// $Id: mul.cpp 3785 2016-02-08 12:53:06Z 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.
-------------------------------------------------------------------------- */

/*
Two old Mul examples now used just for valiadation testing
*/
# include <cppad/cppad.hpp>

namespace { // BEGIN empty namespace

bool MulTestOne(void)
{	bool ok = true;

	using namespace CppAD;

	// independent variable vector, indices, values, and declaration
	CPPAD_TESTVECTOR(AD<double>) U(2);
	size_t s = 0;
	size_t t = 1;
	U[s]     = 3.;
	U[t]     = 2.;
	Independent(U);

	// assign some parameters
	AD<double> zero = 0.;
	AD<double> one  = 1.;

	// dependent variable vector and indices
	CPPAD_TESTVECTOR(AD<double>) Z(5);
	size_t x = 0;
	size_t y = 1;
	size_t z = 2;
	size_t u = 3;
	size_t v = 4;

	// assign the dependent variables
	Z[x] = U[s] * U[t];   // AD<double> * AD<double>
	Z[y] = Z[x] * 4.;     // AD<double> *    double
	Z[z] = 4.   * Z[y];   //    double  * AD<double>
	Z[u] =  one * Z[z];   // multiplication by parameter equal to one
	Z[v] = zero * Z[z];   // multiplication by parameter equal to zero

	// check multipilcation by zero results in a parameter
	ok &= Parameter(Z[v]);

	// create f: U -> Z and vectors used for derivative calculations
	ADFun<double> f(U, Z);
	CPPAD_TESTVECTOR(double) q( f.Domain() );
	CPPAD_TESTVECTOR(double) r( f.Range() );

	// check parameter flag
	ok &= f.Parameter(v);

	// check values
	ok &= ( Z[x] == 3. * 2. );
	ok &= ( Z[y] == 3. * 2. * 4. );
	ok &= ( Z[z] == 4. * 3. * 2. * 4. );
	ok &= ( Z[u] == Z[z] );
	ok &= ( Z[v] == 0. );

	// forward computation of partials w.r.t. s
	q[s] = 1.;
	q[t] = 0.;
	r    = f.Forward(1, q);
	ok &= ( r[x] == U[t] );           // dx/ds
	ok &= ( r[y] == U[t] * 4. );      // dy/ds
	ok &= ( r[z] == 4. * U[t] * 4. ); // dz/ds
	ok &= ( r[u] == r[z] );           // du/ds
	ok &= ( r[v] == 0. );             // dv/ds

	// reverse computation of second partials of z
	CPPAD_TESTVECTOR(double) d2( f.Domain() * 2 );
	r[x] = 0.;
	r[y] = 0.;
	r[z] = 1.;
	r[u] = 0.;
	r[v] = 0.;
	d2   = f.Reverse(2, r);

	// check second order partials
	ok &= ( d2[2 * s + 1] == 0. );             // d^2 z / (ds ds)
	ok &= ( d2[2 * t + 1] == 4. * 4. );        // d^2 z / (ds dt)

	return ok;
}

bool MulTestTwo(void)
{	bool ok = true;

	using namespace CppAD;

	// independent variable vector
	double u0 = .5;
	CPPAD_TESTVECTOR(AD<double>) U(1);
	U[0]      = u0;
	Independent(U);

	AD<double> a = U[0] * 1.; // AD<double> * double
	AD<double> b = a  * 2;    // AD<double> * int
	AD<double> c = 3. * b;    // double     * AD<double>
	AD<double> d = 4  * c;    // int        * AD<double>

	// dependent variable vector
	CPPAD_TESTVECTOR(AD<double>) Z(1);
	Z[0] = U[0] * d;          // AD<double> * AD<double>

	// 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(Value(Z[0]) , u0*4*3*2*u0,  1e-10 , 1e-10);

	// forward computation of partials w.r.t. u
	size_t j;
	size_t p     = 5;
	double jfac  = 1.;
	v[0]         = 1.;
	for(j = 1; j < p; j++)
	{	double value;
		if( j == 1 )
			value = 48. * u0;
		else if( j == 2 )
			value = 48.;
		else	value = 0.;

		jfac *= j;
		w     = f.Forward(j, v);
		ok &= NearEqual(jfac*w[0], value, 1e-10 , 1e-10); // d^jz/du^j
		v[0]  = 0.;
	}

	// reverse computation of partials of Taylor coefficients
	CPPAD_TESTVECTOR(double) r(p);
	w[0]  = 1.;
	r     = f.Reverse(p, w);
	jfac  = 1.;
	for(j = 0; j < p; j++)
	{	double value;
		if( j == 0 )
			value = 48. * u0;
		else if( j == 1 )
			value = 48.;
		else	value = 0.;

		ok &= NearEqual(jfac*r[j], value, 1e-10 , 1e-10); // d^jz/du^j
		jfac *= (j + 1);
	}

	return ok;
}

} // END empty namespace

bool Mul(void)
{	bool ok = true;
	ok &= MulTestOne();
	ok &= MulTestTwo();
	return ok;
}
