RcppAlgos-package {RcppAlgos}

High Performance Tools for Combinatorics and Computational Mathematics

Description

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

Goals

1. The main goal is to encourage fresh and creative approaches to foundational problems. The question that most appropriately summarizes RcppAlgos is: "Can we do better?".

2. Provide highly optimized functions that facilitates a broader spectrum of researchable cases. E.g

   • Investigating the structure of large numbers over wide ranges:

     • primeFactorizeSieve(10^13 - 10^7, 10^13 + 10^7)

     • primeSieve(2^53 - 10^10, 2^53 - 1, nThreads = 32)

   • Easily explore combinations/permutations/partitions that would otherwise be inaccessible due to time of execution/memory constraints:

     • c_iter = comboIter(10000, 100)
       bigSamp = gmp::urand.bigz(3, gmp::log2.bigz(comboCount(10000, 100)))
       c_iter[[bigSamp]] ## flexible iterator allows random sampling

     • p_iter = partitionsIter(5000, 100, target = 6000)
       p_iter[[1e9]] ## start iterating from index = 1e9
       p_iter@nextIter()
       p_iter@nextNIter(1e3)

     • comboGeneral(150, 5, constraintFun = "sum", Parallel = TRUE)

     • parallel::mclapply(seq(...), function(x) {
                   temp = permuteGeneral(15, 10, lower = x, upper = y)
                   ## analyze permutations
                   ## output results
           }, mc.cores = detectCores() - 1))

     • partitionsGeneral(0:80, repetition = TRUE)

     • permuteSample(rnorm(100), 10, freqs = rep(1:4, 25), n = 15, seed = 123)

     • set.seed(123)
       comboGeneral(runif(42, 0, 50), 10,
                    constraintFun = "mean",
                    comparisonFun = c(">","<"),
                    limitConstraints = c(39.876, 42.123))

3. Speed!!!.... You will find that the functions in RcppAlgos are some of the fastest of their type available in R.

Author(s)

Joseph Wood