Multiplying two 2D numpy arrays to a 3D array

Question

I've got two 2D numpy arrays called A and B, where A is M x N and B is M x n. My problem is that I wish to multiply each element of each row of B with corresponding row of A and create a 3D matrix C which is of size M x n x N, without using for-loops.

As an example, if A is:

A = np.array([[1, 2, 3],
              [4, 5, 6]])

and B is

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

Then the resulting multiplication C = A x B would look something like

C = [
     [[1, 2],
      [12, 16]],
     [[2, 4],
      [15, 20]],
     [[3, 6],
      [18, 24]]
     ]

Is it clear what I'm trying to achieve, and is it possible doing without any for-loops? Best, tingis

swimfar2 · Accepted Answer · 2023-08-18 19:31:40Z

6

You can use the NumPy Einstein summation function, einsum():

C=np.einsum('ij,ik->jik',A,B)

edited Aug 18, 2023 at 19:31

swimfar2

1878 bronze badges

answered Aug 20, 2015 at 11:55

yevgeniy

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4 Comments

Tingiskhan Over a year ago

Thanks for the quick answer! This funcition helps a lot, will go with your solution!

yevgeniy Over a year ago

einsum can do wondrous things, i think it is also faster than other numpy vector product methods. Also, by changing the index order after ->, you can do a reshape without an extra call to the actual reshape.

Saullo G. P. Castro Over a year ago

@yevgeniy about being faster, It depends on the size of the array. Usually it is faster for smaller arrays, while for larger arrays I measured speeds comparable to the method using newaxis

yevgeniy Over a year ago

@SaulloCastro. Thanks for running an actual test. I was also following this, where einsum really showed great performance, so it seems at array size >10000 is where one should consider alternative solutions.

Saullo G. P. Castro · Accepted Answer · 2015-08-20 11:54:01Z

4

It is possible by creating a new axis in each array and transposing the modified A:

A[np.newaxis,...].T * B[np.newaxis,...]

giving:

array([[[ 1,  2],
        [12, 16]],

       [[ 2,  4],
        [15, 20]],

       [[ 3,  6],
        [18, 24]]])

answered Aug 20, 2015 at 11:54

Saullo G. P. Castro

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1 Comment

Tingiskhan Over a year ago

Wow, thanks for the quick answer! Going with yev's answer though, as he needs the points ;D

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