_t range_size(size_t k)
	{	size_t p;
		switch(k)
		{	case 0:  p = 1;  break;
			default: assert(0);
		}
		return p;
	}
	size_t number_terms(size_t k)
	{	size_t L;
		switch(k)
		{	case 0:  L = 3;   break;
			default: assert(0);
		}
		return L;
	}
	void index(size_t k, size_t ell, SizeVector&I, SizeVector& J)
	{	assert( I.size() >= 1 );
		assert( J.size() >= 1 );
		I[0] = ell;
		if( ell == 0 )
		{	J[0] = 1;
			return;
		}
		J[0] = ell - 1;
		return;
	}
	// retape function
	bool retape(size_t k)
	{	return retape_; }
	ADVector eval_r(size_t k, const ADVector&  u)
	{
		assert( u.size() == 1 );
		ADVector r(1);
		r[0] = u[0] ;
		return r;
	}
};
} // end empty namespace

bool multiple_solution(void)
{
	bool ok = true;
	// number of independent variables (domain dimension for f and g)
	size_t n = 2;
	// number of constraints (range dimension for g)
	size_t m = 2;
	// initial value of the independent variables
	NumberVector x_i(n);
	NumberVector x_l(n);
	NumberVector x_u(n);

	size_t i = 0;
	for(i = 0; i < n; i++)
	{	x_i[i] = 0.;
		x_l[i] = -1.0;
		x_u[i] = +1.0;
	}

	// lower and upper limits for g
	NumberVector g_l(m);
	NumberVector g_u(m);
	g_l[0] = -1; g_u[0] = 0.;
	g_l[1] = 0.; g_u[1] = 1.;

	// object for evaluating function
	bool retape = false;
	FG_J_changes my_fg_info(retape);
	cppad_ipopt_fg_info *fg_info = &my_fg_info;

	cppad_ipopt_solution solution;
	Ipopt::SmartPtr<Ipopt::TNLP> cppad_nlp = new cppad_ipopt_nlp(
		n, m, x_i, x_l, x_u, g_l, g_u, fg_info, &solution
	);

	// Create an instance of the IpoptApplication
	using Ipopt::IpoptApplication;
	Ipopt::SmartPtr<IpoptApplication> app = new IpoptApplication();

	// turn off any printing
	app->Options()->SetIntegerValue("print_level", 0);
	app->Options()->SetStringValue("sb", "yes");

	// approximate accuracy in first order necessary conditions;
	// see Mathematical Programming, Volume 106, Number 1,
	// Pages 25-57, Equation (6)
	app->Options()->SetNumericValue("tol", 1e-9);
	app->Options()-> SetStringValue("derivative_test", "second-order");

	// Initialize the IpoptApplication and process the options
	Ipopt::ApplicationReturnStatus status = app->Initialize();
	ok    &= status == Ipopt::Solve_Succeeded;

	// Run the IpoptApplication
	status = app->OptimizeTNLP(cppad_nlp);
	ok    &= status == Ipopt::Solve_Succeeded;

	/*
	 Check solution status
	 */
	ok &= solution.status == cppad_ipopt_solution::success;
	ok &= CppAD::NearEqual(solution.x[1], 0., 1e-6, 1e-6);

	return ok;
}
