Rank Partitions/Compositions

Generate the rank (lexicographically) of partitions/compositions. These functions are the complement to partitions/compositionsSample. See the examples below.
GMP support allows for exploration of partitions/compositions of vectors with many elements.

partitionsRank(..., v, repetition = FALSE, freqs = NULL, target = NULL)

compositionsRank(..., v, repetition = FALSE, freqs = NULL,
                 target = NULL, weak = FALSE)

Arguments

...: vectors or matrices to be ranked.
v: Source vector. If v is a positive integer, it will be converted to the sequence 1:v. If v is a negative integer, it will be converted to the sequence v:-1. All atomic types are supported (See is.atomic).
repetition: Logical value indicating whether partitions/compositions should be with or without repetition. The default is FALSE.
freqs: A vector of frequencies used for producing all partitions of a multiset of v. Each element of freqs represents how many times each element of the source vector, v, is repeated. It is analogous to the times argument in rep. The default value is NULL.
target: Number to be partitioned. If NULL, max(v) will be used.
weak: (Compositions only) Logical flag indicating whether to allow terms of the sequence to be zero.

Details

These algorithms rely on efficiently ranking the \(n^{th}\) lexicographical partition.

Value

A vector of class integer, numeric, or bigz determined by the total number of partitions/compositions

References

Lexicographical order ranking/unranking

Author

Joseph Wood

Note

v must be supplied.

Examples

mySamp = partitionsSample(30, 8, TRUE, n = 5, seed = 10, namedSample = TRUE)
myRank = partitionsRank(mySamp, v = 30, repetition = TRUE)
all.equal(as.integer(rownames(mySamp)), myRank)
#> [1] TRUE