Vectorization vs loops in MATLAB - Visual Side-by-Side Comparison

Concept Flow - Vectorization vs loops

Start

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Input Data

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Choose Method

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Loop

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Process

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Output

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End

This flow shows how data can be processed either by loops or vectorized operations, both leading to the output.

Execution Sample

MATLAB

A = 1:5;
B = zeros(1,5);
for i = 1:5
  B(i) = A(i)^2;
end

This code squares each element of A using a loop and stores results in B.

Execution Table

Iteration	i	A(i)	Condition i<=5	Action	B after action
1	1	1	True	B(1) = 1^2 = 1	[1 0 0 0 0]
2	2	2	True	B(2) = 2^2 = 4	[1 4 0 0 0]
3	3	3	True	B(3) = 3^2 = 9	[1 4 9 0 0]
4	4	4	True	B(4) = 4^2 = 16	[1 4 9 16 0]
5	5	5	True	B(5) = 5^2 = 25	[1 4 9 16 25]
6	6	-	False	Exit loop	[1 4 9 16 25]

💡 i reaches 6, condition 6<=5 is False, loop ends

Variable Tracker

Variable	Start	After 1	After 2	After 3	After 4	After 5	Final
i	-	1	2	3	4	5	6
B	[0 0 0 0 0]	[1 0 0 0 0]	[1 4 0 0 0]	[1 4 9 0 0]	[1 4 9 16 0]	[1 4 9 16 25]	[1 4 9 16 25]

Key Moments - 3 Insights

Why does the loop stop after i=5?

Because the condition i<=5 becomes false at i=6, as shown in the last row of the execution_table.

Why do we initialize B with zeros before the loop?

To create space for results and avoid errors when assigning values inside the loop, as seen in the variable_tracker start value.

How does vectorization avoid the loop?

Vectorization applies the operation to the whole array at once, skipping the step-by-step iteration shown in the execution_table.

Visual Quiz - 3 Questions

Look at the execution_table, what is the value of B after iteration 3?

A [1 4 9 0 0]

B [1 4 0 0 0]

C [1 0 0 0 0]

D [0 0 0 0 0]

💡 Hint

Check the 'B after action' column at iteration 3 in the execution_table.

At which iteration does the loop condition become false?

A 5

B 6

C 4

D 1

💡 Hint

Look at the 'Condition i<=5' column in the execution_table and find when it is False.

If we replace the loop with vectorized code B = A.^2, what changes in the execution_table?

A More iterations because vectorization loops internally

B Condition column will have more True values

C No iterations, direct assignment of all values at once

D B will remain zeros

💡 Hint

Vectorization applies operation to whole array at once, skipping loop steps shown in execution_table.

Concept Snapshot

Vectorization vs loops in MATLAB:
- Loops process elements one by one.
- Vectorization applies operations to whole arrays at once.
- Vectorized code is usually faster and cleaner.
- Use vectorization when possible for efficiency.
- Loops are easier to understand but slower for large data.

Full Transcript

This lesson compares vectorization and loops in MATLAB. The flow diagram shows data input, choice between loop or vectorized processing, and output. The sample code uses a loop to square elements of an array A and store results in B. The execution table traces each loop iteration: variable i, current element A(i), condition check, action taken, and B's state after. The loop stops when i exceeds 5. The variable tracker shows how i and B change step by step. Key moments clarify why the loop stops, why B is initialized, and how vectorization skips loops. The quiz tests understanding of B's values after iterations, when the loop ends, and how vectorization changes execution. The snapshot summarizes that vectorization applies operations to whole arrays at once, making code faster and cleaner than loops, which process elements one by one.