Use the `:`

operator to create sequences of numbers, such as for use in vectorizing larger chunks of your code:

```
x <- 1:5
x
## [1] 1 2 3 4 5
```

This works both ways

```
10:4
# [1] 10 9 8 7 6 5 4
```

and even with floating point numbers

```
1.25:5
# [1] 1.25 2.25 3.25 4.25
```

or negatives

```
-4:4
#[1] -4 -3 -2 -1 0 1 2 3 4
```

`seq`

is a more flexible function than the `:`

operator allowing to specify steps other than 1.

The function creates a sequence from the `start`

(default is 1) to the end including that number.

You can supply only the end (`to`

) parameter

```
seq(5)
# [1] 1 2 3 4 5
```

As well as the start

```
seq(2, 5) # or seq(from=2, to=5)
# [1] 2 3 4 5
```

And finally the step (`by`

)

```
seq(2, 5, 0.5) # or seq(from=2, to=5, by=0.5)
# [1] 2.0 2.5 3.0 3.5 4.0 4.5 5.0
```

`seq`

can optionally infer the (evenly spaced) steps when alternatively the desired length of the output (`length.out`

) is supplied

```
seq(2,5, length.out = 10)
# [1] 2.0 2.3 2.6 2.9 3.2 3.5 3.8 4.1 4.4 4.7 5.0
```

If the sequence needs to have the same length as another vector we can use the `along.with`

as a shorthand for `length.out = length(x)`

```
x = 1:8
seq(2,5,along.with = x)
# [1] 2.000000 2.428571 2.857143 3.285714 3.714286 4.142857 4.571429 5.000000
```

There are two useful simplified functions in the `seq`

family: `seq_along`

, `seq_len`

, and `seq.int`

. `seq_along`

and `seq_len`

functions construct the natural (counting) numbers from 1 through N where N is determined by the function argument, the length of a vector or list with `seq_along`

, and the integer argument with `seq_len`

.

```
seq_along(x)
# [1] 1 2 3 4 5 6 7 8
```

Note that `seq_along`

returns the indices of an existing object.

```
# counting numbers 1 through 10
seq_len(10)
[1] 1 2 3 4 5 6 7 8 9 10
# indices of existing vector (or list) with seq_along
letters[1:10]
[1] "a" "b" "c" "d" "e" "f" "g" "h" "i" "j"
seq_along(letters[1:10])
[1] 1 2 3 4 5 6 7 8 9 10
```

`seq.int`

is the same as `seq`

maintained for ancient compatibility.

There is also an old function `sequence`

that creates a vector of sequences from a non negative argument.

```
sequence(4)
# [1] 1 2 3 4
sequence(c(3, 2))
# [1] 1 2 3 1 2
sequence(c(3, 2, 5))
# [1] 1 2 3 1 2 1 2 3 4 5
```

Vectors in R can have different types (e.g. integer, logical, character). The most general way of defining a vector is by using the function `vector()`

.

```
vector('integer',2) # creates a vector of integers of size 2.
vector('character',2) # creates a vector of characters of size 2.
vector('logical',2) # creates a vector of logicals of size 2.
```

However, in R, the shorthand functions are generally more popular.

```
integer(2) # is the same as vector('integer',2) and creates an integer vector with two elements
character(2) # is the same as vector('integer',2) and creates an character vector with two elements
logical(2) # is the same as vector('logical',2) and creates an logical vector with two elements
```

Creating vectors with values, other than the default values, is also possible. Often the function `c()`

is used for this. The c is short for combine or concatenate.

```
c(1, 2) # creates a integer vector of two elements: 1 and 2.
c('a', 'b') # creates a character vector of two elements: a and b.
c(T,F) # creates a logical vector of two elements: TRUE and FALSE.
```

Important to note here is that R interprets any integer (e.g. 1) as an integer vector of size one. The same holds for numerics (e.g. 1.1), logicals (e.g. T or F), or characters (e.g. 'a'). Therefore, you are in essence combining vectors, which in turn are vectors.

Pay attention that you always have to combine similar vectors. Otherwise, R will try to convert the vectors in vectors of the same type.

```
c(1,1.1,'a',T) # all types (integer, numeric, character and logical) are converted to the 'lowest' type which is character.
```

Finding elements in vectors can be done with the `[`

operator.

```
vec_int <- c(1,2,3)
vec_char <- c('a','b','c')
vec_int[2] # accessing the second element will return 2
vec_char[2] # accessing the second element will return 'b'
```

This can also be used to change values

```
vec_int[2] <- 5 # change the second value from 2 to 5
vec_int # returns [1] 1 5 3
```

Finally, the `:`

operator (short for the function `seq()`

) can be used to quickly create a vector of numbers.

```
vec_int <- 1:10
vec_int # returns [1] 1 2 3 4 5 6 7 8 9 10
```

