Main Page
Server Info & Course Info
Loading......
Password
Matrix
Section 1. Matrix
Basic Characteristics
- 2D structure with rows and columns
- Contains same data type elements
- Example matrix:
this_mat = matrix(c(1:9),ncol=3)
this_mat
[,1] [,2] [,3]
[1,] 1 4 7
[2,] 2 5 8
[3,] 3 6 9
Matrix vs Vector vs List
Key Differences
| Type | Dimensions | Data Types |
|---|---|---|
| Vector | 1D | Single type |
| List | Mixed | Multiple types |
| Matrix | 2D | Single type |
Example Comparison
my_vector <- 1:9 # 1D
my_matrix <- matrix(1:9, nrow=3) # 2D
my_list <- list(c(1,2,3), "a", TRUE) # Mixed types
Method 1: matrix() Function
Basic Syntax
matrix(data, nrow, ncol, byrow)
Example 1 - Default
matrix(1:6, nrow=2)
# Output:
# [,1] [,2] [,3]
# [1,] 1 3 5
# [2,] 2 4 6
byrow Parameter
Column-wise vs Row-wise
# Column-wise (default)
matrix(1:4, nrow=2)
# Row-wise
matrix(1:4, nrow=2, byrow=TRUE)
Visual Comparison
Default: byrow=TRUE:
1 3 1 2
2 4 3 4
Method 2: Vector to Matrix
Dimension Assignment
my_vector <- c(5,3,9,1,6,4)
dim(my_vector) <- c(2,3)
Result
[,1] [,2] [,3]
[1,] 5 9 6
[2,] 3 1 4
Method 3: Row/Column Binding
rbind() for Rows
rbind(c(1,2,3), c(4,5,6))
# Output:
# [,1] [,2] [,3]
# [1,] 1 2 3
# [2,] 4 5 6
cbind() for Columns
cbind(c(1,4), c(2,5), c(3,6))
Method 4: Random Matrices
Normal Distribution
matrix(rnorm(4), nrow=2)
# Example output:
# [,1] [,2]
# [1,] -0.5604756 -0.9957987
# [2,] -0.2301775 1.0670417
Matrix Properties: Dimensions
Check Structure
my_matrix <- matrix(1:12, nrow=3)
dim(my_matrix) # Returns c(3,4)
nrow(my_matrix) # Returns 3
ncol(my_matrix) # Returns 4
Matrix Properties: Naming
Add Row/Column Names
rownames(my_matrix) <- c("Alice", "Bob", "Charlie")
colnames(my_matrix) <- c("Math", "Science", "History", "Art")
Result
Math Science History Art
Alice 1 4 7 10
Bob 2 5 8 11
Charlie 3 6 9 12
Create Student Grade Matrix
Question: NROW ? BYROW ?
student_grade= c(85, 90, 78, 92, 88, 95, 76, 89, 92)
student_name= c('Alice','Alice','Alice','Bob','Bob','Bob','Carol','Carol','Carol')
subject_name = c('Math','Biology','English','Math','Biology','English','Math','Biology','English')
NROW = ?
BYROW = ?
grades <- matrix(student_grade, nrow=NROW, byrow=BYROW)
rownames(grades) <- c("Alice", "Bob", "Carol")
colnames(grades) <- c("Math", "Bio", "Chem")
Final Result
Math Bio Chem
Alice 85 90 78
Bob 92 88 95
Carol 76 89 92
Section 2. Matrix Operations in R
1. Creating Matrices
Basic matrix creation example:
# Create a 2x3 matrix
my_matrix <- matrix(1:6, nrow=2)
print(my_matrix)
Output:
[,1] [,2] [,3]
[1,] 1 3 5
[2,] 2 4 6
2. Accessing Elements
Basic Indexing
# Get element at 2nd row, 3rd column
my_matrix[2, 3]
# Get entire first row
my_matrix[1, ]
# Get first and third columns
my_matrix[, c(1,3)]
3. Conditional Filtering
Extract elements meeting conditions:
# Create temperature matrix
temps <- matrix(c(22, 25, 18, 30, 15, 28), nrow=2)
# Find temperatures > 25
hot_days <- temps[temps > 25]
print(hot_days) # Output: 30 28
4. Merging Matrices
Row Binding (rbind)
classA <- matrix(c(80, 75, 90), nrow=1)
classB <- matrix(c(88, 82, 95), nrow=1)
combined <- rbind(classA, classB)
5. Merging Matrices
Column Binding (cbind)
quiz_scores <- matrix(c(15, 18, 20), ncol=1)
exam_scores <- matrix(c(45, 48, 50), ncol=1)
full_scores <- cbind(quiz_scores, exam_scores)
6. Matrix Splitting
Extract matrix subsets:
