norm#
- scipy.sparse.linalg.norm(x, ord=None, axis=None)[source]#
- Norm of a sparse matrix - This function is able to return one of seven different matrix norms, depending on the value of the - ordparameter.- Parameters:
- xa sparse array
- Input sparse array. 
- ord{non-zero int, inf, -inf, ‘fro’}, optional
- Order of the norm (see table under - Notes). inf means numpy’s inf object.
- axis{int, 2-tuple of ints, None}, optional
- If axis is an integer, it specifies the axis of x along which to compute the vector norms. If axis is a 2-tuple, it specifies the axes that hold 2-D matrices, and the matrix norms of these matrices are computed. If axis is None then either a vector norm (when x is 1-D) or a matrix norm (when x is 2-D) is returned. 
 
- Returns:
- nfloat or ndarray
 
 - Notes - Some of the ord are not implemented because some associated functions like, _multi_svd_norm, are not yet available for sparse array. - This docstring is modified based on numpy.linalg.norm. numpy/numpy - The following norms can be calculated: - ord - norm for sparse arrays - 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 - Spectral norm (the largest singular value) - -2 - Not implemented - other - Not implemented - The Frobenius norm is given by [1]: - \(||A||_F = [\sum_{i,j} abs(a_{i,j})^2]^{1/2}\) - References [1]- G. H. Golub and C. F. Van Loan, Matrix Computations, Baltimore, MD, Johns Hopkins University Press, 1985, pg. 15 - Examples - >>> from scipy.sparse import csr_array, diags_array >>> 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_array(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) 6 - The matrix 2-norm or the spectral norm is the largest singular value, computed approximately and with limitations. - >>> b = diags_array([-1, 1], [0, 1], shape=(9, 10)) >>> norm(b, 2) 1.9753...