`sqrt(225)`

`#> [1] 15`

## Learning Objectives

- Know some common functions in R.
- Know how R handles function arguments and named arguments.
- Know how to install, load, and use functions from external R packages.
- Practice programming with functions using the TurtleGraphics package.
## Suggested Readings

- Chapter 3 of Danielle Navarro’s book “Learning Statistics With R”

You can do a lot with the basic operators like `+`

, `-`

, and `*`

, but to do more advanced calculations you’re going to need to start using functions.^{1}

R has a lot of very useful built-in functions. For example, if I wanted to take the square root of 225, I could use R’s built-in square root function `sqrt()`

:

`sqrt(225)`

`#> [1] 15`

Here the letters `sqrt`

are short for “square root,” and the value inside the `()`

is the “argument” to the function. In the example above, the value `225`

is the “argument”.

Keep in mind that not all functions have (or require) arguments:

`date() # Returns the current date and time`

`#> [1] "Mon Aug 5 16:09:33 2024"`

(the date above is the date this page was last built)

Some functions have more than one argument. For example, the `round()`

function can be used to round some value to the nearest integer or to a specified decimal place:

`round(3.14165) # Rounds to the nearest integer`

`#> [1] 3`

`round(3.14165, 2) # Rounds to the 2nd decimal place`

`#> [1] 3.14`

Not all arguments are mandatory. With the `round()`

function, the decimal place is an *optional* input - if nothing is provided, the function will round to the nearest integer by default.

In the case of `round()`

, it’s not too hard to remember which argument comes first and which one comes second. But it starts to get very difficult once you start using complicated functions that have lots of arguments. Fortunately, most R functions use **argument names** to make your life a little easier. For the `round()`

function, for example, the number that needs to be rounded is specified using the `x`

argument, and the number of decimal points that you want it rounded to is specified using the `digits`

argument, like this:

`round(x = 3.1415, digits = 2)`

`#> [1] 3.14`

Notice that the first time I called the `round()`

function I didn’t actually specify the `digits`

argument at all, and yet R somehow knew that this meant it should round to the nearest whole number. How did that happen? The answer is that the `digits`

argument has a **default value** of `0`

, meaning that if you decide not to specify a value for `digits`

then R will act as if you had typed `digits = 0`

.

This is quite handy: most of the time when you want to round a number you want to round it to the nearest *whole* number, and it would be pretty annoying to have to specify the `digits`

argument every single time. On the other hand, sometimes you actually do want to round to something other than the nearest whole number, and it would be even more annoying if R didn’t allow this! Thus, by having `digits = 0`

as the default value, we get the best of both worlds.

Not sure what a function does, how many arguments it has, or what the argument names are? Ask R for help by typing `?`

and then the function name, and R will return some documentation about it. For example, type `?round()`

into the console and R will return information about how to use the `round()`

function.

In the same way that R allows us to put multiple operations together into a longer command (like `1 + 2 * 4`

for instance), it also lets us put functions together and even combine functions with operators if we so desire. For example, the following is a perfectly legitimate command:

`round(sqrt(7), digits = 2)`

`#> [1] 2.65`

When R executes this command, starts out by calculating the value of `sqrt(7)`

, which produces an intermediate value of `2.645751`

. The command then simplifies to `round(2.645751, digits = 2)`

, which rounds the value to `2.65`

.

R has LOTS of functions. Many of the basic math functions are somewhat self-explanatory, but it can be hard to remember the specific function name. Below is a reference table of some frequently used math functions.

