15  Vectorized Operations

Many built-in R functions are vectorized and so are many functions from external packages as well.

A vectorized function operates on all elements of an object.

Vectorization is very efficient: it can save both human (your) time and machine time.

Tip

In many cases, applying a function on all elements simultaneously may seem like the obvious or expected behavior, but since not all functions are vectorized, make sure to check the documentation (and/or test whether a function is vectorized using a simple example).

15.1 Operations between vectors of equal length

Such operations are applied between corresponding elements of each vector:

x <- 1:10
z <- 11:20
x + z

 [1] 12 14 16 18 20 22 24 26 28 30

i.e. the above is equal to c(x[1] + z[1], x[2] + z[2], ..., x[n] + z[n]).

Weight <- rnorm(20, mean = 80, sd = 1.7)
Weight

 [1] 79.36801 81.06268 79.41230 80.10540 80.87167 79.12432 79.71534 79.99593
 [9] 80.22232 78.98860 79.92995 80.51565 76.70282 80.84724 78.15982 81.09863
[17] 76.51254 79.88208 76.89691 80.46485

Height <- rnorm(20, mean = 1.7, sd = .1)
Height

 [1] 1.712619 1.825532 1.740072 1.746919 1.831087 1.634120 1.607686 1.880719
 [9] 1.655010 1.641103 1.686898 1.699648 1.810535 1.694773 1.666255 1.575280
[17] 1.562882 1.463314 1.549886 1.911374

BMI <- Weight/Height^2
BMI

 [1] 27.05975 24.32441 26.22728 26.24921 24.12005 29.63071 30.84177 22.61621
 [9] 29.28829 29.32869 28.08873 27.87161 23.39902 28.14765 28.15145 32.68119
[17] 31.32421 37.30561 32.01175 22.02494

15.2 Operations between a vector and a scalar

In this cases, the scalar is repeated to match the length of the vector, i.e. it is recycled:

x + 10

 [1] 11 12 13 14 15 16 17 18 19 20

x * 2

 [1]  2  4  6  8 10 12 14 16 18 20

x / 10

 [1] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

x ^ 2

 [1]   1   4   9  16  25  36  49  64  81 100

15.3 Operations between vectors of unequal length: value recycling

Operations between a vector and a scalar are a special case of operations between vectors of unequal length. Whenever you perform an operation between two objects of different length, the shorter object’s elements are recycled:

x + c(2:1)

 [1]  3  3  5  5  7  7  9  9 11 11

Caution

Operations between objects of unequal length can occur by mistake. If the shorter object’s length is a multiple of the longer object’s length, there will be no error or warning, as above. Otherwise, there is a warning (which may be confusing at first) BUT recycling still happens and is highly unlikely to be intentional.

x + c(1, 3, 9)

Warning in x + c(1, 3, 9): longer object length is not a multiple of shorter
object length

 [1]  2  5 12  5  8 15  8 11 18 11

15.4 Vectorized matrix operations

Operations between matrices are similarly vectorized, i.e. performed between corresponding elements:

a <- matrix(1:4, nrow = 2)
b <- matrix(11:14, nrow = 2)
a

     [,1] [,2]
[1,]    1    3
[2,]    2    4

b

     [,1] [,2]
[1,]   11   13
[2,]   12   14

a + b

     [,1] [,2]
[1,]   12   16
[2,]   14   18

a * b

     [,1] [,2]
[1,]   11   39
[2,]   24   56

a / b

           [,1]      [,2]
[1,] 0.09090909 0.2307692
[2,] 0.16666667 0.2857143

15.5 Vectorized functions

Some examples of common mathematical operations that are vectorized:

log(x)

 [1] 0.0000000 0.6931472 1.0986123 1.3862944 1.6094379 1.7917595 1.9459101
 [8] 2.0794415 2.1972246 2.3025851

sqrt(x)

 [1] 1.000000 1.414214 1.732051 2.000000 2.236068 2.449490 2.645751 2.828427
 [9] 3.000000 3.162278

sin(x)

 [1]  0.8414710  0.9092974  0.1411200 -0.7568025 -0.9589243 -0.2794155
 [7]  0.6569866  0.9893582  0.4121185 -0.5440211

cos(x)

 [1]  0.5403023 -0.4161468 -0.9899925 -0.6536436  0.2836622  0.9601703
 [7]  0.7539023 -0.1455000 -0.9111303 -0.8390715