Chapter 2 Vectors
Last updated: 2020-08-12 00:35:48
Aims
Our aims in this chapter are:
- Learn how to work with R code files
- Get to know the simplest data structure in R, the vector
- Learn about subsetting, one of the fundamental operations with data
2.1 Editing code
2.1.1 Using code files
In Chapter 1, we typed short and simple expressions into the R console. As we progress, however, the code we write will get longer and more complex. To be able to edit and save longer code, the code is kept in code files.
Computer code is stored in code files as plain text. When writing computer code, we must use a plain text editor, such as Notepad++ or RStudio (Section 1.2). A word processor, such as Microsoft Word, is not a good choice for writing code, because:
- Documents created with a word processor contain elements other than plain text (such as highlighting, font types, sizes and colors, etc.), which are not plain text and therefore not processed by the interpreter, leading to confusion.
- Word processors can automatically correct “mistakes” thereby introducing unintended changes in our code, such as capitalizing:
max(1)→Max(1).
Any plain text file can be used to store R code, though, conventionally, R code files have the *.R file extension. Complete code files can be executed with source (Figure 2.1).
Figure 2.1: Methods of executing R code
For example, we can run the file volcano.R which draws a 3D image of a volcano (Figure 2.2).
Figure 2.2: 3D image of the volcano dataset
Selected parts of code can be executed by marking the section and pressing Ctrl+Enter (in RStudio). Executing a single expression can be done by placing the cursor on the particular line and pressing Ctrl+Enter.
2.1.2 RStudio keyboard stortcuts
RStudio has numerous keyboard shortcuts for making it easier to edit and execute code files. Some useful RStudio keyboard shortcuts are given in Table 2.1.
| Shortcut | Action |
|---|---|
| Alt+Shift+K | List of all shortcuts |
| Ctrl+1 | Moving cursor to the code editor |
| Ctrl+2 | Moving cursor to the console |
| Ctrl+Enter | Running the current selection or line |
| Ctrl+Shift+P | Re-running the last selection |
| Ctrl+Alt+B | Running from top to current line |
| Ctrl+Shift+C | Turn comment on or off |
| Tab | Auto-complete |
| Ctrl+D | Delete line |
| Ctrl+Shift+D | Duplicate line |
| Ctrl+F | Find and replace menu |
| Ctrl+S | Save |
2.2 Assignment
So far we have been using R by typing expressions into the command line and observing the result on screen. That way, R functions as a “calculator”; the results are not kept in computer memory (Figure 2.3).
Figure 2.3: Simple R expressions are evaluated and printed
Storing objects in the temporary computer memory (RAM) is called assignment. In an assignment expression, we are storing an object, under a certain name, in the RAM (Figure 2.4). Assignment is done using the assignment operator. Assignment is an essential operation in programming, because it makes automation possible—reaching the goal step by step, while storing intermediate products. An assignment expression consists of:
- The expression whose result we want to store
- The assignment operator,
=or<- - The name which will be assigned to the object
For example:
Figure 2.4: An assignment expression stores an object in the RAM
When we type an object name in the console, R accesses an object stored under that name in the RAM, and calls the print function on the object (Figure 2.5):
Figure 2.5: Accessing an object stored in the RAM
What happens when we assign a new value to an existing object? The old object gets deleted, and its name is now pointing on the new value:
Note the difference between the == and = operators! = is an assignment operator:
while == is a logical operator for comparison:
Which user-defined objects are currently in memory? The ls function returns a character vector with their names:
Why did we write
ls()and notls?
2.3 Vectors
2.3.1 What is a vector?
A vector, in R, is an ordered collection of values of the same type, such as:
- Numbers—
numericorinterger - Text—
character - Logical—
logical
Recall that these are the same three types of “constant values” we saw in Chapter 1. In fact, a constant value is a vector of length 1.
2.3.2 The c function
Vectors can be created with the c function, which combines the given vectors in the given order:
Here is another example, with character values:
2.3.3 Vector subsetting (individual elements)
We can access individual vector elements using the [ operator and an index; in other words, to get a subset with an individual vector element:
Note that the index starts at 1!
Here is another example:
Note the components of an expression for accessing a vector element (Figure 2.6).
Figure 2.6: Components of expression to access vector elements
We can also assign new values into a vector subset:
In this example, we made an assignment into a subset with a single element. As we will see later on, we can assign values into a subset of any length using the same method (Section 2.3.9).
