/* $Id: cond_exp.cpp 3666 2015-02-28 16:54:17Z 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.
-------------------------------------------------------------------------- */

/*
Comprehensive test built on 08/07 for new user interface to CondExp
*/
// BEGIN C++

# include <cppad/cppad.hpp>

namespace { // Begin empty namespace

bool CondExp_pvvv(void)
{	bool ok = true;

	using namespace CppAD;

	// independent variable vector
	CPPAD_TESTVECTOR(AD<double>) X(3);
	X[0]     = 0.;
	X[1]     = 1.;
	X[2]     = 2.;
	Independent(X);

	// parameter value
	AD<double> one = 1.;

	// dependent variable vector
	CPPAD_TESTVECTOR(AD<double>) Y(5);

	// CondExp(parameter, variable, variable, variable)
	Y[0] = CondExpLt(one, X[0], X[1], X[2]);
	Y[1] = CondExpLe(one, X[0], X[1], X[2]);
	Y[2] = CondExpEq(one, X[0], X[1], X[2]);
	Y[3] = CondExpGe(one, X[0], X[1], X[2]);
	Y[4] = CondExpGt(one, X[0], X[1], X[2]);

	// create f: X -> Y
	ADFun<double> f(X, Y);

	// vectors for function values
	CPPAD_TESTVECTOR(double) v( f.Domain() );
	CPPAD_TESTVECTOR(double) w( f.Range() );

	// vectors for derivative values
	CPPAD_TESTVECTOR(double) dv( f.Domain() );
	CPPAD_TESTVECTOR(double) dw( f.Range() );

	// check original function values
	ok &= Y[0] == X[2];
	ok &= Y[1] == X[2];
	ok &= Y[2] == X[2];
	ok &= Y[3] == X[1];
	ok &= Y[4] == X[1];

	// function values
	v[0] = 2.;
	v[1] = 1.;
	v[2] = 0.;
	w    = f.Forward(0, v);
	ok &= ( w[0] == v[1] );
	ok &= ( w[1] == v[1] );
	ok &= ( w[2] == v[2] );
	ok &= ( w[3] == v[2] );
	ok &= ( w[4] == v[2] );

	// forward mode derivative values
	dv[0] = 1.;
	dv[1] = 2.;
	dv[2] = 3.;
	dw    = f.Forward(1, dv);
	ok   &= (dw[0] == dv[1] );
	ok   &= (dw[1] == dv[1] );
	ok   &= (dw[2] == dv[2] );
	ok   &= (dw[3] == dv[2] );
	ok   &= (dw[4] == dv[2] );

	// reverse mode derivative values
	dw[0] = 1.;
	dw[1] = 2.;
	dw[2] = 3.;
	dw[3] = 4.;
	dw[4] = 5.;
	dv    = f.Reverse(1, dw);
	ok   &= (dv[0] == 0.);
	ok   &= (dv[1] == dw[0] + dw[1] );
	ok   &= (dv[2] == dw[2] + dw[3] + dw[4] );

	return ok;
}
bool CondExp_vpvv(void)
{	bool ok = true;

	using namespace CppAD;

	// independent variable vector
	CPPAD_TESTVECTOR(AD<double>) X(3);
	X[0]     = 0.;
	X[1]     = 1.;
	X[2]     = 2.;
	Independent(X);

	// parameter value
	AD<double> one = 1.;

	// dependent variable vector
	CPPAD_TESTVECTOR(AD<double>) Y(5);

	// CondExp(variable, parameter, variable, variable)
	Y[0] = CondExpLt(X[0], one, X[1], X[2]);
	Y[1] = CondExpLe(X[0], one, X[1], X[2]);
	Y[2] = CondExpEq(X[0], one, X[1], X[2]);
	Y[3] = CondExpGe(X[0], one, X[1], X[2]);
	Y[4] = CondExpGt(X[0], one, X[1], X[2]);

	// create f: X -> Y
	ADFun<double> f(X, Y);

	// vectors for function values
	CPPAD_TESTVECTOR(double) v( f.Domain() );
	CPPAD_TESTVECTOR(double) w( f.Range() );

