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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_TEST_VECTOR<ADComplex>   ADVector;

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

bool JacMinorDet()
{	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_TEST_VECTOR<ADComplex>  X(n * n);
	CPPAD_TEST_VECTOR<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_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> 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