Jacobian: Example and Test
Keywords: jacobian: example test Jacobian

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Jacobian: Example and Test
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    # include <cppad/cppad.hpp>
    namespace { // ---------------------------------------------------------
    // define the template function JacobianCases<Vector> in empty namespace
    template <typename Vector>
    bool JacobianCases()
    {	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.;

    	// compute the derivative at this x
    	Vector jac( m * n );
    	jac = f.Jacobian(x);

    	/*
    	F'(x) = [ 2 * x[0] * exp(x[1]) ,  x[0] * x[0] * exp(x[1]) ]
    	        [ 2 * x[0] * sin(x[1]) ,  x[0] * x[0] * cos(x[1]) ]
    	        [ 2 * x[0] * cos(x[1]) , -x[0] * x[0] * sin(x[i]) ]
    	*/
    	ok &=  NearEqual( 2.*x[0]*exp(x[1]), jac[0*n+0], 1e-10, 1e-10 );
    	ok &=  NearEqual( 2.*x[0]*sin(x[1]), jac[1*n+0], 1e-10, 1e-10 );
    	ok &=  NearEqual( 2.*x[0]*cos(x[1]), jac[2*n+0], 1e-10, 1e-10 );

    	ok &=  NearEqual( x[0] * x[0] *exp(x[1]), jac[0*n+1], 1e-10, 1e-10 );
    	ok &=  NearEqual( x[0] * x[0] *cos(x[1]), jac[1*n+1], 1e-10, 1e-10 );
    	ok &=  NearEqual(-x[0] * x[0] *sin(x[1]), jac[2*n+1], 1e-10, 1e-10 );

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

`

Input File: example/jacobian.cpp