684 lines
27 KiB
Plaintext
684 lines
27 KiB
Plaintext
# Vectors
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## Introduction
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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 underlie data frames. If you've learned R in a more traditional way, you're probably already familiar with vectors, as most R resources 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.
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Vectors are particularly important as most of the functions you will write will work with vectors. It is possible to write functions that work with data frames (like ggplot2, dplyr, tidyr, etc), but the underlying technology is more complex and less consistent. I am working on a system to make to it easier, but it will not be ready in time for the publication of the book. This system will still require you understand vectors, but will help provide a user-friendly layer on top.
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### Prerequisites
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The focus of this chapter is on base R data structures, so you it isn't essential to load any packages. However, the __purrr__ package, which you'll learn more about in [iteration], provides some useful tools to help us see what's going on.
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```{r}
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library(purrr)
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```
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## Vector overview
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There are two types of vectors:
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1. __Atomic__ vectors, which are further broken down into six types:
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__logical__, __integer__, __double__, __character__, __complex__, and
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__raw__. Integer and double vectors are collectively known as
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__numeric__ vectors.
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1. __Lists__, sometimes called recursive vectors, because lists can
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contain other lists. This is the chief difference between atomic vectors
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and lists: atomic vectors are homogeneous, lists can be heterogeneous.
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There's a somewhat related object: `NULL`. `NULL` is 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.
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The structure of the vector types is summarised in the following diagram:
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```{r, echo = FALSE}
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knitr::include_graphics("diagrams/data-structures-overview.png")
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```
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Every vector has two key properties:
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1. Its __type__, which you can determine with `typeof()`.
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```{r}
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typeof(letters)
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typeof(1:10)
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```
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1. Its __length__, which you can determine with `length()`.
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```{r}
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x <- list("a", "b", 1:10)
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length(x)
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```
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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:
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* Factors and dates are built on top of integer vectors.
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* Date-times (POSIXct) are built on of double vectors.
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* Data frames and tibbles are built on top of lists.
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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.
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## Important types of atomic vector
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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.
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### Logical
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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()`:
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```{r}
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c(TRUE, TRUE, FALSE, NA)
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```
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### Numeric
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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:
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```{r}
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typeof(1)
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typeof(1L)
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1.5L
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```
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The distinction between integers and doubles is not usually important. However, there are two important differences that you need to be aware of:
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1. Doubles are approximations.
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1. Integers have one special value: `NA_integer_`, while doubles have four:
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`NA_real_`, `NaN`, `Inf` and `-Inf`
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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?
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```{r}
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x <- sqrt(2) ^ 2
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x
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```
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It certainly looks like R calculates the number we expect: 2. But things are not exactly as they seem:
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```{r}
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x == 2
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x - 2
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```
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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.
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```{r}
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dplyr::near(x, 2)
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```
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Doubles have three special values in addition to `NA`:
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```{r}
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c(NA, -1, 0, 1) / 0
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```
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Avoid using `==` to check for these other special values. Instead use the helper functions `is.finite()`, `is.infinite()`, and `is.nan()`:
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| | 0 | Inf | NA | NaN |
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|------------------|-----|-----|-----|-----|
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| `is.finite()` | x | | | |
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| `is.infinite()` | | x | | |
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| `is.na()` | | | x | x |
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| `is.nan()` | | | | x |
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### Character
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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. You've already learned a lot about working with strings in [strings].
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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()`:
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```{r}
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x <- "This is a reasonably long string."
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pryr::object_size(x)
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y <- rep(x, 1000)
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pryr::object_size(y)
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```
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`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.
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### Missing values
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Each type of atomic vector has its own missing value:
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```{r}
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NA # logical
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NA_integer_ # integer
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NA_real_ # double
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NA_character_ # character
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```
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Normally, you don't need to know about these different types because you can always use `NA` and 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.
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### Exercises
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1. Describe the difference between `is.finite(x)` and `!is.infinite(x)`.
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1. Read the source code for `dplyr::near()`. How does it work?
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1. A logical vector can take 3 possible values. How many possible
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values can an integer vector take? How many possible values can
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a double take? Use google to do some research.
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1. Brainstorm at least four functions that allow you to convert a double to an
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integer. How do they differ? Be precise.
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1. What functions from the readr package allow you to turn a string
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into a logical, integer, or double vector?
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## Using atomic vectors
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Now that you understand the different types of atomic vector, it's useful to review some of the important tools for working with them. These include:
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1. The implicit coercion rules which govern what happen when, for example,
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you use a logical vector in a numeric context.
