Covariance matrices - how to handle singular matrices about refnx HOT 2 CLOSED

check that there are no duplicated parameters present in the varying parameters.

the covariance matrix is only estimated for unique varying parameters.

check that step sizes are correct

scipy.optimize._numdiff.approx_derivative calculates the scaled step sizes correctly. In any case the derivatives (to obtain the Jacobian matrix) are calculated on parameters scaled to unity. This scaling is unwound in the final calculation of the covariance matrix.
A test is run against scipy.optimize.least_squares to check that the Jacobian/Hessian/covariance matrices estimated by objective.covar are correct.

check that it's falling back to the scale calculation when required

The parameters are by default scaled to unity.

is the correct matrix inverse being used?

np.linalg.inv should be applicable to this situation. QR decomposition may provide additional precision if the Hessian is close to being singular.

from refnx.

If there are zero values in the parameters then unscaled parameters are used in the calculation of the Jacobian. approx_derivative can deal with zero parameters, and uses an absolute step instead.

objective.covar now uses a pseudo inverse and removes, and identifies singular parameters.

from refnx.