set {sets}

Sets

Description

Creation and manipulation of sets.

Usage

set(...)
as.set(x)
make_set_with_order(x)
is.set(x)

set_is_empty(x)
set_is_subset(x, y)
set_is_proper_subset(x, y)
set_is_equal(x, y)
set_contains_element(x, e)

set_union(...)
set_intersection(...)
set_symdiff(...)
set_complement(x, y)
set_cardinality(x)
## S3 method for class 'set'
length(x)
## S3 method for class 'set'
lengths(x, use.names = TRUE)
set_power(x)
set_cartesian(...)
set_combn(x, m)

Arguments

x

For as.set() and is.set(): an R object. A set object otherwise.

y

A set object.

e

An R object.

m

Number of elements to choose.

use.names

logical; should the names of x be used in the result?

...

For set(): R objects, and set objects otherwise.

Details

These functions represent basic infrastructure for handling sets of general (R) objects. The set_is_foo() predicates are vectorized. In addition to the methods defined, one can use the following operators: | for the union, - for the difference (or complement), & for the intersection, %D% for the symmetric difference, * and ^n for the (n-fold) cartesian product, 2^ for the power set, %e% for the element-of predicate, < and <= for the (proper) subset predicate, > and >= for the (proper) superset predicate, and == and != for (in)equality. The length method for sets gives the cardinality. The lengths method coerces the set to a list before applying the length method on its elements. set_combn returns the set of all subsets of specified length. The Summary methods do also work if defined for the set elements. The mean and median methods try to convert the object to a numeric vector before calling the default methods.

Because set elements are unordered, it is not allowed to use positional indexing. However, it is possible to do indexing using element labels or simply the elements themselves (useful, e.g., for subassignment). In addition, it is possible to iterate over all elements using for and lapply/sapply.

Note that converting objects to sets may change the internal order of the elements, so that iterating over the original data might give different results than iterating over the corresponding set. The permutation can be obtained using the generic function make_set_with_order, returning both the set and the ordering. as.set simply calls make_set_with_order internally and strips the order information, so user-defined methods for coercion have to be provided for the latter and not for as.set.

Note that set_union, set_intersection, and set_symdiff accept any number of arguments. The n-ary symmetric difference of sets contains just elements which are in an odd number of the sets.

set_contains_element is vectorized in e, that is, if e is an atomic vector or list, the is-element operation is performed element-wise, and a logical vector returned. Note that, however, objects of class tuple are taken as atomic objects to correctly handle sets of tuples.

Value

For the predicate functions, a vector of logicals. For make_set_with_order, a list with two components "set" and "order". For set_cardinality and the length method, an integer value. For the lengths method, an integer vector. For all others, a set.

References

D. Meyer and K. Hornik (2009), Generalized and customizable sets in R, Journal of Statistical Software 31(2), 1–27. doi:10.18637/jss.v031.i02.

See Also

set_outer, gset for generalized sets, and tuple for tuples (“vectors”).

Examples

## constructor
s <- set(1L, 2L, 3L)
s

## named elements
snamed <- set(one = 1, 2, three = 3)
snamed

## indexing by label
snamed[["one"]]

## subassignment
snamed[c(2,3)] <- c("a","b")
snamed

## a more complex set
set(c, "test", list(1, 2, 3))

## converter
s2 <- as.set(2:5)
s2

## converter with order
make_set_with_order(5:1)

## set of sets
set(set(), set(1))

## cartesian product
s * s2
s * s
s ^ 2 # same as above
s ^ 3

## power set
2 ^ s

## tuples
s3 <- set(tuple(1,2,3), tuple(2,3,4))
s3

## Predicates:

## element
1:2 %e% s
tuple(1,2,3) %e% s3

## subset
s <= s2
s2 >= s # same

## proper subset
s < s

## complement, union, intersection, symmetric difference:
s - set(1L)
s + set("a") # or use: s | set("a")
s & s
s %D% s2
set(1,2,3) - set(1,2)
set_intersection(set(1,2,3), set(2,3,4), set(3,4,5))
set_union(set(1,2,3), set(2,3,4), set(3,4,5))
set_symdiff(set(1,2,3), set(2,3,4), set(3,4,5))

## subsets:
set_combn(as.set(1:3),2)

## iterators:
sapply(s, sqrt)
for (i in s) print(i)

## Summary methods
sum(s)
range(s)

## mean / median
mean(s)
median(s)

## cardinality
s <- set(1, list(1, 2))
length(s)
lengths(s)

## vectorization
list(set(1), set(2), set()) == set(1)