| combn {utils} | R Documentation |
Generate all combinations of the elements of x taken m
at a time. If x is a positive integer, returns all
combinations of the elements of seq(x) taken m at a
time. If argument FUN is not NULL, applies a function given
by the argument to each point. If simplify is FALSE, returns
a list; otherwise returns an array, typically a
matrix. ... are passed unchanged to the
FUN function, if specified.
combn(x, m, FUN = NULL, simplify = TRUE, ...)
x |
vector source for combinations, or integer |
m |
number of elements to choose. |
FUN |
function to be applied to each combination; default
|
simplify |
logical indicating if the result should be simplified
to an |
... |
optionally, further arguments to |
a list or array, see the simplify
argument above. In the latter case, the identity
dim(combn(n,m)) == c(m, choose(n,m)) holds.
Scott Chasalow wrote the original in 1994 for S;
R package combinat and documentation by Vince Carey
stvjc@channing.harvard.edu;
small changes by the R core team, notably to return an array in all
cases of simplify = TRUE, e.g., for combn(5,5).
Nijenhuis, A. and Wilf, H.S. (1978) Combinatorial Algorithms for Computers and Calculators; Academic Press, NY.
choose for fast computation of the number of
combinations. expand.grid for creating a data frame from
all combinations of factors or vectors.
combn(letters[1:4], 2)
(m <- combn(10, 5, min)) # minimum value in each combination
mm <- combn(15, 6, function(x) matrix(x, 2,3))
stopifnot(round(choose(10,5)) == length(m),
c(2,3, round(choose(15,6))) == dim(mm))
## Different way of encoding points:
combn(c(1,1,1,1,2,2,2,3,3,4), 3, tabulate, nbins = 4)
## Compute support points and (scaled) probabilities for a
## Multivariate-Hypergeometric(n = 3, N = c(4,3,2,1)) p.f.:
# table.mat(t(combn(c(1,1,1,1,2,2,2,3,3,4), 3, tabulate,nbins=4)))
## Assuring the identity
for(n in 1:7)
for(m in 0:n) stopifnot(is.array(cc <- combn(n, m)),
dim(cc) == c(m, choose(n,m)))