all combinations of k numbers between 0 and n whose sum equals n, speed optimization

Question

I have this R function to generate a matrix of all combinations of k numbers between 0 and n whose sum equals n. This is one of the bottlenecks of my program as it becomes extre

Answer 1

What about something short like:

comb = function(n, k) {
    all = combn(0:n, k)
    sums = colSums(all)
    all[, sums == n]
}

Then something like:

comb(5, 3)

which produces a matrix as you requested:

     [,1] [,2]
[1,]    0    0
[2,]    1    2
[3,]    4    3

---

Thanks to @josilber and the original poster for pointing out that the OP required all the permutations with repetition rather than combinations. A similar approach for the permutations would look like:

perm = function(n, k) {
    grid = matrix(rep(0:n, k), n + 1, k)
    all = expand.grid(data.frame(grid))
    sums = rowSums(all)
    all[sums == n,]
}

Then something like:

perm(5, 3)

produces a matrix as you requested:

    X1 X2 X3
6    5  0  0
11   4  1  0
16   3  2  0
21   2  3  0
26   1  4  0
31   0  5  0
...