Vectorization

Functions in R are often vectorized. For example:

exp(2)

[1] 7.389056

I give it one number, and it returns one number. If instead, I supply a vector, I get this:

exp(c(-3, 0.001, 2, 5, 600, 1, 0))

[1]  4.978707e-02  1.001001e+00  7.389056e+00  1.484132e+02 3.773020e+260
[6]  2.718282e+00  1.000000e+00

So when I supply a regular ol’ number as an argument, the exp function returns a number. When I supply a vector, it returns a vector; the exp function knows to act entry-wise and give me back a vector with the output of each entry-wise computation. In other words, I didn’t have to write a loop to manually do this. The function is vectorized, so it effectively runs the loop for me.

So consider for instance the set of numbers \(A = \{-100, -6, 0.001, \pi, 30\}\), and this stupid function:

\[ f(x) = \ln^2\left|\frac{2x}{1-\sin(x)}\right|. \]

If I wanted to compute the value of \(f\) for each of the arguments in \(A\), I could write a loop that goes entry-by-entry through \(A\) and applies the function \(f\) to it. But in R, because arithmetic operations are vectorized, I can do this:

A = c(-100, -6, 0.001, pi, 30)

log( abs( (2 * A) / ( 1 - sin(A) ) ) ) ^ 2 

[1] 36.051349  7.910714 38.608919  3.377792 11.609009

Dumb!

All of the basic arithmetic operations are vectorized like this:

c(1, 2, 3) + 2

[1] 3 4 5

c(1, 2, 3) + c(1, 2, 3)

[1] 2 4 6

floor(c(4, 5.1, 6.9))

[1] 4 5 6