norm(x, ord=None, axis=None)
This function is able to return one of seven different matrix norms, depending on the value of the ord
parameter.
Some of the ord are not implemented because some associated functions like, _multi_svd_norm, are not yet available for sparse matrix.
This docstring is modified based on numpy.linalg.norm. https://github.com/numpy/numpy/blob/master/numpy/linalg/linalg.py
The following norms can be calculated:
===== ============================ ord norm for sparse matrices ===== ============================ None Frobenius norm 'fro' Frobenius norm inf max(sum(abs(x), axis=1)) -inf min(sum(abs(x), axis=1)) 0 abs(x).sum(axis=axis) 1 max(sum(abs(x), axis=0)) -1 min(sum(abs(x), axis=0)) 2 Not implemented -2 Not implemented other Not implemented ===== ============================
The Frobenius norm is given by :
$||A||_F = [\sum_{i,j} abs(a_{i,j})^2]^{1/2}$
Input sparse matrix.
Order of the norm (see table under Notes
). inf means numpy's :None:None:`inf` object.
If :None:None:`axis` is an integer, it specifies the axis of x along which to compute the vector norms. If :None:None:`axis` is a 2-tuple, it specifies the axes that hold 2-D matrices, and the matrix norms of these matrices are computed. If :None:None:`axis` is None then either a vector norm (when x is 1-D) or a matrix norm (when x is 2-D) is returned.
Norm of a sparse matrix
>>> from scipy.sparse import *
... import numpy as np
... from scipy.sparse.linalg import norm
... a = np.arange(9) - 4
... a array([-4, -3, -2, -1, 0, 1, 2, 3, 4])
>>> b = a.reshape((3, 3))
... b array([[-4, -3, -2], [-1, 0, 1], [ 2, 3, 4]])
>>> b = csr_matrix(b)
... norm(b) 7.745966692414834
>>> norm(b, 'fro') 7.745966692414834
>>> norm(b, np.inf) 9
>>> norm(b, -np.inf) 2
>>> norm(b, 1) 7
>>> norm(b, -1) 6See :
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.sparse.linalg._norm.norm
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