How to efficiently do matrix multiplication for 2 specific dimensions of the tensor?

Hi,

I have a rank-5 tensor A and a rank-2 matrix B, and I want to captured the first two dimentions of A as slices and do the mutiplication with B to form an output C.

I can do it as below by using 3 for loops. But that is not efficient. How can I do it vectorizedly (i.e. without using the for loops)?

Many thanks!

My current code

A=randn(3,4,8,2,14);
B=randn(7,3);

C=zeros(7,4,8,2,14); % (7, 4) is due to matrix mutiplication of (7, 3)x(3, 4)
for i=1:8
    for j=1:2
        for k=1:14
            A_slice=A(:,:,i,j,k);
            C_slice=B*A_slice;
            C(:,:,i,j,k)=C_slice;
        end
    end
end
            
C % the output I want

Answer 1

[James Tursa]

Some FEX options that might work for you (some require an installed C compiler):

https://www.mathworks.com/matlabcentral/fileexchange/37515-mmx

https://www.mathworks.com/matlabcentral/fileexchange/25977-mtimesx-fast-matrix-multiply-with-multi-dimensional-support

https://www.mathworks.com/matlabcentral/fileexchange/8773-multiple-matrix-multiplications-with-array-expansion-enabled