/* $Id: acos.cpp 2506 2012-10-24 19:36:49Z bradbell $ */
/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-12 Bradley M. Bell

CppAD is distributed under multiple licenses. This distribution is under
the terms of the 
                    Eclipse Public License Version 1.0.

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.
-------------------------------------------------------------------------- */

/*
Old Acos examples now used just for valiadation testing
*/
# include <cppad/cppad.hpp>

bool Acos(void)
{	bool ok = true;

	using CppAD::acos;
	using namespace CppAD;

	// independent variable vector
	CPPAD_TESTVECTOR(AD<double>) U(1);
	U[0]     = .5;
	Independent(U);

	// a temporary values
	AD<double> x = cos(U[0]); 

	// dependent variable vector 
	CPPAD_TESTVECTOR(AD<double>) Z(1);
	Z[0] = acos(x); // acos( cos(u) )

	// create f: U -> Z and vectors used for derivative calculations
	ADFun<double> f(U, Z); 
	CPPAD_TESTVECTOR(double) v(1);
	CPPAD_TESTVECTOR(double) w(1);

	// check value 
	ok &= NearEqual(U[0] , Z[0],  1e-10 , 1e-10);

	// forward computation of partials w.r.t. u
	size_t j;
	size_t p     = 5;
	double jfac  = 1.;
	double value = 1.;
	v[0]         = 1.;
	for(j = 1; j < p; j++)
	{	jfac *= j;
		w     = f.Forward(j, v);	
		ok &= NearEqual(jfac*w[0], value, 1e-10 , 1e-10); // d^jz/du^j
		v[0]  = 0.;
		value = 0.;
	}

	// reverse computation of partials of Taylor coefficients
	CPPAD_TESTVECTOR(double) r(p); 
	w[0]  = 1.;
	r     = f.Reverse(p, w);
	jfac  = 1.;
	value = 1.;
	for(j = 0; j < p; j++)
	{	ok &= NearEqual(jfac*r[j], value, 1e-10 , 1e-10); // d^jz/du^j
		jfac *= (j + 1);
		value = 0.;
	}

	return ok;
}
