R: المصفوفات R والمصفوفات العادية

       Mathematics  Chinese Language  English
Alice     85    78    92
Bob     72    88    80
Charlie     90    85    87
Diana     65    70    75
Eve     95    92    88

# 5x3 Matrix
scores <- matrix(c(85, 78, 92,
                   72, 88, 80,
                   90, 85, 87,
                   65, 70, 75,
                   95, 92, 88),
                 nrow = 5, byrow = TRUE)
colnames(scores) <- c("Mathematics", "Chinese Language", "English")
rownames(scores) <- c("Alice", "Bob", "Charlie", "Diana", "Eve")

# 1. Each Student's Total Score(Sum in One Line)
row_sums <- apply(scores, 1, sum)

# 2. Average per subject(Calculate the average for a column)
col_means <- apply(scores, 2, mean)

# 3. Find the highest score in math
top_math <- which.max(scores[, "Mathematics"])

# One-dimensional vector
v <- 1:6
v
# [1] 1 2 3 4 5 6

# Convert to 2 row 3 List of Matrices
m <- matrix(v, nrow = 2, ncol = 3)
m
#      [,1] [,2] [,3]
# [1,]    1    3    5
# [2,]    2    4    6

m <- matrix(1:6, nrow = 2)

dim(m)        # [1] 2 3
nrow(m)       # [1] 2
ncol(m)       # [1] 3
length(m)     # [1] 6  ← Total Number of Elements

matrix(data, nrow = 1, ncol = 1, byrow = FALSE, dimnames = NULL)

# 1. Provide the data directly + Number of rows and columns
m1 <- matrix(1:6, nrow = 2)
#      [,1] [,2] [,3]
# [1,]    1    3    5   ← Fill by column by default
# [2,]    2    4    6

# 2. byrow = TRUE(Fill by Row)
m2 <- matrix(1:6, nrow = 2, byrow = TRUE)
#      [,1] [,2] [,3]
# [1,]    1    2    3
# [2,]    4    5    6

# 3. Add row and column names
m3 <- matrix(1:6, nrow = 2, byrow = TRUE,
            dimnames = list(c("row1", "row2"), c("colA", "colB", "colC")))
#     colA colB colC
# row1   1   2   3
# row2   4   5   6

# 4. Specify only nrow,ncol Automatic Inference
m4 <- matrix(1:6, nrow = 3)  # 3 row 2 col
#      [,1] [,2]
# [1,]    1    4
# [2,]    2    5
# [3,]    3    6

m <- matrix(1:6, nrow = 2, byrow = TRUE)
rownames(m) <- c("Alice", "Bob")
colnames(m) <- c("Mathematics", "Chinese Language", "English")
m
#     Mathematics Chinese Language English
# Alice   1    2    3
# Bob   4    5    6

m <- matrix(1:9, nrow = 3, byrow = TRUE,
            dimnames = list(c("Alice", "Bob", "Charlie"),
                          c("Mathematics", "Chinese Language", "English")))
m
#     Mathematics Chinese Language English
# Alice   1    2    3
# Bob   4    5    6
# Charlie   7    8    9

# A single element
m[2, 3]            # [1] 6
m["Bob", "English"]  # [1] 6

# Entire row
m[1, ]             # Mathematics 1 Chinese Language 2 English 3
m["Alice", ]        # Ibid.

# Align
m[, 1]             # Alice 1 Bob 4 Charlie 7
m[, "Mathematics"]        # Ibid.

# Find the math scores > 5 students
m[m[, "Mathematics"] > 5, ]
#     Mathematics Chinese Language English
# Bob   4 ...   ← Will not be selected
# Charlie   7    8    9

a <- matrix(1:6, nrow = 3, byrow = TRUE)
b <- matrix(7:12, nrow = 3, byrow = TRUE)

# Concatenate by row(Sum of Rows)
rbind(a, b)
#      [,1] [,2]
# [1,]    1    2
# [2,]    3    4
# [3,]    5    6
# [4,]    7    8
# [5,]    9   10
# [6,]   11   12

# Concatenate by Column(Sum of a Series)
cbind(a, b)
#      [,1] [,2] [,3] [,4]
# [1,]    1    2    7    8
# [2,]    3    4    9   10
# [3,]    5    6   11   12

m <- matrix(1:9, nrow = 3)

# Find the sum of each row(No need for a loop)
apply(m, 1, sum)
# [1] 12 15 18

# Find the sum of each column
apply(m, 2, sum)
# [1] 12 15 18

apply(X, MARGIN, FUN)

# 1=row(Process by row),2=col(Process by Column)
apply(m, 1, mean)   # Average per line
apply(m, 2, max)    # Maximum per column

