[Rd] combn(n, k, ...) and all its re-inventions

Peter Dalgaard p.dalgaard at biostat.ku.dk
Tue May 9 13:54:05 CEST 2006

Martin Maechler <maechler at stat.math.ethz.ch> writes:

> tweaks, I have now a version of combn() that is faster than all
> the other implementations {only slightly faster than
> combinations()}, and I plan to add this to R's standard package
> 'utils'. 
> Hopefully, the reinventing can be stopped by this, once people
> can rely on a relatively fast implementation of the
> functionality.
> One might also consider to include a version of the ``one by
> one'' combination generators {as mentioned above} which is
> needed for larger k.
> Opinions ?

While you're in there... combn() has a nice feature that you can apply
a function to each combination, which can be quite useful (and fun) if
you're demonstrating permutation tests:

> x <- combn(20,10,function(i)mean(sleep$extra[i]))
> x <- round(x,2) # this is needed, or you get artifacts
> plot(sort(unique(x)),table(x),type="h")
> plot(sort(x),type="l")
> sum(x <= mean(sleep$extra[1:10])) / length(x)
[1] 0.04072398

However, combn() does its work in sapply() style: First create a list,
then simplify. As this quickly becomes a rather *long* list (e.g., a
slightly larger case with choose(29, 14)==77558760 combinations kills
R for me on a 2GB 64 bit machine), it might be desirable to have an option,
"assume.scalar" or so, to specify that the function always returns a
single scalar.

   O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)                  FAX: (+45) 35327907

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