# Original 4x4 matrix
big_matrix <- matrix(1:16, nrow=4)
# Extract first two rows
top_section <- big_matrix[1:2, ]
7. Basic Math Operations
Element-wise operations:
# Create two matrices
m1 <- matrix(1:4, nrow=2)
m2 <- matrix(5:8, nrow=2)
# Element-wise multiplication
m1 * 2
# Matrix addition
m1 + m2
8. Row & Column Operations
Calculate totals and averages:
# Student score matrix
scores <- matrix(c(80,75,90, 85,88,92), nrow=2)
# Calculate total scores
rowSums(scores)
# Calculate subject averages
colMeans(scores)
9. Transposition
Flip matrix dimensions:
# Original gene matrix (genes x samples)
gene_matrix <- matrix(rnorm(9), nrow=3)
# Transposed matrix (samples x genes)
t(gene_matrix)
10. Dimension Adjustment
Reshaping matrices:
# Original 2x3 matrix
original <- matrix(1:6, nrow=2)
# Reshape to 3x2
dim(original) <- c(3,2)
Summary
- Matrix indexing starts at [1,1]
- Use rbind/cbind for combining data
- rowSums/colMeans for quick statistics
- Transpose with t() for different perspectives
Section 3. apply()
What is apply()?
- Simplifies matrix/array operations
- Avoid writing loops manually
-
Basic syntax:
apply(matrix, margin, function) margin=1: row-wisemargin=2: column-wise
apply() Example 1: Sum Rows
Create a score matrix:
scores <- matrix(c(80, 90, 75,
85, 88, 92,
78, 85, 90), ncol=3)
colnames(scores) <- c("Math", "Science", "English")
Calculate row sums:
apply(scores, 1, sum)
Output:
[1] 245 265 253
apply() Example 2: Find Max Columns
Same score matrix:
scores
Math Science English
[1,] 80 85 78
[2,] 90 88 85
[3,] 75 92 90
Find column maxima:
apply(scores, 2, max)
Math Science English
90 92 90
lapply(): List Processor
Works on lists/vectors:
student_ages <- list(c(18,19,20), c(21,22,19))
Calculate average ages:
lapply(student_ages, mean)
Output:
[[1]]
[1] 19
[[2]]
[1] 20.66667
sapply(): Simplified Output
Same age data:
student_ages <- list(c(18,19,20), c(21,22,19))
Get simplified vector:
sapply(student_ages, mean)
Output:
[1] 19.00000 20.66667
Compare lapply vs sapply
Input list:
weather <- list(rainy_days = c(3,5,2),
sunny_days = c(8,6,7))
lapply output:
[[1]]
[1] 3.333333
[[2]]
[1] 7
sapply output:
rainy_days sunny_days
3.333333 7.000000
tapply(): Group Statistics
Create sample data:
classes <- c("A", "B", "A", "B")
exam_scores <- c(88, 92, 85, 90)
Calculate class averages:
tapply(exam_scores, classes, mean)
Output:
A B
86.5 91.0
Real Case: Gene Matrix
Create sample data:
gene_expr <- matrix(rnorm(15, mean=50, sd=10),
nrow=5)
rownames(gene_expr) <- paste("Gene", 1:5)
Show matrix:
[,1] [,2] [,3]
Gene 1 52.3 48.7 55.1
Gene 2 61.8 43.2 59.4
...
Z-score Standardization
Calculate row-wise Z-scores:
getZ = function(x){
z=(x - mean(x)) / sd(x)
return(z)}
z_scores <- apply(gene_expr, 1, getZ)
Transpose the result:
z_scores <- t(z_scores)
Final matrix:
[,1] [,2] [,3]
Gene 1 0.12 -0.45 0.33
Gene 2 0.87 -1.02 0.15
...
Question: how can we get the averaged expression level (original value) of each gene?
Question: how can we find the highest z-score of each gene?
Summary Table
| Function | Input | Output | Best For |
|---|---|---|---|
| apply() | Matrix | Matrix | 2D calculations |
| lapply() | List/Vector | List | Multiple objects |
| sapply() | List/Vector | Vector | Clean results |
| tapply() | Vector | Vector | Group analysis |
Section 4. Using which() for Matrix Operations in R
What is which()?