This can also be used to subset vectors (from easy to more complex subsets)

```
vec_char <- c('a','b','c','d','e')
vec_char[2:4] # returns [1] "b" "c" "d"
vec_char[c(1,3,5)] # returns [1] "a" "c" "e"
```

Named vector can be created in several ways. With `c`

:

```
xc <- c('a' = 5, 'b' = 6, 'c' = 7, 'd' = 8)
```

which results in:

```
> xc
a b c d
5 6 7 8
```

with `list`

:

```
xl <- list('a' = 5, 'b' = 6, 'c' = 7, 'd' = 8)
```

which results in:

```
> xl
$a
[1] 5
$b
[1] 6
$c
[1] 7
$d
[1] 8
```

With the `setNames`

function, two vectors of the same length can be used to create a named vector:

```
x <- 5:8
y <- letters[1:4]
xy <- setNames(x, y)
```

which results in a named integer vector:

```
> xy
a b c d
5 6 7 8
```

As can be seen, this gives the same result as the `c`

method.

You may also use the `names`

function to get the same result:

```
xy <- 5:8
names(xy) <- letters[1:4]
```

With such a vector it is also possibly to select elements by name:

```
> xy["c"]
c
7
```

This feature makes it possible to use such a named vector as a look-up vector/table to match the values to values of another vector or column in dataframe. Considering the following dataframe:

```
mydf <- data.frame(let = c('c','a','b','d'))
> mydf
let
1 c
2 a
3 b
4 d
```

Suppose you want to create a new variable in the `mydf`

dataframe called `num`

with the correct values from `xy`

in the rows. Using the `match`

function the appropriate values from `xy`

can be selected:

```
mydf$num <- xy[match(mydf$let, names(xy))]
```

which results in:

```
> mydf
let num
1 c 7
2 a 5
3 b 6
4 d 8
```

The `rep`

function can be used to repeat a vector in a fairly flexible manner.

```
# repeat counting numbers, 1 through 5 twice
rep(1:5, 2)
[1] 1 2 3 4 5 1 2 3 4 5
# repeat vector with incomplete recycling
rep(1:5, 2, length.out=7)
[1] 1 2 3 4 5 1 2
```

The each argument is especially useful for expanding a vector of statistics of observational/experimental units into a vector of data.frame with repeated observations of these units.

```
# same except repeat each integer next to each other
rep(1:5, each=2)
[1] 1 1 2 2 3 3 4 4 5 5
```

A nice feature of `rep`

regarding involving expansion to such a data structure is that expansion of a vector to an unbalanced panel can be accomplished by replacing the length argument with a vector that dictates the number of times to repeat each element in the vector:

```
# automated length repetition
rep(1:5, 1:5)
[1] 1 2 2 3 3 3 4 4 4 4 5 5 5 5 5
# hand-fed repetition length vector
rep(1:5, c(1,1,1,2,2))
[1] 1 2 3 4 4 5 5
```

This should expose the possibility of allowing an external function to feed the second argument of `rep`

in order to dynamically construct a vector that expands according to the data.

As with `seq`

, faster, simplified versions of `rep`

are `rep_len`

and `rep.int`

. These drop some attributes that `rep`

maintains and so may be most useful in situations where speed is a concern and additional aspects of the repeated vector are unnecessary.

```
# repeat counting numbers, 1 through 5 twice
rep.int(1:5, 2)
[1] 1 2 3 4 5 1 2 3 4 5
# repeat vector with incomplete recycling
rep_len(1:5, length.out=7)
[1] 1 2 3 4 5 1 2
```

`R`

has a number of build in constants. The following constants are available:

`LETTERS`

: the 26 upper-case letters of the Roman alphabet`letters`

: the 26 lower-case letters of the Roman alphabet`month.abb`

: the three-letter abbreviations for the English month names`month.name`

: the English names for the months of the year`pi`

: the ratio of the circumference of a circle to its diameter

From the letters and month constants, vectors can be created.

**1)** Sequences of letters:

```
> letters
[1] "a" "b" "c" "d" "e" "f" "g" "h" "i" "j" "k" "l" "m" "n" "o" "p" "q" "r" "s" "t" "u" "v" "w" "x" "y" "z"
> LETTERS[7:9]
[1] "G" "H" "I"
> letters[c(1,5,3,2,4)]
[1] "a" "e" "c" "b" "d"
```

**2)** Sequences of month abbreviations or month names:

```
> month.abb
[1] "Jan" "Feb" "Mar" "Apr" "May" "Jun" "Jul" "Aug" "Sep" "Oct" "Nov" "Dec"
> month.name[1:4]
[1] "January" "February" "March" "April"
> month.abb[c(3,6,9,12)]
[1] "Mar" "Jun" "Sep" "Dec"
```

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