Often, when you write a function it will work with a single vector (or a handful of vectors), rather than a data frame. So far we've focussed on tools, like dplyr, that work with data frames, and have talked little about vector. Now it's time to dive deep and learn how you can work with vectors to build your own functions to automate common problems.
This chapter focusses on __vectors__, the most important family of objects in R. They are the most important because you work with them most frequently in a data analysis. You will use other types of objects likes functions and environments, but by and large you don't need to understand the details of these data types. If you are interested in learning the precise details, you'll need to learn about R's underlying C API, which is beyond the scope of this book. <http://adv-r.had.co.nz/C-interface.html#c-data-structures> has some details if you're interested.
There are two types of vectors:
1. __Atomic__ vectors, which are further broken down into six types:
__logical__, __integer__, __double__, __character__, __complex__, and
__raw__. Complex are raw are rarely used and won't be discussed further.
Integer and double vectors are collectively known as __numeric__ vectors.
1. __Lists__, which sometimes called recursive vectors, because lists can
contain other lists. This is the chief difference between atomic vectors
Vectors can also contain arbitrary additional metadata in the form of attributes. These attributes are used to create __augmented vectors__ which build on additional behaviour. There are four important augmented vector types:
* __Factors__ and __dates__ are built on top of integers.
* __Date times__ (POSIXct) are built on of doubles.
* Data frames and __tibbles__ are built on top of lists.
This chapter will introduce you to these important vectors types from simplest to most complicated. You'll start with atomic vectors, then build up to lists, and finally learn about augmented vectors.
The four most important types of atomic vector are logical, integer, double, and character. Integer and double are known collectively as numeric vectors and most of the time the distinction is not important, so we'll discuss them together. They're beyond the scope of this book because they are rarely needed to do data analysis. The following sections describe each type in turn.
Logical vectors are the simplest type of atomic vector because they can take only three possible values: `FALSE`, `TRUE`, and `NA`. Logical vectors are usually constructed with comparison operators, as described in [comparisons]. You can also create them by hand with `c()`:
One of the most useful properties of logical vectors is how they behave in numeric contexts: `TRUE` is converted to `1`, `FALSE` converted to 0. That means the sum of a logical vector is the number of trues, and the mean of a logical vector is the proportion of trues.
Numeric vectors include both integers and doubles (real numbers). In R, numbers are doubles by default. To make an integer, place a `L` after the number:
Doubles represent floating point numbers that can not always be precisely represented with a fixed amount of memory. This means that you should consider all doubles to be approximations, and you should never test for equality. For example, what is square of the square root of two?
This behaviour is common when working with floating point numbers: most calculations include some approximation error. Instead of comparing floating point numbers using `==`, you should use `dplyr::near()` which allows for some numerical tolerance.
Character vectors are the most complex of atomic vectors, because each element of a character vector is a string, and a string can contain an arbitrary amount of data. Strings are such an important data type, they have their own chapter: [strings].
Here I wanted to mention one important feature of the underlying string implementation: it uses a global string pool. This means that each unique string is only stored in memory once, and every use of the string points to that representation. This reduces the amount of memory needed by duplicated strings.
`y` doesn't take up 1,000x as much memory as `x`, because each element of `y` is just a pointer to that same string. A pointer is 8 bytes, so 1000 pointers to a 136 B string is about 8.13 kB.
Note that R does not have "scalars". In R, a single number is a vector of length 1. The impacts of this are mostly on how functions work. Because there are no scalars, most built-in functions are __vectorised__, meaning that they will operate on a vector of numbers. That's why, for example, this code works:
```{r}
1:10 + 2:11
```
In R, basic mathematical operations work with vectors, not scalars like in most programming languages. This means that you should never need to write an explicit for loop when performing simple computations on vectors.
Each type of atomic vector has its own missing value:
```{r}
NA # logical
NA_integer_ # integer
NA_real_ # double
NA_character_ # character
```
Normally, you don't need to know about these different types because you can always use `NA` it will be converted to the correct type. However, there are some functions that are strict about their inputs, so it's useful to have this knowledge sitting in your back pocket so you can use a specific type of missing value when needed.
### Coercion
You can convert another from one type of atomic vector to another with `as.logical()`, `as.integer()`, `as.double()`, and `as.character()`. However, before doing so, you should carefully consider whether you can make the fix upstream, so that the vector never had the wrong type in the first place. For example, you may need to tweak you readr `col_types` specification.
