// $Id: div_eq.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.
-------------------------------------------------------------------------- */

/*
Old DivEq example now used just for valiadation testing
*/
# include <cppad/cppad.hpp>

namespace { // BEGIN empty namespace

bool DivEqTestOne(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;

	// some constants
	AD<double> zero = 0.;
	AD<double> one  = 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
	zero /= Z[y]; // divide into a parameter equal to zero
	Z[y] /= one;  // divide by a parameter equal to one
	Z[y] /= 1.;   // divide by a double equal to one

	// check that zero is still a parameter
	// (must do this before creating f because it erases the tape)
	ok &= Parameter(zero);

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

	// check that none of the components of f are parameters
	size_t i;
	for(i = 0; i < f.Range(); i++)
		ok &= ! f.Parameter(i);

	// check functin values
	ok &= NearEqual(Z[x] , 3. / 2. , 1e-10, 1e-10);
	ok &= NearEqual(Z[y] , 2. / 5. , 1e-10, 1e-10);

	// forward computation of partials w.r.t. t
	v[s] = 0.;
	v[t] = 1.;
	w    = f.Forward(1, v);
	ok &= NearEqual(w[x] , -1.*U[s]/(U[t]*U[t]) , 1e-10, 1e-10); // dx/dt
	ok &= NearEqual(w[y] , 1. / 5.              , 1e-10, 1e-10); // 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 &= NearEqual(r[2 * s + 1]                 // d^2 x / (dt ds)
		 , - 1. / (U[t] * U[t])     , 1e-10 , 1e-10 );
	ok &= NearEqual(r[2 * t + 1]                 // d^2 x / (dt dt)
		, 2. * U[s] / (U[t] * U[t] * U[t])  , 1e-10 , 1e-10 );

	return ok;
}

bool DivEqTestTwo(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] * U[0]; // initial value
	Z[0] /= 2;          // AD<double> /= int
	Z[0] /= 4.;         // AD<double> /= double
	Z[0] /= 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*u0/(2*4*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./8.;
	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./8.;
	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 DivEq(void)
{	bool ok = true;
	ok &= DivEqTestOne();
	ok &= DivEqTestTwo();
	return ok;
}
