cbrnr cbrnr - 4 months ago 13
Python Question

Multiply each column from 2D array with each column from another 2D array

I have two Numpy arrays

x
with shape
(m, i)
and
y
with shape
(m, j)
(so the number of rows is the same). I would like to multiply each column of
x
with each column of
y
element-wise so that the result is of shape
(m, i*j)
.

Example:

import numpy as np

np.random.seed(1)
x = np.random.randint(0, 2, (10, 3))
y = np.random.randint(0, 2, (10, 2))


This creates the following two arrays
x
:

array([[1, 1, 0],
[0, 1, 1],
[1, 1, 1],
[0, 0, 1],
[0, 1, 1],
[0, 0, 1],
[0, 0, 0],
[1, 0, 0],
[1, 0, 0],
[0, 1, 0]])


and
y
:

array([[0, 0],
[1, 1],
[1, 1],
[1, 0],
[0, 0],
[1, 1],
[1, 1],
[1, 1],
[0, 1],
[1, 0]])


Now the result should be:

array([[0, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 1],
[1, 1, 1, 1, 1, 1],
[0, 0, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 1, 1],
[0, 0, 0, 0, 0, 0],
[1, 1, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0]])


Currently, I've implemented this operation with two nested loops over the columns of
x
and
y
:

def _mult(x, y):
r = []
for xc in x.T:
for yc in y.T:
r.append(xc * yc)
return np.array(r).T


However, I'm pretty sure that there must be a more elegant solution that I can't seem to come up with.

Answer

Use NumPy broadcasting -

(y[:,None]*x[...,None]).reshape(x.shape[0],-1)

Explanation

As inputs, we have -

y : 10 x 2
x : 10 x 3

With y[:,None], we are introducing a new axis between the existing two dims, thus creating a 3D array version of it. This keeps the first axis as the first one in 3D version and pushes out the second axis as the third one.

With x[...,None], we are introducing a new axis as the last one by pushing up the two existing dims as the first two dims to result in a 3D array version.

To summarize, with the introduction of new axes, we have -

y : 10 x 1 x 2
x : 10 x 3 x 1

With y[:,None]*x[...,None], there would be broadcasting for both y and x, resulting in an output array with a shape of (10,3,2). To get to the final output array of shape (10,6), we just need to merge the last two axes with that reshape.