12.6: Anonymous Functions

An anonymous function is a short function that is created directly in a script, in the Command Window, or inside another function file. Unlike regular functions, anonymous functions do not need their own separate .m file.

Anonymous functions are useful when you need to define a simple mathematical expression and use it several times. They are especially helpful when working with plotting, numerical integration, root finding, and other numerical methods.

The basic format is:

functionName = @(inputVariable) expression;

The symbol @ tells MATLAB that we are creating a function handle. A function handle is a variable that stores a reference to a function. The input variable is placed inside parentheses after the @ symbol.

For example, to define

\(f(x) = 3*x^2 + 2*x - 1\)

we write:

f = @(x) 3*x.^2 + 2*x - 1;

After creating the anonymous function, we can evaluate it just like we would call any other function.

For example:

f(2)

returns:

12

because:

2^2 + 3(2) + 2 = 12

We can also pass an array of values to the function:

x = 0:5;
y = f(x)

This evaluates the function at every value in the vector x.

Notice the element-by-element operator .^ in the function definition. This allows the function to work with both single numbers and arrays of x-values.

Note

When writing anonymous functions that may receive arrays, use element-by-element operations such as .*, ./, and .^ when appropriate.

Anonymous Functions with More Than One Input

Anonymous functions can also have more than one input. For example, suppose we want to define the area of a rectangle as a function of width and height.

Example \(\PageIndex{1}\)

Calculating the area of one or many rectangles.

% define an anonymous function for area of a rectangle
areaRect = @(width, height) width .* height;

% calculating the area of one rectangle
width = 3;
height = 4;

area = areaRect(width, height)


% Calculating the area of 3 rectangles.
widths = [2 3 4];

heights = [5 6 7];

areas = areaRect(widths, heights)

Solution