Second Partials Reverse Driver: Example and Test
Keywords: second partials reverse driver: example test

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Second Partials Reverse Driver: Example and Test
`

    # include <cppad/cppad.hpp>
    namespace { // -----------------------------------------------------
    // define the template function in empty namespace
    // bool RevTwoCases<VectorBase, VectorSize_t>(void)
    template <class VectorBase, class VectorSize_t>
    bool RevTwoCases()
    {	bool ok = true;
    	using CppAD::AD;
    	using CppAD::NearEqual;
    	using CppAD::exp;
    	using CppAD::sin;
    	using CppAD::cos;

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

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

    	// a calculation between the domain and range values
    	AD<double> Square = X[0] * X[0];

    	// range space vector
    	size_t m = 3;
    	CPPAD_TESTVECTOR(AD<double>)  Y(m);
    	Y[0] = Square * exp( X[1] );
    	Y[1] = Square * sin( X[1] );
    	Y[2] = Square * cos( X[1] );

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

    	// new value for the independent variable vector
    	VectorBase x(n);
    	x[0] = 2.;
    	x[1] = 1.;

    	// set i and j to compute specific second partials of y
    	size_t p = 2;
    	VectorSize_t i(p);
    	VectorSize_t j(p);
    	i[0] = 0; j[0] = 0; // for partials y[0] w.r.t x[0] and x[k]
    	i[1] = 1; j[1] = 1; // for partials y[1] w.r.t x[1] and x[k]

    	// compute the second partials
    	VectorBase ddw(n * p);
    	ddw = f.RevTwo(x, i, j);

    	// partials of y[0] w.r.t x[0] is 2 * x[0] * exp(x[1])
    	// check partials of y[0] w.r.t x[0] and x[k] for k = 0, 1
    	ok &=  NearEqual(      2.*exp(x[1]), ddw[0*p+0], 1e-10, 1e-10 );
    	ok &=  NearEqual( 2.*x[0]*exp(x[1]), ddw[1*p+0], 1e-10, 1e-10 );

    	// partials of y[1] w.r.t x[1] is x[0] * x[0] * cos(x[1])
    	// check partials of F_1 w.r.t x[1] and x[k] for k = 0, 1
    	ok &=  NearEqual(    2.*x[0]*cos(x[1]), ddw[0*p+1], 1e-10, 1e-10 );
    	ok &=  NearEqual( -x[0]*x[0]*sin(x[1]), ddw[1*p+1], 1e-10, 1e-10 );

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

            // Run with VectorSize_t equal to two other cases
            // which are Simple Vectors with elements of type size_t.
    	ok &= RevTwoCases< std::vector <double>, CppAD::vector<size_t> >();
    	ok &= RevTwoCases< std::vector <double>, std::valarray<size_t> >();

    	return ok;
    }

`

Input File: example/rev_two.cpp