Introduction to R

What is matrix?

In R, the matrix() function is a versatile tool for creating matrices.
A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

#matrix(data, nrow, ncol, byrow = FALSE, dimnames = NULL)

Arguements:
• data: A vector containing the elements of the matrix.
• nrow: The desired number of rows.
• ncol: The desired number of columns.
• byrow: A logical value indicating whether the matrix should be filled by row (TRUE) or by column (FALSE, default).
• dimnames: A list of two character vectors, providing row and column names.

3x3 Matrix

Create a 3x3 matrix with numbers 1 to 9, filled by row:

my_matrix <- matrix(1:9, nrow = 3, byrow = TRUE)
print(my_matrix)

##      [,1] [,2] [,3]
## [1,]    1    2    3
## [2,]    4    5    6
## [3,]    7    8    9

Analyze matrices

Box office movies of Star Wars named new_hope, empire_strikes and return_jedi

# 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)
print(box_office)

## [1] 460.998 314.400 290.475 247.900 309.306 165.800

# Construct star_wars_matrix
star_wars_matrix <- matrix(box_office, nrow = 3, byrow = TRUE)
print(star_wars_matrix)

##         [,1]  [,2]
## [1,] 460.998 314.4
## [2,] 290.475 247.9
## [3,] 309.306 165.8

Naming a matrix

The colnames() function in R is a versitile tool used to:

Retrieve Column Names:
• Returns a character vector containing the names of the columns in a data frame or matrix.
Set Column Names:
• Assigns new names to the columns of a data frame or matrix.
The new names must be provided as a character vector of the same length as the number of columns.

The rownames() function in R is used to:

Retrieve Row Names:
• Returns a character vector containing the names of the rows in a data frame or matrix.
Set Row Names:
• Assigns new names to the rows of a data frame or matrix.
The new names must be provided as a character vector of the same length as the number of rows.

# 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)
print(star_wars_matrix)

##         [,1]  [,2]
## [1,] 460.998 314.4
## [2,] 290.475 247.9
## [3,] 309.306 165.8

# 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
print(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  165.8

Calculate: `rowSums()`

The rowSums() function in R is used to calculate the sum of values across each row of a matrix or data frame.

# 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")

# Create a matrix named as star_wars_matrix     
star_wars_matrix <- matrix(box_office, 
                      nrow = 3, byrow = TRUE,
                      dimnames = list(titles, region))

# Display the created matrix
print(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  165.8

# Calculate worldwide box office figures
worldwide_vector <- rowSums(star_wars_matrix)

# Print the rowSums() result
worldwide_vector

##              A New Hope The Empire Strikes Back      Return of the Jedi 
##                 775.398                 538.375                 475.106

Adding Column: `cbind()`

The cbind() function in R is a versatile tool used to combine multiple objects (vectors, matrices, or data frames) by columns.
This means it stacks the objects horizontally, creating a new object with the combined columns.

# 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)
# Print worldwide_vector rowSums
print(worldwide_vector)

##              A New Hope The Empire Strikes Back      Return of the Jedi 
##                 775.398                 538.375                 475.106

# Bind the new variable worldwide_vector as a column to star_wars_matrix
all_wars_matrix <- cbind(star_wars_matrix, worldwide_vector)
# Print result of cbind() of start_wars_matrix and worldwide_vector
print(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          475.106

Calculate: `colSums()`

colSums() in R: Summing Up Columns

The colSums() function in R is a handy tool to calculate the sum of values within each column of a matrix or data frame.

# all_wars_matrix is available in your workspace
print(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          475.106

# Total revenue for US and non-US
total_revenue_vector <- colSums(all_wars_matrix)
  
# Print out total_revenue_vector
print(total_revenue_vector)

##               US           non-US worldwide_vector 
##         1060.779          728.100         1788.879

Adding Row `rbind()`

The rbind() function in R is used to combine multiple objects (vectors, matrices, or data frames) by rows. This means it stacks the objects vertically, creating a new object with the combined rows.

### Adding Row: `rbind()` function
star_wars_vector <- 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 Strike Back", "Return of the Jedi")

star_wars_matrix <- matrix(star_wars_vector,
                           nrow = 3, byrow = TRUE,
                           dimnames = list(titles, region))
print(star_wars_matrix)

##                           US non-US
## A New Hope             461.0  314.4
## The Empire Strike Back 290.5  247.9
## Return of the Jedi     309.3  165.8

star_wars_vector2 <- c(474.5, 552.5, 310.7, 338.7, 380.3, 468.5)
titles2 <- c("The Phantom Menace", "Attack of the Clones", "Revenge of the Sith")

star_wars_matrix2 <- matrix(star_wars_vector2,
                            nrow = 3, byrow = TRUE,
                            dimnames = list(titles2, region))
print(star_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)
# Print all_wars_matrix
print(all_wars_matrix)

##                           US non-US
## A New Hope             461.0  314.4
## The Empire Strike 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

Selection of matrix elements

In R, the matrix[] syntax is a powerful tool for accessing and manipulating specific elements, rows, or columns within a matrix.

matrix[row_index, column_index]

Subsetting a Row

my_matrix[row_index, ]

Subsetting a Column

my_matrix[, column_index]

# all_wars_matrix is available in your workspace
all_wars_matrix

##                           US non-US
## A New Hope             461.0  314.4
## The Empire Strike 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] 281.15

Algorithm on matrix

# all_wars_matrix is available in your workspace
all_wars_matrix

##                           US non-US
## A New Hope             461.0  314.4
## The Empire Strike 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 Strike 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  93.70

Arithmetic with matrices

ticket_price <- c(5.0, 5.0, 6.0, 6.0, 7.0, 7.0, 4.0, 4.0, 4.5, 4.5, 4.9, 4.9)
star_wars_title <- c("A New Hope", "The Empire Strikes Back", "Return of the Jedi",
                     "The Phantom Menace", "Attack of the Clones", "Revenge of the Sith")
region <- c("US", "non-US")

ticket_prices_matrix <- 

ticket_prices_matrix <- matrix(ticket_price, nrow = 6, byrow = TRUE,
                               dimnames = list(star_wars_title, region))

                               
# 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 Strike 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

ticket_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    4.5
## 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

Introduction to R

BotnieData

06 December 2024

What is matrix?

3x3 Matrix

Analyze matrices

Naming a matrix

Calculate: `rowSums()`

Adding Column: `cbind()`

Calculate: `colSums()`

Adding Row `rbind()`

Selection of matrix elements

Subsetting a Row

Subsetting a Column

Algorithm on matrix

Arithmetic with matrices

Introduction to R

BotnieData

06 December 2024

What is matrix?

3x3 Matrix

Analyze matrices

Naming a matrix

Calculate: rowSums()

Adding Column: cbind()

Calculate: colSums()

Adding Row rbind()

Selection of matrix elements

Subsetting a Row

Subsetting a Column

Algorithm on matrix

Arithmetic with matrices

Calculate: `rowSums()`

Adding Column: `cbind()`

Calculate: `colSums()`

Adding Row `rbind()`