Nested subplots with subfigures in Matplotlib - Time & Space Complexity

Time Complexity: Nested subplots with subfigures

O(m * n^2)

Understanding Time Complexity

When creating nested subplots with subfigures in matplotlib, the time to draw the figure depends on how many plots we make.

We want to know how the drawing time grows as we add more subplots inside subfigures.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt

fig = plt.figure(constrained_layout=True)
subfigs = fig.subfigures(2, 1)

for subfig in subfigs:
    axs = subfig.subplots(2, 2)
    for ax in axs.flat:
        ax.plot([1, 2, 3], [1, 4, 9])

plt.show()

This code creates a figure with 2 subfigures stacked vertically. Each subfigure has a 2x2 grid of subplots, and each subplot draws a simple line plot.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Plotting on each subplot inside nested loops.
• How many times: Outer loop runs 2 times (for subfigures), inner loop runs 4 times (for subplots), total 8 plots.

How Execution Grows With Input

As the number of subfigures and subplots per subfigure increases, the total plots grow by multiplying these counts.

Input Size (n = subplots per subfigure)	Approx. Operations (plots)
2 subfigures, 2x2 subplots (4)	8
2 subfigures, 10x10 subplots (100)	200
3 subfigures, 20x20 subplots (400)	1200

Pattern observation: Total plots grow by multiplying number of subfigures and number of subplots per subfigure.

Final Time Complexity

Time Complexity: O(m * n^2)

This means the time grows proportionally to the number of subfigures (m) times the square of the number of subplots per subfigure (n), since subplots are arranged in an n x n grid.

Common Mistake

[X] Wrong: "Adding more subplots inside subfigures only adds a small fixed time, so complexity stays the same."

[OK] Correct: Each subplot requires drawing operations, so total time grows with the total number of subplots, not fixed.

Interview Connect

Understanding how nested plotting scales helps you reason about performance in data visualization tasks, a useful skill in many projects.

Self-Check

"What if we changed the number of subfigures dynamically based on data size? How would the time complexity change?"

Practice

1. What is the main purpose of using fig.subfigures() in matplotlib?

easy

A. To add a single plot to a figure

B. To create large groups inside a figure that can hold their own smaller plots

C. To change the color of a plot

D. To save a figure as an image file

Solution

1. Step 1: Understand the role of fig.subfigures()

   This method creates subfigures, which are large groups inside a main figure.

2. Step 2: Recognize the use of subfigures

   Each subfigure can contain its own grid of smaller plots, helping organize complex layouts.

3. Final Answer:

   To create large groups inside a figure that can hold their own smaller plots -> Option B

4. Quick Check:

   Subfigures = large groups inside figure [OK]

Hint: Subfigures group plots inside a figure [OK]

Common Mistakes:

• Thinking subfigures add only one plot
• Confusing subfigures with saving figures
• Assuming subfigures change plot colors

2. Which of the following is the correct way to create two subfigures side by side in matplotlib?

easy

A. fig.subplots(1, 2)

B. fig.subfigures(2, 1)

C. fig.subfigures(1, 2)

D. fig.subfigures(2, 2)

Solution

1. Step 1: Understand subfigures layout parameters

   The parameters (rows, columns) define the grid of subfigures. For side by side, use 1 row and 2 columns.

2. Step 2: Match parameters to options

   fig.subfigures(1, 2) uses fig.subfigures(1, 2), which creates 1 row and 2 columns, placing subfigures side by side.

