Hessian: Example and Test
Keywords: hessian: example test Hessian

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Hessian: Example and Test
`

    # include <cppad/cppad.hpp>
    namespace { // ---------------------------------------------------------
    // define the template function HessianCases<Vector> in empty namespace
    template <typename Vector>
    bool HessianCases()
    {	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
    	Vector x(n);
    	x[0] = 2.;
    	x[1] = 1.;

    	// second derivative of y[1]
    	Vector hes( n * n );
    	hes = f.Hessian(x, 1);
    	/*
    	F_1       = x[0] * x[0] * sin(x[1])

    	F_1^{(1)} = [ 2 * x[0] * sin(x[1]) , x[0] * x[0] * cos(x[1]) ]

    	F_1^{(2)} = [        2 * sin(x[1]) ,      2 * x[0] * cos(x[1]) ]
    	            [ 2 * x[0] * cos(x[1]) , - x[0] * x[0] * sin(x[1]) ]
    	*/
    	ok &=  NearEqual(          2.*sin(x[1]), hes[0*n+0], 1e-10, 1e-10 );
    	ok &=  NearEqual(     2.*x[0]*cos(x[1]), hes[0*n+1], 1e-10, 1e-10 );
    	ok &=  NearEqual(     2.*x[0]*cos(x[1]), hes[1*n+0], 1e-10, 1e-10 );
    	ok &=  NearEqual( - x[0]*x[0]*sin(x[1]), hes[1*n+1], 1e-10, 1e-10 );

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

`

Input File: example/hessian.cpp