Forward Mode: Example and Test of Multiple Directions
Keywords: forward mode: example test multiple directions orders order

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Forward Mode: Example and Test of Multiple Directions
`

    # include <limits>
    # include <cppad/cppad.hpp>
    bool forward_dir(void)
    {	bool ok = true;
    	using CppAD::AD;
    	using CppAD::NearEqual;
    	double eps = 10. * std::numeric_limits<double>::epsilon();
    	size_t j;

    	// domain space vector
    	size_t n = 3;
    	CPPAD_TESTVECTOR(AD<double>) ax(n);
    	ax[0] = 0.;
    	ax[1] = 1.;
    	ax[2] = 2.;

    	// declare independent variables and starting recording
    	CppAD::Independent(ax);

    	// range space vector
    	size_t m = 1;
    	CPPAD_TESTVECTOR(AD<double>) ay(m);
    	ay[0] = ax[0] * ax[1] * ax[2];

    	// create f: x -> y and stop tape recording
    	CppAD::ADFun<double> f(ax, ay);

    	// initially, the variable values during taping are stored in f
    	ok &= f.size_order() == 1;

    	// zero order Taylor coefficients
    	CPPAD_TESTVECTOR(double) x0(n), y0;
    	for(j = 0; j < n; j++)
    		x0[j] = double(j+1);
    	y0          = f.Forward(0, x0);
    	ok         &= size_t( y0.size() ) == m;
    	double y_0  = 1.*2.*3.;
    	ok         &= NearEqual(y0[0], y_0, eps, eps);

    	// first order Taylor coefficients
    	size_t r = 2, ell;
    	CPPAD_TESTVECTOR(double) x1(r*n), y1;
    	for(ell = 0; ell < r; ell++)
    	{	for(j = 0; j < n; j++)
    			x1[ r * j + ell ] = double(j + 1 + ell);
    	}
    	y1  = f.Forward(1, r, x1);
    	ok &= size_t( y1.size() ) == r*m;

    	// secondorder Taylor coefficients
    	CPPAD_TESTVECTOR(double) x2(r*n), y2;
    	for(ell = 0; ell < r; ell++)
    	{	for(j = 0; j < n; j++)
    			x2[ r * j + ell ] = 0.0;
    	}
    	y2  = f.Forward(2, r, x2);
    	ok &= size_t( y2.size() ) == r*m;
    	//
    	// Y_0 (t)     = F[X_0(t)]
    	//             =  (1 + 1t)(2 + 2t)(3 + 3t)
    	double y_1_0   = 1.*2.*3. + 2.*1.*3. + 3.*1.*2.;
    	double y_2_0   = 1.*2.*3. + 2.*1.*3. + 3.*1.*2.;
    	//
    	// Y_1 (t)     = F[X_1(t)]
    	//             =  (1 + 2t)(2 + 3t)(3 + 4t)
    	double y_1_1   = 2.*2.*3. + 3.*1.*3. + 4.*1.*2.;
    	double y_2_1   = 1.*3.*4. + 2.*2.*4. + 3.*2.*3.;
    	//
    	ok  &= NearEqual(y1[0] , y_1_0, eps, eps);
    	ok  &= NearEqual(y1[1] , y_1_1, eps, eps);
    	ok  &= NearEqual(y2[0] , y_2_0, eps, eps);
    	ok  &= NearEqual(y2[1] , y_2_1, eps, eps);
    	//
    	// check number of orders
    	ok   &= f.size_order() == 3;
    	//
    	// check number of directions
    	ok   &= f.size_direction() == 2;
    	//
    	return ok;
    }

`

Input File: example/forward_dir.cpp