Data Structure

The logical vectors in R Language are the vectors whose elements are TRUE, FALSE, or NA (Not Available). R language allows the easy manipulation of logical (or relational) quantities. The TRUE and FALSE values are often used to represent the conditions or Boolean expressions.

In R, the reserved words TRUE and FALSE are often abbreviated as T and F, respectively. However, the T and F are not reserved words and hence can be overwritten by the user. Therefore, instead of T and F; it is better to use TRUE and FALSE.

Logical vectors in R can be created by:

• Direct assignment of TRUE and FALSE values to the elements of a vector
• By using conditions (use of logical or comparison operators) on elements of the vectors. (Operators in R Language)
• Using ifelse statement

Creating Logical Vectors in R Using Direct Assignment

v1 <- c(TRUE, FALSE, TRUE)
print(v1)
## Output
[1]  TRUE FALSE  TRUE

Creating Logical Vectors using Comparison Operators

x <- 5
y <- 10
v2 <- x > y
print(v2)
## Output
FALSE

data <- c(1, 2, 3, 4, 5)
v3 <- data < 3
print(v3)
## Output
[1]  TRUE  TRUE FALSE FALSE FALSE

Creating Logical Vectors using ifelse Statement

The ifelse statement can also be used to create/generate logical vectors in R Language. For example,

data <- c(3, 4, 6, 8, 4, 4, 6, 10, -5)
v4 <- ifelse(data > 5, TRUE, FALSE)
print(v4)

## Output
[1] FALSE FALSE  TRUE  TRUE FALSE FALSE  TRUE  TRUE FALSE

From the above examples, the logical vectors are usually generated by conditions. The length of the logical vector will be the same as that of the vectors to which the condition is applied. Depending on the condition, the corresponding elements result in FALSE if the element of the vectors does not meet the condition specified and TRUE where it is.

Logical Operators

The following is the list of logical operators

In addition to logical operators, the relational/logical operators are:

Use of Logical Operators

Filtering Data

The logical vectors in R language are commonly used for filtering the data. For example,

data <- data.frame(x = c(1, 2, 3, 4, 5), y = c("a", "b", "c", "d", "e"))
filtered_data <- data[data$x > 3, ]

Ordinary Arithmetic

Logical vectors may be used in ordinary arithmetic, in which case they are coerced into numeric vectors, FALSE becoming 0 and TRUE becoming. For example,

x = c(TRUE, FALSE, FALSE, TRUE)
y = c(5, 10, 6, 15)
x+y

## Output
[1]  6 10  6 16

sum(x)
## Output
[1] 2

Logical vectors in R language are a fundamental tool for working with conditions and Boolean expressions. Understanding how to create, manipulate, and use logical vectors is essential for effective data analysis and programming in R.

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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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