Data Structure

The post is about vector arithmetic in R Language. In R, different mathematical operations can be performed on vectors, that is vectors can be used in arithmetic expressions. The vector arithmetic operations are performed element by element.

It is important to note that vectors occurring in the same mathematical expression need not be of the same length (size). The shorter vectors in the arithmetic expression are recycled until they match the length of the longest vector.

Vector Arithmetic Operations

The vector arithmetic operations can be performed using arithmetic operators and vector functions. The +, -, *, /, and ^ are elementary arithmetic operators. The arithmetic functions are also available, such as, log, exp, sin, cos, tan, sqrt, and so on. The max() and min() functions returns the largest and smallest elements of a vector, respectively. Similarly, the range() function results in a vector of length two having minimum and maximum values from the vector, that is, c(min(x), max(x)).

The length(x) function returns the number of elements (size or number of observations) in a vector say $x$, sum(x) gives the total (sum) of the elements in vector $x$, and prod(x) returns the product of elements.

Instead of performing simple arithmetics (+, -, *, and /), we will use some functions for arithmetic that can be performed on a vector.

Vector Arithmetic in R: Examples

The basic vector arithmetic in R can be performed just like adding numbers on a calculator.

x <- c(1, 2, 3, 4, 5)
y <- c(4, 5, 6, 7, 8)

# Addition
x + y

# Subtraction
x - y

# Multiplication
x * y

# Division
x / y

# Exponentiation
x ^ y

One can compute the average (mean value) of a vector by performing arithmetics on a vector, such as

x <- c(5, 10, 5, 3, 5, 6, 7, 8, 4, 3, 10)
sum(x)/ length(x)

## Output
6

The built-in function for the computation of the average value of a vector is mean(), that is mean(x).

mean(x)

## output
6

The variance can also be computed by performing arithmetics on a vector say $x$.

sum((x - mean(x))^2)/ (length(x)-1)

## Output
6.2

The built-in function for sample variance is var(x). Note that if the argument var() is a $n$-by-$p$ matrix, a $p$-by-$p$ matrix of the sample covariance matrix will return.

var(x)

## Output
6.2

The sort(x) function returns a vector of the same size as $x$ with the elements arranged in increasing order.

sort(x)

## Output
[1]  3  3  4  5  5  5  6  7  8 10 10

The min() and max() functions are used to select the smallest and largest values from the argument, even if the argument contains several vectors.

In summary, Vector arithmetic is a fundamental aspect of R programming, enabling efficient and concise mathematical operations on sequences of elements. By understanding the basic operations, vector recycling, and available functions, you can effectively leverage vectors to solve a wide range of problems in data analysis and scientific computing.

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A vector in R is a set of numbers. A vector can be considered as a single column or a single row of a spreadsheet. The following examples are numbers that are not technically “vectors”. It is because these vectors are not in a column/row structure, however, they are ordered. These vectors can be referred to by index.

Creating Vector in R

# Creating a vector with the c function

c(1, 4, 6, 7, 9)

c(1:5, 10)

A vector in R language can be created using seq() function, it generates a series of numbers.

# Create a vector using seq() function

seq(1, 10, by = 2)
seq(0, 50, length = 11)
seq(1, 50, length = 11)

The vector can be created in R using the colon (:) operator. Following are the examples

# Create vector using : operator

1:10

## Output
[1]  1  2  3  4  5  6  7  8  9 10

5:1

## Output
[1] 5 4 3 2 1

The non-integer sequences can also be created in R Language.

# non-integer sequences
seq(0, 100*pi, by = pi)

One can assign a vector to a variable using the assignment operator (<-) or equal symbol (=). The examples are:

a <- 1:5
b <- seq(15, 3, length=5)
c <- a * b

There are a lot of built-in functions that can be used to perform different computations on vectors. For example,

a <- 1:5

# compute the total of elements of a vector
sum(a)

## Output
15

# product of elements of a vector
prod(a)

## Output
120

# average of the vector
mean(a)

## Output
3

# standard deviation and variance of a vector
sd(a)

## Output 
1.581139

var(a)

## Output
2.5

One can extract the elements of a vector by using square brackets and the index of the component of the vector.

V <- seq(0, 100, by = 10)
V[] # gives all the elements of the vector

## Output
[1]   0  10  20  30  40  50  60  70  80  90 100

V[5] # 5th elements from vector z

## Output
[1] 40

V[c(2, 4, 6, 8)] #2nd, 4th, th, and 8th element

## Output
[1] 10 30 50 70

V[-c(2, 4, 6, 8)] # elements except 2nd, 4th, 6th, and 8th element

## Output
[1]   0  20  40  60  80  90 100

The specific / required elements of a vector can be updated

V[c(2, 4)] <- c(500, 600) # the second and 4th element is updated to 500 and 600

https://itfeature.com

https://gmstat.com

The important points about vectors in R language are:

• Data Types: Vectors can hold logical, integer, double, character, complex, or raw data.
• Creation: Use the c() function to combine elements into a vector.
• Accessing Elements: Use indexing (square brackets) to access individual elements.
• Vector Operations: Perform arithmetic, logical, and comparison operations on vectors.
• Vectorization: R excels at vectorized operations, making calculations efficient.