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1. Tools to test if an function input is a specific type of vector.
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1. R's recycling rules which govern what happens when you work
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with vectors of different lengths.
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1. Naming the elements of a vector.
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1. Subsetting a vector to pull out elements of interest.
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### Coercion
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There are two ways to convert, or coerce, one type of vector to another:
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1. Explicit coercion happens when you call a function like `as.logical()`,
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`as.integer()`, `as.double()`, or `as.character()`. Whenever you find
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yourself using explicit coercion, you should always check whether you can
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make the fix upstream, so that the vector never had the wrong type in
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the first place. For example, you may need to tweak your readr
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`col_types` specification.
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1. Implicit coercion happens when you use a vector in a specific context
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that expects a certain type of vector. For example, when you use a logical
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vector with a numeric summary function, or when you use a double vector
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where an integer vector is expected.
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Because explicit coercion is used relatively rarely (and is largely easy to understand), it's more important to understand implicit coercion.
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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:
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```{r}
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x <- sample(20, 100, replace = TRUE)
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y <- x > 10
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sum(y) # how many are greater than 10?
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mean(y) # what proportion are greater than 10?
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```
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You may see some code (typically older) that relies on the implicit coercion in the opposite direction, from integer to logical:
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```{r, eval = FALSE}
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if (length(x)) {
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# do something
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}
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```
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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 don't recommend it.
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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.
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```{r}
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typeof(c(TRUE, 1L))
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typeof(c(1L, 1.5))
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typeof(c(1.5, "a"))
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```
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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.
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### Test functions
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Sometimes you want to do different things based on the type of vector. 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).
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Base R provides many functions like `is.vector()` and `is.atomic()`, but they often returns surprising results. Instead, it's safer to use the `is_*` functions provided by purrr, which are summarised in the table below.
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| | lgl | int | dbl | chr | list |
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|------------------|-----|-----|-----|-----|------|
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| `is_logical()` | x | | | | |
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| `is_integer()` | | x | | | |
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| `is_double()` | | | x | | |
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| `is_numeric()` | | x | x | | |
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| `is_character()` | | | | x | |
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| `is_atomic()` | x | x | x | x | |
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| `is_list()` | | | | | x |
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| `is_vector()` | x | x | x | x | x |
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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.
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### Scalars and recycling rules
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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.
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This is generally most useful when you are mixing vectors and "scalars". I put scalars in quotes because R doesn't actually have scalars: instead, 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:
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```{r}
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sample(10) + 100
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runif(10) > 0.5
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```
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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 when performing simple mathematical computations.
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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?
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```{r}
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1:10 + 1:2
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```
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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:
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```{r}
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1:10 + 1:3
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```
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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 tidyverse will throw errors when you recycle anything other than a scalar.
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```{r, error = TRUE}
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tibble::tibble(x = 1:4, y = 1:2)
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```
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### Naming vectors
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All types of vectors can be named. You can name them during creation with `c()`:
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```{r}
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c(x = 1, y = 2, z = 4)
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```
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Or after the fact with `purrr::set_names()`:
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```{r}
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purrr::set_names(1:3, c("a", "b", "c"))
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```
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Named vectors are most useful for subsetting, described next.
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### Subsetting {#vector-subsetting}
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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]`. There are four types of thing that you can subset a vector with:
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1. A numeric vector containing only integers. The integers must either be all
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positive, all negative, or zero.
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Subsetting with positive integers keeps the elements at those positions:
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```{r}
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x <- c("one", "two", "three", "four", "five")
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x[c(3, 2, 5)]
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```
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By repeating a position, you can actually make a longer output than
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input:
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```{r}
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x[c(1, 1, 5, 5, 5, 2)]
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```
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Negative values drop the elements at the specified positions:
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```{r}
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x[c(-1, -3, -5)]
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```
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It's an error to mix positive and negative values:
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```{r, error = TRUE}
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x[c(1, -1)]
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```
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The error message mentions subsetting with zero, which returns no values:
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```{r}
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x[0]
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```
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This is not generally useful, but can be helpful if you want to create
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unusual data structures with which to test your functions.
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1. Subsetting with a logical vector keeps all values corresponding to a
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`TRUE` value. This is most often useful in conjunction with a function
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that creates a logical vector.
