Scipy稀疏效率乘以两个矩阵时的警告

debugcn 发表于 Dev

leo_bouts

我正在尝试将稀疏稀疏矩阵与值列表相乘。该代码按预期工作，但我在inv电话中收到这两个警告：

1）SparseEfficiencyWarning：splu需要CSC矩阵格式警告（“ splu需要CSC矩阵格式”，SparseEfficiencyWarning）

2）SparseEfficiencyWarning：当稀疏b为CSC矩阵格式时，spsolve效率更高warn（'当稀疏b时spsolve效率更高'）

L_plus_I矩阵是的类型<class 'scipy.sparse.csr.csr_matrix'>。

from scipy.sparse.linalg import inv
from scipy.sparse import identity
import networkx as nx

no_of_nodes = len(g.nodes)

values = list(nx.get_node_attributes(g, 'value').values())

Laplace = nx.laplacian_matrix(g)
Identity = identity(no_of_nodes)
L_plus_I = Laplace + Identity
Inverse = inv(L_plus_I)

solutions = Inverse * values

很明显这些是因为values只是一个列表而生成的，但是当我尝试使其稀疏时，会在计算中出错。一般而言，如何改善运行时间？

hpaulj

从另一个问题的矩阵开始：

In [74]: A_sp
Out[74]: 
<5x5 sparse matrix of type '<class 'numpy.int64'>'
    with 24 stored elements in Compressed Sparse Row format>
In [75]: A_sp.A
Out[75]: 
array([[7, 4, 2, 9, 0],
       [6, 2, 5, 7, 4],
       [6, 6, 4, 3, 1],
       [5, 6, 5, 1, 2],
       [4, 8, 6, 5, 6]])

在inv你的警告：

In [76]: inv(A_sp)
/usr/local/lib/python3.8/dist-packages/scipy/sparse/linalg/dsolve/linsolve.py:318: SparseEfficiencyWarning: splu requires CSC matrix format
  warn('splu requires CSC matrix format', SparseEfficiencyWarning)
/usr/local/lib/python3.8/dist-packages/scipy/sparse/linalg/dsolve/linsolve.py:215: SparseEfficiencyWarning: spsolve is more efficient when sparse b is in the CSC matrix format
  warn('spsolve is more efficient when sparse b '
Out[76]: 
<5x5 sparse matrix of type '<class 'numpy.float64'>'
    with 25 stored elements in Compressed Sparse Row format>

查看代码，我看到inv(A)的只是`spsolve（A，I）

In [77]: Identity=sparse.identity(5)
In [79]: Identity
Out[79]: 
<5x5 sparse matrix of type '<class 'numpy.float64'>'
    with 5 stored elements (1 diagonals) in DIAgonal format>

In [80]: spsolve(A_sp, Identity)
/usr/local/lib/python3.8/dist-packages/scipy/sparse/linalg/dsolve/linsolve.py:318: SparseEfficiencyWarning: splu requires CSC matrix format
  warn('splu requires CSC matrix format', SparseEfficiencyWarning)
/usr/local/lib/python3.8/dist-packages/scipy/sparse/linalg/dsolve/linsolve.py:215: SparseEfficiencyWarning: spsolve is more efficient when sparse b is in the CSC matrix format
  warn('spsolve is more efficient when sparse b '
Out[80]: 
<5x5 sparse matrix of type '<class 'numpy.float64'>'
    with 25 stored elements in Compressed Sparse Row format>

转换Identity格式：

In [81]: spsolve(A_sp, Identity.tocsc())
/usr/local/lib/python3.8/dist-packages/scipy/sparse/linalg/dsolve/linsolve.py:318: SparseEfficiencyWarning: splu requires CSC matrix format
  warn('splu requires CSC matrix format', SparseEfficiencyWarning)
Out[81]: 
<5x5 sparse matrix of type '<class 'numpy.float64'>'
    with 25 stored elements in Compressed Sparse Row format>

A以及转换：

In [82]: spsolve(A_sp.tocsc(), Identity.tocsc())
Out[82]: 
<5x5 sparse matrix of type '<class 'numpy.float64'>'
    with 25 stored elements in Compressed Sparse Column format>

是的，没有警告:)

In [83]: _.A
Out[83]: 
array([[-1.08108108e+00,  4.59459459e-01,  2.97297297e+00,
        -2.40540541e+00, -1.58603289e-16],
       [ 3.04054054e-02, -1.72297297e-01,  1.35135135e-01,
        -9.79729730e-02,  1.25000000e-01],
       [ 1.42567568e+00, -4.12162162e-01, -4.10810811e+00,
         3.62837838e+00, -2.50000000e-01],
       [ 6.21621622e-01, -1.89189189e-01, -1.45945946e+00,
         1.10810811e+00,  8.54017711e-17],
       [-1.26351351e+00,  4.93243243e-01,  3.16216216e+00,
        -2.81756757e+00,  2.50000000e-01]])

针对密集版本进行测试：

In [84]: np.linalg.inv(A_sp.A)
Out[84]: 
array([[-1.08108108e+00,  4.59459459e-01,  2.97297297e+00,
        -2.40540541e+00, -1.58603289e-16],
       [ 3.04054054e-02, -1.72297297e-01,  1.35135135e-01,
        -9.79729730e-02,  1.25000000e-01],
       [ 1.42567568e+00, -4.12162162e-01, -4.10810811e+00,
         3.62837838e+00, -2.50000000e-01],
       [ 6.21621622e-01, -1.89189189e-01, -1.45945946e+00,
         1.10810811e+00,  8.54017711e-17],
       [-1.26351351e+00,  4.93243243e-01,  3.16216216e+00,
        -2.81756757e+00,  2.50000000e-01]])

实际上inv使用I = _ident_like(A)，所以这就足够了：

In [85]: inv(A_sp.tocsc())
Out[85]: 
<5x5 sparse matrix of type '<class 'numpy.float64'>'
    with 25 stored elements in Compressed Sparse Column format>

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