partitionsCount

Source vector. If <code>v</code> is a positive integer, it will be converted to the sequence <code>1:v</code>. If <code>v</code> is a negative integer, it will be converted to the sequence <code>v:-1</code>. Only integer and numeric vectors are accepted.

Width of the partition. If <code>m = NULL</code>, the length will be determined by the partitioning case (e.g. When we are generating distinct partitions of \(n\), the width will be equal to the smallest \(m\) such that <code>sum(1:m) &gt;= n</code>).

Logical value indicating whether partitions should be with or without repetition. The default is <code>FALSE</code>.

repetition

A vector of frequencies used for producing all partitions of a multiset of <code>v</code>. Each element of <code>freqs</code> represents how many times each element of the source vector, <code>v</code>, is repeated. It is analogous to the <code>times</code> argument in <code><a rd-options="base" href="/link/rep?package=RcppAlgos&version=2.5.0&to=base" data-mini-rdoc="base::rep">rep</a></code>. The default value is <code>NULL</code>.

freqs

target

Calculate the number of partitions of a vector chosen \(m\) at a time with or without replacement. Additionally, these functions can calculate the number of partitions of multisets.

Provides optimized functions and flexible combinatorial iterators
implemented in C++ for solving problems in combinatorics and
computational mathematics. Utilizes the RMatrix class from 'RcppParallel'
for thread safety. There are combination/permutation functions with
constraint parameters that allow for generation of all results of a vector
meeting specific criteria (e.g. generating integer partitions
or finding all combinations such that the sum is between two bounds).
Capable of generating specific combinations/permutations (e.g. retrieve
only the nth lexicographical result) which sets up nicely for
parallelization as well as random sampling. Gmp support permits exploration
where the total number of results is large (e.g. comboSample(10000, 500,
n = 4)). Additionally, there are several high performance number theoretic
functions that are useful for problems common in computational mathematics.
Some of these functions make use of the fast integer division library
'libdivide'. The primeSieve function is based on the segmented sieve of
Eratosthenes implementation by Kim Walisch. It is also efficient for large
numbers by using the cache friendly improvements originally developed by
Tom<c3><a1>s Oliveira. Finally, there is a prime counting function that implements
Legendre's formula based on the work of Kim Walisch.

Joseph Wood

RcppAlgos

High Performance Tools for Combinatorics and Computational
Mathematics

partitionsCount function

A vector of frequencies used for producing all partitions of a multiset of <code>v</code>. Each element of <code>freqs</code> represents how many times each element of the source vector, <code>v</code>, is repeated. It is analogous to the <code>times</code> argument in <code><a rd-options='base' href='rep'>rep</a></code>. The default value is <code>NULL</code>.

partitionsCount: Number of Partitions

Description

Usage

Arguments

Value

See Also

Examples