MATLAB for Beginners: Functions

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Functions

A function is a self-contained block of code that performs a specific task and can be called upon multiple times within your program. In MATLAB, functions can be defined using the function keyword followed by the function name, input arguments (optional), output arguments (optional), and the function body. Here’s the basic structure:

function [output_arguments] = function_name(input_arguments)
  % Function body
  % Your code here...
  % ...
  % Perform calculations, data manipulation, etc.
  % ...
end

Description:

function keyword: This tells MATLAB that you are defining a function.
output_arguments: This is an optional comma-separated list of variables that will store the results of the function’s calculations. These variables will be accessible outside the function.
function_name: This is the name of your function. Choose a descriptive name that reflects what the function does.
input_arguments: This is an optional comma-separated list of variables that will be passed to the function when it is called. These variables will be accessible inside the function.
% Function body: This is the main part of your function, where you write the code that performs the desired task. You can use any MATLAB commands and functions within the function body.
end: This marks the end of your function definition.

Important:

This declaration statement must be the first executable line of the function. Valid function names begin with an alphabetic character, and can contain letters, numbers, or underscores.

While it’s not strictly required, matching the function name and file name in MATLAB is a commonly followed and recommended practice for function files (m-files containing only function definitions).

Example #1: Addition Function

% This function adds two numbers together and returns the sum.
function sumResult = addNumbers(a, b)
    % Define the input arguments:
    % - a: The first number to be added (numerical value)
    % - b: The second number to be added (numerical value)
    
    % Perform addition and store the result in a variable.
    sumResult = a + b;
end

This function takes two numbers as input and returns their sum. You can call the function like this:

y = addNumbers(4,9);
disp(y);

Example #2: Simple function to square a number

function result = square(x)
  result = x * x;
end

This function takes a number as input and returns its square. You can call the function like this:

y = square(5);
disp(y);

The variable y will now contain the value 25.

Example #3: Function to calculate the area of a rectangle

function area = rectangleArea(width, height)
  area = width * height;
end

This function takes the width and height of a rectangle as inputs and returns its area. You can call the function like this:

area = rectangleArea(3, 4);

The variable area will now contain the value 12.

Example #4: Area of a Triangle

function area = calculateTriangleArea(base, height)
    % Calculates the area of a triangle given its base and height
    
    area = 0.5 * base * height;
end

Example #5: Calculates the area of a circle

function area = circle_area(radius)
  % Calculate the area of a circle
  area = pi * radius^2;
end

You can call the function like this:

% Example usage
radius = 5;
my_area = circle_area(radius);
dispg(['The area of the circle is:', num2str(my_area)]);

Example #6: Area and Perimeter of a Rectangle

function [area, perimeter] = rectangleProperties(length, width)
    % Calculates the area and perimeter of a rectangle
    
    % Area
    area = length * width;
    
    % Perimeter
    perimeter = 2 * (length + width);
    
    % Display results
    fprintf('Area: %f\n', area);
    fprintf('Perimeter: %f\n', perimeter);
end

Example #7: Power Function

function result = powerFunction(base, exponent)
    % Calculates the power of a number
    
    result = base ^ exponent;
end

Example #8: Function to convert Celsius to Fahrenheit

function fahrenheit = celsiusToFahrenheit(celsius)
  fahrenheit = (celsius * 9/5) + 32;
end

This function takes a temperature in Celsius as input and returns the equivalent temperature in Fahrenheit. You can call the function like this:

fahrenheit = celsiusToFahrenheit(20);

The variable fahrenheit will now contain the value 68.

Example #9: positive or negative number

function takes a number as input and returns a string indicating whether it is positive, negative, or zero.

function output = positive_or_negative(x)
  % This function determines whether a number is positive, negative, or zero.
  %
  % Args:
  %   x: A number (integer or float).
  %
  % Returns:
  %   A string indicating whether the number is positive, negative, or zero.

  if x > 0
    output = 'positive';
  elseif x < 0
    output = 'negative';
  else
    output = 'zero';
  end
end

Code Explanation:

Takes a single input argument x, which can be any numeric type.
Uses an if statement to check the value of x:
- If x is greater than 0, the function returns the string “positive”.
- If x is less than 0, the function returns the string “negative”.
- Otherwise, the function returns the string “zero”.

