lec02-basic-r.Rmd

---
title: "Introduction to R: Assignment, vectors, functions"
author: Joel Östblom
---

**Copyright (c) Data Carpentry**

*Note: This lecture content was originally created by voluntary contributions to
[Data Carpentry](http://datacarpentry.org) and has been modified to align with
the aims of EEB430. Data Carpentry is an organization focused on data literacy,
with the objective of teaching skills to researchers to enable them to retrieve,
view, manipulate, analyze, and store their and other’s data in an open and
reproducible way in order to extract knowledge from data. For EEB430, we are
making all our content available under the same license, [The Creative
Commons](https://creativecommons.org/), so that anyone in the future
can re-use or modify our course content, without infringing on copyright
licensing issues.*

The above paragraph is made explicit since it is one of the core features of
working with an open language like R. Many smart people willingly and actively
share their material publicly, so that others can modify and build off of the
material themselves.

By being open, we can "stand on the shoulders of giants" and continue to
contribute for others to then stand on our shoulders. Not only does this help
get work done, but it also adds to a feeling of community. In fact, there is a
common saying in the open source world:

> I came for the language and stayed for the community.

This saying captures the spirit, generosity, and fun involved in being a
part of these open source projects.

-----

## Lesson Preamble

> ### Learning Objectives
> 
> - Define the following terms as they relate to R: object, assign, call,
>   function, arguments, options.
> - Create objects and assign values to them.
> - Use comments within code blocks.
> - Do simple arithmetic operations in R using values and objects.
> - Call functions and use arguments to change their default options.
> - Inspect the content of vectors and manipulate their content.
> - Subset and extract values from vectors.
> - Correctly define and handle missing values in vectors.
> - Define our own functions
> - Create for-loops
> 
> ### Lecture outline
> 
> - Setting up the R Notebook (5 min)
> - Creating objects/variables in R (20 min)
> - Vectors and data types (15 min)
> - Subsetting vectors (15 min)
> - Missing data (10 min)
> - Writing functions (10 min)
> - Loops and vectorization (10 min)

-----

## Setting up the R Notebook

Let's remove the template RStudio gives us, and add a title of our own.

```yaml
---
title: Introduction to R
---
```

This header block is called the YAML header. This is where we specify whether we
want to convert this file to a HTML or PDF file. This will be discussed in more
detail in another class. For now, we just care about including the lecture title
here. For now, let's type out a note:

> This lecture covers fundamental R usage, such as assigning values to a
> variable, using functions, commenting code, and more.

Under this sentence, we will insert our first code chunk. You insert a code
chunk by either clicking the "Insert" button or pressing <kbd>Ctrl</kbd> +
<kbd>Alt</kbd> + <kbd>i</kbd> simultaneously. You could also type out the
surrounding backticks, but this would take longer. To run a code chunk, you
press the green arrow, or <kbd>Ctrl</kbd> + <kbd>Shift</kbd> + <kbd>Enter</kbd>.


## Creating objects in R

As we saw in our first class, you can get output from R simply by typing math in
the console:

```{r}
3 + 5
12 / 7
```

However, to do useful and interesting things, we need to assign _values_ to
_objects_. Objects are also referred to as _variables_, and although there
technically are minor differences between them[^objects_variables], we will use
them interchangeably in this class. To create an object, we need to give it a
name followed by the assignment operator `<-`, and the value we want to assign:

[^objects_variables]: https://cran.r-project.org/doc/manuals/r-release/R-lang.html#Objects).

```{r}
x <- 3
x + 5
```

`<-` is the assignment operator. It assigns values on the right to objects on
the left. So, after executing `x <- 3`, the value of `x` is `3`. The arrow can
be read as 3 **goes into** `x`.[^equal_vs_arrow] In RStudio, typing
<kbd>Alt</kbd> + <kbd>-</kbd> will write ` <- ` in a single keystroke.

