Using Eigen To Compute Determinant: Example and Test
Keywords: using eigen to compute determinant: example test determinant

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Using Eigen To Compute Determinant: Example and Test
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    # include <cppad/example/cppad_eigen.hpp>
    # include <cppad/speed/det_by_minor.hpp>
    # include <Eigen/Dense>

    bool eigen_det(void)
    {	bool ok = true;
    	using CppAD::AD;
    	using CppAD::NearEqual;
    	using Eigen::Matrix;
    	using Eigen::Dynamic;
    	//
    	typedef Matrix< double     , Dynamic, Dynamic > matrix;
    	typedef Matrix< AD<double> , Dynamic, Dynamic > a_matrix;
    	//
    	typedef Matrix< double ,     Dynamic , 1>       vector;
    	typedef Matrix< AD<double> , Dynamic , 1>       a_vector;
    	// some temporary indices
    	size_t i, j;

    	// domain and range space vectors
    	size_t size = 3, n  = size * size, m = 1;
    	a_vector a_x(n), a_y(m);
    	vector x(n);

    	// set and declare independent variables and start tape recording
    	for(i = 0; i < size; i++)
    	{	for(j = 0; j < size; j++)
    		{	// lower triangular matrix
    			a_x[i * size + j] = x[i * size + j] = 0.0;
    			if( j <= i )
    				a_x[i * size + j] = x[i * size + j] = double(1 + i + j);
    		}
    	}
    	CppAD::Independent(a_x);

    	// copy independent variable vector to a matrix
    	a_matrix a_X(size, size);
    	matrix X(size, size);
    	for(i = 0; i < size; i++)
    	{	for(j = 0; j < size; j++)
    		{	X(i, j)   = x[i * size + j];
    			// If we used a_X(i, j) = X(i, j), a_X would not depend on a_x.
    			a_X(i, j) = a_x[i * size + j];
    		}
    	}

    	// Compute the log of determinant of X
    	a_y[0] = log( a_X.determinant() );

    	// create f: x -> y and stop tape recording
    	CppAD::ADFun<double> f(a_x, a_y);

    	// check function value
    	double eps = 100. * CppAD::numeric_limits<double>::epsilon();
    	CppAD::det_by_minor<double> det(size);
    	ok &= NearEqual(Value(a_y[0]) , log(det(x)), eps, eps);

    	// compute the derivative of y w.r.t x using CppAD
    	vector jac = f.Jacobian(x);

    	// check the derivative using the formula
    	// d/dX log(det(X)) = transpose( inv(X) )
    	matrix inv_X = X.inverse();
    	for(i = 0; i < size; i++)
    	{	for(j = 0; j < size; j++)
    			ok &= NearEqual(jac[i * size + j], inv_X(j, i), eps, eps);
    	}

    	return ok;
    }

`

Input File: example/eigen_det.cpp