Forward Mode: Example and Test
Keywords: forward mode: example test

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Forward Mode: Example and Test
`

    # include <limits>
    # include <cppad/cppad.hpp>
    namespace { // --------------------------------------------------------
    // define the template function ForwardCases<Vector> in empty namespace
    template <class Vector>
    bool ForwardCases(void)
    {	bool ok = true;
    	using CppAD::AD;
    	using CppAD::NearEqual;
    	double eps = 10. * std::numeric_limits<double>::epsilon();

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

    	// 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[0] * ax[1];

    	// 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 forward mode using notation in forward_zero
    	// use the template parameter Vector for the vector type
    	Vector x0(n), y0(m);
    	x0[0] = 3.;
    	x0[1] = 4.;
    	y0    = f.Forward(0, x0);
    	ok  &= NearEqual(y0[0] , x0[0]*x0[0]*x0[1], eps, eps);
    	ok  &= f.size_order() == 1;

    	// first order forward mode using notation in forward_one
    	// X(t)           = x0 + x1 * t
    	// Y(t) = F[X(t)] = y0 + y1 * t + o(t)
    	Vector x1(n), y1(m);
    	x1[0] = 1.;
    	x1[1] = 0.;
    	y1    = f.Forward(1, x1); // partial F w.r.t. x_0
    	ok   &= NearEqual(y1[0] , 2.*x0[0]*x0[1], eps, eps);
    	ok   &= f.size_order() == 2;

    	// second order forward mode using notation in forward_order
    	// X(t) =           x0 + x1 * t + x2 * t^2
    	// Y(t) = F[X(t)] = y0 + y1 * t + y2 * t^2 + o(t^3)
    	Vector x2(n), y2(m);
    	x2[0]      = 0.;
    	x2[1]      = 0.;
    	y2         = f.Forward(2, x2);
    	double F_00 = 2. * y2[0]; // second partial F w.r.t. x_0, x_0
    	ok         &= NearEqual(F_00, 2.*x0[1], eps, eps);
    	ok         &= f.size_order() == 3;

    	return ok;
    }
    } // End empty namespace
    # include <vector>
    # include <valarray>
    bool Forward(void)
    {	bool ok = true;
    	// Run with Vector equal to three different cases
    	// all of which are Simple Vectors with elements of type double.
    	ok &= ForwardCases< CppAD::vector  <double> >();
    	ok &= ForwardCases< std::vector    <double> >();
    	ok &= ForwardCases< std::valarray  <double> >();
    	return ok;
    }

`

Input File: example/forward.cpp