[^equal_vs_arrow]: For historical reasons, you can also use `=` for assignments,
but not in every context. Because of the
[slight](http://blog.revolutionanalytics.com/2008/12/use-equals-or-arrow-for-assignment.html)
[differences](https://web.archive.org/web/20130610005305/https://stat.ethz.ch/pipermail/r-help/2009-March/191462.html)
in syntax, it is good practice to always use `<-` for assignments.

You can name an object in R almost anything you want:

```{r}
joel <- 3
joel + 5
```

> #### Challenge
>
> So far, we have created two variables, `joel` and `x`. What is the sum of these variables?
> 
> ```{r}
> joel + x
> ```

Objects can be given any name such as `x`, `current_temperature`, or
`subject_id`. You want your object names to be explicit and not too long. They
cannot start with a number (`2x` is not valid, but `x2` is). R is case sensitive
(e.g., `joel` is different from `Joel`). There are some names that cannot be
used because they are they are reserved for fundamental functions in R
(`?Reserved` lists these words). In general, even if it's allowed, it's best to
not use other function names (e.g., `c`, `T`, `mean`, `data`, `df`, `weights`).
If in doubt, check the help or use tab completion to see if the name is already
in use. It's also best to avoid dots (`.`) within a variable name as in
`my.dataset`. Historically, there are many functions in R with dots in their
name, but since dots have a [special meaning](http://adv-r.had.co.nz/S3.html) in
R, it's better to not use them and instead use underscores (`_`). It is also
recommended to use nouns for variable names, and verbs for function names. It's
important to be consistent in the styling of your code (where you put spaces,
how you name variables, etc.). Using a consistent coding style[^coding_style]
makes your code clearer to read for your future self and your collaborators.
RStudio will format code for you if you highlight a section of code and press
<kbd>Ctrl</kbd> + <kbd>Shift</kbd> + <kbd>a</kbd>.

[^coding_style]: Refer to the [class resources
page](https://uoftcoders.github.io/rcourse/resources.html) for which style to
adhere to.

When assigning a value to an object, R does not print anything. You can force R
to print the value by using parentheses or by typing the object name:

```{r}
weight_kg <- 55    # doesn't print anything
(weight_kg <- 55)  # but putting parenthesis around the call prints the value of `weight_kg`
weight_kg          # and so does typing the name of the object
```

The variable `weight_kg` is stored in the computer's memory where R can access
it, and we can start doing arithmetic with it efficiently. For instance, we may
want to convert this weight into pounds (weight in pounds is 2.2 times the
weight in kg):

```{r}
2.2 * weight_kg
```

We can also change a variable's value by assigning it a new one:

```{r}
weight_kg <- 57.5
2.2 * weight_kg
```

This means that assigning a value to one variable does not change the values of
other variables.  For example, let's store the animal's weight in pounds in a
new variable, `weight_lb`:

```{r}
weight_lb <- 2.2 * weight_kg
```

and then change `weight_kg` to 100.

```{r}
weight_kg <- 100
```

> #### Challenge
>
> What do you think is the current content of the object `weight_lb`? 126.5 or 220?
> 
> ```{r}
> weight_lb
> ```


### Comments

A comment is piece of text in your code that will not be executed with the rest
of the code, but its purpose is to be a note to the person reading the code.
Traditionally, comments have been the only way to make notes alongside your
code, but since we are using the R Notebook format, we can also write notes in
Markdown. Therefore, comments are not as important for us, but they are still
the best method of leaving short notes and explanations for specific lines of
code. The comment character in R is `#`, anything to the right of a `#` in a
script will be ignored by R.