Function | Description | Example input | Example output |
---|---|---|---|

`round(x, digits=0)` |
Round `x` to the `digits` decimal place |
`round(3.1415, digits=2)` |
`3.14` |

`floor(x)` |
Round `x` down the nearest integer |
`floor(3.1415)` |
`3` |

`ceiling(x)` |
Round `x` up the nearest integer |
`ceiling(3.1415)` |
`4` |

`abs()` |
Absolute value | `abs(-42)` |
`42` |

`min()` |
Minimum value | `min(1, 2, 3)` |
`1` |

`max()` |
Maximum value | `max(1, 2, 3)` |
`3` |

`sqrt()` |
Square root | `sqrt(64)` |
`8` |

`exp()` |
Exponential | `exp(0)` |
`1` |

`log()` |
Natural log | `log(1)` |
`0` |

`factorial()` |
Factorial | `factorial(5)` |
`120` |

You will often need to check the data type of objects and convert them to other types. To handle this, use these patterns:

- Check the type of
`x`

:`is.______()`

- Convert the type of
`x`

:`as.______()`

In each of these patterns, replace “`______`

” with:

`character`

`logical`

`numeric`

/`double`

/`integer`

You can convert an object from one type to another using `as.______()`

, replacing “`______`

” with a data type:

Convert **numeric** types:

`as.numeric("3.1415")`

`#> [1] 3.1415`

`as.double("3.1415")`

`#> [1] 3.1415`

`as.integer("3.1415")`

`#> [1] 3`

Convert **non-numeric** types:

`as.character(3.1415)`

`#> [1] "3.1415"`

`as.logical(3.1415)`

`#> [1] TRUE`

A few notes to keep in mind:

- When converting from a
**numeric**to a**logical**,`as.logical()`

will always return`TRUE`

for any numeric value other than`0`

, for which it returns`FALSE`

.

`as.logical(7)`

`#> [1] TRUE`

`as.logical(0)`

`#> [1] FALSE`

The reverse is also true

`as.numeric(TRUE)`

`#> [1] 1`

`as.numeric(FALSE)`

`#> [1] 0`

- Not everything can be converted. For example, if you try to coerce a character that contains letters into a number, R will return
`NA`

, because it doesn’t know what number to choose:

`as.numeric('foo')`

`#> Warning: NAs introduced by coercion`

`#> [1] NA`

- The
`as.integer()`

function behaves the same as`floor()`

:

`as.integer(3.14)`

`#> [1] 3`

`as.integer(3.99)`

`#> [1] 3`

Similar to the `as.______()`

format, you can check if an object is a specific data type using `is.______()`

, replacing “`______`

” with a data type.

Checking **numeric** types:

`is.numeric(3.1415)`

`#> [1] TRUE`

`is.double(3.1415)`

`#> [1] TRUE`

`is.integer(3.1415)`

`#> [1] FALSE`

Checking **non-numeric** types:

`is.character(3.1415)`

`#> [1] FALSE`

`is.logical(3.1415)`

`#> [1] FALSE`

One thing you’ll notice is that `is.integer()`

often gives you a surprising result. For example, why did `is.integer(7)`

return `FALSE`

?. Well, this is because numbers are *doubles* by default in R, so even though `7`

*looks* like an integer, R thinks it’s a double.

The safer way to check if a number is an integer in *value* is to compare it against itself converted into an integer:

`7 == as.integer(7)`

`#> [1] TRUE`

When you start R, it only loads the “Base R” functions (e.g. `sqrt()`

, `round()`

, etc.), but there are thousands and thousands of additional functions stored in external **packages**.

To install a package, use the `install.packages()`

function. Make sure you put the package name in quotes:

```
install.packages("packagename") # This works
install.packages(packagename) # This doesn't work
```

Just like most software, you only need to *install* a package once.

After installing a package, you can’t immediately use the functions that the package contains. This is because when you start up R only the “base” functions are loaded. If you want R to also load the functions inside a package, you have to *load* that package, which you do with the `library()`

function. In contrast to the `install.packages()`

function, you don’t need quotes around the package name to load it:

```
library("packagename") # This works
library(packagename) # This also works
```

Here’s a helpful image to keep the two ideas of *installing* vs *loading* separate:

As an example, try installing the Wikifacts package, by Keith McNulty:

`install.packages("wikifacts") # Remember - you only have to do this once!`

Now that you have the package installed on your computer, try loading it using `library(wikifacts)`

, then trying using some of it’s functions:

`library(wikifacts) # Load the library`

`wiki_randomfact()`

`#> [1] "Did you know that endocrinologist Reginald Hall, who studied the thyroid gland and its diseases, received a heart transplant in 1984? (Courtesy of Wikipedia)"`

`wiki_didyouknow()`

`#> [1] "I got nothin'"`

In case you’re wondering, the only thing this package does is generate messages containing random facts from Wikipedia.

