Gradient of Determinant Using Expansion by Minors: Example and Test
Keywords: gradient determinant using expansion minors: example test minors

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Gradient of Determinant Using Expansion by Minors: Example and Test
`

    # include <cppad/cppad.hpp>
    # include <cppad/speed/det_by_minor.hpp>
    # include <complex>

    typedef std::complex<double>     Complex;
    typedef CppAD::AD<Complex>       ADComplex;
    typedef CPPAD_TESTVECTOR(ADComplex)   ADVector;

    // ----------------------------------------------------------------------------

    bool JacMinorDet(void)
    {	bool ok = true;

    	using namespace CppAD;

    	size_t n = 2;

    	// object for computing determinant
    	det_by_minor<ADComplex> Det(n);

    	// independent and dependent variable vectors
    	CPPAD_TESTVECTOR(ADComplex)  X(n * n);
    	CPPAD_TESTVECTOR(ADComplex)  D(1);

    	// value of the independent variable
    	size_t i;
    	for(i = 0; i < n * n; i++)
    		X[i] = Complex(int(i), -int(i));

    	// set the independent variables
    	Independent(X);

    	// comupute the determinant
    	D[0] = Det(X);

    	// create the function object
    	ADFun<Complex> f(X, D);

    	// argument value
    	CPPAD_TESTVECTOR(Complex)     x( n * n );
    	for(i = 0; i < n * n; i++)
    		x[i] = Complex(2 * i, i);

    	// first derivative of the determinant
    	CPPAD_TESTVECTOR(Complex) J( n * n );
    	J = f.Jacobian(x);

    	/*
    	f(x)     = x[0] * x[3] - x[1] * x[2]
    	f'(x)    = ( x[3], -x[2], -x[1], x[0] )
    	*/
    	Complex Jtrue[] = { x[3], -x[2], -x[1], x[0] };
    	for(i = 0; i < n * n; i++)
    		ok &= Jtrue[i] == J[i];

    	return ok;

    }

`

Input File: example/jac_minor_det.cpp