In R, a matrix is a collection of elements of the same data type (numeric, character, or logical) arranged into a fixed number of rows and columns. Since you are only working with rows and columns, a matrix is called two-dimensional.
You can construct a matrix in R with the matrix() function. Consider the following example:
matrix(1:9, byrow = TRUE, nrow = 3)In the matrix() function:
The first argument is the collection of elements that R will arrange into the rows and columns of the matrix. Here, we use 1:9 which is a shortcut for c(1, 2, 3, 4, 5, 6, 7, 8, 9).
The argument byrow indicates that the matrix is filled by the rows. If we want the matrix to be filled by the columns, we just place byrow = FALSE.
The third argument nrow indicates that the matrix should have three rows.
Instructions
Construct a matrix with 3 rows containing the numbers 1 up to 9, filled row-wise.
# Construct a matrix with 3 rows that contain the numbers 1 up to 9
matrix(1:9, byrow = TRUE, nrow = 3)## [,1] [,2] [,3]
## [1,] 1 2 3
## [2,] 4 5 6
## [3,] 7 8 9It is now time to get your hands dirty. In the following exercises you will analyze the box office numbers of the Star Wars franchise. May the force be with you!
In the editor, three vectors are defined. Each one represents the box office numbers from the first three Star Wars movies. The first element of each vector indicates the US box office revenue, the second element refers to the Non-US box office (source: Wikipedia).
In this exercise, you’ll combine all these figures into a single vector. Next, you’ll build a matrix from this vector.
Instructions
Use c(new_hope, empire_strikes, return_jedi) to combine the three vectors into one vector. Call this vector box_office.
Construct a matrix with 3 rows, where each row represents a movie. Use the matrix() function to do this. The first argument is the vector box_office, containing all box office figures. Next, you’ll have to specify nrow = 3 and byrow = TRUE. Name the resulting matrix star_wars_matrix.
# Box office Star Wars (in millions!)
new_hope <- c(460.998, 314.4)
empire_strikes <- c(290.475, 247.900)
return_jedi <- c(309.306, 165.8)
# Create box_office
box_office <- c(new_hope,empire_strikes,return_jedi)
# Construct star_wars_matrix
star_wars_matrix <- matrix(box_office, byrow = TRUE, nrow =3)
star_wars_matrix## [,1] [,2]
## [1,] 460.998 314.4
## [2,] 290.475 247.9
## [3,] 309.306 165.8To help you remember what is stored in star_wars_matrix, you would like to add the names of the movies for the rows. Not only does this help you to read the data, but it is also useful to select certain elements from the matrix.
Similar to vectors, you can add names for the rows and the columns of a matrix
Two vectors region, and titles have been created. You will need these vectors to name the columns and rows of star_wars_matrix, respectively.
Instructions
# Box office Star Wars (in millions!)
new_hope <- c(460.998, 314.4)
empire_strikes <- c(290.475, 247.900)
return_jedi <- c(309.306, 165.8)
# Construct matrix
star_wars_matrix <- matrix(c(new_hope, empire_strikes, return_jedi), nrow = 3, byrow = TRUE)
# Vectors region and titles, used for naming
region <- c("US", "non-US")
titles <- c("A New Hope", "The Empire Strikes Back", "Return of the Jedi")
# Name the columns with region
colnames(star_wars_matrix) <- region
# Name the rows with titles
rownames(star_wars_matrix) <- titles
# Print out star_wars_matrix
star_wars_matrix## US non-US
## A New Hope 460.998 314.4
## The Empire Strikes Back 290.475 247.9
## Return of the Jedi 309.306 165.8The single most important thing for a movie in order to become an instant legend in Tinseltown is its worldwide box office figures.
To calculate the total box office revenue for the three Star Wars movies, you have to take the sum of the US revenue column and the non-US revenue column.
In R, the function rowSums() conveniently calculates the totals for each row of a matrix. This function creates a new vector:
rowSums(my_matrix)Instructions
Calculate the worldwide box office figures for the three movies and put these in the vector named worldwide_vector.
# Construct star_wars_matrix
box_office <- c(460.998, 314.4, 290.475, 247.900, 309.306, 165.8)
region <- c("US", "non-US")
titles <- c("A New Hope",
"The Empire Strikes Back",
"Return of the Jedi")
star_wars_matrix <- matrix(box_office,
nrow = 3, byrow = TRUE,
dimnames = list(titles, region))
# Calculate worldwide box office figures
worldwide_vector <- rowSums(star_wars_matrix)
worldwide_vector## A New Hope The Empire Strikes Back Return of the Jedi
## 775.398 538.375 475.106In the previous exercise you calculated the vector that contained the worldwide box office receipt for each of the three Star Wars movies. However, this vector is not yet part of star_wars_matrix.
