Log scale and symlog scale in Matplotlib - Mini Project: Build & Apply

Plotting with Log Scale and Symlog Scale in Matplotlib

📖 Scenario: You are working with a small business that tracks daily sales and wants to visualize the data clearly. Some days have very low sales, and some days have very high sales. To better understand the trends, you will create plots using log scale and symlog scale.

🎯 Goal: Build two line plots using matplotlib: one with a log scale on the y-axis and another with a symmetric log scale (symlog) on the y-axis. This will help visualize data that varies widely and includes zero or negative values.

📋 What You'll Learn

Create a list called days with values from 1 to 10.

Create a list called sales with these exact values: 0, 1, 10, 100, 1000, 10000, 100000, -10, -100, 0.

Create a variable called linthresh and set it to 20.

Plot days vs sales using plt.plot().

Set the y-axis scale to log using plt.yscale('log') for the first plot.

Create a second plot with y-axis scale set to symlog using plt.yscale('symlog', linthresh=linthresh).

Show both plots with plt.show().

💡 Why This Matters

🌍 Real World

Businesses often have data that varies a lot in size, like sales or website visits. Using log or symlog scales helps visualize such data clearly, especially when some values are zero or negative.

💼 Career

Data scientists and analysts use log and symlog scales to explore and present data effectively, making it easier to spot trends and outliers.

1

Create the data lists for days and sales

Create a list called days with values from 1 to 10, and a list called sales with these exact values: 0, 1, 10, 100, 1000, 10000, 100000, -10, -100, 0.

Matplotlib

# Create the days and sales lists
# Your code here

Hint

Use square brackets to create lists. Make sure the values match exactly.

2

Set the linthresh variable for symlog scale

Create a variable called linthresh and set it to 20.

Matplotlib

days = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
sales = [0, 1, 10, 100, 1000, 10000, 100000, -10, -100, 0]
# Create linthresh variable and set it to 20
# Your code here

Hint

Just assign the number 20 to the variable linthresh.

3

Plot days vs sales with log scale and symlog scale

Import matplotlib.pyplot as plt. Plot days vs sales using plt.plot(). Then set the y-axis scale to log using plt.yscale('log'). Create a new figure with plt.figure(), plot the same data again, and set the y-axis scale to symlog using plt.yscale('symlog', linthresh=linthresh).

Matplotlib

days = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
sales = [0, 1, 10, 100, 1000, 10000, 100000, -10, -100, 0]
linthresh = 20
# Import matplotlib.pyplot as plt
# Plot days vs sales with log scale
# Create new figure and plot days vs sales with symlog scale
# Your code here

Hint

Remember to import matplotlib.pyplot as plt first. Use plt.plot() to draw the lines. Use plt.yscale() to set the scale.

4

Show the plots

Use plt.show() to display both plots.

Matplotlib

import matplotlib.pyplot as plt

days = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
sales = [0, 1, 10, 100, 1000, 10000, 100000, -10, -100, 0]
linthresh = 20

plt.plot(days, sales)
plt.yscale('log')

plt.figure()
plt.plot(days, sales)
plt.yscale('symlog', linthresh=linthresh)
# Show the plots
# Your code here

Hint

Use plt.show() once after all plots are ready to display them.

Practice

1. What is the main difference between a log scale and a symlog scale in matplotlib?

easy

A. Log scale only works for positive values, while symlog can handle negative and zero values.

B. Log scale can handle negative values, but symlog cannot.

C. Symlog scale is only for categorical data, log scale is for numerical data.

D. Log scale and symlog scale are exactly the same.

Solution

1. Step 1: Understand log scale limitations

   Log scale transforms data using logarithms and only supports positive values because logarithm of zero or negative numbers is undefined.

2. Step 2: Understand symlog scale features

   Symlog scale combines linear and logarithmic scales to handle negative, zero, and positive values by using a linear region around zero.

3. Final Answer:

   Log scale only works for positive values, while symlog can handle negative and zero values. -> Option A

4. Quick Check:

   Log scale positive only, symlog includes negatives [OK]

Hint: Log scale = positive only; symlog = includes negatives and zero [OK]

Common Mistakes:

• Thinking log scale supports zero or negative values
• Confusing symlog with linear scale
• Assuming symlog is only for positive values

2. Which of the following is the correct way to set the y-axis to a symlog scale in matplotlib?

easy

A. ax.set_scale('symlog')

B. ax.set_yscale('logarithm')

C. ax.set_yscale('symlog')

D. ax.set_scale('log')

Solution

1. Step 1: Recall matplotlib scale setting methods

   Matplotlib uses ax.set_xscale() or ax.set_yscale() to set axis scales.

2. Step 2: Identify correct scale name and method

   To set y-axis to symlog, use ax.set_yscale('symlog'). Other options are either incorrect method names or scale names.