	// vectors for derivative values
	CPPAD_TESTVECTOR(double) dv( f.Domain() );
	CPPAD_TESTVECTOR(double) dw( f.Range() );

	// check original function values
	ok &= Y[0] == X[1];
	ok &= Y[1] == X[1];
	ok &= Y[2] == X[2];
	ok &= Y[3] == X[2];
	ok &= Y[4] == X[2];

	// function values
	v[0] = 2.;
	v[1] = 1.;
	v[2] = 0.;
	w    = f.Forward(0, v);
	ok &= ( w[0] == v[2] );
	ok &= ( w[1] == v[2] );
	ok &= ( w[2] == v[2] );
	ok &= ( w[3] == v[1] );
	ok &= ( w[4] == v[1] );

	// forward mode derivative values
	dv[0] = 1.;
	dv[1] = 2.;
	dv[2] = 3.;
	dw    = f.Forward(1, dv);
	ok   &= (dw[0] == dv[2] );
	ok   &= (dw[1] == dv[2] );
	ok   &= (dw[2] == dv[2] );
	ok   &= (dw[3] == dv[1] );
	ok   &= (dw[4] == dv[1] );

	// reverse mode derivative values
	dw[0] = 1.;
	dw[1] = 2.;
	dw[2] = 3.;
	dw[3] = 4.;
	dw[4] = 5.;
	dv    = f.Reverse(1, dw);
	ok   &= (dv[0] == 0.);
	ok   &= (dv[1] == dw[3] + dw[4] );
	ok   &= (dv[2] == dw[0] + dw[1] + dw[2] );

	return ok;
}
bool CondExp_vvpv(void)
{	bool ok = true;

	using namespace CppAD;

	// independent variable vector
	CPPAD_TESTVECTOR(AD<double>) X(3);
	X[0]     = 0.;
	X[1]     = 1.;
	X[2]     = 2.;
	Independent(X);

	// parameter value
	AD<double> three = 3.;

	// dependent variable vector
	CPPAD_TESTVECTOR(AD<double>) Y(5);

	// CondExp(variable, variable, parameter, variable)
	Y[0] = CondExpLt(X[0], X[1], three, X[2]);
	Y[1] = CondExpLe(X[0], X[1], three, X[2]);
	Y[2] = CondExpEq(X[0], X[1], three, X[2]);
	Y[3] = CondExpGe(X[0], X[1], three, X[2]);
	Y[4] = CondExpGt(X[0], X[1], three, X[2]);

	// create f: X -> Y
	ADFun<double> f(X, Y);

	// vectors for function values
	CPPAD_TESTVECTOR(double) v( f.Domain() );
	CPPAD_TESTVECTOR(double) w( f.Range() );

	// vectors for derivative values
	CPPAD_TESTVECTOR(double) dv( f.Domain() );
	CPPAD_TESTVECTOR(double) dw( f.Range() );

	// check original function values
	ok &= Y[0] == three;
	ok &= Y[1] == three;
	ok &= Y[2] == X[2];
	ok &= Y[3] == X[2];
	ok &= Y[4] == X[2];

	// function values
	v[0] = 2.;
	v[1] = 1.;
	v[2] = 0.;
	w    = f.Forward(0, v);
	ok &= ( w[0] == v[2] );
	ok &= ( w[1] == v[2] );
	ok &= ( w[2] == v[2] );
	ok &= ( w[3] == three );
	ok &= ( w[4] == three );

	// forward mode derivative values
	dv[0] = 1.;
	dv[1] = 2.;
	dv[2] = 3.;
	dw    = f.Forward(1, dv);
	ok   &= (dw[0] == dv[2] );
	ok   &= (dw[1] == dv[2] );
	ok   &= (dw[2] == dv[2] );
	ok   &= (dw[3] == 0.    );
	ok   &= (dw[4] == 0.    );

