RcppAlgos (version 0.2.1)

primeFactorizationList: Generate Prime Factorization for all Integers up to \(n\)

Description

Efficiently generates the prime factorization of all integers up to \(n\) using Rcpp.

Usage

primeFactorizationList(n = 100L)

Arguments

n

Positive integer or numeric value.

Value

Returns a list of integer vectors where each index, \(j\), represents the prime factorization of \(j\) (E.g. gmp::factorize(j)).

Details

This function is useful when many prime factorizations are needed. Instead of generating the prime factorization on the fly, one can reference the indices of the generated list.

See Also

divisorsList, factorize, primeFactors

Examples

# NOT RUN {
## Generate some random data
set.seed(28)
mySamp <- sample(10^6, 5*10^5)

## Quickly generate prime factorizations up 
## to 10^6 (max element from mySamp)
system.time(allPFacs <- primeFactorizationList(10^6))

## Use generated prime factorization for further
## analysis by accessing the index of allPFacs
for (s in mySamp) {
    pFac <- allPFacs[[s]]
    ## Continue algorithm
}

## Generating the prime factorization on the fly is much 
## slower despite 1. gmp::factorize being one of the fastest
## stand alone factoring algorithms and 2. there are fewer
## factorizations being performed (allPFacs above contains
## 10^6 factorizations and the below only generates the
## factorizations of the numbers in mySamp (5*10^5 elements)).

# }
# NOT RUN {
system.time(mySampPFacs <- lapply(mySamp, gmp::factorize))
# }