Multiplying a 2d array with each slice of 3d array - Numpy

Question

I am looking for an optimized way of computing a element wise multiplication of a 2d array by each slice of a 3d array (using numpy).

for example:

w = np.array([[1,5], [4,9], [12,15]]) y = np.ones((3,2,3))

I want to get a result as a 3d array with the same shape as y.

Broadcasting using the * operator is not allowed. In my case, the third dimensions is very long and a for loop is not convenient.

Answer 1

Given arrays

import numpy as np

w = np.array([[1,5], [4,9], [12,15]])

print(w)

[[ 1  5]
 [ 4  9]
 [12 15]]

and

y = np.ones((3,2,3))

print(y)

[[[ 1.  1.  1.]
  [ 1.  1.  1.]]

 [[ 1.  1.  1.]
  [ 1.  1.  1.]]

 [[ 1.  1.  1.]
  [ 1.  1.  1.]]]

We can multiple the arrays directly,

z = ( y.transpose() * w.transpose() ).transpose()

print(z)

[[[  1.   1.   1.]
  [  5.   5.   5.]]

 [[  4.   4.   4.]
  [  9.   9.   9.]]

 [[ 12.  12.  12.]
  [ 15.  15.  15.]]]

We might note that this produces the same result as np.einsum('ij,ijk->ijk',w,y), perhaps with a little less effort and overhead.