All possible combinations of adding two matrices elementwise

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.

Answer 1

[John D'Errico]

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

[Linus Kron]

great, exactly what i needed!

[Andrei Bobrov]

+1

Answer 2

[Matt J]

You can use my tensorsum function

reshape(tensorsum(A,B),[N,N,N,N]);

where

function X = tensorsum(A,B)
%TENSORSUM
%
% Modification of Laurent Sorber's KRON

[I J] = size(A);
[K L] = size(B);
if ~issparse(A) && ~issparse(B)
    A = reshape(A,[1 I 1 J]);
    B = reshape(B,[K 1 L 1]);
    X = reshape(bsxfun(@plus,A,B),[I*K J*L]);
else

      [ia,ja,sa] = find(A); ia=ia(:); ja=ja(:); sa=sa(:);
      [ib,jb,sb] = find(B); ib=ib(:); jb=jb(:); sb=sb(:);

      ix = bsxfun(@plus,K*(ia-1).',ib);
      jx = bsxfun(@plus,L*(ja-1).',jb);

      X = sparse(ix,jx,bsxfun(@plus,sb,sa.'),I*K,J*L);

Answer 3

[Matt J]

In R2016b and higher you could also just do this

out = reshape(B(:)+A(:).', [N,N,N,N]);

It will give a somewhat different order than my previous answer

[Linus Kron]

great, thanks!