RStudio makes it easy to comment or uncomment a paragraph: after selecting the
lines you want to comment, press at the same time on your keyboard
<kbd>Ctrl</kbd> + <kbd>Shift</kbd> + <kbd>C</kbd>. If you only want to comment
out one line, you can put the cursor at any location of that line (i.e. no need 
to select the whole line), then press <kbd>Ctrl</kbd> + <kbd>Shift</kbd> + 
<kbd>C</kbd>.

```{r}
weight_lb <- 2.2 * weight_kg # Actually, 1 kg = 2.204623 lbs
```

> #### Challenge
>
> What are the values after each statement in the following?
> 
> ```{r}
> mass <- 47.5            
> age  <- 122            
> mass <- mass * 2.0      # mass?
> age  <- age - 20        # age?
> mass_index <- mass/age  # mass_index?
> ```


### Functions and their arguments

Functions can be thought of as recipes. You give a few ingredients as input to a
function, and it will generate an output based on these ingredients. Just as
when baking, both the ingredients and the actual recipe will influence what
comes out of the recipe in the end, will it be a cake or a loaf of bread? In R,
the inputs to a function are not called ingredients, but rather *arguments*, and
the output is called the *return value* of the function. A function does not
technically have to return a value, but often does so. Functions are used to
automate more complicated sets of commands and many of them are already
predefined in R. A typical example would be the function `sqrt()`. The input
(the argument) must be a number, and the return value (in fact, the output) is
the square root of that number. Executing a function ('running it') is called
*calling* the function. An example of a function call is:

```{r}
sqrt(9)
```

Which is the same as assigning the value to a variable and then passing that
variable to the function:

```{r}
a <- 9
b <- sqrt(a)
b
```

Here, the value of `a` is given to the `sqrt()` function, the `sqrt()` function
calculates the square root, and returns the value which is then assigned to
variable `b`. This function is very simple, because it takes just one argument.

The return 'value' of a function need not be numerical (like that of `sqrt()`),
and it also does not need to be a single item: it can be a set of things, or
even a dataset, as we will see later on.

Arguments can be anything, not only numbers or filenames, but also other
objects. Exactly what each argument means differs per function, and must be
looked up in the documentation (see below). Some functions take arguments which
may either be specified by the user, or, if left out, take on a *default* value:
these are called *options*. Options are typically used to alter the way the
function operates, such as whether it ignores 'bad values', or what symbol to
use in a plot. However, if you want something specific, you can specify a value
of your choice which will be used instead of the default.

To access help about `sqrt`, we are first going to learn about tab-completion.
Type `s` and press <kbd>Tab</kbd>.

```{r, eval=FALSE}
s<tab>q
```

You can see that R gives you suggestions of what functions and variables are
available that start with the letter `s`, and thanks to RStudio they are
formatted in this nice list. There are *many* suggestions here, so let's be a
bit more specific and append a `q`, to find what we want. If we press enter or
tab again, R will insert the selected option.

You can see that R inserts a pair of parenthesis together with the name of the
functions. This is how the function syntax looks for R and many other
programming languages, and it means that within these parentheses, we will
specify all the arguments (the ingredients) that we want to pass to this
function.

If we press tab again, R will helpfully display all the available parameters for
this function that we can pass an argument to. The word *parameter* is used to
describe the name that the argument can be passed to. More on that later.

```{r, eval=FALSE}
sqrt(<tab>
```

There are many things in this list, but only one of them is marked in purple.
Purple here means that it is parameter we can use for the function and yellow
means that it is a variable that we defined earlier.[^R-symbols]

[^R-symbols]: There are a few other symbols as well, all of which can be viewed
at the end of [this post about RStudio code
completion](https://support.rstudio.com/hc/en-us/articles/205273297-Code-Completion).

To read the full help about `sqrt`, we can use the question mark, or type it
directly into the help document browser.

```{r, eval=FALSE}
?sqrt
```

As you can see, `sqrt()` takes only one argument, `x`, which needs to be a
*numerical vector*. Don't worry too much about that is says *vector* here, I
will talk more about that later. Briefly, a numerical vector is one or more
numbers. Every number is a vector, so you don't have to do anything special to
create a vector. More on vectors later.


Let's try a function that can take multiple arguments: `round()`.

```{r, eval=FALSE}
round(<tab>
?round
```

If we try round with a value:

```{r}
round(3.14159)
```

Here, we've called `round()` with just one argument, `3.14159`, and it has
returned the value `3`. That's because the default is to round to the nearest
whole number, or integer. If we want more digits we can pass an argument to the
`digits` parameter, to specify how many decimals we want to round to.

```{r}
round(3.14159, digits = 2)
```

So, above we pass the *argument* `2`, to the *parameter* `digits`. Knowing this
nomenclature is not essential for doing your own data analysis, but it will be
very helpful when you are reading through help documents online and in RStudio.

