乘法和点积与邻接矩阵(numpy)

时间:2017-07-03 00:03:02

标签: python numpy networkx numpy-broadcasting numpy-ufunc

当我发现以下奇怪之处时,我正在使用以下网络代码块。在第一种情况下,我在稀疏矩阵上使用了ufunc multiply(*),它意外地正确地给了我一个度序列。然而,当使用普通矩阵完成相同的操作时,它会给我一个10 x 10矩阵,正如预期的那样,np.dot(...)给出了正确的结果。

import numpy as np
import networks as nx

ba = nx.barabasi_albert_graph(n=10, m=2)

A = nx.adjacency_matrix(ba)
# <10x10 sparse matrix of type '<class 'numpy.int64'>'
# with 32 stored elements in Compressed Sparse Row format>

A * np.ones(10)

# output: array([ 5.,  3.,  4.,  5.,  4.,  3.,  2.,  2.,  2.,  2.])

nx.degree(ba)

# output {0: 5, 1: 3, 2: 4, 3: 5, 4: 4, 5: 3, 6: 2, 7: 2, 8: 2, 9: 2}

B = np.ones(100).reshape(10, 10)

B * np.ones(10)

array([[ 1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.],
   [ 1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.],
   [ 1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.],
   [ 1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.],
   [ 1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.],
   [ 1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.],
   [ 1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.],
   [ 1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.],
   [ 1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.],
   [ 1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.]])

np.dot(B, np.ones(10))
# array([ 10.,  10.,  10.,  10.,  10.,  10.,  10.,  10.,  10.,  10.])

我原以为我应该做np.dot(A, np.ones(10))但是会​​返回一个10,10 x 10矩阵的数组

array([ <10x10 sparse matrix of type '<class 'numpy.float64'>'
with 32 stored elements in Compressed Sparse Row format>,
   <10x10 sparse matrix of type '<class 'numpy.float64'>'
with 32 stored elements in Compressed Sparse Row format>,
   <10x10 sparse matrix of type '<class 'numpy.float64'>'
with 32 stored elements in Compressed Sparse Row format>,
   <10x10 sparse matrix of type '<class 'numpy.float64'>'
with 32 stored elements in Compressed Sparse Row format>,
   <10x10 sparse matrix of type '<class 'numpy.float64'>'
with 32 stored elements in Compressed Sparse Row format>,
   <10x10 sparse matrix of type '<class 'numpy.float64'>'
with 32 stored elements in Compressed Sparse Row format>,
   <10x10 sparse matrix of type '<class 'numpy.float64'>'
with 32 stored elements in Compressed Sparse Row format>,
   <10x10 sparse matrix of type '<class 'numpy.float64'>'
with 32 stored elements in Compressed Sparse Row format>,
   <10x10 sparse matrix of type '<class 'numpy.float64'>'
with 32 stored elements in Compressed Sparse Row format>,
   <10x10 sparse matrix of type '<class 'numpy.float64'>'
with 32 stored elements in Compressed Sparse Row format>], dtype=object)

这里的细微差别是什么?

1 个答案:

答案 0 :(得分:0)

对于常规numpy数组,*乘以元素(broadcasting)。 np.dot是矩阵乘积,即乘积和。对于np.matrix子类*,矩阵乘积为dotsparse.matrix不是子类,但它以此为模型。 *是矩阵产品。

In [694]: A = sparse.random(10,10,.2, format='csr')
In [695]: A
Out[695]: 
<10x10 sparse matrix of type '<class 'numpy.float64'>'
    with 20 stored elements in Compressed Sparse Row format>
In [696]: A *np.ones(10)
Out[696]: 
array([ 0.6349177 ,  0.        ,  1.25781168,  1.12021258,  2.43477065,
        1.10407149,  1.95096264,  0.6253589 ,  0.44242708,  0.50353061])

稀疏矩阵具有dot方法,其行为相同:

In [698]: A.dot(np.ones(10))
Out[698]: 
array([ 0.6349177 ,  0.        ,  1.25781168,  1.12021258,  2.43477065,
        1.10407149,  1.95096264,  0.6253589 ,  0.44242708,  0.50353061])

密集版本:

In [699]: np.dot(A.A,np.ones(10))
Out[699]: 
array([ 0.6349177 ,  0.        ,  1.25781168,  1.12021258,  2.43477065,
        1.10407149,  1.95096264,  0.6253589 ,  0.44242708,  0.50353061])

我认为np.dot应该正确处理稀疏矩阵,这与他们自己的方法不同。但是np.dot(A,np.ones(10))没有做到这一点,产生了2个稀疏矩阵的对象数组。我可以深入研究为什么,但现在,避免它。

通常,使用稀疏矩阵的稀疏函数和方法。不要认为numpy函数会正确使用它们。

当两个数组都稀疏时,

np.dot工作正常,

In [702]: np.dot(A,A)
Out[702]: 
<10x10 sparse matrix of type '<class 'numpy.float64'>'
    with 32 stored elements in Compressed Sparse Row format>
In [703]: np.dot(A,A.T)
Out[703]: 
<10x10 sparse matrix of type '<class 'numpy.float64'>'
    with 31 stored elements in Compressed Sparse Row format>

In [705]: np.dot(A, sparse.csr_matrix(np.ones(10)).T)
Out[705]: 
<10x1 sparse matrix of type '<class 'numpy.float64'>'
    with 9 stored elements in Compressed Sparse Row format>
In [706]: _.A
Out[706]: 
array([[ 0.6349177 ],
       [ 0.        ],
       [ 1.25781168],
       [ 1.12021258],
       [ 2.43477065],
       [ 1.10407149],
       [ 1.95096264],
       [ 0.6253589 ],
       [ 0.44242708],
       [ 0.50353061]])

使用这种矩阵产品执行稀疏sum的价值是什么:

In [708]: A.sum(axis=1)
Out[708]: 
matrix([[ 0.6349177 ],
        [ 0.        ],
        [ 1.25781168],
        [ 1.12021258],
        [ 2.43477065],
        [ 1.10407149],
        [ 1.95096264],
        [ 0.6253589 ],
        [ 0.44242708],
        [ 0.50353061]])