You can add a column or multiple columns to a matrix with the cbind() function, which merges matrices and/or vectors together by column. For example:
big_matrix <- cbind(matrix1, matrix2, vector1 ...)Instructions
Add worldwide_vector as a new column to the star_wars_matrix and assign the result to all_wars_matrix. Use the cbind() function.
# Construct star_wars_matrix
box_office <- c(460.998, 314.4, 290.475, 247.900, 309.306, 165.8)
region <- c("US", "non-US")
titles <- c("A New Hope",
"The Empire Strikes Back",
"Return of the Jedi")
star_wars_matrix <- matrix(box_office,
nrow = 3, byrow = TRUE,
dimnames = list(titles, region))
# The worldwide box office figures
worldwide_vector <- rowSums(star_wars_matrix)
# Bind the new variable worldwide_vector as a column to star_wars_matrix
all_wars_matrix <- cbind(star_wars_matrix, worldwide_vector)
all_wars_matrix## US non-US worldwide_vector
## A New Hope 460.998 314.4 775.398
## The Empire Strikes Back 290.475 247.9 538.375
## Return of the Jedi 309.306 165.8 475.106After adding column to a matrix, the logical next step is adding rows.
Just like every action has a reaction, every cbind() has an rbind(). (We admit, we are pretty bad with metaphors.)
Your R workspace, where all variables you defined ‘live’ (check out what a workspace is), has already been initialized and contains two matrices:
Explore these matrices in the console if you want to have a closer look. If you want to check out the contents of the workspace, you can type ls() in the console.
Instructions
Use rbind() to paste together star_wars_matrix and star_wars_matrix2, in this order. Assign the resulting matrix to all_wars_matrix.
# Construct star_wars_matrix
box_office <- c(461.0, 314.4, 290.5, 247.9, 309.3, 165.8)
region <- c("US", "non-US")
titles <- c("A New Hope",
"The Empire Strikes Back",
"Return of the Jedi")
star_wars_matrix <- matrix(box_office,
nrow = 3, byrow = TRUE,
dimnames = list(titles, region))
# Construct star_wars_matrix2
box_office2 <- c(474.5, 552.5, 310.7, 338.7, 380.3, 468.5)
region2 <- c("US", "non-US")
titles2 <- c("The Phantom Menace",
"Attack of the Clones",
"Revenge of the Sith")
star_wars_matrix2 <- matrix(box_office2,
nrow = 3, byrow = TRUE,
dimnames = list(titles2, region2))
# star_wars_matrix and star_wars_matrix2 are now available in your workspace
star_wars_matrix ## US non-US
## A New Hope 461.0 314.4
## The Empire Strikes Back 290.5 247.9
## Return of the Jedi 309.3 165.8star_wars_matrix2 ## US non-US
## The Phantom Menace 474.5 552.5
## Attack of the Clones 310.7 338.7
## Revenge of the Sith 380.3 468.5# Combine both Star Wars trilogies in one matrix
all_wars_matrix <- rbind(star_wars_matrix, star_wars_matrix2)
all_wars_matrix## US non-US
## A New Hope 461.0 314.4
## The Empire Strikes Back 290.5 247.9
## Return of the Jedi 309.3 165.8
## The Phantom Menace 474.5 552.5
## Attack of the Clones 310.7 338.7
## Revenge of the Sith 380.3 468.5Continue with the next exercise and see how you can combine the results of the rbind() function with the colSums() function!
Just like cbind() has rbind(), colSums() has rowSums().
Your R workspace already contains the all_wars_matrix that you constructed in the previous exercise; type all_wars_matrix to have another look. Let’s now calculate the total box office revenue for the entire saga.
all_wars_matrix## US non-US
## A New Hope 461.0 314.4
## The Empire Strikes Back 290.5 247.9
## Return of the Jedi 309.3 165.8
## The Phantom Menace 474.5 552.5
## Attack of the Clones 310.7 338.7
## Revenge of the Sith 380.3 468.5knitr::kable(all_wars_matrix)| US | non-US | |
|---|---|---|
| A New Hope | 461.0 | 314.4 |
| The Empire Strikes Back | 290.5 | 247.9 |
| Return of the Jedi | 309.3 | 165.8 |
| The Phantom Menace | 474.5 | 552.5 |
| Attack of the Clones | 310.7 | 338.7 |
| Revenge of the Sith | 380.3 | 468.5 |
Instructions
Calculate the total revenue for the US and the non-US region and assign total_revenue_vector. You can use the colSums() function.
Print out total_revenue_vector to have a look at the results.
