Creating Functions

Overview

Teaching: 30 min
Exercises: 0 min
Questions
  • How do I make a function?

  • How can I test my functions?

  • How should I document my code?

Objectives
  • Define a function that takes arguments.

  • Return a value from a function.

  • Test a function.

  • Set default values for function arguments.

  • Explain why we should divide programs into small, single-purpose functions.

If we only had one data set to analyze, it would probably be faster to load the file into a spreadsheet and use that to plot some simple statistics. But we have twelve files to check, and may have more in the future. In this lesson, we’ll learn how to write a function so that we can repeat several operations with a single command.

Defining a Function

Let’s start by defining a function fahrenheit_to_kelvin that converts temperatures from Fahrenheit to Kelvin:

fahrenheit_to_kelvin <- function(temp_F) {
  temp_K <- ((temp_F - 32) * (5 / 9)) + 273.15
  return(temp_K)
}

We define fahrenheit_to_kelvin by assigning it to the output of function. The list of argument names are contained within parentheses. Next, the body of the function–the statements that are executed when it runs–is contained within curly braces ({}). The statements in the body are indented by two spaces, which makes the code easier to read but does not affect how the code operates.

When we call the function, the values we pass to it are assigned to those variables so that we can use them inside the function. Inside the function, we use a return statement to send a result back to whoever asked for it.

Automatic Returns

In R, it is not necessary to include the return statement. R automatically returns whichever variable is on the last line of the body of the function. Since we are just learning, we will explicitly define the return statement.

Let’s try running our function. Calling our own function is no different from calling any other function:

# freezing point of water
fahrenheit_to_kelvin(32)
[1] 273.15
# boiling point of water
fahrenheit_to_kelvin(212)
[1] 373.15

We’ve successfully called the function that we defined, and we have access to the value that we returned.

Composing Functions

Now that we’ve seen how to turn Fahrenheit into Kelvin, it’s easy to turn Kelvin into Celsius:

kelvin_to_celsius <- function(temp_K) {
  temp_C <- temp_K - 273.15
  return(temp_C)
}

#absolute zero in Celsius
kelvin_to_celsius(0)
[1] -273.15

What about converting Fahrenheit to Celsius? We could write out the formula, but we don’t need to. Instead, we can compose the two functions we have already created:

fahrenheit_to_celsius <- function(temp_F) {
  temp_K <- fahrenheit_to_kelvin(temp_F)
  temp_C <- kelvin_to_celsius(temp_K)
  return(temp_C)
}

# freezing point of water in Celsius
fahrenheit_to_celsius(32.0)
[1] 0

This is our first taste of how larger programs are built: we define basic operations, then combine them in ever-larger chunks to get the effect we want. Real-life functions will usually be larger than the ones shown here–typically half a dozen to a few dozen lines–but they shouldn’t ever be much longer than that, or the next person who reads it won’t be able to understand what’s going on.

Chaining Functions

This example showed the output of fahrenheit_to_kelvin assigned to temp_K, which is then passed to kelvin_to_celsius to get the final result. It is also possible to perform this calculation in one line of code, by “chaining” functions together, like so:

# freezing point of water in Celsius
kelvin_to_celsius(fahrenheit_to_kelvin(32.0))
[1] 0

Create a Function

In the last lesson, we learned to combine elements into a vector using the c function, e.g. x <- c("A", "B", "C") creates a vector x with three elements. Furthermore, we can extend that vector again using c, e.g. y <- c(x, "D") creates a vector y with four elements. Write a function called fence that takes two vectors as arguments, called original and wrapper, and returns a new vector that has the wrapper vector at the beginning and end of the original:

best_practice <- c("Write", "programs", "for", "people", "not", "computers")
asterisk <- "***"  # R interprets a variable with a single value as a vector
                   # with one element.
fence(best_practice, asterisk)
[1] "***"       "Write"     "programs"  "for"       "people"    "not"      
[7] "computers" "***"      

Solution

fence <- function(original, wrapper) {
  answer <- c(wrapper, original, wrapper)
  return(answer)
}

If the variable v refers to a vector, then v[1] is the vector’s first element and v[length(v)] is its last (the function length returns the number of elements in a vector). Write a function called outside that returns a vector made up of just the first and last elements of its input:

dry_principle <- c("Don't", "repeat", "yourself", "or", "others")
outside(dry_principle)
[1] "Don't"  "others"

Solution

outside <- function(v) {
  first <- v[1]
   last <- v[length(v)]
   answer <- c(first, last)
   return(answer)
}

The Call Stack

For a deeper understanding of how functions work, you’ll need to learn how they create their own environments and call other functions. Function calls are managed via the call stack. For more details on the call stack, have a look at the supplementary material.

