Reshaping arrays in MATLAB - Step-by-Step Execution

Concept Flow - Reshaping arrays

Start with original array

↓

Specify new shape dimensions

↓

Check total elements match?

No→Error: Cannot reshape

Yes↓

Rearrange elements into new shape

↓

Output reshaped array

This flow shows how MATLAB reshapes an array by checking if the total number of elements stays the same, then rearranging elements into the new shape.

Execution Sample

MATLAB

A = [1 2 3 4 5 6];
B = reshape(A, 2, 3);
disp(B);

This code reshapes a 1x6 array into a 2x3 matrix and displays it.

Execution Table

Step	Action	Array Shape	Total Elements	Result / Output
1	Create A	1x6	6	[1 2 3 4 5 6]
2	Specify new shape (2,3)	-	-	-
3	Check total elements match (6 == 2*3)	1x6 and 2x3	6	Match, proceed
4	Reshape A to 2x3	2x3	6	[1 2 3; 4 5 6] (column-wise filling)
5	Display B	2x3	6	1 3 5 2 4 6

💡 Execution stops after displaying reshaped array B.

Variable Tracker

Variable	Start	After Step 1	After Step 4	Final
A	undefined	[1 2 3 4 5 6]	[1 2 3 4 5 6]	[1 2 3 4 5 6]
B	undefined	undefined	[1 2 3; 4 5 6]	[1 2 3; 4 5 6]

Key Moments - 3 Insights

Why does MATLAB fill the reshaped array column-wise, not row-wise?

MATLAB stores arrays in column-major order, so reshape fills elements down columns first, as shown in step 4 of the execution_table.

What happens if the total elements don't match when reshaping?

MATLAB throws an error because the reshape function requires the total number of elements to stay the same, as checked in step 3.

Does reshape change the original array A?

No, reshape creates a new array B with the new shape; A remains unchanged, as seen in variable_tracker.

Visual Quiz - 3 Questions

Look at the execution_table at step 4, what is the value of B(2,1)?

A 3

B 4

C 2

D 5

💡 Hint

Check the reshaped array values in step 4 of execution_table.

At which step does MATLAB verify if the reshape is possible?

A Step 2

B Step 4

C Step 3

D Step 5

💡 Hint

Look for the step where total elements are compared in execution_table.

If A had 8 elements instead of 6, what would happen at step 3?

A Error because total elements don't match

B Reshape proceeds normally

C Array B becomes larger

D Original array A changes shape

💡 Hint

Refer to the explanation in key_moments about element count matching.

Concept Snapshot

reshape(array, rows, cols)
- Changes array shape without changing data order
- Total elements must match (rows*cols = numel(array))
- MATLAB fills reshaped array column-wise
- Original array stays unchanged
- Errors if sizes mismatch

Full Transcript

This visual trace shows how MATLAB reshapes arrays. First, the original array A is created with 6 elements. Then, the new shape 2 rows by 3 columns is specified. MATLAB checks if the total elements match (6 == 2*3). Since they match, it rearranges elements column-wise into the new 2x3 array B. The original array A remains unchanged. The reshaped array B is displayed with elements filled down columns. If the total elements did not match, MATLAB would give an error. This process helps change how data is organized without changing the data itself.

Practice

1. What does the MATLAB function reshape do to an array?

easy

A. Sorts the array elements in ascending order

B. Changes the data values but keeps the shape the same

C. Deletes elements from the array

D. Changes the shape of the array without changing its data

Solution

1. Step 1: Understand the purpose of reshape

   The reshape function changes how the array is organized in terms of rows and columns but does not modify the actual data values.

2. Step 2: Confirm data remains unchanged

   The total number of elements stays the same, so no data is lost or changed, only rearranged.

3. Final Answer:

   Changes the shape of the array without changing its data -> Option D

4. Quick Check:

   reshape changes shape, not data [OK]

Hint: Remember reshape only rearranges elements, data stays same [OK]

Common Mistakes:

• Thinking reshape changes data values
• Assuming reshape deletes elements
• Confusing reshape with sorting

2. Which of the following is the correct syntax to reshape a 1x6 vector A into a 2x3 matrix in MATLAB?

easy

A. reshape(A, 2, 3)

B. reshape(2, 3, A)

C. reshape(A, [3 2])

D. reshape(A, 3, 2)

Solution

1. Step 1: Recall reshape syntax

   The correct syntax is reshape(array, rows, columns). So the array comes first, then the new dimensions.

2. Step 2: Check dimensions for 2x3

   To reshape into 2 rows and 3 columns, use reshape(A, 2, 3). Options with swapped dimensions or wrong order are incorrect.

3. Final Answer:

   reshape(A, 2, 3) -> Option A

4. Quick Check:

   reshape(array, rows, cols) [OK]

Hint: Syntax is reshape(array, rows, columns) [OK]

Common Mistakes:

• Putting dimensions before the array
• Swapping rows and columns
• Using brackets incorrectly

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

A = 1:6;
B = reshape(A, 3, 2);
disp(B);

medium

A. [1 4; 2 5; 3 6]

B. [1 2; 3 4; 5 6]

C. [1 3 5; 2 4 6]

D. [1 2 3; 4 5 6]

Solution

1. Step 1: Understand reshape fills column-wise

   MATLAB fills the reshaped matrix column by column from the original vector. The vector A = [1 2 3 4 5 6].

2. Step 2: Fill 3 rows and 2 columns

   Fill first column: 1, 2, 3; second column: 4, 5, 6. So matrix B is:
   [1 4;
   2 5;
   3 6]

3. Final Answer:

   [1 4; 2 5; 3 6] -> Option A

4. Quick Check:

   reshape fills column-wise [OK]

Hint: Remember MATLAB fills columns first in reshape [OK]

Common Mistakes:

• Assuming row-wise filling
• Mixing up rows and columns
• Confusing output format

4. Identify the error in this MATLAB code:

A = 1:8;
B = reshape(A, 3, 3);

medium

A. Variable A is not defined correctly

B. reshape dimensions do not match number of elements

C. Syntax error in reshape function

D. No error, code runs fine

Solution

1. Step 1: Count elements in A

   Vector A has 8 elements (1 to 8).

2. Step 2: Check reshape target size

   reshape tries to make a 3x3 matrix which needs 9 elements, but A has only 8.

3. Final Answer:

   reshape dimensions do not match number of elements -> Option B

4. Quick Check:

   Elements must match reshape size [OK]

Hint: Check total elements before reshaping [OK]

Common Mistakes:

• Ignoring element count mismatch
• Assuming reshape pads missing elements
• Thinking reshape auto adjusts size

5. Given a 3D array A of size 2x3x4, which MATLAB command correctly reshapes it into a 6x4 matrix without changing the order of elements?

hard

A. reshape(A, [2 3 4])

B. reshape(A, 4, 6)

C. reshape(A, [6 4])

D. reshape(A, [4 6])

Solution

1. Step 1: Calculate total elements

   Original size is 2x3x4 = 24 elements total.

2. Step 2: Confirm reshape size matches total elements

   6x4 = 24 elements, so reshape to [6 4] is valid.

3. Step 3: Use correct syntax for reshape with vector size

   reshape accepts size as a vector, so reshape(A, [6 4]) is correct and clearer for multi-dimensional arrays.

4. Final Answer:

   reshape(A, [6 4]) -> Option C

5. Quick Check:

   Use vector size for multi-dim reshape [OK]

Hint: Use reshape(A, [rows cols]) for multi-dim arrays [OK]

Common Mistakes:

• Swapping rows and columns
• Using wrong syntax without brackets
• Ignoring total element count