/* $Id: log.cpp 3684 2015-05-10 14:01:21Z 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 log examples now used just for validation testing
*/

# include <cppad/cppad.hpp>

namespace { // BEGIN empty namespace

bool LogTestOne(void)
{	bool ok = true;

	using CppAD::log;
	using namespace CppAD;

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

	// dependent variable vector, indices, and values
	CPPAD_TESTVECTOR(AD<double>) Z(2);
	size_t x = 0;
	size_t y = 1;
	Z[x]     = log(U[s]);
	Z[y]     = log(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] , log(2.),  1e-10 , 1e-10);
	ok &= NearEqual(Z[y] , log( log(2.) ),  1e-10 , 1e-10);

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

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

	using CppAD::log;
	using namespace CppAD;

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

	// a temporary values
	AD<double> x = exp(U[0]);

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

	// 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(U[0] , Z[0],  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 log(void)
{	bool ok = true;
	ok &= LogTestOne();
	ok &= LogTestTwo();
	return ok;
}
