Multiply a 3D matrix with a 2D matrix

Question

Suppose I have an AxBxC matrix X and a BxD matrix Y.

Is there a non-loop method by which I can multiply each of the C AxB matrices with Y?

Answer 1

As a personal preference, I like my code to be as succinct and readable as possible.

Here's what I would have done, though it doesn't meet your 'no-loops' requirement:

for m = 1:C      Z(:,:,m) = X(:,:,m)*Y;  end 

This results in an A x D x C matrix Z.

And of course, you can always pre-allocate Z to speed things up by using Z = zeros(A,D,C);.

Answer 2

You can do this in one line using the functions NUM2CELL to break the matrix X into a cell array and CELLFUN to operate across the cells:

Z = cellfun(@(x) x*Y,num2cell(X,[1 2]),'UniformOutput',false); 

The result Z is a 1-by-C cell array where each cell contains an A-by-D matrix. If you want Z to be an A-by-D-by-C matrix, you can use the CAT function:

Z = cat(3,Z{:}); 

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NOTE: My old solution used MAT2CELL instead of NUM2CELL, which wasn't as succinct:

[A,B,C] = size(X); Z = cellfun(@(x) x*Y,mat2cell(X,A,B,ones(1,C)),'UniformOutput',false);