How to create a list of uniformly spaced numbers using a logarithmic scale with Python?

Last Updated : 15 Mar, 2021

In this article, we will create a list of uniformly spaced numbers using a logarithmic scale. It means on a log scale difference between two adjacent samples is the same. The goal can be achieved using two different functions from the Python Numpy library.

Functions Used:

numpy.logspace: This function returns number scaled evenly on logarithmic scale.

Parameters:

start: Starting value of sequence is base**start
stop: If endpoint is True then ending value of sequence is base**stop
num (Optional): Specifies the number of samples to generate
endpoint (Optional): It can either be true or false with default value true
base (Optional): Specifies the base of log sequence. Default value is 10.
dtype (Optional): Specifies the type of output array
axis (Optional): The axis in the result to store the samples.

Return: It returns array of samples equally spaced on log scale.

numpy.geomspace: This function is similar to logspace function only difference being end points are specified directly. In Output sample every output is obtained by multiplying previous output by same constant.

Parameters:

start: It is the starting value of sequence

stop: If endpoint is True then it is the ending value of sequence

num (Optional): Specifies the number of samples to generate

endpoint (Optional): It can either be true or false with default value true

dtype (Optional): Specifies the type of output array

axis (Optional): The axis in the result to store the samples.

Return: It returns array of samples equally spaced on log scale.

Example 1: This example uses logspace function. In this example, start is passed as 1 and the stop is passed as 3 with the base being 10. So starting point of the sequence will be 10**1 = 10 and the ending point of the sequence will be 10**3 = 1000.

Python3

# importing the library
import numpy as np
import matplotlib.pyplot as plt

# Initializing variable
y = np.ones(10)

# Calculating result
res = np.logspace(1, 3, 10, endpoint = True)

# Printing the result
print(res)

# Plotting the graph
plt.scatter(res, y, color = 'green')
plt.title('logarithmically spaced numbers')
plt.show()

Output:

Example 2: This example generates the same list as the previous example using geomspace function. Here we directly passed 10 and 1000 as starting and ending points

Python3

# importing the library
import numpy as np
import matplotlib.pyplot as plt

# Initializing variable
y = np.ones(10)

# Calculating result
res = np.geomspace(10, 1000, 10, endpoint = True)

# Printing the result
print(res)

# Plotting the graph
plt.scatter(res, y, color = 'green')
plt.title('logarithmically spaced numbers')
plt.show()

Output:

Example 3: In this example, endpoint is set to false so it will generate n+1 sample and return only first n sample i.e. stop will not be included in the sequence.