How do I create every sum of column entries of a m x n matrix?

I would like to create the sums of a mxn matrix that have m summands, one of each row - using a for loop to generate every possible combination. For my 3x3 Matrix A my code would look like this:

for i=1:3
    for j=1:3
        for k=1:3
            S=A(1,i)+A(2,j)+A(3,k);
        end
    end
end

Now I need this to work for any mxn Matrix. How? Do I need a recursive function or is there any other way?

Answer 1

[Viktor von den Brincken]

Figured another way:

close
clear
clc
A = [1 2 3; 4 5 6;7 8 9];
[Zeile,Spalte] = size(A);
S=MatAdd(A,1);

with

function [Summe] = MatAdd(A,aktuelleZeile)
Summe=[];
[AnzahlZeilen,AnzahlSpalten] = size(A);
if aktuelleZeile==AnzahlZeilen
    Summe=A(aktuelleZeile,:)';
else
    Summanden=MatAdd(A,aktuelleZeile+1);
    for i=1:AnzahlSpalten
        Summe=[Summe;Summanden+A(aktuelleZeile,i);];
    end
end
end

Answer 2

[Jos (10584)]

read the help of sum, and take a look at the dimension argument

    help sum
    M = randi(10,3,4)
    sum(M,1) % sum along rows

[Viktor von den Brincken]

this way I get max 3 Sums of my expected 27 for the 3x3 matrix.

[Jos (10584)]

O, sorry, I misunderstood your question. So you have n-columns, each with m values (hence the the m-by-n matrix) and you want the sum of the m^n possible combinations ...

Answer 3

[Jos (10584)]

A = magic(3)
[m,n] = size(A)

% get the row indices into A for every combination
clear r
[r{n:-1:1}] = ndgrid(1:m)
r = reshape(cat(n+1,r{:}),[],n)
% or use PERMN from the file exchange

% get the columns indices
c = repmat(1:n,size(r,1),1) ;

% transform into linear indices
idx = sub2ind([m,n],r,c) ;

% get the summands for each combination
B = A(idx) 
% and sum
out = sum(B,2)

[Viktor von den Brincken]

this looks promising. I'll look into it and try to understand. Thank you very much!!