## What is a Vector?

A vector is a collection of elements, all the same type (similar to an array in other programming languages but more versatile).

When using R, you will frequently encounter the four basic vector types viz. logical, character, integer and double (often called numeric).

## Create a vector

In R, there are several different ways to create a new vector.

The simplest one is the `c()`

function.

Example: Create basic vectors

```
> # integer vector
> c(1, 2, 3, 4, 5, 6)
[1] 1 2 3 4 5 6
```

```
> # double vector
> c(1*pi, 2*pi, 3*pi, 4*pi)
[1] 3.141593 6.283185 9.424778 12.566371
```

```
> # character vector
> c("red", "green", "blue")
[1] "red" "green" "blue"
```

```
> # logical vector
> c(TRUE, FALSE, TRUE, FALSE)
[1] TRUE FALSE TRUE FALSE
```

As a vector contains elements of the same type, if you try to combine different type of elements, the `c()`

function converts (coerces) them into a single type.

Example: c() function converts all elements into a single type

```
> # numerics are converted to characters
> v <- c(1, 2, 3, "a", "b", "c")
> v
[1] "1" "2" "3" "a" "b" "c"
```

```
> # logical are turned to numerics
> v <- c(1, 2, 3, TRUE, FALSE)
> v
[1] 1 2 3 1 0
```

You can check the type of a vector using `typeof()`

function.

## Create a Sequence

You can also create a vector using:

### The : Operator

You can generate an equally spaced sequence of numbers, by using the `:`

sequence operator.

Example: Create a sequence of numbers from 1 to 10

```
> 1:10
[1] 1 2 3 4 5 6 7 8 9 10
```

### The seq() Function

The `seq()`

function works the same as the `:`

operator, except you can specify a different increment (step size).

Example: Create a sequence of numbers from 1 to 10 with increment of 2

```
> seq(from=1,to=10,by=2)
[1] 1 3 5 7 9
```

### The rep() Function

With `rep()`

function you can generate a sequence by simply repeating certain values.

Example:

```
> # repeat a value 6 times
> rep(x=1,times=6)
[1] 1 1 1 1 1 1
> # repeat a vector 3 times
> rep(x=c(1,2,3),times=3)
[1] 1 2 3 1 2 3 1 2 3
```

## Change the Vector Type

By using the `as.vector()`

function, you can change the vector type.

Example: Turn numerical vector to character

```
> v <- c(0, 1, 2, 3, 4, 5)
> as.vector(v, mode="character")
[1] "0" "1" "2" "3" "4" "5"
```

Example: Turn numerical vector to logical

```
> v <- c(0, 1, 2, TRUE, FALSE)
> as.vector(v, mode="logical")
[1] FALSE TRUE TRUE TRUE FALSE
```

## Naming a Vector

Each element of a vector can have a name. It allows you to access individual elements by names.

You can give a name to the vector element with the `names()`

function.

Example: Name each vector element using names() function

```
> v <- c("Apple", "Banana", "Cherry")
> names(v) <- c("A", "B", "C")
> v
A B C
"Apple" "Banana" "Cherry"
```

You can also give a name to the vector element while creating a vector.

Example: Name each vector element while creation

```
> v <- c("A"="Apple", "B"="Banana", "C"="Cherry")
> v
A B C
"Apple" "Banana" "Cherry"
```

## Subsetting Vectors

There are several ways to subset a vector (extract a value from the vector)

You can do this by combining square brackets `[]`

with:

- Positive integers
- Negative integers
- Logical values
- Names

### Subsetting with Positive Integers

Subsetting with positive integers returns the elements at the specified positions.

Note that vector positioning starts from 1.

Example:

```
> v <- c("a","b","c","d","e","f")
> # select 3rd element
> v[3]
[1] "c"
> # select 5th element
> v[5]
[1] "e"
```

You can select multiple elements at once by using a vector of indexes.

