/* $Id: pow.cpp 3735 2015-10-01 13:43:46Z 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.
-------------------------------------------------------------------------- */

/*
$begin pow.cpp$$
$spell
$$

$section The AD Power Function: Example and Test$$

$code
$verbatim%example/pow.cpp%0%// BEGIN C++%// END C++%1%$$
$$

$end
*/
// BEGIN C++

# include <cppad/cppad.hpp>
# include <cmath>

bool pow(void)
{	bool ok = true;

	using CppAD::AD;
	using CppAD::NearEqual;
	double eps = 10. * std::numeric_limits<double>::epsilon();

	// domain space vector
	size_t n  = 2;
	double x = 0.5;
	double y = 2.;
	CPPAD_TESTVECTOR(AD<double>) axy(n);
	axy[0]      = x;
	axy[1]      = y;

	// declare independent variables and start tape recording
	CppAD::Independent(axy);

	// range space vector
	size_t m = 3;
	CPPAD_TESTVECTOR(AD<double>) az(m);
	az[0] = CppAD::pow(axy[0], axy[1]); // pow(variable, variable)
	az[1] = CppAD::pow(axy[0], y);      // pow(variable, parameter)
	az[2] = CppAD::pow(x,     axy[1]);  // pow(parameter, variable)

	// create f: axy -> az and stop tape recording
	CppAD::ADFun<double> f(axy, az);

	// check value
	double check = std::pow(x, y);
	size_t i;
	for(i = 0; i < m; i++)
		ok &= NearEqual(az[i] , check,  eps, eps);

	// forward computation of first partial w.r.t. x
	CPPAD_TESTVECTOR(double) dxy(n);
	CPPAD_TESTVECTOR(double) dz(m);
	dxy[0] = 1.;
	dxy[1] = 0.;
	dz    = f.Forward(1, dxy);
	check = y * std::pow(x, y-1.);
	ok   &= NearEqual(dz[0], check, eps, eps);
	ok   &= NearEqual(dz[1], check, eps, eps);
	ok   &= NearEqual(dz[2],    0., eps, eps);

	// forward computation of first partial w.r.t. y
	dxy[0] = 0.;
	dxy[1] = 1.;
	dz    = f.Forward(1, dxy);
	check = std::log(x) * std::pow(x, y);
	ok   &= NearEqual(dz[0], check, eps, eps);
	ok   &= NearEqual(dz[1],    0., eps, eps);
	ok   &= NearEqual(dz[2], check, eps, eps);

	// reverse computation of derivative of z[0] + z[1] + z[2]
	CPPAD_TESTVECTOR(double)  w(m);
	CPPAD_TESTVECTOR(double) dw(n);
	w[0]  = 1.;
	w[1]  = 1.;
	w[2]  = 1.;
	dw    = f.Reverse(1, w);
	check = y * std::pow(x, y-1.);
	ok   &= NearEqual(dw[0], 2. * check, eps, eps);
	check = std::log(x) * std::pow(x, y);
	ok   &= NearEqual(dw[1], 2. * check, eps, eps);

	// use a VecAD<Base>::reference object with pow
	CppAD::VecAD<double> v(2);
	AD<double> zero(0);
	AD<double> one(1);
	v[zero]           = axy[0];
	v[one]            = axy[1];
	AD<double> result = CppAD::pow(v[zero], v[one]);
	ok               &= NearEqual(result, az[0], eps, eps);

	return ok;
}

// END C++
