First Order Reverse Mode: Example and Test
Keywords: first order reverse mode: example test

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First Order Reverse Mode: Example and Test
`

    # include <cppad/cppad.hpp>
    namespace { // ----------------------------------------------------------
    // define the template function reverse_one_cases<Vector> in empty namespace
    template <typename Vector>
    bool reverse_one_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 first order reverse mode to evaluate derivative of y[0]
    	// and use the values in X for the independent variables.
    	CPPAD_TESTVECTOR(double) w(m), dw(n);
    	w[0] = 1.;
    	dw   = f.Reverse(1, w);
    	ok  &= NearEqual(dw[0] , 2.*X[0]*X[1], 1e-10, 1e-10);
    	ok  &= NearEqual(dw[1] ,    X[0]*X[0], 1e-10, 1e-10);

    	// use zero order forward mode to evaluate y at x = (3, 4)
    	// and 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 reverse mode to evaluate derivative of y[0]
    	// and using the values in x for the independent variables.
    	w[0] = 1.;
    	dw   = f.Reverse(1, w);
    	ok  &= NearEqual(dw[0] , 2.*x[0]*x[1], 1e-10, 1e-10);
    	ok  &= NearEqual(dw[1] ,    x[0]*x[0], 1e-10, 1e-10);

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

`

Input File: example/reverse_one.cpp