Numpy Elementwise Multiplication, with Multiple Columns [duplicate]

Question

I have the following numpy code. I have one array (a) with 3d points and another with weights (b). I need to multiply each row in a by each weight in b in the corresponding row. I am hoping to make this code more understandable and eliminate the loops.

a = np.array([[1, 2, 3], [4, 5, 6]])
b = np.array([[7, 8, 9, 10], [11, 12, 13, 14]])
c = np.zeros((2, 4, 3))

for i, row in enumerate(b):
    for j, col in enumerate(row):
        print('Mult:', a[i, :], '*', col)
        c[i, j, :] = a[i, :] * col

print(c[0, :, :])
print(c[1, :, :])

Here's the output.

Mult: [1 2 3] * 7
Mult: [1 2 3] * 8
Mult: [1 2 3] * 9
Mult: [1 2 3] * 10
Mult: [4 5 6] * 11
Mult: [4 5 6] * 12
Mult: [4 5 6] * 13
Mult: [4 5 6] * 14
[[ 7. 14. 21.]
 [ 8. 16. 24.]
 [ 9. 18. 27.]
 [10. 20. 30.]]
[[44. 55. 66.]
 [48. 60. 72.]
 [52. 65. 78.]
 [56. 70. 84.]]

willeM_ Van Onsem · Accepted Answer · 2019-09-05 13:17:48Z

4

You can shape the matrices differently, and then perform an element-wise multiplication:

a[:,None,:] * b[:,:,None]

So if a is an m×n-matrix and b is an m×p-matrix, we obtain an m×p×n-tensor. For the given sample data, we get:

>>> a[:,None,:] * b[:,:,None]
array([[[ 7, 14, 21],
        [ 8, 16, 24],
        [ 9, 18, 27],
        [10, 20, 30]],

       [[44, 55, 66],
        [48, 60, 72],
        [52, 65, 78],
        [56, 70, 84]]])

answered Sep 5, 2019 at 13:17

willeM_ Van Onsem

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5 Comments

Dan Grahn Over a year ago

Perfect. I'll accept as soon as I can. Thanks, I didn't know about that syntax.

Giacomo Alzetta Over a year ago

@DanGrahnJust FYI: you should not accept answers "as soon as you can". There is a time limit specifically because people tend to accept too early. If you wait some hours/1 or 2 days other answerers have a chance to provide better, more accurate solutions. Accepting the first thing that you think solves the problem is generally a bad idea. Nothing happens if you wait tomorrow to accept this answer except possibly getting an even better answer. (Not saying that in this specific instance Willem probably has the best solution, I want to make a general statement)

Mad Physicist Over a year ago

@DanGrahn. Look into broadcasting. None inserts a unit dimension wherever it appears in the index. Broadcasting lets you perform an element-wise operation between a dimension with one element and multiple elements.

Mad Physicist Over a year ago

@Giacomo. This answer is perfect.

Dan Grahn Over a year ago

@GiacomoAlzetta I agree with MadPhysicist. It's exactly what I asked for and it's clear. I just couldn't figure out the NP syntax.

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