Axis control and formatting in MATLAB - Time & Space Complexity

Time Complexity: Axis control and formatting

O(n)

Understanding Time Complexity

When we control and format axes in MATLAB plots, some commands run repeatedly depending on the data size.

We want to know how the time to set axis properties grows as the data or plot size increases.

Scenario Under Consideration

Analyze the time complexity of the following MATLAB code snippet.

x = 1:n;
y = rand(1, n);
plot(x, y);
axis([0 n 0 1]);
set(gca, 'XTick', linspace(0, n, 11));
set(gca, 'YTick', 0:0.1:1);
xlabel('X Axis');
ylabel('Y Axis');
title('Sample Plot');

This code plots n points and sets axis limits, tick marks, and labels.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Plotting n points with plot(x, y) which processes each data point.
• How many times: The plot function internally handles each of the n points once.
• Axis settings: Setting axis limits and ticks runs a fixed number of times, not depending on n.

How Execution Grows With Input

The time to draw the plot grows as the number of points n increases, because each point is processed.

Input Size (n)	Approx. Operations
10	About 10 operations for plotting points + fixed axis settings
100	About 100 operations for plotting points + fixed axis settings
1000	About 1000 operations for plotting points + fixed axis settings

Pattern observation: The plotting time grows roughly in direct proportion to n, while axis formatting time stays about the same.

Final Time Complexity

Time Complexity: O(n)

This means the time to create and format the plot grows linearly with the number of points plotted.

Common Mistake

[X] Wrong: "Changing axis limits or ticks takes longer as the number of data points grows."

[OK] Correct: Axis formatting commands run a fixed number of times regardless of data size; only plotting points depends on n.

Interview Connect

Understanding how plotting and axis formatting scale helps you write efficient visualization code and explain performance in real projects.

Self-Check

"What if we added a loop to update axis ticks inside the plotting loop? How would the time complexity change?"

Practice

1. What does the MATLAB command axis([0 10 0 5]) do to a plot?

easy

A. Sets the x-axis limits from 0 to 10 and y-axis limits from 0 to 5

B. Sets the axis color to RGB values [0 10 0 5]

C. Creates a grid with 10 rows and 5 columns

D. Labels the axes with numbers 0, 10, 0, and 5

Solution

1. Step 1: Understand the axis function input

   The axis function with a vector of four numbers sets axis limits: [xmin xmax ymin ymax].

2. Step 2: Apply the given limits

   Here, [0 10 0 5] means x-axis from 0 to 10 and y-axis from 0 to 5.

3. Final Answer:

   Sets the x-axis limits from 0 to 10 and y-axis limits from 0 to 5 -> Option A

4. Quick Check:

   axis([xmin xmax ymin ymax]) = set axis limits [OK]

Hint: Remember axis([xmin xmax ymin ymax]) sets axis limits [OK]

Common Mistakes:

• Confusing axis limits with colors
• Thinking axis sets labels or grid size
• Using axis without four numbers

2. Which of the following is the correct syntax to set the x-axis label to 'Time (s)' in MATLAB?

easy

A. labelx('Time (s)')

B. xlabel('Time (s)')

C. setxlabel('Time (s)')

D. xaxislabel('Time (s)')

Solution

1. Step 1: Recall MATLAB function for x-axis label

   The function to set x-axis label is xlabel with the label text as input.

2. Step 2: Check syntax correctness

   xlabel('Time (s)') correctly sets the label. Other options are invalid function names.

3. Final Answer:

   xlabel('Time (s)') -> Option B

4. Quick Check:

   Use xlabel('text') to label x-axis [OK]

Hint: Use xlabel('text') exactly to label x-axis [OK]

Common Mistakes:

• Using wrong function names like setxlabel
• Forgetting quotes around label text
• Confusing xlabel with axis or title

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

plot(1:5, [2 4 6 8 10]);
axis([0 6 0 12]);
xticks([0 2 4 6]);
yticks([0 6 12]);

medium

A. Plot points with x-axis from 0 to 6, y-axis from 0 to 12, x-ticks at 0,2,4,6 and y-ticks at 0,6,12

B. Plot points with default axis limits and ticks

C. Error because xticks and yticks require vectors of length 5

D. Plot with reversed axes limits

Solution

1. Step 1: Analyze axis limits

   axis([0 6 0 12]) sets x-axis from 0 to 6 and y-axis from 0 to 12.

