solve_inverse_covariance_matrices

sofia_redux.toolkit.resampling.solve_inverse_covariance_matrices(phi, error, residuals, weights, error_weighted_amat=None, rank=None, calculate_error=True, calculate_residual=True, estimate_covariance=False)

Inverse covariance matrices on fit coefficients from errors and residuals.

A utility function to calculate the inverse covariance matrices of the fit coefficients (\(c\)) based on the \(1\sigma\) error values of the sample measurements and/or the residuals of the fit \(y - c \cdot \Phi\).

The function used to calculate the error covariance may be either estimated_covariance_matrix_inverse() or covariance_matrix_inverse(). However, estimated_covariance_matrix_inverse() will always be used to calculate the covariance matrix derived from residuals.

Parameters:

phinumpy.ndarray (nterms, N)

The polynomial terms for each of the N samples.

errornumpy.ndarray (N,)

The 1-sigma error values for each sample.

residualsnumpy.ndarray (N,)

The residuals of the fit y - c.phi.

weightsnumpy.ndarray (N,)

The weighting of each sample in the fit.

error_weighted_amatnumpy.ndarray (nterms, nterms), optional

The matrix \(A = \Phi^T W Var(y) W \Phi\), optionally passed in for speed if pre-calculated.

rankint or float, optional

The rank of error_weighted_amat, if provided, and it’s rank was pre-calculated. Otherwise, it will be solved for.

calculate_errorbool, optional

If True, calculate the covariance of the fit coefficients based upon the error values.

calculate_residualbool, optional

If True, calculate the covariance of the fit coefficients based upon residuals of the fit.

estimate_covariancebool, optional

If True, calculate the covariance of the fit coefficients from the error values using estimated_covariance_matrix_inverse(). Otherwise, use covariance_matrix_inverse().

Returns:

e_inv, r_invnumpy.ndarray, numpy.ndarray

The inverse covariance calculated from error, and the inverse covariance calculated from residuals. If calculate_error is True, the shape of e_cov will be (nterms, nterms) or (0, 0) otherwise. The same is true for calculate_residual and r_cov.