R语言从基础入门到提高（四）matrices（矩阵）

第1程序

What's a matrix（矩阵）?

100xp

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（二维）.

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:（三个参数说明）

#mark#重点理解

• 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（快捷方式） for c(1, 2, 3, 4, 5, 6, 7, 8, 9).
• The argument byrow indicates（表明） that the matrix is filled by the rows（行）. If we want the matrix to be filled by the columns（列）, we just place byrow = FALSE.
• The third argument nrow indicates that the matrix should have three rows.
• 注意这里都是 =   不是   = =   ！！！

要求：

Construct a matrix with 3 rows containing the numbers 1 up to 9, filled row-wise.

源程序：

# Construct a matrix with 3 rows that contain the numbers 1 up to 9

matrix ( 1:9, byrow = TRUE, nrow = 3 )

console：

> # 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    9

第2程序

Analyzing matrices, you shall

100xp

It is now time to get your hands dirty. In the following exercises you will analyze the box office numbers of the Star Wars franchise（选举）. May the force（闹剧） be with you!

In the editor, three vectors are defined. Each one represents（展现） the box office numbers from the first three Star Wars movies. The first element of each vector indicates the US box office revenue（税收）, 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.

要求：

• 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 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.

源程序：

# 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

console：

> # 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,] 309.306 165.8

第3程序：

Naming a matrix

100xp

To 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（特定） elements from the matrix.

Similar to vectors, you can add names for the rows and the columns of a matrix

rownames(my_matrix) <- row_names_vectorcolnames(my_matrix) <- col_names_vector

We went ahead and prepared two vectors for you: region, and titles. You will need these vectors to name the columns and rows of star_wars_matrix, respectively.

#mark#重点理解

这里使用的是  rownames ( ) ,和 colnames ( )

要求：

• Use colnames() to name the columns of star_wars_matrixwith the region vector.
• Use rownames() to name the rows of star_wars_matrix with the titles vector.
• Print out star_wars_matrix to see the result of your work.

源程序：

# 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)

#mark#重点理解

#这个地方已经把整个矩阵绘出来啦，只需指明 行，列名称。注意了解几行几列 ！！！

# 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

#对star_wars_matrix 指明列名 ，把region 向量赋给它

# Name the rows with titles

rownames( star_wars_matrix ) <- titles

#对star_wars_matrix 指明行名 ，把titles 向量赋给它

# Print out star_wars_matrix

star_wars_matrix

console：

> # 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  165.8

第4程序：

Calculating the worldwide（世界范围的） box office

100xp

The single most important thing for a movie in order to become an instant（快速） legend in Tinseltown（ 浮华城 ）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（方便的） calculates the totals for each row of a matrix. This function creates a new vector:

rowSums(my_matrix)

要求：

Calculate the worldwide box office figures for the three movies and put these in the vector named worldwide_vector.

源程序：

# Construct star_wars_matrix

box_office <- c(460.998, 314.4, 290.475, 247.900, 309.306, 165.8)

star_wars_matrix <- matrix(box_office, nrow = 3, byrow = TRUE,

                           dimnames = list(c("A New Hope", "The Empire Strikes Back", "Return of the Jedi"),

                                           c("US", "non-US")))

#mark#重点理解

# 这个地方用到了一个未知函数dimnames,6个数据，3行，每一行行名为list（）里的第一个向量里的参数，列名为第二个向量里的参数。

# Calculate worldwide box office figures

worldwide_vector <- rowSums (star_wars_matrix)

#这里输出时没有指定格式，它应该是默认啦

worldwide_vector

console：

> # Construct star_wars_matrix

> box_office <- c(460.998, 314.4, 290.475, 247.900, 309.306, 165.8)

> star_wars_matrix <- matrix(box_office, nrow = 3, byrow = TRUE,

                           dimnames = list(c("A New Hope", "The Empire Strikes Back", "Return of the Jedi"),

                                           c("US", "non-US")))

>

> # 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                 475.106

 

第5程序：

Adding a column for the Worldwide box office

100xp

In the previous exercise you calculated the vector that contained（包含） the worldwide box office receipt（收据） 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（多个） columns to a matrix with the cbind()function, which merges（合并） matrices and/or vectors together by column. For example:

big_matrix <- cbind(matrix1, matrix2, vector1 ...)

我的理解的简写：

cbind ( ) columns combine data 

rbind ( )  rows combine data

要求：

Add worldwide_vector as a new column to the star_wars_matrixand assign the result to all_wars_matrix. Use the cbind() function.

源程序：

# Construct star_wars_matrix

box_office <- c(460.998, 314.4, 290.475, 247.900, 309.306, 165.8)

star_wars_matrix <- matrix(box_office, nrow = 3, byrow = TRUE,

                           dimnames = list(c("A New Hope", "The Empire Strikes Back", "Return of the Jedi"), 

                                           c("US", "non-US")))

# 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

console：

> # Construct star_wars_matrix

> box_office <- c(460.998, 314.4, 290.475, 247.900, 309.306, 165.8)

> star_wars_matrix <- matrix(box_office, nrow = 3, byrow = TRUE,

                           dimnames = list(c("A New Hope", "The Empire Strikes Back", "Return of the Jedi"), 

                                           c("US", "non-US")))

> 

> # 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          475.106

第6程序：

Adding a row

100xp

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:

• star_wars_matrix that we have used all along, with data on the first trilogy（三部曲）,
• star_wars_matrix2, with similar data for the second trilogy.