# all_wars_matrix is available in your workspace
all_wars_matrix## US non-US
## A New Hope 461.0 314.4
## The Empire Strikes Back 290.5 247.9
## Return of the Jedi 309.3 165.8
## The Phantom Menace 474.5 552.5
## Attack of the Clones 310.7 338.7
## Revenge of the Sith 380.3 468.5# Total revenue for US and non-US
total_revenue_vector <- colSums(all_wars_matrix)
# Print out total_revenue_vector
total_revenue_vector## US non-US
## 2226.3 2087.8Similar to vectors, you can use the square brackets [ ] to select one or multiple elements from a matrix. Whereas vectors have one dimension, matrices have two dimensions. You should therefore use a comma to separate the rows you want to select from the columns. For example:
If you want to select all elements of a row or a column, no number is needed before or after the comma, respectively:
Back to Star Wars with this newly acquired knowledge! As in the previous exercise, all_wars_matrix is already available in your workspace.
Instructions
# all_wars_matrix is available in your workspace
all_wars_matrix## US non-US
## A New Hope 461.0 314.4
## The Empire Strikes Back 290.5 247.9
## Return of the Jedi 309.3 165.8
## The Phantom Menace 474.5 552.5
## Attack of the Clones 310.7 338.7
## Revenge of the Sith 380.3 468.5# Select the non-US revenue for all movies
non_us_all <- all_wars_matrix[,2]
# Average non-US revenue
mean(non_us_all)## [1] 347.9667# Select the non-US revenue for first two movies
non_us_some <- all_wars_matrix[1:2,2]
# Average non-US revenue for first two movies
mean(non_us_some)## [1] 281.15Similar to what you have learned with vectors, the standard operators like +, -, /, , etc. work in an element-wise way on matrices in R.
For example, 2 * my_matrix multiplies each element of my_matrix by two.
As a newly-hired data analyst for Lucasfilm, it is your job to find out how many visitors went to each movie for each geographical area. You already have the total revenue figures in all_wars_matrix. Assume that the price of a ticket was 5 dollars. Simply dividing the box office numbers by this ticket price gives you the number of visitors.
Instructions
# all_wars_matrix is available in your workspace
all_wars_matrix## US non-US
## A New Hope 461.0 314.4
## The Empire Strikes Back 290.5 247.9
## Return of the Jedi 309.3 165.8
## The Phantom Menace 474.5 552.5
## Attack of the Clones 310.7 338.7
## Revenge of the Sith 380.3 468.5# Estimate the visitors
visitors <- all_wars_matrix / 5
# Print the estimate to the console
visitors## US non-US
## A New Hope 92.20 62.88
## The Empire Strikes Back 58.10 49.58
## Return of the Jedi 61.86 33.16
## The Phantom Menace 94.90 110.50
## Attack of the Clones 62.14 67.74
## Revenge of the Sith 76.06 93.70What do these results tell you? A staggering 92 million people went to see A New Hope in US theaters!
Just like 2 * my_matrix multiplied every element of my_matrix by two, my_matrix1 * my_matrix2 creates a matrix where each element is the product of the corresponding elements in my_matrix1 and my_matrix2.
After looking at the result of the previous exercise, big boss Lucas points out that the ticket prices went up over time. He asks to redo the analysis based on the prices you can find in ticket_prices_matrix (source: imagination).
Those who are familiar with matrices should note that this is not the standard matrix multiplication for which you should use * in R.
Instructions
# Construct star_wars_matrix
box_office3 <- c(5.0, 5.0, 6.0,6.0,7.0,7.0,4.0,4.0,4.5,4.4,4.9,4.9)
region3 <- c("US", "non-US")
titles3 <- c("A New Hope",
"The Empire Strikes Back",
"Return of the Jedi",
"The Phantom Menace",
"Attack of the Clones",
"Revenge of the Sith")
ticket_prices_matrix <- matrix(box_office3,
nrow = 6, byrow = TRUE,
dimnames = list(titles3, region3))
# all_wars_matrix and ticket_prices_matrix are available in your workspace
all_wars_matrix## US non-US
## A New Hope 461.0 314.4
## The Empire Strikes Back 290.5 247.9
## Return of the Jedi 309.3 165.8
## The Phantom Menace 474.5 552.5
## Attack of the Clones 310.7 338.7
## Revenge of the Sith 380.3 468.5ticket_prices_matrix## US non-US
## A New Hope 5.0 5.0
## The Empire Strikes Back 6.0 6.0
## Return of the Jedi 7.0 7.0
## The Phantom Menace 4.0 4.0
## Attack of the Clones 4.5 4.4
## Revenge of the Sith 4.9 4.9# Estimated number of visitors
visitors <- all_wars_matrix / ticket_prices_matrix
# US visitors
us_visitors <- visitors[,1]
# Average number of US visitors
mean(us_visitors)## [1] 75.01401