Introduction to MATLAB Array: An Ultimate Guide

MATLAB Arrays are the backbone of efficient data computation and visualisation in various scientific and engineering applications. These enable users to handle large datasets, perform complex calculations, and easily represent multidimensional data. These provide a powerful Data Structure that enables efficient computation and visualisation of data in a wide range of scientific and engineering applications. Thus, for professionals entering the Web Development domain must learn about the powerful Data Structures. In this blog, we will explore what is a MATLAB Array, its types, operations, examples and a list of prebuilt functions. 

Table of Contents  

1) What are MATLAB Arrays?  

2) Array creation in MATLAB 

3) Operating on MATLAB Arrays

4) Types of MATLAB Array  

5) List of Array functions  

6) MATLAB Array examples

7) Conclusion  

What are MATLAB Arrays?  

MATLAB Arrays are a fundamental Data Structure representing collections of elements organised in a grid-like format. Unlike traditional Arrays, these can have multiple dimensions, making them suitable for handling complex data sets. They provide a versatile framework for storing and manipulating data, whether a single number, a vector, a matrix, or higher-dimensional data.   

One of their key advantages of MATLAB arrays is their ability to handle data in multiple dimensions. They can be called Matrices or Grids, where elements are arranged in rows and columns. MATLAB Arrays can have any number of dimensions, allowing for efficient storage and analysis of multidimensional data, such as images, signals, and 3D models.   

MATLAB projects provides indexing and slicing capabilities to access specific elements or subsets. Indexing allows users to retrieve specific elements by specifying their positions in the array using indices. Slicing, on the other hand, enables you to extract subsets of the Array by defining ranges or conditions. These operations empower you to selectively extract and manipulate the data you need for further analysis.

Array creation in MATLAB

Here are some common ways to create arrays in MATLAB:

Direct assignment

Let's see how directly assigning the data set help in the creation of Arrays:

1) Using square brackets:

myArray = [1 2 3 4 5];  % Creates a row vector myMatrix = [1 2 3; 4 5 6];  % Creates a 2x3 matrix

 

2) Using linspace:
 

evenlySpaced = linspace(1, 10, 5);  % Creates 5 evenly spaced points between 1 and 10

 

Using built-in functions

1) zeroes

zeroArray = zeros(3, 4);  % Creates a 3x4 matrix of zeros

 

2) ones

 

onesVector = ones(1, 6);  % Creates a row vector of ones

3) rand
 

randomMatrix = rand(2, 2);  % Creates a 2x2 matrix of random numbers between 0 and 1

 

Using colon operator

Generating sequences
 

sequence = 1:5;  % Creates a row vector with numbers 1 to 5

 

Combining Arrays

Concatenation

array1 = [1 2 3]; array2 = [4 5 6]; combined = [array1; array2];  % Concatenates vertically

 

Generating specific patterns

Eye

identityMatrix = eye(3);  % Creates a 3x3 identity matrix

 

Using functions

 

identityMatrix = eye(3);  % Creates a 3x3 identity matrix

 

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Operating on MATLAB Arrays  

MATLAB Arrays offer various built-in functions and operators for mathematical and logical operations. These operations can be applied element-wise, across entire matrices, or using broadcasting techniques. By leveraging these operations, features of MATLAB Arrays empower you to perform complex computations and transformations on your data efficiently. Whether you are conducting basic arithmetic or implementing advanced operations like Matlab Convolation for signal processing, MATLAB's array capabilities provide a versatile and powerful environment for a wide range of mathematical and computational tasks.

Whether you need to analyse data, solve equations, simulate systems, or perform statistical analysis, MATLAB Commands provides indexing and slicing capabilities to access specific elements or subsets of an array

Element-wise operations  

MATLAB allows you to perform arithmetic operations (addition, subtraction, multiplication, division) on arrays element-wise using operators (+, -, *, /). Element-wise logical operations (logical AND, OR, NOT) can be performed using operators (&, |, ~). Further, it provides functions such as sin, cos, exp, and log that can be applied element-wise to arrays.   

Matrix operations  

MATLAB Arrays support standard matrix operations, including matrix multiplication (* operator) and matrix power (^ operator). The .* and ./ operators perform element-wise multiplication and division between two arrays of the same size. MATLAB's dot and cross functions compute the dot product and cross product of vectors, respectively. 

Array broadcasting  

MATLAB enables Array broadcasting, a powerful feature that automatically extends arrays to match dimensions for element-wise operations. This allows you to perform operations between arrays of different sizes, making the code more concise and efficient. 

Statistical and mathematical functions  

MATLAB provides an extensive collection of statistical and mathematical functions that operate on Arrays. Functions such as mean, std, min, max, sum, and prod can be applied to Arrays to calculate statistical measures. Mathematical functions like sqrt, abs, round, and floor can be used for various numerical computations.

Types of MATLAB Array  

Now, let's dive deeper into the working of MATLAB Arrays, exploring indexing techniques, special array types, multidimensional arrays, and a fascinating mathematical concept called the Magic Square:

Indexing Array  

MATLAB Arrays are indexed using parentheses and square brackets. The indices start from 1, unlike many programming languages that start indexing from 0. This indexing convention aligns with mathematical notation and simplifies working with Arrays in MATLAB.   

To access the individual elements of an array, you can specify the indices corresponding to the row and column positions of the desired element. For example, to access the element at the second row and third column of matrix A, you would use syntax A(2, 3).   

