The simplest thing you could do with R is do arithmetic:
1 + 100
[1] 101
Here, we’ve added 1 and 100 together to make 101. The [1] preceding this we will explain in a minute. For now, think of it as something that indicates output.
Order of operations is the same as in maths class (from highest to lowest precedence):
Brackets
Exponents
Divide
Multiply
Add
Subtract
What will this evaluate to?
3 + 5 * 2
The “caret” symbol (or “hat”) is the exponent (to-the-power-of) operator (read x ^ y as “x to the power of y”). What will this evaluate to?
3 + 5 * 2 ^ 2
Use brackets (actually parentheses) to group to force the order of evaluation if it differs from the default, or to set your own order.
(3 + 5) * 2
[1] 16
But this can get unwieldy when not needed:
(3 + (5 * (2 ^ 2))) # hard to read
3 + 5 * 2 ^ 2 # easier to read, once you know rules
3 + 5 * (2 ^ 2) # if you forget some rules, this might help
See ?Arithmetic for more information, and two more operators (you can also get there by ?"+" (note the quotes)
If R thinks that the statement is incomplete, it will change the prompt from > to + indicating that it is expecting more input. This is not an addition sign! Press "Esc" if you want to cancel this statement and return to the prompt.
The usual sort of comparison operators are available:
1 == 1 # equality (note two equals signs, read as "is equal to")
[1] TRUE
1 != 2 # inequality (read as "is not equal to")
[1] TRUE
1 < 2 # less than
[1] TRUE
1 <= 1 # less than or equal to
[1] TRUE
1 > 0 # greater than
[1] TRUE
1 >= -9 # greater than or equal to
[1] TRUE
See ?Comparison for more information (you can also get there by help("==").
Really small numbers get a scientific notation:
2/10000
[1] 2e-04
which you can write in too:
2e-04
[1] 2e-04
Read e-XX as “multiplied by 10^XX”, so 2e-4 is 2 * 10^(-4).
### Mathematical functions
R has many built in mathematical functions that will work as you would expect:
sin(1) # trig functions
[1] 0.8415
asin(1) # inverse sin (also for cos and tan)
[1] 1.571
log(1) # natural logarithm
[1] 0
log10(10) # base-10 logarithm
[1] 1
log2(100) # base-2 logarithm
[1] 6.644
exp(0.5) # e^(1/2)
[1] 1.649
Plus things like probability density functions for many common distributions, and other mathematical functions (e.g., Gamma, Beta, Bessel). If you need it, it’s probably there.
You can assign values to variables using the assignment operator <-, like this:
x <- 1/40
And now the variable x contains the value 0.025:
x
[1] 0.025
(note that it does not contain the fraction 1/40, it contains a decimal approximation of this fraction. This appears exact in this case, but it is not. These decimal approximations are called “floating point numbers” and at some point you will probably end up having to learn more about them than you’d like).
Look up at the top right pane of RStudio, and you’ll see that this has appeared in the “Workspace” pane.
Our variable x can be used in place of a number in any calculation that expects a number.
log(x)
[1] -3.689
sin(x)
[1] 0.025
The right hand side of the assignment can be any valid R expression.
x <- 100
Notice that assignment does not print a value.
Notice also that variables can be reassigned (x used to contain the value 0.025 and and now it has the value 100).
It is sometimes possible to use the = operator for assignment, though I don't fully understand when this is allowed and when not. Most people avoid the issue by always using the arrow <-.
Assignment values can contain the variable being assigned to: What will x contain after running this?
x <- x + 1
The right hand side is fully evaluated before the assignment occurs.
Variable names can contain letters, numbers, underscores and periods. They cannot start with a number. They cannot contain spaces at all. Different people use different conventions for long variable names, these include
periods.between.words
underscores_between_words
camelCaseToSeparateWords
What you use is up to you, but be consistent.
Exercise:
Compute the difference in years between now and the year that you started University. Divide this by the difference between now and the year when you were born. Multiply this by 100 to get the percentage of your life spent at university. Use parentheses if you need them, use assignment if you need it.
This problem is as much about thinking about formalising the ingredients of a problem as much as actually getting the syntax correct.
R was designed for people who do data analysis. As a result in R all data types are actually vectors (Think of vectors as containers for data, not as geometric vectors in coordinate space. More precisely, in R a vector is defined as a one-dimensional array). So the number ‘1’ is actually a vector of numbers that happens to be of length 1.
1
[1] 1
length(1)
[1] 1
To build a vector, use the c function (c stands for “concatenate” or “create”).
x <- c(1, 2, 40, 1234)
We have assigned this vector to the variable x.
x
[1] 1 2 40 1234
length(x)
[1] 4
(notice how RStudio has updated its description of x. If you click it, you’ll get an option to alter it, which is rarely what you want to do).