3. Final Answer:

   fig.subfigures(1, 2) -> Option C

4. Quick Check:

   Side by side = 1 row, 2 columns [OK]

Hint: Rows first, columns second in subfigures() [OK]

Common Mistakes:

• Swapping rows and columns
• Using subplots() instead of subfigures()
• Choosing more rows than needed

3. What will be the output shape of the axes array when running this code?

fig = plt.figure()
subfigs = fig.subfigures(2, 1)
ax1 = subfigs[0].subplots(1, 3)
ax2 = subfigs[1].subplots(2, 2)
print(ax1.shape, ax2.shape)

medium

A. (1, 3) (4,)

B. (3,) (4,)

C. (3,) (2, 2)

D. (1, 3) (2, 2)

Solution

1. Step 1: Analyze subfigures and their subplot grids

   First subfigure has 1 row and 3 columns, so ax1 shape is (1, 3). Second subfigure has 2 rows and 2 columns, so ax2 shape is (2, 2).

2. Step 2: Confirm shapes printed

   Printing ax1.shape and ax2.shape outputs (1, 3) and (2, 2) respectively.

3. Final Answer:

   (1, 3) (2, 2) -> Option D

4. Quick Check:

   Subplots shape = (rows, columns) [OK]

Hint: Shape matches (rows, columns) in subplots() [OK]

Common Mistakes:

• Confusing flat arrays with 2D arrays
• Mixing up rows and columns
• Assuming subfigures affect shape differently

4. Identify the error in this code snippet for creating nested subplots with subfigures:

fig = plt.figure()
subfigs = fig.subfigures(1, 2)
ax = subfigs.subplots(2, 2)

medium

A. subfigs.subplots() should be called on each subfigure, not on the list

B. fig.subfigures() requires 3 arguments, missing one

C. subfigs is a list, so subfigs.subplots() is invalid

D. subfigures cannot have nested subplots

Solution

1. Step 1: Understand the type of subfigs

   fig.subfigures(1, 2) returns a list or array of subfigure objects, not a single subfigure.

2. Step 2: Correct method call for subplots

   We must call subplots() on each individual subfigure, not on the entire list subfigs.

3. Final Answer:

   subfigs.subplots() should be called on each subfigure, not on the list -> Option A

4. Quick Check:

   Call subplots() on single subfigure [OK]

Hint: Call subplots() on one subfigure, not list [OK]

Common Mistakes:

• Calling subplots() on the list of subfigures
• Assuming subfigures() needs 3 args
• Thinking subfigures can't have subplots

5. You want to create a figure with 2 subfigures stacked vertically. The top subfigure should have a 2x2 grid of plots, and the bottom subfigure a single plot. Which code correctly achieves this?

hard

A. fig = plt.figure()
subfigs = fig.subfigures(2, 1)
axs_top = subfigs[0].subplots(2, 2)
axs_bottom = subfigs[1].subplots(1, 1)

B. fig = plt.figure()
subfigs = fig.subfigures(1, 2)
axs_top = subfigs[0].subplots(2, 2)
axs_bottom = subfigs[1].subplots(1, 1)

C. fig = plt.figure()
subfigs = fig.subfigures(2, 1)
axs_top = subfigs.subplots(2, 2)
axs_bottom = subfigs.subplots(1, 1)

D. fig = plt.figure()
subfigs = fig.subfigures(1, 2)
axs_top = subfigs.subplots(2, 2)
axs_bottom = subfigs.subplots(1, 1)

Solution

1. Step 1: Set subfigures layout vertically

   Two subfigures stacked vertically means 2 rows and 1 column, so fig.subfigures(2, 1).

2. Step 2: Create subplots inside each subfigure

   Top subfigure gets a 2x2 grid, bottom subfigure gets a single plot (1x1). Call subplots() on each subfigure individually.

3. Final Answer:

   fig = plt.figure() subfigs = fig.subfigures(2, 1) axs_top = subfigs[0].subplots(2, 2) axs_bottom = subfigs[1].subplots(1, 1) -> Option A

4. Quick Check:

   Vertical stack = (2,1), call subplots() on each subfigure [OK]

Hint: Vertical stack = (2,1), subplots() on each subfigure [OK]

Common Mistakes:

• Using (1,2) for vertical stacking
• Calling subplots() on the list of subfigures
• Not matching subplot grids to subfigures