R — Vectors

What is a vector?

A vector is the most basic data structure in R — an ordered collection of values of the same type:

numbers <- c(1, 2, 3, 4, 5)
fruits <- c("apple", "banana", "cherry")
flags <- c(TRUE, FALSE, TRUE)

Even a single value is a vector of length 1:

x <- 42
length(x)  # 1

Creating vectors

# c() — combine values
v1 <- c(1, 2, 3)
v2 <- c("a", "b", "c")

# : operator — sequences
v3 <- 1:10        # 1 2 3 4 5 6 7 8 9 10
v4 <- 10:1        # 10 9 8 7 6 5 4 3 2 1

# seq() — flexible sequences
seq(1, 10)              # 1 2 3 4 5 6 7 8 9 10
seq(1, 10, by = 2)      # 1 3 5 7 9
seq(1, 10, length.out = 5)  # 1.0 3.25 5.50 7.75 10.00
seq(0, 1, by = 0.25)    # 0.00 0.25 0.50 0.75 1.00

# rep() — repetition
rep(1, 5)            # 1 1 1 1 1
rep(c(1, 2), 3)      # 1 2 1 2 1 2
rep(c("a", "b"), each = 3)  # a a a b b b

# Special vectors
numeric(5)    # 0 0 0 0 0
character(3)  # "" "" ""
logical(4)    # FALSE FALSE FALSE FALSE

Accessing elements

x <- c(10, 20, 30, 40, 50)

# By position
x[1]        # 10
x[5]        # 50

# Multiple positions
x[c(1, 3, 5)]  # 10 30 50

# Negative index — exclude
x[-1]       # 20 30 40 50
x[c(-1, -3)] # 20 40 50

# Range
x[2:4]      # 20 30 40

Subsetting with logical vectors

x <- c(10, 20, 30, 40, 50)

# Logical vector
x[c(TRUE, FALSE, TRUE, FALSE, TRUE)]  # 10 30 50

# Condition — creates a logical vector
x > 25       # FALSE FALSE TRUE TRUE TRUE
x[x > 25]    # 30 40 50

# Multiple conditions
x[x > 20 & x < 50]  # 30 40
x[x < 20 | x > 40]  # 10 50

# which() — get indices
which(x > 25)  # 3 4 5

Named vectors

scores <- c(Alice = 90, Bob = 85, Charlie = 95)

scores["Alice"]     # 90
scores[c("Alice", "Charlie")]  # 90 95

names(scores)        # "Alice" "Bob" "Charlie"
names(scores) <- c("A", "B", "C")

Modifying vectors

x <- c(1, 2, 3, 4, 5)

# Change elements
x[1] <- 10        # 10 2 3 4 5
x[c(2, 4)] <- 0   # 10 0 3 0 5

# Add elements
x <- c(x, 6)      # append
x <- c(0, x)      # prepend

# Remove elements
x <- x[-1]        # remove first
x <- x[x != 3]    # remove all 3s

# Replace with condition
x[x < 0] <- 0     # replace negatives with 0

Vector functions

x <- c(3, 1, 4, 1, 5, 9, 2, 6)

length(x)     # 8
sum(x)        # 31
mean(x)       # 3.875
min(x)        # 1
max(x)        # 9
range(x)      # 1 9
prod(x)       # 6480
cumsum(x)     # 3 4 8 9 14 23 25 31
cumprod(x)    # 3 3 12 12 60 540 1080 6480

sort(x)             # 1 1 2 3 4 5 6 9
sort(x, decreasing = TRUE)  # 9 6 5 4 3 2 1 1
rev(x)              # 6 2 9 5 1 4 1 3

# Unique values
unique(x)     # 3 1 4 5 9 2 6
duplicated(x) # FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE

# Table of counts
table(x)
# x
# 1 2 3 4 5 6 9
# 2 1 1 1 1 1 1

Vectorized functions

Many functions work element-wise:

x <- c(1, 4, 9, 16, 25)

sqrt(x)       # 1 2 3 4 5
log(x)        # 0.00 1.39 2.20 2.77 3.22
log10(x)      # 0.00 0.60 0.95 1.20 1.40
exp(x)        # 2.72 54.60 8103.08 ...
abs(c(-1, 2, -3))  # 1 2 3
round(c(1.2, 2.5, 3.7), 0)  # 1 3 4
ceiling(c(1.2, 2.5, 3.7))   # 2 3 4
floor(c(1.2, 2.5, 3.7))     # 1 2 3

Recycling

When vectors have different lengths, R repeats the shorter one:

c(1, 2, 3) + 10      # 11 12 13
c(1, 2, 3) * c(10, 20)  # 10 40 30 — recycled!

Recycling is powerful but can cause subtle bugs. R warns when the lengths aren't multiples.

Combining vectors

a <- c(1, 2, 3)
b <- c(4, 5, 6)

c(a, b)          # 1 2 3 4 5 6
append(a, b)     # 1 2 3 4 5 6
append(a, b, after = 1)  # 1 4 5 6 2 3

String vectors

words <- c("hello", "world", "foo", "bar")

nchar(words)          # 5 5 3 3
toupper(words)        # "HELLO" "WORLD" "FOO" "BAR"
tolower(words)        # "hello" "world" "foo" "bar"
paste(words, collapse = " ")  # "hello world foo bar"
strsplit("a,b,c", ",")       # list with "a" "b" "c"
grep("o", words)             # 1 2 — indices matching "o"
gsub("o", "0", words)        # "hell0" "w0rld" "f00" "bar"

Common patterns

# Generate random data
rnorm(10)           # 10 random normal values
runif(10)           # 10 random uniform values (0-1)
sample(1:100, 10)   # 10 random integers from 1-100

# Sequences for iteration
for (i in 1:10) {
  print(i^2)
}

# Filtering
x <- c(10, 20, 30, 40, 50)
x[x > 25 & x < 45]  # 30 40

Mini Practice

1. Create a vector of the first 20 prime numbers
2. Calculate the cumulative sum of 1:100
3. Use logical subsetting to filter a vector to values between 10 and 50
4. Create a named vector mapping five students to their grades
5. Use sample() to simulate rolling a die 100 times and count occurrences with table()

Next: lists — collections of anything →