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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()
{	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_TEST_VECTOR< AD<Complex> >  X(n * n);
	CPPAD_TEST_VECTOR< 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_TEST_VECTOR<Complex>     x( n * n );
	for(i = 0; i < n * n; i++)
		x[i] = Complex(2 * i, i);

	// first derivative of the determinant
	CPPAD_TEST_VECTOR<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