Gradient of Determinant Using LU Factorization: Example and Test
Keywords: gradient determinant using lu factorization: example test

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Gradient of Determinant Using LU Factorization: Example and Test
`

    # include <cppad/cppad.hpp>
    # include <cppad/speed/det_by_lu.hpp>

    bool HesLuDet(void)
    {	bool ok = true;

    	using namespace CppAD;

    	typedef std::complex<double> Complex;

    	size_t n = 2;

    	// object for computing determinants
    	det_by_lu< AD<Complex> > Det(n);

    	// independent and dependent variable vectors
    	CPPAD_TESTVECTOR(AD<Complex>)  X(n * n);
    	CPPAD_TESTVECTOR(AD<Complex>)  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);

    	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) H( n * n * n * n );
    	H = f.Hessian(x, 0);

    	/*
    	f(x)     = x[0] * x[3] - x[1] * x[2]
    	f'(x)    = ( x[3], -x[2], -x[1], x[0] )
    	*/
    	Complex zero(0., 0.);
    	Complex one(1., 0.);
    	Complex Htrue[]  = {
    		zero, zero, zero,  one,
    		zero, zero, -one, zero,
    		zero, -one, zero, zero,
    		 one, zero, zero, zero
    	};
    	for( i = 0; i < n*n*n*n; i++)
    		ok &= NearEqual( Htrue[i], H[i], 1e-10 , 1e-10 );

    	return ok;
    }

`

Input File: example/hes_lu_det.cpp