	// reverse mode derivative values
	dw[0] = 1.;
	dw[1] = 2.;
	dw[2] = 3.;
	dw[3] = 4.;
	dw[4] = 5.;
	dv    = f.Reverse(1, dw);
	ok   &= (dv[0] == 0.);
	ok   &= (dv[1] == 0.);
	ok   &= (dv[2] == dw[0] + dw[1] + dw[2] );

	return ok;
}
bool CondExp_vvvp(void)
{	bool ok = true;

	using namespace CppAD;

	// independent variable vector
	CPPAD_TESTVECTOR(AD<double>) X(3);
	X[0]     = 0.;
	X[1]     = 1.;
	X[2]     = 2.;
	Independent(X);

	// parameter value
	AD<double> three = 3.;

	// dependent variable vector
	CPPAD_TESTVECTOR(AD<double>) Y(5);

	// CondExp(variable, variable, variable, parameter)
	Y[0] = CondExpLt(X[0], X[1], X[2], three);
	Y[1] = CondExpLe(X[0], X[1], X[2], three);
	Y[2] = CondExpEq(X[0], X[1], X[2], three);
	Y[3] = CondExpGe(X[0], X[1], X[2], three);
	Y[4] = CondExpGt(X[0], X[1], X[2], three);

	// create f: X -> Y
	ADFun<double> f(X, Y);

	// vectors for function values
	CPPAD_TESTVECTOR(double) v( f.Domain() );
	CPPAD_TESTVECTOR(double) w( f.Range() );

	// vectors for derivative values
	CPPAD_TESTVECTOR(double) dv( f.Domain() );
	CPPAD_TESTVECTOR(double) dw( f.Range() );

	// check original function values
	ok &= Y[0] == X[2];
	ok &= Y[1] == X[2];
	ok &= Y[2] == three;
	ok &= Y[3] == three;
	ok &= Y[4] == three;

	// function values
	v[0] = 2.;
	v[1] = 1.;
	v[2] = 0.;
	w    = f.Forward(0, v);
	ok &= ( w[0] == three );
	ok &= ( w[1] == three );
	ok &= ( w[2] == three );
	ok &= ( w[3] == v[2]  );
	ok &= ( w[4] == v[2]  );

	// forward mode derivative values
	dv[0] = 1.;
	dv[1] = 2.;
	dv[2] = 3.;
	dw    = f.Forward(1, dv);
	ok   &= (dw[0] == 0.    );
	ok   &= (dw[1] == 0.    );
	ok   &= (dw[2] == 0.    );
	ok   &= (dw[3] == dv[2] );
	ok   &= (dw[4] == dv[2] );

	// reverse mode derivative values
	dw[0] = 1.;
	dw[1] = 2.;
	dw[2] = 3.;
	dw[3] = 4.;
	dw[4] = 5.;
	dv    = f.Reverse(1, dw);
	ok   &= (dv[0] == 0.);
	ok   &= (dv[1] == 0.);
	ok   &= (dv[2] == dw[3] + dw[4] );

	return ok;
}

# include <limits>
bool SecondOrderReverse(void)
{	// Bradley M. Bell 2009-07-04
	// Reverse mode for CExpOp was only modifying the highest order partial
	// This test demonstrated the bug
	bool ok = true;
	using CppAD::AD;
	using CppAD::NearEqual;
	double eps = 10. * std::numeric_limits<double>::epsilon();

	size_t n = 1;
	CPPAD_TESTVECTOR(AD<double>) X(n);
	X[0] = 2.;
	CppAD::Independent(X);

	size_t m = 2;
	CPPAD_TESTVECTOR(AD<double>) Y(m);

	AD<double> left = X[0];
	AD<double> right = X[0] * X[0];
	AD<double> exp_if_true  = left;
	AD<double> exp_if_false = right;

	// Test of reverse mode using exp_if_true case
	// For this value of X, should be the same as Z = X[0]
	AD<double> Z = CondExpLt(left, right, exp_if_true, exp_if_false);
	Y[0] = Z * Z;

	// Test of reverse mode  using exp_if_false case
	exp_if_false = left;
	exp_if_true  = right;
	Z            = CondExpGt(left, right, exp_if_true, exp_if_false);
	Y[1]         = Z * Z;

