// $Id: sub_eq.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.
-------------------------------------------------------------------------- */

/*
Two old SubEq examples now used just for valiadation testing
*/
# include <cppad/cppad.hpp>

namespace { // BEGIN empty namespace

bool SubEqTestOne(void)
{	bool ok = true;

	using namespace CppAD;

	// independent variable vector, indices, values, and declaration
	CPPAD_TESTVECTOR(AD<double>) U(2);
	size_t s = 0;
	size_t t = 1;
	U[s] = 3.;
	U[t] = 2.;
	Independent(U);

	// dependent variable vector and indices
	CPPAD_TESTVECTOR(AD<double>) Z(2);
	size_t x = 0;
	size_t y = 1;

	// dependent variable values
	Z[x]  = U[s];
	Z[y]  = U[t];
	Z[x] -= U[t];  // AD<double> -= AD<double>
	Z[y] -= 5.;    // AD<double> -= double

	// create f: U -> Z and vectors used for derivative calculations
	ADFun<double> f(U, Z);
	CPPAD_TESTVECTOR(double) v( f.Domain() );
	CPPAD_TESTVECTOR(double) w( f.Range() );

	// check function values
	ok &= ( Z[x] == 3. - 2. );
	ok &= ( Z[y] == 2. - 5. );

	// forward computation of partials w.r.t. t
	v[s] = 0.;
	v[t] = 1.;
	w = f.Forward(1, v);
	ok &= ( w[x] == -1. );  // dx/dt
	ok &= ( w[y] == 1. );   // dy/dt

	// reverse computation of second partials of x
	CPPAD_TESTVECTOR(double) r( f.Domain() * 2 );
	w[x] = 1.;
	w[y] = 0.;
	r = f.Reverse(2, w);
	ok &= ( r[2 * s + 1] == 0. );  // d^2 x / (ds ds)
	ok &= ( r[2 * t + 1] == 0. );  // d^2 x / (ds dt)

	return ok;
}

bool SubEqTestTwo(void)
{	bool ok = true;

	using namespace CppAD;

	// independent variable vector
	double u0 = .5;
	CPPAD_TESTVECTOR(AD<double>) U(1);
	U[0]      = u0;
	Independent(U);

	// dependent variable vector
	CPPAD_TESTVECTOR(AD<double>) Z(1);
	Z[0] = U[0];       // initial value
	Z[0] -= 2;         // AD<double> -= int
	Z[0] -= 4.;        // AD<double> -= double
	Z[0] -= 2 * U[0];  // AD<double> -= AD<double>

	// create f: U -> Z and vectors used for derivative calculations
	ADFun<double> f(U, Z);
	CPPAD_TESTVECTOR(double) v(1);
	CPPAD_TESTVECTOR(double) w(1);

	// check value
	ok &= NearEqual(Z[0] , u0-2-4-2*u0,  1e-10 , 1e-10);

	// forward computation of partials w.r.t. u
	size_t j;
	size_t p     = 5;
	double jfac  = 1.;
	double value = -1.;
	v[0]         = 1.;
	for(j = 1; j < p; j++)
	{	jfac *= j;
		w     = f.Forward(j, v);
		ok &= NearEqual(jfac*w[0], value, 1e-10 , 1e-10); // d^jz/du^j
		v[0]  = 0.;
		value = 0.;
	}

	// reverse computation of partials of Taylor coefficients
	CPPAD_TESTVECTOR(double) r(p);
	w[0]  = 1.;
	r     = f.Reverse(p, w);
	jfac  = 1.;
	value = -1.;
	for(j = 0; j < p; j++)
	{	ok &= NearEqual(jfac*r[j], value, 1e-10 , 1e-10); // d^jz/du^j
		jfac *= (j + 1);
		value = 0.;
	}

	return ok;
}

} // END empty namespace

bool SubEq(void)
{	bool ok = true;
	ok &= SubEqTestOne();
	ok &= SubEqTestTwo();
	return ok;
}
