Multiplying a small matrix by a big matrix

问题:

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?

回答1:

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))));

回答2:

If you have the image processing toolbox, you can try blkproc:

>> A = magic(4)
A =
    16     2     3    13
     5    11    10     8
     9     7     6    12
     4    14    15     1
>> B = [1 0; 0 0];
>> C = blkproc(A,size(B),@(x) x.*B)
C =
    16     0     3     0
     0     0     0     0
     9     0     6     0
     0     0     0     0