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CppAD Speed: Gradient of Determinant Using Lu Factorization

Specifications
See link_det_lu .

Implementation
 
# include <cppad/vector.hpp>
# include <cppad/speed/det_by_lu.hpp>
# include <cppad/speed/uniform_01.hpp>

bool link_det_lu(
	size_t                           size     , 
	size_t                           repeat   , 
	CppAD::vector<double>           &matrix   ,
	CppAD::vector<double>           &gradient )
{
	// -----------------------------------------------------
	// setup
	typedef CppAD::AD<double>           ADScalar; 
	typedef CppAD::vector<ADScalar>     ADVector; 
	CppAD::det_by_lu<ADScalar>          Det(size);

	size_t i;               // temporary index
	size_t m = 1;           // number of dependent variables
	size_t n = size * size; // number of independent variables
	ADVector   A(n);        // AD domain space vector
	ADVector   detA(m);     // AD range space vector
	
	// vectors of reverse mode weights 
	CppAD::vector<double> w(1);
	w[0] = 1.;

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

	while(repeat--)
	{	// get the next matrix
		CppAD::uniform_01(n, matrix);
		for( i = 0; i < n; i++)
			A[i] = matrix[i];

		// declare independent variables
		Independent(A);

		// AD computation of the determinant
		detA[0] = Det(A);

		// create function object f : A -> detA
		CppAD::ADFun<double> f(A, detA);

		// evaluate and return gradient using reverse mode
		gradient = f.Reverse(1, w);
	}
	return true;
}

Input File: speed/cppad/det_lu.cpp