Multiplying a small matrix by a big matrix
linear-algebra, matlab, matrix, matrix-multiplication
Solution
One possibility is to use `repmat` to repeat the small matrix as many times as necessary:
C = repmat(A,size(B,1)/size(A,1),size(B,2)/size(A,2)).*B
Another possibility, which avoids `repmat`: cut up the large matrix, arrange the pieces in the third and fourth dimensions, and use `bsxfun` to do the multiplication:
[m n] = size(A);
[M N] = size(B);
T = permute(reshape(B,M,n,[]), [2 1 3]);
T = permute(reshape(T,n,m,[],size(T,3)),[2 1 3 4]);
C = cell2mat(squeeze(mat2cell(bsxfun(@times,T,A),m,n,ones(1,M/m),ones(1,N/n))));
(The two lines `T = ...` do the cutting, and are due to A. Donda.)
The advantage of this approach is that, if memory is an issue, you can overwrite `B` instead of defining `T`, thus saving memory:
[m n] = size(A);
[M N] = size(B);
B = permute(reshape(B,M,n,[]),[2 1 3]);
B = permute(reshape(B,n,m,[],size(B,3)),[2 1 3 4]);
C = cell2mat(squeeze(mat2cell(bsxfun(@times,B,A),m,n,ones(1,M/m),ones(1,N/n))));
Problem
I'm trying to multiply every element in a small matrix (let's say 2x2) with every position in a big matrix (let's say 4x4), element by element. So I want: ``` 1 2 3 4 1 0 3 0 1 0 1 2 3 4 0 0 0 0 0 0 'x' 1 2 3 4 = 1 0 3 0 1 2 3 4 0 0 0 0 ``` The small matrix is applied as many times as it fits, and the multiplication is element by element. I've tried a bunch of loops, but that doesn't feel right in MATLAB, there must be prettier ways of doing it?