scipy.sparse点在Python中非常慢

问题描述

以下代码甚至无法在我的系统上完成:

The following code will not even finish on my system:

import numpy as np
from scipy import sparse
p = 100
n = 50
X = np.random.randn(p,n)
L = sparse.eye(p,p, format='csc')
X.T.dot(L).dot(X)

有什么解释为什么这个矩阵乘法挂起了吗?

Is there any explanation why this matrix multiplication is hanging?

推荐答案

X.T.dot(L)不是50x100的矩阵，而是100x100的50x100稀疏矩阵的数组

X.T.dot(L) is not, as you may think, a 50x100 matrix, but an array of 50x100 sparse matrices of 100x100

>>> X.T.dot(L).shape
(50, 100)
>>> X.T.dot(L)[0,0]
<100x100 sparse matrix of type '<type 'numpy.float64'>'
    with 100 stored elements in Compressed Sparse Column format>

问题似乎是X的dot方法(它是一个数组)不知道稀疏矩阵.因此，您必须使用其todense或toarray方法将稀疏矩阵转换为稠密矩阵.前者返回matrix对象，后者返回array:

It seems that the problem is that X's dot method, it being an array, doesn't know about sparse matrices. So you must either convert the sparse matrix to dense using its todense or toarray method. The former returns a matrix object, the latter an array:

>>> X.T.dot(L.todense()).dot(X)
matrix([[  81.85399873,    3.75640482,    1.62443625, ...,    6.47522251,
            3.42719396,    2.78630873],
        [   3.75640482,  109.45428475,   -2.62737229, ...,   -0.31310651,
            2.87871548,    8.27537382],
        [   1.62443625,   -2.62737229,  101.58919604, ...,    3.95235372,
            1.080478  ,   -0.16478654],
        ...,
        [   6.47522251,   -0.31310651,    3.95235372, ...,   95.72988689,
          -18.99209596,   17.31774553],
        [   3.42719396,    2.87871548,    1.080478  , ...,  -18.99209596,
          108.90045569,  -16.20312682],
        [   2.78630873,    8.27537382,   -0.16478654, ...,   17.31774553,
          -16.20312682,  105.37102461]])

或者，稀疏矩阵具有dot知道数组的方法:

Alternatively, sparse matrices have a dot method that knows about arrays:

>>> X.T.dot(L.dot(X))
array([[  81.85399873,    3.75640482,    1.62443625, ...,    6.47522251,
           3.42719396,    2.78630873],
       [   3.75640482,  109.45428475,   -2.62737229, ...,   -0.31310651,
           2.87871548,    8.27537382],
       [   1.62443625,   -2.62737229,  101.58919604, ...,    3.95235372,
           1.080478  ,   -0.16478654],
       ...,
       [   6.47522251,   -0.31310651,    3.95235372, ...,   95.72988689,
         -18.99209596,   17.31774553],
       [   3.42719396,    2.87871548,    1.080478  , ...,  -18.99209596,
         108.90045569,  -16.20312682],
       [   2.78630873,    8.27537382,   -0.16478654, ...,   17.31774553,
         -16.20312682,  105.37102461]])

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