Heatmap with plt.imshow in Matplotlib - Time & Space Complexity

Time Complexity: Heatmap with plt.imshow

O(n²)

Understanding Time Complexity

We want to understand how the time to create a heatmap grows as the data size increases.

How does the plotting time change when the matrix gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt
import numpy as np

# Create a random matrix of size n x n
n = 100
data = np.random.rand(n, n)

# Plot heatmap
plt.imshow(data, cmap='viridis')
plt.colorbar()
plt.show()

This code creates a heatmap from a square matrix of size n by n using plt.imshow.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Rendering each cell of the n x n matrix as a colored pixel.
• How many times: Once for each of the n² cells in the matrix.

How Execution Grows With Input

As the matrix size n grows, the number of cells to draw grows with n squared.

Input Size (n)	Approx. Operations
10	100
100	10,000
1000	1,000,000

Pattern observation: Doubling n makes the work about four times bigger because the area grows with n squared.

Final Time Complexity

Time Complexity: O(n²)

This means the time to draw the heatmap grows roughly with the square of the matrix size.

Common Mistake

[X] Wrong: "The time grows linearly with n because we just loop once over the data."

[OK] Correct: The data is two-dimensional, so we actually process n times n cells, not just n.

Interview Connect

Understanding how plotting time grows with data size helps you explain performance in data visualization tasks clearly and confidently.

Self-Check

"What if we changed the data from a square matrix to a long vector? How would the time complexity change?"

Practice

1. What does the plt.imshow function do in matplotlib when given a 2D array?

easy

A. It prints the array values as text on the plot.

B. It plots a line graph of the array values.

C. It creates a heatmap by showing the array values as colors.

D. It creates a pie chart from the array values.

Solution

1. Step 1: Understand plt.imshow input

   The function takes a 2D array and maps its values to colors in a grid.

2. Step 2: Recognize heatmap behavior

   This color mapping creates a heatmap, showing patterns visually.

3. Final Answer:

   It creates a heatmap by showing the array values as colors. -> Option C

4. Quick Check:

   plt.imshow = heatmap colors [OK]

Hint: plt.imshow shows 2D data as colored grids [OK]

Common Mistakes:

• Thinking plt.imshow plots lines or text
• Confusing heatmap with pie chart
• Assuming plt.imshow prints numbers

2. Which of these is the correct way to add a color bar to a heatmap created with plt.imshow?

easy

A. plt.colorbar()

B. plt.addcolor()

C. plt.showcolor()

D. plt.colorheat()

Solution

1. Step 1: Recall color bar function

   Matplotlib uses plt.colorbar() to add a color scale next to images.

2. Step 2: Check other options

   Other options are not valid matplotlib functions.

3. Final Answer:

   plt.colorbar() -> Option A

4. Quick Check:

   Color bar function = plt.colorbar() [OK]

Hint: Use plt.colorbar() to add color scale [OK]

Common Mistakes:

• Using non-existent functions like plt.addcolor()
• Forgetting to call plt.colorbar() after plt.imshow()
• Trying to add color bar before plotting heatmap

3. What will the following code display?

import matplotlib.pyplot as plt
import numpy as np

data = np.array([[1, 2], [3, 4]])
plt.imshow(data, cmap='hot')
plt.colorbar()
plt.show()

medium

A. A scatter plot of points (1,2) and (3,4) with hot colors.

B. A line plot of the numbers 1, 2, 3, 4 with a color bar.

C. An error because cmap='hot' is invalid.

D. A 2x2 heatmap with colors from black to red to yellow, and a color bar showing values 1 to 4.

Solution

1. Step 1: Understand plt.imshow with cmap='hot'

   The data array is 2x2, so plt.imshow creates a 2x2 grid colored by values using the 'hot' color map (black to red to yellow).

2. Step 2: Effect of plt.colorbar()

   The color bar shows the scale from the minimum value 1 to maximum 4, helping interpret colors.

3. Final Answer:

   A 2x2 heatmap with colors from black to red to yellow, and a color bar showing values 1 to 4. -> Option D

4. Quick Check:

   plt.imshow + cmap='hot' + colorbar = heatmap with hot colors [OK]

Hint: cmap='hot' colors low to high values black-red-yellow [OK]

Common Mistakes:

• Thinking plt.imshow plots lines or scatter
• Believing cmap='hot' causes error
• Ignoring color bar meaning

4. The code below is intended to show a heatmap but does not display the color bar. What is the error?

import matplotlib.pyplot as plt
import numpy as np

data = np.random.rand(3,3)
plt.imshow(data)
plt.colorbar
plt.show()

medium

A. plt.colorbar is missing parentheses, so color bar is not shown.

B. plt.imshow needs a cmap argument to show color bar.

C. plt.show() must come before plt.colorbar().

D. np.random.rand(3,3) creates invalid data for heatmap.

Solution

1. Step 1: Identify plt.colorbar usage

   The code uses plt.colorbar without parentheses, so the function is not called.

2. Step 2: Correct function call

   Adding parentheses plt.colorbar() calls the function and displays the color bar.

3. Final Answer:

   plt.colorbar is missing parentheses, so color bar is not shown. -> Option A

4. Quick Check:

   Call plt.colorbar() with () to show color bar [OK]

Hint: Always call plt.colorbar() with parentheses [OK]

Common Mistakes:

• Forgetting parentheses on plt.colorbar
• Thinking cmap is required for color bar
• Calling plt.show() before plt.colorbar

5. You have a 4x4 matrix with values from 0 to 15. You want to create a heatmap using plt.imshow that shows the values clearly with a color bar, but you want the color scale to always be from 0 to 20 regardless of data. Which code snippet correctly does this?

hard

A. plt.imshow(matrix, vmin=0, vmax=15)
plt.colorbar()
plt.show()

B. plt.imshow(matrix, vmin=0, vmax=20)
plt.colorbar()
plt.show()

C. plt.imshow(matrix, cmap='gray')
plt.colorbar()
plt.show()

D. plt.imshow(matrix)
plt.colorbar(vmin=0, vmax=20)
plt.show()

Solution

1. Step 1: Set color scale limits in plt.imshow

   Use vmin=0 and vmax=20 in plt.imshow to fix color scale from 0 to 20.

2. Step 2: Add color bar normally

   Call plt.colorbar() to show the color scale matching the fixed limits.

3. Final Answer:

   plt.imshow(matrix, vmin=0, vmax=20) plt.colorbar() plt.show() -> Option B

4. Quick Check:

   Set vmin/vmax in imshow, then add colorbar [OK]

Hint: Use vmin and vmax in plt.imshow to fix color scale [OK]

Common Mistakes:

• Setting vmin/vmax in plt.colorbar instead of plt.imshow
• Not setting vmax to 20, so scale auto adjusts
• Using wrong vmin/vmax values