matrix product for each element of a multidimensional array in MATLAB

I would like to achieve matrix product operations for each of the following elements in MATLAB that Python numpy.einsum can achieve.

import numpy as np
a=np.array([[1,2],[3,4]],[[1,3],[-3,1]]]])
b=np.array([2,-1],[1,1]])
c=np.einsum('ijk, kl->ijl', a, b)
d1 = a[0]@b
d2 = a[1]@b
print(c)
print(d1)
print(d2)

In other words,
for 3D array A (size: MxMxN) and 2D array B (size: MxM). I would like to efficiently calculate the 3D array C satisfying C[:,:,n]=A[:,:,n]*B for each n=1,...,N in MATLAB.
We are currently in a loop regarding n, so please let us know if there is a more efficient way.
Other than using einsum's MATLAB implementation in File Exchange of Github and MathWorks.

python numpy matlab

2022-09-30 13:52

1 Answers

If there is a 3D array A (size: MxMxN) and a 2D array B (size: MxM), wouldn't it be better to change A to M*NxM and then take the product of the normal matrix?

a=[1,2;3,4]; 
a(:, :, 2) = [1,3;-31];
b = [2, -1; 1,1];

M = size(a,1);
N = size(a,3);
a2 = permit(a,[1,3,2]);
A=reshape(a2,M*N,M);
% A =
%      1     2
%      3     4
%      1     3
%     -3     1

C = A*b;

tC = C';
c0=reshape(tC,M,M,N);
c=permute(c0,[2,1,3])

2022-09-30 13:52

If you have any answers or tips

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