// $Id: cond_exp.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 cond_exp.cpp$$
$spell
	Cpp
	cstddef
	CondExp
$$

$section Conditional Expressions: Example and Test$$
$mindex CondExp$$


$head Description$$
Use $code CondExp$$ to compute
$latex \[
	f(x) = \sum_{j=0}^{m-1} x_j \log( x_j )
\] $$
and its derivative at various argument values
( where $latex x_j \geq 0$$ )
with out having to re-tape; i.e.,
using only one $cref ADFun$$ object.
Note that $latex x_j \log ( x_j ) \rightarrow 0 $$
as $latex x_j \downarrow 0$$ and
we need to handle the case $latex x_j = 0$$
in a special way to avoid multiplying zero by infinity.

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

$end
*/
// 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;
	using CppAD::abs;
	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.;

	// function value
	y   = f.Forward(0, x);
	ok &= NearEqual(y[0], check, eps, eps);

	// check derivative of y[0]
	f.check_for_nan(false);
	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
		{	// Note that in case where dw has type AD<double> and is a variable
			// this dw[j] can be nan (zero times nan is not zero).
			ok &= NearEqual(dw[j], 0.0, eps, eps);
		}
	}

	return ok;
}
// END C++
