pypcga.ghep#

pypcga.ghep(A: ndarray[tuple[Any, ...], dtype[float64]] | LinearOperator, B: ndarray[tuple[Any, ...], dtype[float64]] | LinearOperator, Binv: ndarray[tuple[Any, ...], dtype[float64]] | LinearOperator, r: int, d: int, single_pass: bool = True, keep_neg_eigvals: bool = False) → Tuple[ndarray[tuple[Any, ...], dtype[float64]], ndarray[tuple[Any, ...], dtype[float64]]][source]#

Randomized Eigen Value Decomposition (EVD).

TODO: add ref. :cite:t:`halkoFindingStructureRandomness2010`_.

Parameters:

  • A (NDArrayFloat) – A ∈ RN×N

  • r (int) – Desired rank.

  • d (int) – Oversampling parameter. Typically, d is chosen to be less than 20 following the arguments in [5, 7]. The improvement in the approximation error with increasing p is verified in both theory and experiment (Sections 4 and 5)

  • N (5. Halko)

  • PG (Martinsson)

  • randomness (Tropp JA. Finding structure with)

  • decompositions. (probabilistic algorithms for constructing approximate matrix)

  • 53(2) (SIAM Review 2011;)

  • G (Stadler)

  • governed (Wilcox LC. Extreme-scale UQ for Bayesian inverse problems)

  • Performance (by PDEs. In Proceedings of the International Conference on High)

  • Computing

  • Networking

  • Press (Storage and Analysis. IEEE Computer Society)

  • Portland

  • OR

  • E (2012; 3. 7. Liberty)

  • F (Woolfe)

  • PG

  • V (Rokhlin)

:param : :param Tygert M. Randomized algorithms for the low-rank approximation of matrices.: :param Proceedings of the National Academy of Sciences 2007; 104(51): :type Proceedings of the National Academy of Sciences 2007; 104(51): 20167–20172. :param Output: :type Output: low-rank approximation ̃ A of A

On this page