Secondary axes in Matplotlib - Step-by-Step Execution

Concept Flow - Secondary axes

Create main plot

↓

Add secondary axis

↓

Define transform functions

↓

Plot data on secondary axis

↓

Show combined plot

First, create a main plot. Then add a secondary axis with transformation functions. Plot data on both axes and display the combined figure.

Execution Sample

Matplotlib

import matplotlib.pyplot as plt
fig, ax = plt.subplots()
ax.plot([0, 1, 2], [0, 1, 4])
secax = ax.secondary_yaxis('right', functions=(lambda x: x/2, lambda x: x*2))
secax.set_ylabel('Secondary axis')
plt.show()

This code plots data on the main y-axis and adds a secondary y-axis on the right with a scaling transform.

Execution Table

Step	Action	Main axis data	Secondary axis transform	Secondary axis label	Plot shown
1	Create figure and main axis	Empty	null	null	No
2	Plot data on main axis	[0,1,4]	null	null	No
3	Add secondary y-axis on right	[0,1,4]	Forward: x/2, Inverse: x*2	null	No
4	Set label for secondary axis	[0,1,4]	Forward: x/2, Inverse: x*2	Secondary axis	No
5	Show plot with both axes	[0,1,4]	Forward: x/2, Inverse: x*2	Secondary axis	Yes

💡 Plot displayed with main and secondary y-axes after step 5

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 4	After Step 5
fig	null	Figure object created	Figure object created	Figure object created	Figure object created
ax	null	Axes object created	Axes object created	Axes object created	Axes object created
secax	null	null	SecondaryAxis object created	SecondaryAxis object created	SecondaryAxis object created
main_data	null	[0,1,4]	[0,1,4]	[0,1,4]	[0,1,4]
secax_label	null	null	null	'Secondary axis'	'Secondary axis'

Key Moments - 2 Insights

Why do we need two functions when adding a secondary axis?

The secondary axis needs a forward function to convert main axis values to secondary axis values, and an inverse function to convert back. This ensures correct scaling and interaction, as shown in step 3 of the execution_table.

Does plotting on the main axis automatically update the secondary axis?

No, the secondary axis is linked by the transform functions but does not plot data itself unless explicitly plotted. Step 2 shows main axis plotting, step 3 adds the secondary axis without plotting data on it.

Visual Quiz - 3 Questions

Look at the execution_table at step 3, what is the inverse transform function for the secondary axis?

A x / 2

B x + 2

C x * 2

D x - 2

💡 Hint

Check the 'Secondary axis transform' column at step 3 in the execution_table.

At which step is the secondary axis label set?

A Step 4

B Step 2

C Step 3

D Step 5

💡 Hint

Look at the 'Secondary axis label' column in the execution_table.

If we remove the inverse function in step 3, what happens to the secondary axis?

A It will work the same as before

B It will not display correctly or may cause errors

C The main axis data will change

D The secondary axis label will disappear

💡 Hint

Inverse function is needed for proper scaling as explained in key_moments and shown in step 3.

Concept Snapshot

Secondary axes in matplotlib allow adding an extra axis sharing the same x or y axis.
Use ax.secondary_xaxis or ax.secondary_yaxis with two functions: forward and inverse transforms.
Plot main data on the original axis; secondary axis shows transformed scale.
Set labels on secondary axis for clarity.
Useful for showing data in different units or scales side-by-side.

Full Transcript

This visual execution shows how to add a secondary axis in matplotlib. First, a figure and main axis are created. Then data is plotted on the main axis. Next, a secondary y-axis is added on the right side with two transform functions: one to convert main axis values to secondary axis values, and one to convert back. The secondary axis label is set. Finally, the plot is displayed showing both axes. The key point is that the secondary axis uses transform functions to link scales correctly. The execution table tracks each step and variable changes. The quiz tests understanding of transform functions, labeling, and the role of inverse functions.