MATLAB: All the combinations of sums of rows of matrices

adding rows of matricessums of rows

Hello, I looked for this problem but I couldn't find any convenient solution. Assume that I have k matrices whose dimensions are m(1)xn, m(2)xn, … m(k)xn. I need all the possible sums of rows of these k matrices.
For example, let us have 3 different matrices.
A =
      1   0   2   1
      2   4   1   3
      0   1   3   2
     
B =
      1   3   0   5
C =
      2   1   3   0
      1   4   0   3
Then the result should be the following.
Result = 
         4   4   5   6   ( A(1,:) + B(1,:) + C(1,:) )
         3   7   2   8   ( A(1,:) + B(1,:) + C(2,:) )
         5   8   4   8   ( A(2,:) + B(1,:) + C(1,:) )
         4  11   1  10   ( A(2,:) + B(1,:) + C(2,:) )
         3   5   6   7   ( A(3,:) + B(1,:) + C(1,:) )
         2   8   3   9   ( A(3,:) + B(1,:) + C(2,:) )
I hope that I could explain my problem. If there is an ambigous part, please ask me to fix your confusion.
Thanks for your efforts.

Best Answer

Code for arbitrary number of matrix
A=[...
    1   0   2   1
    2   4   1   3
    0   1   3   2];
B=[...
    1   3   0   5];
C=[...
    2   1   3   0
    1   4   0   3];
% Start from here
CA = {A,B,C}; % add more matrices if needed
CA = CA(:);
s1 = cellfun('size',CA,1);
c = arrayfun(@(n) 1:n, s1, 'unif', 0);
[c{:}] = ndgrid(c{:});
n = length(CA);
c = reshape(cat(n+1,c{:}),[],n)';
c = c + cumsum([0;s1(1:n-1)]);
AA = cell2mat(CA);
R = reshape(AA(c,:),n,[],size(A,2));
R = reshape(sum(R,1),[],size(A,2))
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