Descriptions of exercises are in green.
Homeworks are in pink

What is R?

R is an extremely powerful programming language, broadly used in science for:

R installation

To install R for Windows, follow the link and then click on “Download R – version_number – for Windows”.
To install R for OS X (Macs), follow the link and then click on “Download R for (Mac) OS X”
To install R for Linux, type the lines below in the terminal.

Run R. You should see a window similar to the one below.

It is the so-called R console. Anything written and executed within a console will be interpreted (calculated) by R, and the result or message will be printed out in the console.

Note on Programming Vocabulary

RStudio

RStudio is a shell and programming environment for the R language. It makes working with R much easier and more intuitive by providing a user interface to R features originally hidden behind R functions. However, remember that all actions can also be performed within the classical R console.

RStudio installation

Follow the link, choose the appropriate operating system, and install free RStudio Desktop. Have in mind that R needs to be installed first.

The RStudio interface is divided into four main panels, but today we will focus only on the Console panel, located in the lower-left corner. In the following classes, we will explore the other three panels and learn how to use them effectively.

R as a typical calculator

R understands standard mathematical operators: + (addition), - (subtraction), * (multiplication), / (division), and ^ (power). We can perform mathematical operations on single values – numbers, as well as other objects made up of numbers.

Exercise 1

Sum up all numbers from 1 to 10 using the + operator.
Expected result:

## [1] 55

Exercise 2

Raise the result of exercise 1 to the power of 5.
Expected result:

## [1] 503284375

R also provides 2 additional operators:
%% - modulo - returns the reminder from the division
%/% - integer division - returns how many times one number fits into another

Exercise 3

For numbers 10, 156, 557, 777, and 1055, check which are divisible by 7.
Expected result:

## [1] 3
## [1] 2
## [1] 4
## [1] 0
## [1] 5

Exercise 4

Calculate the area of a circle if the radius equals 40 meters.

Tip: Due to its unique role in science π value can be obtained just by typing ‘pi’.
Expected result:

## [1] 5026.548

Advice: R follows the standard order of mathematical operations. However, it is usually a good practice to use parentheses.

Apart from that, there are also commonly used mathematical functions as:

log() - natural logarithm
log10() - logarithm base 10
exp() - exponent, Euler number raised to a given power
sin(), cos(), tan() - trigonometric functions
abs() - absolute value

You can use them by including the desired number inside the parentheses, e.g. exponent of e for exp() or an angle in radians for any of the trigonometric functions.

Exercise 5

Using the equation for Shannon - Wiener index and species frequencies shown below, calculate diversity for both populations separately. Which is more diverse (higher values reflect more diverse populations)?

\[ H_{SW} = \sum_{i=1}^{S} p_i \cdot \ln\left(\frac{1}{p_i}\right) \]

Where:

  • \(H_{SW}\) is the Shannon-Wiener diversity index,
  • \(S\) is the total number of species,
  • \(p_i\) is the frequency of the given species,
  • \(\ln\) is the natural logarithm.
Species Population 1 Population 2
species 1 0.8 0.2
species 2 0.1 0.2
species 3 0.1 0.6

Expected result:

## [1] 0.6390319
## [1] 0.9502705

Variables

Until you name something, it does not exist in a computer memory! Any outcome of the execution of a command within the console perishes when the calculation is finished, unless it is assigned to a given name. Named objects within the computer memory are called variables. You can create one by using the arrow (assignment symbol) in the following manner:

chosen_name <- object_to_be_saved

You can easily recall the value of the variable later on by typing its name.

Exercise 6

Try to save 5 as a variable. Choose a variable name on your own. Then, type your variable’s name and press Enter.

Expected result:

## [1] 5

Advice: The variable name is case sensitive and cannot contain blank spaces or start with a digit. When you want to combine several words into one name, use the underscore (\_). By convention, dots are used for function names and should be used with caution.

Since the variable is saved, its name can replace the actual value in any R commands, e.g. if 2 is assigned to x, both 2+3 and x+3 would result in 5.

Exercise 7

Using the table from exercise 5, calculate the range of species frequencies for both populations and save them as separate variables. Then, using chosen names, calculate the absolute difference between ranges. Save it to a variable called range_diff and call it.

Expected result:

## [1] 0.3

Variables can also be overwritten. It is done by assigning a new object to the already used variable’s name. Remember, however, that once you overwrite the variable, the old value disappears for good.

