SVDFixedLengthTruncation
- class boulderopal.noise_reconstruction.SVDFixedLengthTruncation(singular_value_count=None)
Configuration for noise reconstruction with the singular value decomposition (SVD) method using fixed-length truncation.
- Parameters:
singular_value_count (int or None, optional) – The number of singular values to retain. It must be greater or equal to 1. Defaults to None, in which case no truncation is performed.
Notes
The singular value decomposition (SVD) method first finds a low rank approximation of the matrix of weighted filter functions \(F^\prime\):
\[F^\prime \approx U \Sigma V ,\]where matrices \(U\) and \(V\) satisfy that \(U^\dagger U = VV^\dagger = \mathbb{I}_{n_{\mathrm{sv}} \times n_{\mathrm{sv}}}\), and \(\Sigma\) is a diagonal matrix of \(n_{\mathrm{sv}}\) truncated singular values, which are determined by the singular_value_count that you provided.
The SVD method then estimates the noise power spectral density (PSD) \(\mathbf S\) as:
\[{\mathbf S}_{\mathrm{est}} = V^\dagger\Sigma^{-1}U^\dagger{\mathbf I} .\]This method calculates the uncertainties in estimation using error propagation if you provide measurement uncertainties.