Question

Suppose I want perform a simulation using the following function:

fn1 <- function(N) {
  res <- c()
  for (i in 1:N) {
    x <- rnorm(2)
    res <- c(res, x[2]-x[1])
  }
  res
}

For very large N, computation appears to hang. Are there better ways of doing this?

(Inspired by: https://stat.ethz.ch/pipermail/r-help/2008-February/155591.html)

Answer 1

For loops in R are notoriously slow, but here there’s another issue. It’s much faster to preallocate the results vector, res, rather append to res at each iteration.

Below we can compare the speed of the above version with a version that simply starts with a vector, res, of length N and changes the ith element during the loop.

fn1 <- function(N) {
  res <- c()
  for (i in 1:N) {
     x <- rnorm(2)
     res <- c(res,x[2]-x[1])
  }
  res
}
fn2 <- function(N) {
  res <- rep(0,N)
  for (i in 1:N) {
     x <- rnorm(2)
     res[i] <- x[2]-x[1]
  }
  res
}
> N <- 50000
> system.time(res1 <- fn1(N))
   user  system elapsed 
  6.568   0.256   6.826 
> system.time(res2 <- fn2(N))
   user  system elapsed 
  0.452   0.004   0.496 

Also, as Sharpie points out, we can make this slightly faster by using R functions like apply (or its relatives, sapply and lapply).

fn3 <- function(N) {
  sapply( 1:N, function( i ){ x <- rnorm(2); return( x[2] - x[1] ) } )
}
> system.time(res3 <- fn3(N))
   user  system elapsed 
  0.397   0.004   0.397