---
title: R's Atomic Data Types and Vectorization
layout: default_with_disqus
author: Eric C. Anderson
output: bookdown::html_chapter
---

# Atomic Data Types and Coercion {#r-data-types-and-coercion}


## Basic Data "Modes" of R  {#basic-modes}
There are four main "modes" of scalar data, in order from least to most general:

1. `logical` can take two values: `TRUE` and `FALSE`, which can be abbreviated, when you type them as `T` and `F`.
1. The `numeric` mode comes in two flavors: "integer" and "numeric" (real numbers).  Examples: `1`, `3.14`, `8.2`, `10`, etc.
1. `complex`: these are complex numbers of the form $a + bi$ where $a$ and $b$ are real numbers
and $i=\sqrt{-1}.$ Examples: `3.2+7.3i`,  `4+0i`
1. `character`: these take values that are often called "strings" in other languages.  Examples: `"fred"`, `"foo"`, `"bar"`, `"boing"`.
There is also a `raw` mode which refers to raw bytes of data, but we won't concern ourselves with that for now.

### Atomic Vectors
A fundamental data structure in R: a vector in which every element is of the same mode. Like
```{r}
x <- c(1,2,3,5,7)
x
```
Pretty basic stuff, until you start accidentally, or intentionally mixing modes.
```{r}
x <- c(1,2,3,5,7,"11")
x
```
The mode of everything is _coerced_ to the mode of the element with the most general mode, and this can really bite you in the rear if you don't watch out!


## Coercion {#coercion}

* All the data in an atomic vector _must be of the same mode_
* If data are added so that modes are mixed, then _the whole vector
gets changed so that everything is of the most general mode_
* Example:
    ```{r}
    # simple atomic vector of mode numeric
    x <- 1:6
    x

    # now change one to mode character and see what happens
    x[1] <- "tweezer"
    x
    
    ```

### Coercion Up One Step

* logical to numeric:
    * `TRUE` ==> `1`
    * `FALSE` ==> `0`
*  numeric to complex:
    * `6.4` ==> `6.4+0i`
    * `5` ==> `5+0i`
*  complex to character:
    * `6.4+0i` ==> `"6.4+0i"`


### Coercion Up Two Or More Steps
Note that the coercion sometimes "jumps over the intermediate steps"

* logical to complex
    * `TRUE` ==> `1+0i`
    * `FALSE` ==> `0+0i`
*  logical to character (it _does not_ go FALSE ==> 0 ==> "0")
    * `TRUE` ==> `"TRUE"`
    * `FALSE` ==> `"FALSE"`
*  numeric to character
    * `7` ==> `"7"`
    * `3.1415` ==> `"3.1415"`


### Coercion down one step

Sometimes things get coerced "downards" (i.e., toward less general
data types).

If the coercion doesn't make sense you end up with `NA` which is how R denotes missing data

* numeric to logical (0 ==> FALSE, anything else ==> TRUE); _Always "makes sense"_
    * `0` ==> `FALSE`
    * `1` ==> `TRUE`
    * `78.2` ==> `TRUE`
    * `0.0001` ==> `TRUE`
    * `-563.3` ==> `TRUE`
*  complex to numeric (discards complex part and warns about it!)
      * `3.4+0i` ==> `3.4`
      * `5.6+7.6i` ==> `5.6` (+ a warning)
        ```{r}
        # witness a warning:
        as.numeric(7.4+5i)
        ```
*  character to complex
      * `"3.4+4i"` ==> `3.4+4i`
      * `"a"` -> `NA` (you can't coerce `"a"` to any number, reasonably)

### Coercion down more than one step
Important point: it doesn't _necessarily_ go through intermediate steps:

* complex to logical (0 ==>FALSE, anything else ==> TRUE)
    * `0+0i` ==> `FALSE`
    * `0+2i` ==> `TRUE`
    * `5+0i` ==> `TRUE`
    * `5+9i` ==> `TRUE`
* character to logical
    * `"TRUE"` ==> `TRUE`
    * `"FALSE"` ==> `FALSE`
    * `"1"` ==> `NA`  (_yikes! if it went through numeric you'd get something different!_)
    * `"0"` ==> `NA`
*  character to numeric
    * `"56.764"` ==> `56.764`
    * `"4+8i"` ==> `4` (with a warning that the complex part was dropped)
    * `"fred"` -> `NA`


### Functions For Explicit Coercion
There is a whole family for coercing objects between different modes (or different types) that take the form `as.something`:

* `as.logical(x)`
* `as.numeric(x)`
* `as.integer(x)` # not a mode, (this is a subclass of the `numeric` mode)
* `as.complex(x)`
* `as.character(x)`


As expected, these are vectorized---they coerce every element of the vector to the desired mode.



## Missing Data and Special Values in R {#missing-data}
We saw `NA` up above.  That means "Not Available" and it denotes missing data.    

There are also two more interesting values:

1. `Inf` (-Inf) means $\infty$ (or $-\infty$) and arises from things like: 1/0 or log(0).
1. `NaN` means "Not a Number" and it arises from situations where you can't evaluate something and it doesn't have an obvious limit.  Like 0/0 or Inf/-Inf  or 0*Inf.

* If you wish to test whether something is NaN, or NA you have: `is.na(x)` and `is.nan(x)` which return logical vectors.
* The same goes for testing if things are finite or infinite:
    ```{r}
    x <- c(NA, 2, Inf, 4, NaN, 6)
    
    is.nan(x) # only the NaN
    
    is.na(x) # both NA and NaN
    
    is.infinite(x) # only Inf or -Inf
    ```


### Modes of Missing Data
Here is something to be aware of: missing values, like non-missing values, carry around their mode. Try this:
```{r}
x <- c(1, 2, NA, 4, "5")
x

x[3]  # this extracts the third element of x

c(10,20,30,x[3])

c(10, 20, 30, NA)  # this is a "fresh" NA, no coercion
```


## Vectorization {#vectorization}

* In R, the term _vectorization_ refers to the fact that, in many
cases, when you apply a function to a vector, it applies the function
to every element of the vector. 
* This is apparent in many of the _operators_ and we will see it in plenty
of other functions, too.


### Most Operators are Vectorized
This is _incredibly important_!  All the mathematical operators, like `+`, `-`, `*`, and the logical operators, like  `&` (AND), `|` (OR), and the comparison operators, like `<` and `>` are hungry to operate _element-wise_ on every _element_ of a vector.  Example:
```{r}
fish.lengths <- c(121, 95, 87, 142)
fish.weights <- c(1011, 505, 702, 900)
fish.fatness <- fish.weights / fish.lengths
fish.fatness
```

### Vectorization is so important...
That we are going to go to open up a whole new lecture that starts with it.