nevp#

Bases: NEVP

Beyn's integral method for solving NEVP.¹

This is implemented along the lines of what is described in ².

Parameters:

• r_o (float) –

  The outer radius of the annulus for the contour integration.

• r_i (float) –

  The inner radius of the annulus for the contour integration.

• m_0 (int) –

  Guess for the number of eigenvalues that lie in the subspace.

• num_quad_points (int) –

  The number of quadrature points to use for the contour integration.

• num_threads_contour (int, default: 1024 ) –

  The number of cuda threads to use for the contour integration kernel. Only relevant for GPU computations.

• eig_compute_location (str, default: 'numpy' ) –

  The location where to compute the eigenvalues and eigenvectors. Can be either "numpy" or "cupy" or "nvmath".

• project_compute_location (str, default: 'numpy' ) –

  The location where to compute the singular value or qr decomposition for the projector. Can be either "numpy" or "cupy".

• use_qr (bool, default: False ) –

  Whether to use QR decomposition for the projector instead of SVD. Default is False.

• contour_batch_size (int, default: None ) –

  The batch size for the contour integration kernel. If None, the batch size is set to num_quad_points.

• use_pinned_memory (bool, default: True ) –

  Whether to use pinnend memory if cupy is used. Default is True.

Methods:

• __call__ –

  Solves the polynomial eigenvalue problem through contour integration.

__call__(a_xx: tuple[NDArray, ...]) -> tuple[NDArray, NDArray]

Bases: NEVP

An NEVP solver based on linearization.

Implemented along the lines of what is described in ¹.

Parameters:

• eig_compute_location (str, default: 'numpy' ) –

  The location where to compute the eigenvalues and eigenvectors. Can be either "numpy" or "cupy" or "nvmath".

• use_pinned_memory (bool, default: True ) –

  Whether to use pinned memory if cupy is used. Default is True.

• reduce (bool, default: False ) –

  Whether to reduce the problem size by eliminating columns that are zero in the first and last coefficient blocks. These columns correspond to eigenvalues that are infinity or zero.

• a_xx_sparsity (tuple[csc_matrix, ...] or None, default: None ) –

  The sparsity patterns of the coefficient blocks of the NEVP. If reduce is True, this can be provided at instantiation to identify the zero columns and perform the reduction. If reduce is True and a_xx is not provided, the zero columns will be identified at runtime, which may introduce some overhead.

Methods:

• __call__ –

  Solves the polynomial eigenvalue problem through linearization.

__call__(a_xx: tuple[NDArray, ...]) -> tuple[NDArray, NDArray]

Bases: ABC

Abstract base class for the non-linear eigenvalue solvers.

Methods:

• __call__ –

  Solves the polynomial eigenvalue problem.

__call__(a_xx: tuple[NDArray, ...]) -> tuple