low_rank_toolbox.cssp.oversampling_sqdeim
Oversampling Strong QDEIM algorithm.
Author: Benjamin Carrel, University of Geneva, 2024
Functions
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Oversampling sQDEIM - Oversampled version of sQDEIM |
- low_rank_toolbox.cssp.oversampling_sqdeim.oversampling_sQDEIM(U, oversampling_size, tol=None, return_projection=False, return_inverse=False)[source]
Oversampling sQDEIM - Oversampled version of sQDEIM
Reference: ACCURACY AND STABILITY OF CUR DECOMPOSITIONS WITH OVERSAMPLING (Taejun Park and Yuji Nakatsukasa)
- Parameters:
U (ndarray) – Orthonormal matrix of size n x k
oversampling_size (int) – Oversampling size p < k such that m = k + p
tol (float) – Tolerance for the strong rank-revealing QR factorization If None, use the rank-revealing QR factorization with eta=2
return_projection (bool) – If True, return also the matrix U @ pseudoinv(U[S, :])
return_inverse (bool) – If True, return also the inverse of U[S, :]
- Return type:
ndarray|Tuple[ndarray,ndarray] |Tuple[ndarray,ndarray,ndarray]- Returns:
p (list) – Selection of m = k + oversampling_size row indices.
P_U (ndarray (n x m) (optional)) – Matrix U @ pseudoinv(U[p, :]) where U[p, :] is the (m x k) submatrix. Only returned if return_projection=True.
inv_U (ndarray (k x m) (optional)) – Matrix U.T @ P_U, representing the pseudoinverse relationship. Only returned if return_inverse=True (requires return_projection=True).