Type the name of these matrices in the console and hit Enter if you want to have a closer look. If you want to check out the contents（目录） of the workspace, you can type ls() in the console.

要求：

Use rbind() to paste together star_wars_matrix and star_wars_matrix2, in this order. Assign the resulting matrix to all_wars_matrix.

源程序：

# star_wars_matrix and star_wars_matrix2 are available in your workspace

star_wars_matrix  

star_wars_matrix2 

# Combine both Star Wars trilogies in one matrix

all_wars_matrix <- rbind(star_wars_matrix,star_wars_matrix2)

all_wars_matrix

console:

> # star_wars_matrix and star_wars_matrix2 are available in your workspace

> # mark# 重点理解

> # 这个地方已经初始化完两个矩阵啦，直接使用。

> 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  165.8

> 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)

> 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

第7程序：

The total box office revenue for the entire （完整）saga（故事）

100xp

Just like every cbind() has a rbind(), every colSums() has a 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.

要求：

• Calculate the total revenue for the US and the non-US region and assign （赋值）total_revenue_vector. You can use the colSums()function.
• Print out total_revenue_vector to have a look at the results.

源程序：

# all_wars_matrix is available in your workspace

all_wars_matrix

#已经初始化完啦，可直接使用

# Total revenue for US and non-US

total_revenue_vector <- colSums(all_wars_matrix)

# Print out total_revenue_vector

total_revenue_vector

console：

> # 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

> #已经初始化完啦，可直接使用

> 

> # 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 2087.8

第8程序：

Selection of matrix elements

100xp

Similar to vectors, you can use the square brackets [ ] to select one or multiple elements from a matrix. Whereas（然而） vectors have one dimension（维度）, matrices have two dimensions. You should therefore use a comma（逗号） to separate（分离） that what to select from the rows from that what you want to select from the columns. For example:

#mark#重点理解

• my_matrix[1,2] selects the element at the first row and second column.
• 选择的是第一行，第二列 注意矩阵是二维的
• 第一个参数是行，第二个参数是列
• my_matrix[1:3,2:4] results in a matrix with the data on the rows 1, 2, 3 and columns 2, 3, 4.

If you want to select all elements of a row or a column, no number is needed before or after the comma, respectively:

     如果想选择全部行或列，那么就可以空着不写，只写逗号。

• my_matrix[,1] selects all elements of the first column.
• my_matrix[1,] selects all elements of the first row.

Back to Star Wars with this newly acquired knowledge! As in the previous exercise, all_wars_matrix is already available in your workspace.

要求：

• Select the non-US revenue for all movies (the entire second column of all_wars_matrix), store the result as non_us_all.
• Use mean() on non_us_all to calculate the average non-US revenue for all movies. Simply print out the result.
• This time, select the non-US revenue for the first two movies in all_wars_matrix. Store the result as non_us_some.
• Use mean() again to print out the average of the values in non_us_some.

源程序：

# all_wars_matrix is available in your workspace

all_wars_matrix

# Select the non-US revenue for all movies

non_us_all <- all_wars_matrix[ , 2]

# Average non-US revenue

mean( non_us_all )

# 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 )

console：

> # 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

> # 这个地方说明啦，说要的是  non-US的 前两个

> non_us_some <- all_wars_matrix[ 1:2, 2]

>   

> # Average non-US revenue for first two movies

> mean( non_us_some )

[1] 281.15

> ls()

[1] "all_wars_matrix" "non_us_all"      "non_us_some"  

> #这个地方使用 ls() 查看 当前所有变量 

第9程序：

A little arithmetic（计算） with matrices

100xp

Similar to what you have learned with vectors, the standard（标准） operators（运算符） 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.

所有元素都乘以2

As a newly-hired data analyst for Lucasfilm卢卡斯电影公司

it is your job is to find out how many visitors went to each movie for each geographical area（地理位置）. 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.

要求：

• Divide（除以） all_wars_matrix by 5, giving you the number of visitors in millions. Assign the resulting matrix to visitors.
• Print out visitors so you can have a look.

源程序：

# all_wars_matrix is available in your workspace

all_wars_matrix

# Estimate the visitors

visitors <- all_wars_matrix / 5

# Print the estimate to the console

visitors

console：

> # 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  93.70

第10程序：

A little arithmetic with matrices (2)

100xp

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（相应） elements in my_matrix1 and my_matrix2.

相当于矩阵相乘，线性代数里的知识点啦，不会的同学需要复习一下啦

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（重做） 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.

这个地方说两个相同矩阵相乘应该使用 %*%  

要求：

• Divide all_wars_matrix by ticket_prices_matrix to get the estimated（估计） number of US and non-US visitors for the six movies. Assign the result to visitors.
• From the visitors matrix, select the entire first column, representing （描述）the number of visitors in the US. Store this selection as us_visitors.
• Calculate the average number of US visitors; print out the result.

源程序：

# all_wars_matrix and ticket_prices_matrix are available in your workspace

all_wars_matrix

ticket_prices_matrix

# 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 )

console：

> # 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  468.5

> 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