Subset of Second Order Partials: Example and Test
Keywords: subset second order partials: example test partial

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Subset of Second Order Partials: Example and Test
`

    # include <cppad/cppad.hpp>
    namespace { // -----------------------------------------------------
    // define the template function in empty namespace
    // bool ForTwoCases<VectorBase, VectorSize_t>(void)
    template <class VectorBase, class VectorSize_t>
    bool ForTwoCases()
    {	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 j and k to compute specific second partials of y
    	size_t p = 2;
    	VectorSize_t j(p);
    	VectorSize_t k(p);
    	j[0] = 0; k[0] = 0; // for second partial w.r.t. x[0] and x[0]
    	j[1] = 0; k[1] = 1; // for second partial w.r.t x[0] and x[1]

    	// compute the second partials
    	VectorBase ddy(m * p);
    	ddy = f.ForTwo(x, j, k);
    	/*
    	partial of y w.r.t x[0] is
    	[ 2 * x[0] * exp(x[1]) ]
    	[ 2 * x[0] * sin(x[1]) ]
    	[ 2 * x[0] * cos(x[1]) ]
    	*/
    	// second partial of y w.r.t x[0] and x[1]
    	ok &=  NearEqual( 2.*exp(x[1]), ddy[0*p+0], 1e-10, 1e-10 );
    	ok &=  NearEqual( 2.*sin(x[1]), ddy[1*p+0], 1e-10, 1e-10 );
    	ok &=  NearEqual( 2.*cos(x[1]), ddy[2*p+0], 1e-10, 1e-10 );

    	// second partial of F w.r.t x[0] and x[1]
    	ok &=  NearEqual( 2.*x[0]*exp(x[1]), ddy[0*p+1], 1e-10, 1e-10 );
    	ok &=  NearEqual( 2.*x[0]*cos(x[1]), ddy[1*p+1], 1e-10, 1e-10 );
    	ok &=  NearEqual(-2.*x[0]*sin(x[1]), ddy[2*p+1], 1e-10, 1e-10 );

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

    	return ok;
    }

`

Input File: example/for_two.cpp