RcppAlgos

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A collection of high performance functions implemented in C++ with Rcpp for solving problems in combinatorics and computational mathematics. Utilizes the RcppThread library for easy access to thread safe multithreading. We also make use of the RMatrix.h header file from RcppParallel for thread safe accessors for Rcpp matrices.

The primeSieve function and the primeCount function are both based off of the excellent work by Kim Walisch. The respective repos can be found here: kimwalisch/primesieve; kimwalisch/primecount

Additionally, many of the sieving functions make use of the fast integer division library libdivide by ridiculousfish.

Installation

install.packages("RcppAlgos")

## install the development version
devtools::install_github("jwood000/RcppAlgos")

Basic Usage

## Generate prime numbers
primeSieve(50, 100)
[1] 53 59 61 67 71 73 79 83 89 97


## Count prime numbers less than n
primeCount(1e10)
[1] 455052511


## Find all 3-tuples combinations of 1:4 
comboGeneral(4, 3)
     [,1] [,2] [,3]
[1,]   1    2    3
[2,]   1    2    4
[3,]   1    3    4
[4,]   2    3    4


## Pass any atomic type vector
permuteGeneral(letters, 3, upper = 4)
     [,1] [,2] [,3]
[1,] "a"  "b"  "c" 
[2,] "a"  "b"  "d" 
[3,] "a"  "b"  "e" 
[4,] "a"  "b"  "f" 


## Generate a reproducible sample
comboSample(10, 8, TRUE, n = 5, seed = 84)
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,]    3    3    3    6    6   10   10   10
[2,]    1    3    3    4    4    7    9   10
[3,]    3    7    7    7    9   10   10   10
[4,]    3    3    3    9   10   10   10   10
[5,]    1    2    2    3    3    4    4    7


## Get combinations such that the product is between
## 3600 and 4000 (including 3600 but not 4000)
comboGeneral(5, 7, TRUE, constraintFun = "prod",
             comparisonFun = c(">=","<"),
             limitConstraints = c(3600, 4000),
             keepResults = TRUE)
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,]    1    2    3    5    5    5    5 3750
[2,]    1    3    3    4    4    5    5 3600
[3,]    1    3    4    4    4    4    5 3840
[4,]    2    2    3    3    4    5    5 3600
[5,]    2    2    3    4    4    4    5 3840
[6,]    3    3    3    3    3    3    5 3645
[7,]    3    3    3    3    3    4    4 3888

Further Reading

Contact

I welcome any and all feedback. If you would like to report a bug, have a question, or have suggestions for possible improvements, please file an issue.