R Data Structures In Depth -- R Programming

M1

Matrices and Arrays

Concept 1

Creating and Indexing Matrices

A matrix is a 2-dimensional vector — all elements same type, filled column-by-column by default.

R

m <- matrix(1:12, nrow=3, ncol=4)
#      [,1] [,2] [,3] [,4]
# [1,]   1    4    7   10
# [2,]   2    5    8   11
# [3,]   3    6    9   12

# Access [row, col] — both can be vectors
m[2, 3]        # 8
m[1, ]         # row 1: 1 4 7 10
m[, 2]         # col 2: 4 5 6
m[1:2, 3:4]    # submatrix

# Matrix operations
t(m)           # transpose
A <- matrix(c(1,2,3,4), 2,2)
solve(A)       # inverse
det(A)         # determinant = -2
A %*% t(A)     # matrix multiply

# apply over rows(1) or cols(2)
apply(m, 1, sum)   # row sums: 22 26 30
apply(m, 2, mean)  # col means: 2 5 8 11

Solved Examples

Example 1 Create a 4x4 matrix filled with 1:16, then extract the top-right 2x2 submatrix.

R

m <- matrix(1:16, 4, 4)
m[1:2, 3:4]
#      [,1] [,2]
# [1,]    9   13
# [2,]   10   14

Self-Assessment (2 questions)

Q1. In R, matrices are filled:

Q2. Which operator performs matrix multiplication in R?

M2

Lists and Data Frames

Concept 2

Lists — Flexible Containers

A list can hold any mix of types, including other lists. They're the backbone of model objects and API responses.

R

student <- list(
  name   = "Aarav Mehta",
  grade  = 11,
  scores = c(92, 88, 95),
  passed = TRUE
)

# Three equivalent access methods
student$name          # "Aarav Mehta"  ($ notation)
student[["grade"]]    # 11             ([[ ]] by name)
student[[3]]          # c(92,88,95)    ([[ ]] by position)

# [ ] returns a list; [[ ]] returns the element
student[1]            # list of length 1
student[[1]]          # the actual element (character)

# Modify / add
student$school <- "Vidaara Academy"
student[["grade"]] <- 12

# Apply functions over lists
score_lists <- list(a=1:5, b=6:10, c=11:15)
lapply(score_lists, mean)   # returns list: 3, 8, 13
sapply(score_lists, mean)   # returns named vector

Solved Examples

Example 1 Create a nested list: info <- list(student=list(name='Kavya', scores=c(88,92)), year=2024). Access Kavya's first score.

R

info <- list(student=list(name='Kavya', scores=c(88,92)), year=2024)
info$student$scores[1]   # 88
# or
info[["student"]][["scores"]][1]  # 88

Self-Assessment (2 questions)

Q1. What is the difference between list[1] and list[[1]] in R?

Q2. Which function applies a function to each list element and always returns a list?

Concept 3

Data Frames — Tabular Data

A data frame is R's primary structure for tabular data — a list of equal-length vectors treated as columns.

R

df <- data.frame(
  student = c("Aarav","Kavya","Rohan","Ananya"),
  score   = c(92, 88, 95, 78),
  grade   = c("A","B","A","C"),
  stringsAsFactors = FALSE   # modern default
)

# Inspect
nrow(df); ncol(df); dim(df)   # 4 3 | 4 3
str(df)       # structure and types
head(df, 2)   # first 2 rows
glimpse(df)   # tidyverse version of str()

# Access columns
df$score              # numeric vector
df[["student"]]       # same

# Filter rows
df[df$score >= 90, ]  # students scoring 90+
subset(df, score >= 90 & grade == "A") 

# Add column
df$passed <- df$score >= 80

# Tibbles (tidyverse data frames) — nicer printing
library(tibble)
tbl <- as_tibble(df)

Solved Examples

Example 1 From a data frame with columns name, math, english, science, find the student with the highest total score.

R

df <- data.frame(
  name    = c('Aarav','Kavya','Rohan'),
  math    = c(92,88,75),
  english = c(85,90,82),
  science = c(88,85,91)
)
df$total <- df$math + df$english + df$science
df[which.max(df$total), 'name']  # 'Aarav' with 265

Self-Assessment (2 questions)

Q1. How do you access the 'score' column of data frame df?

Q2. What does str(df) show?

M3

Factors and Dates

Concept 4

Factors for Categorical Data

Factors store categorical data as integer codes with a levels attribute. Essential for statistical models and ordered plots.

R

# Unordered factor
grade <- factor(c("A","B","A","C","B","A"))
levels(grade)    # "A" "B" "C" (alphabetical default)
table(grade)     # frequency table
nlevels(grade)   # 3

# Ordered factor (for comparisons)
size <- factor(c("Small","Large","Medium","Large"),
               levels=c("Small","Medium","Large"),
               ordered=TRUE)
size[1] < size[2]   # TRUE: Small < Large

# forcats package for manipulation
library(forcats)
fct_count(grade)              # frequency table as tibble
fct_relevel(grade, "C","B","A")  # reorder levels
fct_lump(grade, n=2)             # keep top 2, lump rest as 'Other'
fct_reorder(grade, score, mean)  # reorder by mean of another var

Solved Examples

Example 1 You have a factor experience with levels 'Junior','Senior','Lead' appearing in wrong order in a ggplot2 bar chart. Fix it.

R

experience <- factor(c('Senior','Junior','Lead','Junior','Senior'))
# Reorder for logical progression:
experience <- fct_relevel(experience, 'Junior','Senior','Lead')
levels(experience)  # 'Junior' 'Senior' 'Lead'
# Now ggplot2 bars appear in this order

Self-Assessment (2 questions)

Q1. When is an ordered factor appropriate?

Q2. Which package provides fct_relevel() and fct_lump()?