- Finds positions where condition is TRUE
- Works with vectors, matrices, and arrays
- Returns numeric indices
# Simple vector example
scores <- c(78, 92, 85, 100, 65)
which(scores == 100) # Returns 4
which.max() - Find Maximum
- Fast way to find highest value position
exam_scores <- matrix(c(80, 92, 75,
100, 88, 82,
73, 95, 67), ncol=3)
which.max(exam_scores) # Returns position 4 (value 100)
Basic Position Finding
- Find exact matches in matrix
# Create sample score matrix
mat <- matrix(c(80, 100, 75,
100, 85, 90,
95, 88, 100), nrow=3)
# Find all perfect scores
perfect <- which(mat == 100)
print(perfect) # Returns positions 2, 4, 9
Combined Conditions
-
Use logical operators: & (AND), (OR)
# Students with math >80 AND english <60
math_scores <- c(85, 92, 78, 88)
english_scores <- c(55, 58, 72, 61)
which(math_scores > 80 & english_scores < 60)
# Returns positions 1 and 2
Matrix Filter Example
- Find students with total score >250
# Create score matrix (5 students x 3 subjects)
student_scores <- matrix(c(80, 75, 90,
92, 88, 85,
78, 82, 95,
85, 90, 88,
90, 92, 94), nrow=5, byrow=TRUE)
# Get row indices where sum >250
good_students <- which(rowSums(student_scores) > 250)
print(good_students) # Returns 2,3,4,5
Creating Sub-matrices
- Extract rows meeting criteria
# Continue from previous matrix
high_scores <- student_scores[which(rowSums(student_scores) > 250), ]
print(high_scores)
# Shows rows for students 2,3,4,5
Real-world Application
- Filter experimental data
# Gene expression matrix (genes x samples)
gene_data <- matrix(rnorm(100, mean=10), ncol=5)
rownames(gene_data)=paste0('gene',c(1:20))
Question: how can we find genes with high expression (>10) in all samples ?
Hint: use “min()”
Section 5. R Programming Practical Cases
Case 1: Student Grade Analysis System
Step 1: Create Grade Matrix
# Create matrix with 5 students' scores for 3 subjects
grades <- matrix(c(85, 92, 78,
90, 95, 88,
78, 89, 92,
95, 91, 87,
82, 93, 84),
nrow = 5, byrow = TRUE)
colnames(grades) <- c("Math", "Science", "English")
rownames(grades) <- paste("Student", 1:5)
Step 2: Calculate Total Scores
# Using apply() to calculate row sums
total_scores <- apply(grades, 1, sum)
names(total_scores) <- rownames(grades)
total_scores
Output:
Student 1 Student 2 Student 3 Student 4 Student 5
255 273 259 273 259
Step 3: Calculate Average Scores
# Using apply() with mean function
average_scores <- apply(grades, 1, mean)
round(average_scores, 1) # round to 1 decimal place
Output:
Student 1 Student 2 Student 3 Student 4 Student 5
85.0 91.0 86.3 91.0 86.3
Step 4: Find Math High Achievers
# Using which() to find high scorers
math_scores <- grades[, "Math"] # or grades[,1]
top_math <- which(math_scores >= 90)
grades[top_math, ]
Output:
Math Science English
Student 2 90 95 88
Student 4 95 91 87
Case 2: Gene Expression Data Cleaning
Step 1: Create Simulation Data
# Generate 100 genes x 10 samples matrix
set.seed(123)
gene_expr <- matrix(rnorm(1000, mean = 7, sd = 3),
nrow = 100)
colnames(gene_expr) <- paste("Sample", 1:10)
rownames(gene_expr) <- paste("Gene", 1:100)
Step 2: Filter Low Expression Genes
# Calculate row means and filter
row_means <- apply(gene_expr, 1, mean)
high_expr_genes <- gene_expr[row_means > 7, ]
dim(high_expr_genes)
Output:
[1] 52 10 # 52 genes remaining
Step 3: Log2 Transformation
# Apply log2 transformation column-wise
log2trans<-function(x){
result=log2(x + 1)
return(result)
}
log2_expr <- apply(high_expr_genes, 2, log2trans)
head(log2_expr[, 1:3])
Step 4: Find Top Expressed Genes
# Find top 10 genes by mean expression
top10_idx <- order(row_means, decreasing = TRUE)[1:10]
gene_expr[top10_idx, 1:3] # Show first 3 samples
Question: what’s the function of “order()” ?
Question: please check the function of “rank()” after class.
Key Functions Recap
apply():
MARGIN = 1for row operationsMARGIN = 2for column operations
which():
- Returns indices meeting conditions
- Works with matrices and vectors
rbind():
- Combine matrices vertically
- Ensure same number of columns