Discrete colorbars in Matplotlib - Time & Space Complexity

Time Complexity: Discrete colorbars

O(n)

Understanding Time Complexity

We want to understand how the time to create a discrete colorbar changes as we increase the number of color segments.

How does adding more color steps affect the work matplotlib does?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt
import numpy as np
from matplotlib.colors import BoundaryNorm

levels = np.linspace(0, 100, 11)  # 10 intervals
cmap = plt.get_cmap('viridis', len(levels) - 1)
norm = BoundaryNorm(levels, ncolors=cmap.N)

fig, ax = plt.subplots()
cb = plt.colorbar(plt.cm.ScalarMappable(norm=norm, cmap=cmap), ax=ax)
plt.show()

This code creates a discrete colorbar with 10 color segments using matplotlib.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Generating and drawing each color segment in the colorbar.
• How many times: Once for each color segment, which equals the number of intervals (here 10).

How Execution Grows With Input

As the number of color segments increases, matplotlib draws more rectangles and labels for the colorbar.

Input Size (n)	Approx. Operations
10	10 drawing steps
100	100 drawing steps
1000	1000 drawing steps

Pattern observation: The work grows directly with the number of color segments.

Final Time Complexity

Time Complexity: O(n)

This means the time to create the discrete colorbar grows linearly with the number of color segments.

Common Mistake

[X] Wrong: "Adding more color segments does not affect the drawing time much because it's just one colorbar."

[OK] Correct: Each color segment requires separate drawing and labeling, so more segments mean more work.

Interview Connect

Understanding how visual elements scale with input size helps you reason about performance in data visualization tasks.

Self-Check

What if we changed the colorbar to use a continuous colormap instead of discrete segments? How would the time complexity change?

Practice

1. What is the main purpose of using a discrete colorbar in a matplotlib plot?

easy

A. To increase the size of the plot figure

B. To create a continuous gradient of colors for smooth data

C. To add labels to the x-axis of a plot

D. To show data with distinct color steps for clear category separation

Solution

1. Step 1: Understand colorbar types

   Continuous colorbars show smooth color changes, while discrete colorbars use fixed color steps.

2. Step 2: Identify the purpose of discrete colorbars

   Discrete colorbars help separate data into clear categories using distinct colors.

3. Final Answer:

   To show data with distinct color steps for clear category separation -> Option D

4. Quick Check:

   Discrete colorbar = distinct color steps [OK]

Hint: Discrete colorbars separate categories with fixed colors [OK]

Common Mistakes:

• Confusing discrete with continuous colorbars
• Thinking colorbars change plot size
• Mixing colorbar purpose with axis labeling

2. Which of the following code snippets correctly creates a discrete colorbar with 3 color steps using matplotlib?

easy

A. cmap = ListedColormap(['red', 'green', 'blue'])
norm = Normalize(0, 3)

B. cmap = LinearSegmentedColormap(['red', 'green', 'blue'])
norm = Normalize(0, 3)

C. cmap = ListedColormap(['red', 'green', 'blue'])
norm = BoundaryNorm([0, 1, 2, 3], cmap.N)

D. cmap = LinearSegmentedColormap(['red', 'green', 'blue'])
norm = BoundaryNorm([0, 1, 2, 3], cmap.N)

Solution

1. Step 1: Identify correct colormap for discrete colors

   ListedColormap is used for discrete colors, LinearSegmentedColormap is for continuous gradients.

2. Step 2: Check normalization method

   BoundaryNorm with boundaries defines discrete steps; Normalize is for continuous scaling.

3. Final Answer:

   cmap = ListedColormap(['red', 'green', 'blue'])\nnorm = BoundaryNorm([0, 1, 2, 3], cmap.N) -> Option C

4. Quick Check:

   ListedColormap + BoundaryNorm = discrete colorbar [OK]

Hint: Use ListedColormap + BoundaryNorm for discrete colorbars [OK]

Common Mistakes:

• Using Normalize instead of BoundaryNorm
• Using LinearSegmentedColormap for discrete colors
• Incorrect boundary list length

