Source code for sknetwork.linalg.normalizer

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created in November 2019
@author: Nathan de Lara <nathan.delara@polytechnique.org>
"""
from typing import Union

import numpy as np
from scipy import sparse
from scipy.sparse.linalg import LinearOperator


[docs] def diagonal_pseudo_inverse(weights: np.ndarray) -> sparse.csr_matrix: """Compute :math:`\\text{diag}(w)^+`, the pseudo-inverse of the diagonal matrix with diagonal elements given by the weights :math:`w`. Parameters ---------- weights: The weights to invert. Returns ------- sparse.csr_matrix """ diag: sparse.csr_matrix = sparse.diags(weights, format='csr') diag.data = 1 / diag.data return diag
def get_norms(matrix: Union[sparse.csr_matrix, np.ndarray, LinearOperator], p=1): """Get the norms of rows of a matrix. Parameters ---------- matrix : numpy array or sparse CSR matrix or LinearOperator, shape (n_rows, n_cols) Input matrix. p : Order of the norm (1 or 2). Returns ------- norms : np.array, shape (n_rows,) Vector norms """ n_row, n_col = matrix.shape if isinstance(matrix, np.ndarray): input_matrix = sparse.csr_matrix(matrix) elif isinstance(matrix, sparse.csr_matrix): input_matrix = matrix.copy() else: input_matrix = matrix if p == 1: if not isinstance(matrix, LinearOperator): input_matrix.data = np.abs(input_matrix.data) return input_matrix.dot(np.ones(n_col)) elif p == 2: if isinstance(matrix, LinearOperator): raise ValueError('Only norm 1 is available for linear operators.') input_matrix.data = input_matrix.data**2 return np.sqrt(input_matrix.dot(np.ones(n_col))) else: raise ValueError('Only norms 1 and 2 are available.')
[docs] def normalize(matrix: Union[sparse.csr_matrix, np.ndarray, LinearOperator], p=1): """Normalize the rows of a matrix so that all have norm 1 (or 0; null rows remain null). Parameters ---------- matrix : Input matrix. p : Order of the norm. Returns ------- normalized matrix : Normalized matrix (same format as input matrix). """ norms = get_norms(matrix, p) diag = diagonal_pseudo_inverse(norms) if hasattr(matrix, 'left_sparse_dot') and callable(matrix.left_sparse_dot): return matrix.left_sparse_dot(diag) return diag.dot(matrix)