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```{r}
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x <- c(10, 3, NA, 5, 8, 1, NA)
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# All non-missing values of x
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x[!is.na(x)]
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# All even (or missing!) values of x
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x[x %% 2 == 0]
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```
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1. If you have a named vector, you can subset it with a character vector""
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```{r}
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x <- c(abc = 1, def = 2, xyz = 5)
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x[c("xyz", "def")]
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```
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Like with positive integers, you can also use a character vector to
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duplicate individual entries.
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1. The simplest type of subsetting is nothing, `x[]`, which returns the
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complete `x`. This is not useful for subsetting vectors, but it is useful
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when subsetting matrices (and other high dimensional structures) because
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it lets you select all the rows or all the columns, by leaving that
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index blank. For example, if `x` is 2d, `x[1, ]` selects the first row and
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all the columns, and `x[, -1]` selects all rows and all columns except
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the first.
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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.
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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.
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### Exercises
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1. Carefully read the documentation of `is.vector()`. What does it actually
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test for? Why does `is.atomic()` not agree with the definition of
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atomic vectors above?
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1. Create functions that take a vector as input and returns:
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1. The last value. Should you use `[` or `[[`?
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1. The elements at even numbered positions.
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1. Every element except the last value.
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1. Only even numbers (and no missing values).
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1. Why is `x[-which(x > 0)]` not the same as `x[x <= 0]`?
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1. What happens when you subset with a positive integer that's bigger
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than the length of the vector? What happens when you subset with a
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name that doesn't exist?
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## Recursive vectors (lists) {#lists}
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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()`:
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```{r}
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x <- list(1, 2, 3)
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x
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```
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A very useful tool for working with lists is `str()` because it focusses on the **str**ucture, not the contents.
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```{r}
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str(x)
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x_named <- list(a = 1, b = 2, c = 3)
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str(x_named)
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```
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Unlike atomic vectors, `lists()` can contain a mix of objects:
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```{r}
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y <- list("a", 1L, 1.5, TRUE)
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str(y)
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```
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Lists can even contain other lists!
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```{r}
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z <- list(list(1, 2), list(3, 4))
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str(z)
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```
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### Visualising lists
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To explain more complicated list manipulation functions, it's helpful to have a visual representation of lists. For example, take these three lists:
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```{r}
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x1 <- list(c(1, 2), c(3, 4))
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x2 <- list(list(1, 2), list(3, 4))
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x3 <- list(1, list(2, list(3)))
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```
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I'll draw them as follows:
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```{r, echo = FALSE, out.width = "75%"}
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knitr::include_graphics("diagrams/lists-structure.png")
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```
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There are three principles:
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1. Lists have rounded corners. Atomic vectors have square corners.
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1. Children are drawn inside their parent, and have a slightly darker
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background to make it easier to see the hierarchy.
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1. The orientation of the children (i.e. rows or columns) isn't important,
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so I'll pick a row or column orientation to either save space or illustrate
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an important property in the example.
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### Subsetting
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There are three ways to subset a list, which I'll illustrate with `a`:
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```{r}
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a <- list(a = 1:3, b = "a string", c = pi, d = list(-1, -5))
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```
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* `[` extracts a sub-list. The result will always be a list.
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```{r}
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str(a[1:2])
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str(a[4])
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```
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Like with vectors, you can subset with a logical, integer, or character
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vector.
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* `[[` extracts a single component from a list. It removes a level of
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hierarchy from the list.
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```{r}
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str(y[[1]])
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str(y[[4]])
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```
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* `$` is a shorthand for extracting named elements of a list. It works
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similarly to `[[` except that you don't need to use quotes.
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```{r}
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a$a
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a[["a"]]
|
|
```
|
|
|
|
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.
|
|
|
|
```{r, echo = FALSE, out.width = "75%"}
|
|
knitr::include_graphics("diagrams/lists-subsetting.png")
|
|
```
|
|
|
|
### Lists of condiments
|
|
|
|
The difference between `[` and `[[` is very important, but it's easy to get confused. A few months ago I stayed at a hotel with a rather 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. `list(a, b, list(c, d), list(e, f))`
|
|
1. `list(list(list(list(list(list(a))))))`
|
|
|
|
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?
|
|
|
|
## Attributes
|
|
|
|
Any vector can contain arbitrary additional metadata through its __attributes__. 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()`.
|
|
|
|
```{r}
|
|
x <- 1:10
|
|
attr(x, "greeting")
|
|
attr(x, "greeting") <- "Hi!"