Exercise 8

Change variable range_diff by increasing its value by 20%. Call it.

Expected result:

## [1] 0.36

Variables can store not only numbers. The other very popular type of data is a string. It is a text that behaves as a single object regardless of its length. To distinguish strings from variable names, R requires the use of quotation marks ("") around them.

Exercise 9

Save your name to the variable my_name. Call it.

Expected result:

## [1] "Your Name"

Functions

One of the usual ways to deal with your data in R is to use functions. They are simply lines of code saved in a computer memory that perform desired operations and often return a result. Some functions are built into R, and some require additional tools called packages to be installed. Think apps pre-loaded on your phone, like a calculator or a calendar, vs apps for specific uses you need to download separately. We will talk about packages in the next class.

Functions we used before take only a single argument, e.g., log() takes a number. However, it is rarely the case. The list of the function’s arguments and the way of usage can be found in the function’s manual. It can be reached by typing a question mark (?) followed by the function’s name.

Exercise 10

Open the manual for the paste() function.

Usually, the manual consists of 7 sections:

  • DESCRIPTION - the aim of the function
  • USAGE - the syntax
  • ARGUMENTS - arguments passed to the function and their meaning
  • DETAILS - detailed description of the function behaviour
  • VALUE - outcome of the function
  • REFERENCES - often the scientific article function is based on
  • EXAMPLES

Exercise 11

Use the paste() function to stick the following words together: ’I’m’, ‘using’, and ‘R’. Don’t forget about quotation marks ("").

Expected result:

## [1] "I’m using R"

Arguments passed to functions often have their own names. Distinctive names are crucial because many functions take multiple arguments that need to be distinguished. Such named arguments are passed in the following pattern: argument_name = argument_value.

Exercise 12

Use the same function as above, but set another argument called sep (separator) to ’_’.

Expected result:

## [1] "I’m_using_R"

Note that the blank space was replaced with an underscore. However, where did the blank spaces in the Exercise 11 result come from? The answer is that some arguments have their default values that would be taken if no value is put into the function. In the above case, the default value for the sep argument is a blank space (” “).

Advice: It is a good practice to use argument names while calling a function. Although R can “guess” the argument name by the order in which arguments are typed, it can work improperly when the number of arguments is not strictly defined (… sign in function description).

Vectors

A vector is a series of numbers (or strings) that are saved as a single variable. A new vector can be created with c() function in the following manner: c(value_1,value_2,value_3,…).

Exercise 13

Create a vector containing integers from 5 to 10 and save it to a variable. Call it.

Expected result:

## [1]  5  6  7  8  9 10

Tip: To create a vector of consecutive integers, you can type the limits of the range separated by a colon.

Exercise 14

Create a vector containing integers from 1 to 100 and save it to a variable one_to_hundred. Call it.

Expected result:

##   [1]   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18
##  [19]  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36
##  [37]  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54
##  [55]  55  56  57  58  59  60  61  62  63  64  65  66  67  68  69  70  71  72
##  [73]  73  74  75  76  77  78  79  80  81  82  83  84  85  86  87  88  89  90
##  [91]  91  92  93  94  95  96  97  98  99 100

Advice: Note that concerning ranges, R is fully inclusive, which means that both limits of the range will be included in the outcome.

To create a vector of consecutive numbers that differ by a given value, use the seq() function. Note that the function will return a vector, so there is no need to use c().

Exercise 15

Access the seq() manual. Using the seq() function, create a vector of numbers between 0 and 1 that differ by 0.1.

Expected result:

##  [1] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

To create a vector of repeated values, use the rep() function.

Exercise 16

Access the rep() manual. Using the rep() function, create a vector consisting of 1,2, and 3 repeated 20 times. Save it as a variable repeated. Call it.

##  [1] 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2
## [39] 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

Exercise 17

Create a vector from 1 to 4 with odd numbers typed as digits and even numbers typed as words. What is the outcome? Vector of integers or vector of strings?

Expected result:

## [1] "1"    "two"  "3"    "four"

Vector machinations

Useful functions:
min() - minimum value
max()- maximum value
sum() - sum up all numbers in a vector
prod() - multiply all numbers in a vector
mean() - average value
median() - central value
length() - number of elements in a vector
sort() - sort values (default is ascending order, use decreasing argument to sort in descending order)
unique() - return unique values
round() - round numbers (to integers by default)

Exercise 18

Having a vector one_to_hundred calculate its mean and median.