### Named vectors
All types of vectors can be named. You can either name them during creation with `c()`:
Compared to the base R functions, they only inspect the type of the object, not its attributes. This means they tend to be less surprising:
```{r}
is.atomic(NULL)
is_atomic(NULL)
is.vector(factor("a"))
is_vector(factor("a"))
```
I recommend using these instead of the base functions.
Each predicate also comes with "scalar" and "bare" versions. The scalar version checks that the length is 1 and the bare version checks that the object is a bare vector with no S3 class.
```{r}
y <- factor(c("a", "b", "c"))
is_integer(y)
is_scalar_integer(y)
is_bare_integer(y)
```
### Exercises
1. Carefully read the documentation of `is.vector()`. What does it actually
test for?
### Subsetting
Before we continue on to a richer data structure, the list, we need to take a brief detour to talk about subsetting vectors. So far, we've focussed on data frames, which are most easily subset with `dplyr::filter()`. `filter()`, however, does not work with vectors, so we need to learn a new tool: `[`.
`[` is the subsetting function, and is called like `x[a]`. We're not going to cover data structures that are 2d or higher in detail, but the idea generalised to `x[a, b]`, `x[a, b, c]` and so on. When working with individual vectors, it's important to understand how `[` works and how you can use it to extract elements of interest.
There are three four types of thing you can use to subset a vector:
1. The simplest type of subsetting is nothing, `x[]`, which returns the
complete `x`. This is not useful for subsetting vectors, but it is useful
when subsetting matrices (and other high dimensional structures) because
it lets you select all the rows or all the columns, by leaving that
index blank.
1. A numeric vector. If you subset with a numeric vector, it must either
be all positive, all negative, or zero.
Subsetting with a positive vector keeps the elements at those positions:
```{r}
x <- c("one", "two", "three", "four", "five")
x[c(3, 2, 5)]
```
By repeating a position, you can actually make an longer output than
input:
```{r}
x[c(1, 1, 5, 5, 5, 2)]
```
Negative values drop the elements at the specified positions:
```{r}
x[c(-1, -3, -5)]
```
It's an error to mix position and negative values:
```{r, error = TRUE}
x[c(1, -1)]
```
The error message mentions subsetting with zero, which returns no values:
```{r}
x[0]
```
This is not generally useful, but can be helpful if you want to create
unusual data structures with which to test your functions.
1. Subsetting with a logical vector keeps all values corresponding to a
`TRUE` value. This is most often useful in conjunction with a function
that creates a logical vector.
```{r, eval = FALSE}
# All non-missing values of x
x[!is.na(x)]
# All even values of x
x[x %% 2 == 0]
```
1. If you have a named vector, you can subset it with a character vector.
```{r}
x <- c(abc = 1, def = 2, xyz = 5)
x[c("xyz", "def")]
```
Like with positive integers, you can also use a character vector to
duplicate individual entries.
I'd recommend reading <http://adv-r.had.co.nz/Subsetting.html#applications> to learn more about how you can use subsetting to achieve various goals. If you are working with data frames, you can typically use a dplyr function to achieve these goals, but the techniques are useful to know about when you are writing your own functions.
There is an important variation of `[` called `[[`. `[[` only ever extracts a single element, and always drops names. It's a good idea to use it whenever you want to make it clear that you're extracting one thing, as in a for loop. The distinction between `[` and `[[` is most important for lists, as we'll see shortly.
### Exercises
1. Create functions that take a vector as input and returns:
1. What happens when you subset with a positive integer that's bigger
than the length of the vector? What happens when you subset with a
name that doesn't exist?
## Null
Null is a special object. Represents a "generic" vector of length 0. Often used to represent the absense of a vector (as opposed to `NA` which is used to represent the absence of a value in a vector). NULL is a singleton.
Subsetting NULL always gives you a null.
## Recursive vectors (lists)
Lists are a fundamentally richer than atomic vectors, because lists can contain other lists. This makes them suitable for representing hierarchical or tree-like structures. You create a list with `list()`:
The distinction between `[` and `[[` is really important for lists, because `[[` drills down into the list while `[` returns a new, smaller list. Compare the code and output above with the visual representation below.
It's easy to get confused between `[` and `[[`, but it's important to understand the difference. A few months ago I stayed at a hotel with a pretty interesting pepper shaker that I hope will help you remember these differences:
```{r, echo = FALSE, out.width = "25%"}
knitr::include_graphics("images/pepper.jpg")
```
If this pepper shaker is your list `x`, then, `x[1]` is a pepper shaker containing a single pepper packet:
```{r, echo = FALSE, out.width = "25%"}
knitr::include_graphics("images/pepper-1.jpg")
```
`x[2]` would look the same, but would contain the second packet. `x[1:2]` would be a pepper shaker containing two pepper packets.
