The Art of R Programming

[1] 0.5031

user system elapsed

2.936 0.004 3.027

In spite of the many benefits of functional programming, this approach

usingapply()didn’t help. Instead, things got worse. Since this could be sim-

ply due to random sampling variation, I ran the code several times again,

with similar results.

So, let’s look at vectorizing this simulation.

1 sim3 <- function(nreps) {
2 nb1 <- 10
3 nb2 <- 6
4 n1 <- 18
5 n2 <- 13
6 u <- matrix(c(runif(2*nreps)),nrow=nreps,ncol=2)
7 # set up the condition vector
8 cndtn <- u[,1] <= nb1/n1 & u[,2] <= (nb2+1)/n2 |
9 u[,1] > nb1/n1 & u[,2] <= nb2/n2
10 return(mean(cndtn))
11 }

The main work is done in this statement:

cndtn <- u[,1] <= nb1/n1 & u[,2] <= (nb2+1)/n2 |

u[,1] > nb1/n1 & u[,2] <= nb2/n2

To get that, we reasoned out which conditions would lead to choosing

a blue marble on the second pick, coded them, and then assigned them to

cndtn.

Remember that<=and&are functions; in fact, they are vector functions,

so they should be fast. Sure enough, this brings quite an improvement:

> system.time(print(sim3(10000)))

[1] 0.4987

user system elapsed

0.060 0.016 0.076

In principle, the approach we took to speed up the code here could be

applied to many other Monte Carlo simulations. However, it’s clear that the

analog of the statement that computescndtnwould quickly become quite

complex, even for seemingly simple applications.

Moreover, the approach would not work in “infinite-stage” situations,

meaning an unlimited number of time steps. Here, we are considering the

marble example as being two-stage, with two columns to the matrixu.

Performance Enhancement: Speed and Memory 311