multiplying 2 2d matrices and get a 3d matrix out

Question

import numpy as np

a = np.array([[1,2],[3,4]])

print(a.shape)

c = np.array([[1,2,3]])

print(c.shape)


#wanted result multiplication of a*c would return 2,2,3 shape matrix

final = np.array([[[1,2,3],[2,4,6]],[[3,6,9],[4,8,12]]])

print(final.shape)
print(final)

I would like to multiply two matrices with different shapes and basically get a result which would be a 3d matrix. I hope you get the pattern from the code. Is there any simple numpyic way for this? I would appreciate it.

Answer 1

You can use NumPy broadcasting for this:

a[...,None] * c

array([[[ 1,  2,  3],
        [ 2,  4,  6]],

       [[ 3,  6,  9],
        [ 4,  8, 12]]])

---

The following basically alings the dimensions so the multiplication is broadcast to the desired output shape:

a[...,None].shape
(2, 2, 1)

Answer 2

Try np.einsum

out = np.einsum('ij,kl->klj',c,a)

Out[35]:
array([[[ 1,  2,  3],
        [ 2,  4,  6]],

       [[ 3,  6,  9],
        [ 4,  8, 12]]])

In [36]: out.shape
Out[36]: (2, 2, 3)