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// SPDX-License-Identifier: EPL-2.0 OR GPL-2.0-or-later
// SPDX-FileCopyrightText: Bradley M. Bell <bradbell@seanet.com>
// SPDX-FileContributor: 2003-22 Bradley M. Bell
// ----------------------------------------------------------------------------
/*
{xrst_begin forward_dir.cpp}
Forward Mode: Example and Test of Multiple Directions
#####################################################
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end forward_dir.cpp}
*/
// 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++
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