Data structures

Data stuctures

The table below shows the most important R data structures, organised by their dimensionality and whether they're homogeneous (all contents must be of the same type) or heterogeneous (the contents can be of different types):

	Homogenous	Heterogenous
1d	Atomic vector	List
2d	Matrix	Data frame
nd	Array

Given an arbitrary object in R, str (short for structure), is probably the most useful function: it will give a compact human readable description of any R data structure.

1d: vectors

The basic data structure in R is the vector, which comes in two basic flavours: atomic vectors and lists. Vectors have three properties: their typeof() (what it is), length() (how long it is) and attributes() (additional arbitrary metadata). The most common attribute is names().

Beware is.vector(): for historical reasons returns TRUE only if the object is a vector with no attributes apart from names. Use is.atomic(x) || is.list(x) instead.

Atomic vectors

Atomic vectors can be logical, integer, double (often called numeric), or character, or less commonly complex or raw. Atomic vectors are typically created with c:

logical <- c(T, FALSE, TRUE, FALSE)
numeric <- c(1, 2.5, 4.5)
# Note the L suffix which distinguishes numeric from integers
integer <- c(1L, 6L, 10L)
character <- c("these are", "some strings")

Atomic vectors are flat, and nesting c() just creates a flat vector:

c(1, c(2, c(3, 4)))

Types and tests

Given a vector, you can determine what type it is using typeof(), or a specific tests: is.character(), is.double(), is.integer(), is.logical(), or generically is.atomic().

Beware is.numeric(): it's a general test for the "numberliness" of a vector, not a specific test for double vectors, which are commonly called numeric. is.numeric() is an S3 generic.

typeof(integer)
is.integer(integer)
is.double(integer)
is.numeric(integer)

typeof(numeric)
is.integer(numeric)
is.double(numeric)
is.numeric(numeric)

Coercion

An atomic vector can only be of one type, so when you attempt to combine different types they will be coerced into one type, picking the first matching class from character, double, integer and logical.

c("a", 1)

When a logical vector is coerced to double or integer, TRUE becomes 1 and FALSE becomes 0. This is very useful in conjunction with sum() and mean()

c("a", T)
c(1, T, F)
# Total number of TRUEs
sum(mtcars$cyl == 4)
# Proportion of TRUEs
mean(mtcars$cyl == 4)

You can also manually force one type of vector to another using a coercion function: as.character(), as.double(), as.integer(), as.logical().

Coercion also happens automatically. Most mathematical functions (+, log, abs, etc.) will coerce to a double or integer, and most logical operations (&, |, any, etc) will coerce to a logical. You will usually get a warning message if the coercion might lose information.

Lists

Lists are different from atomic vectors in that they can contain any other type of vector. You construct them using list() instead of c()

x <- list(1:3, "a", c(T, F, T), c(2.3, 5.9))
str(x)

Lists are sometimes called recursive vectors, because a list can contain other lists. This makes them fundamentally different from atomic vectors.

x <- list(list(list(list())))
str(x)
is.recursive(x)

The typeof() a list is list, and you can test and coerce with is.list() and as.list().

Lists are used to build up most more complicated datastructures in R: both data frames (described below), and linear models are lists:

is.list(mtcars)
names(mtcars)
str(mtcars$mpg)

mod <- lm(mpg ~ wt, data = mtcars)
is.list(mod)
names(mod)
str(mod$qr)

Attributes

All object can have additional arbitrary attributes. These can be thought of as a named list (although the names must be unique). Attributes can be accessed individually with attr() or all at once (as a list) with attributes().

y <- 1:10
attr(y, "comment") <- "This is a vector"
attr(y, "comment")
str(attributes(y))

The structure() returns a new object with modified attributes:

structure(1:10, comment = "This is a vector")

By default, most attributes are lost when modifying a vector:

y + 1
y[1]
sum(y)

The exceptions are for the most common attributes:

• names()
• class(), used to implement the S3 object system.
• dim(), used to turn vectors into high-dimensional structures

When an accessor function is available, it's usually better to use that: get the names of the vector using names(x), not attr(x, "names").

Higher dimensions

Atomic vectors and lists are the building blocks for higher dimensional data structures. Atomic vectors extend to matrices anda arrays, and lists are used to create data frames.

Matrices and arrays

A vector becomes a matrix (2d) or array (>2d) with the addition of a dim() attribute. They can be created using the matrix() and array() functions, or by using the replacement form of dim():

a <- matrix(1:6, ncol = 3)
b <- array(1:12, c(2, 3, 2))

c <- 1:6
dim(c) <- c(3, 2)
c
dim(c) <- c(2, 3)
c

length() generalises to nrow() and ncol() for matrices, and dim() for arrays. names() generalises to rownames() and colnames() for matrices, and dimnames() for arrays.

length(a)
nrow(a)
ncol(a)
rownames(a) <- c("A", "B")
colnames(a) <- c("a", "b", "c")
a

length(b)
dim(b)
dimnames(b) <- list(c("one", "two"), c("a", "b", "c"), c("A", "B"))
b

You can test if an object is a matrix or array using is.matrix() and is.array(), or by looking at the length of the dim(). Because of the behaviour described above, is.vector() will return FALSE for matrices and arrays, but it is not generally a safe test. as.matrix() and as.array() make it easy to turn an existing vector into a matrix or array.

Becareful of the difference between vectors, row vectors, column vectors, and 1d arrays:

vec <- 1:3
col_vec <- matrix(1:3, ncol = 1)
row_vec <- matrix(1:3, nrow = 1)
arr <- array(1:3, 3)

While atomic vectors are most commonly turned into matrices, the dimension attribute can also be set on lists to make list-matrices or list-arrays:

l <- list(1:3, "a", T, 1.0)
dim(l) <- c(2, 2)
l

Data frames

A data frame is a list of vectors, where each vector represents a column, and must have the same length. This makes it a 2d dimensional structure, so it shares the properties of a matrix and a list.

This means that a data frame has names(), colnames() and rownames(), although names() and colnames() are the same thing. The length() of a data frame is the length of the underlying list and so is the same as ncol(), nrow() gives the number of rows.

Since a data frame is a list of vectors, it is possible for a data frame to have a column that is a list:

df <- data.frame(x = 1:3)
df$y <- list(1:2, 1:3, 1:4)
df

(Note that this is not recommended as many functions that work with data frames assume that you can not have a list in a column.)