R nested loop slow

Question

I have no idea why something like this should be slow:

steps=500
samples=100000
s_0=2.1
r=.02
sigma=.2
k=1.9

at<-matrix(nrow=(steps+1),ncol=samples)
at[1,]=s_0

for(j in 1:samples)
{
  for(i in 2:(steps+1))
  {
    at[i,j]=at[(i-1),j] + sigma*sqrt(.0008)*rnorm(1)
  }
}

I tried to rewrite this using sapply, but it was still awful from a performance standpoint.

Am I missing something here? This would be seconds in c++ or even the bloated c#.

Answer 1

R can vectorize certain operations. In your case you can get rid of the outer loop by doing a following change.

for(i in 2:(steps + 1))
{
    at[i,] = at[(i - 1),] + sigma * sqrt(.0008) * rnorm(samples)
}

According to system.time the original version for samples = 1000 takes 6.83s, while the modified one 0.09s.