4  Custom Functions

4.1 Introduction

R allows users to create their own functions, called custom functions, to perform specific tasks. In this section, we show how to define custom functions in R using the function keyword.

4.2 Defining a custom function

We use the keyword function() to define a custom function in R. The general syntax for defining a function is as follows:

my_function <- function(arg1, arg2, ...) {
  # code to execute
  return(result)
}

Here, my_function is the name of the function. The arguments are arg1, arg2, and ..., where ... allows for additional arguments to be passed to the function. The code block contains the instructions to be executed when the function is called. The return() statement specifies the value to be returned by the function.

As an example, we consider a function to compute the \(L_p\) distance between two vectors. The \(L_p\) distance is defined as: \[ d_p(x, y) = \left( \sum_{i=1}^{n} |x_i - y_i|^p \right)^{1/p}. \] where \(x\) and \(y\) are vectors of length \(n\), and \(p\) is a positive real number.

We can define a custom function in R to compute the \(L_p\) distance as follows:

lp_distance <- function(x, y, p) {
  if (length(x) != length(y)) {
    stop("Vectors must be of the same length")
  }
  sum(abs(x - y)^p)^(1/p)
}

The lp_distance function takes three arguments: x, y, and p. It first checks if the lengths of the vectors x and y are the same. If not, it stops execution and returns an error message. Otherwise, it computes the \(L_p\) distance using the formula provided. The return statement is implicit here, as the last evaluated expression is returned by default. If we want to explicitly return the result, we can modify the function as follows:

lp_distance <- function(x, y, p) {
  if (length(x) != length(y)) {
    stop("Vectors must be of the same length")
  }
  result <- sum(abs(x - y)^p)^(1/p)
  return(result)
}

If there are multiple outputs to return, we can use a list to return them. In the following example, we return both the computed distance and the input vectors as part of a list.

lp_distance_with_details <- function(x, y, p) {
  if (length(x) != length(y)) {
    stop("Vectors must be of the same length")
  }
  distance <- sum(abs(x - y)^p)^(1/p)
  details <- list(vector_x = x, vector_y = y, p_value = p)
  return(list(distance = distance, details = details))
}

4.3 Calling a custom function

We can call the lp_distance function with two vectors and a value for p.

vector1 <- c(1, 2, 3)
vector2 <- c(4, 5, 6)
p_value <- 2
distance <- lp_distance(vector1, vector2, p_value)
print(distance)

[1] 5.196152

We can also use named arguments when calling the function:

distance <- lp_distance(x=vector1, y=vector2, p=p_value)
distance

[1] 5.196152

The order of named arguments does not matter as shown in the following call.

distance <- lp_distance(p=p_value, y=vector2, x=vector1)
distance

[1] 5.196152

In the case of the lp_distance_with_details function, we can call it and access both the distance and the details as follows:

result <- lp_distance_with_details(vector1, vector2, p_value)
print(result$distance)

[1] 5.196152

print(result$details)

$vector_x
[1] 1 2 3

$vector_y
[1] 4 5 6

$p_value
[1] 2