Numpy matrix multiplication between a 2D array and each vector in 3D array

Question

I have one 3 x 3 numpy.ndarray, i.e. H, and one M x N x 3 numpy.ndarray, i.e. A.

What I want to do is multiplying H with each vector in A.

import numpy as np

H = np.array([[1, 2, 3],
              [4, 5, 6],
              [7, 8, 9]])  # 3 x 3 matrix

A = np.array([[[1, 2, 3],
               [4, 5, 6],
               [7, 8, 9]],

              [[10, 11, 12],
               [13, 14, 15],
               [16, 17, 18]]])  # 2 x 3 x 3 matrix

For example, in the above code, I want to apply matrix and vector multiplication between H and [1, 2, 3], [4, 5, 6], ..., [16, 17, 18], which are vector elements of A.

Therefore, the result would be

np.array([[[14, 32, 50],     # H @ A[0, 0]
           [32, 77, 122],    # H @ A[0, 1]
           [50, 122, 194]],  # H @ A[0, 2]

          [[68, 167, 266],   # H @ A[1, 0]
           [86, 212, 338],   # H @ A[1, 1]
           [104, 257, 410]]] # H @ A[1, 2]
        )

When I broadcast H @ A, H @ A[0] and H @ A[1] are applied, which is not that I expected.

Is there a way to broadcast in the way I want?

np.einsum('ij, klj -> kli', H, A)

Michael Szczesny
– Michael Szczesny

2022-04-27 08:42:40 +00:00
Commented Apr 27, 2022 at 8:42 — Michael Szczesny
– Michael Szczesny, Commented Apr 27, 2022 at 8:42

Onyambu · Accepted Answer · 2022-04-27 09:37:33Z

4

You could use the @ operator:

A @ H.T
 
array([[[ 14,  32,  50],
        [ 32,  77, 122],
        [ 50, 122, 194]],

       [[ 68, 167, 266],
        [ 86, 212, 338],
        [104, 257, 410]]])

answered Apr 27, 2022 at 9:37

Onyambu

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