MATLAB: All possible combinations of adding two matrices elementwise

combinationsmatrix operations

I want to calculate all possible combinations of adding elements in two NxN matrices, resulting in a NxNxNxN (or N^2xN^2) matrix. My current method uses 4 for-loops, like "sum(i,j,k,l)=A(i,j)-B(k,l), where i,j,k,l=1:N ", but it is quite time-consuming and I'm guessing using matrix multiplication in some way would be more effective, but I can't figure how to do it.

Best Answer

Easy, peasy, that is, IF you have a current MATLAB release. A one line solution...
A = rand(2,2)
A =
    0.37803      0.80787
    0.21181      0.90728
B = [1 2;3 4];
C = A + reshape(B,[1 1, size(A)])
C(:,:,1,1) =
      1.378       1.8079
     1.2118       1.9073
C(:,:,2,1) =
      3.378       3.8079
     3.2118       3.9073
C(:,:,1,2) =
      2.378       2.8079
     2.2118       2.9073
C(:,:,2,2) =
      4.378       4.8079
     4.2118       4.9073
size(C)
ans =
     2     2     2     2
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