Anonymous functions in MATLAB - Step-by-Step Execution

Concept Flow - Anonymous functions

Define anonymous function

↓

Call function with input

↓

Function executes expression

↓

Return output value

↓

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.

Practice

1. What is an anonymous function in MATLAB?

easy

A. A quick, unnamed function created using the '@' symbol.

B. A function saved in a separate file with a name.

C. A function that can only be used inside loops.

D. A function that requires no input arguments.

Solution

1. Step 1: Understand the definition of anonymous functions

   Anonymous functions in MATLAB are small, unnamed functions created using the '@' symbol.

2. Step 2: Compare options with the definition

   A quick, unnamed function created using the '@' symbol. correctly describes anonymous functions as quick, unnamed functions created with '@'. Other options describe named functions or incorrect properties.

3. Final Answer:

   A quick, unnamed function created using the '@' symbol. -> Option A

4. Quick Check:

   Anonymous function = unnamed function with '@' [OK]

Hint: Look for '@' symbol to identify anonymous functions [OK]

Common Mistakes:

• Confusing anonymous functions with regular named functions
• Thinking anonymous functions must have no inputs
• Assuming anonymous functions are saved in separate files

2. Which of the following is the correct syntax to create an anonymous function that squares its input x?

easy

A. f = @(x) x^2;

B. f = function(x) x^2;

C. f = @x x^2;

D. f = (x) => x^2;

Solution

1. Step 1: Recall MATLAB anonymous function syntax

   The correct syntax uses '@(args) expression;' so for squaring x, it is '@(x) x^2;'.

2. Step 2: Check each option

   f = @(x) x^2; matches the correct syntax. f = function(x) x^2; uses incorrect keyword 'function'. f = @x x^2; misses parentheses. f = (x) => x^2; uses arrow syntax from other languages.

3. Final Answer:

   f = @(x) x^2; -> Option A

4. Quick Check:

   Anonymous function syntax = @(args) expression [OK]

Hint: Remember '@(x) expression;' for anonymous functions [OK]

Common Mistakes:

• Omitting parentheses around input arguments
• Using 'function' keyword inside anonymous function
• Using arrow syntax from other languages

3. What is the output of the following MATLAB code?

f = @(x) x + 5;
result = f(10);
disp(result);

medium

A. 5

B. 10

C. 15

D. Error

Solution

1. Step 1: Understand the anonymous function definition

   The function f adds 5 to its input x.

2. Step 2: Calculate the function output for input 10

   f(10) = 10 + 5 = 15.

3. Final Answer:

   15 -> Option C

4. Quick Check:

   10 + 5 = 15 [OK]

Hint: Apply input to expression inside @(x) function [OK]

Common Mistakes:

• Confusing input and output values
• Expecting function to multiply instead of add
• Thinking anonymous functions cause errors without file

4. Identify the error in this MATLAB anonymous function:

g = @x x^2 + 3;

medium

A. Anonymous functions cannot use addition.

B. Missing parentheses around input argument x.

C. The '@' symbol is not allowed here.

D. The function must be saved in a separate file.

Solution

1. Step 1: Check anonymous function syntax

   Anonymous functions require parentheses around input arguments, like '@(x)'.

2. Step 2: Identify the syntax error

   The code uses '@x' without parentheses, which is invalid syntax.

3. Final Answer:

   Missing parentheses around input argument x. -> Option B

4. Quick Check:

   Anonymous function input must be in parentheses [OK]

Hint: Always use @(input) with parentheses [OK]

Common Mistakes:

• Omitting parentheses around inputs
• Thinking '@' can be used without parentheses
• Believing anonymous functions need separate files

5. You want to create an anonymous function h that takes two inputs x and y and returns x squared plus y cubed. Which is the correct way to write this?

hard

A. h = @(x y) x^2 + y^3;

B. h = @(x,y) x^2 * y^3;

C. h = @(x,y) (x^2), (y^3);

D. h = @(x,y) x^2 + y^3;

Solution

1. Step 1: Understand multiple inputs in anonymous functions

   Multiple inputs are separated by commas inside parentheses: @(x,y).

2. Step 2: Check the expression for correct operations

   The function should return x squared plus y cubed, so use '+' operator, not '*'.

3. Final Answer:

   h = @(x,y) x^2 + y^3; -> Option D

4. Quick Check:

   Multiple inputs use commas; '+' adds results [OK]

Hint: Separate inputs with commas and use correct operators [OK]

Common Mistakes:

• Omitting commas between inputs
• Using wrong operators like multiplication instead of addition
• Trying to separate expressions with commas outside parentheses