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Lab 7: Simple Functions and Conditionals

Gaston Sanchez

Learning Objectives

  • Learn how to write simple functions
  • Get into the habit of writing simple functions
  • Get into the habit of documenting functions
  • Make sure your functions work
  • Use conditionals if-then-else

Introduction

In this lab you will practice writing simple functions, and some basic examples to make sure that the functions work as expected. Later in the course we will see how to write assertions (i.e. tests) for your functions in a more formal way.

In addition to writing the functions, you should also practice documenting your functions. Writing this type of documentation should become second nature. To do this, include roxygen comments such as:

  • #' @title Name of your function
  • #' @description What the function does
  • #' @param x input(s) of your function
  • #' @return output of your function

Before you start ...

If you use an Rmd file to write narrative and code for this practice, you must include a code chunk at the top of your file like the one in the following screen capture:

By setting the global option error = TRUE you avoid the knitting process to be stopped in case a code chunk generates an error.

Since you willl be writing a couple of functions with stop() statements, it is essential that you set up error = TRUE, otherwise "knitr" will stop knitting your Rmd file if it encounters an error.

Toy Example

Here's an example of how to write a function with its documentation:

#' @title area of rectangle
#' @description calculates the area of a rectangle
#' @param len length of the rectangle (numeric)
#' @param wid width of the rectangle (numeric)
#' @return computed area
rect_area <- function(len = 1, wid = 1) {
  if (len < 0) {
    stop("len must be positive")
  }
  if (wid < 0) {
    stop("wid must be positive")
  }
  area <- len * wid
  return(area)
}

Some tests:

# default
rect_area()
## [1] 1

# len=2, wid=3
rect_area(len = 2, wid = 3)
## [1] 6

# bad len
rect_area(len = -2, wid = 3)
## Error in rect_area(len = -2, wid = 3): len must be positive

Simple Math Functions

Consider the following mathematical functions:

  • f(x)=x2
  • g(x)=2x + 5

Write two functions f() and g() based on the previous equations. Don't forget to include roxygen comments to document your function!

# your function f()
# your function g()

Test your functions with:

f(2)     # 4
f(-5)    # 25

g(0)     # 5
g(-5/2)  # 0

Use your functions f() and g() to create the following composite functions:

  • fog() for the composite function: f ∘ g(x)
  • gof() for the composite function: g ∘ f(x)
# your function fog()
# your function gof()

Test your composite functions with:

fog(2)     # 81
fog(-5)    # 25

gof(0)     # 5
gof(-5/2)  # 17.5

Pythagoras

The pythagoras formula is used to compute the length of the hypotenuse, c, of a right triangle with legs of length a and b.

hypotenuse

Write a function pythagoras() that takes two arguments a and b, and returns the length of the hypotenuse. Don't forget to include roxygen comments to document your function!

# your pythagoras() function

Test your pythagoras() with two leg values: pythagoras(3, 4)

# test pythagoras(3, 4)

Modify your function pythagoras() so that argument b takes the same value of argument a. Test it with just one leg value: pythagoras(5)

# test pythagoras(5)

Area of a circle

Consider a circle with radius = 2. The area of this circle can be computed in R as:

# area of circle with radius 2
r <- 2
area <- pi * r^2
area
## [1] 12.56637

Write a function circle_area() that calculates the area of a circle. This function must take one argument radius. Give radius a default value of 1. Don't forget to include roxygen comments to document your function!

For example:

# default (radius 1)
circle_area()

# radius 3
circle_area(radius = 3)

Modify your circle_area() function in order to include a stop() statement. If radius is negative, then the function should stop with a message like: "radius cannot be negative".

Test your modified circle_area() with radius = -2; the function should return a stop message:

# bad radius
circle_area(radius = -2)

Area of a cylinder

For a given cylinder of radius r and height h the area A is:

A = 2πrh + 2π**r2

For example. Say you have a cylinder with radius = 2, and height = 3.

# cylinder variables
r = 2  # radius
h = 3  # height

# area of cylinder
2 * pi * r * h + 2 * pi * r^2
## [1] 62.83185

Notice that the formula of the area of a cylinder includes the area of a circle: π**r2. Write a function cylinder_area(), that calls circle_area(), to compute the area of a cylinder.

This function must take two arguments: radius and height. Give both arguments a default value of 1. In addition, the function should stop if any of radius or height are negative.

For instance:

# default (radius 1, height 1)
cylinder_area()

# radius 2, height 3
cylinder_area(radius = 2, height = 3)

These should return an error message:

# bad radius
cylinder_area(radius = -2, height = 1)

# bad height
cylinder_area(radius = 2, height = -1)

# bad radius and height
cylinder_area(radius = -2, height = -1)

Volume of a cylinder

For a given cylinder of radius r and height h the volume V is:

V = π**r2h

Write a function cylinder_volume(), that calls circle_area(), to compute the volume of a cylinder. This function must take two arguments: radius and height. Give both arguments a default value of 1.