We can leave out the word `digits` since we know it comes as the
second parameter, after `x`.

```{r}
round(3.14159, 2)
```

As you notice, we have been leaving out `x` from the beginning. If you provide
the names for both the arguments, we can switch their order:

```{r}
round(digits = 2, x = 3.14159)
```

It's good practice to put the non-optional arguments (like the number you're
rounding) first in your function call, and to specify the names of all optional
arguments. If you don't, someone reading your code might have to look up the
definition of a function with unfamiliar arguments to understand what you're
doing.


## Vectors and data types

A vector is the most common and basic data type in R, and is pretty much the
workhorse of R. A vector is composed by a series of values, which can be either
numbers or characters. We can assign a series of values to a vector using the
`c()` function, which stands for "concatenate (combine/connect one after
another) values into a vector" For example we can create a vector of animal
weights and assign it to a new object `weight_g`:

```{r}
weight_g <- c(50, 60, 65, 82) # Concatenate/Combine values into a vector
weight_g
```

You can also use the built-in command `seq`, to create a sequence of numbers
without typing all of them in manually.

```{r}
seq(0, 30) # This is the same as just `0:30`
seq(0, 30, 3) # Every third number
```

A vector can also contain characters:

```{r}
animals <- c('mouse', 'rat', 'dog')
animals
```

The quotes around "mouse", "rat", etc. are essential here and can be either
single or double quotes. Without the quotes R will assume there are objects
called `mouse`, `rat` and `dog`. As these objects don't exist in R's memory,
there will be an error message.

There are many functions that allow you to inspect the content of a
vector. `length()` tells you how many elements are in a particular vector:

```{r}
length(weight_g)
length(animals)
```

An important feature of a vector is that all of the elements are the same type
of data. The function `class()` indicates the class (the type of element) of an
object:

```{r}
class(weight_g)
class(animals)
```

The function `str()` provides an overview of the structure of an object and its
elements. It is a useful function when working with large and complex
objects:

```{r}
str(weight_g)
str(animals)
```

You can use the `c()` function to add other elements to your vector:

```{r}
weight_g <- c(weight_g, 90) # add to the end of the vector
weight_g <- c(30, weight_g) # add to the beginning of the vector
weight_g
```

In the first line, we take the original vector `weight_g`,
add the value `90` to the end of it, and save the result back into
`weight_g`. Then we add the value `30` to the beginning, again saving the result
back into `weight_g`.

We can do this over and over again to grow a vector, or assemble a dataset.
As we program, this may be useful to add results that we are collecting or
calculating.

An **atomic vector** is the simplest R **data type** and it is a linear vector
of a single type, e.g. all numbers. Above, we saw 2 of the 6 main **atomic
vector** types  that R uses: `"character"` and `"numeric"` (or `"double"`).
These are the basic building blocks that all R objects are built from. The other
4 **atomic vector** types are:

* `"logical"` for `TRUE` and `FALSE` (the boolean data type)
* `"integer"` for integer numbers (e.g., `2L`, the `L` indicates to R that it's an integer)
* `"complex"` to represent complex numbers with real and imaginary parts (e.g.,
  `1 + 4i`) and that's all we're going to say about them
* `"raw"` for bitstreams that we won't discuss further

Vectors are one of the many **data structures** that R uses. Other important
ones are lists (`list`), matrices (`matrix`), data frames (`data.frame`),
factors (`factor`) and arrays (`array`). In this class, we will focus on data
frames, which is most commonly used one for data analyses.

