SVDEntropyTruncation

class boulderopal.noise_reconstruction.SVDEntropyTruncation(rounding_threshold=0.5)

Configuration for noise reconstruction with the singular value decomposition (SVD) method using entropy truncation.

Parameters

rounding_threshold (float , optional) – The rounding threshold of the entropy, between 0 and 1 (inclusive). Defaults to 0.5.

Notes

The singular value decomposition (SVD) method first finds a low rank approximation of the matrix of weighted filter functions $F^\prime$:

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 in the entropy truncation method are determined by the entropy of the singular values $E$.

The entropy truncation method calculates the value $2^E$ and rounds the value to an integer $n_{\mathrm{sv}}$. When rounding the value $2^E$, the floor of $2^E$ plus the rounding threshold that you chose is taken. Therefore a small value leads to rounding down, while a large value leads to rounding up. The $n_{\mathrm{sv}}$ is then used as the truncation value.

The SVD method then estimates the noise power spectral density (PSD) $\mathbf S$ as:

This method calculates the uncertainties in estimation using error propagation if you provide measurement uncertainties.