comboGroupsCount

Calculate the number of partitions of a vector into groups. See the related integer sequences A025035-A025042 at <a href="https://oeis.org">OEIS</a> (E.g. <a href="https://oeis.org/A025036">A025036</a> for Number of partitions of \( 1, 2, ..., 4n \) into sets of size 4.)

partitions

combinatorics

comboGroups

Provides optimized functions and flexible iterators implemented in
C++ for solving problems in combinatorics and computational mathematics.
Handles various combinatorial objects including combinations, permutations,
integer partitions and compositions, Cartesian products, unordered
Cartesian products, and partition of groups. Utilizes the RMatrix class
from 'RcppParallel' for thread safety. The combination and permutation
functions contain constraint parameters that allow for generation of all
results of a vector meeting specific criteria (e.g. finding all
combinations such that the sum is between two bounds). Capable of
ranking/unranking combinatorial objects efficiently (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
Tomás 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

comboGroupsCount function

<dl> <dt>v</dt>
<dd>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>. All atomic types are supported (See <code><a href="/link/is.atomic?package=RcppAlgos&version=2.9.3" data-mini-rdoc="RcppAlgos::is.atomic">is.atomic</a></code>).</dd> <dt>numGroups</dt>
<dd>An Integer. The number of groups that the vector will be partitioned into. The default is <code>NULL</code>. If provided and <code>grpSize</code> is <code>NULL</code>, it must divide the length of v (if v is a vector) or v (if v is a scalar).</dd> <dt>grpSizes</dt>
<dd>A vector of whole numbers representing the size of each group. The default is <code>NULL</code>. If provided, the sum of the elements must total the length of v (if v is a vector) or v (if v is a scalar).</dd></dl>

Arguments

Author

Calculate the number of partitions of a vector into groups. See the related integer sequences A025035-A025042 at <a href='https://oeis.org'>OEIS</a> (E.g. <a href='https://oeis.org/A025036'>A025036</a> for Number of partitions of \( 1, 2, ..., 4n \) into sets of size 4.)

Number of Partitions of a Vector into Groups — comboGroupsCount

<dl>

 <dt>v</dt>
<dd>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>. All atomic types are supported (See <code><a href='https://rdrr.io/r/base/is.recursive.html'>is.atomic</a></code>).</dd>

 <dt>numGroups</dt>
<dd>An Integer. The number of groups that the vector will be partitioned into. The default is <code>NULL</code>. If provided and <code>grpSize</code> is <code>NULL</code>, it must divide the length of v (if v is a vector) or v (if v is a scalar).</dd>

 <dt>grpSizes</dt>
<dd>A vector of whole numbers representing the size of each group. The default is <code>NULL</code>. If provided, the sum of the elements must total the length of v (if v is a vector) or v (if v is a scalar).</dd>

</dl>

comboGroupsCount: Number of Partitions of a Vector into Groups

Description

Usage

Value

Arguments

Author

References

Examples