/* $Id: fun_check.cpp 3214 2014-03-18 20:50:38Z bradbell $ */
/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-14 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.
-------------------------------------------------------------------------- */
/*
! WARNING: This file is used as an example by FunConstruct and Dependent

$begin fun_check.cpp$$
$spell
	abs
$$

$section ADFun Check and Re-Tape: Example and Test$$

$index FunCheck, example$$
$index example, FunCheck$$
$index test, FunCheck$$

$index ADFun, example$$
$index example, ADFun$$
$index test, ADFun$$

$index Dependent, example$$
$index example, Dependent$$
$index test, Dependent$$

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

$end
*/
// BEGIN C++
# include <cppad/cppad.hpp>

namespace { // -----------------------------------------------------------
// define the template function object Fun<Type,Vector> in empty namespace
template <class Type, class Vector>
class Fun {
private:
	size_t n;
public:
	// function constructor
	Fun(size_t n_) : n(n_)
	{ }
	// function evaluator
	Vector operator() (const Vector &x)
	{	Vector y(n);
		size_t i;
		for(i = 0; i < n; i++)
		{	// This operaiton sequence depends on x
			if( x[i] >= 0 ) 
				y[i] = exp(x[i]);
			else	y[i] = exp(-x[i]);
		}
		return y;
	}	
};
// template function FunCheckCases<Vector, ADVector> in empty namespace
template <class Vector, class ADVector>
bool FunCheckCases(void)
{	bool ok = true;
	using CppAD::AD;
	using CppAD::ADFun;
	using CppAD::Independent;

	// use the ADFun default constructor
	ADFun<double> f;

	// domain space vector
	size_t n = 2;
	ADVector X(n);
	X[0] = -1.;
	X[1] = 1.;

	// declare independent variables and starting recording
	Independent(X);

	// create function object to use with AD<double>
	Fun< AD<double>, ADVector > G(n);

	// range space vector
	size_t m = n;
	ADVector Y(m);
	Y = G(X);

	// stop tape and store operation sequence in f : X -> Y
	f.Dependent(X, Y);
	ok &= (f.size_order() == 0);  // no implicit forward operation

	// create function object to use with double
	Fun<double, Vector> g(n);

	// function values should agree when the independent variable 
	// values are the same as during recording
	Vector x(n);
	size_t j;
	for(j = 0; j < n; j++)
		x[j] = Value(X[j]);
	double r = 1e-10; 
	double a = 1e-10;
	ok      &= FunCheck(f, g, x, a, r);

	// function values should not agree when the independent variable
	// values are the negative of values during recording
	for(j = 0; j < n; j++)
		x[j] = - Value(X[j]);
	ok      &= ! FunCheck(f, g, x, a, r);

	// re-tape to obtain the new AD of double operation sequence
	for(j = 0; j < n; j++)
		X[j] = x[j];
	Independent(X);
	Y = G(X);

	// stop tape and store operation sequence in f : X -> Y
	f.Dependent(X, Y);
	ok &= (f.size_order() == 0);  // no implicit forward with this x

	// function values should agree now
	ok      &= FunCheck(f, g, x, a, r);

	return ok;
}
} // End empty namespace 
# include <vector>
# include <valarray>
bool FunCheck(void)
{	bool ok = true;
	typedef CppAD::vector<double>                Vector1;
	typedef CppAD::vector< CppAD::AD<double> > ADVector1;
	typedef   std::vector<double>                Vector2;
	typedef   std::vector< CppAD::AD<double> > ADVector2;
	typedef std::valarray<double>                Vector3;
	typedef std::valarray< CppAD::AD<double> > ADVector3;
	// Run with Vector and ADVector equal to three different cases
	// all of which are Simple Vectors with elements of type 
	// double and AD<double> respectively.
	ok &= FunCheckCases< Vector1, ADVector2 >();
	ok &= FunCheckCases< Vector2, ADVector3 >();
	ok &= FunCheckCases< Vector3, ADVector1 >();
	return ok;
}
// END C++