> #### Challenge
>
> * We’ve seen that atomic vectors can be of type character, numeric (or
double), integer, and logical. But what happens if we try to mix these types in 
>   a single vector? Find out by using `class` to test these examples.
> 
> ```{r}
> num_char <- c(1, 2, 3, 'a')
> num_logical <- c(1, 2, 3, TRUE)
> char_logical <- c('a', 'b', 'c', TRUE)
> tricky <- c(1, 2, 3, '4')
> ```
> 
> <!-- * _Answer_: R implicitly converts them to all be the same type -->
>
> 
> - This happens because vectors can be of only one data type. Instead of
>  throwing an error and saying that you are trying to mix different types in
>  the same vector, R tries to convert (coerce) the content of this vector to
>  find a "common denominator". A logical can be turn into 1 or 0, and a number
>  can be turned into a string/character representation. It would be difficult
>  to do it the other way around: would 5 be TRUE or FALSE? What number would
>  't' be?
> 
> - In R, we
>   call converting objects from one class into another class
>   _coercion_. These conversions happen according to a hierarchy,
>   whereby some types get preferentially coerced into other
>   types. Can you draw a diagram that represents the hierarchy of how
>   these data types are coerced?
> <!-- * _Answer_: `logical -> numeric -> character <-- logical` -->


## Subsetting vectors

If we want to extract one or several values from a vector, we must provide one
or several indices in square brackets. For instance:

```{r}
animals <- c("mouse", "rat", "dog", "cat")
animals[2]
animals[c(3, 2)]
```

We can also repeat the indices to create an object with more elements than the
original one:

```{r}
more_animals <- animals[c(1, 2, 3, 2, 1, 4)]
more_animals
```

R indices start at 1. Programming languages like Fortran, MATLAB, Julia, and R
start counting at 1, because that's what human beings typically do. Languages in
the C family (including C++, Java, Perl, and Python) count from 0 because that
was historically simpler for computers and can allow for more elegant code.


### Conditional subsetting

Another common way of subsetting is by using a logical vector. `TRUE` will
select the element with the same index, while `FALSE` will not:

```{r}
weight_g <- c(21, 34, 39, 54, 55)
weight_g[c(TRUE, FALSE, TRUE, TRUE, FALSE)]
```

Typically, these logical vectors are not typed by hand, but are the output of
other functions or logical tests. For instance, if you wanted to select only the
values above 50:

```{r}
weight_g > 50    # will return logicals with TRUE for the indices that meet the condition
## so we can use this to select only the values above 50
weight_g[weight_g > 50]
```

You can combine multiple tests using `&` (both conditions are true, AND) or `|`
(at least one of the conditions is true, OR), similar to how you can do when
using search engines online:

```{r}
weight_g[weight_g < 30 | weight_g > 50]
weight_g[weight_g >= 30 & weight_g == 21]
```

Here, `<` stands for "less than", `>` for "greater than", `>=` for "greater than
or equal to", and `==` for "equal to". The double equal sign `==` is a test for
numerical equality between the left and right hand sides, and should not be
confused with the single `=` sign, which performs variable and parameter
assignment (similar to `<-`).

A common task is to search for certain strings in a vector.  One could use the
"or" operator `|` to test for equality to multiple values, but this can quickly
become tedious. The function `%in%` allows you to test if any of the elements of
a search vector are found:

```{r}
animals <- c("mouse", "rat", "dog", "cat")
animals[animals == "cat" | animals == "rat"] # returns both rat and cat
animals %in% c("rat", "cat", "dog", "duck", "goat")
animals[animals %in% c("rat", "cat", "dog", "duck", "goat")]
```

> #### Challenge
>
> * Can you figure out why `"four" > "five"` returns `TRUE`?

```{r, echo=FALSE, eval=FALSE}
## Answers
## * When using ">" or "<" on strings, R compares their alphabetical order. Here
##   "four" comes after "five", and therefore is "greater than" it.
```


## Missing data

As R was designed to analyze datasets, it includes the concept of missing data
(which is uncommon in other programming languages). Missing data are represented
in vectors as `NA`.