# Custom Functions
apply(m, 1, function(x) max(x) - min(x))  # Range per row

# lapply Back to List
numbers <- list(a = 1:3, b = 4:6, c = 7:9)
result_l <- lapply(numbers, sum)
# $a 6
# $b 15
# $c 24

# sapply Return Vector(More commonly used)
result_s <- sapply(numbers, sum)
#  a  b  c
#  6 15 24

# 5 Students 3 Course Grades, grouped by "Gender"
scores <- c(85, 78, 92, 72, 88, 80, 90, 85, 87, 65, 70, 75, 95, 92, 88)
gender <- c("M", "F", "M", "M", "F", "F", "M", "M", "F", "M", "F", "M", "F", "M", "F")

# Calculate the average by gender
tapply(scores, gender, mean)
#   F   M 
# 84.6 81.5

# Sum the corresponding elements of two vectors
mapply(function(a, b) a + b, 1:3, 10:12)
# [1] 11 13 15

# 2x3x4 a three-dimensional array
arr <- array(1:24, dim = c(2, 3, 4))

# 1st 2x3 Matrix
arr[, , 1]
#      [,1] [,2] [,3]
# [1,]    1    3    5
# [2,]    2    4    6

# apply Supports multidimensional operations
apply(arr, c(1, 2), mean)  # Regarding No. 3 Find the average

m <- matrix(1:4, nrow = 2)
#      [,1] [,2]
# [1,]    1    3
# [2,]    2    4

# Transpose
t(m)
#      [,1] [,2]
# [1,]    1    2
# [2,]    3    4

# Matrix Multiplication (use m %*% m)
m %*% m
#      [,1] [,2]
# [1,]    7   15
# [2,]   10   22

# Inverse
solve(m)
#      [,1] [,2]
# [1,]   -2  1.5
# [2,]    1 -0.5

# ============================================
# Comprehensive Analysis of Class Performance
# Features:5 Student 3 A Comprehensive Analysis of the Course Grade Matrix
# ============================================

# 1. Create a Grade Matrix(Fill by Row:One student per line)
scores <- matrix(c(
  85, 78, 92,   # Alice
  72, 88, 80,   # Bob
  90, 85, 87,   # Charlie
  65, 70, 75,   # Diana
  95, 92, 88    # Eve
), nrow = 5, byrow = TRUE)

# Add row and column names
rownames(scores) <- c("Alice", "Bob", "Charlie", "Diana", "Eve")
colnames(scores) <- c("Mathematics", "Chinese Language", "English")

cat("=== Grade Matrix ===\n")
print(scores)

# 2. Each Student's Total Score(Sum by Row)
cat("\n=== Student's Total Score ===\n")
row_totals <- apply(scores, 1, sum)
print(row_totals)

# 3. Average per subject/Highest/Lowest(Tally by Column)
cat("\n=== Statistics by Subject ===\n")
col_stats <- apply(scores, 2, function(x) {
  c(mean = round(mean(x), 2),
    max = max(x),
    min = min(x),
    sd = round(sd(x), 2))
})
print(col_stats)

# 4. Average score per student(Calculate the average by row)
cat("\n=== Average Student Score ===\n")
row_means <- apply(scores, 1, mean)
print(round(row_means, 2))

# 5. Identify the student with the highest math score
top_math <- which.max(scores[, "Mathematics"])
cat("\nHighest Score in Math:", rownames(scores)[top_math], "(", max(scores[, "Mathematics"]), "min)\n")

# 6. Identify the student with the highest total score
top_total <- which.max(row_totals)
cat("Highest Total Score:", rownames(scores)[top_total], "(", max(row_totals), "min)\n")

# 7. Find a single subject < 70 students(Using Logical Indexes)
fail <- scores < 70
cat("\nFailed Courses(< 70):\n")
print(scores)
cat("\nDid I fail?(TRUE = Fail):\n")
print(fail)

# 8. Overall Ranking
cat("\n=== Overall Ranking(Sort by total score in descending order)===\n")
ranking <- order(row_totals, decreasing = TRUE)
result <- data.frame(
  Ranking = 1:5,
  Name = rownames(scores)[ranking],
  Total Score = row_totals[ranking],
  Average = round(row_totals[ranking] / 3, 2)
)
print(result)

=== Grade Matrix ===
    Mathematics Chinese Language English
Alice   85   78   92
Bob   72   88   80
Charlie   90   85   87
Diana   65   70   75
Eve   95   92   88

=== Student's Total Score ===
Alice Bob Charlie Diana Eve
255  240  262  210  275

=== Average Student Score ===
Alice   Bob   Charlie   Diana   Eve
85.00  80.00  87.33  70.00  91.67

=== Overall Ranking(Sort by total score in descending order)===
  Ranking Name Total Score Average
1   1 Eve  275 91.67
2   2 Charlie  262 87.33
3   3 Alice  255 85.00
4   4 Bob  240 80.00
5   5 Diana  210 70.00