All possible combinations of adding two matrices elementwise
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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.
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John D'Errico
2017-12-9
编辑：John D'Errico
2017-12-9
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
更多回答（2 个）
Matt J
2017-12-9
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);
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
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