Data-structures.rmd

---
title: Data structures
layout: default
---

# Data structures

This chapter summarises the most important data structures in base R. I assume you've used many (if not all) of them before, but you may not have thought deeply about how they are interrelated.  It is a brief overview: the goal is not to discuss individual types in depth, but to show how they fit together as a whole. I also expect that you'll read the documentation if you want more details on any of the specific functions used in the chapter.

R's base data structures are summarised in the table below, 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):

|    | Homogeneous   | Heterogeneous |
|----|---------------|---------------|
| 1d | Atomic vector | List          |
| 2d | Matrix        | Data frame    |
| nd | Array         |               |

Note that R has no scalar, or 0-dimensional, types. All scalars (single numbers or strings) are length-one vectors.

Almost all other objects in R are built upon these foundations, and in the [OO field guide](OO-essentials.html) you'll see how R's object oriented tools build on top of these basics. There are also a few types of more esoteric objects that I don't describe here, but you'll learn about in depth in other parts of the book:

* [functions](Functions.html), including closures and promises
* [environments](Environments.html) 
* names/symbols, calls and expression objects, for [metaprogramming](metaprogramming.html)

When trying to understand the structure of an arbitrary object in R your most important tool is `str()`, short for structure: it gives a compact human readable description of any R data structure.

The chapter starts by describing R's 1d structures (atomic vectors and lists), then detours to discuss attributes (R's flexible metadata specification) and factors, before returning to discuss high-d structures (matrices, arrays and data frames).

## Quiz

Take this short quiz to determine if you need to read this chapter. If you can bring the answers to mind quickly, you can comfortably skip this chapter.

* What are the three properties of a vector? (apart from its contents)
* What are the four common types of atomic vector? What are the two rarer types?
* What are attributes? How do you get and set them?
* How is a list different to a vector?
* How is a matrix different to a data frame?
* Can you have a list that is a matrix?
* Can a data frame have a column that is a list?

## Vectors

The basic data structure in R is the vector, which comes in two basic flavours: atomic vectors and lists. They differ in their content: the contents of an atomic  vector must all be the same type, the contents of a list can have different types. As well as their content, vectors have three properties: `typeof()` (what it is), `length()` (how long it is) and `attributes()` (additional arbitrary metadata). The most common attribute is `names()`.

Each type of vector comes with an `as.*` coercion function and an `is.*` testing function. But beware `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)` to test if an object is actually a vector.

### Atomic vectors

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

```{r}
numeric <- c(1, 2.5, 4.5)
# Note the L suffix distinguishes doubles from integers
integer <- c(1L, 6L, 10L)
# Use T and F or TRUE and FALSE to create logical vectors 
logical <- c(T, FALSE, TRUE, FALSE)
character <- c("these are", "some strings")
```

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

```{r}
c(1, c(2, c(3, 4)))
# the same as 
c(1, 2, 3, 4)
```

Missing values are specified with `NA`, which is a logical vector of length 1. `NA` will always be coerced to the correct type with `c()`, or you can use create NA's of specific types with `NA_real_` (double), `NA_integer_` and `NA_character_`.

#### Types and tests

Given a vector, you can determine what type it is with `typeof()`, or with a specific test: `is.character()`, `is.double()`, `is.integer()`, `is.logical()`, or, more generally, `is.atomic()`.  

NB: `is.numeric()` which is a general test for the "numberliness" of a vector, not a specific test for double vectors, which are often called numeric. It returns `TRUE` for integers:

```{r}
integer <- c(1L, 6L, 10L)
typeof(integer)
is.integer(integer)
is.double(integer)
is.numeric(integer)

numeric <- c(1, 2.5, 4.5)
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 present type from character, double, integer and logical.

```{r}
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()`

```{r}
as.numeric(c(F, F, T))
# 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 often 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 confusion is likely, it's better to explicitly coerce.

### Lists

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()`.

