# Vector Indexing

An important aspect of working with R objects is knowing how to “index” them Indexing means selecting a subset of the elements in order to use them in further analysis or possibly change them Here we focus just on three kinds of vector indexing: positional, named reference, and logical Any of these indexing techniques works the same for all classes of vectors

## Positional indexing

If we start with a simple vector, we can extract each element from the vector by placing its position in brackets:

c("a", "b", "c")[1]

## [1] "a"

c("a", "b", "c")[2]

## [1] "b"

c("a", "b", "c")[3]

## [1] "c"


Indices in R start at 1 for the first item in the vector and continue up to the length of the vector. (Note: In some languages, indices start with the first item being indexed as 0.) This means that we can even index a one-element vector:

4[1]

## [1] 4


But, we will get a missing value if we try to index outside the length of a vector:

length(c(1:3))

## [1] 3

c(1:3)[9]

## [1] NA


Positional indices can also involve an R expression For example, you may want to extract the last element of a vector of unknown length To do that, you can embed the length function in the the [] brackets.

a <- 4:12
a[length(a)]

## [1] 12


Or, you can express any other R expression, for example to get the second-to-last element:

a[length(a) - 1]

## [1] 11


It is also possible to extra multiple elements from a vector, such as the first two elements:

a[1:2]

## [1] 4 5


You can use any vector of element positions:

a[c(1, 3, 5)]

## [1] 4 6 8


This means that you could also return the same element multiple times:

a[c(1, 1, 1, 2, 2, 1)]

## [1] 4 4 4 5 5 4


But note that positions outside of the length of vector will be returned as missing values:

a[c(5, 25, 26)]

## [1]  8 NA NA


It is also possible to index a vector, less a vector of specified elements, using the - symbol For example, to get all elements except the first, on could simply index with -1:

a[-1]

## [1]  5  6  7  8  9 10 11 12


Or, to obtain all elements except the last element, we can combine - with length:

a[-length(a)]

## [1]  4  5  6  7  8  9 10 11


Or, to obtain all elements except the second and third:

a[-c(2, 3)]

## [1]  4  7  8  9 10 11 12


Note: While in general 2:3 is the same as c(2,3), this is not the case in indexing

## Named indexing

A second approach to indexing that is not particularly common for vectors is named indexing Vector elements can assigned names, such that each element has a value but also a name attached to it:

b <- c(x = 1, y = 2, z = "4")
b

##   x   y   z
## "1" "2" "4"


This is the same as:

b <- c(x = 1, y = 2, z = "4")
b

##   x   y   z
## "1" "2" "4"


In this type of vector we can still use positional indexing:

b[1]

##   x
## "1"


But we can also index based on the names of the vector elements:

b["x"]

##   x
## "1"


And, just with positional indexing, we can extract multiple elements at once:

b[c("x", "z")]

##   x   z
## "1" "4"


But, it's not possible to use the - indexing that we used with element positions. For example, b[-'x'] would return an error. If a vector has names, this provides a way to extract elements without knowing their relative position in the order of vector elements. If you want to know which name is in which position, we can also get just the names of the vector elements:

names(b)

## [1] "x" "y" "z"


And we can use positional indexing on the names(b) vector, e.g. to get the first element's name:

names(b)[1]

## [1] "x"


## Logical indexing

The final way to index a vector involves logicals. Positional indexing allowed us to use any R expression to extract one or more elements. Logical indexing allows us to extract elements that meet specified criteria, as specified by an R logical expression. Thus, with a given vector, we could, for example, extract elements that are equal to a particular value:

c <- 10:3
c[c == 5]

## [1] 5


This works by first constructing a logical vector and then using that to return elements where the logical is TRUE:

c == 5

## [1] FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE

c[c == 5]

## [1] 5


We can use an exclamation point (!) to negate the logical and thus return an opposite set of vector elements This is similar to the - indexing from positional indexing:

!c == 5

## [1]  TRUE  TRUE  TRUE  TRUE  TRUE FALSE  TRUE  TRUE

c[!c == 5]

## [1] 10  9  8  7  6  4  3


We do not need to restrict ourselves to logical equivalences. We can also use other comparators:

c[c > 5]

## [1] 10  9  8  7  6

c[c <= 7]

## [1] 7 6 5 4 3


We can also use boolean operators (i.e., AND &, OR |) to combine multiple criteria:

c < 9 & c > 4

## [1] FALSE FALSE  TRUE  TRUE  TRUE  TRUE FALSE FALSE

c[c < 9 & c > 4]

## [1] 8 7 6 5

c > 8 | c == 3

## [1]  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE  TRUE

c[c > 8 | c == 3]

## [1] 10  9  3


Here we can see how different logical criteria translate into a logical vector that is then used to index our target vector Some potentially unexpected behavior can happen if we try to index with a logical vector of a different length than our target vector:

c[TRUE]  #' returns all elements

## [1] 10  9  8  7  6  5  4  3

c[c(TRUE, TRUE)]  #' returns all elements

## [1] 10  9  8  7  6  5  4  3

c[FALSE]  #' returns an empty vector

## integer(0)


Just with positional indexing, if the logical vector is longer than our target vector, missing values will be appended to the end:

d <- 1:3
d[c(TRUE, TRUE, TRUE, TRUE)]

## [1]  1  2  3 NA


Because 0 and 1 values can be coerced to logicals, we can also use some shorthand to get the same indices as logical values:

as.logical(c(1, 1, 0))

## [1]  TRUE  TRUE FALSE

d[c(TRUE, TRUE, FALSE)]

## [1] 1 2

d[as.logical(c(1, 1, 0))]

## [1] 1 2


## Blank index

Note: A blank index like e[] is treated specially in R. It refers to all elements in a vector.

e <- 1:10
e[]

##  [1]  1  2  3  4  5  6  7  8  9 10


This is of course redundant to just saying e, but might produce unexpected results during assignment:

e[] <- 0
e

##  [1] 0 0 0 0 0 0 0 0 0 0


This replaces all values of e with 0, which may or may not be intended.