MATLAB: How to perform tensor summation without using “for” loop

tensor summation

Hi. I have a matrix A with n*4 dimentions, I want to sum each element of the first row with all the elements of the 2nd row to obtain a matrix B with 4.^2 elements and then, to sum each element of the 3rd row of matrix A with all the elements of matrix B to obtain a matrix C with 4.^3 elements. The process should continue until we have a matrix with 4.^n elements. I want to do this without for loop to increase the speed.
For example A=[1 2 3 4; 5 6 7 8; 9 10 11 12]
then B is:
B=[6 7 8 9; 7 8 9 10; 8 9 10 11; 9 10 11 12]
and C=C_0' is:
C_0=[15 16 17 18 16 17 18 19 17 18 19 20 18 19 20 21; 16 17 18 19 17 18 19 20 18 19 20 21 19 20 21 22; 17 18 19 20 18 19 20 21 19 20 21 22 20 21 22 23; 18 19 20 21 19 20 21 22 20 21 22 23 21 22 23 24]
Thank you in advance

Best Answer

A = [1 2 3 4; 5 6 7 8; 9 10 11 12];
rows = num2cell(A, 2);  %split A, keeping columns together
[rows{:}] = ndgrid(rows{:});  %calculate cartesian product of all the rows
result = reshape(sum(cat(numel(rows) + 1, rows{:}), numel(rows) + 1), [], size(A, 2))'  %sum the cartesian product and reshape into desired output format
Note that the above iterates over the elements of row1, then row2, ... then rown. If you want the reverse, then change the second line to:
[rows{:}] = ndgrid(rows{end:-1:1});
Your example is ambiguous in that respect.
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