low_rank_toolbox.cssp.gpode

low_rank_toolbox.cssp.gpode(U, oversampling_size, return_projector=False, return_inverse=False, **extra_args)[source]

Gappy POD+E - Greedy algorithm for the selection of m rows of U Minimize the norm of the pseudoinverse of U[S, :] Total cost is O(k^2 + m^2) + QR of U.T.conj() of cost O(nk^2)

Reference

Stability of discrete empirical interpolation and gappy proper orthogonal decomposition with randomized and deterministic sampling points Benjamin Peherstorfer, Zlatko Drmač, and Serkan Gugercin SIAM Journal on Scientific Computing, 42(5), A2837-A2864.

Parameters:

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

  • oversampling_size (int) – Oversampling size p such that m = k + p

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

  • return_inverse (bool) – If True, return also the inverse of U[p, :]

  • extra_args (dict) –

    Additional arguments:
    qr_kwargs: dict

    Additional arguments for the QR factorization

    lstsq_kwargs: dict

    Additional arguments for the lstsq function

Return type:

tuple | list

Returns:

  • p (list) – Selection of m row indices

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

  • inv_U (ndarray (k x k) (optional)) – Inverse of U[p, :]