R help - Dec 2008 - generate combination multiset (set with repetition)

Hi,

This has been asked before but not sufficiently answered from what I
could find. How do you create combinations
with repetitions (multisets) in R?

If I have
> set <- array(1:3)
And I want to choose all combinations of picking 2 numbers, I want to
get a print out like

     [,1] [,2]
[1,]    1    1
[2,]    1    2
[3,]    1    3
[4,]    2    2
[5,]    2    3
[6,]    3    3

subsets(set, 2, allow.repeat=T) should work, but I can't get the
multic package to install, t(combn(set,2)) was suggested but it
doesn't produce repetitions; expand.grid(rep(list(1:3), 2)) was also
suggested, but it produces permuations, not combinations.
Additionally, I would like to iterate through each resultant set for
large n (similar to the description for getNextSet {pcalg}). Any
suggestions?

Reuben Cummings

Hi,

Perhaps you can use expand.grid and then remove the mirror combinations,
> values <- 1:3
> tmp <- expand.grid(values, values)
> unique.combs <- tmp[tmp[, 1]<=tmp[, 2], ]
> unique.combs[do.call(order, unique.combs), ] # reorder if you wish
>   Var1 Var2
> 1    1    1
> 4    1    2
> 7    1    3
> 5    2    2
> 8    2    3
> 9    3    3
I vaguely recall a discussion a few months ago on extending this  
approach to a variable number of arguments to expand.grid.

Hope this helps,

baptiste

On 11 Dec 2008, at 17:00, Reuben Cummings wrote:
> Hi,
>
> This has been asked before but not sufficiently answered from what I
> could find. How do you create combinations
> with repetitions (multisets) in R?
>
> If I have
>> set <- array(1:3)
>
> And I want to choose all combinations of picking 2 numbers, I want to
> get a print out like
>
>     [,1] [,2]
> [1,]    1    1
> [2,]    1    2
> [3,]    1    3
> [4,]    2    2
> [5,]    2    3
> [6,]    3    3
>
> subsets(set, 2, allow.repeat=T) should work, but I can't get the
> multic package to install, t(combn(set,2)) was suggested but it
> doesn't produce repetitions; expand.grid(rep(list(1:3), 2)) was also
> suggested, but it produces permuations, not combinations.
> Additionally, I would like to iterate through each resultant set for
> large n (similar to the description for getNextSet {pcalg}). Any
> suggestions?
>
> Reuben Cummings
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
_____________________________

Baptiste Augui?

School of Physics
University of Exeter
Stocker Road,
Exeter, Devon,
EX4 4QL, UK

Phone: +44 1392 264187

http://newton.ex.ac.uk/research/emag

Dear Reuben,


On Thu, Dec 11, 2008 at 12:53 PM, baptiste auguie <ba208 at exeter.ac.uk>
wrote:
> Hi,
>
> Perhaps you can use expand.grid and then remove the mirror combinations,
>
>> values <- 1:3
>> tmp <- expand.grid(values, values)
>> unique.combs <- tmp[tmp[, 1]<=tmp[, 2], ]
>> unique.combs[do.call(order, unique.combs), ] # reorder if you wish
>>  Var1 Var2
>> 1    1    1
>> 4    1    2
>> 7    1    3
>> 5    2    2
>> 8    2    3
>> 9    3    3
>
> I vaguely recall a discussion a few months ago on extending this approach
to
> a variable number of arguments to expand.grid.
>
> Hope this helps,
>
> baptiste
>

Here is another way:

library(prob)
urnsamples(1:3, size = 2, ordered = FALSE, replace = TRUE)

You can convert to a matrix with as.matrix(), if desired.

Regards,
Jay


-- 

***************************************************
G. Jay Kerns, Ph.D.
Associate Professor
Department of Mathematics & Statistics
Youngstown State University
Youngstown, OH 44555-0002 USA
Office: 1035 Cushwa Hall
Phone: (330) 941-3310 Office (voice mail)
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E-mail: gkerns at ysu.edu
http://www.cc.ysu.edu/~gjkerns/

On Thu, 11 Dec 2008, Reuben Cummings wrote:
> Hi,
>
> This has been asked before but not sufficiently answered from what I
> could find. How do you create combinations
> with repetitions (multisets) in R?
>
> If I have
>> set <- array(1:3)
Why wrap 1:3 in array() ??
>
> And I want to choose all combinations of picking 2 numbers, I want to
> get a print out like
>
>     [,1] [,2]
> [1,]    1    1
> [2,]    1    2
> [3,]    1    3
> [4,]    2    2
> [5,]    2    3
> [6,]    3    3
>
For small problems (n < 100, say) :

 	 which( lower.tri( diag( n ), diag=TRUE), arr.ind=TRUE )[,2:1]

For larger problems, something like :

foo <- function(n) {
 	brks <- cumsum( n:1 )
 	k <- 1:choose( n+1, 2 )
 	j <- findInterval( k, brks+1 ) + 1
 	i <- k - ( brks-brks[1] )[ j ]
 	cbind( j, i ) }

If the number in 'set' are not 1:n, you can do a lookup using the
results
from above.


HTH,

Chuck


> subsets(set, 2, allow.repeat=T) should work, but I can't get the
> multic package to install, t(combn(set,2)) was suggested but it
> doesn't produce repetitions; expand.grid(rep(list(1:3), 2)) was also
> suggested, but it produces permuations, not combinations.
> Additionally, I would like to iterate through each resultant set for
> large n (similar to the description for getNextSet {pcalg}). Any
> suggestions?
>
> Reuben Cummings
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
Charles C. Berry                            (858) 534-2098
                                             Dept of Family/Preventive Medicine
E mailto:cberry at tajo.ucsd.edu	            UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/  La Jolla, San Diego 92093-0901