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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 fabs.cpp}
AD Absolute Value Function: Example and Test
############################################
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end fabs.cpp}
*/
// BEGIN C++
# include <cppad/cppad.hpp>
bool fabs(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
// domain space vector
size_t n = 1;
CPPAD_TESTVECTOR(AD<double>) ax(n);
ax[0] = 0.;
// declare independent variables and start tape recording
CppAD::Independent(ax);
// range space vector
size_t m = 3;
CPPAD_TESTVECTOR(AD<double>) ay(m);
ay[0] = fabs(ax[0] - 1.);
ay[1] = fabs(ax[0]);
ay[2] = fabs(ax[0] + 1.);
//
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f(ax, ay);
// check values
ok &= (ay[0] == 1.);
ok &= (ay[1] == 0.);
ok &= (ay[2] == 1.);
//
// forward computation of partials w.r.t. a positive x[0] direction
size_t p = 1;
CPPAD_TESTVECTOR(double) dx(n), dy(m);
dx[0] = 1.;
dy = f.Forward(p, dx);
ok &= (dy[0] == - dx[0]);
ok &= (dy[1] == 0. );
ok &= (dy[2] == + dx[0]);
//
// forward computation of partials w.r.t. a negative x[0] direction
dx[0] = -1.;
dy = f.Forward(p, dx);
ok &= (dy[0] == - dx[0]);
ok &= (dy[1] == 0. );
ok &= (dy[2] == + dx[0]);
//
// reverse computation of derivative of y[0]
p = 1;
CPPAD_TESTVECTOR(double) w(m), dw(n);
w[0] = 1.; w[1] = 0.; w[2] = 0;
dw = f.Reverse(p, w);
ok &= (dw[0] == -1.);
// reverse computation of derivative of y[1]
w[0] = 0.; w[1] = 1.; w[2] = 0;
dw = f.Reverse(p, w);
ok &= (dw[0] == 0.);
// reverse computation of derivative of y[3]
w[0] = 0.; w[1] = 0.; w[2] = 1;
dw = f.Reverse(p, w);
ok &= (dw[0] == 1.);
// use a VecAD<Base>::reference object with fabs
CppAD::VecAD<double> av(1);
AD<double> az(0);
av[az] = -1;
AD<double> a_result = fabs(av[az]);
ok &= a_result == 1.0;
return ok;
}
// END C++
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