	CppAD::ADFun<double> f(X, Y);

	// first order forward
	CPPAD_TESTVECTOR(double) dx(n);
	size_t p = 1;
	dx[0]    = 1.;
	f.Forward(p, dx);

	// second order reverse (test exp_if_true case)
	CPPAD_TESTVECTOR(double) w(m), dw(2 * n);
	w[0] = 1.;
	w[1] = 0.;
	p    = 2;
	dw = f.Reverse(p, w);

	// check first derivative in dw
	double check = 2. * Value( X[0] );
	ok &= NearEqual(dw[0], check, eps, eps);

	// check second derivative in dw
	check = 2.;
	ok &= NearEqual(dw[1], check, eps, eps);

	// test exp_if_false case
	w[0] = 0.;
	w[1] = 1.;
	p    = 2;
	dw = f.Reverse(p, w);

	// check first derivative in dw
	check = 2. * Value( X[0] );
	ok &= NearEqual(dw[0], check, eps, eps);

	// check second derivative in dw
	check = 2.;
	ok &= NearEqual(dw[1], check, eps, eps);

	return ok;
}

double Infinity(double zero)
{       return 1. / zero; }

bool OldExample(void)
{	bool ok = true;

	using CppAD::AD;
	using CppAD::NearEqual;
	using CppAD::log;
	using CppAD::abs;
	double eps = 100. * std::numeric_limits<double>::epsilon();

	// domain space vector
	size_t n = 5;
	CPPAD_TESTVECTOR(AD<double>) X(n);
	size_t j;
	for(j = 0; j < n; j++)
		X[j] = 1.;

	// declare independent variables and start tape recording
	CppAD::Independent(X);

	// sum with respect to j of log of absolute value of X[j]
	// sould be - infinity if any of the X[j] are zero
	AD<double> MinusInfinity = - Infinity(0.);
	AD<double> Sum           = 0.;
	AD<double> Zero(0);
	for(j = 0; j < n; j++)
	{	// if X[j] > 0
		Sum += CppAD::CondExpGt(X[j], Zero, log(X[j]),     Zero);

		// if X[j] < 0
		Sum += CppAD::CondExpLt(X[j], Zero, log(-X[j]),    Zero);

		// if X[j] == 0
		Sum += CppAD::CondExpEq(X[j], Zero, MinusInfinity, Zero);
	}

	// range space vector
	size_t m = 1;
	CPPAD_TESTVECTOR(AD<double>) Y(m);
	Y[0] = Sum;

	// create f: X -> Y and stop tape recording
	CppAD::ADFun<double> f(X, Y);

	// 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 abs( x[j] ) > 0 for all j
	double check  = 0.;
	double sign   = 1.;
	for(j = 0; j < n; j++)
	{	sign *= -1.;
		x[j] = sign * double(j + 1);
		check += log( abs( x[j] ) );
	}

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

	// compute 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], 1./abs( x[j] ), eps, eps);
		else	ok &= NearEqual(dw[j], -1./abs( x[j] ), eps, eps);
	}

	// a case where x[0] is equal to zero
	sign = 1.;
	for(j = 0; j < n; j++)
	{	sign *= -1.;
		x[j] = sign * double(j);
	}

	// function value
	y   = f.Forward(0, x);
	ok &= ( y[0] == -Infinity(0.) );

	// compute 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], 1./abs( x[j] ), eps, eps);
		else if( x[j] < 0. )
			ok &= NearEqual(dw[j], -1./abs( x[j] ), eps, eps);
		else
			ok &= NearEqual(dw[j], 0.0, eps, eps);
	}

	return ok;
}
} // end empty namespace

bool CondExp(void)
{	bool ok  = true;
	ok      &= CondExp_pvvv();
	ok      &= CondExp_vpvv();
	ok      &= CondExp_vvpv();
	ok      &= CondExp_vvvp();
	ok      &= SecondOrderReverse();
	ok      &= OldExample();
	return ok;
}
// END C++
