Y cx055 x x y 1 100 50 30 60 055 100 50 30 60 10 100

y <- c(x,0.55, x, x)
y
[1] 10.0 5.0 3.0 6.0 0.55 10.0 5.0 3.0 6.0
[10] 10.0 5.0 3.0 6.0
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CHAPTER 2. DATA OBJECTS 2.2. DATA STRUCTURES
Typing the name of an object in the commands window results in printing the object.
The numbers between square brackets indicate the position of the following element in
the vector.
Use the function round to round the numbers in a vector.
round (y,3) # round to 3 decimals
Mathematical calculations on vectors
Calculations on (numerical) vectors are usually performed on each element. For example,
x*x results in a vector which contains the squared elements of x .
x
[1] 10 5 3 6
z <- x*x
z
[1] 100 25 9 36
The symbols for elementary arithmetic operations are + , - , * , / . Use the ^ symbol to
raise power. Most of the standard mathematical functions are available in R. These
functions also work on each element of a vector. For example the logarithm of x:
log(x)
[1] 2.302585 1.609438 1.098612 1.791759
Function name Operation
abs absolute value
asin acos atan inverse geometric functions
asinh acosh atanh inverse hyperbolic functions
exp log exponent and natural logarithm
floor ceiling trunc creates integers from floating point numbers
gamma lgamma gamma and log gamma function
log10 logarithm with basis 10
round rounding
sin cos tan geometric functions
sinh cosh tanh hyperbolic functions
sqrt square root
Table 2.1: Some mathematical functions that can be applied on vectors
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CHAPTER 2. DATA OBJECTS 2.2. DATA STRUCTURES
The recycling rule
It is not necessary to have vectors of the same length in an expression. If two vectors
in an expression are not of the same length then the shorter one will be repeated until
it has the same length as the longer one. A simple example is a vector and a number
(which is a vector of length one).
sqrt(x) + 2
[1] 5.162278 4.236068 3.732051 4.449490
In the above example the 2 is repeated 4 times until it has the same length as x and then
the addition of the two vectors is carried out. In the next example, x has to be repeated
1.5 times in order to have the same length as y . This means the first two elements of x
are added to x and then x*y is calculated.
x <- c(1,2,3,4)
y <- c(1,2,3,4,5,6)
z <- x*y
Warning message:
longer object length
is not a multiple of shorter object length in: x * y
> z
[1] 1 4 9 16 5 12
Generating vectors
Regular sequences of numbers can be very handy for all sorts of reasons. Such sequences
can be generated in different ways. The easiest way is to use the column operator ( : ).
index <- 1:20
index
[1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
A descending sequence is obtained by 20:1 . The function seq together with its arguments
from, to, by or length is used to generate more general sequences. Specify the beginning
and end of the sequence and either specify the length of the sequence or the increment.
u <- seq(from=-3,to=3,by =0.5)
u
[1] -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0
30