# 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.

--------
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
```