Here are the exercises on loops and applying functions to data structures:
12.4.1 Exercise 1
Fibonacci loop and functions
Look up the term Fibonacci numbers and use a
forloop to create a numeric vector of the first 25 Fibonacci numbers (for a series of numbers starting with
forloop into a
fibonaccifunction that returns a numeric vector of the first
nFibonacci numbers. Test your function for
fibonacci(n = 25).
fibonaccifunction to also accept the first 2 elements (
e2) as inputs to the series and then create the first
nFibonacci numbers given these initial elements. Test your function for
fibonacci(e1 = 1, e2 = 3, n = 25).
12.4.2 Exercise 2
184.108.40.206 Looping for divisors
- Write a
forloop that prints out all positive divisors of the number 1000.
N %% x == 0 to test whether
x is a divisor of
How many iterations did your loop require? Could you achieve the same results with fewer iterations?
divisorsfunction that uses a
forloop to return a numeric vector containing all positive divisors of a natural number
Hint: Note that we do not know the length of the resulting vector.
divisorsfunction to answer the question: Does the number 1001 have fewer or more divisors than the number 1000?
divisorsfunction and another
forloop to answer the question: Which prime numbers exist between the number 111 and the number 1111?
Hint: A prime number (e.g., 13) has only 2 divisors: 1 and the number itself.
12.4.3 Exercise 3
Implement a function
dicethat uses the base R function
sample()to simulate a throw of a dice (i.e., yielding an integer from 1 to 6 with equal probability).
Add an argument
n(for the number of throws) to your function and modify it by using a
forloop to throw the dice
ntimes, and returning a vector of length
nthat shows the results of the
whileloop to throw
dice(n = 1)until you throw the number 6 twice in a row and show the sequence of all throws up to this point.
Hint: Given a sequence
n-th element is
throws[n]. Hence, the last element of
- Use your solution of 3. to conduct a simulation that addresses the following question:
- How many times on average do we need to throw
dice(1)to obtain the number 6 twice in a row?
Hint: Use a
for loop to run your solution to 3. for
N = 10000 times and store the length of the individual
throws in a numeric vector.
12.4.4 Exercise 4
Mapping functions to data
Write code that uses a function of the base R
apply or purrr
map family of functions to:
- Compute the mean of every column in
- Determine the type of each column in
- Compute the number of unique values in each column of
- Generate 10 random normal numbers for each of
μ = −100, 0, and 100.
12.4.5 Exercise 5
In this exercise, we will standardize an entire table of data (using a
for loop, an
apply, and a
map function). We will first write a utility function that achieves the desired transformation for a vector and then compare and contrast different ways of applying this function to a table of data.
In case you are not familiar with the notion of a z score or standard score, look up these terms (e.g., on Wikipedia).
Write a function called
z_transthat takes a vector
vas input and returns the z-transformed (or standardized) values as output if
vis numeric and returns
vunchanged if it is non-numeric.
Hint: Remember that
z <- (v - mean(v)) / sd(v)), but beware that
# Load data: falsePosPsy <- ds4psy::falsePosPsy_all # from ds4psy package # falsePosPsy <- readr::read_csv("http://rpository.com/ds4psy/data/falsePosPsy_all.csv") # online falsePosPsy #> # A tibble: 78 x 19 #> study ID aged aged365 female dad mom potato when64 kalimba cond #> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <chr> #> 1 1 1 6765 18.5 0 49 45 0 0 1 cont… #> 2 1 2 7715 21.1 1 63 62 0 1 0 64 #> 3 1 3 7630 20.9 0 61 59 0 1 0 64 #> 4 1 4 7543 20.7 0 54 51 0 0 1 cont… #> 5 1 5 7849 21.5 0 47 43 0 1 0 64 #> 6 1 6 7581 20.8 1 49 50 0 1 0 64 #> 7 1 7 7534 20.6 1 56 55 0 0 1 cont… #> 8 1 8 6678 18.3 1 45 45 0 1 0 64 #> 9 1 9 6970 19.1 0 53 51 1 0 0 pota… #> 10 1 10 7681 21.0 0 53 51 0 1 0 64 #> # … with 68 more rows, and 8 more variables: root <dbl>, bird <dbl>, #> # political <dbl>, quarterback <dbl>, olddays <dbl>, feelold <dbl>, #> # computer <dbl>, diner <dbl>
- Use an appropriate
mapfunction to to create a single vector that — for each column in
falsePosPsy— indicates whether or not it is a numeric variable?
Hint: The function
is.numeric tests whether a vector is numeric.
Use this vector to select only the numeric columns of
falsePosPsyinto a new tibble
forloop to apply your
fpp_numericto standardize all of its columns:
Turn your resulting data structure into a tibble
out_1and print it.
- Repeat the task of 2. (i.e., applying
z_transto all numeric columns of
falsePosPsy) by using the base R
applyfunction, rather than a
forloop. Save and print your resulting data structure as a tibble
Hint: Remember to set the
MARGIN argument to apply
z_trans over all columns, rather than rows.
- Repeat the task of 2. and 3. (i.e., applying
z_transto all numeric columns of
falsePosPsy) by using an appropriate version of a
mapfunction from the purrr package. Save and print your resulting data structure as a tibble
Hint: Note that the desired output structure is a rectangular data table, which is also a list.
all.equalto verify that your results of 2., 3. and 4. (i.e.,
out_3) are all equal.
Hint: If a tibble
t1 lacks variable names, you can add those of another tibble
t2 by assigning
names(t1) <- names(t2).
12.4.6 Exercise 6
Cumulative savings revisited
In Exercise 2 of Chapter 1: Basic R concepts and commands, we computed the cumulative sum of an initial investment amount
a = 1000, given an annual interest rate of
int of .1%, and an annual rate of inflation
inf of 2%, after a number of
n full years (e.g.,
n = 10):
# Task parameters: a <- 1000 # initial amount: $1000 int <- .1/100 # annual interest rate of 0.1% inf <- 2/100 # annual inflation rate 2% n <- 10 # number of years
Our solution in Chapter 1 consisted in an arithmetic formula which computes a new
total based on the current task parameters:
# Previous solution (see Exercise 2 of Chapter 1): total <- a * (1 + int - inf)^n total #>  825.4487
Given our new skills about writing loops and functions (from Chapter 11), we can solve this task in a variety of ways. This exercise illustrates some differences between loops, a function that implements the formula, and a vector-based solution. Although all these approaches solve the same problem, they differ in important ways.
- Write a
forloop that iteratively computes the current value of your investment after each of
1:nyears (with \(n \geq 1\)).
Hint: Express the new value of your investment
a as a function of its current value
a and its change based on
int in each year.
- Write a function
nas its arguments, and directly computes and returns the cumulative total after
Hint: Translate the arithmetic solution (shown above) into a function that directly computes the new total. Use sensible default values for your function.
forloop that iteratively calls your function
compute_value()for every year
Check whether your
compute_value()function also works for a vector of year values
n. Then discuss the differences between the solutions to Exercise 6.1, 6.3, and 6.4.
This concludes our exercises on loops and applying functions to data structures.