Arrays in R

Introduction

An array is a homogeneous data structure used to store elements of the same data type in multiple dimensions. An array is a generalization of a matrix: while a matrix is always two-dimensional, an array can have two, three, or more dimensions.

Arrays are useful for storing and manipulating multidimensional data such as:

• Marks of students in different subjects and semesters
• Temperature readings over days, months, and years
• Pixel values of images (height × width × color channels)
• Scientific and statistical data

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Characteristics of Arrays

• Homogeneous (all elements are of the same type).
• Can have two or more dimensions.
• Elements are stored column-wise.
• Elements are accessed by indices.
• Support element-wise arithmetic operations.
• Created using the array() function.

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Syntax

array(data, dim)

where:

• data : vector containing the elements.
• dim : dimensions of the array.

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One-Dimensional Array

A <- array(c(10,20,30,40))

print(A)

Output

[1] 10 20 30 40

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Two-Dimensional Array

A <- array(c(10,20,30,40,50,60), dim=c(2,3))

print(A)

Output

     [,1] [,2] [,3]
[1,]   10   30   50
[2,]   20   40   60

Since R stores elements column-wise:

10 30 50
20 40 60

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Three-Dimensional Array

A <- array(1:24, dim=c(3,4,2))

print(A)

Output

, , 1

     [,1] [,2] [,3] [,4]
[1,]    1    4    7   10
[2,]    2    5    8   11
[3,]    3    6    9   12

, , 2

     [,1] [,2] [,3] [,4]
[1,]   13   16   19   22
[2,]   14   17   20   23
[3,]   15   18   21   24

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Determining Array Properties

class()

A <- array(1:12, dim=c(3,4))

class(A)

Output

[1] "matrix"       # because it is 2-dimensional

For three-dimensional arrays:

A <- array(1:24, dim=c(3,4,2))

class(A)

Output

[1] "array"

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length()

Returns total number of elements.

length(A)

Output

[1] 24

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dim()

Returns dimensions.

dim(A)

Output

[1] 3 4 2

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Accessing Elements

Consider

A <- array(1:12, dim=c(3,4))

Output

     [,1] [,2] [,3] [,4]
[1,]    1    4    7   10
[2,]    2    5    8   11
[3,]    3    6    9   12

Access Individual Elements

A[2,3]

Output

[1] 8

(Row 2, Column 3)

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Access Entire Row

A[2,]

Output

[1] 2 5 8 11

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Access Entire Column

A[,3]

Output

[1] 7 8 9

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Access Elements of a 3D Array

A <- array(1:24, dim=c(3,4,2))

Access:

A[2,3,1]

Output

[1] 8

(Row 2, Column 3, Layer 1)

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Naming Dimensions

A <- array(
  1:12,
  dim=c(2,3,2),
  dimnames=list(
    Row=c("R1","R2"),
    Col=c("C1","C2","C3"),
    Layer=c("L1","L2")
  )
)

print(A)

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Array Arithmetic

A <- array(1:6, dim=c(2,3))
B <- array(7:12, dim=c(2,3))

print(A+B)

Output

     [,1] [,2] [,3]
[1,]    8   12   16
[2,]   10   14   18

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Subtraction

A-B

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Multiplication

A*B

Element-wise multiplication.

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Scalar Operations

A <- array(1:6, dim=c(2,3))

print(A+10)

Output

     [,1] [,2] [,3]
[1,]   11   13   15
[2,]   12   14   16

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Summation

sum(A)

Output

[1] 21

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Mean

mean(A)

Output

[1] 3.5

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Maximum and Minimum

max(A)
min(A)

Output

[1] 6

[1] 1

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Applying Functions Along Dimensions

Row Sums

A <- array(1:12, dim=c(3,4))

apply(A,1,sum)

Output

[1] 22 26 30

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Column Sums

apply(A,2,sum)

Output

[1]  6 15 24 33

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Modifying Elements

A <- array(1:6, dim=c(2,3))

A[2,3] <- 100

print(A)

Output

     [,1] [,2] [,3]
[1,]    1    3    5
[2,]    2    4  100

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Difference Between Vector, Matrix and Array

Structure	Dimensions
Vector	One-dimensional
Matrix	Two-dimensional
Array	Two or more dimensions

Example:

Vector

v <- c(1,2,3,4)

Matrix

M <- matrix(1:6, nrow=2)

Array

A <- array(1:24, dim=c(2,3,4))

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Example: Monthly Sales Data

Suppose sales of 3 products are recorded for 4 quarters during 2 years.

sales <- array(
    1:24,
    dim=c(3,4,2),
    dimnames=list(
      Product=c("P1","P2","P3"),
      Quarter=c("Q1","Q2","Q3","Q4"),
      Year=c("2024","2025")
    )
)

print(sales)

Find total sales:

sum(sales)

Find average sales:

mean(sales)

Find sales in 2025:

sales[,,2]

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Useful Functions

Function	Purpose
array()	Create array
dim()	Dimensions
length()	Number of elements
class()	Class of array
sum()	Sum
mean()	Average
max()	Maximum
min()	Minimum
apply()	Apply function
dimnames()	Dimension names

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Applications of Arrays

• Image processing
• Machine learning datasets
• Scientific computing
• Weather forecasting
• Financial data analysis
• Time-series data
• Multidimensional statistical data

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Conclusion

Arrays are multidimensional homogeneous data structures that extend vectors and matrices to higher dimensions. They provide an efficient way to organize and manipulate multidimensional data and support powerful element-wise and statistical operations. Arrays are widely used in scientific computing, machine learning, and data analysis.