Chapter 5 Sequences of Numbers
In this lesson, you’ll learn how to create sequences of numbers in R.
The simplest way to create a sequence of numbers in R is by using the : operator (i.e., the ‘colon’ operator). Type 1:20 to see how it works.
That gave us every integer between (and including) 1 and 20. We could also use it to create a sequence of real numbers (i.e., continuous values that thus can include decimals). For example, try pi:10.
The result is a vector of real numbers starting with pi (3.142…) and increasing in increments of 1. The upper limit of 10 is never reached, since the next number in our sequence would be greater than 10.
What happens if we do 15:1? Give it a try to find out.
It counted backwards in increments of 1! It’s unlikely we’d want this behavior, but nonetheless it’s good to know how it could happen.
Remember that if you have questions about a particular R function, you can access its documentation with a question mark followed by the function name: ?function_name_here. However, in the case of an operator like the colon used above, you must enclose the symbol in backticks or regular quotes. (NOTE: The backtick (`) key is generally located in the top left corner of a keyboard, above the Tab key)
Pull up the documentation for : now.
Often, we’ll desire more control over a sequence we’re creating than what the : operator gives us. The seq() function serves this purpose.
The most basic use of seq() does exactly the same thing as the : operator. Try seq(1, 20) to see this.
This gives us the same output as 1:20. However, let’s say that instead we want a vector of numbers ranging from 0 to 10, incremented by 0.5. seq(0, 10, by=0.5) does just that. Try it out.
seq(0, 10, by=0.5)
## [1] 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0Or maybe we don’t care what the increment is and we just want a sequence of 30 numbers between 5 and 10. seq(5, 10, length=30) does the trick. Give it a shot now and store the result in a new variable called my_seq.
To confirm that my_seq has length 30, we can use the length() function. Try it now.
Let’s pretend we don’t know the length of my_seq, but we want to generate a sequence of integers from 1 to N, where N represents the length of the my_seq vector. In other words, we want a new vector (1, 2, 3, …) that is the same length as my_seq.
There are several ways we could do this. One possibility is to combine the : operator and the length() function like this: 1:length(my_seq). Give that a try.
1:length(my_seq)
## [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30Another option is to use seq(along.with = my_seq). Give that a try.
seq(along.with = my_seq)
## [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30However, as is the case with many common tasks, R has a separate built-in function for this purpose called seq_along(). Type seq_along(my_seq) to see it in action.
seq_along(my_seq)
## [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30There are often several approaches to solving the same problem, particularly in R. Simple approaches that involve less typing are generally best. It’s also important for your code to be readable, so that you and others can figure out what’s going on without too much hassle.
If R has a built-in function for a particular task, it’s likely that function is highly optimized for that purpose and is your best option. As you become a more advanced R programmer, you’ll design your own functions to perform tasks when there are no better options. We’ll explore writing your own functions in future lessons.
One more function related to creating sequences of numbers is rep(), which stands for ‘replicate’. Let’s look at a few uses.
If we’re interested in creating a vector that contains 40 zeros, we can use rep(0, times = 40). Try it out.
rep(0, times = 40)
## [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0If instead we want our vector to contain 10 repetitions of the vector (0, 1, 2), we can do rep(c(0, 1, 2), times = 10). Go ahead.
Finally, let’s say that rather than repeating the vector (0, 1, 2) over and over again, we want our vector to contain 10 zeros, then 10 ones, then 10 twos. We can do this with the each argument. Try rep(c(0, 1, 2), each = 10).
You’ve successfully completed this lesson!