When should you write a function?

suppressPackageStartupMessages(library("tidyverse"))

package 㤼㸱tidyverse㤼㸲 was built under R version 3.6.3

suppressPackageStartupMessages(library("lubridate"))

1.Why is TRUE not a parameter to rescale01()? What would happen if x contained a single missing value, and na.rm was FALSE?

The code for rescale01() is reproduced below.

rescale01 <- function(x) {
  rng <- range(x, na.rm = TRUE, finite = TRUE)
  (x - rng[1]) / (rng[2] - rng[1])
}

If x contains a single missing value and na.rm = FALSE, then this function stills return a non-missing value.

rescale01_alt <- function(x, na.rm = FALSE) {
  rng <- range(x, na.rm = na.rm, finite = TRUE)
  (x - rng[1]) / (rng[2] - rng[1])
}
rescale01_alt(c(NA, 1:5), na.rm = FALSE)

[1]   NA 0.00 0.25 0.50 0.75 1.00

rescale01_alt(c(NA, 1:5), na.rm = TRUE)

[1]   NA 0.00 0.25 0.50 0.75 1.00

The option finite = TRUE to range() will drop all non-finite elements, and NA is a non-finite element.

However, if both finite = FALSE and na.rm = FALSE, then this function will return a vector of NA values. Recall, arithmetic operations involving NA values return NA.

rescale01_alt2 <- function(x, na.rm = FALSE, finite = FALSE) {
  rng <- range(x, na.rm = na.rm, finite = finite)
  (x - rng[1]) / (rng[2] - rng[1])
}
rescale01_alt2(c(NA, 1:5), na.rm = FALSE, finite = FALSE)

[1] NA NA NA NA NA NA

2. In the second variant of rescale01(), infinite values are left unchanged. Rewrite rescale01() so that -Inf is mapped to 0, and Inf is mapped to 1.

rescale01 <- function(x) {
  rng <- range(x, na.rm = TRUE, finite = TRUE)
  y <- (x - rng[1]) / (rng[2] - rng[1])
  y[y == -Inf] <- 0
  y[y == Inf] <- 1
  y
}

rescale01(c(Inf, -Inf, 0:5, NA))

[1] 1.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0  NA

3. Practice turning the following code snippets into functions. Think about what each function does. What would you call it? How many arguments does it need? Can you rewrite it to be more expressive or less duplicative?

mean(is.na(x))

x / sum(x, na.rm = TRUE)

sd(x, na.rm = TRUE) / mean(x, na.rm = TRUE)

mean(is.na(x)) code calculates the proportion of NA values in a vector. I will write it as a function named prop_na() that takes a single argument x, and returns a single numeric value between 0 and 1.

prop_na <- function(x) {
  mean(is.na(x))
}
prop_na(c(0, 1, 2, NA, 4, NA))

[1] 0.3333333

x / sum(x, na.rm = TRUE) standardizes a vector so that it sums to one. I’ll write a function named sum_to_one(), which is a function of a single argument, x, the vector to standardize, and an optional argument na.rm. The optional argument, na.rm, makes the function more expressive, since it can handle NA values in two ways (returning NA or dropping them). Additionally, this makes sum_to_one() consistent with sum(), mean(), and many other R functions which have a na.rm argument. While the example code had na.rm = TRUE, I set na.rm = FALSE by default in order to make the function behave the same as the built-in functions like sum() and mean() in its handling of missing values.

sum_to_one <- function(x, na.rm = FALSE) {
  x / sum(x, na.rm = na.rm)
}
# no missing values
sum_to_one(1:5)

[1] 0.06666667 0.13333333 0.20000000 0.26666667 0.33333333

# if any missing, return all missing
sum_to_one(c(1:5, NA))

[1] NA NA NA NA NA NA

# drop missing values when standardizing
sum_to_one(c(1:5, NA), na.rm = TRUE)

[1] 0.06666667 0.13333333 0.20000000 0.26666667 0.33333333         NA

sd(x, na.rm = TRUE) / mean(x, na.rm = TRUE) calculates the coefficient of variation (assuming that x can only take non-negative values), which is the standard deviation divided by the mean. I’ll write a function named coef_variation(), which takes a single argument x, and an optional na.rm argument.

coef_variation <- function(x, na.rm = FALSE) {
  sd(x, na.rm = na.rm) / mean(x, na.rm = na.rm)
}
coef_variation(1:5)

[1] 0.5270463

coef_variation(c(1:5, NA))

[1] NA

coef_variation(c(1:5, NA), na.rm = TRUE)

[1] 0.5270463

4. Follow https://nicercode.github.io/intro/writing-functions.html to write your own functions to compute the variance and skew of a numeric vector.

