RcppAlgos-package

RcppAlgos

The RcppAlgos package attacks age-old problems in combinatorics and computational mathematics.

 package

Provides optimized functions implemented in C++ with 'Rcpp'
for solving problems in combinatorics and computational mathematics.
Utilizes parallel programming via 'RcppThread' for maximal performance.
Also makes use of the RMatrix class from the 'RcppParallel' library.
There are combination/permutation functions with constraint parameters
that allow for generation of all combinations/permutations of a vector
meeting specific criteria (e.g. 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' by <http://ridiculousfish.com>. 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 algorithm by Kim Walisch.

Joseph Wood

High Performance Tools for Combinatorics and Computational
Mathematics

RcppAlgos-package function

<ol>
<li>The main goal is to encourage fresh and creative approaches to foundational problems. The question that most appropriately summarizes <code>RcppAlgos</code> is: "Can we do better?".</li>
<li>Provide highly optimized functions that facilitates a broader spectrum of researchable cases. E.g
 <ul>
<li>Investigating the structure of large numbers over wide ranges:
 <ul>
<li><code>primeFactorizeSieve(10^13 - 10^7, 10^13 + 10^7)</code></li>
<li><code>primeSieve(2^53 - 10^10, 2^53 - 1, nThreads = 8)</code></li>
</ul></li>
<li>Easily explore combinations/permutations that would otherwise be inaccessible due to time of execution/memory constraints:
 <ul>
<li><pre>comboGeneral(primeSieve(1000), m = 5, repetition = TRUE,
 constraintFun = "prod", comparisonFun = "&lt;",
 limitConstraints = 500000, upper = 10^5)</pre></li>
<li><pre>parallel::mclapply(seq(...), function(x) {
 temp = permuteGeneral(15, 10, lower = x, upper = y)
 ## analyze permutations
 ## output results
 }, mc.cores = detectCores() - 1))</pre></li>
<li><code>permuteSample(rnorm(100), 10, freqs = rep(1:4, 25), n = 15, seed = 123)</code></li>
</ul></li>
</ul></li>
<li>Speed!!!.... You will find that the functions in <code>RcppAlgos</code> are some of the fastest of their type available in <code>R</code>.</li>
</ol>

RcppAlgos-package: High Performance Tools for Combinatorics and Computational Mathematics

Description

Arguments

Goals