Dot product of tensor

Hi, I have two tensors A and B, of sizes (ma, na, 3), and (mb, nb, 3).

I would like to create C of size(ma, na, mb, nb) with C(i,j,k,h) = dot(A(i,j,:),B(k,h,:));

What is the fastest and most memory efficient way of achieving this? Many thanks!

Answer 1

[Bruno Luong]

If you have the R2022a, a single statement will do

A=rand(2,3,3);
B=rand(4,5,3);

C=tensorprod(A,B,3);
size(C)

ans = 1×4

2 3 4 5

[Leonardo Mutti]

Hi, thanks! Is there anything similar for sums instead of dot product? This way I'm not opening a new question.

[Bruno Luong]

I don't know what you meant by "sums" but MATLAB auto-expansion and reshape is like tensor operators

A=rand(2,3,3);
B=rand(4,5,3);
C = sum(A,3) + reshape(sum(B,3),[1 1 size(B,1) size(B,2)])
% or this?
C = reshape(A, [size(A,1) size(A,2) 1 1 size(A,3)]) + ...
    reshape(B, [1 1 size(B)])

[Leonardo Mutti]

Okay perfect, the second works well, many thanks.

Answer 2

[Matt J]

Ar=reshape(A,[],3);
Br=reshape(B,[],3);

C=reshape( Ar*Br.'  ,ma,na,mb,nb);