In addition to accessing individual elements, MATLAB supports indexing to extract subsets of an Array. You can specify a range of indices to create a subarray or use logical expressions to select elements that satisfy specific conditions. This flexibility in indexing allows for efficient manipulation and data analysis within Arrays. 

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Special arrays  

MATLAB provides several functions to create special arrays with specific values or patterns. These functions simplify the process of initialising Arrays with predefined characteristics, saving time and effort. Here are a few commonly used special array functions:   

a) zeros() function: Creates an Array filled with zeros of a specified size.   

b) ones() function: Generates an Array filled with ones of a specified size.   

c) eye() function: This function in MATLAB generates an identity matrix, which is a square matrix where the diagonal elements are ones, while all other elements are zeros.   

d) rand() function: The "rand" function in MATLAB creates an Array filled with random values drawn from a uniform distribution between 0 and 1.   

These special array functions are particularly useful when initialising Arrays before performing calculations or when creating arrays with specific properties. Here's how Special Array functions work:

Multidimensional Array  

MATLAB Arrays can have more than two dimensions, making them suitable for handling complex data structures. Multidimensional Arrays represent higher-dimensional data, such as images, videos, and spatial-temporal datasets.   

To create a multidimensional array, you can specify the size of each dimension when defining the array. For example, a 3D Array can be created by specifying the number of rows, columns, and depth.   

Working with multidimensional arrays involves accessing and manipulating elements across multiple dimensions. MATLAB provides powerful tools for multidimensional arrays, including indexing, slicing, and reshaping operations. These operations allow for the selective extraction of data from specific dimensions or subarrays, making it convenient to analyse and process complex datasets.   

Magic Square  

A fascinating mathematical concept related to Arrays in MATLAB is the "Magic Square". It is a square matrix of size N x N that contains unique integers from 1 to N^2. The sum of elements in each column, row, and diagonal is equal in this square.  

MATLAB provides a built-in function called magic() that generates magic squares of various sizes. For example, calling magic(3) generates a 3x3 magic square. Magic squares have interesting properties and are often used in recreational mathematics and puzzle solving. Here's an example of Magic Square.

These squares showcase the versatility of MATLAB Arrays in representing and manipulating structured data. Moreover, they serve as an example of MATLAB's mathematical and computational capabilities. 

List of Array functions  

MATLAB provides a rich set of built-in functions designed to operate on Arrays. These functions extend the capabilities of MATLAB Arrays, enabling efficient data manipulation, analysis, and visualisation. Let's explore some of the key Array functions available in MATLAB. 

a) size(): Returns the size of an array along each dimension.  

b) length(): Returns the length of the largest dimension of an Array.  

c) numel(): Returns the total number of elements in an array.  

d) ndims(): This function returns the number of dimensions of an Array.  

e) reshape(): Changes the shape and size of an Array while preserving the total number of elements.  

f) cat(): Concatenates arrays along a specified dimension.  

g) repmat(): Replicates and tiles an array to create a larger Array.  

h) squeeze(): Removes singleton dimensions from an array.  

i) permute(): Rearranges the dimensions of an array.  

j) flip(): Flips the order of elements along a specified dimension.  

k) fliplr(): Flips the order of columns in a matrix.  

l) flipud(): Flips the order of rows in a matrix.  

m) diag(): Extracts or creates diagonal matrices from an Array.  

n) sort(): Sorts the array elements in ascending or descending order.  

o) unique(): Returns the unique elements of an Array.  

p) find(): Returns the indices of nonzero elements in an Array.  

q) max(): Returns the biggest value in an Array.  

r)  min(): Returns the smallest value in an Array.  

s)  mean(): Computes the mean value of an Array.  

t) sum(): Computes the sum of elements in an Array.  

u) prod(): Computes the product of elements in an Array.  

v) median(): Computes the median value of an Array.  

w) std(): Computes the standard deviation of an Array.  

x) cov(): Computes the covariance matrix of an Array.  

y) corrcoef(): Computes the correlation coefficient matrix of an Array.  

z) repmat(): Replicates and tiles an array to create a larger Array.  

These are just a few examples of the array functions available in MATLAB. The MATLAB documentation provides a comprehensive list of array functions and detailed usage explanations.  

Using these functions, MATLAB users can efficiently perform complex computations, data analysis, and visualisation tasks on arrays, making MATLAB a powerful tool for scientific and engineering applications.  

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MATLAB Array examples

Here are a few common examples of MATLAB Arrays:

Row vector

This code snippet creates a single row Array comprising 4 elements.
 

rowVector = [1 5 7 3];

 

1

5

7

3

 

Column vector

This command creates a single column Array with fourelements in it. The semicolon in the syntax is used to separate the roles:
 

columnVector = [4; 8; 2; 9];
4
8
2
9

 

Matrix

The following command creates a 3x3 matrix with 9 elements in it. The elements are arranged in 3 rows and 3 columns:

matrix = [1 6 2; 4 5 8; 3 9 7];

 

1	6	2
4	5	8
3	9	7

 

Empty Array

This creates an empty Array with no elements. It can be used as a placeholder or to initialise arrays later in your code.

emptyArray = [];

Conclusion 

MATLAB Array is a powerful and versatile Data Structure fundamental in scientific and engineering applications. It enables efficient computation, data manipulation, and visualisation. Throughout this blog, we have explored the key aspects of MATLAB Arrays, including operations, indexing techniques, Multidimensional Arrays, accessing data in Cell Arrays, and a range of essential functions.

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