A function is a set of statements organized together to perform a specific task. R has a large number of in-built functions but we may as well create functions by our own.

R has many in-built functions which can be directly called without
defining them beforehand. In base R your find, functions such as `seq()`

, `mean()`

, `max()`

, `min()`

, `sum()`

, `paste()`

, `length()`

and `sample()`

, among others.

```
s <- seq(1:5000)
mean(s)
```

`## [1] 2500.5`

`max(s)`

`## [1] 5000`

`min(s)`

`## [1] 1`

`sum(s)`

`## [1] 12502500`

`paste("The sequence 's' contains", length(s), "components")`

`## [1] "The sequence 's' contains 5000 components"`

A function consists of different parts:

*Function Name*: This is the actual name of the function. It is stored in the R environment as an object with this name.*Arguments*: An argument is a placeholder. When a function is invoked, you pass a value to the argument. Arguments are optional; that is, a function may contain no arguments. Also arguments can have default values.*Function Body*: The function body contains a collection of statements that defines what the function does.*Return Value*: The return value of a function is the last expression in the function body to be evaluated. Or it is specified explicitly by the`return()`

command.

Consider the `sample()`

function, which takes a sample of the specified size from the elements of a vector (either with or without replacement). Type `help("sample")`

into your console for further information.

We may ask R for the arguments of the `sample()`

function by using the `args()`

command.

`args(sample)`

```
## function (x, size, replace = FALSE, prob = NULL)
## NULL
```

If we want to retrieve the function body we we just type the function
name (without parenthesis!) into the R console. With respect to our
example, we type `sample`

into our console.

`sample`

```
## function (x, size, replace = FALSE, prob = NULL)
## {
## if (length(x) == 1L && is.numeric(x) && is.finite(x) && x >=
## 1) {
## if (missing(size))
## size <- x
## sample.int(x, size, replace, prob)
## }
## else {
## if (missing(size))
## size <- length(x)
## x[sample.int(length(x), size, replace, prob)]
## }
## }
## <bytecode: 0x000000000b798540>
## <environment: namespace:base>
```

In order to apply the `sample()`

function to pick 5 numbers with replacement from the sequence `s`

, which we defined above, we type `sample(s, size = 5, replace = TRUE)`

into the R console.

`sample(s, size = 5, replace = TRUE)`

`## [1] 1754 2549 3693 42 186`

It is very easy to create user-defined functions in R. A function in R is created by using the keyword `function`

. The basic syntax of a function definition is as follows

```
function_name <- function(arg_1, arg_2, ...) {
Function body
}
```

Let us create a function to print the cube of the number 3 $({3}^{3})$. Note that this function does not need any arguments.

```
print.cube3 <- function() {
rv <- 3^3 # return value
print(rv)
}
```

In order to call the function `print.cube3()`

we simply type `print.cube3()`

into the R console.

`print.cube3()`

`## [1] 27`

This function is for sure not of much use, hence we extend the function and compute the cube of any scalar given by the user $({x}^{3})$.

```
print.cube <- function(s) {
cubed <- s^3
print(cubed)
}
```

In order to call the function `print.cube()`

, this time we have to provide the argument `s`

.

`print.cube(2)`

`## [1] 8`

**Calling a Function with Argument Values (by position and by name)**

For real life applications functions often have several arguments. It is worth noting, that in R the arguments to a function call can be supplied in the same sequence as defined in the function or they can be supplied in a different sequence but assigned to the names of the arguments.

To showcase this behavior we define a function to do some simple computations.

```
my.function <- function(a,b,c) {
result <- a * b - c
print(result)
}
```

Now, we can call the function by position of arguments, where `a = 2`

, `b = 10`

and `c = 1`

. We have to make sure that the numbers are given to the function in correct order.

`my.function(2,10,1)`

`## [1] 19`

We would get the same result by calling the function by names of the arguments, however, this time we do not need to care about the specific order of the given arguments.

`my.function(b = 10, c = 1, a = 2)`

`## [1] 19`

**Calling a Function with Default Argument**

Another convenient feature of a function is that we can define the value of the arguments in the function definition and call the function without supplying any argument to get the default result. But we can also call such functions by supplying new values of the argument and get non default result.

```
# Create a function with arguments.
my.multiply <- function(a = 15, b = 3) {
result <- a * b
print(result)
}
```

Now we can either call the function without giving any argument.

`my.multiply()`

`## [1] 45`

Or we may call the the function and provide new values for the arguments.

`my.multiply(5, 5)`

`## [1] 25`