Lesson 05: User-Defined Functions
Objectives
- Learn how to create and use your own MATLAB functions
- Learn how to create and use anonymous functions
Background
A user-defined function is a MATLAB program that is created by the user and saves as a function file. It can be used like a built-in function. A function usually has input arguments (or parameters) and/or output variables (or parameters). Both parameters can be scalars, vectors, matrices of any size. In MATLAB, a function can has any number of input and output parameters, also including zero.
5.1 Create a Function Files
Both scripts and function files allow you to reuse sequences of commands by storing them in program files. Script files are the simplest type of program, since they store commands exactly as you would type them at the command line. Function files provide more flexibility, primarily because you can pass input values and return output values. For example, this function named fact computes the factorial of a number (n) and returns the result (f).
function f = fact(n)
f = prod(1:n);
end
A function must be define within a file, not at the command line, and the function is usually stored in its own file. When creating a function file, the filename must be the same as the function name, since MATLAB associates the program with the filename. You can save the file either in the current project folder, or in a folder on the MATLABN search path.
You can call the function from the command line, using the same syntax rules that apply to MATLAB built-in functions. For instance, calculate the factorial of 5:
>> x = 5;
>> y = fact(5)
y = 120
To create a function file, you can click 
icon, then select 
icon to create a function.
function [outputArg1,outputArg2] = untitled(inputArg1,inputArg2)
%UNTITLED Summary of this function goes here
% Detailed explanation goes here
outputArg1 = inputArg1;
outputArg2 = inputArg2;
end
- untitled: (required) the name of the user-defined function
Valid function names follow the same rules as variable names. They must start with a letter, and can contain letters, digits, or underscores. - inputArg1, inputArg2: (optional) input parameters
- outoutArg1, outputArg2: (optional) output parameters
The parentheses are needed even if the function has no input parameter.
To avoid confusion, use the same name for both the function file and the first function within the file. MATLAB associates your program with the file name, not the function name.
Function with One Output
Function with One Output
If your function returns one output, you can specify the output name after the function keyword.
function myOutput = myFunction(x)
Example
Define a function in a file named average.m that accepts an input vector, calculates the average of the values, and returns a single result.
function ave = average(x)
ave = sum(x(:))/numel(x);
end
Call the function from the command line.
>> z = 1:99;
>> ave = average(z)
ave = 50
Function with Multiple Inputs
Function with Multiple Inputs
If your function accepts any inputs, enclose their names in parentheses after the function name. Separate inputs with commas.
function y = myFunction(one,two,three)
Example
Define a function to multiply x and y together.
function output = g(x,y)
a = x .* y;
output = a;
end
Call the function from the command line.
>> x = 1:5; y = 5:9;
>> g(x,y)
ans = 5 12 21 32 45
Function with Multiple Outputs
Function with Multiple Outputs
If your function returns more than one output, enclose the output names in square brackets.
function [one,two,three] = myFunction(x)
Example
Define a function in a file named stat.m that returns the mean and standard deviation of an input vector.
function [m,s] = stat(x)
n = length(x);
m = sum(x)/n;
s = sqrt(sum((x-m).^2/n));
end
Call the function from the command line.
>> values = [12.7, 45.4, 98.9, 26.6, 53.1];
>> [ave,stdev] = stat(values)
ave = 47.3400
stdev = 29.4124
Function with No Output and/or No Input
Function with No Output
If there is no output, you can omit it.
function myFunction(x)
Or you can use empty square brackets.
function [] = myFunction(x)
Function with No Output and No Input
If there is no output and no input, you can omit it.
function myFunction()
Or you can use empty square brackets.
function [] = myFunction()
Example
Define a function in a file named star.m that draw a star in polar coordinates.
function [] = star()
theta = pi/2:0.8*pi:4.8*pi;
r = ones(1,6);
polarplot(theta,r)
end
Call the function from the command line.
| >> star |  |
There are no returned values, but a figure window opens showing a star drawn in polar coordinates.
