How can I replace 1s in one matrix with another sub matrix?

Question

I have a matrix-like

[[1, 2],
 [3, 4]]

and I want to replace the 1s in another matrix:

[[1, 0],
 [1, 1]]

to make this matrix:

[[1, 2, 0, 0],
 [3, 4, 0, 0],
 [1, 2, 1, 2],
 [3, 4, 3, 4]]

The 1s in the second matrix can be in any position, this is just an example.

How can I do this?

Answer 1

Use scipy.linalg.kron

from scipy.linalg import kron

m1 = np.array([[1, 2],[3, 4]])
m2 = np.array([[1, 0], [1, 1]])

output:
kron(m2, m1)
array([[1, 2, 0, 0],
       [3, 4, 0, 0],
       [1, 2, 1, 2],
       [3, 4, 3, 4]])

How does it work?

It takes two arrays of M, N and P, Q dimensions. Here, m2 and m1 with 2, 2 and 2, 2 dimensions.

Next, it multiplies the arrays in the following way:

m2[0,0]*m1    m2[0,1]*m1  ... m2[0,-1]*m1
m2[1,0]*m1    m2[1,1]*m1  ... m2[1,-1]*m1
        ...
m2[-1,0]*m1   m2[-1,1]*m1 ... m2[-1,-1]*m1

To create a single array of dimensions (M*P, N*Q)

Answer 2

You can do that elegantly with a mathematical operation called Kronecker product which is implemented in numpy (or in scipy using numpy underneath).

import numpy as np # or from scipy import linealg
a = np.array([[1, 0], 
              [1, 1]])
b = np.array([[1, 2], 
              [3, 4]])
np.kron(a, b) # or linealg.kron(a, b)
# returns
# array([[1, 2, 0, 0],
#        [3, 4, 0, 0],
#        [1, 2, 1, 2],
#        [3, 4, 3, 4]])

And here is what the Kronecker product does mathematically:

In other words, with the matrix A (or numpy array a) we indicate if the entries of B shall be added (if 1) or not (if 0).