Is the “*apply” family really not vectorized?

Question

So we are used to say to every R new user that \"apply isn\'t vectorized, check out the Patrick Burns R Inferno Circle 4\" which says (I quote):

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Answer 1

To me, vectorisation is primarily about making your code easier to write and easier to understand.

The goal of a vectorised function is to eliminate the book-keeping associated with a for loop. For example, instead of:

means <- numeric(length(mtcars))
for (i in seq_along(mtcars)) {
  means[i] <- mean(mtcars[[i]])
}
sds <- numeric(length(mtcars))
for (i in seq_along(mtcars)) {
  sds[i] <- sd(mtcars[[i]])
}

You can write:

means <- vapply(mtcars, mean, numeric(1))
sds   <- vapply(mtcars, sd, numeric(1))

That makes it easier to see what's the same (the input data) and what's different (the function you're applying).

A secondary advantage of vectorisation is that the for-loop is often written in C, rather than in R. This has substantial performance benefits, but I don't think it's the key property of vectorisation. Vectorisation is fundamentally about saving your brain, not saving the computer work.