Figure and Axes mental model in Matplotlib - Time & Space Complexity

Time Complexity: Figure and Axes mental model

O(n)

Understanding Time Complexity

When working with matplotlib, it is helpful to understand how the figure and axes objects behave in terms of time cost.

We want to know how the time to create and update plots grows as we add more axes or figures.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt

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

This code creates a 3 by 3 grid of axes and plots a simple line on each axes.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Looping over each axes to plot data.
• How many times: Once for each axes, here 9 times (3 rows x 3 columns).

How Execution Grows With Input

As the number of axes increases, the time to plot on each axes grows linearly.

Input Size (number of axes)	Approx. Operations
10	10 plotting calls
100	100 plotting calls
1000	1000 plotting calls

Pattern observation: Doubling the number of axes roughly doubles the work done.

Final Time Complexity

Time Complexity: O(n)

This means the time to create and plot on axes grows directly with the number of axes.

Common Mistake

[X] Wrong: "Adding more axes does not affect plotting time much because each plot is simple."

[OK] Correct: Even simple plots take time, and plotting on many axes adds up linearly.

Interview Connect

Understanding how plotting time grows with the number of axes helps you design efficient visualizations and manage resources well.

Self-Check

"What if we changed the code to plot multiple lines on each axes? How would the time complexity change?"

Practice

1. What does the Figure represent in matplotlib's Figure and Axes model?

easy

A. A single data point on the plot

B. The area where data points are drawn

C. The entire image or window that contains all plots

D. The color scheme of the plot

Solution

1. Step 1: Understand the role of Figure

   The Figure is the whole container or window that holds one or more plots.

2. Step 2: Differentiate Figure from Axes

   Axes is the part inside the Figure where data is drawn, not the entire window.

3. Final Answer:

   The entire image or window that contains all plots -> Option C

4. Quick Check:

   Figure = whole window [OK]

Hint: Figure is the whole plot window, not just the data area [OK]

Common Mistakes:

• Confusing Figure with Axes
• Thinking Figure is a single plot line
• Mixing Figure with plot colors

2. Which of the following is the correct way to create a Figure and Axes in matplotlib?

easy

A. fig, ax = plt.subplots()

B. fig = plt.figure(), ax = plt.plot()

C. ax = plt.figure(), fig = plt.axes()

D. plt.create_figure(), plt.create_axes()

Solution

1. Step 1: Recall matplotlib syntax

   The standard way to create Figure and Axes together is using plt.subplots().

2. Step 2: Check each option

   fig, ax = plt.subplots() correctly assigns Figure and Axes from plt.subplots(). Others misuse functions or assign incorrectly.

3. Final Answer:

   fig, ax = plt.subplots() -> Option A

4. Quick Check:

   Use plt.subplots() to get Figure and Axes [OK]

Hint: Use plt.subplots() to get both Figure and Axes [OK]

Common Mistakes:

• Using plt.plot() to create Axes
• Confusing plt.figure() with plt.subplots()
• Trying non-existent functions like plt.create_figure()

3. What will be the output type of the variable ax after running this code?

import matplotlib.pyplot as plt
fig, ax = plt.subplots()

medium

A. A matplotlib Figure object

B. A matplotlib Axes object

C. A list of Axes objects

D. A NumPy array

Solution

1. Step 1: Understand plt.subplots() return values

   It returns a tuple: (Figure object, Axes object or array of Axes).

2. Step 2: Check variable assignment

   Here, ax is assigned the second element, which is a single Axes object.

3. Final Answer:

   A matplotlib Axes object -> Option B

4. Quick Check:

   ax = Axes object from plt.subplots() [OK]

Hint: plt.subplots() returns (Figure, Axes) tuple [OK]

Common Mistakes:

• Thinking ax is a Figure
• Assuming ax is a list without multiple plots
• Confusing Axes with NumPy arrays

4. Identify the error in this code snippet:

import matplotlib.pyplot as plt
fig = plt.figure()
ax = plt.axes()
ax.plot([1, 2, 3], [4, 5, 6])
plt.show()

medium

A. plt.axes() should be called on the Figure object

B. plt.axes() creates a new Figure, not Axes

C. plt.figure() must be called after plt.axes()

D. No error, code runs fine

Solution

1. Step 1: Understand plt.figure() and plt.axes()

   plt.figure() creates a Figure and sets it as current. plt.axes() creates Axes in the current Figure using default positioning.

2. Step 2: Verify code execution

   The plot is correctly added to ax and plt.show() displays the figure. The code runs without errors.

3. Final Answer:

   No error, code runs fine -> Option D

4. Quick Check:

   plt.axes() adds to current Figure [OK]

Hint: plt.figure() sets current figure for plt.axes() [OK]

Common Mistakes:

• Calling plt.axes() without linking to Figure
• Assuming plt.axes() auto-links to last Figure
• Calling plt.figure() after plt.axes()

5. You want to create a figure with two side-by-side plots sharing the same y-axis. Which code correctly uses the Figure and Axes model to achieve this?

hard

A. fig, (ax1, ax2) = plt.subplots(1, 2, sharey=True)
ax1.plot([1,2,3], [4,5,6])
ax2.plot([1,2,3], [6,5,4])

B. fig = plt.figure()
ax1 = fig.add_subplot(1, 2, 1)
ax2 = fig.add_subplot(1, 2, 2)
ax1.sharey(ax2)

C. fig, ax = plt.subplots(2, 1)
ax[0].plot([1,2,3], [4,5,6])
ax[1].plot([1,2,3], [6,5,4])

D. fig, ax = plt.subplots(1, 2)
ax[0].plot([1,2,3], [4,5,6])
ax[1].plot([1,2,3], [6,5,4])

Solution

1. Step 1: Understand subplots with shared axes

   Using plt.subplots(1, 2, sharey=True) creates one row, two columns of Axes sharing the y-axis.

2. Step 2: Check code correctness

   fig, (ax1, ax2) = plt.subplots(1, 2, sharey=True) ax1.plot([1,2,3], [4,5,6]) ax2.plot([1,2,3], [6,5,4]): fig, (ax1, ax2) = plt.subplots(1, 2, sharey=True) ax1.plot([1,2,3], [4,5,6]) ax2.plot([1,2,3], [6,5,4]) correctly unpacks two Axes and plots data with shared y-axis. fig, ax = plt.subplots(1, 2) ax[0].plot([1,2,3], [4,5,6]) ax[1].plot([1,2,3], [6,5,4]) omits sharey=True. fig = plt.figure() ax1 = fig.add_subplot(1, 2, 1) ax2 = fig.add_subplot(1, 2, 2) ax1.sharey(ax2) calls non-existent sharey() method. fig, ax = plt.subplots(2, 1) ax[0].plot([1,2,3], [4,5,6]) ax[1].plot([1,2,3], [6,5,4]) creates vertical subplots.

3. Final Answer:

   fig, (ax1, ax2) = plt.subplots(1, 2, sharey=True) ax1.plot([1,2,3], [4,5,6]) ax2.plot([1,2,3], [6,5,4]) -> Option A

4. Quick Check:

   Use sharey=True in plt.subplots() for shared y-axis [OK]

Hint: Use sharey=True in plt.subplots() for shared y-axis [OK]

Common Mistakes:

• Trying to call sharey() on Axes objects
• Creating vertical subplots instead of horizontal
• Not unpacking multiple Axes correctly