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combn: Generate All Combinations of n Elements, Taken m at a Time

combn

R Documentation

Generate All Combinations of n Elements, Taken m at a Time

Description

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.

Usage

combn(x, m, FUN = NULL, simplify = TRUE, ...)

Arguments

`x`	vector source for combinations, or integer `n` for `x <- seq_len(n)`.
`m`	number of elements to choose.
`FUN`	function to be applied to each combination; default `NULL` means the identity, i.e., to return the combination (vector of length `m`).
`simplify`	logical indicating if the result should be simplified to an `array` (typically a `matrix`); if FALSE, the function returns a `list`. Note that when `simplify = TRUE` as by default, the dimension of the result is simply determined from `FUN(1st combination)` (for efficiency reasons). This will badly fail if `FUN(u)` is not of constant length.
`...`	optionally, further arguments to `FUN`.

Details

Factors x are accepted.

Value

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.

Author(s)

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).

References

Nijenhuis, A. and Wilf, H.S. (1978) Combinatorial Algorithms for Computers and Calculators; Academic Press, NY.

Examples

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), is.array(m), # 1-dimensional
          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)),
                         identical(cc, combn(n, m, identity)) || m == 1)