Combinations from a given set without repetition

Question

Suppose I have a matrix defined as follows

M = [C1 C2 C3 C4]

Where the C's are column vectors I want some efficient (i.e. no for loops) way of producing A vector such that

ResultVec = [C1 C2; 
             C1 C3; 
             C1 C4;
             C2 C3; 
             C2 C4; 
             C3 C4]

Thanks in advance!

Answer 1

That is, what nchoosek does:

M = [ 1 2 3 4 ];

R = nchoosek(M,2);

returns:

R =

     1     2
     1     3
     1     4
     2     3
     2     4
     3     4

I don't know if it's your intention but nchoosek is Matlabs implementation of The number of k-combinations from a given set S of n elements without repetition (Wikipedia)

The function nchoosek is performance wise not very efficient though. But there are equivalents on File Exchange, which are much(!!) faster and doing the same.

---

Just to make it clear, it's not just working for the fairly simple example above, and is not returning any indices. It directly transforms the matrix as desired.

M = [ 21 42 123 17 ];

returns:

R =

    21    42
    21   123
    21    17
    42   123
    42    17
   123    17

Answer 2

This is the simplest way I've come up with:

n = size(M, 2);
[j, i] = ind2sub([n n], find(~triu(ones(n))));
ResultVec = M(:, [i j]);
ResultVec = reshape(ResultVec, [], 2)