// $Id: forward_dir.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.
-------------------------------------------------------------------------- */

/*
$begin forward_dir.cpp$$
$spell
	Cpp
$$

$section Forward Mode: Example and Test of Multiple Directions$$
$mindex orders order$$

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

$end
*/
// BEGIN C++
# include <limits>
# include <cppad/cppad.hpp>
bool forward_dir(void)
{	bool ok = true;
	using CppAD::AD;
	using CppAD::NearEqual;
	double eps = 10. * std::numeric_limits<double>::epsilon();
	size_t j;

	// domain space vector
	size_t n = 3;
	CPPAD_TESTVECTOR(AD<double>) ax(n);
	ax[0] = 0.;
	ax[1] = 1.;
	ax[2] = 2.;

	// declare independent variables and starting recording
	CppAD::Independent(ax);

	// range space vector
	size_t m = 1;
	CPPAD_TESTVECTOR(AD<double>) ay(m);
	ay[0] = ax[0] * ax[1] * ax[2];

	// create f: x -> y and stop tape recording
	CppAD::ADFun<double> f(ax, ay);

	// initially, the variable values during taping are stored in f
	ok &= f.size_order() == 1;

	// zero order Taylor coefficients
	CPPAD_TESTVECTOR(double) x0(n), y0;
	for(j = 0; j < n; j++)
		x0[j] = double(j+1);
	y0          = f.Forward(0, x0);
	ok         &= size_t( y0.size() ) == m;
	double y_0  = 1.*2.*3.;
	ok         &= NearEqual(y0[0], y_0, eps, eps);

	// first order Taylor coefficients
	size_t r = 2, ell;
	CPPAD_TESTVECTOR(double) x1(r*n), y1;
	for(ell = 0; ell < r; ell++)
	{	for(j = 0; j < n; j++)
			x1[ r * j + ell ] = double(j + 1 + ell);
	}
	y1  = f.Forward(1, r, x1);
	ok &= size_t( y1.size() ) == r*m;

	// secondorder Taylor coefficients
	CPPAD_TESTVECTOR(double) x2(r*n), y2;
	for(ell = 0; ell < r; ell++)
	{	for(j = 0; j < n; j++)
			x2[ r * j + ell ] = 0.0;
	}
	y2  = f.Forward(2, r, x2);
	ok &= size_t( y2.size() ) == r*m;
	//
	// Y_0 (t)     = F[X_0(t)]
	//             =  (1 + 1t)(2 + 2t)(3 + 3t)
	double y_1_0   = 1.*2.*3. + 2.*1.*3. + 3.*1.*2.;
	double y_2_0   = 1.*2.*3. + 2.*1.*3. + 3.*1.*2.;
	//
	// Y_1 (t)     = F[X_1(t)]
	//             =  (1 + 2t)(2 + 3t)(3 + 4t)
	double y_1_1   = 2.*2.*3. + 3.*1.*3. + 4.*1.*2.;
	double y_2_1   = 1.*3.*4. + 2.*2.*4. + 3.*2.*3.;
	//
	ok  &= NearEqual(y1[0] , y_1_0, eps, eps);
	ok  &= NearEqual(y1[1] , y_1_1, eps, eps);
	ok  &= NearEqual(y2[0] , y_2_0, eps, eps);
	ok  &= NearEqual(y2[1] , y_2_1, eps, eps);
	//
	// check number of orders
	ok   &= f.size_order() == 3;
	//
	// check number of directions
	ok   &= f.size_direction() == 2;
	//
	return ok;
}
// END C++