For example:

# default (radius 1, height 1)
cylinder_volume()

cylinder_volume(radius = 3, height = 10)
cylinder_volume(height = 10, radius = 3)

Unit Conversion Formulas

The following exercises involve writing simple functions to convert from one type of unit to other.

Miles to Kilometers

Write a function miles2kms() that converts miles into kilometers: 1 mile is equal to 1.6 kilometers. Give the argument a default value of 1.

miles2kms <- function() {
  # fill in
}

Use miles2kms() to obtain mile conversions, in order to create a table (i.e. data frame) like the one below. The first ten rows range from 1 to 10 miles, and then from 10 to 100 in 10 mile steps. The second column corresponds to kms.

miles kms
1 1.6
2 3.2
... ...
10 16
20 32
... ...
100 160

Gallons to Liters, and viceversa

Write a function gallon2liters() that converts gallons to liters: 1 gallon is equal to 3.78541 liters:

# your gallons2liters() function

Use gallon2liters() to make an inverse function liters2gallons().

# your liters2gallons() function

Use liters2gallons() to obtain liter conversions, in order to create a table (i.e. data frame) like the one below. The first ten rows range from 1 to 10 liters, and then from 10 to 100 in 10 liter steps. The second column corresponds to gallons.

liters gallons
1 0.2641722
2 0.5283444
... ...
10 2.6417218
20 5.283444
... ...
100 26.417218

Seconds to Years

According to Wikipedia, in 2015 the life expectancy of a person born in the US was 79 years. Consider the following question: Can a newborn baby in USA expect to live for one billion (109) seconds?

To answer this question, write a function seconds2years() that takes a number in seconds and returns the equivalent number of years. Test the function with seconds2years(1000000000)

# your code

Gaussian Function

The Gaussian (Normal) function, given in the equation below, is one of the most widely used functions in science and statistics:

gaussian function

The parameters σ and μ are real numbers, where σ must be greater than zero.

Make a function gaussian() that takes three arguments: x, m, and s. Evaluate the function with m = 0, s = 2, and x = 1.

# your code

Test your gaussian() function and compare it with the R function dnorm()

# compare with dnorm()
dnorm(x = 1, mean = 0, sd = 2)
## [1] 0.1760327

Now try gaussian() with a vector seq(-4.5, 4.5, by = 0.1), and pass the values to plot() to get a normal curve. Here's code with values obtained from dnorm()

# you should get a plot like this one
x_values <- seq(from = -4.5, to = 4.5, by = 0.1)
y_values <- dnorm(x_values, mean = 0, sd = 2)
plot(x_values, y_values, las = 1, type = "l", lwd = 2)

Your turn:

# your code

Polynomials

In this problem we want to see whether the graph of a given polynomial will cross or touch the x axis in a given interval.

Let's begin with the polynomial: f(x)=x2(x − 1). The first thing to do is write a function for the polynomial, for instance:

poly1 <- function(x) {
  (x^2) * (x - 1)
}

Once you have a function for the polynomial, you can create a set of pairs of points x and y = f(x), and then use them to graph the polynomial

# set of points
x <- seq(-4, 4, length.out = 20)
y <- poly1(x)

# graph polynomial
plot(x, y, type = 'l', lwd = 3, col = "#FB7215", las = 1)
abline(h = 0, v = 0, col = '#888888aa', lwd = 1.5)
title(main = expression(paste(f(x), ' = ', x^2, (x - 1))))

Write functions and graph the following polynomials in the x-axis interval -4 to 4:

  1. f(x)=x3
  2. f(x)=(x2 − 1)(x + 3)3
  3. f(x)=(x2 − 1)(x2 − 9)

Descriptive Statistics

Write a function descriptive() that takes a numeric vector as input, and returns a named vector with the following descriptive statistics:

  • min: minimum
  • q1: first quartile (Q2)
  • median: median
  • mean: mean
  • q3: third quartile (Q3)
  • max: maximum
  • range: range or span (max - min)
  • iqr: interquartile range (IQR)
  • sd: standard deviation
# your descriptive() function
descriptive <- function() {
  # fill in

}

If Conditionals

Write R code that will "squish" a number into the interval [0, 100], so that a number less than 0 is replaced by 0 and a number greater than 100 is replaced by 100.

z <- 100*pi
# Fill in the following if-else statements. You may (or may not) 
# have to add or subtract else if or else statements.
if (TRUE) { # Replace TRUE with a condition.
  
} else if (TRUE) { # Replace TRUE with a condition.
  
