Anonymous functions in MATLAB - Step-by-Step Execution

Concept Flow - Anonymous functions

Define anonymous function

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Call function with input

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Function executes expression

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Return output value

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End

Anonymous functions are small, unnamed functions defined in one line and used immediately or stored in variables.

Execution Sample

MATLAB

f = @(x) x^2 + 3;
y = f(4);

Defines an anonymous function f that squares input x and adds 3, then calls f with 4.

Execution Table

Step	Action	Expression/Value	Result
1	Define anonymous function f	f = @(x) x^2 + 3	f is a function handle
2	Call f with x=4	f(4)	Calculates 4^2 + 3
3	Compute 4^2	4^2	16
4	Add 3	16 + 3	19
5	Return result	19	y = 19

💡 Function call completes and y stores the result 19

Variable Tracker

Variable	Start	After Step 2	After Step 5
f	undefined	function handle @(x) x^2 + 3	function handle @(x) x^2 + 3
x	undefined	4 (input to f)	undefined (local to function)
y	undefined	undefined	19

Key Moments - 3 Insights

Why don't we see a function name when defining an anonymous function?

Anonymous functions are unnamed by design; they are stored in variables like f, as shown in step 1 of the execution_table.

How does MATLAB know what x is inside the anonymous function?

When calling f(4) in step 2, the input 4 is assigned to x locally inside the function for that call.

Why is the variable x not tracked after the function call?

x is local to the anonymous function and does not exist outside it, so variable_tracker shows it only during the call.

Visual Quiz - 3 Questions

Look at the execution_table, what is the value of y after step 5?

A 16

B 19

C 7

D undefined

💡 Hint

Check the 'Result' column in row with Step 5 in execution_table

At which step is the input x assigned the value 4?

A Step 1

B Step 3

C Step 2

D Step 5

💡 Hint

Look at the 'Action' and 'Expression/Value' columns in execution_table row Step 2

If we change the function to f = @(x) x + 3, what would y be when calling f(4)?

A 7

B 19

C 16

D 12

💡 Hint

Refer to how the function expression affects output in execution_table steps 3 and 4

Concept Snapshot

Anonymous functions in MATLAB:
- Defined with @(input) expression
- No separate function file needed
- Input variable is local
- Used immediately or stored in variables
- Example: f = @(x) x^2 + 3; y = f(4);

Full Transcript

Anonymous functions in MATLAB are small functions defined in one line using the syntax @(input) expression. They do not have a name but are stored in variables like f. When you call f with a value, that value is assigned to the input variable locally inside the function. The function then computes the expression and returns the result. For example, defining f = @(x) x^2 + 3 creates a function that squares x and adds 3. Calling f(4) computes 4 squared plus 3, resulting in 19. The input variable x exists only during the function call and is not accessible outside. This makes anonymous functions handy for quick calculations without creating full function files.