# include "ode_problem.hpp"

namespace { // BEGIN empty namespace -----------------------------------------
using namespace cppad_ipopt;

template <class FG_info>
void ipopt_ode_case(
	bool  retape        ,
	const SizeVector& N ,
	NumberVector&     x )
{	bool ok = true;
	size_t i, j;

	// compute the partial sums of the number of grid points
	assert( N.size() == Nz + 1);
	assert( N[0] == 0 );
	SizeVector S(Nz+1);
	S[0] = 0;
	for(i = 1; i <= Nz; i++)
		S[i] = S[i-1] + N[i];
	
	// number of components of x corresponding to values for y
	size_t ny_inx = (S[Nz] + 1) * Ny;
	// number of constraints (range dimension of g)
	size_t m      = ny_inx;
	// number of components in x (domain dimension for f and g)
	size_t n      = ny_inx + Na;
	// the argument vector for the optimization is 
	// y(t) at t[0] , ... , t[S[Nz]] , followed by a
	NumberVector x_i(n), x_l(n), x_u(n);
	for(j = 0; j < ny_inx; j++)
	{	x_i[j] = 0.;       // initial y(t) for optimization
		x_l[j] = -1.0e19;  // no lower limit
		x_u[j] = +1.0e19;  // no upper limit
	}
	for(j = 0; j < Na; j++)
	{	x_i[ny_inx + j ] = .5;       // initiali a for optimization
		x_l[ny_inx + j ] =  -1.e19;  // no lower limit
		x_u[ny_inx + j ] =  +1.e19;  // no upper
	}
	// all of the difference equations are constrained to the value zero
	NumberVector g_l(m), g_u(m);
	for(i = 0; i < m; i++)
	{	g_l[i] = 0.;
		g_u[i] = 0.;
	}

	// object defining the objective f(x) and constraints g(x)
	FG_info fg_info(retape, N);

	// create the CppAD Ipopt interface
	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 Ipopt application
	using Ipopt::IpoptApplication;
	Ipopt::SmartPtr<IpoptApplication> app = new IpoptApplication();

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

	// maximum number of iterations
	app->Options()->SetIntegerValue("max_iter", 30);

	// 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);

	// Derivative testing is very slow for large problems
	// so comment this out if you use a large value for N[].
	app->Options()-> SetStringValue( "derivative_test", "second-order");
	app->Options()-> SetNumericValue( "point_perturbation_radius", 0.);

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

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

	// return the solution
	x.resize( solution.x.size() );
	for(j = 0; j < x.size(); j++)
		x[j] = solution.x[j];

	return;
}
} // END empty namespace ----------------------------------------------------