RcppAlgos (version 0.2.1)

divisorsList: Generate Complete Factorization of all Integers up to \(n\)

Description

Rcpp sieve implementation that quickly generates the complete factorization of all integers up to \(n\).

Usage

divisorsList(n = 100L)

Arguments

n

Positive integer or numeric value.

Value

Returns a list of integer vectors where each index, \(m\), represents the complete factorization of \(m\).

E.g. (1:m)[m%%(1:m)==0]

Details

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

See Also

primeFactorizationList, divisors

Examples

# NOT RUN {
## Generate some random data
set.seed(33550336)
mySamp <- sample(10^5, 5*10^4)

## Quickly generate complete factorizations up 
## to 10^5 (max element from mySamp)
system.time(allFacs <- divisorsList(10^5))

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

## Generating the complete factorization on the fly is much slower.
## See below for a couple of examples that are not as efficient.

# }
# NOT RUN {
## Brute Force... very slow
system.time(mySampFacs <- lapply(mySamp, function(x) (1:x)[x%%(1:x)==0L]))

## Using numbers::divisors... better than brute force, but still
## much slower than calling divisorList
system.time(mySampFacs <- lapply(mySamp, function(x) numbers::divisors))
# }