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

Question

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.

Divakar · Accepted Answer · 2016-08-02 14:13:45Z

7

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.

edited Aug 2, 2016 at 14:13

answered Aug 2, 2016 at 8:26

Divakar

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3 Comments

Colonel Beauvel Over a year ago

"complicated" hack but very concise! +1

kmario23 Over a year ago

can you add some explanation here? it's concise but not explanatory.

Divakar Over a year ago

@kmario23 Added some explanation, check it out!

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