2.3.4 Calling functions on a vector
There are various functions for calculating vector properties. For example:
Other functions operate on each vector element, returning a vector of results having the same length as the input:
Why does the output of
sqrt(x)containNaN?
2.3.5 The recycling rule (arithmetic)
Binary operations, such as arithmetic and logical operators, applied on two vectors are done element-by-element, and a vector of the results is returned:
What happens when the input vector lengths do not match? The shorter vector gets “recycled”. For example, when one of the vectors is of length 3 and the other vector is of length 6, then the shorter vector (of length 3) is replicated 2 times until it matches the longer vector (Figure 2.7):
Figure 2.7: Vector recycling
When one of the vectors is of length 1 and the other is of length 4, the shorter vector (of length 1) is replicated 4 times:
When one of the vectors is of length 2 and the other is of length 6, the shorter vector (of length 2) is replicated 3 times:
When longer vector length is not a multiple of the shorter one, the result comes with a warning message that recycling is “incomplete”:
2.3.6 Consecutive and repetitive vectors
2.3.6.1 Introduction
Other than the c function, there are three commonly used methods for creating consecutive or repetitive vectors:
- The
:operator - The
seqfunction - The
repfunction
2.3.6.2 Consecutive vectors
The : operator is used to create a vector of consecutive vectors in steps of 1 or -1:
The seq function provides a more general way to create a consecutive vector with any step size. The three most useful parameters of the seq function are:
from—Where to startto—When to endby—Step size
For example:
2.3.6.3 Repetitive vectors
The rep function replicates its argument to create a repetitive vector:
x—What to replicatetimes—How many times to repeatx
For example:
2.3.7 Function calls
Using the seq function, we will demonstrate three properties of function calls. First, we can omit parameter names as long as the arguments are passed in the default order:
Second, we can use any argument order as long as parameter names are specified:
Third, we can omit parameters that have a default argument as part of the function definition. For example, the by parameter of seq has a default value of 1:
To find out what are the parameters of a particular function, their order or their default values, we can look into the documentation:
2.3.8 Vector subsetting (general)
So far, we created vector subsets using a numeric index which consists of a single value, such as:
We can also use a vector of length >1 as an index. For example:
Note that the vector does not need to be consecutive, and can include repetitions:
Here is another example (Figure 2.8):
Figure 2.8: Vector subsetting with a vector of indices (1:3)
And here is one more example (Figure 2.9):
Figure 2.9: Vector subsetting with a vector of indices (c(1:3, 7:9))
For the next examples, let’s create a vector of all even numbers between 1 and 100:
x = seq(2, 100, 2)
x
## [1] 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38
## [20] 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76
## [39] 78 80 82 84 86 88 90 92 94 96 98 100What is the meaning of the numbers in square brackets when printing the vector?
How many elements does x have?
What is the value of the last element in x?
Which of the last two expressions is preferable and why?
How can we get the entire vector using subsetting with a numeric index?
x[1:length(x)]
## [1] 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38
## [20] 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76
## [39] 78 80 82 84 86 88 90 92 94 96 98 100How can we get the entire vector except for the last element?
x[1:(length(x)-1)]
## [1] 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
## [26] 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98What
numericindex can we use to get a reversed vector?
Note that there is a special function named rev for reversing a vector:
rev(x)
## [1] 100 98 96 94 92 90 88 86 84 82 80 78 76 74 72 70 68 66 64
## [20] 62 60 58 56 54 52 50 48 46 44 42 40 38 36 34 32 30 28 26
## [39] 24 22 20 18 16 14 12 10 8 6 4 2When requesting an index beyond vector length, we get NA (Not Available). For example:
2.3.9 The recycling rule (assignment)
Earlier, we saw the recycling rule with arithmetic operators. The rule also applies to assignment. For example, here NA is replicated six times, to match the subset length 6:
Here, c(NA, 99) is replicated three times, also to match the subset length 6:
2.3.10 Logical vectors
2.3.10.1 Creating logical vectors
The third common type of vectors are logical vectors. A logical vector is composed of logical values: TRUE and FALSE. For example:
Usually, we will not be creating logical vectors manually, but through applying a logical operator on a numeric or character vector. Note how the recycling rule applies to logical operators as well:
When arithmetic operations are applied to a logical vector, the logical vector is converted to a numeric one, where TRUE becomes 1 and FALSE becomes 0. For example:
What is the meaning of the values
4and0.4in the above example?