Example Usage:

number = 5;
result = positive_or_negative(number);
disp(result); % This will print "positive"

Example #10: Function to find the minimum value in a list:**

function minValue = findMin(data)
  minValue = data(1);
  for i = 2:length(data)
    if data(i) < minValue
      minValue = data(i);
    end
  end
end

This function takes a list of numbers as input and returns the smallest number in the list. You can call the function like this:

data = [5, 1, 8, 3];
minVal = findMin(data);

The variable minVal will now contain the value 1.

Intermediate

Example #11: Factorial Calculator

function fact = factorialCalc(n)
    % Calculates the factorial of a non-negative integer
    
    if n == 0
        fact = 1;
    else
        fact = 1;
        for i = 1:n
            fact = fact * i;
        end
    end

Example #12: Fibonacci Sequence Generator

function fibSeq = fibonacci(n)
    % Generates the first n terms of the Fibonacci sequence
    
    fibSeq = zeros(1, n);
    fibSeq(1) = 0;
    fibSeq(2) = 1;
    
    for i = 3:n
        fibSeq(i) = fibSeq(i-1) + fibSeq(i-2);
    end
end

Example #13: Least common multiple (LCM)

This function takes two positive integers as input and returns their LCM using the Euclidean algorithm.

function lcm = leastCommonMultiple(a, b)
  if a == 0 || b == 0
    lcm = 0;
  else
    while b ~= 0
      tmp = b;
      b = mod(a, b);
      a = tmp;
    end
    lcm = a;
  end
end

Example #14: Function for Grade Conversion

function grade = grade_converter(score)

if score < 0 || score > 100
    error('Score must be between 0 and 100');
end

if score >= 90
    grade = 'A';
elseif score >= 80
    grade = 'B';
elseif score >= 70
    grade = 'C';
elseif score >= 60
    grade = 'D';
else
    grade = 'F';
end

end

Using the ‘@’ Operator

Anonymous function: An anonymous function is a function that is not stored in a program file, but is associated with a variable whose data type is function_handle. Anonymous functions can accept multiple inputs and return one output. They can contain only a single executable statement. ¹

Example Usage:

score = 85;
grade = grade_converter(score);

fprintf('Score: %d, Grade: %s', score,grade)

Syntax:

function_handle = @(input_arguments) expression

Example #: Basic Anonymous function

square = @(x) x^2;  % Function to square a number

result = square(5);  % Call the function, result will be 25

Example #: Anonymous Function with Multiple Inputs

g = @(x, y) x + y;

sumResult = g(3, 5);  % Evaluating the function with x=3 and y=5

Example #: Using Built-in Functions with Anonymous Functions

h = @(a, b) sqrt(a^2 + b^2);

hypotenuse = h(3, 4);  % Evaluating the hypotenuse of a right triangle

True/False (Mark T for True and F for False)

Functions can only return one output value. True or False
The order of arguments matters when calling a function. True or False
Variables defined within a function are local to that function. True or False
MATLAB functions can only be called from other functions, not from script files. True or False
Anonymous functions can accept multiple input arguments, but they can only directly return a single output value in MATLAB. True or False

Multiple Choice (Select the best answer)

What is the purpose of the “function” keyword in MATLAB? a. Declares a variable b. Defines a loop c. Marks the beginning of a function d. Specifies a data type

How can you return multiple values from a MATLAB function? a. Use a semicolon between values b. Separate values with commas c. Enclose values in square brackets d. Use square brackets and commas

What is the purpose of input arguments in a MATLAB function? a. They define the function’s name b. They determine the output of the function c. They provide values for computation within the function d. They are optional and not necessary

Which command is used to call a function in MATLAB? a. call b. run c. execute d. The function name itself

What is the primary difference between a function and a script in MATLAB? a) Functions can return values, while scripts cannot. b) Functions have their own workspace, while scripts share the base workspace. c) Functions can be called multiple times, while scripts can only run once. d) All of the above.

