Vectorize many matrix multiplications using the third dimension

I have collections of matrices, say two collections A and B of n matrices each, implemented as cell arrays. I would like to produce a third collection C by multiplying the matrices from the first two collections:

C = cell(1, n);
for i = 1:n
    C{i} = A{i} * B{i};
end

Is it possible instead to use 3D arrays to vectorize this operation? Suppose that A and B are m x m x n arrays, where the ith page (where i ranges from 1 to n) of the arrays are the same as the ith cell in the previous example. Then, is it possible to write something that would look like

C = A * B;

to perform the multiplications in a way that is transparent for the pages of A and B?

Answer 1

[James Tursa]

See this link:

https://www.mathworks.com/matlabcentral/answers/456711-how-can-i-do-matrix-multiplication-on-sets-of-data-in-an-array-without-looping

And see these FEX submissions:

MTIMESX: (mex, needs C-compiler)

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

MMX: (mex, needs C-compiler)

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

MULTIPROD: (M-code)

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

[Alec Poulin]

Your function does exactly what I need and I was able to compile it without too much trouble. Thank you a lot!

[Alec Poulin]

Another question: Would there be a way to do the same thing with mldivide? I saw that there are pre-operations available for the matrices, but there is no inverse among them.