So far this book has focussed on data frames and packages that work with them. But as you start to write your own functions, and dig deeper into R, you need to learn about vectors, the objects that underpin data frames. If you've learned R in a more traditional way, you're probably familiar with vectors already, as most R resource start with vectors and work their way up to data frames. I think it's better to start with data frames because they're immediately useful, and then work your way down to the underlying components.
Vectors are particularly important as its to learn to write functions that work with vectors, rather than data frames. The technology that lets ggplot2, tidyr, dplyr etc work with data frames is considerably more complex and not currently standardised. While I'm currently working on a new standard that will make life much easier, it's unlikely to be ready in time for this book.
There's a somewhat related object: `NULL`. It's often used to represent the absence of a vector (as opposed to `NA` which is used to represent the absence of a value in a vector). `NULL` typically behaves like a vector of length 0.
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 types of augmented vector:
This chapter will introduce you to these important vectors 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. Raw and complex are rarely used during a data analysis, so I won't discuss them here.
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 be specific when needed.
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()`:
Integer and double vectors are known collectively as numeric vectors. In R, numbers are doubles by default. To make an integer, place a `L` after the number:
Most of the time the distinction between integers and doubles is not important. However, there are two important differences that you need to be aware of:
1. Integers have one special value: `NA_integer_`, while doubles have four:
`NA_real_`, `NaN`, `Inf` and `-Inf`
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. 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 type of atomic vector, 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: R 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. You can see this behaviour in practice with `pryr::object_size()`:
`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 8 * 1000 + 136 = 8.13 kB.
Because explicit coercion is used relatively rarely (and is largely easy to understand), it's more important to understand implicit coercion.
The most important type of implicit coercion is using a logical vector in a numeric context. In this case `TRUE` is converted to `1` and `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:
You may see some code (typically older) that relies on the implicit coercion in the opposite direction, from integer to logical:
```{r, eval = FALSE}
if (length(x)) {
# do something
}
```
In this case, 0 is converted to `FALSE` and everything else is converted to `TRUE`. I think this makes it harder to understand your code, and I recommend it.
It's also important to understand what happens when you try and create a vector containing multiple types with `c()`: the most complex type always wins.
An atomic vector can not have a mix of different types because the type is a property of the complete vector, not of the individual elements. If you need to mix multiple types in the same vector, you should use a list, which you'll learn about shortly.
Sometimes you want to do different things based on the type of vector you get. One option is to use `typeof()`. Another is to use a test function which returns a `TRUE` or `FALSE` (broadly, functions that return a single logical value are often called __predicate__ functions).
Base R provides many functions like `is.vector()` and `is.atomic()`, but they are often surprising. Instead, it's safer to use the `is_*` functions provided by purrr, which are summarised in the table below.
Each predicate also comes with a "scalar" version, which checks that the length is 1. This is useful if you want to check (for example) that the inputs to your function are as you expect.
As well as implicitly coercion the types of vectors to be compatible, R will also implicit coerce the length of vectors. This is called vector "recycling", because the shorter vector is repeated, or __recycled__, to be the same length as the longer vector.
This is generally most useful when you are mixing vectors and "scalars". But note that R does not actually have scalars. In R, a single number is a vector of length 1. 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}
sample(10) + 100
runif(10) > 0.5
```
In R, basic mathematical operations work with vectors, not scalars like in most programming languages. This means that you should never need to perform explicit iteration (either with a loop or a map function) performing simple mathematical computations.
It's intuitive what should happen if you add two vectors of the same length, or a vector and a "scalar", but what happens if you add two vectors of different lengths?
```{r}
1:10 + 1:2
```
Here, R will expand the shortest vector to the same length as the longest, so called __recycling__. This is silent except in the case where the length of the longer is not an integer multiple of the length of the longer:
```{r}
1:10 + 1:3
```
While vector recycling can be used to create very succinct, clever code, it can also silently conceal problems. For this reason, the vectorised functions in dplyr, purrr, etc will throw errors when you recycle anything other than a scalar.
So far we've used `dplyr::filter()` to filter the rows in a data frame. `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 2d and higher data structures here, but the idea generalises in a straightforward way: `x[a, b]` for 2d, `x[a, b, c]` for 3d, and so on.
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.
Lists are a step up in complexity from 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]]`:
Atomic vectors and lists are the building blocks for four other important vector types: factors, dates, date times, and data frames. I call these __augmented vectors__, because they are vectors with additional __attributes__.
Attributes are a way of adding arbitrary additional metadata to a vector. You can think of attributes as named list of vectors that can be attached to any object. You can get and set individual attribute values with `attr()` or see them all at once with `attributes()`.
Class is particularly important because it changes what __generic functions__ do with the object. Generic functions are key to object oriented programming in R, and are what make augmented vectors behave differently to the vector they are built on top of. A detailed discussion of the S3 object oriented system is beyond the scope of this book, but you can read more about it at <http://adv-r.had.co.nz/OO-essentials.html#s3>.
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__, a function, based on the class of the first argument. (All methods are functions; not all functions are methods). 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:
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 modelling. 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 character vector.
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].