3. Final Answer:

   ax.set_yscale('symlog') -> Option C

4. Quick Check:

   Use set_yscale with 'symlog' string [OK]

Hint: Use ax.set_yscale('symlog') to set y-axis symlog scale [OK]

Common Mistakes:

• Using ax.set_scale instead of ax.set_yscale
• Using wrong scale name like 'logarithm'
• Trying to set scale on x-axis when y-axis is intended

3. What will be the output of the following code snippet?

import matplotlib.pyplot as plt
import numpy as np

x = np.array([-100, -10, -1, 0, 1, 10, 100])
y = x

fig, ax = plt.subplots()
ax.plot(x, y)
ax.set_xscale('symlog', linthresh=1)
plt.show()

medium

A. A plot with x-axis on a linear scale only.

B. A plot with x-axis showing only positive values on a logarithmic scale, negative values ignored.

C. A runtime error because negative values cannot be plotted on log scale.

D. A plot with x-axis showing a linear scale near zero and logarithmic scale away from zero, including negative values.

Solution

1. Step 1: Understand symlog scale behavior

   Symlog scale allows negative and zero values by using a linear region around zero defined by linthresh.

2. Step 2: Analyze code and data

   The x values include negative, zero, and positive numbers. Setting x-axis to symlog with linthresh=1 means values between -1 and 1 are linear, outside are logarithmic.

3. Final Answer:

   A plot with x-axis showing a linear scale near zero and logarithmic scale away from zero, including negative values. -> Option D

4. Quick Check:

   Symlog handles negatives with linear region near zero [OK]

Hint: Symlog mixes linear near zero and log away, including negatives [OK]

Common Mistakes:

• Expecting error due to negative values on log scale
• Thinking symlog is fully logarithmic without linear region
• Assuming negative values are ignored or cause crash

4. The following code throws a ValueError: "Data has no positive values, and therefore can not be log-scaled." How can you fix it?

import matplotlib.pyplot as plt
import numpy as np

x = np.array([-10, -5, -1, 0])
y = np.arange(4)

fig, ax = plt.subplots()
ax.plot(x, y)
ax.set_xscale('log')
plt.show()

medium

A. Change ax.set_xscale('log') to ax.set_xscale('symlog').

B. Remove negative values from x before plotting.

C. Change y-axis scale instead of x-axis scale.

D. Use ax.set_xscale('linear') instead.

Solution

1. Step 1: Identify cause of error

   Log scale requires positive values only. The x array has negative and zero values, causing the error.

2. Step 2: Apply symlog scale to handle negatives

   Symlog scale supports negative and zero values by combining linear and log scales, so changing to symlog fixes the error.

3. Final Answer:

   Change ax.set_xscale('log') to ax.set_xscale('symlog'). -> Option A

4. Quick Check:

   Use symlog for negative values on log scale [OK]

Hint: Use symlog scale to plot negative or zero values on log axis [OK]

Common Mistakes:

• Trying to plot negative values on log scale directly
• Removing data instead of changing scale
• Changing unrelated axis scale

5. You have a dataset with values ranging from -1000 to 1000, including zero. You want to plot it using matplotlib so that the axis shows a logarithmic scale for large values but remains linear near zero to avoid distortion. Which approach is best?

hard

A. Use ax.set_xscale('log') and filter out negative and zero values.

B. Use ax.set_xscale('symlog', linthresh=10) to combine linear and log scales.

C. Use ax.set_xscale('linear') because log scales cannot handle negatives.

D. Use ax.set_xscale('log') with linthresh=10 parameter.

Solution

1. Step 1: Understand data range and requirements

   Data includes negative, zero, and positive values from -1000 to 1000. We want log scale for large values but linear near zero to avoid distortion.

2. Step 2: Choose appropriate scale and parameters

   Log scale cannot handle negatives or zero. Symlog scale supports negatives and zero by mixing linear region near zero (controlled by linthresh) and log scale outside.

3. Step 3: Evaluate options

   Use ax.set_xscale('symlog', linthresh=10) to combine linear and log scales. uses symlog with linthresh=10, which fits the requirement. Use ax.set_xscale('log') and filter out negative and zero values. filters data, losing information. Use ax.set_xscale('linear') because log scales cannot handle negatives. uses linear scale only, losing log benefits. Use ax.set_xscale('log') with linthresh=10 parameter. is invalid because log scale does not accept linthresh.

4. Final Answer:

   Use ax.set_xscale('symlog', linthresh=10) to combine linear and log scales. -> Option B

5. Quick Check:

   Symlog with linthresh mixes linear near zero and log away [OK]

Hint: Use symlog with linthresh to mix linear near zero and log away [OK]

Common Mistakes:

• Trying to use log scale with negative values
• Filtering out negative values instead of using symlog
• Using linear scale only losing log benefits
• Using invalid parameters with log scale