For loops

There are two important properties of for loops. First, results are not printed inside a loop unless you explicitly call the print() function. Second, the indexing variable used within a for loop will be changed, in order, after each iteration. Furthermore, to stop iterating you can use the keyword break, and to skip to the next iteration you can use the next command.

For this first example, we create a vector of characters called words, and iterate through each of its elements in order using the for (word in words) syntax. Doing so will take the first element in words, assign it to word, and pass it through the expression defined in the block defined by the curly braces, which in this case print the word to the console, as well as the number of characters in the word. When the iteration is finished, word will be updated with the next word, and the loop will be repeated this way until all words have been used:

words <- c("Hello", "there", "dear", "reader")
for (word in words) {
    print(word)
    print(nchar(word))
}
#> [1] "Hello"
#> [1] 5
#> [1] "there"
#> [1] 5
#> [1] "dear"
#> [1] 4
#> [1] "reader"
#> [1] 6

Interesting behavior can be achieved by using nested for loops which are for loops inside other for loops. In this case, the same logic applies, when we encounter a for loop we execute it until completion. It's easier to see the result of such behavior than explaining it, so take a look at the behavior of the following code:

for (i in 1:5) {
    print(i)
    for (j in 1:3) {
        print(paste("   ", j))
    }
}
#> [1] 1
#> [1] " 1"
#> [1] " 2"
#> [1] " 3"
#> [1] 2
#> [1] " 1"
#> [1] " 2"
#> [1] " 3"
#> [1] 3
#> [1] " 1"
#> [1] " 2"
#> [1] " 3"
#> [1] 4
#> [1] " 1"
#> [1] " 2"
#> [1] " 3"
#> [1] 5
#> [1] " 1"
#> [1] " 2"
#> [1] " 3"

Using such nested for loops is how people perform matrix-like operations when using languages that do not offer vectorized operations. Luckily, we can use the syntax shown in previous sections to perform those operations without having to use nested for-loops ourselves which can be tricky at times.

Now, we will see how to use the sapply() and lapply() functions to apply a function to each element of a vector. In this case, we will call use the nchar() function on each of the elements in the words vector we created before. The difference between the sapply() and the lapply() functions is that the first one returns a vector, while the second returns a list. Finally, note that explicitly using any of these functions is unnecessary, since, as we have seen before in this chapter, the nchar() function is already vectorized for us:

sapply(words, nchar)
#> Hello there dear reader
#> 5     5     4    6
lapply(words, nchar)
#> [[1]]
#> [1] 5
#>
#> [[2]]
#> [1] 5
#>
#> [[3]]
#> [1] 4
#>
#> [[4]]
#> [1] 6
nchar(words)
#> [1] 5 5 4 6

When you have a function that has not been vectorized, like our distance() function. You can still use it in a vectorized way by making use of the functions we just mentioned. In this case we will apply it to the x list which contains three different numeric vectors. We will use the lapply() function by passing it the list, followed by the function we want to apply to each of its elements (distance() in this case). Note that in case the function you are using receives other arguments apart from the one that will be taken from x and which will be passed as the first argument to such function, you can pass them through after the function name, like we do here with the c(1, 1, 1) and l1_norm arguments, which will be received by the distance() function as the y and norm arguments, and will remain fixed for all the elements of the x list:

x <- list(c(1, 2, 3), c(4, 5, 6), c(7, 8, 9))
lapply(x, distance, c(1, 1, 1), l1_norm)
#> [[1]]
#> [1] 3
#>
#> [[2]]
#> [1] 12
#>
#> [[3]]
#> [1] 21