} else {
  
}
## NULL

Multiple If's

A common situation involves working with multiple conditions at the same time. You can chain multiple if-else statements:

y <- 1 # Change this value!

if (y > 0) {
  print("positive")
} else if (y < 0) {
  print("negative")
} else {
  print("zero?")
}
## [1] "positive"

Even number

Write a function is_even() that determines whether a number is even (i.e. multiple of 2). If the input number is even, the output should be TRUE. If the input number is odd, the output should be FALSE. If the input is not a number, the output should be NA

Test your function:

# even number
is_even(10)

# odd number
is_even(33)

# not a number
is_even('a')

Odd number

Use your function is_even() to write a function is_odd() that determines if a number is odd (i.e. not a multiple of 2). If a number is odd, the output should be TRUE; if a number is even the output should be FALSE; if the input is not a number the output should be NA

Test is_odd() with the following cases:

# odd number
is_odd(1)

# even number
is_odd(4)

# not a number
is_odd('a')

Switch

Working with multiple chained if's becomes cumbersome. Consider the following example that uses several if's to convert a day of the week into a number:

# Convert the day of the week into a number.
day <- "Tuesday" # Change this value!

if (day == 'Sunday') {
  num_day <- 1
} else {
  if (day == "Monday") {
    num_day <- 2
  } else {
    if (day == "Tuesday") {
      num_day <- 3
    } else {
      if (day == "Wednesday") {
        num_day <- 4
      } else {
        if (day == "Thursday") {
          num_day <- 5
        } else {
          if (day == "Friday") {
            num_day <- 6
          } else {
            if (day == "Saturday") {
              num_day <- 7
            }
          }
        }
      }
    }
  }
}


num_day
## [1] 3

Working with several nested if's like in the example above can be a nigthmare.

In R, you can get rid of many of the braces like this:

# Convert the day of the week into a number.
day <- "Tuesday" # Change this value!

if (day == 'Sunday') {
  num_day <- 1
} else if (day == "Monday") {
  num_day <- 2
} else if (day == "Tuesday") {
  num_day <- 3
} else if (day == "Wednesday") {
  num_day <- 4
} else if (day == "Thursday") {
  num_day <- 5
} else if (day == "Friday") {
  num_day <- 6
} else if (day == "Saturday") {
  num_day <- 7
}

num_day
## [1] 3

Your turn: a grading function

Write a function grade() that takes a score argument (i.e. a numeric value between 0 and 100), and returns a letter grade (i.e. character) based on the following grading scheme:

score grade
[90 - 100] "A"
[80 - 90) "B"
[70 - 80) "C"
[60 - 70) "D"
< 60 "F"

You should be able to call your grade() function like this:

# grade "A"
grade(score = 90)

# grade "B"
grade(score = 89.9999)

# grade "C"
grade(score = 70.0000001)

# grade "F"
grade(score = 50)

Modify your grade() function to include a stop() condition when the input score value is less than zero or greater than 100. The error message should say something like:

"score must be a number between 0 and 100"

The switch() function

Consider again the chain of if-then-else's used to convert a name day into a number dat. We have too many if's, and there's a lot of repetition in the code. If you find yourself using many if-else statements with identical structure for slightly different cases, you may want to consider a switch statement instead:

# Convert the day of the week into a number.
day <- "Tuesday" # Change this value!

switch(day, # The expression to be evaluated.
  Sunday = 1,
  Monday = 2,
  Tuesday = 3,
  Wednesday = 4,
  Thursday = 5,
  Friday = 6,
  Saturday = 7,
  NA) # an (optional) default value if there are no matches
## [1] 3

Switch statements can also accept integer arguments, which will act as indices to choose a corresponding element:

# Convert a number into a day of the week.
day_num <- 3 # Change this value!

switch(day_num,
  "Sunday",
  "Monday",
  "Tuesday",
  "Wednesday",
  "Thursday",
  "Friday",
  "Saturday")
## [1] "Tuesday"

Converting Miles to other units

The table below shows the different formulas for converting miles (mi) into other scales:

Units Formula
Inches mi x 63360
Feet mi x 5280
Yards mi x 1760
Meters mi / 0.00062137
Kms mi / 0.62137

Write the following five functions for each type of conversion. Each function must take one argument x with default value: x = 1.

  • miles2inches()
  • miles2feet()
  • miles2yards()
  • miles2meters()
  • miles2kms()

For example:

miles2inches(2)
miles2feet(2)
miles2yards(2)
miles2meters(2)
miles2kms(2)

Using switch()

Create a function convert() that converts miles into the specified units. Use switch() and the previously defined functions---miles2inches(), miles2feet(), ..., miles2kms---to define convert(). Use two arguments: x and to, like this:

convert(40, to = "in")

By default, to = "km", but it can take values such as "in", "ft", "yd", or "m".

Test convert() with:

convert(3, "in")
convert(3, "ft")
convert(3, "yd")
convert(3, "m")
convert(3, "km")