[R] combinatorics again

[Jacques VESLOT]

combinations(5,3,rep=T)

Robin Hankin a écrit :

> Thank you Jacques
>
> but your solution  misses (eg) c(1,1,2) which I need.
>
> best wishes
>
> Robin
>
>
>
> On 6 Mar 2006, at 09:17, Jacques VESLOT wrote:
>
>> > 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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>>>
>>>
>
> -- 
> Robin Hankin
> Uncertainty Analyst
> National Oceanography Centre, Southampton
> European Way, Southampton SO14 3ZH, UK
>  tel  023-8059-7743
>
>