low_rank_toolbox.cssp.deim

Discrete Empirical Interpolation Method (DEIM).

Author: Benjamin Carrel, University of Geneva, 2024

Functions

DEIM(U[, return_projector, return_inverse])

DEIM - Discrete empirical interpolation method
low_rank_toolbox.cssp.deim.DEIM(U, return_projector=False, return_inverse=False, **extra_args)[source]

DEIM - Discrete empirical interpolation method

Construct a matrix P = [e_p1, e_p2, …, e_pk] where the indexes pi are obtained via the DEIM procedure.

Reference

Nonlinear Model Reduction via Discrete Empirical Interpolation Saifon Chaturantabut and Danny C. Sorensen SIAM Journal on Scientific Computing 2010 32:5, 2737-2764

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 inverse matrix inv(U[S, :])

  • extra_args (dict) –

    Additional arguments:
    solve_kwargs: dict

    Additional arguments for the solve function

Return type:

list | tuple

Returns:

  • p (list) – List of indexes selected by DEIM

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

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