What happens if you try to call a function with fewer arguments than it expects? a) The function calls the input function to prompt for missing values. b) The function uses default values for missing arguments. c) The function generates an error. d) The function uses random values for missing arguments.

How do you define a function in MATLAB? a. for b. function c. if d. while

How is a function file named in MATLAB typically saved?

With a “.m” extension

With a “.mat” extension

With a “.func” extension

Without any file extension

In MATLAB, what is the role of the “end” keyword inside a function?

Marks the end of the function definition

Specifies the end of a loop or conditional statement

Ends the execution of the entire script

Indicates the end of a variable assignment

How can you call a MATLAB function that is saved in a separate file?

Use the “call” command

Execute the function file directly

Import the function into the script

Use the function name in the script

What is the output of the following MATLAB code snippet?

function result = multiply_numbers(a, b)
    result = a * b;
end

x = 3;
y = 4;
z = multiply_numbers(x, y);
disp(z);

Which of the following correctly defines an anonymous function in MATLAB?

function_name = @(input_arguments) expression
function function_name(input_arguments) expression
anonymous_func = function(input_arguments) expression
function(input_arguments) expression

What is the output of the following code?

square = @(x) x^2;
result = square(4);
disp(result);

Which of the following is a valid way to create an anonymous function with two input arguments?

myfun = @(x, y) x * y;
myfun = function(x, y) x * y;
myfun(x, y) = x * y;
myfun = inline(‘x * y’, ‘x’, ‘y’);

Exercises

Write a function sum3(num1,num3,num3) that takes three numbers as input and returns the sum.
Write a function that calculates the area of a circle, given its radius.
Write a function SumNum(num1) that takes a number as input and returns the sum of numbers from 1 to that number (num1).
Write a function sumSquares(x) that takes a vector of numbers as input and returns the sum of their squares.
Write a function isEven(x) that takes a number as input and returns true if it is even, and false otherwise.
Write a program with three functions:
1. isEven(n): This function takes an integer n as input and returns True if n is even and False otherwise. You can use the modulo operator (%) to check for evenness.
2. printTable(n): This function takes an integer n as input and prints its multiplication table. The table should show the product of n with each number from 1 to 10, formatted like n * i = n * i, where i is the current number in the loop.
3. main: The main program should:
  - Prompt the user to enter an integer.
  - Use the isEven(n) function to check if the entered number is even.
  - If the number is even, call the printTable(n) function to print its multiplication table.
  - If the number is odd, print a message indicating the number is odd and not eligible for printing a table.

Example output:

Enter an integer: 4
is even! Here's its multiplication table:
* 1 = 4
* 2 = 8
* 3 = 12
...
* 10 = 40

Write a function findMax(data) that takes a list of numbers as input and returns the maximum value in the list.
Write a function findSum(data) that takes a list of numbers as input and returns the sum of allthe numbers in the list.
Write a function findProduct(data) that takes a list of numbers as input and returns the product of all the numbers in the list.
Write a function avgPositive(data) that takes a list of numbers as input and returns the average of all positive numbers in the list.

Review Questions

What is a function in MATLAB?
How do you define a function in MATLAB? Provide an example.
How do you define a function in MATLAB? What are the essential components of a function definition?
How do functions return output values?
What is the difference between a function and a script in MATLAB?
Describe the process of calling a function, including argument passing and return value handling.
What happens if you try to call a function with the wrong number of arguments?
How can you create plots within a function and display them to the user?
How can you pass plotting options as arguments to functions to customize visualizations?
Demonstrate how to pass multiple input arguments and return multiple output values.
Define an anonymous function in MATLAB and provide an example to explain its usage.

References and Bibliography

Declare function name, inputs, and outputs - MathWorks Help Center

Anonymous Functions - Mathworks ↩