The sample variance is defined as,

\(Var(x) = \frac{1}{n-1} \sum \limits_{i = 1}^n { \left( {x_i - \bar x} \right)^2 }\)

where \(\bar x = \frac{1}{n} \sum\limits_{i=1}^n {x_i}\) is the sample mean. The corresponding function is:

variance <- function(x, na.rm = TRUE) {
  n <- length(x)
  m <- mean(x, na.rm = TRUE)
  sq_err <- (x - m)^2
  sum(sq_err) / (n - 1)
}
var(1:10)

[1] 9.166667

variance(1:10)

[1] 9.166667

There are multiple definitions for skewness, but we will use the following one,

\(Skew(x) = \frac{\frac{1}{n-2} \sum \limits_{i = 1}^n { \left( {x_i - \bar x} \right)^3}}{{Var(x)}^{3/2}}\)

The corresponding function is:

skewness <- function(x, na.rm = FALSE) {
  n <- length(x)
  m <- mean(x, na.rm = na.rm)
  v <- var(x, na.rm = na.rm)
  (sum((x - m)^3) / (n - 2)) / v^(3 / 2)
}
skewness(c(1, 2, 5, 100))

[1] 1.494554

5. Write both_na(), a function that takes two vectors of the same length and returns the number of positions that have an NA in both vectors.

both_na <- function(x, y) {
  sum(is.na(x) & is.na(y))
}

both_na(
  c(NA, NA, 1, 2),
  c(NA, 1, NA, 2)
)

[1] 1

both_na(
  c(NA, NA, 1, 2, NA, NA, 1),
  c(NA, 1, NA, 2, NA, NA, 1)
)

[1] 3

6. What do the following functions do? Why are they useful even though they are so short?

is_directory <- function(x) file.info(x)$isdir
is_readable <- function(x) file.access(x, 4) == 0

The function is_directory() checks whether the path in x is a directory. The function is_readable() checks whether the path in x is readable, meaning that the file exists and the user has permission to open it. These functions are useful even though they are short because their names make it much clearer what the code is doing.

7. Read the complete lyrics to Little Bunny Foo Foo’’. There’s a lot of duplication in this song. Extend the initial piping example to recreate the complete song, and use functions to reduce the duplication.

The lyrics of one of the most common versions of this song are

Little bunny Foo Foo Hopping through the forest Scooping up the field mice And bopping them on the head

Down came the Good Fairy, and she said “Little bunny Foo Foo I don’t want to see you Scooping up the field mice

And bopping them on the head. I’ll give you three chances, And if you don’t stop, I’ll turn you into a GOON!” And the next day…

The verses repeat with one chance fewer each time. When there are no chances left, the Good Fairy says

“I gave you three chances, and you didn’t stop; so….” POOF. She turned him into a GOON! And the moral of this story is: hare today, goon tomorrow.

Here’s one way of writing this

threat <- function(chances) {
  give_chances(
    from = Good_Fairy,
    to = foo_foo,
    number = chances,
    condition = "Don't behave",
    consequence = turn_into_goon
  )
}

lyric <- function() {
  foo_foo %>%
    hop(through = forest) %>%
    scoop(up = field_mouse) %>%
    bop(on = head)

  down_came(Good_Fairy)
  said(
    Good_Fairy,
    c(
      "Little bunny Foo Foo",
      "I don't want to see you",
      "Scooping up the field mice",
      "And bopping them on the head."
    )
  )
}

lyric()
threat(3)
lyric()
threat(2)
lyric()
threat(1)
lyric()
turn_into_goon(Good_Fairy, foo_foo)