Generating all combinations with repetition using MATLAB

We can use the bijection mentioned in the wikipedia article, which maps combinations without repetition of type n+k-1 choose k to k-multicombinations of size n. We generate the combinations without repetition and map them using bsxfun(@minus, nchoosek(1:n+k-1,k), 0:k-1);. This results in the following function:

function combs = nmultichoosek(values, k)
%// Return number of multisubsets or actual multisubsets.
if numel(values)==1 
    n = values;
    combs = nchoosek(n+k-1,k);
else
    n = numel(values);
    combs = bsxfun(@minus, nchoosek(1:n+k-1,k), 0:k-1);
    combs = reshape(values(combs),[],k);
end

Thanks to Hans Hirse for a correction.

Brute-force approach: generate all tuples and then keep only those that are sorted. Not suitable for large values of n or k.

values = 1:3;                               %//  data
k = 3;                                      %//  data
n = numel(values);                          %//  number of values
combs = values(dec2base(0:n^k-1,n)-'0'+1);  %//  generate all tuples
combs = combs(all(diff(combs.')>=0, 1),:);  %'// keep only those that are sorted