Lists

The most flexible of structures

Last Time

1. Comments mark text that R will not evaluate.
2. Subsetting can be used to change a vector in place.
3. A matrix is a vector with a dimension attribute.
4. Matrices are subset by [row, col] or by [el].
5. Row- and column-wise summaries operate on whole margins.

Key Ideas for Today

1. A list is a non-atomic vector: types can be mixed.
2. [] subsets a list and returns a list.
3. [[ ]] and $ return the object inside the list.
4. Lists can nest, so subsetting can be chained.
5. $ allows subsetting by name.

Concept Acquisition

1. Atomic means one type and no nesting; lists relax both restrictions.
2. A list is still a vector: it has a length and an order.
3. [] preserves the container; [[ ]] and $ extract the contents.
4. Elements of a list can be named, and named lists can be subset by name.
5. Lists can contain lists, which is what makes them a recursive structure.

Tool Acquisition

1. list(), length(), typeof().
2. x[i], x[-i], x[c("a", "b")], x[log_vec].
3. x[[i]], x$name.
4. str() for peering into nested lists.

Concept Application

1. Predict whether an expression returns a list or the object inside it.
2. Draw the train diagram for a given subsetting expression.
3. Write the shortest expression that extracts a value from a nested list.

One more way to subset a vector…

x <- 1:3
x[-2]

[1] 1 3

Negative indexing will drop that element (or set of elements) from the vector.

Discuss with a neighbor

Which of the following four objects are the same?

seq(1, 6)
seq(1, 3) + seq(4, 6)
c(seq(1, 3), seq(4, 6))
c(c(seq(1, 3), seq(4, 6)))

01:30

Draw attention to why the last two are the same: c() flattens, so nesting c() inside c() buys you nothing. That is the constraint we relax today.

Discuss with a neighbor

Which of the following four objects are the same?

seq(1, 6)

[1] 1 2 3 4 5 6

seq(1, 3) + seq(4, 6)

[1] 5 7 9

c(seq(1, 3), seq(4, 6))

[1] 1 2 3 4 5 6

c(c(seq(1, 3), seq(4, 6)))

[1] 1 2 3 4 5 6

Atomic Vectors

By atomic we mean:

1. All elements of the same type
2. Cannot contain other vectors

On the board: the row of boxes from two lectures ago, with a note under it listing the two restrictions. Today we cross both of them out.

Introducing Lists

Lists, defined

List

A non-atomic vector that can contain atomic vectors of different types, as well as other lists. Created with list().

list(1, "rabbit")

[[1]]
[1] 1

[[2]]
[1] "rabbit"

Read the printed output together — the [[1]] and [[2]] headers are new, and they are the first hint that a list element is a container rather than a value.

“Contains atomic vectors of different types”

list(1, "rabbit")

[[1]]
[1] 1

[[2]]
[1] "rabbit"

list(1:3, "a", 4:6)

[[1]]
[1] 1 2 3

[[2]]
[1] "a"

[[3]]
[1] 4 5 6

Ask for length() of the right-hand list before running it. Three, not seven — each element is one slot no matter how much it holds. That is the idea the train metaphor will make concrete.

Subsetting with []

Subsetting with []

[] extracts elements of a vector (atomic or non-atomic) using a subsetting (atomic) vector.

• Atomic vectors and matrices return atomic vectors

vec <- 1:4
vec[1:2]

[1] 1 2

mat <- matrix(vec, nrow = 2)
mat

     [,1] [,2]
[1,]    1    3
[2,]    2    4

mat[2]

[1] 2

Subsetting with []

[] extracts elements of a vector (atomic or non-atomic) using a subsetting (atomic) vector.

• Atomic vectors and matrices return atomic vectors
• Lists return lists

x <- list(1:3, "a", 4:6)
x[1]

[[1]]
[1] 1 2 3

x[2:3]

[[1]]
[1] "a"

[[2]]
[1] 4 5 6

The key line is x[1]: it returns a list of length one, not the vector 1:3. Everything students know about subsetting vectors still applies — index, negative index, name, logical — the only new thing is what comes back.

Yes, you can name elements of a list

named_x <- list("Ape" = 1:3, "Boy" = "a", "Cat" = 4:6)
named_x

$Ape
[1] 1 2 3

$Boy
[1] "a"

$Cat
[1] 4 5 6

named_x[c("Boy", "Cat")]

$Boy
[1] "a"

$Cat
[1] 4 5 6

Yes, it works with logicals too

named_x[c(FALSE, TRUE, FALSE)]

$Boy
[1] "a"

But what if you want the actual data structure inside the list?

Subsetting with [[ ]]

Subsetting single elements with [[ ]]

[[i]] extracts the original object inside the list.

x <- list(1:3, "a", 4:6)
x[[1]]

[1] 1 2 3

To tell [] and [[ ]] apart, let’s use a metaphor of a train.

Sketch first of the following image slides.

Guess the metaphor

A list is like a train: an ordered line of cars, each holding cargo of whatever kind. [] gives you back a train; [[ ]] gives you the cargo.

Draw the appropriate train or car for each of the following

1. x[1:2]
2. x[[3]]
3. x[-2]
4. x[c(1, 1)]
5. c(x[[3]], x[[1]])

02:30

Subsetting with $

Subsetting single elements with $

$ will extract a single element of a list by name.

named_x <- list("Ape" = 1:3, "Boy" = "a", "Cat" = 4:6)
named_x$Cat

[1] 4 5 6

named_x$C

[1] 4 5 6

Permits partial matching.

Partial matching is convenient at the console and dangerous in a script: adding an element named Cow later would break named_x$C. [[ ]] requires the full name, which is why it is the safer choice in saved code.

Nesting

Lists, defined

A list is a non-atomic vector that can contain:

1. Atomic vectors of different types
2. Other lists

list(1, "rabbit", list(TRUE, 1:3))

[[1]]
[1] 1

[[2]]
[1] "rabbit"

[[3]]
[[3]][[1]]
[1] TRUE

[[3]][[2]]
[1] 1 2 3

Point at the nested [[3]][[1]] labels in the printed output. R is telling you the path you would type to get there.

Implications for subsetting

y <- list(1, "rabbit", list(TRUE, 1:3))

Draw the train:

Drop:

1. length(y[3]) vs. length(y[[3]])

Your Turn

y <- list(1, "rabbit", list(TRUE, 1:3))

Draw the train, then write the R code to extract:

1. The list containing the character vector with "rabbit"
2. The vector "rabbit"
3. The second element of the list element in y
4. The vector 1:3
5. The element 2

02:00

The last one is trickiest: y[[3]][[2]][2] chains all three operations.

Key Ideas for Today

1. A list is a non-atomic vector: types can be mixed.
2. [] subsets a list and returns a list.
3. [[ ]] and $ return the object inside the list.
4. Lists can nest, so subsetting can be chained.
5. $ matches by name, and permits partial matching.

For Next Time

1. Good luck on Quiz 1!
2. Work through the lists questions on the problem set.
3. Work through Project 1: Sampson’s Monks.
4. Read Advanced R, Ch. 3.3.

References

• Train diagrams from Advanced R by Hadley Wickham.