class boulderopal.noise_reconstruction.SVDEntropyTruncation(rounding_threshold=0.5)

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


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


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

FUΣV, F^\prime \approx U \Sigma V ,

where matrices UU and VV{n{\mathrm{sv}} \times n_{\mathrm{sv}}},and, and \Sigmaisadiagonalmatrixof is a diagonal matrix of n_{\mathrm{sv}}truncatedsingularvalues,whichintheentropytruncationmethodaredeterminedbytheentropyofthesingularvalues truncated singular values, which in the entropy truncation method are determined by the entropy of the singular values

The entropy truncation method calculates the value 2E2^E and rounds the value to an integer nsvn_{\mathrm{sv}}. When rounding the value 2E2^E, the floor of 2E2^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 nsvn_{\mathrm{sv}}

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

Sest=VΣ1UI. {\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.

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