Multiple Functions in a Function File
Multiple Functions in a Function File
Define two functions in a file named stat2.m, where the first function calls the second.
function [m,s] = stat2(x)
n = length(x);
m = avg(x,n);
s = sqrt(sum((x-m).^2/n));
end
function m = avg(x,n)
m = sum(x)/n;
end
Function avg is a local function. Local functions are only available to other functions within the same file.
Call function stat2 from the command line.
>> values = [12.7, 45.4, 98.9, 26.6, 53.1];
>> [ave,stdev] = stat2(values)
ave = 47.3400
stdev = 29.4124
Function with Argument Validation
Function with Argument Validation
Define a function that restricts input to a numeric vector that contains no Inf or NaN elements. This function uses the arguments keyword, which is valid for MATLAB versions R2019b and later.
function [m,s] = stat3(x)
arguments
x (1,:) {mustBeNumeric, mustBeFinite}
end
n = length(x);
m = avg(x,n);
s = sqrt( sum((x-m).^2/n) );
end
function m = avg(x,n)
m = sum(x)/n;
end
In the arguments code block, (1,:) indicates that x must be a vector. The validation functions, {mustBeNumeric, mustBeFinite}, restrict the elements in x to numeric values that are not Inf or NaN. For more information, see Function Argument Validation.
Calling the function with a vector that contains an element that is NaN violates the input argument declaration. This violation results in an error being thrown by the mustBeFinite validation function.
>> values = [12.7, 45.4, 98.9, NaN, 53.1];
>> [ave,stdev] = stat3(values)
Invalid input argument at position 1. Value must be finite.
Practice Exercise 5.1
- Assuming that the matrix dimensions agree, create and test MATLAB functions to evaluate the following simple mathematical functions with multiple input vectors and a single output vector:
- $z(a,b,c) = a{b^c}$
- $z(w,x,y) = w{e^{(x/y)}}$
- $z(p,t)={}^{p}\!\!\diagup\!\!{}_{\sin (t)}\;$
- Assuming that the matrix dimensions agree, create and test MATLAB functions to evaluate the following simple mathematical functions with a single input vector and multiple output vectors:
- $f(x)=\cos (x)$
$f(x)=\sin (x)$ - $f(x)=5{{x}^{2}}+2$
$f(x)=\sqrt{5{{x}^{2}}+2}$ - $f(x)=\exp (x)$
$f(x)=\ln (x)$
- $f(x)=\cos (x)$
- Assuming that the matrix dimensions agree, create, and test MATLAB functions to evaluate the following simple mathematical functions with multiple input vectors and multiple output vectors:
- $f(x,y)=x+y$
$f(x,y)=x-y$ - $f(x,y)=y{{e}^{x}}$
$f(x,y)=x{{e}^{y}}$
- $f(x,y)=x+y$
5.5 Function in a Script File
To create a script file, you can
- Click New Script icon
. - or, click icon, then select
icon to create function.
Another option for storing function is to include them at the end of a script file. For instance, create a file named mystates.m with a few commands and two functions, fact and perm. The script calculates the permutation of (3,2).
x = 3;
y = 2;
z = perm(x,y)
function p = perm(n,r)
p = fact(n) * fact(n-1);
end
function f = fact(n)
f = prod(1:n);
end
Call the script from the command line.
>> mystates
z = 6
Questions
- Perhaps the most famous equation in physics is
$E=m{{c}^{2}}$
which relates energy E to mass m. The speed of light in a vacuum, c, is the property that links the two together. The speed of light in a vacuum is $2.9979\times {{10}^{8}}$ m/s.- Create a function called energy to find the energy corresponding to a given mass in kilograms. Your result will be in joules, since $1\,kg{}^{{{m}^{2}}}\!\!\diagup\!\!{}_{{{s}^{2}}}\;=1\,J$.
- Use your function to find the energy corresponding to masses from 1 kg to 106 kg. Use the logspace function (consult help logspace) to create an appropriate mass vector.
- Create four anonymous functions to represent the function $6{{e}^{3\cos {{x}^{2}}}}$, which is composed of the functions $h(z)=6{{e}^{z}}$, $g(y)=3\cos y$, and $f(x)={{x}^{2}}$. Use the anonymous function to plot $6{{e}^{3\cos {{x}^{2}}}}$ over the range 0 ≤ x ≤ 4.