Second Order Reverse ModeExample and Test
Keywords: second order reverse modeexample test example

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Second Order Reverse ModeExample and Test
`

    # include <cppad/cppad.hpp>
    namespace { // ----------------------------------------------------------
    // define the template function reverse_two_cases<Vector> in empty namespace
    template <typename Vector>
    bool reverse_two_cases(void)
    {	bool ok = true;
    	using CppAD::AD;
    	using CppAD::NearEqual;

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

    	// declare independent variables and start recording
    	CppAD::Independent(X);

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

    	// create f : X -> Y and stop recording
    	CppAD::ADFun<double> f(X, Y);

    	// use zero order forward mode to evaluate y at x = (3, 4)
    	// use the template parameter Vector for the vector type
    	Vector x(n), y(m);
    	x[0]  = 3.;
    	x[1]  = 4.;
    	y     = f.Forward(0, x);
    	ok    &= NearEqual(y[0] , x[0]*x[0]*x[1], 1e-10, 1e-10);

    	// use first order forward mode in x[0] direction
    	// (all second order partials below involve x[0])
    	Vector dx(n), dy(m);
    	dx[0] = 1.;
    	dx[1] = 1.;
    	dy    = f.Forward(1, dx);
    	double check = 2.*x[0]*x[1]*dx[0] + x[0]*x[0]*dx[1];
    	ok   &= NearEqual(dy[0], check, 1e-10, 1e-10);

    	// use second order reverse mode to evalaute second partials of y[0]
    	// with respect to (x[0], x[0]) and with respect to (x[0], x[1])
    	Vector w(m), dw( n * 2 );
    	w[0]  = 1.;
    	dw    = f.Reverse(2, w);

    	// check derivative of f
    	ok   &= NearEqual(dw[0*2+0] , 2.*x[0]*x[1], 1e-10, 1e-10);
    	ok   &= NearEqual(dw[1*2+0] ,    x[0]*x[0], 1e-10, 1e-10);

    	// check derivative of f^{(1)} (x) * dx
    	check = 2.*x[1]*dx[1] + 2.*x[0]*dx[1];
    	ok   &= NearEqual(dw[0*2+1] , check, 1e-10, 1e-10);
    	check = 2.*x[0]*dx[1];
    	ok   &= NearEqual(dw[1*2+1] , check, 1e-10, 1e-10);

    	return ok;
    }
    } // End empty namespace
    # include <vector>
    # include <valarray>
    bool reverse_two(void)
    {	bool ok = true;
    	ok &= reverse_two_cases< CppAD::vector  <double> >();
    	ok &= reverse_two_cases< std::vector    <double> >();
    	ok &= reverse_two_cases< std::valarray  <double> >();
    	return ok;
    }

`

Input File: example/reverse_two.cpp