Chapter 2 Vectors
Last updated: 2021-03-31 00:23:35
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).
For example, we can run the file volcano.R
which draws a 3D image of a volcano (Figure 2.2). The file is contained in the book materials, see Appendix A for the complete list of files and the download link.
Download the file
volcano.R
from the book materials, open it in RStudio, and run the code to produce the 3D image (Figure 2.2).
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 |
---|---|
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).
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:
= (6617747987 - 6617746521) / 10 rateEstimate
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):
rateEstimate## [1] 146.6
print(rateEstimate)
## [1] 146.6
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:
= 55
x
x## [1] 55
= "Hello"
x
x## [1] "Hello"
Note the difference between the ==
and =
operators! =
is an assignment operator:
= 1
one = 2
two = two
one
one## [1] 2
two## [1] 2
while ==
is a logical operator for comparison:
= 1
one = 2
two == two
one ## [1] FALSE
Which user-defined objects are currently in memory? The ls
function returns a character vector with their names:
ls()
Why did we write
ls()
and notls
?
2.3 Vectors
2.3.1 What is a vector?
The vector is the simplest data structure in R, and the first we learn about in this book. A vector, in R, is an ordered collection of values of the same type, such as:
- Numbers—
numeric
(numbers with a decimal point) orinteger
(whole numbers) - Text—
character
- Logical—
logical
Recall that these are the same three types of “constant values” we saw in Chapter 1. In fact, R doesn’t have a special class for individual constant values. A constant value in R is represented by a vector of length 1.
The distinction between the numeric
and integer
classes (Section 1.3.11) is not very important for our purposes. Both of these two classes are used to represent numbers, and R can convert from one another automatically, as needed. We are mentioning both only because you may encounter either one when working with numbers. In this book, we will refer to both numeric
and integer
vectors as “numeric,” for convenience.
2.3.2 The c
function
Vectors can be created with the c
function, which combines the given vectors, in the specified order. For example:
= c(1, 2, 3)
x
x## [1] 1 2 3
Note that the c
function is not restricted to combining individual values (i.e., vectors of length 1). It can be used to combine any number of vectors, of any length. For example, the following expression combines four vectors—of length 3, 1, 3 and 2—into a new vector of length 9:
c(x, 84, x, c(-1, -2))
## [1] 1 2 3 84 1 2 3 -1 -2
Here is another example of using the c
function, this time to combine four character
values into a vector of length 4:
= c("cat", "dog", "mouse", "apple")
y
y## [1] "cat" "dog" "mouse" "apple"
2.3.3 Vector subsetting (individual elements)
We can access individual vector elements using the [
operator and a numeric index. That way, we can get a subset with an individual vector element:
1]
y[## [1] "cat"
2]
y[## [1] "dog"
3]
y[## [1] "mouse"
4]
y[## [1] "apple"
Note that numeric indices in R start at 1
10!
Here is another example:
= c(2, 0, 3, 1, 3, 2, 9, 0, 2, 1, 11, 2)
counts 4]
counts[## [1] 1
Note the three components of an expression for accessing a vector element (Figure 2.6):
- The vector being subsetted
- Square brackets
- The index
We can also make an assignment into a vector subset, for example to replace an individual element:
= c(1, 2, 3)
x
x## [1] 1 2 3
2] = 300
x[
x## [1] 1 300 3
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 numerous functions for calculating vector properties in R. The length
, min
, max
, range
, mean
and sum
are most commonly used. For example:
= c(1, 6, 3, -8, 2)
x
x## [1] 1 6 3 -8 2
length(x) # Number of elements
## [1] 5
min(x) # Minimum
## [1] -8
max(x) # Maximum
## [1] 6
range(x) # Minimum and maximum
## [1] -8 6
mean(x) # Average
## [1] 0.8
sum(x) # Sum
## [1] 4
In what way is the
range
function different from the other functions shown above?
Contrariwise, there are functions that operate on each vector element, separately, returning a vector of results having the same length as the input:
abs(x) # Absolute value
## [1] 1 6 3 8 2
sqrt(x) # Square root
## Warning in sqrt(x): NaNs produced
## [1] 1.000000 2.449490 1.732051 NaN 1.414214
Why does the output of
sqrt(x)
containNaN
?
Note that the last expression produced a warning. A warning, in R, signals to the user that something suspicious or notable has happened. A warning differs from an error (Section 1.3.7) in that the when a warning is raised, the expression is executed nevertheless. However, when an error is raised, code evaluation stops and the expression is not executed by the interpreter.
