// $Id: exp.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 exp example now used just for validation testing.
*/
# include <cppad/cppad.hpp>

# include <cmath>

namespace { // BEGIN empty namespace

bool ExpTestOne(void)
{	bool ok = true;

	using CppAD::exp;
	using namespace CppAD;

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

	// dependent variable vector, indices, and values
	CPPAD_TESTVECTOR(AD<double>) Z(2);
	size_t x = 0;
	size_t y = 1;
	Z[x]     = exp(U[s]);
	Z[y]     = exp(Z[x]);

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

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

	// forward computation of partials w.r.t. s
	v[s] = 1.;
	w    = f.Forward(1, v);
	ok &= NearEqual(w[x], Z[x],            1e-10 , 1e-10); // dx/ds
	ok &= NearEqual(w[y], Z[y] * Z[x],     1e-10 , 1e-10); // dy/ds

	// reverse computation of partials of y
	w[x] = 0.;
	w[y] = 1.;
	v    = f.Reverse(1,w);
	ok &= NearEqual(v[s], Z[y] * Z[x],     1e-10 , 1e-10); // dy/ds

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

	// reverse computation of second partials of y
	CPPAD_TESTVECTOR(double) r( f.Domain() * 2 );
	w[x] = 0.;
	w[y] = 1.;
	r    = f.Reverse(2, w);
	ok &= NearEqual(      // d^2 y / (ds ds)
		r[2 * s + 1] ,
		Z[y] * Z[x] * Z[x] + Z[y] * Z[x],
		1e-10 ,
		1e-10
	);

	return ok;
}
bool ExpTestTwo(void)
{	bool ok = true;

	using CppAD::exp;
	using namespace CppAD;

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

	// dependent variable vector
	CPPAD_TESTVECTOR(AD<double>) Z(1);
	Z[0] = exp(U[0]);

	// 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
	double exp_u = exp( Value(U[0]) );
	ok &= NearEqual(exp_u, Value(Z[0]),  1e-10 , 1e-10);

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

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

	return ok;
}

} // END empty namespace

bool Exp(void)
{	bool ok = true;
	ok &= ExpTestOne();
	ok &= ExpTestTwo();
	return ok;
}
