# Re: [R] Generating groupings of ordered observations

From: Gabor Grothendieck <ggrothendieck_at_gmail.com>
Date: Sat, 21 Jun 2008 17:58:24 -0400

I meant 0:31, not 0:15.

On Sat, Jun 21, 2008 at 5:56 PM, Gabor Grothendieck <ggrothendieck_at_gmail.com> wrote:
> On Sat, Jun 21, 2008 at 12:40 PM, Gavin Simpson <gavin.simpson@ucl.ac.uk> wrote:
>> Dear List,
>>
>> I have a problem I'm finding it difficult to make headway with.
>>
>> Say I have 6 ordered observations, and I want to find all combinations
>> of splitting these 6 ordered observations in g groups, where g = 1, ...,
>> 6. Groups can only be formed by adjacent observations, so observations 1
>> and 4 can't be in a group on their own, only if 1,2,3&4 are all in the
>> group.
>>
>> For example, with 6 observations, the columns of the matrices below
>> represent the groups that can be formed by placing the 6 ordered
>> observations into 2-5 groups. Think of the columns of these matrices as
>> being an indicator of group membership. We then cbind these matrices
>> with the trivial partitions into 1 and 6 groups:
>>
>> mat2g <- matrix(c(1,1,1,1,1,
>> 2,1,1,1,1,
>> 2,2,1,1,1,
>> 2,2,2,1,1,
>> 2,2,2,2,1,
>> 2,2,2,2,2),
>> nrow = 6, ncol = 5, byrow = TRUE)
>>
>> mat3g <- matrix(c(1,1,1,1,1,1,1,1,1,1,
>> 2,2,2,2,1,1,1,1,1,1,
>> 3,2,2,2,2,2,2,1,1,1,
>> 3,3,2,2,3,2,2,2,2,1,
>> 3,3,3,2,3,3,2,3,2,2,
>> 3,3,3,3,3,3,3,3,3,3),
>> nrow = 6, ncol = 10, byrow = TRUE)
>>
>> mat4g <- matrix(c(1,1,1,1,1,1,1,1,1,1,
>> 2,2,2,2,2,2,1,1,1,1,
>> 3,3,3,2,2,2,2,2,2,1,
>> 4,3,3,3,3,2,3,3,2,2,
>> 4,4,3,4,3,3,4,3,3,3,
>> 4,4,4,4,4,4,4,4,4,4),
>> nrow = 6, ncol = 10, byrow = TRUE)
>>
>> mat5g <- matrix(c(1,1,1,1,1,
>> 2,2,2,2,1,
>> 3,3,3,2,2,
>> 4,4,3,3,3,
>> 5,4,4,4,4,
>> 5,5,5,5,5),
>> nrow = 6, ncol = 5, byrow = TRUE)
>>
>> cbind(rep(1,6), mat2g, mat3g, mat4g, mat5g, 1:6)
>>
>> I'd like to be able to do this automagically, for any (reasonable,
>> small, say n = 10-20) number of observations, n, and for g = 1, ..., n
>> groups.
>>
>> I can't see the pattern here or a way forward. Can anyone suggest an
>> approach?
>>
>
> Peter Wolf has APL-style encode/decode functions on his web site that
> can readily be used for this. The output of the encode below are the binary
> digits expansions of the numbers 0:15, one per column, and the remainder
> transforms that matrix to the required one (but columns are in a different
> order than yours):
>
>> source("http://www.wiwi.uni-bielefeld.de/~wolf/software/R-wtools/decodeencode/decodeencode.R")
>> n <- 6
>> n1 <- n-1
>> apply(rbind(1, encode(0:(2^n1-1), rep(2, n1))), 2, cumsum)
> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
> [,13] [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23]
> [,24] [,25] [,26]
> [1,] 1 1 1 1 1 1 1 1 1 1 1 1
> 1 1 1 1 1 1 1 1 1 1 1 1
> 1 1
> [2,] 1 1 1 1 1 1 1 1 1 1 1 1
> 1 1 1 1 2 2 2 2 2 2 2 2
> 2 2
> [3,] 1 1 1 1 1 1 1 1 2 2 2 2
> 2 2 2 2 2 2 2 2 2 2 2 2
> 3 3
> [4,] 1 1 1 1 2 2 2 2 2 2 2 2
> 3 3 3 3 2 2 2 2 3 3 3 3
> 3 3
> [5,] 1 1 2 2 2 2 3 3 2 2 3 3
> 3 3 4 4 2 2 3 3 3 3 4 4
> 3 3
> [6,] 1 2 2 3 2 3 3 4 2 3 3 4
> 3 4 4 5 2 3 3 4 3 4 4 5
> 3 4
> [,27] [,28] [,29] [,30] [,31] [,32]
> [1,] 1 1 1 1 1 1
> [2,] 2 2 2 2 2 2
> [3,] 3 3 3 3 3 3
> [4,] 3 3 4 4 4 4
> [5,] 4 4 4 4 5 5
> [6,] 4 5 4 5 5 6
>

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