Scipy 稀疏矩阵 - 仅对非零元素进行逐元素乘法和除法

Question

I have three sparse matrices A , B , and C , and I want to compute the element-wise result of: (A*B)/C , ie element-wise multiply A with B , then element-wise divide by C .

Naturally, since C is sparse, division by zero results in most of the matrix elements set to infinity/nan. However, I am not interested in these elements since for my needs A is essentially a mask, and all zero indices in A should stay zeros in the result. In practice, scipy does calculate these items even though they could be masked if we decide that 0/0=0 .

What is the best way to avoid the redundant calculations of elements that are zeros in A ?

Example for concreteness:

A = sparse.csr_matrix(np.identity(100))
B = sparse.csr_matrix(np.identity(100) * 2)
C = sparse.csr_matrix(np.identity(100) * 5)

Z = ((A*B)/C)

Z[0,0]
>>> 0.4
Z[0,1]
>>> nan

Required result:

Z[0,0]
>>> 0.4
Z[0,1]
>>> 0.0

Note: I am mostly interested in the performance of this operation.

Answer 1

This is the best way to do this but if C.data has any 0s in it they'll still come out as NaN . How you choose to handle this probably depends on what exactly you're doing.

A = sparse.csr_matrix(np.identity(100))
B = sparse.csr_matrix(np.identity(100) * 2)
C = sparse.csr_matrix(np.identity(100) * 5)

C.data = 1 / C.data

Z = A*B*C

>>> Z
<100x100 sparse matrix of type '<class 'numpy.float64'>'
    with 100 stored elements in Compressed Sparse Row format>

>>> Z[0,0]
0.4
>>> Z[0,1]
0.0