Forward Mode: Example and Test of Multiple Orders
Keywords: forward mode: example test multiple orders

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Forward Mode: Example and Test of Multiple Orders
`

    # include <limits>
    # include <cppad/cppad.hpp>
    bool forward_order(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;

    	// Compute three forward orders at one
    	size_t q = 2, q1 = q+1;
    	CPPAD_TESTVECTOR(double) xq(n*q1), yq;
    	xq[q1*0 + 0] = 3.;    xq[q1*1 + 0] = 4.; // x^0 (order zero)
    	xq[q1*0 + 1] = 1.;    xq[q1*1 + 1] = 0.; // x^1 (order one)
    	xq[q1*0 + 2] = 0.;    xq[q1*1 + 2] = 0.; // x^2 (order two)
    	// X(t) =   x^0 + x^1 * t + x^2 * t^2
    	//      = [ 3 + t, 4 ]
    	yq  = f.Forward(q, xq);
    	ok &= size_t( yq.size() ) == m*q1;
    	// Y(t) = F[X(t)]
    	//      = (3 + t) * (3 + t) * 4
    	//      = y^0 + y^1 * t + y^2 * t^2 + o(t^3)
    	//
    	// check y^0 (order zero)
    	CPPAD_TESTVECTOR(double) x0(n);
    	x0[0] = xq[q1*0 + 0];
    	x0[1] = xq[q1*1 + 0];
    	ok  &= NearEqual(yq[q1*0 + 0] , x0[0]*x0[0]*x0[1], eps, eps);
    	//
    	// check y^1 (order one)
    	ok  &= NearEqual(yq[q1*0 + 1] , 2.*x0[0]*x0[1], eps, eps);
    	//
    	// check y^2 (order two)
    	double F_00 = 2. * yq[q1*0 + 2]; // second partial F w.r.t. x_0, x_0
    	ok   &= NearEqual(F_00, 2.*x0[1], eps, eps);

    	// check number of orders per variable
    	ok   &= f.size_order() == 3;

    	return ok;
    }

`

Input File: example/forward_order.cpp