### Performance Improvements in R: Vectorization & Memoisation

Full of potential coding improvements, Efficient R Programming: A Practical Guide to Smarter Programming, the book makes two suggestions that are notable. Vectorization, explained here and here, and memoisation, caching prior results albeit with additional memory use, were relevant and significant.

What follows is a demonstration of the speed improvements that might be achieved using these concepts.

The result of the first pass shows that vectorization provides a vast improvement over a standard for loop, and that memoise provides little of an improvement over that.

That said, on a a second pass over the same loops, memoisation is vastly faster, returning values in zero (0) seconds.

What follows is a demonstration of the speed improvements that might be achieved using these concepts.

```
################################
# performance
# vectorization and memoization
################################
# clear memory between changes
rm(list = ls())
#load memoise
#install.packages('memoise')
library(memoise)
# create test function
monte_carlo = function(N) {
hits = 0
for (i in seq_len(N)) {
u1 = runif(1)
u2 = runif(1)
if (u1 ^ 2 > u2)
hits = hits + 1
}
return(hits / N)
}
# memoise test function
monte_carlo_memo <- memoise(monte_carlo)
# vectorize function
monte_carlo_vec <- function(N) mean(runif(N) ^ 2 > runif(N))
# memoise vectorized function
monte_carlo_vec_memo <- memoise(monte_carlo_vec)
# run test - pass 1
n <- 999999
plainFor <- system.time(monte_carlo(n))
memoised <- system.time(monte_carlo_memo(n))
vectorised <- system.time(monte_carlo_vec(n))
both <- system.time(monte_carlo_vec_memo(n))
# results - pass 1
result <- cbind(plainFor, memoised, vectorised, both)
display <- format(result, digits = 3, nsmall = 3)
View(display)
```

The result of the first pass shows that vectorization provides a vast improvement over a standard for loop, and that memoise provides little of an improvement over that.

```
# run test - pass 2
plainFor <- system.time(monte_carlo(n))
memoised <- system.time(monte_carlo_memo(n))
vectorised <- system.time(monte_carlo_vec(n))
both <- system.time(monte_carlo_vec_memo(n))
# results - pass 2
result <- cbind(plainFor, memoised, vectorised, both)
display <- format(result, digits = 3, nsmall = 3)
View(display)
```

That said, on a a second pass over the same loops, memoisation is vastly faster, returning values in zero (0) seconds.