# [R] all combinations with replacement not ordered

Bert Gunter gunter.berton at gene.com
Thu Nov 7 19:06:01 CET 2013

```Well, you can create the expand.grid data frame programmatically via:

u <- 1:3
len <- length(u)
v <-do.call(expand.grid, split(rep(u,len),rep(seq_len(len),e=len)))

And then you can use unique.array to get the unique rows after the sort:

unique(t(apply(v,1,sort)))

However, I agree with your sentiments. Not only does this seem
inelegant, but it will not scale well.

I would imagine a recursive approach would be more efficient -- as
then only the sets you need would be produced and there'd be no
sorting, etc. -- but I have neither the time nor interest to work it
out.

... and I bet someone already has done this in some R package anyway.

Cheers,
Bert

On Thu, Nov 7, 2013 at 9:04 AM, Ted Harding <Ted.Harding at wlandres.net> wrote:
> On 07-Nov-2013 13:38:29 Konstantin Tretiakov wrote:
>> Hello!
>>
>> I need to obtain all possible combinations with replacement when
>> order is not important.
>> E.g. I have a population x{1,2,3}.
>> So I can get (choose(3+3-1,3)=) 10 combinations from this population
>> with 'size=3'.
>> How can I get a list of all that combinations?
>>
>> I have tried 'expand.grid()' and managed to get only samples where
>> order is important.
>> 'combn()' gave me samples without replacement.
>>
>> Best regards,
>> Konstantin Tretyakov.
>
> >From your description I infer that, from {1,2,3}, you want the result:
>
>   1 1 1
>   1 1 2
>   1 1 3
>   1 2 2
>   1 2 3
>   1 3 3
>   2 2 2
>   2 2 3
>   2 3 3
>   3 3 3
>
> The following will do that:
>
> u <- c(1,2,3)
> unique(t(unique(apply(expand.grid(u,u,u),1,sort),margin=1)))
>
> #      [,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
> # [9,]    2    3    3
> #[10,]    3    3    3
>
> There may be a simpler way!
> Ted.
>
> -------------------------------------------------
> E-Mail: (Ted Harding) <Ted.Harding at wlandres.net>
> Date: 07-Nov-2013  Time: 17:04:50
> This message was sent by XFMail
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> and provide commented, minimal, self-contained, reproducible code.

--

Bert Gunter
Genentech Nonclinical Biostatistics

(650) 467-7374

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