Introduction
To R

Vector Arithmetic

Simple arithmetical calculations work on vectors one element at a time. Some examples:

> x <- 1:10
> x + 2
 [1]  3  4  5  6  7  8  9 10 11 12
> x * 2
 [1]  2  4  6  8 10 12 14 16 18 20
> sqrt(x)
 [1] 1.000000 1.414214 1.732051 2.000000 2.236068 2.449490 2.645751 2.828427
 [9] 3.000000 3.162278

If you operate on two vectors, the calculations are also done one element at a time:

> x <- 1:10
> y <- 21:30
>  x+y
 [1] 22 24 26 28 30 32 34 36 38 40

But what if the vectors are different lengths? In this case, R will always repeat the shorter vector until it is long enough:

> x <- 1:10
> y <- c(1,2)
> x+y
 [1]  2  4  4  6  6  8  8 10 10 12

Here R has repeated y five times, and added that to x, like this:

 x  :  1  2  3  4  5  6  7  8  9 10
 y  :  1  2  1  2  1  2  1  2  1  2  (repeated)
-----------------------------------
x+y :  2  4  4  6  6  8  8 10 10 12

However, if the length of the longer vector isn't an integer multiple of the length of the shorter vector, R will warn you:

> x <- 1:10
> y <- c(1,2,1)
> x + y
 [1]  2  4  4  5  7  7  8 10 10 11
Warning message: 
longer object length is not a multiple of shorter object 
length in: x + y

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