[R] combinatorial programming problem

[Martin Maechler]

>>>>> "SpG" == Spencer Graves <spencer.graves at pdf.com>
>>>>>     on Sun, 28 May 2006 16:21:53 -0700 writes:

    SpG> 	  I'm not sure I understand your question, but
    SpG> are you asking how to index choose(k, r) objects?
    SpG> Almost 3 years ago, I asked a question like this.  Andy
    SpG> Liaw referred me to nchoosek(vsn)
    SpG> (http://finzi.psych.upenn.edu/R/Rhelp02a/archive/12518.html).
    SpG> This produces a matrix of dimension (r, choose(k, r)).
    SpG> With this matrix, you could convert an integer between
    SpG> 1 and choose(k, r) into an r-vector by table look-up.
    SpG> Reading the code for nchoosek might help you further if
    SpG> this does not seem appropriate for you.

Note that *if* the above is the answer,
I'd rather recommend to use  combn() from package "combinat",
since a (slightly improved) version of combn() has been part of R-devel
(to become R 2.4.0 in October) for a while.  Also, combn() from
"combinat" precedes nchoosek() historically and is also faster.

Martin Maechler, ETH Zurich

    SpG> 	  I found this just now using 'RSiteSearch("all
    SpG> subsets of a size")', which produced 102 hits.  Another
    SpG> one that looked like it might help you is
    SpG> "http://finzi.psych.upenn.edu/R/Rhelp02a/archive/1717.html".

    SpG> 	  Hope this helps, Spencer Graves

    SpG> Kjetil Brinchmann Halvorsen wrote:
    >> Hola!
    >> 
    >> I am programming a class (S3) "symarray" for storing the
    >> results of functions symmetric in its k
    >> arguments. Intended use is for association indices for
    >> more than two variables, for instance coresistivity
    >> against antibiotics.
    >> 
    >> There is one programming problem I haven't solved, making
    >> an inverse of the index function indx() --- se code
    >> below. It could for instance return the original k
    >> indexes in strictly increasing order, to make indx()
    >> formally invertible.
    >> 
    >> Any ideas?
    >> 
    >> Kjetil
    >> 
    >> 
    >> Code:
    >> 
    >> 
    >> # Implementing an S3 class for symarrays with array rank
    >> r for dimension # [k, k, ..., k] with k>=r repeated r
    >> times. We do not store the diagonal.
    >> 
    >> # Storage requirement is given by {r, k}= choose(k, r) #
    >> where r=array rank, k=maximum index
    >> 
    >> symarray <- function(data=NA, dims=c(1,1)){ r <- dims[1]
    >> k <- dims[2] if(r > k) stop("symarray needs dimension
    >> larger than array rank") len <- choose(k, r) out <-
    >> data[1:len] attr(out, "dims") <- dims class(out) <-
    >> "symarray" out }
    >> 
    >> # Index calculation:
    >> 
    >> indx <- function(inds, k){ r <- length(inds) if(r==1)
    >> return(inds) else { if(inds[1]==1) { return(
    >> indx(inds[-1]-1, k-1 ) ) } else { return(
    >> indx(c(inds[1]-1, seq(from=k-r+2, by=1, to=k)), k) +
    >> indx( inds[-1]-inds[1], k-inds[1] )) } } } # end indx
    >> 
    >> # Methods for assignment and indexing:
    >> 
    >> "[.symarray" <- function(x, inds, drop=FALSE){ dims <-
    >> attr(x, "dims") k <- dims[2] inds <- indx(inds, k) res <-
    >> NextMethod("[", x) res }
    >> 
    >> "[<-.symarray" <- function(x, inds, value){ dims <-
    >> attr(x, "dims") k <- dims[2] inds <- indx(inds, k) res <-
    >> NextMethod("[<-", x) res }
    >> 
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    SpG> ______________________________________________
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