MATLAB tutorial for beginners

What MATLAB is and who uses it

MATLAB ("matrix laboratory") began as a tool by Cleve Moler for easy access to linear algebra libraries and became a commercial product of MathWorks. It combines a language, an interactive desktop, plotting, and toolboxes for signal processing, control systems, optimization, statistics, image processing and machine learning. Simulink, a companion product, models dynamic systems with block diagrams.

MATLAB is widely used in engineering and science courses, research labs, and industries such as automotive, aerospace and finance. It requires a paid license (many universities provide one). GNU Octave is free software with largely compatible syntax; it covers the core language and many functions but not MathWorks toolboxes or Simulink.

Install and run Hello, world

Install MATLAB from MathWorks, use MATLAB Online in a browser, or install GNU Octave from octave.org (Windows, macOS, Linux). Code is saved in .m files. A script is a file of commands; you run it by typing its name, without .m, in the Command Window.

% hello.m
disp('Hello, world!')

matlab -batch "hello"   # MATLAB from a terminal
octave hello.m          # GNU Octave
# Hello, world!

Comments start with %. A line that ends without a semicolon prints its result, so x = 5 shows x = 5, while x = 5; stays silent.

Variables and basic types

Variables are created by assignment and need no declaration. Numbers are double (64-bit floating point) by default, and even a single number is a 1-by-1 matrix.

x = 10;
y = 3;
x / y              % 3.3333
mod(x, y)          % 1
x ^ 2              % 100
name = 'Ana';
fprintf('%s is %d years old\n', name, 30)
% Ana is 30 years old
class(x)           % 'double'

Vectors and matrices

Square brackets build arrays: spaces or commas separate columns, semicolons separate rows. Indexing uses parentheses and starts at 1; end means the last index and : means "all".

v = [3 1 4 1 5];
v(1)               % 3
v(end)             % 5
v(2:4)             % [1 4 1]
v * 2              % [6 2 8 2 10]
v(v > 2)           % [3 4 5]   logical indexing
A = [1 2; 3 4];
A(2, :)            % second row: [3 4]
A'                 % transpose:  [1 3; 2 4]
A * A              % matrix product: [7 10; 15 22]
A .* A             % element-wise:   [1 4; 9 16]
b = [5; 11];
x = A \ b          % solves A*x = b: [1; 2]
z = zeros(2, 3);   % also ones, eye, rand
r = 0:0.25:1;      % [0 0.25 0.5 0.75 1]

Operators with a dot (.*, ./, .^) work element by element; without the dot they follow the rules of linear algebra. The backslash operator solves linear systems and is more accurate than computing inv(A) * b.

Control flow

score = 85;
if score >= 90
    disp('A')
elseif score >= 80
    disp('B')
else
    disp('C')
end

total = 0;
for k = 1:10
    total = total + k;
end
fprintf('total = %d\n', total)   % total = 55

n = 3;
while n > 0
    n = n - 1;
end

switch 'red'
    case {'red', 'green'}
        disp('a color')
    otherwise
        disp('unknown')
end

Every block ends with end. Many loops can be replaced by a vectorized expression: the loop above is the same as sum(1:10), which is shorter and usually faster. If you must build an array in a loop, preallocate it first, for example result = zeros(1, 1000);.

Functions and anonymous functions

A function lives in its own file whose name matches the function name. A function can return several outputs. Scripts can also contain local functions at the end of the file in recent MATLAB versions.

% stats.m
function [m, s] = stats(x)
%STATS Mean and sample standard deviation of a vector.
    m = mean(x);
    s = std(x);
end

[m, s] = stats([2 4 4 5 7])   % m = 4.4000, s = 1.8166
[biggest, where] = max([3 9 2])   % biggest = 9, where = 2

f = @(x) x.^2 + 1;            % anonymous function
f(3)                          % 10
f([1 2 3])                    % [2 5 10]
fzero(@(x) x.^2 - 2, 1)       % 1.4142, a root near 1
integral(f, 0, 1)             % 1.3333

Anonymous functions, created with @, are often passed to other functions such as fzero, integral, arrayfun or optimization routines. Write them with element-wise operators (.^) so they also work on vectors.

Structs and cell arrays

person.name = 'Ana';
person.age = 30;
fprintf('%s is %d\n', person.name, person.age)   % Ana is 30

c = {'Ana', 30, [1 2 3]};   % cell array with mixed types
c{2}                         % 30 (curly braces get the content)
class(c(2))                  % 'cell' (parentheses get a sub-cell)
names = {'Ana', 'Ben', 'Cleo'};
numel(names)                 % 3
upper(names{1})              % 'ANA'

MATLAB also has a table type for column-oriented data with named variables, similar to a spreadsheet; readtable loads CSV and Excel files into it.

Error handling

Raise an error with error, optionally with an identifier such as 'demo:negative', and handle it with try ... catch. The caught object (an MException in MATLAB) has identifier and message fields.

% safe_sqrt.m
function r = safe_sqrt(x)
    if x < 0
        error('demo:negative', 'Input must be non-negative, got %g', x);
    end
    r = sqrt(x);
end

try
    safe_sqrt(-4);
catch err
    fprintf('%s: %s\n', err.identifier, err.message)
end
% demo:negative: Input must be non-negative, got -4

Use warning(...) for problems that should not stop the program. Without the check, sqrt(-4) would not fail at all: it returns the complex number 0 + 2i.

A small complete program: analyze and plot data

% temps.m - analyze a week of temperatures
temps = [21.5 23.0 19.8 25.1 24.3 18.9 22.7];
days = 1:numel(temps);

avg = mean(temps);
[hottest, idx] = max(temps);
above = days(temps > avg);

fprintf('Average: %.2f\n', avg)
fprintf('Hottest: %.1f on day %d\n', hottest, idx)
fprintf('Days above average: %s\n', mat2str(above))

plot(days, temps, '-o')
hold on
plot(days, avg * ones(size(days)), '--')
xlabel('Day'); ylabel('Temperature (C)')
title('Temperatures this week')
legend('Daily', 'Average')
% Average: 22.19
% Hottest: 25.1 on day 4
% Days above average: [2 4 5 7]

The script uses logical indexing to find the days above the average without a loop, then draws a line chart with markers and a dashed average line. The same code runs in GNU Octave.

Where to go next

• The MATLAB documentation from MathWorks, starting with the getting-started pages.
• MATLAB Onramp, the free interactive introductory course from MathWorks.
• The GNU Octave manual if you use Octave, including its notes on MATLAB compatibility.
• Learn vectorization, readtable for data files and the plotting functions next.