```{r}
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.

```{r}
x <- list(list(list(list())))
str(x)
is.recursive(x)
```

`c()` will combine several lists into one. If given a combination of atomic vectors and lists, c() will coerce the vectors to list before combining them. Compare the results of `list()` and `c()`:

```{r}
x <- list(list(1, 2), c(3, 4))
y <- c(list(1, 2), c(3, 4))
str(x)
str(y)
```

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

Lists are used to build up many of the more complicated data structures in R: both data frames (described below), and linear models (as produced by `lm()`) are lists:

```{r}
is.list(mtcars)
names(mtcars)
str(mtcars$mpg)

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

You can turn a list back into an atomic vector using `unlist()`: this uses the same implicit coercion rules as for `c()`.

### Exercises

1. What are the six types of atomic vectors? How does a list differ from an 
   atomic vector?
   
2. What makes `is.vector()` and `is.numeric()` fundamentally different to 
   `is.list()` and `is.character()`?
   
3. Test your knowledge of vector coercion rules by predicting the output of
   the following uses of `c()`:
   
    ```{r}
    c(1, F)
    c("a", 1)
    c(list(1), "a")
    c(T, 1L)    
    ```
    
4. Why is `1 == "1"` true? Why is `-1 < 0` true? Why is `"one" < 2` false?

5. Why is the default (and shortest) `NA` a logical vector? What's special
   about logical vectors?

## Attributes

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

```{r}
y <- 1:10
attr(y, "my_attribute") <- "This is a vector"
attr(y, "my_attribute")
str(attributes(y))
```

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

```{r}
structure(1:10, my_attribute = "This is a vector")
```

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

```{r}
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, described in the next section.
* `dim()`, used to turn vectors into high-dimensional structures

You should always get and get these attributes with their accessor functions: use `names(x)`, `class(x)` and `dim(x)`, not `attr(x, "names")`, `attr(x, "class")`, and `attr(x, "dim")`.

#### Names

You can give a vector names in three ways:

* During creation: `x <- c(a = 1, b = 2, c = 3)`
* By modifying a vector in place: `x <- 1:3; names(x) <- c("a", "b", "c")`
* By creating a modified vector: `x <- setNames(1:3, c("a", "b", "c"))`

Names should be unique, because character subsetting (see [subsetting](Subsetting.html)), the biggest reason to use names, will only return the first match.

Not all elements of a vector have to have names. If some names are missing, `names()` will return an empty string for those elements. If all names are missing, `names()` will return NULL.

```{r}
y <- c(a = 1, 2, 3)
names(y)

z <- c(1, 2, 3)
names(z)
```

You can create a vector without names using `unname(x)`, or remove names in place with `names(x) <- NULL`.

### Factors

The factor is a vector that can contain only predefined values, and is R's structure for dealing with qualitative data. A factor is not a basic vector, but is build on top of an integer vector using the S3 class system, as described in the [OO-field-guide.html#s3]. Factors have two key attributes: their `class()`, "factor", which controls their behaviour; and their `levels()`, the set of allowed values.

```{r}
x <- factor(c("a", "b", "b", "a"))
x
class(x)
levels(x)

# You can't use values not in levels
x[2] <- "c"
x

# NB: you can't combine factors
c(factor("a"), factor("b"))
```

While factors look (and often behave) like character vectors, they are actually integers under the hood, and you need to be careful when treating them like strings. Some string methods (like `gsub()` and `grepl()`) will coerce factors to strings, while others (like `nchar()`) will throw an error, and still others will use the underlying integer ids (like `c()`). For this reason, it's usually best to explicitly convert factors to strings when modifying their levels.

Factors are useful when you know the possible values a variable may take, even if you don't see them in the dataset. Using a factor instead of a character vector makes it obvious when some groups contain no observations:

```{r}
sex_char <- c("m", "m", "m")
sex_factor <- factor(sex_char, levels = c("m", "f"))

table(sex_char)
table(sex_factor)
```

Someimes when you read a data frame from a file, a column you'd thought would be numeric is actually a factor, with the numeric values appearing in the levels. This is caused by a non-numeric value in that column, often from a non-standard missing value. To remedy this you have two options. The best option is to discover what caused the problem and fix it in your data loading code (often by using the `na.value` argument to `read.csv()`). If you can't do that, you'll need to first coerce the factor to a character vector and then to numeric:

```{r}
z <- factor(c(12, 1, 9))
# Oops, that's not right
as.numeric(z)
# Perfect :)
as.numeric(as.character(z))
```

Unfortunately, most data loading functions in R automatically convert character vectors to factors. This is suboptimal, because there's no way for those functions to know the set of all possible levels and their optimal order. Instead, use the argument `stringsAsFactors = FALSE` to suppress this behaviour, and then manually convert character vectors to factors using your knowledge of the data. A global option (`options(stringsAsFactors = FALSE`) is available to control this behaviour, but it's not recommended - it may have unexpected consequences when combined with other code (either from packages, or code that you're `source()`ing.) In early versions of R, there was a memory advantage to using factors; that is no longer the case.

