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1 Built-In Functions

Functions take in input(s) and produce output(s). There are plenty of built-in functions in Octave which do something based on what they are given, here are some examples:

format compact

% Return the square root of the given number
sqrt(2)

% Convert the string to lowercase
lower('HELLO, WORLD!')

% Return a 1x7 matrix of random numbers sampled from the interval (0, 1)
rand(1, 7)

% Return the current date
date

% Convert the current date into ISO 8601 format
datestr(date, 29)

% Return the data type of a variable
typeinfo(42)
## ans = 1.4142
## ans = hello, world!
## ans =
##    0.718787   0.806083   0.978761   0.860265   0.231144   0.612126   0.048602
## 
## ans = 07-Aug-2023
## ans = 2023-08-07
## ans = scalar

2 Custom Functions

In Octave, there are script files and function files, both of which have the .m extension. A function file starts with a function declaration (it only has empty lines or comments above this) whereas the first code in a script file (not counting empty lines or comments) is anything other than a function declaration. It’s good practice to start script files with some variation of clc; clear; close;, not just because those commands are useful but because this will ensure that the file is not mistaken by Octave for a function file.

Here’s an example of a function being defined and then being called in a script file:

% Prevent Octave from thinking that this is a function file
clc; clear; close;

% Create a custom function
function [root1, root2] = quadratic_formula(a, b, c)
    % Quadratic root finder
    % ax² + bx + c = 0
    % https://en.wikipedia.org/wiki/Quadratic_formula
    discriminant = b^2 - 4 * a * c;
    root1 = (-b + sqrt(discriminant)) / (2 * a);
    root2 = (-b - sqrt(discriminant)) / (2 * a);
endfunction

% Call a custom function
[root1, root2] = quadratic_formula(5, 6, 1);

% Display the results
root1
root2
## root1 = -0.2000
## root2 = -1

3 Function Files

If the above function declaration is moved into its own file that will then be a function file:

% quadratic_formula.m

% Quadratic root finder
% ax² + bx + c = 0
% https://en.wikipedia.org/wiki/Quadratic_formula

function [root1, root2] = quadratic_formula(a, b, c)
    discriminant = b^2 - 4 * a * c;
    root1 = (-b + sqrt(discriminant)) / (2 * a);
    root2 = (-b - sqrt(discriminant)) / (2 * a);
endfunction

This can now be called from within a script file. Note that it is the name of the function file that is called, not the name of the function itself that is called. For this reason, it is good practice to make the name of a function file (the part before the .m extension) be the same as that of the function that is defined within it. Indeed, Octave will print a warning if this is not the case.

For our example, both the function file and the function are called quadratic_formula. This can be called from within a script file as follows:

% Prevent Octave from thinking that this is a function file
clc; clear; close;

% Call a custom function from an external function file
% 5x² + 6x + 1 = 0
[root1, root2] = quadratic_formula(5, 6, 1);

% Display the results
root1
root2
## root1 = -0.2000
## root2 = -1

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