Calculate the filter factors \(f_{\lambda, i}\).
The filter factors are diagonal elements of the filter matrix \(\mathbf{F}_\lambda\),
and can be expressed with SVD components as follows:
\[f_{\lambda, i} = \left( 1 + \frac{\lambda}{\sigma_i^2} \right)^{-1}.\]
- Parameters:
- beta
float Regularization parameter.
- Returns:
- (
r, ) array 1-D array containing filter factors, the length of which is the same as the number of
singular values.