low_rank_toolbox.cssp.qdeim

QR-based Discrete Empirical Interpolation Method (QDEIM).

Author: Benjamin Carrel, University of Geneva, 2024

Functions

QDEIM(U[, return_projector, return_inverse])

QDEIM - QR based DEIM of U (size n x k)

low_rank_toolbox.cssp.qdeim.QDEIM(U, return_projector=False, return_inverse=False, **extra_args)

QDEIM - QR based DEIM of U (size n x k)

Reference

A new selection operator for the discrete empirical interpolation method - improved a priori error bound and extensions. Zlatko Drmač and Serkan Gugercin. SIAM Journal on Scientific Computing, 38(2), A631-A648.

Original Matlab code from Zlatko Drmač

Parameters:

• U (ndarray) – Orthonormal matrix of size n x k

• return_projector (bool) – If True, return also the matrix U @ inv(U[S, :])

• return_inverse (bool) – If True, return also the matrix inv(U[S, :])

• extra_args (dict) –

  Additional arguments:

  qr_kwargs: dict

  Additional arguments for the QR factorization

  solve_kwargs: dict

  Additional arguments for the solve function

Return type:

ndarray | tuple

Returns:

• p (list) – Selection of m row indices with guaranteed upper bound: norm(inv(U[S,:])) <= sqrt(n-k+1) * O(2^m).

• P_U (ndarray (n x k) (optional)) – Matrix U @ inv(U[S, :])

• inv_U (ndarray (k x k) (optional)) – Matrix inv(U[S, :])