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Data structures
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.
Take this short quiz to determine if you need to read this chapter or not:
- What are the three properties of a vector? (apart from its contents)
- What are the four common atomic vectors? What are the two rarer atomic vectors?
- How is a list different to a vector?
- How is a matrix different to a data frame?
- Can a data frame have a column that is a list?
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 of is.vector(): for historical reasons it 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 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)))Given a vector, you can determine what type it is with typeof(), or with the specific tests: is.character(), is.double(), is.integer(), is.logical(), or, more generically, is.atomic().
Beware of 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, and returns TRUE for integers.
typeof(integer)
is.integer(integer)
is.double(integer)
is.numeric(integer)
typeof(numeric)
is.integer(numeric)
is.double(numeric)
is.numeric(numeric)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 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. If there's any possible confusion, it's usually better to explicitly coerce.
Lists are different from atomic vectors in that they can contain any other type of vector, including lists. 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 data structures 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)All objects 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() function 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(), character vector of element 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: use names(x), class(x) and dim(x), not attr(x, "names"), attr(x, "class"), and attr(x, "dim").
Atomic vectors and lists are the building blocks for higher dimensional data structures. Atomic vectors extend to matrices and arrays, and lists are used to create data frames.
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)
clength() 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"))
bc() generalises to cbind() and rbind() for matrices, and to abind::abind() for arrays.
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, even though they are implemented as vectors internally. as.matrix() and as.array() make it easy to turn an existing vector into a matrix or array.
Be careful 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)They may print similarly, but will behave differently.
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)
lA data frame is a list of equal-length vectors. 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.
You create a data frame using data.frame(), which takes named vectors as input:
df <- data.frame(x = 1:3, y = c("a", "b", "c"))
str(df)Beware the default behaviour of data.frame() to convert strings into factors. Use stringAsFactors = FALSE to suppress this behaviour:
df <- data.frame(
x = 1:3,
y = c("a", "b", "c"),
stringsAsFactors = FALSE)
str(df)Because a data frame is an S3 class, the type of a data frame reflects the underlying vector used to build it: list. Instead you can look at its class() or test for a data frame with is.data.frame():
typeof(df)
class(df)
is.data.frame(df)You can combine data frames using cbind() and rbind():
cbind(df, data.frame(y = 4))
rbind(df, data.frame(x = 10))When combining by column, the rows must match (or match with vector recycling), when combining by rows, the columns must match. If you want to combine data frames that may not have all the same rows, see plyr::rbind.fill()
It's a common mistake to try and create a data frame by cbind()ing vectors together:
bad <- data.frame(cbind(a = 1:3, b = c("a", "b", "c")))
str(bad)But this doesn't work because cbind() will create a matrix unless one of the arguments is already a data frame. The conversion rules for cbind() are complicated and best avoided by ensuring all the inputs are of the same type.
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)
dfHowever, when a list is given to data.frame(), it tries to put each item of the list into its own column, so this fails:
data.frame(x = 1:3, y = list(1:2, 1:3, 1:4))A workaround is to use I() which causes data.frame to treat the list as one unit:
data.frame(x = 1:3, y = I(list(1:2, 1:3, 1:4)))Similarly, it's also possible to have a column of a data frame that's a matrix or array, as long as the number of rows matches:
data.frame(x = 1:3, y = I(matrix(1:9, nrow = 3)))
df[2,"y"]Both list and array columns might be better avoided, since many functions that work with data frames assume that all columns are atomic vectors.
As described in the following chapter, you can subset a data frame like a 1d structure (where it behaves like a list), or a 2d structure (where it behaves like a matrix).