Example:

```
> v <- c("a","b","c","d","e","f")
> # select elements from index 2 to 5
> v[2:5]
[1] "b" "c" "d" "e"
> # select elements from index 1 to 6 by increment 2
> v[seq(from=1,to=6,by=2)]
[1] "a" "c" "e"
```

The indexing vector need not be a simple sequence. You can select elements anywhere within the vector.

Example:

```
> v <- c("a","b","c","d","e","f")
> # select 1st, 3rd, 5th and 6th element
> v[c(1,3,5,6)]
[1] "a" "c" "e" "f"
```

### Subsetting by Negative Integer

Subsetting with negative integers will omit the elements at the specified positions.

Example:

```
> v <- c("a","b","c","d","e","f")
> # omit first element
> v[-1]
[1] "b" "c" "d" "e" "f"
> # omit elements from index 2 to 5
> v[-2:-5]
[1] "a" "f"
> # omit 1st, 3rd and 5th element
> v[c(-1,-3,-5)]
[1] "b" "d" "f"
```

### Subsetting by Logical Values

Subsetting with logical values will return the elements where the corresponding logical value is TRUE.

Example:

```
> v <- c(1,2,3,4,5,6)
> v[c(TRUE,FALSE,TRUE,FALSE,TRUE,FALSE)]
[1] 1 3 5
```

You can also use a logical vector to select elements based on a condition.

Example:

```
> # select even elements
> v <- c(1,2,3,4,5,6,7,8,9)
> v[v %% 2 == 0]
[1] 2 4 6 8
> # skip values from 4 to 7
> v <- c(1,2,3,4,5,6,7,8,9)
> v[v < 4 | v > 7]
[1] 1 2 3 8 9
```

### Subsetting by Names

Subsetting with names will return the elements having the matching names.

Example:

```
> v <- c("A"="Apple", "B"="Banana", "C"="Cherry")
> v
A B C
"Apple" "Banana" "Cherry"
> # select element 'A'
> v["A"]
A
"Apple"
> # select element 'B'
> v["B"]
B
"Banana"
```

## Modify Vector Elements

Modifying a vector element is pretty straightforward.

You use the `[]`

to access the element, and simply assign a new value.

Example: Modify 3rd vector element

```
> v <- c("a","b","c","d","e","f")
> v[3] <- 1
> v
[1] "a" "b" "1" "d" "e" "f"
```

You can also modify more than one element at once.

Example: Modify multiple vector elements

```
> v <- c("a","b","c","d","e","f")
> v[1:3] <- c(1,2,3)
> v
[1] "1" "2" "3" "d" "e" "f"
```

## Add Elements to a Vector

The `c()`

function can also be used to add elements to a vector.

Example:

```
> v <- c(1,2,3)
> # Add a single value to v
> v <- c(v,4)
> v
[1] 1 2 3 4
> # Append an entire vector to v
> w <- c(5,6,7,8)
> v <- c(v,w)
> v
[1] 1 2 3 4 5 6 7 8
```

## Insert Element into a Vector

To insert an element into the middle of a vector, use `append()`

function.

Example: Insert 99 after 5th element

```
> append(1:10, 99, after=5)
[1] 1 2 3 4 5 99 6 7 8 9 10
```

Example: Insert 99 at the start

```
> append(1:10, 99, after=0)
[1] 99 1 2 3 4 5 6 7 8 9 10
```

## Combine Multiple Vectors

If the arguments to the `c()`

function are vectors, it flattens them and combines them into one single vector.

Example: Combine three vectors

```
> v1 <- c(1, 2, 3)
> v2 <- c(4, 5, 6)
> v3 <- c(7, 8, 9)
> c(v1, v2, v3)
[1] 1 2 3 4 5 6 7 8 9
```

Example: Combine a vector and a sequence

```
> v <- c(1, 2, 3)
> c(v, 4:9)
[1] 1 2 3 4 5 6 7 8 9
```

## Vector Arithmetic

Vector operations are one of R’s great strengths.