Expected results:

## [1] 50.5
## [1] 50.5

Exercise 19

Having a vector repeated sort it and return unique values.

Expected results:

##  [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [39] 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [1] 1 2 3

Vectors can also be used in typical mathematical operations. However, there is one important rule: the shorter vector will be repeated until it reaches the length of the longer one (a single number is treated as a vector of length 1).

Examples:

c(1,2,3,4) + 5   # 5 is added to each element, the same as c(1,2,3,4) + c(5,5,5,5)
## [1] 6 7 8 9
c(1,2,3,4) + c(1,2)   # the same as c(1,2,3,4) + c(1,2,1,2)
## [1] 2 4 4 6
paste("text", seq(1:10))   # Similarly here - the shorter vector including 1 element ("text") is repeated 10 times to reach the length of the longer vector.
##  [1] "text 1"  "text 2"  "text 3"  "text 4"  "text 5"  "text 6"  "text 7" 
##  [8] "text 8"  "text 9"  "text 10"

The result:

##  [1] "cat 1"   "dog 2"   "mouse 3" "cat 4"   "dog 5"   "mouse 6" "cat 7"  
##  [8] "dog 8"   "mouse 9" "cat 10"

Exercise 20

Having a vector one_to_hundred, raise each element to the power of 3. Save it to a variable called power_3.

Expected result:

##   [1]       1       8      27      64     125     216     343     512     729
##  [10]    1000    1331    1728    2197    2744    3375    4096    4913    5832
##  [19]    6859    8000    9261   10648   12167   13824   15625   17576   19683
##  [28]   21952   24389   27000   29791   32768   35937   39304   42875   46656
##  [37]   50653   54872   59319   64000   68921   74088   79507   85184   91125
##  [46]   97336  103823  110592  117649  125000  132651  140608  148877  157464
##  [55]  166375  175616  185193  195112  205379  216000  226981  238328  250047
##  [64]  262144  274625  287496  300763  314432  328509  343000  357911  373248
##  [73]  389017  405224  421875  438976  456533  474552  493039  512000  531441
##  [82]  551368  571787  592704  614125  636056  658503  681472  704969  729000
##  [91]  753571  778688  804357  830584  857375  884736  912673  941192  970299
## [100] 1000000

Accessing elements of a vector

A vector can be subsetted (=accessed or displayed at a specific point) in the following manner: vector_name[element_index]. Index is the position of the value in the vector, e.g., 1st, 3rd, 25th, etc.

Exercise 21

Return the 15th element of the vector power_3.

Expected result:

## [1] 3375

Exercise 22

Return the 2nd to 20th element of the vector power_3.

Tip: Colon can be used for ranges just as for vector creation.

Expected result:

##  [1]    8   27   64  125  216  343  512  729 1000 1331 1728 2197 2744 3375 4096
## [16] 4913 5832 6859 8000

Exercise 23

Return the 15th, 30th, and 45th elements of the vector power_3.

Tip: To obtain multiple values, put a vector instead single position index.

Expected result:

## [1]  3375 27000 91125

Exercise 24

Create a vector including numbers from 1 to 10, 40 and 55. Save it to a variable. Return corresponding elements of the vector power_3 with the use of previously saved variable.

Tip: While creating a vector, you can combine both ranges and single indexes with c() function.

Expected result:

##  [1]      1      8     27     64    125    216    343    512    729   1000
## [11]  64000 166375

Before leaving

If you want to save your code written during the class, type the commands below to save the R history.

savehistory(file = "my_history.txt")     # saves your R history to the file "my_history.txt"
getwd()                                  # displays where the file was saved

Homework

Please save all your R commands in a plain text file and call it “class_1_homework_Your_Name.txt” (replace “Your_Name” with your actual name). Then, upload the file to the Class 1 tab on the Pegaz platform.
1. Create a vector of the number of days in each month called days. The vector should have 12 elements and contain only numbers. Assume it is not a leap year.
2. Using vector days, find the median number of days in a month and save it to a new variable called median_days.
3. Using vector days, find the difference (in days) between the longest and shortest month and save it to a new variable called range_days. Find the longest and shortest month using R functions. 4. Using vector days, get a vector of unique month lengths and call a new vector month_length.
5. Overwrite the days vector by replacing it with the number of minutes in each month.