letrs <- c(
'y', 'd', 'g', 'a', 'b', 'w', 'k', 'n', 'r', 's',
'a', 'u', 'u', 'j', 'v', 'n', 'j', 'g', 'i', 'o',
'u', 'e', 'i', 'y', 'n', 'e', 'e', 'b', 'j', 'y',
'l', 'o', 'a', 't', 'c', 'f', 'j', 'j', 'f', 'o',
't', 't', 'z', 'l', 'y', 'w', 'f', 'y', 'h', 'l',
'y', 'w', 'x', 'f', 'z', 'g', 's', 'j', 'f', 'x',
'n', 'b', 'm', 'r', 'v', 'n', 'f', 'a', 's', 's',
'h', 'f', 'w', 'l', 'f', 'h', 'g', 'k', 'q', 'd',
'm', 'h', 'y', 'p', 'y', 'w', 'n', 't', 'g', 'm',
'v', 'l', 'p', 'a', 'm', 'u', 'f', 'q', 'i', 'g'
)Practice: Loops
Stat 133
Learning Objectives
- Get familiar with the syntax of a
forloop - Write simple
forloops
1 About Loops
Many times we need to perform a procedure several times
In other words, we have to perform the same operation several times as long as some condition is fulfilled
For this purpose we use loops
The main idea is that of iteration or repetition
R provides three basic paradigms to handle this situations:
for()loops,whileloops, andrepeatloops.
2 Examples: Counting Letters
Consider the following vector letrs which contains various letters:
2.1 Counting a’s with vectorized code
Say we are interested in counting the number of letters "a". This can be easily done in R with some vectorized code:
sum(letrs == 'a')[1] 5For learning purposes, we are going to ask you to forget about vectorization for a moment. And instead let’s see how to use loops.
2.2 Counting a’s with a for loop
Alternatively, we can also write a for loop that iterates through each element of letrs, testing whether we have an "a", and if yes, the count increases by one.
# start at count zero
count_a = 0
for (pos in 1:length(letrs)) {
# increase count if letter is an 'a'
if (letrs[pos] == 'a') {
count_a = count_a + 1
}
}
count_a[1] 52.3 Counting x, y and z with a for loop
Say we are interested in counting the number of x, y and z letters, using a for loop. Here’s one possibility:
# start at count zero
count_xyz = 0
for (pos in 1:length(letrs)) {
# increase count if letter is x, y, or z
if (letrs[pos] %in% c('x', 'y', 'z')) {
count_xyz = count_xyz + 1
}
}
count_xyz[1] 122.4 Stopping a loop with break
Say we are interested in counting the number of x, y and z letters, using a for loop, but this time, we only want to count until we get the fifth occurrence.
# start at count zero
count_xyz = 0
for (pos in 1:length(letrs)) {
# increase count if letter is x, y, or z
if (letrs[pos] %in% c('x', 'y', 'z')) {
count_xyz = count_xyz + 1
}
# break loop if count gets to fifth occurrence
if (count_xyz == 5) {
break
}
}
count_xyz[1] 5Notice the use of the break statement to decide whether the loop should stop from iterating.
3 Your Turn: Counting Letters
3.1 Number of letters different from "b"
Consider the vector letrs defined in the previous section. Write a for loop in order to count the number of letters different from "b"
Show answer
# start count at zero
count_not_b = 0
for (pos in 1:length(letrs)) {
# increase count if letter is not a 'b'
if (letrs[pos] != 'b') {
count_not_b = count_not_b + 1
}
}
count_not_b3.2 Number of "f" or "w" in even positions
Consider the vector letrs. Write a for loop in order to count the number of letters equal to f or w that are in even positions (e.g. 2, 4, …, 100). Hint: the function seq() is your friend.
Show answer
# start count at zero
count_fw = 0
for (pos in seq(2, 100, by = 2)) {
# increase count if letter is 'f' or 'w'
if (letrs[pos] == 'f' | letrs[pos] == 'w') {
count_fw = count_fw + 1
}
}
count_fw3.3 Counting vowels
Consider the vector letrs. Write a for loop in order to count the number of vowels, until reaching exactly 15 vowels. How many iterations were necessary to obtain 15 vowels?
Show answer
# start count at zero
count_vowels = 0
for (pos in 1:length(letrs)) {
# increase count if letter is a vowel
if (letrs[pos] %in% c('a', 'e', 'i', 'o', 'u')) {
count_vowels = count_vowels + 1
}
if (count_vowels == 15) {
break
}
}
# number of iterations
pos4 Summation Series
- Write a for loop to compute the following series. Test your code with different values for \(n\). Does the sum of the series converge as \(n\) increase?
\[ \sum_{k=0}^{n} \frac{1}{2^k} = 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots + \frac{1}{2^n} \]
Show answer
# Summation Series of 1/2
n = 10
series = 0
sum_series = 0
for (k in 0:n) {
term = 1 / (2^k)
series[k+1] = term
sum_series = sum_series + term
}
# with n=10, the series is
series
# the sum of the series is
sum_series- Write a for loop to compute the following series. Test your code with different values for \(n\). Does the sum of the series converge as \(n\) increase?
\[ \sum_{k=0}^{n} \frac{1}{9^k} =1 + \frac{1}{9} + \frac{1}{81} + \dots + \frac{1}{9^n} \]
Show answer
# Summation Series of 1/9
n = 20
# outputs
series = 0
sum_series = 0
# iterations
for (k in 0:n) {
term = 1 / (9^k)
series[k+1] = term
sum_series = sum_series + term
}
# with n=10, the series is
series
# the sum of the series is
sum_series4.1 Arithmetic Series
Consider the following arithmetic series
\[ a_n = a_1 + (n-1)d \]
Write a for loop to compute this series when \(a_1 = 3\), and \(d = 3\). For instance: \(3 + 6 + 12 + 24 + \dots\). Test your code with different values for \(n\). Does the series converge as \(n\) increase?
Show answer
# inputs
a1 = 3
d = 3
num = 10
# outputs
series = rep(0, num)
sum_series = 0
# iterations
for (n in 1:num) {
an = a1 + (n-1)*d
series[n] = an
sum_series = sum_series + an
}
# series does not converge as 'n' increases4.2 Geometric Sequence
A sequence such as \(3, 6, 12, 24, 48\) is an example of a geometric sequence. In this type of sequence, the \(n\)-th term is obtained as:
\[ a_n = a_1 \times r^{n-1} \]
where: \(a_1\) is the first term, \(r\) is the common ratio, and \(n\) is the number of terms.
Write a for loop to compute the sum of the first \(n\) terms of: \(3 + 6 + 12 + 24 + \dots\). Test your code with different values for \(n\). Does the series converge as \(n\) increase?
Show answer
# inputs
a1 = 3
r = 2
# outputs
summ = 0
for (n in 1:10) {
an = a1 * r^(n-1)
summ = summ + an
}
# series does not converge as 'n' increases