When doing operations on numbers, most functions will return `NA` if the data
you are working with include missing values. This feature
makes it harder to overlook the cases where you are dealing with missing data.
You can add the argument `na.rm=TRUE` to calculate the result while ignoring
the missing values.

```{r}
heights <- c(2, 4, 4, NA, 6)
mean(heights)
max(heights)
mean(heights, na.rm = TRUE)
max(heights, na.rm = TRUE)
```

If your data include missing values, you may want to become familiar with the
functions `is.na()`, `na.omit()`, and `complete.cases()`. See below for
examples. Prefixing with `!` returns the opposite Boolean values (i.e. `FALSE` instead of `TRUE` and `TRUE` instead of `FALSE`).

```{r}
## Extract those elements which are not missing values.
heights[!is.na(heights)]

## Returns the object with incomplete cases removed. The returned object is an atomic vector of type `"numeric"` (or `"double"`).
na.omit(heights)

## Extract those elements which are complete cases. The returned object is an atomic vector of type `"numeric"` (or `"double"`).
heights[complete.cases(heights)]
```
Recall that you can use the `class()` function to find the type of your atomic vector.

> #### Challenge
>
> 1. Using this vector of length measurements, create a new vector with the NAs
> removed.
>
> ```{r}
> lengths <- c(10,24,NA,18,NA,20)
> ```
>
> 2. Use the function `median()` to calculate the median of the `lengths` vector.


## Writing functions

In this class, you will be working a lot with functions, especially those that
someone else has already written. When you type `sum`, `c()`, or `mean()`, you
are using a function that has been made previously and built into R. To remove
some of the magic around these functions, we will go through how to make a basic
function of our own. Let's start with a simple example where we add two numbers
together:

```{r}
add_two_numbers <- function(num1, num2) {
    return(num1 + num2)
}
add_two_numbers(4, 5)
```

As you can see, running this function on two numbers returns their sum. We
could also assign to a variable in the function and return the function.

```{r}
add_two_numbers <- function(num1, num2) {
    my_sum <- num1 + num2
    return(my_sum)
}
add_two_numbers(4, 5)
```

> #### Challenge
>
> Can you write a function that calculates the mean of 3 numbers?
> 
> ```{r}
> mean_of_three_numbers <- function(num1, num2, num3) {
>    my_sum <- num1 + num2 + num3
>    my_mean <- my_sum / 3
>    return(my_mean)
> }
> mean_of_three_numbers(2, 4, 6)
> ```


## Loops and vectorization

Loop, or for-loops, are essential to programming in general. However, in R, you
should avoid them as often as possible because there are more efficient ways of
doing things that you should use instead. It is still important that you
understand the concept of loops and you might also use them in some of your own
functions if there is no vectorized way of going about what you want to do.

You can think of a for-loop as: "for each number contained in a list/vector,
perform this operation" and the syntax basically says the same thing:

```{r}
v <- c(2, 4, 6)
for (num in v) {
    print(num)
}
```

Instead of printing out every number to the console, we could also add numbers
cumulatively, to calculate the sum of all the numbers in the vector:

```{r}
# To increment `w` each time, we must first create the variable,
# which we do by setting `w <- 0`, referred to as initializing.
# This also ensures that `w` is zero at the start of the loop and
# doesn't retain the value from last time we ran this code.
w <- 0
for (num in v) {
    w <- w + num
}
w
```

If we put what we just did inside a function, we have essentially recreated the
`sum` function in R.

```{r}
my_sum <- function(input_vector) {
    vector_sum <- 0
    for (num in input_vector){
        vector_sum <- vector_sum + num
    }
    return(vector_sum)
}

my_sum(v)
```

Although this gives us the same output as the built-in function `sum`, the
built-in function has many more optimizations so it is much faster than our
function. In R, it is always faster to try to find a way of doing things without
writing a loop yourself. When you are reading about R, you might see suggestions
that you should try to *vectorize* your code to make it faster. What people are
referring to, is that you should not write for loops in R and instead use the
ready-made functions that are much more efficient in working with vectors and
essentially performs operations on entire vector at once instead of
one number at a time. If anyone is interested in more details about how this
works, please ask me after class, but conceptually loops operate on one element
at a time while vectorized code operate on all elements of a vector at once.