[R] combinatorics again

[Jacques VESLOT]

 > library(gtools)
 > combinations(5,3)
      [,1] [,2] [,3]
 [1,]    1    2    3
 [2,]    1    2    4
 [3,]    1    2    5
 [4,]    1    3    4
 [5,]    1    3    5
 [6,]    1    4    5
 [7,]    2    3    4
 [8,]    2    3    5
 [9,]    2    4    5
[10,]    3    4    5


Robin Hankin a écrit :

>Hi
>
>I want to enumerate all vectors of length "J", whose elements are
>integers in the range 1 to S, without regard to ordering.
>
>With J=S=3, the combinations are as follows:
>
>
>        [,1] [,2] [,3]
>  [1,]    1    1    1
>  [2,]    1    1    2
>  [3,]    1    1    3
>  [4,]    1    2    2
>  [5,]    1    2    3
>  [6,]    1    3    3
>  [7,]    2    2    2
>  [8,]    2    2    3
>  [9,]    2    3    3
>[10,]    3    3    3
>
>
>Note that (eg) c(1,2,1) is not on the list because we already have
>c(1,1,2) which would be equivalent [because the problem is to
>enumerate the cases without regard to ordering] and I do not want
>repeats.
>
>The best I can do is to create all S^J possibilities and weed out the
>repeats, using unique() ; code below.
>
>Why is this no good?  Well, even for the tiny case of J=S=10, this
>would require a matrix of 10^10 rows, and my little linux machine
>refuses to cooperate, complaining about allocating a vector of
>length 1410065408.  For these values of J and S, I happen to know
>that the are 6360 distinct combinations, which is eminently handleable.
>
>
>Anyone got any better ideas?
>
>
>
>
>
>
>allcomb <- function(J,S){
>
>   f <- function(...) {
>     1:S
>   }
>   out <- as.matrix(do.call("expand.grid", lapply(1:J, FUN = f)))
>   out <- t(apply(out,1,sort))
>   unique(out)
>}
>
>
>--
>Robin Hankin
>Uncertainty Analyst
>National Oceanography Centre, Southampton
>European Way, Southampton SO14 3ZH, UK
>  tel  023-8059-7743
>
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>
>  
>