**Vectors**, which constitute an ordered collection of values, are a class basic to the functioning of R.

The term "values" in R is broader in scope than what we normally take the term to mean. A value in R can be a numerical value (e.g., `1.2, 5, -79.843`

), but it can also be a character or string of characters(e.g., `"a", "alice", "trial_4"`

). Values can also be logical values (i.e., `TRUE`

or `FALSE`

). The important thing for a vector, however, is that all of its values are of the same type. Thus, you can't mix numerical values and strings of characters, for instance.

The name of a vector (or any variable, for that matter) can be any sequence of letters, numbers, and the dot (i.e., period character) or underline characters that starts with a letter or a dot not followed by a number. Names such as "`.2way`

" are not valid, and neither are the reserved words given in the list below.

TRUE NA if in FALSE NA_integer_ else next NULL NA_real_ repeat break Inf NA_complex_ while NaN NA_character_ function

To create a vector and assign it to a variable, we use the `c()`

function and the `=`

assignment operator, as the next couple of examples illustrate. Note the `=`

operator does not mean what it means in mathematics. It means instead to take the element specified on its right side and store it in the specified element on its left side.

> myNumericalVector = c(1,2,3) > myNumericalVector [1] 1 2 3 > myStringVector = c("alpha","beta","gamma") > myStringVector [1] "alpha" "beta" "gamma" > myLogicalVector = c(TRUE,FALSE,FALSE,FALSE) > myLogicalVector [1] TRUE FALSE FALSE FALSE

In the case where we only wish to store a single value, we may do so in a manner that requires slightly less typing. However, the result is still a vector.

> x = 5 # yields exactly the same output as: x = c(5) > x [1] 5

In the case where we wish to store a vector whose consecutive elements have a common difference of one (e.g., $(4,5,6,7,8)$), we can use a colon to more quickly define the vector, as shown below.

> a = 4:8 # yields exactly the same output as: a = c(4,5,6,7,8) > a [1] 4 5 6 7 8

To create a vector whose elements form an arithmetic sequence with a common difference other than one, we can use the `seq()`

function:

> b = seq(from=6,to=18,by=2) # here we specify the common difference with "by=" > b [1] 6 8 10 12 14 16 18 > c = seq(from=6,to=26,length.out=11) # the number of elements is determined by "length.out=" > c [1] 6 8 10 12 14 16 18 20 22 24 26

Vectors can be concatenated together easily by simply using them as arguments to the `c()`

function (which by the way stands for "combine").

> v1 = c(1,2,3) > v1 [1] 1 2 3 > v2 = 4:6 > v2 [1] 4 5 6 > v3 = c(v1,v2,7) > v3 [1] 1 2 3 4 5 6 7

To create a vector containing repeated values, we use the `rep()`

function

> rep(x=1,times=4) [1] 1 1 1 1 > rep(x=c(1,2,3),each=2) [1] 1 1 2 2 3 3 > rep(x=c(1,2,3),times=3,each=2) [1] 1 1 2 2 3 3 1 1 2 2 3 3 1 1 2 2 3 3

We can use vectors to create other vectors too. What follows gives some examples of this (but it is certainly not an exhaustive list):

- Use the sort() function to put a vector's elements in increasing or decreasing order:
> data = c(3,2,9,5,4,1,6,8,7) > sort(data, decreasing=FALSE) [1] 1 2 3 4 5 6 7 8 9 > sort(data, decreasing=TRUE) [1] 9 8 7 6 5 4 3 2 1

- Use the sqrt() function to take square roots of the elements of a vector:
> squares = c(1,4,9,16,25) > sqrt(squares) [1] 1 2 3 4 5

- You can add two vectors together, which adds their corresponding elements. Similar things happen with other arithmetic operators.
> vec = c(1,2,3) + c(4,5,6) > vec [1] 5 7 9

- Adding a value to a vector creates a new vector formed by adding the value
to each of the original vector's values. Similar things happen with other arithmetic operators.
> vec = c(1,2,3,4) > vec+3 [1] 4 5 6 7

- As an extension of the previous idea -- or more precisely, as its explanation -- when you combine two vectors of different sizes, the smaller one expands to the size of the larger through the repetition of its elements, and then the vectors are combined component-wise. This is called
**recycling**.If the longer vector's length is not a multiple of the smaller vector length - while the calculation will proceed - R will issue a warning.

> c(1,2,3,4,5,6) + c(1,2,3) [1] 2 4 6 5 7 9 > c(1,2,3,4,5,6,7,8) + c(1,2,3) [1] 2 4 6 5 7 9 8 10 Warning message: In c(1, 2, 3, 4, 5, 6, 7, 8) + c(1, 2, 3) : longer object length is not a multiple of shorter object length

We can find the number of elements in a given vector with the `length()`

function:

> nums = c(5,8,3,2) > length(nums) [1] 4

Sometimes one might be interested in the value at a particular position in a vector. Extracting such an element, or a group of such elements is called **subsetting**, and can be accomplished through an appropriate use of square brackets, as illustrated below.

> nums = c(5,8,3,2) > nums[1] # The 1st element is at position 1, which is contrary to how vectors are treated in some other programming languages [1] 5 > nums[2] [1] 8 > nums[length(nums)] [1] 2 > nums[c(2:4)] [1] 8 3 2

One can also use square brackets to remove elements from a vector. The difference between this use of square brackets and subsetting is that here we use negative values inside of the brackets. Each negative value indicates a position in the original vector with its absolute value (e.g., $-3$ corresponds to position $3$, $-5$ corresponds to position $5$, and so on).

The result is a new vector with the elements of the original vector at the indicated positions removed. Note, actually altering the original vector will require another assignment, as shown below:

> nums = c(4,5,6,7,8,9,10,11,12) > nums[-3] # create vector identical to nums but with 3rd element removed [1] 4 5 7 8 9 10 11 12 > nums # nums is left unchanged [1] 4 5 6 7 8 9 10 11 12 > nums = nums[-c(1,6:8)] # remove elements in 1st, 6th, 7th, and 8th postions and reassign this new vector to nums > nums # now nums has been altered [1] 5 6 7 8 9