How can we compute batch matrix-matrix product of matrices (3-D tensors) in MATLAB?

I have two 3-D tensors of size b*n*m and b*m*p. I need the product of these two tensors to get the output size as b*n*p. I have used direct matrix multiplication using * operator. Moreover, I have used 'pagetimes'. But it is not working. Is there any function in MATLAB like 'torch.bmm' in python as shown in link: https://pytorch.org/docs/stable/generated/torch.bmm.html to do the matrix multiplication of two 3-D tensors.

Answer 1

[Bruno Luong]

b = 2;
n = 3;
m = 4;
p = 5;
A = rand(b,n,m);
B = rand(b,  m,p);

AA = permute(A, [2 3 1]);
BB = permute(B, [2 4 1 3]);
AB=pagemtimes(AA, BB);
AB=permute(AB,[3 1 4 2]);

size(AB)

ans = 1×3

2 3 5

AB

AB = 
AB(:,:,1) =

    1.1069    0.9331    1.2839
    0.4248    1.0635    1.2576


AB(:,:,2) =

    1.3688    1.5129    1.6656
    0.6568    1.2286    1.3592


AB(:,:,3) =

    1.0351    1.2450    1.3362
    0.4743    1.1831    1.3162


AB(:,:,4) =

    1.2485    1.0840    1.4573
    0.7987    1.7168    1.7815


AB(:,:,5) =

    0.5739    0.7361    0.7294
    0.9621    1.9460    2.0458

[BIPIN SAMUEL]

Thank You @Bruno Luong. While using permute to BB and AB why the size of dimorder is 4? It is converting the tensor to 4D. Could you please tell why BB is converted to 4D? How the dimorder verctor is selected, i.e, in BB=permute(B, [2 4 1 3]) what does 4 represents because B is 3D matrix.

[Bruno Luong]

MATLAB can implicitly extend 3d array to 4d array by consider the 4th dimension is 1.

And generally it can extend forever with trailing dimensions as length of 1.

So B in my code is considered by MATLAB as as b*m*p*1

BB after permute of B is then m*1*b*p.

(I could achieve the same thing with BB = permute(B, [2 1 3]) then BB = reshape(BB, [m, 1, b, p]) as well, but it is shorter to use implicit trailing dimension)

AA is n*m*b

When calling pagemtimes, it iterates on dimensions 3 & 4 and do matrix multiplication for each pages the first two dimensions

(n*m) x (m*1) => (n*1)

So the reult of the before last instruction is of size

(n*1*b*p)

The last permute bring AB to

b*n*p*1

or

b*n*p (trailing dimension of length 1 is "ignored "by MATLAB)

[BIPIN SAMUEL]

Thank You @Bruno Luong Can it be used for customizing a layer because the input will be formatted dlarray?

[Bruno Luong]

Sorry I don't know dlarray, and I'm not sure what layer do you refer to.

[BIPIN SAMUEL]

I refer to the deep learning layer where input is 3-D tensor in the formatted dlarray and I want to do these operations as a part of forming that layer.