2.3.10.2 Subsetting with logical vectors
A logical vector can be used as an index for subsetting. For example:
The logical vector counts<3 specifies whether to include each of the elements of counts in the resulting subset (Figure 2.10).
Figure 2.10: Subsetting with a logical vector
Here are some more examples of subsetting with a logical index:
What does the output
integer(0)we got in the last expression mean? Why do you think we got this result?
The next example is slightly more complex; we select the elements of z whose square is larger than 8:
Let’s go over this step-by-step. First, z^2 gives a vector of squared z values (2 is recycled):
Then, each of the squares is compared to 8 (8 is recycled):
Finally, the logical vector z^2>8 is used for subsetting z.
2.3.11 Missing values
The is.na function is used to detect missing (NA) values in a vector:
- Accepts a vector of any type
- Returns a logical vector with
TRUEin place ofNAvalues andFALSEin place of non-NAvalues
For example:
Many functions that summarize vector properties, such as sum and mean, have a parameter called na.rm. The na.rm parameter is used to determine whether NA values are excluded from the calculation. The default is na.rm=FALSE, meaning that NA values are not excluded. For example:
Why do we get
NAin the first expression?
What do you think will be the result of
length(x)?
How can we replace the
NAvalues inxwith the mean of its non-NAvalues?
2.4 Some useful functions
2.4.1 any and all
Sometimes we want to figure out whether a logical vector:
- contains at least one
TRUEvalue; or - is entirely composed of
TRUEvalues.
We can use the any and all functions, respectively, to do those things.
The any function returns TRUE if at least one of the input vector values is TRUE, otherwise it returns FALSE. For example, let’s take a numeric vector x:
The expression any(x > 5) returns TRUE, which means that the vector x > 5 contains at least one TRUE value, i.e., at least one element of x is greater than 5:
The expression any(x > 88) returns FALSE, which means that the vector x > 88 contains no TRUE values, i.e., none of the elements of x is greater than 88:
The all function returns TRUE if all of the input vector values are TRUE, otherwise it returns FALSE. For example, the expression all(x > 5) returns FALSE, which means that the vector x > 5 contains at least one FALSE value, i.e., not all elements of x are greater than 5:
The expression all(x > -1) returns TRUE, which means that x > -1 is composed entirely of TRUE values, i.e., all elements of x are greater than -1:
In a way, any and all are inverse:
anydetermines if the logical vector contains at least oneTRUEvalue.alldetermines if the logical vector contains at least oneFALSEvalue.
2.4.2 which
The which function converts a logical vector to a numeric one with the indices of TRUE values. That way, we can find out the index of values that satisfy a given condition. For example, considering the vector x:
the expression which(x > 2.3) returns the indices of TRUE elements in x > 2.3, i.e., the indices of x elements which are greater than 2.3:
2.4.3 which.min and which.max
Related functions which.min and which.max return the index of the (first!) minimal or maximal value in a vector, respectively. For example, considering the vector x:
using which.min we can find out that the minimal value of x is in the 5th position:
while using which.max we can find out that the maximal value of x is in the 2nd position:
What expression can we use to find all indices (
2,7) of the maximal value inx?
2.4.4 The order function
The order function returns ordered vector indices, based on the order of vector values. In other words, order gives the index of the smallest value, the index of the second smallest value, etc., up to the index of the largest value. For example, given the vector x:
order(x) returns the indices 1:length(x), ordered from smallest to largest value:
This result tells us that the 5th element of x is the smallest, the 6th is the second smallest, and so on.
We can also get the reverse order with decreasing=TRUE:
How can we get a sorted vector of elements from
x, as shown below, using theorderfunction?
## [1] 0 1 2 2 3 6 62.4.5 paste and paste0
The paste function is used to “paste” text values. Its sep parameter determines the separating character(s), with default sep=" " (space). For example:
paste("There are", "5", "books.")
## [1] "There are 5 books."
paste("There are", "5", "books.", sep = "_")
## [1] "There are_5_books."Non-character vectors are automatically converted to character before pasting:
The recycling rule applies in paste too:
paste("image", 1:5, ".tif", sep = "")
## [1] "image1.tif" "image2.tif" "image3.tif" "image4.tif" "image5.tif"The paste0 function is a shortcut for paste with sep="":