Subplot for multiple panels in MATLAB - Time & Space Complexity

Time Complexity: Subplot for multiple panels

O(n)

Understanding Time Complexity

When creating multiple plots in MATLAB using subplots, it is important to understand how the time to draw these plots grows as the number of panels increases.

We want to know how the total work changes when we add more subplot panels.

Scenario Under Consideration

Analyze the time complexity of the following MATLAB code that creates multiple subplot panels.

for i = 1:n
    subplot(1, n, i);
    plot(rand(1, 100));
end
    

This code creates n subplot panels arranged in a 1-by-n grid and plots random data in each panel.

Identify Repeating Operations

Look at what repeats in the code.

• Primary operation: The for loop runs n times, creating and plotting in each subplot.
• How many times: Each plotting operation happens once per subplot, so n times total.

How Execution Grows With Input

As you increase the number of subplots, the total work grows roughly in direct proportion.

Input Size (n)	Approx. Operations
10	10 plotting calls
100	100 plotting calls
1000	1000 plotting calls

Pattern observation: Doubling the number of subplots roughly doubles the total work.

Final Time Complexity

Time Complexity: O(n)

This means the time to create and plot all subplots grows linearly with the number of panels.

Common Mistake

[X] Wrong: "Adding more subplots does not affect the total time much because each plot is small."

[OK] Correct: Each subplot requires separate plotting work, so more panels add up and increase total time linearly.

Interview Connect

Understanding how plotting multiple panels scales helps you write efficient visualization code and explain performance in real projects.

Self-Check

What if we changed the plotting data size from 100 points to 1000 points per subplot? How would the time complexity change?

Practice

1. What does the MATLAB function subplot(2, 3, 4) do?

easy

A. Plots data in the 2nd row and 3rd column of a figure.

B. Creates a 2x3 matrix and fills it with the number 4.

C. Clears the 4th subplot in a 2 by 3 grid.

D. Divides the figure into 2 rows and 3 columns, then selects the 4th panel for plotting.

Solution

1. Step 1: Understand subplot grid parameters

   The first two numbers (2, 3) define the grid size: 2 rows and 3 columns.

2. Step 2: Identify the panel number

   The third number (4) selects the 4th panel in row-wise order for plotting.

3. Final Answer:

   Divides the figure into 2 rows and 3 columns, then selects the 4th panel for plotting. -> Option D

4. Quick Check:

   subplot(m, n, p) = grid m x n, panel p [OK]

Hint: Remember subplot(m,n,p) means m rows, n columns, p panel [OK]

Common Mistakes:

• Confusing the order of rows and columns
• Thinking subplot creates a matrix of numbers
• Assuming subplot clears panels automatically

2. Which of the following is the correct syntax to create a 3x1 subplot and plot in the second panel?

easy

A. subplot(3, 1, 2); plot(x, y);

B. subplot(1, 3, 2); plot(x, y);

C. subplot(3, 2, 1); plot(x, y);

D. subplot(2, 3, 2); plot(x, y);

Solution

1. Step 1: Identify the grid layout

   A 3x1 subplot means 3 rows and 1 column, so subplot(3, 1, p) is correct.

2. Step 2: Select the second panel

   The third argument '2' selects the second panel in the vertical stack.

3. Final Answer:

   subplot(3, 1, 2); plot(x, y); -> Option A

4. Quick Check:

   3 rows, 1 column, panel 2 = subplot(3,1,2) [OK]

Hint: Rows first, then columns, then panel number [OK]

Common Mistakes:

• Swapping rows and columns in subplot arguments
• Using wrong panel number for desired position
• Confusing subplot grid with plot commands

3. What will be the output of the following MATLAB code?

subplot(1,2,1); plot(1:3, [2 4 6]);
subplot(1,2,2); plot(1:3, [1 3 5]);

medium

A. Two plots side by side: first with points (1,2),(2,4),(3,6), second with (1,1),(2,3),(3,5).

B. One plot with both data sets overlaid.

C. Error because subplot indices are incorrect.

D. Two plots stacked vertically.

Solution

1. Step 1: Understand subplot grid

   subplot(1,2,1) creates a grid with 1 row and 2 columns, selecting the first panel.

2. Step 2: Plot data in each panel

   The first plot shows points (1,2), (2,4), (3,6). The second subplot(1,2,2) plots points (1,1), (2,3), (3,5).

3. Final Answer:

   Two plots side by side: first with points (1,2),(2,4),(3,6), second with (1,1),(2,3),(3,5). -> Option A

4. Quick Check:

   subplot(1,2,p) = two side-by-side plots [OK]

Hint: subplot(1,2,p) means two plots side by side [OK]

Common Mistakes:

• Thinking plots overlay in one panel
• Assuming vertical stacking instead of horizontal
• Misreading subplot indices

4. Identify the error in this MATLAB code snippet:

subplot(2,2,5);
plot(rand(5));

medium

A. plot function cannot be used inside subplot.

B. Panel index 5 is invalid for a 2x2 grid.

C. Missing semicolon after subplot command.

D. rand(5) is incorrect syntax.

Solution

1. Step 1: Check subplot grid size

   A 2x2 grid has only 4 panels numbered 1 to 4.

2. Step 2: Validate panel index

   Using 5 as the panel index is invalid and causes an error.

3. Final Answer:

   Panel index 5 is invalid for a 2x2 grid. -> Option B

4. Quick Check:

   Panel number must be ≤ rows*columns [OK]

Hint: Panel number must not exceed total grid cells [OK]

Common Mistakes:

• Using panel number larger than grid size
• Thinking semicolon affects subplot indexing
• Believing plot can't be inside subplot

5. You want to create a 2x2 grid of plots showing sine waves with different frequencies. Which code correctly sets up the subplots and plots the waves?

hard

A. subplot(2,2);
for k = 1:4
plot(sin(k*x));
end

B. for k = 1:4
subplot(4,1,k);
x = linspace(0,2*pi,100);
plot(x, sin(k*x));
end

C. for k = 1:4
subplot(2,2,k);
x = linspace(0,2*pi,100);
plot(x, sin(k*x));
end

D. for k = 1:4
subplot(2,2,k+1);
x = linspace(0,2*pi,100);
plot(x, sin(k*x));
end

Solution

1. Step 1: Set up correct subplot grid

   subplot(2,2,k) correctly creates a 2x2 grid and selects each panel from 1 to 4.

2. Step 2: Plot sine waves with increasing frequency

   Inside the loop, x is defined and sin(k*x) is plotted in each subplot panel.

3. Step 3: Check other options for errors

   for k = 1:4 subplot(4,1,k); x = linspace(0,2*pi,100); plot(x, sin(k*x)); end uses 4x1 grid, not 2x2. subplot(2,2); for k = 1:4 plot(sin(k*x)); end calls subplot once without panel index. for k = 1:4 subplot(2,2,k+1); x = linspace(0,2*pi,100); plot(x, sin(k*x)); end uses k+1 which causes invalid panel 5.

4. Final Answer:

   for k = 1:4 subplot(2,2,k); x = linspace(0,2*pi,100); plot(x, sin(k*x)); end -> Option C

5. Quick Check:

   Loop with subplot(2,2,k) plots 4 panels correctly [OK]

Hint: Use subplot(2,2,k) inside loop k=1 to 4 [OK]

Common Mistakes:

• Using wrong subplot grid size
• Not specifying panel index in subplot
• Using invalid panel numbers