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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.cpp}
Forward Mode: Example and Test
##############################
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end forward.cpp}
*/
// BEGIN C++
# include <limits>
# include <cppad/cppad.hpp>
namespace { // --------------------------------------------------------
// define the template function ForwardCases<Vector> in empty namespace
template <class Vector>
bool ForwardCases(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;
CPPAD_TESTVECTOR(AD<double>) ax(n);
ax[0] = 0.;
ax[1] = 1.;
// 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[0] * ax[1];
// 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 forward mode using notation in forward_zero
// use the template parameter Vector for the vector type
Vector x0(n), y0(m);
x0[0] = 3.;
x0[1] = 4.;
y0 = f.Forward(0, x0);
ok &= NearEqual(y0[0] , x0[0]*x0[0]*x0[1], eps, eps);
ok &= f.size_order() == 1;
// first order forward mode using notation in forward_one
// X(t) = x0 + x1 * t
// Y(t) = F[X(t)] = y0 + y1 * t + o(t)
Vector x1(n), y1(m);
x1[0] = 1.;
x1[1] = 0.;
y1 = f.Forward(1, x1); // partial F w.r.t. x_0
ok &= NearEqual(y1[0] , 2.*x0[0]*x0[1], eps, eps);
ok &= f.size_order() == 2;
// second order forward mode using notation in forward_order
// X(t) = x0 + x1 * t + x2 * t^2
// Y(t) = F[X(t)] = y0 + y1 * t + y2 * t^2 + o(t^3)
Vector x2(n), y2(m);
x2[0] = 0.;
x2[1] = 0.;
y2 = f.Forward(2, x2);
double F_00 = 2. * y2[0]; // second partial F w.r.t. x_0, x_0
ok &= NearEqual(F_00, 2.*x0[1], eps, eps);
ok &= f.size_order() == 3;
return ok;
}
} // End empty namespace
# include <vector>
# include <valarray>
bool Forward(void)
{ bool ok = true;
// Run with Vector equal to three different cases
// all of which are Simple Vectors with elements of type double.
ok &= ForwardCases< CppAD::vector <double> >();
ok &= ForwardCases< std::vector <double> >();
ok &= ForwardCases< std::valarray <double> >();
return ok;
}
// END C++
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