3. What will be the output color for a value of 1.5 in this discrete colorbar setup?

import matplotlib.pyplot as plt
from matplotlib.colors import ListedColormap, BoundaryNorm

cmap = ListedColormap(['yellow', 'orange', 'red'])
norm = BoundaryNorm([0, 1, 2, 3], cmap.N)
color = cmap(norm(1.5))
print(color)

medium

A. (1.0, 1.0, 0.0, 1.0) # yellow color

B. (1.0, 0.647, 0.0, 1.0) # orange color

C. (1.0, 0.0, 0.0, 1.0) # red color

D. (0.5, 0.5, 0.5, 1.0) # gray color

Solution

1. Step 1: Understand BoundaryNorm mapping

   BoundaryNorm maps values 0-1 to first color (yellow), 1-2 to second (orange), 2-3 to third (red).

2. Step 2: Find color for value 1.5

   1.5 lies between 1 and 2, so it maps to the second color: orange (RGB approx (1.0, 0.647, 0.0, 1.0)).

3. Final Answer:

   (1.0, 0.647, 0.0, 1.0) # orange color -> Option B

4. Quick Check:

   Value 1.5 in 1-2 range = orange [OK]

Hint: Check which boundary interval the value falls into [OK]

Common Mistakes:

• Choosing first or third color incorrectly
• Confusing Normalize with BoundaryNorm behavior
• Misreading boundary intervals

4. Identify the error in this code that tries to create a discrete colorbar with 4 colors:

import matplotlib.pyplot as plt
from matplotlib.colors import ListedColormap, BoundaryNorm

cmap = ListedColormap(['blue', 'green', 'yellow', 'red'])
norm = BoundaryNorm([0, 1, 2, 3], cmap.N)
plt.colorbar(plt.cm.ScalarMappable(norm=norm, cmap=cmap))
plt.show()

medium

A. Boundary list length should be one more than number of colors

B. ListedColormap cannot have more than 3 colors

C. plt.colorbar requires a continuous colormap

D. ScalarMappable is not compatible with BoundaryNorm

Solution

1. Step 1: Check boundary list length

   BoundaryNorm boundaries must have length = number of colors + 1 to define intervals correctly.

2. Step 2: Compare boundaries and colors

   Here, 4 colors but only 4 boundaries given; should be 5 boundaries like [0,1,2,3,4].

3. Final Answer:

   Boundary list length should be one more than number of colors -> Option A

4. Quick Check:

   Boundaries = colors + 1 [OK]

Hint: Boundaries count = colors count + 1 for discrete colorbars [OK]

Common Mistakes:

• Using equal boundaries and colors length
• Thinking ScalarMappable is incompatible
• Believing ListedColormap limits colors

5. You have data with 5 categories labeled 0 to 4. You want a discrete colorbar with distinct colors for each category and labels shown on the colorbar ticks. Which approach correctly achieves this in matplotlib?

hard

A. Use ListedColormap with 5 colors, BoundaryNorm with boundaries [0,1,2,3,4,5], and set colorbar ticks at [0.5,1.5,2.5,3.5,4.5] with labels ['0','1','2','3','4']

B. Use LinearSegmentedColormap with 5 colors and Normalize from 0 to 4, then set colorbar ticks at [0,1,2,3,4]

C. Use ListedColormap with 4 colors, BoundaryNorm with boundaries [0,1,2,3,4], and set colorbar ticks at [0,1,2,3]

D. Use ListedColormap with 5 colors, Normalize from 0 to 5, and set colorbar ticks at [0,1,2,3,4]

Solution

1. Step 1: Set colormap and boundaries for 5 categories

   ListedColormap with 5 colors matches 5 categories; BoundaryNorm boundaries must be length 6 for 5 intervals.

2. Step 2: Position ticks between boundaries

   Ticks at midpoints like 0.5,1.5,... label categories clearly on discrete colorbar.

3. Final Answer:

   Use ListedColormap with 5 colors, BoundaryNorm with boundaries [0,1,2,3,4,5], and set colorbar ticks at [0.5,1.5,2.5,3.5,4.5] with labels ['0','1','2','3','4'] -> Option A

4. Quick Check:

   Boundaries + mid-ticks label discrete categories [OK]

Hint: Use boundaries + midpoints for ticks to label categories [OK]

Common Mistakes:

• Using continuous colormap for discrete data
• Setting ticks at boundaries instead of midpoints
• Mismatching number of colors and boundaries