|
|
attr(x, "farewell") <- "Bye!"
|
|
attributes(x)
|
|
```
|
|
|
|
There are three very important attributes that are used to implement fundamental parts of R:
|
|
|
|
1. __Names__ are used to name the elements of a vector.
|
|
1. __Dimensions__ (dims, for short) make a vector behave like a matrix or array.
|
|
1. __Class__ is used to implement the S3 object oriented system.
|
|
|
|
You've seen names above, and we won't cover dimensions because we don't use matrices in this book. It remains to describe the class, which controls how __generic functions work__. Generic functions are key to object oriented programming in R, making different types of vector act differently. 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:
|
|
|
|
```{r}
|
|
as.Date
|
|
```
|
|
|
|
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()`:
|
|
|
|
```{r}
|
|
methods("as.Date")
|
|
```
|
|
|
|
For example, if `x` is a character vector, `as.Date()` will call `as.Date.charcter()`; if it's a factor, it'll call `as.Date.factor()`.
|
|
|
|
You can see the specific implementation of a method with `getS3method()`:
|
|
|
|
```{r}
|
|
getS3method("as.Date", "default")
|
|
getS3method("as.Date", "numeric")
|
|
```
|
|
|
|
The most important S3 generic is `print()`: it controls how the object is printed when you type its name at the console. Other important generics are the subsetting functions `[`, `[[`, and `$`.
|
|
|
|
## Augmented vectors
|
|
|
|
Atomic vectors and lists are the building blocks for other important vector types like factors and dates. I call these __augmented vectors__, because they are vectors with additional __attributes__. Generic methods make augmented vectors behave differently, depending on their class. In this book, we make use of four important augmented vectors:
|
|
|
|
* Factors.
|
|
* Date-times and times.
|
|
* Tibbles.
|
|
|
|
These are described below.
|
|
|
|
### Factors
|
|
|
|
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:
|
|
|
|
```{r}
|
|
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 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".
|
|
|
|
Factors aren't common in the tidyverse, 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 place. 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.
|
|
|
|
```{r}
|
|
x <- factor(letters[1:5])
|
|
is.factor(x)
|
|
as.factor(letters[1:5])
|
|
```
|
|
|
|
Otherwise, you might try my __forcats__ package, which provides handy functions for working with factors (forcats = tools **for** **cat**egorical variables, and is an anagram of factors!). At the time of writing it was only available on github, <https://github.com/hadley/forcats>, but it may have made it to CRAN by the time you read this book.
|
|
|
|
### 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. It controls how the time is printed, not what absolute time it refers to.
|
|
|
|
```{r}
|
|
attr(x, "tzone") <- "US/Pacific"
|
|
x
|
|
|
|
attr(x, "tzone") <- "US/Eastern"
|
|
x
|
|
```
|
|
|
|
There is another type of date-times called POSIXlt. These are built on top of named lists:
|
|
|
|
```{r}
|
|
y <- as.POSIXlt(x)
|
|
typeof(y)
|
|
attributes(y)
|
|
```
|
|
|
|
POSIXlts are rare inside the tidyverse. They do crop up in base R, because they are needed to extract specific components of a date (like the year or month). Since lubridate provides helpers for you to do this instead, you don't need them. 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()`.
|
|
|
|
### Tibbles
|
|
|
|
Tibbles are augmented lists: they have class "tbl_df" + "tbl" + "data.frame", and `names` (column) and `row.names` attributes:
|
|
|
|
```{r}
|
|
tb <- tibble::tibble(x = 1:5, y = 5:1)
|
|
typeof(tb)
|
|
attributes(tb)
|
|
```
|
|
|
|
The difference between a tibble and a list is that all the elements of a data frame must be the same length. All functions that work with tibbles enforce this constraint.
|
|
|
|
Traditional data.frames have a very similar structure:
|
|
|
|
```{r}
|
|
df <- data.frame(x = 1:5, y = 5:1)
|
|
typeof(df)
|
|
attributes(df)
|
|
```
|
|
|
|
The main difference is the class. The class of tibble includes "data.frame" which means tibbles inherit the regular data frame behaviour by default.
|
|
|
|
### Exercises
|
|
|
|
1. What does `hms::hms(3600)` return? How does it print? What primitive
|
|
type is the augmented vector built on top of? What attributes does it
|
|
use?
|
|
|
|
1. Try and make a tibble that has columns with different lengths. What
|
|
happens?
|