Vector

Basic skills in R: Working with data structures

Vector

Content

What is a vector in R?
Creating a vector in R
Arithmetic with vectors
Selecting components of vectors and assigning values
Ordering components of a vector

What is a vector in R? You can store more than just one value inside a variable. You can, for example, make a variable called "ages_of_friends" and store a row of numeric values inside this variable. A variable that holds a row of values of the same data type, is called a vector. You can make numerical, character and logical vectors.

Creating a vector in R

Explanation

You create a vector with the function c() (c is short for combine or concatenate). Within the parentheses you list the values that you want in your vector, separated by a comma.

Don't forget to give a name to your new variable and to enter a sequence of basic objects there. With no argument, you only specify that you are creating a vector object Look at the example to see how you could it.

There are also special instructions to create specific vectors. For example, v1 <- 2:4 creates the vector \((2,3,4)\)
v2 <- seq(from=3, to=10, by=2) creates the vector \((3,5,7,9)\).

In simulations one make extensive use of vectors with randomly generated numbers, i.e., with random numbers. There are several instructions for this purpose.

`runif()`	random numbers between 0 and 1 using a uniform distribution
`sample()`	objects randomly taken from a vector
`rnorm()`	random numbers using a normal distribution

Sample script

# create a numerical vector 
num_vector <- c(20, 19, 21, 19) 
print(num_vector)
# output: 20, 19, 21, 19

# create a character vector 
char_vector <- c("Skye", "Leopold", "Jemma")
print(char_vector)
# output: "Skye" "Leopold" "Jemma" 

# create a logical vector
logical_vector <- c(T, F, T, T)
print(logical_vector)
# output: TRUE FALSE TRUE TRUE

# create a vector of 3 randomly genenerated
# numbers between 0 and 1
runif(3, min=0, max=1)
# output: this could look like
# [1] 0.4422001 0.7989248 0.1218993 

# 3 random numbers via standard normal distriution
rnorm(3)
# output: this could look like
# [1] -0.4721671 1.7665132 0.8769968

\(\phantom{x)}\)

The function length()

With the function length() function you can find out how many components a vector has. This can be useful if, for example, you want to check whether you did not make any typo's or forgot to include a component. In addition, it might be useful in some calculations: for example, to compute the mean of a numerical vector by basic functions in R, you could add all components and divide the result by the number of components in the vector (i.e., the length of your vector). See the sample session to the right.

sample session

More special constructions

Via the functions numeric() en logical() you can quickly generate a vector of certain length and filled with default values.

A vector of repeated values can be easily created via the function rep() (short for replicate)

You can also concatenate vector into a single vector object. For this purpose the function c() is also used.

When discussing the use of R in statistics we will see that there are also several functions for creating vectors with randomly generated numbers.

vector creation

Missing data

We wrote that a vector can only contain components of one and the same data type. But what about missing data? R has a special object for it, which is called NA (Not Available). The type of this object is in fact 'logical'. But it can easily be interpreted to be of numeric or character type, and that is what R does automatically when used in a vector.

You can easily filter out all missing data via the R function is.na() and the logical negation prefix operator !. You can also use is.na() to substitute a default value for missing data. See the sample session to the right.

NA (not availabe)

Practice

Vectors are by definition variables that contain exclusively values of the same data type. But what happens if we try to make a "vector" that contains mixed data types? Let's try:

Create an object via the function c() that contains two numbers and one word (don't forget the quotes), and give it a name.
What is the data type of this object? (use the function str())
What did R do to the vector? (If you are looking for a way to store values of multiple data types into one variable, take a look at the Working with Lists theory page)

Arithmetic with vectors

Explanation

Just as with variables with only one value stored in them, you can do math with vectors. When you add, subtract, multiply, or divide vectors, R will do the calculation for components at the same position. See the first example tot the right

But what if you want to add different numbers to each component of your vector? For example, you have the vector v1 <- c(1,2,3) and want to add 2 to the first component, 6 to the second and 4 to the third component. You can do this by creating another vector and adding this vector to your original vector. Take a look at the second example to the right to get an idea.

Sample script

# Arithmetics with one numeric vector 
# create one numeric vector
v1 <- c(1, 2, 3)

# add 5 to the components of the vector
v1 + 5 
#output: 6, 7, 8

# multiply the vector by 2 
print(v1*2) 
#output: 2, 4, 6

# Arithmetics with two vectors 
# Create two numeric vectors
v1 <- c(1, 2, 3)
v2 <- c(4, 5, 6)

# add these vectors
added_vectors <- v1 + v2
print(added_vectors)
# output: 5 7 9

# multiply the vectors componentwise
multiplied_vectors <- v1 * v2
print(multiplied_vectors)
# output: 4 10 18

\(\phantom{x}\)

Practice

Enter instructions in R and look at the output
1. Create a numeric vector and divide the vector by 4. Check for yourself that R just gives the expected output (no errors).
2. Convert the numerical vector to character type with the function as.character().
3. Check that the data type of the variable is now indeed "chr" with the function str().
4. Try to divide this character vector by 4. You will get an error. What does this error mean? Why could R not do the arithmetic calculation here?
Suppose that you have two vectors of different lengths:
```
v1 <- c(3, 6, 4) 
v2 <- c(9, 7, 6, 5)
```
1. What is the output when you add these two vectors?
2. How did R treat the last component of v2?

Selecting components of vectors and assigning values

Explanation

Vectors are subscriptable and mutable objects. This means that components of a vector (also called elements) can be accessed via a positional index and that you can change a vector also by assigning a value to a single component. Indexing starts at 1 and that there smart methods to create some vectors. Look at the first sample session to the right for selection of components.

You may want to ask R to give you all values in a vector that meet a certain condition. For example, you want to see all values in a vector that are greater than a particular value. You do that by telling R the name of the vector and including the condition you want the values to meet within square brackets.

In fact you use then logical indexing (with values TRUE and FALSE) to select components of vectors. You need relational operators for this, such as the ones in the table below.

`==`	equal to
`<`	less than
`>`	greater than
`<=`	less than or equal to
`>=`	greater than or equal to
`!=`	not equal to

You can also combine multiple logical expressions. Logical operators are listed below.

`&` or `&&`	and
`\|` or `\|\|`	or
`xor()`	exclusive or
`!`	not (logical negation)

The second interactive sample session to the right shows an example of a selection of components of a vector via logical expressions.

Components to which you refer can also be assigned new values. By in-line assignments you cannot change the structure of the vector. See the third interactive sample session to the right to discover how you can assign components of a vector.

Sample sessions

Session 1

Session 2

Session 3

& vs &&, | vs || There is a subtle difference between & and &&: The shorter form & performs componentwise comparisons in much the same way as arithmetic operators. The longer form && evaluates left to right examining only the first element of each vector. The same hold for the or operators | and ||.

Ordering components of a vector

Explanation

To sort the values from lowest to highest value you can use the function sort(). To sort from highest to lowest, you can either include the decreasing = TRUE option when using the function sort(), or first sort the vector using sort() and then reverse the sorted vector using the function rev().

Perhaps a more useful task would be to sort one vector according to the values of another vector. To do this you use the function order() in combination with selection via [].

See the interactive sample sessions to the right.

Sample sessions