2. Step 2: Analyze tick settings

   xticks([0 2 4 6]) sets x-axis ticks at 0, 2, 4, 6; yticks([0 6 12]) sets y-axis ticks at 0, 6, 12.

3. Final Answer:

   Plot points with x-axis from 0 to 6, y-axis from 0 to 12, x-ticks at 0,2,4,6 and y-ticks at 0,6,12 -> Option A

4. Quick Check:

   axis + xticks + yticks control limits and ticks [OK]

Hint: axis sets limits; xticks/yticks set tick marks [OK]

Common Mistakes:

• Assuming default ticks remain after setting axis
• Thinking xticks/yticks need same length as data
• Confusing axis limits with tick positions

4. Identify the error in this MATLAB code snippet for setting axis limits and fix it:

plot(1:3, [5 10 15])
axis(0 3 0 20)

medium

A. Limits must be strings; use axis('0 3 0 20')

B. axis function does not set limits; use xlim and ylim instead

C. Missing square brackets around limits; should be axis([0 3 0 20])

D. No error; code runs fine

Solution

1. Step 1: Check axis function syntax

   The axis function requires a vector input for limits, enclosed in square brackets.

2. Step 2: Identify missing brackets

   The code uses axis(0 3 0 20) without brackets, causing syntax error.

3. Final Answer:

   Missing square brackets around limits; should be axis([0 3 0 20]) -> Option C

4. Quick Check:

   axis([xmin xmax ymin ymax]) needs brackets [OK]

Hint: Always use square brackets for axis limits [OK]

Common Mistakes:

• Omitting brackets around axis limits
• Using strings instead of numeric vectors
• Confusing axis with xlim or ylim functions

5. You want to create a plot with x-axis from -5 to 5, y-axis from -10 to 10, and custom ticks every 2 units on both axes. Which MATLAB code correctly achieves this?

hard

A. plot(x,y); axis([-5 5 -10 10]); xticks([-5 2 5]); yticks([-10 2 10]);

B. plot(x,y); axis([-5 5 -10 10]); xticks(-5:5); yticks(-10:10);

C. plot(x,y); xlim([-5 5]); ylim([-10 10]); ticks([-5 5], [-10 10]);

D. plot(x,y); axis([-5 5 -10 10]); xticks(-5:2:5); yticks(-10:2:10);

Solution

1. Step 1: Set axis limits correctly

   axis([-5 5 -10 10]) sets x-axis and y-axis limits as required.

2. Step 2: Set ticks every 2 units

   xticks(-5:2:5) creates ticks at -5, -3, -1, 1, 3, 5; similarly for y-axis with yticks(-10:2:10).

3. Step 3: Check other options

   plot(x,y); axis([-5 5 -10 10]); xticks([-5 2 5]); yticks([-10 2 10]); sets ticks incorrectly (missing intermediate values). plot(x,y); xlim([-5 5]); ylim([-10 10]); ticks([-5 5], [-10 10]); uses invalid ticks function. plot(x,y); axis([-5 5 -10 10]); xticks(-5:5); yticks(-10:10); sets ticks every 5 units, not 2.

4. Final Answer:

   plot(x,y); axis([-5 5 -10 10]); xticks(-5:2:5); yticks(-10:2:10); -> Option D

5. Quick Check:

   Use axis for limits and colon operator for ticks [OK]

Hint: Use colon operator for ticks: start:step:end [OK]

Common Mistakes:

• Setting ticks with wrong intervals
• Using non-existent ticks() function
• Confusing axis limits with tick values