`x[[1]]` is:
```{r, echo = FALSE, out.width = "25%"}
knitr::include_graphics("images/pepper-2.jpg")
```
If you wanted to get the content of the pepper package, you'd need `x[[1]][[1]]`:
```{r, echo = FALSE, out.width = "25%"}
knitr::include_graphics("images/pepper-3.jpg")
```
### Exercises
1. Draw the following lists as nested sets.
1. Generate the lists corresponding to these nested set diagrams.
1. What happens if you subset a data frame as if you're subsetting a list?
What are the key differences between a list and a data frame?
There are four important types of vector that are built on top of atomic vectors: factors, dates, date times, and data frames. I call these augmented vectors, because they are atomic vectors with additional __attributes__. Attributes are a way of adding arbitrary additional metadata to a vector. Each attribute is a named vector. You can get and set individual attribute values with `attr()` or see them all at once with `attributes()`.
* "names" are used to name the elements of a vector.
* "dims" make a vector behave like a matrix or array.
* "class" is used to implemenet the S3 object oriented system.
Class is particularly important because it changes what __generic functions__ do with the object. Generic functions are key to OO in R. Here's what a typical generic function looks like:
The call to "UseMethod" means that this is a generic function, and it will call a specific __method__, based on the class of the first argument. You can list all the methods for a generic with `methods()`:
The most important S3 generic is `print()`: it controls how the object is printed when you type its name on the console. Other important generics are the subsetting functions `[`, `[[`, and `$`.
Factors are designed to represent categorical data that can take a fixed set of possible values. Factors are built on top of integers, and have a levels attribute:
x <- factor(c("ab", "cd", "ab"), levels = c("ab", "cd", "ef"))
typeof(x)
attributes(x)
```
Historically, factors were much easier to work with than characters so many functions in base R automatically convert characters to factors (controlled by the dread `stringsAsFactors` argument). To get more historical context, you might want to read [stringsAsFactors: An unauthorized biography](http://simplystatistics.org/2015/07/24/stringsasfactors-an-unauthorized-biography/) by Roger Peng or [stringsAsFactors = \<sigh\>](http://notstatschat.tumblr.com/post/124987394001/stringsasfactors-sigh) by Thomas Lumley. The motivation for factors is the modelling context. If you're going to fit a model to categorical data, you need to know in advance all the possible values. There's no way to make a prediction for "green" if all you've ever seen is "red", "blue", and "yellow"
The packages in this book keep characters as is, but you will need to deal with them if you are working with base R or many other packages. When you encounter a factor, you should first check to see if you can avoid creating it in the first. Often there will be `stringsAsFactors` argument that you can set to `FALSE`. Otherwise, you can apply `as.character()` to the column to explicitly turn back into a factor.
```{r}
x <- factor(letters[1:5])
is.factor(x)
as.factor(letters[1:5])
```
### Dates and date times
Dates in R are numeric vectors (sometimes integers, sometimes doubles) that represent the number of days since 1 January 1970.
```{r}
x <- as.Date("1971-01-01")
unclass(x)
typeof(x)
attributes(x)
```
Date times are numeric vectors (sometimes integers, sometimes doubles) that represent the number of seconds since 1 January 1970:
```{r}
x <- lubridate::ymd_hm("1970-01-01 01:00")
unclass(x)
typeof(x)
attributes(x)
```
The `tzone` is optional, and only controls the way the date is printed not what it means.
There is another type of datetimes called POSIXlt. These are built on top of named lists.
```{r}
y <- as.POSIXlt(x)
typeof(y)
attributes(y)
```
If you use the packages outlined in this book, you should never encounter a POSIXlt. They do crop up in base R, because they are used extract specific components of a date (like the year or month). However, lubridate provides helpers for you to do this instead. Otherwise POSIXct's are always easier to work with, so if you find you have a POSIXlt, you should always convert it to a POSIXct with `as.POSIXct()`.
### Data frames and tibbles
Data frames are augmented lists: they have class "data.frame", and `names` (column) and `row.names` attributes:
```{r}
df1 <- data.frame(x = 1:5, y = 5:1)
typeof(df1)
attributes(df1)
```
The difference between a data frame and a list is that all the elements of a data frame must be the same length. All functions that work with data frames enforce this constraint.
In this book, we use tibbles, rather than data frames. Tibbles are identical to data frames, except that they have two additional components in the class:
```{r}
df2 <- dplyr::data_frame(x = 1:5, y = 5:1)
typeof(df2)
attributes(df2)
```
These extra components give tibbles the helpful behaviours defined in [tibbles].