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.

### Exercises

* An early draft used this code to illustrate `structure()`:

    ```{r}
    structure(1:5, comment = "my attribute")
    ```
    
    But when you print that object you don't see the comment attribute.
    Why? Is the attribute missing, or is there something else special about
    it? (Hint: try using help)

## 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()`:

```{r}
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.

```{r}
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
```

`c()` 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()` (NB: `dim()` returns `NULL` when applied to a vector). `as.matrix()` and `as.array()` make it easy to turn an existing vector into a matrix or array.

Beware that there are a few different ways to create a 1d datastructure: you can have a vector, row vector, column vector, or a 1d array. They may print similarly, but will behave differently. As always, use `str()` to reveal the differences.

```{r}
str(list(
  vector = 1:3,
  col_vector = matrix(1:3, ncol = 1),
  row_vector = matrix(1:3, nrow = 1),
  array = 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:

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

These are relatively esoteric data structures, but can be useful if you want to arrange objects into a grid-like structure. For example, if you're running models on a spatio-temporal grid, it might be natural to preserve the grid structure by storing the models in a 3d array.

## Data frames

A data frame is the most common way of storing data in R, and if [used systematically](http://vita.had.co.nz/papers/tidy-data.pdf) make data analysis easier. Under the hood, a data frame is a list of equal-length vectors. This makes it a 2d dimensional structure, so it shares properties of both the matrix and the 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.

As described in [subsetting](subsetting.html), 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).

### Creation

You create a data frame using `data.frame()`, which takes named vectors as input:

```{r}
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:

```{r}
df <- data.frame(
  x = 1:3, 
  y = c("a", "b", "c"), 
  stringsAsFactors = FALSE)
str(df)
```

### Testing and coercion

Because data frame is an S3 class, it's type 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()`:

```{r}
typeof(df)
class(df)
is.data.frame(df)
```

You can coerce an object to a data frame with `as.data.frame()`:

* a vector will yield a one-column data frame
* a list will yield one column for each element; it's an error if they're not all the same length
* a matrix will yield a data frame with the same number of columns

### Combining data frames

You can combine data frames using `cbind()` and `rbind()`:

```{r}
cbind(df, data.frame(z = 3:1))
rbind(df, data.frame(x = 10, y = "z"))
```

When combining column-wise, only the number of rows needs to match, and rownames are ignored. When combining row-wise, the column names must match. If you want to combine data frames that may not have all the same variables, use `plyr::rbind.fill()`

It's a common mistake to try and create a data frame by `cbind()`ing vectors together. This doesn't work because `cbind()` will create a matrix unless one of the arguments is already a data frame. Instead use `data.frame()` directly:

```{r}
bad <- data.frame(cbind(a = 1:2, b = c("a", "b")))
str(bad)
good <- data.frame(a = 1:2, b = c("a", "b"), 
  stringsAsFactors = FALSE)
str(good)
```

The conversion rules for `cbind()` are complicated and best avoided by ensuring all inputs are of the same type. 

### Special columns

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

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

However, when a list is given to `data.frame()`, it tries to put each item of the list into its own column, so this fails:

```{r, error = TRUE}
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:

```{r}
dfl <- data.frame(x = 1:3, y = I(list(1:2, 1:3, 1:4)))
str(dfl)
dfl[2, "y"]
```

`I()` adds the `AsIs` class to its input, but this additional attribute can usually be safely ignored.

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 the data frame:

```{r}
dfm <- data.frame(x = 1:3, y = I(matrix(1:9, nrow = 3)))
str(dfm)
dfm[2, "y"]
```

Use list and array columns with caution: many functions that work with data frames assume that all columns are atomic vectors.