2.3.5 The recycling rule (arithmetic)
Binary operations, such as arithmetic (Section 1.3.2) and conditional (Section 1.3.4) operators, when applied on two vectors, are done element-by-element. The result is, then, a vector of the respective results:
c(11, 2, 3) + c(10, 20, 30)
## [1] 21 22 33
c(11, 2, 3) * c(10, 20, 30)
## [1] 110 40 90
c(11, 2, 3) > c(10, 20, 30)
## [1] TRUE FALSE FALSE
c(11, 2, 3) < c(10, 20, 30)
## [1] FALSE TRUE TRUE
What happens when the input vector lengths do not match? In such case, 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 two times, until it matches the longer vector (Figure 2.7). Thus, the expression:
c(1, 2, 3) + c(1, 2, 3, 4, 5, 6)
## [1] 2 4 6 5 7 9
is equivalent to the expression:
c(1, 2, 3, 1, 2, 3) + c(1, 2, 3, 4, 5, 6)
## [1] 2 4 6 5 7 9
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:
2 * c(1, 2, 3, 4)
## [1] 2 4 6 8
c(2, 2, 2, 2) * c(1, 2, 3, 4)
## [1] 2 4 6 8
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:
c(10, 100) + c(1, 2, 3, 4, 5, 6)
## [1] 11 102 13 104 15 106
c(10, 100, 10, 100, 10, 100) + c(1, 2, 3, 4, 5, 6)
## [1] 11 102 13 104 15 106
What happens when the longer vector length is not a multiple of the shorter vector length? In such case, recycling is “incomplete,” as indicated by a warning message:
c(1, 2) * c(1, 2, 3)
## Warning in c(1, 2) * c(1, 2, 3): longer object length is not a multiple of
## shorter object length
## [1] 1 4 3
c(1, 2, 1) * c(1, 2, 3)
## [1] 1 4 3
Incomplete recycling is rarely something we want to do in practice. Therefore, the latter warning is usually an indication of something wrong in our code.
2.3.6 Consecutive and repetitive vectors
2.3.6.1 Introduction
Other than the c
function (Section 2.3.2), there are three commonly used methods for creating consecutive or repetitive vectors:
2.3.6.2 Consecutive vectors
The :
operator is used to create a vector of consecutive values in steps of 1
:
1:10
## [1] 1 2 3 4 5 6 7 8 9 10
or in steps of -1
:
55:43
## [1] 55 54 53 52 51 50 49 48 47 46 45 44 43
The seq
function provides a more general way to create a consecutive vector with any step size, not necessarily 1
or -1
. The three most useful parameters of the seq
function are:
from
—Where to startto
—When to endby
—Step size
For example:
seq(from = 100, to = 150, by = 10)
## [1] 100 110 120 130 140 150
seq(from = 100, to = 80, by = -5)
## [1] 100 95 90 85 80
The above examples of the seq
function are the first case we encounter where more than one argument is passed to a function as part of a function call (Section 1.3.6). You may also have noticed that the arguments are named. We are going to elaborate on the syntax rules of using more than one argument, in a function call in R, in a moment (Section 2.3.7).
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 replicate
For example:
rep(x = 22, times = 10)
## [1] 22 22 22 22 22 22 22 22 22 22
rep(x = c(18, 0, 9), times = 3)
## [1] 18 0 9 18 0 9 18 0 9
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. For example, the following two function calls are identical, because the default order of the (first three) seq
function parameters is from
, to
and by
:
seq(from = 5, to = 10, by = 1)
## [1] 5 6 7 8 9 10
seq(5, 10, 1)
## [1] 5 6 7 8 9 10
Second, we can use any argument order as long as parameter names are specified. The following three function calls are identical, even though argument order is not the same, since the arguments are named:
seq(to = 10, by = 1, from = 5)
## [1] 5 6 7 8 9 10
seq(by = 1, from = 5, to = 10)
## [1] 5 6 7 8 9 10
seq(from = 5, by = 1, to = 10)
## [1] 5 6 7 8 9 10
Third, we can omit parameters that have a default argument, specified as part of the function definition. For example, the by
parameter of seq
has a default value of 1
:
seq(5, 10, 1)
## [1] 5 6 7 8 9 10
seq(5, 10)
## [1] 5 6 7 8 9 10
The parameters of a particular function, their order, and their default values (if any), can be found in the help file of every function (Section 1.3.12):
?seq
2.3.8 Vector subsetting (general)
So far, we created vector subsets using a numeric
index which consists of a single value (Section 2.3.3), as in:
= c(43, 85, 10)
x 3]
x[## [1] 10
We can also use a vector of length >1 as an index. For example, the following expression returns the first and second elements of x
, since the index is the the vector c(1,2)
(which we create using the :
operator) (Section 2.3.6.2):
1:2]
x[## [1] 43 85
Note that the vector of indices can consist of any combination of indices whatsoever. It does not have to be consecutive, and it can even include repetitions:
c(1, 1, 3, 2)]
x[## [1] 43 43 10 85
Here is another example (Figure 2.8):
= c(2, 0, 3, 1, 3)
counts 1:3]
counts[## [1] 2 0 3
And here is one more example where the index is not consecutive (Figure 2.9):
= c(2, 0, 3, 1, 3, 2, 9, 0, 2, 1, 11, 2)
counts c(1:3, 7:9)]
counts[## [1] 2 0 3 9 0 2
For the next examples, let’s create a vector of all even numbers between 1 and 100:
= seq(2, 100, 2)
x
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 98 100
What is the meaning of the numbers in square brackets when printing the vector?
