ó î&]\c@`sdZddlmZmZmZddlZddlmZddl m Z m Z m Z dgZ d„Zddd„ZdS( sSparse matrix norms. i(tdivisiontprint_functiontabsolute_importN(tissparse(tInftsqrttabstnormcC`sUtj|jtjƒr6t|ƒjdƒjƒ}n|jdƒjƒ}t|ƒS(Ni(tnpt issubdtypetdtypetcomplexfloatingRtpowertsumR(txtsqnorm((s8lib/python2.7/site-packages/scipy/sparse/linalg/_norm.pyt_sparse_frobenius_normsc C`s t|ƒstdƒ‚n|dkr=|dkr=t|ƒS|jƒ}|dkr^d}nlt|tƒsÊd}yt|ƒ}Wntk r¢t|ƒ‚nX||kr¾t|ƒ‚n|f}nd}t|ƒdkr|\}}| |ko|kno%| |ko#|knsDt d||j fƒ‚n||||krgt d ƒ‚n|dkr|t ‚q|d kr‘t ‚q|dkrÃt |ƒj d |ƒjd |ƒdS|tkrõt |ƒj d |ƒjd |ƒdS|d kr't |ƒj d |ƒjd |ƒdS|t krZt |ƒj d |ƒjd |ƒdS|dkrpt|ƒSt d ƒ‚nt|ƒdkr|\}| |ko²|knsÓt d||j fƒ‚n|tkrút |ƒjd |ƒ} n |t kr"t |ƒjd |ƒ} ná|dkrI|dkj d |ƒ} nº|dkrpt |ƒj d |ƒ} n“|dkr¦tt |ƒjdƒj d |ƒƒ} n]y |dWntk rÑt dƒ‚nXtjt |ƒj|ƒj d |ƒd|ƒ} | jjƒSt dƒ‚dS(sF Norm of a sparse matrix This function is able to return one of seven different matrix norms, depending on the value of the ``ord`` parameter. Parameters ---------- x : a sparse matrix Input sparse matrix. 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 ------- n : float or ndarray Notes ----- 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 [1]_: :math:`||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 * >>> 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) 6 s*input is not sparse. use numpy.linalg.normtfrotfiis6'axis' must be None, an integer or a tuple of integersis*Invalid axis %r for an array with shape %rsDuplicate axes given.iþÿÿÿtaxisiÿÿÿÿs Invalid norm order for matrices.sInvalid norm order for vectors.s&Improper number of dimensions to norm.N(NRR(ii(ii(ii(ii(ii(NRR(iN(Rt TypeErrortNoneRttocsrt isinstancettupletinttlent ValueErrortshapetNotImplementedErrorRR tmaxRtminRR RtAtravel( RtordRtmsgtint_axistndtrow_axistcol_axistatM((s8lib/python2.7/site-packages/scipy/sparse/linalg/_norm.pyRszX         :     & & & &        *  1 (t__doc__t __future__RRRtnumpyRt scipy.sparseRt numpy.coreRRRt__all__RRR(((s8lib/python2.7/site-packages/scipy/sparse/linalg/_norm.pyts