How to define a vectorized function in R

Question

As the title, I\'d like to know how to define a vectorized function in R.

• Is it just by using a loop in the function?
• Is this method efficient?
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Answer 1

A loop at the R level is not vectorized. An R loop will be calling the same R code for each element of a vector, which will be inefficient. Vectorized functions usually refer to those that take a vector and operate on the entire vector in an efficient way. Ultimately this will involve some for of loop, but as that loop is being performed in a low-level language such as C it can be highly efficient and tailored to the particular task.

Consider this silly function to add pairwise the elements of two vectors

sillyplus <- function(x, y) {
    out <- numeric(length = length(x))
    for(i in seq_along(x)) {
        out[i] <- x[i] + y[i]
    }
    out
}

It gives the right result

R> sillyplus(1:10, 1:10)
 [1]  2  4  6  8 10 12 14 16 18 20

and is vectorised in the sense that it can operate on entire vectors at once, but it is not vectorised in the sense I describe above because it is exceptionally inefficient. + is vectorised at the C level in R so we really only need 1:10 + 1:10, not an explicit loop in R.

The usual way to write a vectorised function is to use existing R functions that are already vectorised. If you want to start from scratch and the thing you want to do with the function doesn't exist as a vectorised function in R (odd, but possible) then you will need to get your hands dirty and write the guts of the function in C and prepare a little wrapper in R to call the C function you wrote with the vector of data you want it to work on. There are ways with functions like Vectorize() to fake vectorisation for R functions that are not vectorised.

C is not the only option here, FORTRAN is a possibility as is C++ and, thanks to Dirk Eddelbuettel & Romain Francois, the latter is much easier to do now with the rcpp package.

Answer 2

A vectorized function will return a vector of the same length as one of its arguments. Generally one can get such a function by using combinations of built-in functions like "+", cos or exp that are vectorized as well.

vecexpcos <- function(x) exp(cos(x))
vecexpcos( (1:10)*pi )
>    vecexpcos( (1:10)*pi )
# [1] 0.3678794 2.7182818 0.3678794 2.7182818 0.3678794 2.7182818 0.3678794 2.7182818 0.3678794 2.7182818

If you need to use a non-vectorized function like sum, you may need to invoke mapply or Vectorize in order to get the desired behavior.