Named Variables and the Scope of Variables

  • Functions can accept arguments explicitly assigned to a variable name in in the function call functionName(variable = value), as well as arguments by order:
input_1 <- 20
mySum <- function(input_1, input_2 = 10) {
  output <- input_1 + input_2
  return(output)
}
  1. Given the above code was run, which value does mySum(input_1 = 1, 3) produce?
    1. 4
    2. 11
    3. 23
    4. 30
  2. If mySum(3) returns 13, why does mySum(input_2 = 3) return an error?

Testing and Documenting

Once we start putting things in functions so that we can re-use them, we need to start testing that those functions are working correctly. To see how to do this, let’s write a function to center a dataset around a particular value:

center <- function(data, desired) {
  new_data <- (data - mean(data)) + desired
  return(new_data)
}

We could test this on our actual data, but since we don’t know what the values ought to be, it will be hard to tell if the result was correct. Instead, let’s create a vector of 0s and then center that around 3. This will make it simple to see if our function is working as expected:

z <- c(0, 0, 0, 0)
z
[1] 0 0 0 0
center(z, 3)
[1] 3 3 3 3

That looks right, so let’s try center on our real data. We’ll center the inflammation data from day 4 around 0:

dat <- read.csv(file = "data/inflammation-01.csv", header = FALSE)
centered <- center(dat[, 4], 0)
head(centered)
[1]  1.25 -0.75  1.25 -1.75  1.25  0.25

It’s hard to tell from the default output whether the result is correct, but there are a few simple tests that will reassure us:

# original min
min(dat[, 4])
[1] 0
# original mean
mean(dat[, 4])
[1] 1.75
# original max
max(dat[, 4])
[1] 3
# centered min
min(centered)
[1] -1.75
# centered mean
mean(centered)
[1] 0
# centered max
max(centered)
[1] 1.25

That seems almost right: the original mean was about 1.75, so the lower bound from zero is now about -1.75. The mean of the centered data is 0. We can even go further and check that the standard deviation hasn’t changed:

# original standard deviation
sd(dat[, 4])
[1] 1.067628
# centered standard deviation
sd(centered)
[1] 1.067628

Those values look the same, but we probably wouldn’t notice if they were different in the sixth decimal place. Let’s do this instead:

# difference in standard deviations before and after
sd(dat[, 4]) - sd(centered)
[1] 0

Sometimes, a very small difference can be detected due to rounding at very low decimal places. R has a useful function for comparing two objects allowing for rounding errors, all.equal:

all.equal(sd(dat[, 4]), sd(centered))
[1] TRUE

It’s still possible that our function is wrong, but it seems unlikely enough that we should probably get back to doing our analysis. We have one more task first, though: we should write some documentation for our function to remind ourselves later what it’s for and how to use it.

A common way to put documentation in software is to add comments like this:

center <- function(data, desired) {
  # return a new vector containing the original data centered around the
  # desired value.
  # Example: center(c(1, 2, 3), 0) => c(-1, 0, 1)
  new_data <- (data - mean(data)) + desired
  return(new_data)
}

Writing Documentation

Formal documentation for R functions is written in separate .Rd using a markup language similar to LaTeX. You see the result of this documentation when you look at the help file for a given function, e.g. ?read.csv. The roxygen2 package allows R coders to write documentation alongside the function code and then process it into the appropriate .Rd files. You will want to switch to this more formal method of writing documentation when you start writing more complicated R projects.

Functions to Create Graphs

Write a function called analyze that takes a filename as an argument and displays the three graphs produced in the previous lesson (average, min and max inflammation over time). analyze("data/inflammation-01.csv") should produce the graphs already shown, while analyze("data/inflammation-02.csv") should produce corresponding graphs for the second data set. Be sure to document your function with comments.

Solution

analyze <- function(filename) {
  # Plots the average, min, and max inflammation over time.
  # Input is character string of a csv file.
  dat <- read.csv(file = filename, header = FALSE)
  avg_day_inflammation <- apply(dat, 2, mean)
  plot(avg_day_inflammation)
  max_day_inflammation <- apply(dat, 2, max)
  plot(max_day_inflammation)
  min_day_inflammation <- apply(dat, 2, min)
  plot(min_day_inflammation)
}

Rescaling

Write a function rescale that takes a vector as input and returns a corresponding vector of values scaled to lie in the range 0 to 1. (If $L$ and $H$ are the lowest and highest values in the original vector, then the replacement for a value $v$ should be $(v-L) / (H-L)$.) Be sure to document your function with comments.

