solve_rchi2_from_error¶

sofia_redux.toolkit.resampling.solve_rchi2_from_error(residuals, weights, errors, weightsum=None, rank=1)[source]¶

Return the reduced chi-squared given residuals and sample errors.

For weights \(w\), errors \(\sigma\), and residuals \(r\) where \(r = y - f(x)\), the reduced chi-squared is given as:

\[\chi_r^2 = \frac{N}{N - M} \frac{\sum_{i=1}^{N}{w_i r_i^2 / \sigma_i^2}} {\sum_{i=1}^{N}{w_i}}\]

where \(M\) is given by rank.

Parameters:

residualsnumpy.ndarray (N,): The residuals to the fit, or y - f(x).
weightsnumpy.ndarray (N,): The weights to each sample in the fit.
errorsnumpy.ndarray (N,): The 1-sigma measurement errors for each sample in the fit.
weightsumint or float, optional: The sum of the sample weights, optionally passed in for speed.
rankint or float, optional: The degrees of freedom used in the reduced chi-squared value is taken as N - rank. The default is 1 and applies the Bessel correction. If N < rank, rank is automatically set to N - 1.

Returns: