MATLAB - Array Functions

MATLAB - Essential Array Functions

MATLAB is a matrix-based language, meaning arrays (vectors and matrices) are first-class citizens. Efficiently creating and manipulating arrays is the most critical skill for any MATLAB user. This tutorial covers the fundamental functions for array creation, inspection, and manipulation.

I. Array Creation Functions

These functions are used to initialize arrays of a specific size and content.

Function Name	Description
zeros	Creates an array of all zeros.
ones	Creates an array of all ones.
eye	Creates an identity matrix (ones on the diagonal, zeros elsewhere).
rand	Creates an array of uniformly distributed random numbers between 0 and 1.
randn	Creates an array of normally distributed (Gaussian) random numbers with mean 0 and variance 1.
linspace	Creates a vector of linearly spaced points between two endpoints.
magic	Creates a magic square matrix (for demonstration purposes).

Example: Creating Various Arrays

% Create a 3x4 matrix of zeros
A = zeros(3, 4);

% Create a 2x2 matrix of ones
B = ones(2, 2);

% Create a 4x4 identity matrix
I = eye(4);

% --- Reproducible Random Numbers ---
% Best Practice: Set the random seed for reproducible results
rng('default');

% Create a 2x5 matrix of uniformly distributed random numbers
U = rand(2, 5);

% Create a 3x1 column vector of normally distributed random numbers
N = randn(3, 1);

II. Array Information & Manipulation

Once an array exists, you need to query its properties and change its shape.

Function Name	Description
size	Returns the dimensions of the array as a row vector.
length	Returns the length of the largest dimension.
numel	Returns the total number of elements in the array.
reshape	Changes the dimensions of an array without changing its data.
' (apostrophe)	Performs the complex conjugate transpose. For real matrices, this is the simple transpose.
transpose	Performs the non-conjugate transpose.

Example: Inspecting and Reshaping

% Create a sample matrix
M = [1, 2, 3; 4, 5, 6];

% Get size information
dims = size(M)       % Result: [2, 3]
num_elements = numel(M) % Result: 6

% Reshape the 2x3 matrix into a 3x2 matrix
M_reshaped = reshape(M, 3, 2);
% Result:
%   1   5
%   4   3
%   2   6

% Transpose the matrix
M_transposed = M'; % Use the apostrophe operator for transpose
% Result:
%   1   4
%   2   5
%   3   6

III. Mathematical and Statistical Functions

MATLAB provides a rich library of functions that operate on entire arrays at once, a concept known as vectorization.

Function Name	Description & Key Usage
sum	sum(A) sums each column. sum(A, 2) sums each row. sum(A, 'all') sums all elements.
mean	mean(A) finds the mean of each column. Use dimensions like sum for other cases.
max	max(A) finds the maximum of each column. [M, I] = max(A) also returns the index.
min	Finds the minimum element, similar syntax to max.
sort	sort(A) sorts each column. sort(A, 'descend') sorts in descending order.
unique	Returns the unique elements of an array, sorted.

Example: Data Analysis on a Matrix

% Let's analyze a matrix of grades for 3 students across 4 tests
grades = [85, 92, 78, 88; ...
          95, 89, 91, 94; ...
          76, 81, 85, 79];

% Calculate the average grade for each test (mean of each column)
avg_test_grade = mean(grades)
% Result: [85.33, 87.33, 84.67, 87.00]

% Calculate the average grade for each student (mean of each row)
avg_student_grade = mean(grades, 2)
% Result:
%   85.75
%   92.25
%   80.25

% Find the highest grade on each test (max of each column)
[highest_grades, student_id] = max(grades)
% Result:
%   highest_grades = [95, 92, 91, 94]
%   student_id     = [2, 1, 2, 2]  (Student 2 got the highest on 3 tests)

% Find the total score for all tests combined
total_score = sum(grades, 'all')
% Result: 1018

Best Practice: Vectorization

A core principle of effective MATLAB programming is vectorization. This means using array-wide operations instead of for loops whenever possible. Vectorized code is more concise, readable, and significantly faster.

% --- The Slow, Non-Vectorized Way (AVOID) ---
x = 1:1000;
y = zeros(size(x));
for i = 1:length(x)
    y(i) = sin(x(i));
end

% --- The Fast, Vectorized MATLAB Way (PREFER) ---
x = 1:1000;
y = sin(x); % Apply sin directly to the entire vector