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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 cond_exp.cpp}
Conditional Expressions: Example and Test
#########################################
See Also
********
:ref:`optimize_conditional_skip.cpp-name`
Description
***********
Use ``CondExp`` to compute
.. math::
f(x) = \sum_{j=0}^{m-1} x_j \log( x_j )
and its derivative at various argument values
( where :math:`x_j \geq 0` )
with out having to re-tape; i.e.,
using only one :ref:`ADFun-name` object.
Note that :math:`x_j \log ( x_j ) \rightarrow 0`
as :math:`x_j \downarrow 0` and
we need to handle the case :math:`x_j = 0`
in a special way to avoid returning zero times minus infinity.
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end cond_exp.cpp}
*/
// BEGIN C++
# include <cppad/cppad.hpp>
# include <limits>
bool CondExp(void)
{ bool ok = true;
using CppAD::isnan;
using CppAD::AD;
using CppAD::NearEqual;
using CppAD::log;
double eps = 100. * CppAD::numeric_limits<double>::epsilon();
// domain space vector
size_t n = 5;
CPPAD_TESTVECTOR(AD<double>) ax(n);
size_t j;
for(j = 0; j < n; j++)
ax[j] = 1.;
// declare independent variables and start tape recording
CppAD::Independent(ax);
AD<double> asum = 0.;
AD<double> azero = 0.;
for(j = 0; j < n; j++)
{ // if x_j > 0, add x_j * log( x_j ) to the sum
asum += CppAD::CondExpGt(ax[j], azero, ax[j] * log(ax[j]), azero);
}
// range space vector
size_t m = 1;
CPPAD_TESTVECTOR(AD<double>) ay(m);
ay[0] = asum;
// create f: x -> ay and stop tape recording
CppAD::ADFun<double> f(ax, ay);
// vectors for arguments to the function object f
CPPAD_TESTVECTOR(double) x(n); // argument values
CPPAD_TESTVECTOR(double) y(m); // function values
CPPAD_TESTVECTOR(double) w(m); // function weights
CPPAD_TESTVECTOR(double) dw(n); // derivative of weighted function
// a case where x[j] > 0 for all j
double check = 0.;
for(j = 0; j < n; j++)
{ x[j] = double(j + 1);
check += x[j] * log( x[j] );
}
// function value
y = f.Forward(0, x);
ok &= NearEqual(y[0], check, eps, eps);
// compute derivative of y[0]
w[0] = 1.;
dw = f.Reverse(1, w);
for(j = 0; j < n; j++)
ok &= NearEqual(dw[j], log(x[j]) + 1., eps, eps);
// a case where x[3] is equal to zero
check -= x[3] * log( x[3] );
x[3] = 0.;
ok &= std::isnan( x[3] * log( x[3] ) );
// function value
y = f.Forward(0, x);
ok &= NearEqual(y[0], check, eps, eps);
// check derivative of y[0]
w[0] = 1.;
dw = f.Reverse(1, w);
for(j = 0; j < n; j++)
{ if( x[j] > 0 )
ok &= NearEqual(dw[j], log(x[j]) + 1., eps, eps);
else
ok &= NearEqual(dw[j], 0.0, eps, eps);
}
return ok;
}
// END C++
|