Sometimes you may only want to use a single function from a library without having to load the whole thing. To do so, use this recipe:

packagename::functionname()

Here I use the name of the *package* followed by `::`

to tell R that I’m looking for a function that is in that package. For example, if I didn’t want to load the whole **wikifacts** library but still wanted to use the `wiki_randomfact()`

function, I could do this:

`::wiki_randomfact() wikifacts`

`#> [1] "Did you know that Jenny Morton discovered that sheep can recognise human faces? (Courtesy of Wikipedia)"`

Where this is particularly handy is when two packages have a function with the same name. If you load both library, R might not know which function to use. In those cases, it’s best to also provide the **package** name. For example, let’s say there was a package called **apples** and another called **bananas**, and each had a function named `fruitName()`

. If I wanted to use each of them in my code, I would need to specify the package names like this:

```
::fruitName()
apples::fruitName() bananas
```

Turtle graphics is a classic teaching tool in computer science, originally invented in the 1960s and re-implemented over and over again in different programming languages.

In R, there is a similar package called **TurtleGraphics**. To get started, install the package (remember, you only need to do this once on your computer):

`install.packages('TurtleGraphics')`

Once installed, load the package (remember, you have to load this every time you restart R to use the package!):

`library(TurtleGraphics)`

`#> Loading required package: grid`

Here’s the idea. You have a turtle, and she lives in a nice warm terrarium. The terrarium is 100 x 100 units in size, where the lower-left corner is at the `(x, y)`

position of `(0, 0)`

. When you call `turtle_init()`

, the turtle is initially positioned in the center of the terrarium at `(50, 50)`

:

`turtle_init()`

You can move the turtle using a variety of movement functions (see `?turtle_move()`

), and she will leave a trail where ever she goes. For example, you can move her 10 units forward from her starting position:

```
turtle_init()
turtle_forward(distance = 10)
```

You can also make the turtle jump to a new position (without drawing a line) by using the `turtle_setpos(x, y)`

, where `(x, y)`

is a coordinate within the 100 x 100 terrarium:

```
turtle_init()
turtle_setpos(x=10, y=10)
```

Simple enough, right? But what if I want my turtle to draw a more complicated shape? Let’s say I want her to draw a hexagon. There are six sides to the hexagon, so the most natural way to write code for this is to write a `for`

loop that loops over the sides (if this doesn’t make sense yet, go read ahead to the chapter on iteration!). At each iteration within the loop, I’ll have the turtle walk forwards, and then turn 60 degrees to the left. Here’s what happens:

```
turtle_init()
for (side in 1:6) {
turtle_forward(distance = 10)
turtle_left(angle = 60)
}
```

Cool! As you draw more complex shapes, you can speed up the process by wrapping your turtle commands inside the `turtle_do({})`

function. This will skip the animations of the turtle moving and will jump straight to the final position. For example, here’s the hexagon again without animations:

```
turtle_init()
turtle_do({
for (side in 1:6) {
turtle_forward(distance = 10)
turtle_left(angle = 60)
} })
```

Some content on this page has been modified from other courses, including:

- Danielle Navarro’s book “Learning Statistics With R”
- Danielle Navarro’s website “R for Psychological Science”
- Jenny Bryan’s STAT 545 Course
- RStudio primers
- Xiao Ping Song’s Intro2R crash course

Technically speaking, operators are functions in R: the addition operator

`+`

is a convenient way of calling the addition function`'+'()`

. Thus`10+20`

is equivalent to the function call`'+'(20, 30)`

. Not surprisingly, no-one ever uses this version.↩︎