All the basic arithmetic operators can be performed on pairs of vectors.

Each operation is performed in an element-by-element manner.

Example: Arithmetic operations on two vectors

```
> v1 <- c(11,12,13,14,15)
> v2 <- c(1,2,3,4,5)
> # addition
> v1 + v2
[1] 12 14 16 18 20
> # subtraction
> v1 - v2
[1] 10 10 10 10 10
> # multiplication
> v1 * v2
[1] 11 24 39 56 75
> # division
> v1 / v2
[1] 11.000000 6.000000 4.333333 3.500000 3.000000
> # exponents
> v1 ^ v2
[1] 11 144 2197 38416 759375
```

If one operand is a vector and the other is a scalar, then the operation is performed between every vector element and the scalar.

Example: Arithmetic operations on a vector and a scalar

```
> v <- c(1,2,3,4,5)
> # addition
> v + 2
[1] 3 4 5 6 7
> # subtraction
> v - 2
[1] -1 0 1 2 3
> # multiplication
> v * 2
[1] 2 4 6 8 10
> # division
> v / 2
[1] 0.5 1.0 1.5 2.0 2.5
> # exponents
> v ^ 2
[1] 1 4 9 16 25
```

You can also apply a function on each element of a vector.

Example: Find square root and log of each vector element

```
> v <- c(1,2,3,4,5)
> sqrt(v)
[1] 1.000000 1.414214 1.732051 2.000000 2.236068
> log(v)
[1] 0.0000000 0.6931472 1.0986123 1.3862944 1.6094379
```

## The Recycling Rule

Arithmetic operations are performed in an element-by-element manner. That works well when both vectors have the same length.

But, when the vectors have **unequal lengths**, R’s Recycling Rule kicks in.

If we apply arithmetic operations to two vectors of unequal length, then the elements of the shorter vector are recycled to match the longest vector.

Example: Elements of the short vector are recycled to match the long vector

```
> long <- c(1,2,3,4,5,6)
> short <- c(1,2,3)
> long + short
[1] 2 4 6 5 7 9
```

Here, the elements of `long`

and `short`

are added together starting from the first element of both vectors.

When R reaches the end of the `short`

vector, it starts again at the first element of `short`

and continues until it reaches the last element of the `long`

vector.

## Sort a Vector

You can sort a vector using the `sort()`

function.

You can also specify the order in which you want to sort a vector.

Example: Sort an integer vector

```
> v <- c(2,7,3,6,1,5,9)
> sort(v,decreasing=FALSE)
[1] 1 2 3 5 6 7 9
> sort(v,decreasing=TRUE)
[1] 9 7 6 5 3 2 1
```

Example: Sort a character vector

```
> v <- c("f","c","g","a","d","e","b")
> sort(v,decreasing=FALSE)
[1] "a" "b" "c" "d" "e" "f" "g"
> sort(v,decreasing=TRUE)
[1] "g" "f" "e" "d" "c" "b" "a"
```

## Find a Vector Length

To find the length of a vector, use `length()`

function.

Example: Find the total number of elements in a vector

```
> v <- c(1,2,3,4,5)
> length(v)
[1] 5
```

## Calculate Basic Statistics

You can calculate basic statistics by using below simple R functions.

Statistic | Function |

mean | mean(x) |

median | median(x) |

standard deviation | sd(x) |

variance | var(x) |

correlation | cor(x, y) |

covariance | cov(x, y) |

Ordinarily, these functions take a vector of numbers as an argument and return the calculated statistic.

Example: Calculate mean, median, standard deviation, variance, correlation and covariance

```
> v <- c(1,2,3,4,5,6)
> # mean
> mean(v)
[1] 3.5
> # median
> median(v)
[1] 3.5
> # standard deviation
> sd(v)
[1] 1.870829
> # variance
> var(v)
[1] 3.5
> # correlation
> cor(v, 2:7)
[1] 1
> # covariance
> cov(v, 2:7)
[1] 3.5
```