Python - Matrix outer product

Question

Given two matrices

A: m * r
B: n * r

I want to generate another matrix C: m * n, with each entry C_ij being a mat

Answer 1

Simple Solution with Numpy Array Broadcasting

Since, you want C_ij = A_i * B_j, this can be achieved simply by numpy broadcasting on element-wise-product of column-vector-A and row-vector-B, as shown below:

# import numpy as np
# A = [[1, 2], [3, 4]]
# B = [[3, 1], [1, 2]]
A, B = np.array(A), np.array(B)
C = A.reshape(-1,1) * B.reshape(1,-1)
# same as: 
# C = np.einsum('i,j->ij', A.flatten(), B.flatten())
print(C)

Output:

array([[ 3,  1,  1,  2],
       [ 6,  2,  2,  4],
       [ 9,  3,  3,  6],
       [12,  4,  4,  8]])

You could then get your desired four sub-matrices by using numpy.dsplit() or numpy.array_split() as follows:

np.dsplit(C.reshape(2, 2, 4), 2)
# same as:
# np.array_split(C.reshape(2,2,4), 2, axis=2)

Output:

[array([[[ 3,  1],
         [ 6,  2]],

        [[ 9,  3],
         [12,  4]]]), 
array([[[1, 2],
         [2, 4]],

        [[3, 6],
         [4, 8]]])]