eigensolvers

meanas.eigensolvers

Solvers for eigenvalue / eigenvector problems

power_iteration

power_iteration(
    operator: spmatrix,
    guess_vector: NDArray[complex128] | None = None,
    iterations: int = 20,
) -> tuple[complex, NDArray[numpy.complex128]]

Use power iteration to estimate the dominant eigenvector of a matrix.

Parameters:

Name	Type	Description	Default
operator	spmatrix	Matrix to analyze.	required
guess_vector	NDArray[complex128] | None	Starting point for the eigenvector. Default is a randomly chosen vector.	None
iterations	int	Number of iterations to perform. Default 20.	20

Returns:

Type	Description
tuple[complex, NDArray[complex128]]	(Largest-magnitude eigenvalue, Corresponding eigenvector estimate)

rayleigh_quotient_iteration

rayleigh_quotient_iteration(
    operator: spmatrix | LinearOperator,
    guess_vector: NDArray[complex128],
    iterations: int = 40,
    tolerance: float = 1e-13,
    solver: Callable[..., NDArray[complex128]]
    | None = None,
) -> tuple[complex, NDArray[numpy.complex128]]

Use Rayleigh quotient iteration to refine an eigenvector guess.

Parameters:

Name	Type	Description	Default
operator	spmatrix | LinearOperator	Matrix to analyze.	required
guess_vector	NDArray[complex128]	Eigenvector to refine.	required
iterations	int	Maximum number of iterations to perform. Default 40.	40
tolerance	float	Stop iteration if (A - I*eigenvalue) @ v < num_vectors * tolerance, Default 1e-13.	1e-13
solver	Callable[..., NDArray[complex128]] | None	Solver function of the form x = solver(A, b). By default, use scipy.sparse.spsolve for sparse matrices and scipy.sparse.bicgstab for general LinearOperator instances.	None

Returns:

Type	Description
tuple[complex, NDArray[complex128]]	(eigenvalues, eigenvectors)

signed_eigensolve

signed_eigensolve(
    operator: spmatrix | LinearOperator,
    how_many: int,
    negative: bool = False,
) -> tuple[
    NDArray[numpy.complex128], NDArray[numpy.complex128]
]

Find the largest-magnitude positive-only (or negative-only) eigenvalues and eigenvectors of the provided matrix.

Parameters:

Name	Type	Description	Default
operator	spmatrix | LinearOperator	Matrix to analyze.	required
how_many	int	How many eigenvalues to find.	required
negative	bool	Whether to find negative-only eigenvalues. Default False (positive only).	False

Returns:

Type	Description
NDArray[complex128]	(sorted list of eigenvalues, 2D ndarray of corresponding eigenvectors)
NDArray[complex128]	eigenvectors[:, k] corresponds to the k-th eigenvalue