How do I vectorize this is_prime function in R? - r

Question

I have created this function that takes number and return TRUE or FALSE depending whether the number is prime or not.
is.prime <- function(num) {
if (num == 2) {
TRUE
} else if (any(num %% 2:(num-1) == 0)) {
FALSE
} else {
TRUE
}
}
However, this function takes only one value, for example this works fine:
> is_prime(17)
[1] TRUE
If I plug in a vector, I want to see TRUE or FALSE for each element. For example,
> is_prime(c(17,5,10,22,109,55))
[1] TRUE
Warning messages:
1: In if (x == 1) { :
the condition has length > 1 and only the first element will be used
2: In 2:(floor(x/2)) :
numerical expression has 6 elements: only the first used
3: In x%%2:(floor(x/2)) :
longer object length is not a multiple of shorter object length
This is evaluated for the first element, but I would want to see
TRUE TRUE FALSE FALSE TRUE FALSE
for the vector
is_prime(c(17,5,10,22,109,55))
How would I modify the function to vectorize using the same algorithm?

Answer 1

Half Vectorized
It is possible to vectorize some of the function by dealing with even numbers (and a few other numbers) in a vectorized fashion. The rest is taken care of using vapply.
helper <- function(x) {
for (k in seq(3, round(sqrt(x)) + 1, 2)) {
if (x %% k == 0)
return(FALSE)
}
return(TRUE)
}
is.prime <- function(v) {
out <- rep(TRUE, length(v))
out[v %% 2 == 0 | v %in% c(1)] <- FALSE
out[v %in% c(2, 3, 5)] <- TRUE
indices <- which(v > 5 && v == FALSE)
out[indices] <- vapply(v[indices], helper, logical(1))
return(out)
}
is.prime(c(17,5,10,22,109,55))
# [1] TRUE TRUE FALSE FALSE TRUE FALSE
Full Vectorized
If performance is at stake, you might consider using `Rcpp`:
c++ file
#include <Rcpp.h>
#include <math.h>
using namespace Rcpp;
bool is_prime(int n) {
if ((n == 2) || (n == 3) || (n == 5)) {
return true;
}
if ((n % 2 == 0) || (n == 1)) {
return false;
}
int i = 3;
while (i < round(sqrt(n)) + 1) {
if (n % i == 0) {
return false;
}
i += 2;
}
return true;
}
// [[Rcpp::export]]
LogicalVector is_prime(IntegerVector v) {
int n = v.length();
LogicalVector out = LogicalVector(n);
for (int i = 0; i < n; i++) {
out[i] = is_prime(v[i]);
}
return out;
}
R File
library(Rcpp)
sourceCpp('prime_fun.cpp') # if cpp file in same dir
is_prime(c(17,5,10,22,109,55))
# [1] TRUE TRUE FALSE FALSE TRUE FALSE

Answer 2

Technically, you cannot vectorize the function but you can use methods to apply is.prime function to vectors.
For example, use sapply :
sapply(c(17,5,10,22,109,55), is.prime)
#[1] TRUE TRUE FALSE FALSE TRUE FALSE
Or use Vectorize which is a wrapper around mapply :
vec.is.prime <- Vectorize(is.prime)
vec.is.prime(c(17,5,10,22,109,55))
#[1] TRUE TRUE FALSE FALSE TRUE FALSE

Answer 3

R is an inherently vectorized language, you just have to not break that when you write functions...
is.prime <- function(num){
res<-rep(TRUE, length(num))
for(i in 2:(max(num)-1) ){
res[(i < num) & ((num %% i) == 0) ] <- FALSE
}
return(res)
}
x<-c(2, 5, 17, 109, 10, 22, 55, 93)
print("Primes:")
print(x[ is.prime(x) ] )
Output:
> source('~/.active-rstudio-document')
[1] "Primes:"
[1] 2 5 17 109