Multiply a 3D matrix with a 2D matrix
matlab, matrix, matrix-multiplication, vectorization
Solution
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{:});
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);
Problem
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`?