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Computing the covariance matrix of best fit parameters

int gsl_multifit_covar (const gsl_matrix * J, double epsrel, gsl_matrix * covar) Function
This function uses the Jacobian matrix J to compute the covariance matrix of the best-fit parameters, covar. The parameter epsrel is used to remove linear-dependent columns when J is rank deficient.

The covariance matrix is given by,

and is computed by QR decomposition of J with column-pivoting. Any columns of R which satisfy

are considered linearly-dependent and are excluded from the covariance matrix (the corresponding rows and columns of the covariance matrix are set to zero).