How to calculate and store the sum of different column combinations in a matrix?

We have a matrix a(i,j) with i:1:M and j:1:N

We want to calculate the sum of all column combinations of N elements each from a distinct column and store them in a new array/matrix. This new matrix/array will have M^N elements. We need to also store which combination yeild this sum.

suppose M=3 and N=4

a = [1,2,3,4;5,6,7,8;9,10,11,12]

a(1,1)+a(1,2)+a(1,3)+a(1,4)--> sum of first element of every column

a(1,1)+a(2,2)+a(1,3)+a(1,4)--> sum of first element of column 1, 3 and 4 and 2nd element of column 2

a(1,1)+a(3,2)+a(1,3)+a(1,4)--> sum of first element of column 1, 3 and 4 and 3rd element of column 2

.

There will be 3^4 combinations.

The goal is to find out which sum combination yields the maximum and be able to report the location of elements of that combination in the main matrix a.

Answer 1

[edward holt]

A similar question has been asked here.

Finding out which combination yields the maximum can be done without summing all possible combinations.

m = 5
n = 4

a = randi(10,m,n)

[coltots, where] = max(a);
tot = sum(coltots)
%gives maximum value
where
%and which rows it came form

For summing and organising all possible pairs

combos = zeros(m,m,m,m);
% will be an N dimensional array, with lengths M

% need N many loops
for i1 = 1:m
    for i2 = 1:m
        for i3 = 1:m
            for i4 = 1:m
                combos(i1,i2,i3,i4) = a(i1,1) + a(i2,2) + a(i3,3) + a(i4,4);               
             end
        end
    end
end

combos == tot

I'm sure there is a better way, that's beyond my skillset. It's a nice problem to think on.