partitionsRank

compositionsRank

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

random

sample

rank

partitions

integer

combinatorics

unrank

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

partitionsRank function

<dl> <dt>...</dt>
<dd>vectors or matrices to be ranked.</dd> <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>repetition</dt>
<dd>Logical value indicating whether partitions/compositions should be with or without repetition. The default is <code>FALSE</code>.</dd> <dt>freqs</dt>
<dd>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 href="/link/rep?package=RcppAlgos&version=2.9.3" data-mini-rdoc="RcppAlgos::rep">rep</a></code>. The default value is <code>NULL</code>.</dd> <dt>target</dt>
<dd>Number to be partitioned. If <code>NULL</code>, <code>max(v)</code> will be used.</dd> <dt>weak</dt>
<dd>(Compositions only) Logical flag indicating whether to allow terms of the sequence to be zero.</dd> </dl>

Arguments

Author

Rank Partitions/Compositions — partitionsRank

<dl>

 <dt>...</dt>
<dd>vectors or matrices to be ranked.</dd>

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

 <dt>freqs</dt>
<dd>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 href='https://rdrr.io/r/base/rep.html'>rep</a></code>. The default value is <code>NULL</code>.</dd>

 <dt>target</dt>
<dd>Number to be partitioned. If <code>NULL</code>, <code>max(v)</code> will be used.</dd>

 <dt>weak</dt>
<dd>(Compositions only) Logical flag indicating whether to allow terms of the sequence to be zero.</dd>

 </dl>

Rank Partitions/Compositions

partitionsRank: Rank Partitions/Compositions

Description

Usage

Value

Arguments

Author

Details

References

See Also

Examples