Log scale and symlog scale in Matplotlib - Step-by-Step Execution

Concept Flow - Log scale and symlog scale

Start: Plot data

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Choose axis scale

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Linear scale

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Log scale

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Symlog scale

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Apply scale to axis

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Render plot with scale

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Show plot output

The flow shows how data is plotted, then a scale type is chosen (linear, log, or symlog), applied to the axis, and finally the plot is rendered with that scale.

Execution Sample

Matplotlib

import matplotlib.pyplot as plt
import numpy as np
x = np.linspace(-10, 10, 100)
y = x**3
plt.plot(x, y)
plt.yscale('symlog', linthresh=100)
plt.show()

This code plots y = x^3 with a symmetric log scale on the y-axis, allowing negative and positive values with a linear region near zero.

Execution Table

Step	Action	x values sample	y values sample	Axis scale applied	Plot effect
1	Generate x values	[-10, -5, 0, 5, 10]	[...]	None	Data ready for plotting
2	Calculate y = x^3	[-10, -5, 0, 5, 10]	[-1000, -125, 0, 125, 1000]	None	y values computed
3	Plot x vs y	[-10, -5, 0, 5, 10]	[-1000, -125, 0, 125, 1000]	None	Plot with default linear scale
4	Set y-axis scale to 'symlog' with linthresh=100	[-10, -5, 0, 5, 10]	[-1000, -125, 0, 125, 1000]	symlog	Negative and positive y shown with linear zone near 0
5	Render and show plot	[-10, -5, 0, 5, 10]	[-1000, -125, 0, 125, 1000]	symlog	Plot displayed with symlog y-axis scale

💡 Plot is shown with y-axis using symlog scale, handling negative and positive values smoothly.

Variable Tracker

Variable	Start	After Step 2	After Step 4	Final
x	None	[-10, -5, 0, 5, 10]	[-10, -5, 0, 5, 10]	[-10, -5, 0, 5, 10]
y	None	[-1000, -125, 0, 125, 1000]	[-1000, -125, 0, 125, 1000]	[-1000, -125, 0, 125, 1000]
axis_scale	linear (default)	linear (default)	symlog (linthresh=100)	symlog (linthresh=100)

Key Moments - 2 Insights

Why can't we use a normal log scale when y has negative values?

Log scale only works with positive values because log of zero or negative numbers is undefined. The symlog scale solves this by combining linear scale near zero and log scale away from zero, allowing negative values.

What does the 'linthresh' parameter do in symlog scale?

'linthresh' sets the range around zero where the scale is linear instead of logarithmic. This prevents extreme compression near zero and helps visualize values close to zero clearly.

Visual Quiz - 3 Questions

Look at the execution table at Step 4, what axis scale is applied?

A Linear scale

B Log scale

C Symlog scale

D No scale applied

💡 Hint

Check the 'Axis scale applied' column in Step 4 of the execution table.

According to variable_tracker, what is the value of y after Step 2 for x=5?

A 25

B 125

C 5

D -125

💡 Hint

Look at the 'y' row and 'After Step 2' column in variable_tracker.

If we set linthresh=10 instead of 100 in symlog, what changes in the plot effect?

A The linear zone near zero becomes smaller

B The linear zone near zero becomes larger

C Negative values are not shown

D The plot switches to linear scale

💡 Hint

Refer to the key_moments explanation about 'linthresh' parameter.

Concept Snapshot

Log scale: axis uses logarithm, only positive values allowed.
Symlog scale: combines linear near zero and log away from zero.
Use symlog to plot data with negative and positive values.
Set 'linthresh' to control linear region size near zero.
In matplotlib: plt.yscale('log') or plt.yscale('symlog', linthresh=...)
Symlog helps visualize wide range including negatives.

Full Transcript

This visual execution shows how to plot data using log and symlog scales in matplotlib. First, x values are generated and y values calculated as x cubed. Then the plot is created with default linear scale. Next, the y-axis scale is changed to symlog with a linear threshold of 100, allowing negative and positive y values to be displayed properly. The plot is rendered showing the effect of symlog scale. Variables x and y remain the same, but the axis scale changes from linear to symlog. Key points include that log scale cannot handle negative values, while symlog can by using a linear region near zero controlled by linthresh. The quizzes test understanding of axis scale applied, y values, and effect of linthresh parameter.