Source code for sknetwork.linalg.eig_solver

#!/usr/bin/env python3
# coding: utf-8
"""
Created on July 9 2019
@author: Nathan De Lara <nathan.delara@polytechnique.org>
"""
from abc import ABC
from typing import Union

import numpy as np
from scipy import sparse
from scipy.sparse.linalg import eigsh
from sknetwork.base import Algorithm


class EigSolver(Algorithm, ABC):
    """Generic class for eigensolvers.

    Parameters
    ----------
    which: str
        Which eigenvectors and eigenvalues to find:

        * ``'LM'`` : Largest (in magnitude) eigenvalues.
        * ``'SM'` : Smallest (in magnitude) eigenvalues.

    Attributes
    ----------
    eigenvectors_: np.ndarray
        Two-dimensional array, each column is an eigenvector of the input.
    eigenvalues_: np.ndarray
        Eigenvalues associated to each eigenvector.
    """
    def __init__(self, which='LM'):
        self.which = which

        self.eigenvectors_ = None
        self.eigenvalues_ = None


[docs]class LanczosEig(EigSolver): """Eigenvalue solver using Lanczos method. Parameters ---------- which : str Which eigenvectors and eigenvalues to find: * ``'LM'`` : Largest (in modulus) eigenvalues. * ``'SM'`` : Smallest (in modulus) eigenvalues. * ``'LA'`` : Largest (algebraic) eigenvalues. * ``'SA'`` : Smallest (algebraic) eigenvalues. n_iter : int Maximum number of Arnoldi update iterations allowed. Default = 10 * nb of rows. tol : float Relative accuracy for eigenvalues (stopping criterion). Default = 0 (machine precision). Attributes ---------- eigenvectors_: np.ndarray Two-dimensional array, each column is an eigenvector of the input. eigenvalues_: np.ndarray Eigenvalues associated to each eigenvector. See Also -------- scipy.sparse.linalg.eigsh """ def __init__(self, which='LM', n_iter: int = None, tol: float = 0.): super(LanczosEig, self).__init__(which=which) self.n_iter = n_iter self.tol = tol
[docs] def fit(self, matrix: Union[sparse.csr_matrix, sparse.linalg.LinearOperator], n_components: int = 2): """Perform spectral decomposition on symmetric input matrix. Parameters ---------- matrix : sparse.csr_matrix or linear operator Matrix to decompose. n_components : int Number of eigenvectors to compute Returns ------- self: :class:`EigSolver` """ self.eigenvalues_, self.eigenvectors_ = eigsh(matrix.astype(float), n_components, which=self.which, maxiter=self.n_iter, tol=self.tol) return self