This is a deep piece of engineering in the design; most of R thinks quite happily in terms of vectors. If you wanted to double all the values in the vector, just multiply it by 2:
2 * x
[1] 2 4 80 2468
You can get the maximum value…
max(x)
[1] 1234
…minimum value…
min(x)
[1] 1
…sum…
sum(x)
[1] 1277
…mean value…
mean(x)
[1] 319.2
…and so on. There are huge numbers of functions that operate on vectors. It is more common that functions will work with vectors than that they won’t.
Vectors can be summed together:
y <- c(0.1, 0.2, 0.3, 0.4)
x + y
[1] 1.1 2.2 40.3 1234.4
And they can be concatenated together:
c(x, y)
[1] 1.0 2.0 40.0 1234.0 0.1 0.2 0.3 0.4
and scalars can be added to them
x + 0.1
[1] 1.1 2.1 40.1 1234.1
Be careful though: if you add/multiply together vectors that are of different lengths, but the lengths factor, R will silently “recycle” the length of the shorter one:
x
[1] 1 2 40 1234
x * c(-2, 2)
[1] -2 4 -80 2468
(note how the first and third element have been multiplied by -2 while the second and fourth element are multiplied by 2).
If the lengths to not factor (i.e., the length of the shorter vector is not a factor of the length of the longer vector) you will get a warning, but the calculation will happen anyway:
x * c(-2, 0, 2)
Warning: longer object length is not a multiple of shorter object length
[1] -2 0 80 -2468
This is almost never what you want. Pay attention to warnings. Note that Warnings are different to Errors. We just saw a warning, where what happened is (probably) undesirable but not fatal. You’ll get errors where what happened has been deemed unrecoverable. For example
x + z # fails because there is no variable z
Error: object 'z' not found
Just as with the scalars, as well as doing arithmetic operators we can do comparisons. This returns a new vector of TRUE and FALSE indicating which elements are less than 10:
x < 10
[1] TRUE TRUE FALSE FALSE
You can do vector-vector comparisons too:
x < y # all false as y is quite small.
[1] FALSE FALSE FALSE FALSE
And combined arithmetic operations with comparison operations. Both sides of the expression are fully evaluated before the comparison takes place.
x > 1/y
[1] FALSE FALSE TRUE TRUE
Be careful with comparisons: This compares the first element with -20, the second with 20, the third with -20 and the fourth with 20.
x >= c(-20, 20)
[1] TRUE FALSE TRUE TRUE
This does nothing sensible, really, and warns you again:
x == c(-2, 0, 2)
Warning: longer object length is not a multiple of shorter object length
[1] FALSE FALSE FALSE FALSE
All the comparison operators work in fairly predictable ways:
x == 40
[1] FALSE FALSE TRUE FALSE
x != 2
[1] TRUE FALSE TRUE TRUE
Sequences are easy to make, and often useful. Integer sequences can be made with the colon operator:
3:10 # sequence 3, 4, ..., 10
[1] 3 4 5 6 7 8 9 10
Which also works backwards
10:3 # the reverse
[1] 10 9 8 7 6 5 4 3
Step in different sizes
seq(3, 10, by=2)
[1] 3 5 7 9
seq(3, 10, length=10)
[1] 3.000 3.778 4.556 5.333 6.111 6.889 7.667 8.444 9.222 10.000
Now we will see the meaning of the [1] term – this indicates that you’re looking at the first element of a vector. If you make a really long vector, you’ll see new numbers:
seq(3, by=2, length=100)
[1] 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35
[18] 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69
[35] 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99 101 103
[52] 105 107 109 111 113 115 117 119 121 123 125 127 129 131 133 135 137
[69] 139 141 143 145 147 149 151 153 155 157 159 161 163 165 167 169 171
[86] 173 175 177 179 181 183 185 187 189 191 193 195 197 199 201
One thing you can do with sequences is you can very informally look at convergent sequences. For example, the sum of squares of the reciprocals of integers:
- What is the sum of the first four squares?
- What is the sum of the first 100?
- …of the first 10,000?
- if x is the answer to 3, what is the square root of 6 * x?
Exercise 1
1 + 1/4 + 1/9 + 1/16 # starting to get tedious to type
[1] 1.424
Exercise 2
squares <- (1:100)^2
sum(1/squares)
[1] 1.635
Exercise 3
sum(1 / (1:10000)^2)
[1] 1.645
Exercise 4
x <- sum(1 / (1:10000)^2)
sqrt(x * 6)
[1] 3.141