bsxfun-like for matrix product

Question

I need to multiply a matrix A with n matrices, and get n matrices back. For example, multiply a 2x2 matrix with 3 2x2 matrices stacked as a 2x2x3 Matlab array. bsxfun is what I usually use for such situations, but it only applies for element-wise operations. I could do something like:

blkdiag(a, a, a) * blkdiag(b(:,:,1), b(:,:,2), b(:,:,3))

but I need a solution for arbitrary n - ?

Cindacindee

mathworks.com/matlabcentral/newsreader/view_thread/311944 check out the comments for FEX links – Inhospitality

Cannot test now, but in the example times is used, perhaps mtimes can be substituted here. – Amphiprostyle

Answer 1

You can reshape the stacked matrices. Suppose you have k-by-k matrix a and a stack of m k-by-k matrices sb and you want the product a*sb(:,:,ii) for ii = 1..m. Then all you need is

sza = size(a);
b = reshape( b, sza(2), [] ); % concatenate all matrices aloong the second dim
res = a * b; 
res = reshape( res, sza(1), [], size(sb,3) ); % stack back to 3d

Inferno

+1 Well thought. But you need to store size(sb,3) before reshaping b, in order to use it at the end – Clift

@LuisMendo if you pay close attention I have two variables: sb for the "stacked" version and just b for the resized one. – Inferno

Oh I see. I thought you were using (and overwriting) b. – Clift

@LuisMendo but you are right that when reshaping and messing with arrays' sizes one better keep track of what is going on... – Inferno

@Inferno In this case it should be b = reshape( sb, sza(2), [] ); – Omarr

BTW, what if I'd like to calculate sb(:,:,ii)*a? – Omarr

Answer 2

Your solution can be adapted to arbitrary size using comma-saparated lists obtained from cell arrays:

[k m n] = size(B);
Acell = mat2cell(repmat(A,[1 1 n]),k,m,ones(1,n));
Bcell = mat2cell(B,k,m,ones(1,n));
blkdiag(Acell{:}) * blkdiag(Bcell{:});

You could then stack the blocks on a 3D array using this answer, and keep only the relevant ones.

But in this case a good old loop is probably faster:

C = NaN(size(B));
for nn = 1:n
    C(:,:,nn) = A * B(:,:,nn);
end

Clift

Answer 3

For large stacks of matrices and/or vectors over which to execute matrix multiplication, speed can start becoming an issue. To avoid re-inventing the wheel, you could simply compile and use the following fast MEX code: MTIMESX - Mathworks. As a rule of thumb, MATLAB is often quite inefficient at executing for loops over large numbers of operations which look like they should be vectorizable; I cannot think of a straightforward way of generalising Shai's answer to this case.

Celinecelinka

While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. – Elodia

Given that the link itself is to the mathworks page for downloading code developed by a 3rd party ( mtimesx - GitHub ), it would not be appropriate for me to claim any part of their work as my own answer. If the link becomes broken, I would naturally attempt to replace it or else delete my answer. – Celinecelinka