Test that your rescale function is working properly using min, max, and plot.

Solution

rescale <- function(v) {
  # Rescales a vector, v, to lie in the range 0 to 1.
  L <- min(v)
  H <- max(v)
  result <- (v - L) / (H - L)
  return(result)
}

Defining Defaults

We have passed arguments to functions in two ways: directly, as in dim(dat), and by name, as in read.csv(file = "data/inflammation-01.csv", header = FALSE). In fact, we can pass the arguments to read.csv without naming them:

dat <- read.csv("data/inflammation-01.csv", FALSE)

However, the position of the arguments matters if they are not named.

dat <- read.csv(header = FALSE, file = "data/inflammation-01.csv")
dat <- read.csv(FALSE, "data/inflammation-01.csv")
Error in read.table(file = file, header = header, sep = sep, quote = quote, : 'file' must be a character string or connection

To understand what’s going on, and make our own functions easier to use, let’s re-define our center function like this:

center <- function(data, desired = 0) {
  # return a new vector containing the original data centered around the
  # desired value (0 by default).
  # Example: center(c(1, 2, 3), 0) => c(-1, 0, 1)
  new_data <- (data - mean(data)) + desired
  return(new_data)
}

The key change is that the second argument is now written desired = 0 instead of just desired. If we call the function with two arguments, it works as it did before:

test_data <- c(0, 0, 0, 0)
center(test_data, 3)
[1] 3 3 3 3

But we can also now call center() with just one argument, in which case desired is automatically assigned the default value of 0:

more_data <- 5 + test_data
more_data
[1] 5 5 5 5
center(more_data)
[1] 0 0 0 0

This is handy: if we usually want a function to work one way, but occasionally need it to do something else, we can allow people to pass an argument when they need to but provide a default to make the normal case easier.

The example below shows how R matches values to arguments

display <- function(a = 1, b = 2, c = 3) {
  result <- c(a, b, c)
  names(result) <- c("a", "b", "c")  # This names each element of the vector
  return(result)
}

# no arguments
display()
a b c 
1 2 3 
# one argument
display(55)
 a  b  c 
55  2  3 
# two arguments
display(55, 66)
 a  b  c 
55 66  3 
# three arguments
display (55, 66, 77)
 a  b  c 
55 66 77 

As this example shows, arguments are matched from left to right, and any that haven’t been given a value explicitly get their default value. We can override this behavior by naming the value as we pass it in:

# only setting the value of c
display(c = 77)
 a  b  c 
 1  2 77 

Matching Arguments

To be precise, R has three ways that arguments are supplied by you are matched to the formal arguments of the function definition:

  1. by complete name,
  2. by partial name (matching on initial n characters of the argument name), and
  3. by position.

Arguments are matched in the manner outlined above in that order: by complete name, then by partial matching of names, and finally by position.

With that in hand, let’s look at the help for read.csv():

?read.csv

There’s a lot of information there, but the most important part is the first couple of lines:

read.csv(file, header = TRUE, sep = ",", quote = "\"",
         dec = ".", fill = TRUE, comment.char = "", ...)

This tells us that read.csv() has one argument, file, that doesn’t have a default value, and six others that do. Now we understand why the following gives an error:

dat <- read.csv(FALSE, "data/inflammation-01.csv")
Error in read.table(file = file, header = header, sep = sep, quote = quote, : 'file' must be a character string or connection

It fails because FALSE is assigned to file and the filename is assigned to the argument header.

A Function with Default Argument Values

Rewrite the rescale function so that it scales a vector to lie between 0 and 1 by default, but will allow the caller to specify lower and upper bounds if they want. Compare your implementation to your neighbor’s: do the two functions always behave the same way?

Solution

rescale <- function(v, lower = 0, upper = 1) {
  # Rescales a vector, v, to lie in the range lower to upper.
  L <- min(v)
  H <- max(v)
  result <- (v - L) / (H - L) * (upper - lower) + lower
  return(result)
}

Key Points

  • Define a function using name <- function(...args...) {...body...}.

  • Call a function using name(...values...).

  • R looks for variables in the current stack frame before looking for them at the top level.

  • Use help(thing) to view help for something.

  • Put comments at the beginning of functions to provide help for that function.

  • Annotate your code!

  • Specify default values for arguments when defining a function using name = value in the argument list.

  • Arguments can be passed by matching based on name, by position, or by omitting them (in which case the default value is used).