Discrete colorbars in Matplotlib - Step-by-Step Execution

Concept Flow - Discrete colorbars

Define color levels

↓

Create colormap with discrete colors

↓

Normalize data to levels

↓

Plot data with colormap

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Add colorbar with discrete ticks

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Display plot

This flow shows how to create a colorbar with distinct color segments by defining levels, mapping colors discretely, and displaying the colorbar.

Execution Sample

Matplotlib

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

levels = [0, 1, 2, 3, 4]
cmap = plt.get_cmap('viridis', len(levels)-1)
norm = BoundaryNorm(levels, cmap.N)

fig, ax = plt.subplots()
img = ax.imshow(np.array([[0.5,1.5],[2.5,3.5]]), cmap=cmap, norm=norm)
fig.colorbar(img, boundaries=levels, ticks=levels)
plt.show()

This code creates a 2x2 image with values mapped to discrete color levels and shows a colorbar with distinct color segments.

Execution Table

Step	Action	Input/Variable	Result/Output
1	Define levels	levels = [0,1,2,3,4]	Levels set for color boundaries
2	Create colormap	cmap = viridis with 4 colors	Colormap with 4 discrete colors created
3	Create normalization	norm = BoundaryNorm(levels, cmap.N)	Normalization maps data to discrete colors
4	Prepare data	data = [[0.5,1.5],[2.5,3.5]]	Data ready for plotting
5	Plot image	imshow with cmap and norm	Image colored with discrete colors
6	Add colorbar	colorbar with boundaries=levels, ticks=levels	Colorbar shows 4 discrete color segments
7	Display plot	plt.show()	Plot with discrete colorbar displayed

💡 Plot displayed with discrete colorbar matching defined levels

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	After Step 5	After Step 6	Final
levels	undefined	[0,1,2,3,4]	[0,1,2,3,4]	[0,1,2,3,4]	[0,1,2,3,4]	[0,1,2,3,4]	[0,1,2,3,4]	[0,1,2,3,4]
cmap	undefined	undefined	viridis with 4 colors	viridis with 4 colors	viridis with 4 colors	viridis with 4 colors	viridis with 4 colors	viridis with 4 colors
norm	undefined	undefined	undefined	BoundaryNorm object	BoundaryNorm object	BoundaryNorm object	BoundaryNorm object	BoundaryNorm object
data	undefined	undefined	undefined	undefined	[[0.5,1.5],[2.5,3.5]]	[[0.5,1.5],[2.5,3.5]]	[[0.5,1.5],[2.5,3.5]]	[[0.5,1.5],[2.5,3.5]]
img	undefined	undefined	undefined	undefined	undefined	AxesImage object	AxesImage object	AxesImage object

Key Moments - 3 Insights

Why do we use BoundaryNorm instead of a simple normalization?

BoundaryNorm maps data values to discrete color intervals defined by levels, ensuring each color segment corresponds exactly to a range, as shown in step 3 of the execution_table.

Why do the colorbar ticks match the levels list?

The colorbar uses the boundaries and ticks parameters set to levels, so each tick aligns with a color segment boundary, as seen in step 6.

What happens if data values fall between levels?

BoundaryNorm assigns colors based on which interval the value falls into, so values like 0.5 map to the first color segment between 0 and 1, demonstrated in step 5.

Visual Quiz - 3 Questions

Look at the execution_table step 3. What does BoundaryNorm do with the levels?

A Creates a continuous gradient colormap

B Sets the colorbar labels only

C Maps continuous data to discrete color intervals

D Normalizes data between 0 and 1

💡 Hint

Refer to step 3 where norm is created with BoundaryNorm using levels.

At which step is the image data assigned colors based on discrete levels?

A Step 4

B Step 5

C Step 2

D Step 6

💡 Hint

Step 5 shows plotting with imshow using cmap and norm.

If we add a new level 5 to levels, how does the colorbar change?

A It shows 5 discrete color segments instead of 4

B It remains with 4 color segments

C It becomes a continuous gradient

D It removes all ticks

💡 Hint

Check variable_tracker for levels and cmap size relation.

Concept Snapshot

Discrete colorbars in matplotlib:
- Define levels as boundaries for colors
- Use BoundaryNorm to map data to these levels
- Create colormap with number of colors = len(levels)-1
- Plot data with cmap and norm
- Add colorbar with boundaries and ticks matching levels
- Result: colorbar shows distinct color segments matching data ranges

Full Transcript

This example shows how to create a discrete colorbar in matplotlib. First, we define the levels that separate color segments. Then, we create a colormap with a fixed number of colors matching the intervals between levels. BoundaryNorm is used to map data values to these discrete color intervals. We plot the data using imshow with the colormap and normalization. Finally, we add a colorbar with boundaries and ticks set to the levels, so the colorbar shows distinct color blocks. This helps visualize data categories clearly instead of a smooth gradient.

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