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

It is hard to tell if it will be useful unless you answer my question regarding your typical values for n and k (please do.) Here is a version using recursion that seems to be faster than josilber's using his benchmark test:

sum.comb3 <- function(n, k) {

   stopifnot(k > 0L)

   REC <- function(n, k) {
      if (k == 1L) list(n) else
      unlist(lapply(0:n, function(i)Map(c, i, REC(n - i, k - 1L))),
             recursive = FALSE)
   }

   matrix(unlist(REC(n, k)), ncol = k, byrow = TRUE)
}

microbenchmark(sum.comb(3, 10), sum.comb2(3, 10), sum.comb3(3, 10))
# Unit: milliseconds
#              expr      min       lq   median       uq      max neval
#  sum.comb2(3, 10) 39.55612 40.60798 41.91954 44.26756 70.44944   100
#  sum.comb3(3, 10) 25.86008 27.74415 28.37080 29.65567 34.18620   100