Discrete colorbars in Matplotlib

Introduction

Discrete colorbars help show clear steps of colors instead of smooth gradients. This makes it easier to see distinct groups or categories in data.

When you want to show categories or groups with different colors.

When your data has specific ranges that need clear color separation.

When you want to avoid confusion from smooth color changes in a legend.

When presenting data like survey results with fixed answer choices.

When visualizing data like temperature ranges or risk levels with clear steps.

Syntax

Matplotlib

import matplotlib.pyplot as plt
import numpy as np
import matplotlib.colors as mcolors

# Define discrete colors and boundaries
cmap = mcolors.ListedColormap(['blue', 'green', 'yellow', 'red'])
bounds = [0, 10, 20, 30, 40]
norm = mcolors.BoundaryNorm(bounds, cmap.N)

# Create colorbar with discrete steps
fig, ax = plt.subplots(figsize=(6, 1))
fig.colorbar(plt.cm.ScalarMappable(norm=norm, cmap=cmap), cax=ax, orientation='horizontal')
plt.show()

Use ListedColormap to set specific colors for each step.

BoundaryNorm defines the edges of each color step.

Examples

This example creates a horizontal discrete colorbar with three colors: red, yellow, and green.

Matplotlib

import matplotlib.pyplot as plt
import matplotlib.colors as mcolors

cmap = mcolors.ListedColormap(['red', 'yellow', 'green'])
bounds = [0, 5, 10, 15]
norm = mcolors.BoundaryNorm(bounds, cmap.N)

fig, ax = plt.subplots(figsize=(5, 1))
fig.colorbar(plt.cm.ScalarMappable(norm=norm, cmap=cmap), cax=ax, orientation='horizontal')
plt.show()

This example uses four colors with boundaries at 0, 25, 50, 75, and 100 to show discrete steps.

Matplotlib

import matplotlib.pyplot as plt
import numpy as np
import matplotlib.colors as mcolors

cmap = mcolors.ListedColormap(['navy', 'cyan', 'lime', 'orange'])
bounds = [0, 25, 50, 75, 100]
norm = mcolors.BoundaryNorm(bounds, cmap.N)

fig, ax = plt.subplots(figsize=(6, 1))
fig.colorbar(plt.cm.ScalarMappable(norm=norm, cmap=cmap), cax=ax, orientation='horizontal')
plt.show()

Sample Program

This program creates a horizontal discrete colorbar with four color steps representing value ranges 0-10, 10-20, 20-30, and 30-40.

Matplotlib

import matplotlib.pyplot as plt
import numpy as np
import matplotlib.colors as mcolors

# Data values
values = np.array([5, 12, 18, 27, 33])

# Define discrete colormap and boundaries
colors = ['blue', 'green', 'yellow', 'red']
cmap = mcolors.ListedColormap(colors)
bounds = [0, 10, 20, 30, 40]
norm = mcolors.BoundaryNorm(bounds, cmap.N)

# Create a figure and axis
fig, ax = plt.subplots(figsize=(6, 1))

# Create a ScalarMappable for the colorbar
sm = plt.cm.ScalarMappable(cmap=cmap, norm=norm)
sm.set_array([])  # Needed for colorbar

# Add discrete colorbar
cbar = fig.colorbar(sm, cax=ax, orientation='horizontal')
cbar.set_label('Value ranges')

plt.show()

Important Notes

Make sure the number of colors matches the number of intervals defined by bounds minus one.

Use set_array([]) on ScalarMappable to avoid warnings when creating colorbars without data.

Summary

Discrete colorbars show clear color steps for distinct data ranges.

Use ListedColormap and BoundaryNorm to create discrete colorbars.

They help make legends easier to read when data has categories or fixed ranges.

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