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Recently I had several discussions about using for loops in GNU R and how they compare to *apply family in terms of speed. I have not seen a direct benchmark comparing them so I decided to execute one (warning: some of the code presented today takes long time to execute).

First I have started by comparing the speed of assignment operator for lists vs. numeric vectors in standard for loops. Here is the code:
```speed.test <- function(n) {
gc()
x1 <- numeric(n)
x2 <- vector(n, mode = "list")
c(system.time(for (i in 1:n) { x1[i] <- i })[3],
system.time(for (i in 1:n) { x2[[i]] <- i })[3])
}

n <- seq(10 ^ 4, 10 ^ 6, len = 5)
result <- t(sapply(n, speed.test))
par(mar=c(4.5, 4.5, 1, 1))
matplot(n / 1000, result, type = "l" , col = 1:2, lty = 1,
xlab = "n ('000)", ylab = "time")
legend("topleft", legend = c("numeric", "list"),
col = 1:2, lty = 1)```
The picture showing the result of the comparison is the following:
As we can see - operation numeric vectors are significantly faster than list, especially for large vector sizes.

But how does this relate to *apply family of functions? The issue is that the workhorse function there is lapply and it works on lists. Other functions from this family call lapply internally.

So I have run the second test comparing: (a) lapply, (b) for loop working on lists and (c) for loop working on numeric vectors. Here is the code:
```aworker <- function(n) {
r <- lapply(1:n, identity)
return(NULL)
}

lworker <- function(n) {
r <- vector(n, mode = "list")
for (i in 1:n) {
r[[i]] <- identity(i)
}
return(NULL)
}

nworker <- function(n) {
r <- numeric(n)
for (i in 1:n) {
r[i] <- identity(i)
}
return(NULL)
}

run <- function(n, worker) {
gc()
unname(system.time(worker(n))[3])
}

compare <- function(n) {
c(lapply = run(n, aworker),
list = run(n, lworker),
numeric = run(n, nworker))
}

n <- rep(c(10 ^ 6, 10 ^ 7), 10)
result <- t(sapply(n, compare))
par(mfrow = c(1,2), mar = c(3,3,3,1))
for (i in n[1:2]) {
boxplot(result[n == i,],
main = format(i, scientific = F, big.mark = ","))
}```
On the picture below we can see the result. For 1,000,000 elements in a vector lapply is the fastest. The reason it that it executes looping in compiled C code. However for 10,000,000 elements for loop using numeric vector is faster as it avoids conversion to list.
Of course probably on other machines than my notebook the difference in speed would manifest itself for other number of elements in a vector.
However one can draw a general conclusion: if you have large AND numeric vectors and need to do a lot of number crunching for loop will be faster than lapply.