How can we check how many elements does x
have? Recall the length
function (Section 2.3.4):
length(x)
## [1] 50
Using this knowledge, here are two expression that return the value of the last element in x
:
50]
x[## [1] 100
length(x)]
x[## [1] 100
Which of the last two expressions is preferable? Why?
Which index can we use to get back the entire vector? We can use an index that contains all of the vector element indices, starting from 1
and up to length(x)
:
1:length(x)]
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 98 100
What index can we use to get the entire vector except for the last two elements?
What index 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 2
Note that, when requesting an element, or elements, beyond the vector length, we get NA
(Not Available) value(s). For example:
55]
x[## [1] NA
1:80]
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 98 100 NA NA NA NA NA NA NA
## [58] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [77] NA NA NA NA
2.3.9 The recycling rule (assignment)
Earlier, we saw how the recycling rule applies to arithmetic and conditional operators (Section 2.3.5). The rule also applies to assignment.
For example, here we assign a vector of length 1 (NA
) into a subset of length 6 (c(1:3,7:9)
). As a result, NA
is replicated six times, to match the subset:
= c(2, 0, 3, 1, 3, 2, 9, 0, 2, 1, 11, 2)
counts
counts## [1] 2 0 3 1 3 2 9 0 2 1 11 2
c(1:3, 7:9)] = NA
counts[
counts## [1] NA NA NA 1 3 2 NA NA NA 1 11 2
Here, c(NA,99)
is replicated three times, also to match the subset of length 6:
c(1:3, 7:9)] = c(NA, 99)
counts[
counts## [1] NA 99 NA 1 3 2 99 NA 99 1 11 2
2.3.10 Logical vectors
2.3.10.1 Creating logical vectors
The third common type of vectors, in addition to numeric
and character
vectors, are logical
vectors. A logical vector is composed of logical
values (Section 1.3.4), TRUE
and FALSE
(or NA
). For example:
c(TRUE, FALSE, FALSE)
## [1] TRUE FALSE FALSE
rep(TRUE, 7)
## [1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE
Usually, we will not be creating logical
vectors manually, but through applying a conditional operator (Section 1.3.4) on a numeric
or character
vector. For example:
= 1:10
x
x## [1] 1 2 3 4 5 6 7 8 9 10
>= 7
x ## [1] FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE TRUE TRUE
Note how the recycling rule applies to conditional operators in the above expression.
An important property of logical
vectors is, that, when arithmetic operations are applied, the logical
vector is automatically converted to a numeric one, where TRUE
becomes 1
and FALSE
becomes 0
. For example:
TRUE + FALSE
## [1] 1
sum(x >= 7)
## [1] 4
mean(x >= 7)
## [1] 0.4
What is the meaning of the values
4
and0.4
in the above example?
2.3.10.2 Subsetting with logical vectors
So far, we used a numeric vector of indices when subsetting a vector (Sections 2.3.3 and 2.3.8). A logical
vector can also be used as an index for subsetting. When using a logical
vector of indices, the subset contains those elements which are in the same positions as the TRUE
elements in the index. This means that the logical
vector of indices needs to match the length of the vector being subsetted. If this is not the case, the logical
vector is recycled.
For example:
= c(2, 0, 3, 1, 3) counts
c(TRUE, FALSE, TRUE, FALSE, FALSE)]
counts[## [1] 2 3
Here is another example, where the logical
vector of indices is created from the same vector being subsetted:
< 3]
counts[counts ## [1] 2 0 1
In this example, the logical vector counts<3
:
< 3
counts ## [1] TRUE TRUE FALSE TRUE FALSE
specifies whether to include each of the elements of counts
in the resulting subset (Figure 2.10).
What does the expression
counts[counts<3]
do, in plain language?
