Figure size and DPI in Matplotlib - Time & Space Complexity

Time Complexity: Figure size and DPI

O(width x height x dpi²)

Understanding Time Complexity

We want to understand how changing figure size and DPI affects the time matplotlib takes to create a figure.

How does the work grow when we increase these settings?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt

fig = plt.figure(figsize=(width, height), dpi=dpi)
ax = fig.add_subplot(111)
ax.plot(data_x, data_y)
plt.show()

This code creates a figure with a given size and resolution, then plots data on it.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Drawing pixels on the figure canvas based on size and DPI.
• How many times: Number of pixels = width x height x dpi² (because DPI scales pixels per inch).

How Execution Grows With Input

As figure size or DPI increases, the number of pixels to draw grows, making rendering take longer.

Input Size (width x height x dpi²)	Approx. Operations
10 x 10 x 50²	~250,000
20 x 20 x 100²	~4,000,000
30 x 30 x 200²	~36,000,000

Pattern observation: Operations grow roughly with the square of DPI and linearly with figure size.

Final Time Complexity

Time Complexity: O(width x height x dpi²)

This means the time to draw the figure grows with the area times the square of the DPI setting.

Common Mistake

[X] Wrong: "Increasing DPI only slightly increases drawing time because it's just a setting."

[OK] Correct: Higher DPI means many more pixels to draw, so time grows much faster than expected.

Interview Connect

Understanding how figure size and DPI affect rendering time helps you explain performance in data visualization tasks clearly and confidently.

Self-Check

"What if we keep figure size fixed but double the DPI? How would the time complexity change?"

Practice

1. What does the figsize parameter control in a matplotlib figure?

easy

A. The physical size of the figure in inches

B. The color of the figure background

C. The resolution of the figure in dots per inch

D. The font size of the plot labels

Solution

1. Step 1: Understand the role of figsize

   The figsize parameter sets the width and height of the figure in inches.

2. Step 2: Differentiate from DPI

   DPI controls resolution, not size. Color and font size are unrelated to figsize.

3. Final Answer:

   The physical size of the figure in inches -> Option A

4. Quick Check:

   Figure size = physical dimensions [OK]

Hint: Remember: figsize = inches size, DPI = sharpness [OK]

Common Mistakes:

• Confusing DPI with figure size
• Thinking figsize controls resolution
• Mixing up color or font size with figsize

2. Which of the following is the correct way to create a matplotlib figure with size 8 inches wide and 4 inches tall?

easy

A. plt.figure(dpi=(8, 4))

B. plt.figure(size=(8, 4))

C. plt.figure(figsize=(8, 4))

D. plt.figure(shape=(8, 4))

Solution

1. Step 1: Recall correct parameter name

   The parameter to set figure size is figsize, which takes a tuple (width, height).

2. Step 2: Check syntax correctness

   Only plt.figure(figsize=(8, 4)) uses figsize correctly. Others use invalid parameter names.

3. Final Answer:

   plt.figure(figsize=(8, 4)) -> Option C

4. Quick Check:

   Use figsize=(width, height) [OK]

Hint: Use figsize=(width, height) tuple in plt.figure() [OK]

Common Mistakes:

• Using wrong parameter names like size or shape
• Passing DPI values instead of size
• Not using a tuple for figsize

3. What will be the DPI of the figure created by this code?

fig = plt.figure(figsize=(6, 3), dpi=150)

medium

A. 100

B. 150

C. 6

D. 3

Solution

1. Step 1: Identify the DPI parameter value

   The code explicitly sets dpi=150 when creating the figure.

2. Step 2: Understand DPI meaning

   DPI means dots per inch, so the figure resolution is 150 dots per inch.

3. Final Answer:

   150 -> Option B

4. Quick Check:

   DPI parameter sets resolution [OK]

Hint: DPI is set by dpi= value in plt.figure() [OK]

Common Mistakes:

• Confusing DPI with figure size
• Choosing width or height as DPI
• Assuming default DPI without checking code

4. Identify the error in this code snippet:

plt.figure(figsize=8, dpi=100)

medium

A. No error, code is correct

B. dpi must be a tuple, not an integer

C. plt.figure does not accept figsize parameter

D. figsize must be a tuple, not a single integer

Solution

1. Step 1: Check the type of figsize argument

   figsize expects a tuple (width, height), but 8 is a single integer.

2. Step 2: Verify dpi argument

   dpi accepts an integer, so dpi=100 is correct.

3. Final Answer:

   figsize must be a tuple, not a single integer -> Option D

4. Quick Check:

   figsize = (width, height) tuple [OK]

Hint: Always pass figsize as (width, height) tuple [OK]

Common Mistakes:

• Passing single int instead of tuple to figsize
• Thinking dpi needs a tuple
• Assuming figsize can be a single number

5. You want to save a plot image that is 10 inches wide and 5 inches tall with a resolution of 300 DPI. Which code snippet correctly creates and saves this figure?

hard

A. fig = plt.figure(figsize=(10, 5))
plt.plot([1, 2, 3])
fig.savefig('plot.png', dpi=300)

B. fig = plt.figure(figsize=(10, 5), dpi=100)
plt.plot([1, 2, 3])
fig.savefig('plot.png')

C. fig = plt.figure(dpi=300)
plt.plot([1, 2, 3])
fig.savefig('plot.png', figsize=(10, 5))

D. fig = plt.figure(figsize=10, dpi=300)
plt.plot([1, 2, 3])
fig.savefig('plot.png')

Solution

1. Step 1: Understand figure creation and saving

   Setting figsize in plt.figure() controls size on screen, but saving with specific DPI requires passing dpi to savefig().

2. Step 2: Analyze each option

   fig = plt.figure(figsize=(10, 5), dpi=100) plt.plot([1, 2, 3]) fig.savefig('plot.png') sets DPI in figure but saving uses default DPI, so output may differ. fig = plt.figure(figsize=(10, 5)) plt.plot([1, 2, 3]) fig.savefig('plot.png', dpi=300) sets size in figure and DPI in savefig, ensuring correct size and resolution. fig = plt.figure(dpi=300) plt.plot([1, 2, 3]) fig.savefig('plot.png', figsize=(10, 5)) wrongly passes figsize to savefig, which is invalid. fig = plt.figure(figsize=10, dpi=300) plt.plot([1, 2, 3]) fig.savefig('plot.png') passes single int to figsize, causing error.

3. Final Answer:

   fig = plt.figure(figsize=(10, 5)) plt.plot([1, 2, 3]) fig.savefig('plot.png', dpi=300) -> Option A

4. Quick Check:

   Set size in figure, DPI in savefig for correct output [OK]

Hint: Set figsize in figure, dpi in savefig to control size and resolution [OK]

Common Mistakes:

• Setting dpi only in figure but not in savefig
• Passing figsize to savefig instead of figure
• Using single int instead of tuple for figsize