Here are some more examples of subsetting with a logical
index:
= 1:10
x
x## [1] 1 2 3 4 5 6 7 8 9 10
>= 3] # Elements of 'x' greater or equal than 3
x[x ## [1] 3 4 5 6 7 8 9 10
!= 2] # Elements of 'x' not equal to 2
x[x ## [1] 1 3 4 5 6 7 8 9 10
> 4 | x < 2] # Elements of 'x' greater than 4 or smaller than 2
x[x ## [1] 1 5 6 7 8 9 10
> 4 & x < 2] # Elements of 'x' greater than 4 and smaller than 2
x[x ## integer(0)
What does the output
integer(0)
, which we got in the last expression, mean?
The next example is slightly more complex; we select the elements of z
whose square is larger than 8:
= c(5, 2, -3, 8)
z ^2 > 8]
z[z## [1] 5 -3 8
Let’s go over this step-by-step. First, z^2
gives a vector of squared z
values (2
is recycled):
^2
z## [1] 25 4 9 64
Then, each of the squares is compared to 8 (8
is recycled):
^2 > 8
z## [1] TRUE FALSE TRUE TRUE
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 (Section 1.3.5) in a vector. It
- accepts a vector, of any type, and
- returns a
logical
vector, withTRUE
in place ofNA
values andFALSE
in place of non-NA
values.
For example, suppose we have a vector x
where some of the values are missing:
= c(28, 58, NA, 31, 39, NA, 9)
x
x## [1] 28 58 NA 31 39 NA 9
The is.na
function can be used to detect which values are missing:
is.na(x)
## [1] FALSE FALSE TRUE FALSE FALSE TRUE FALSE
How can we use the above expression to subset the non-missing values of
x
?
Many of the functions that summarize vector properties (Section 2.3.4), 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:
= c(28, 58, NA, 31, 39, NA, 9)
x mean(x)
## [1] NA
mean(x, na.rm = TRUE)
## [1] 33
Why do we get
NA
in the first expression?
What do you think will be the result of
length(x)
?
How can we replace the
NA
values inx
with the mean of its non-NA
values?
2.4 Additional useful functions
2.4.1 any
and all
Sometimes we want to figure out whether a logical
vector:
- contains at least one
TRUE
value; or - is entirely composed of
TRUE
values.
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
:
= c(2, 6, 2, 3, 0, 1, 6)
x
x## [1] 2 6 2 3 0 1 6
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
:
> 5
x ## [1] FALSE TRUE FALSE FALSE FALSE FALSE TRUE
any(x > 5)
## [1] TRUE
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
are greater than 88
:
> 88
x ## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE
any(x > 88)
## [1] FALSE
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
:
> 5
x ## [1] FALSE TRUE FALSE FALSE FALSE FALSE TRUE
all(x > 5)
## [1] FALSE
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
:
> -1
x ## [1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE
all(x > -1)
## [1] TRUE
In a way, any
and all
are inverse:
any
determines if the logical vector contains at least oneTRUE
value.all
determines if the logical vector contains at least oneFALSE
value.
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
:
x## [1] 2 6 2 3 0 1 6
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
:
> 2.3
x ## [1] FALSE TRUE FALSE TRUE FALSE FALSE TRUE
which(x > 2.3)
## [1] 2 4 7
2.4.3 which.min
and which.max
Related to which
(Section 2.4.2) are functions which.min
and which.max
. The latter two functions return the index of the (first!) minimal or maximal value in a vector, respectively. For example, considering the vector x
:
x## [1] 2 6 2 3 0 1 6
using which.min
we can find out that the minimal value of x
is in the 5th position:
which.min(x)
## [1] 5
while using which.max
we can find out that the maximal value of x
is in the 2nd position:
which.max(x)
## [1] 2
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
:
x## [1] 2 6 2 3 0 1 6
order(x)
returns the indices 1:length(x)
, ordered from smallest to largest value:
order(x)
## [1] 5 6 1 3 4 2 7
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
:
order(x, decreasing = TRUE)
## [1] 2 7 4 1 3 6 5
How can we get a sorted vector of elements from
x
, as shown below, using theorder
function?
## [1] 0 1 2 2 3 6 6
2.4.5 paste
and paste0
The paste
function is used to “paste” text values. Its sep
parameter determines the separating character(s), with the default being sep=" "
(a 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:
paste("There are", 80, "books.")
## [1] "There are 80 books."
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=""
:
paste0("image", 1:5, ".tif")
## [1] "image1.tif" "image2.tif" "image3.tif" "image4.tif" "image5.tif"
Unlike Python and C, and many other programming languages, where numeric indices start at 0.↩︎