How to Calculate a Sigmoid Function in Python (With Examples)


A sigmoid function is a mathematical function that has an “S” shaped curve when plotted.

The most common example of a sigmoid function is the logistic sigmoid function, which is calculated as:

F(x) = 1 / (1 + e-x)

The easiest way to calculate a sigmoid function in Python is to use the expit() function from the SciPy library, which uses the following basic syntax:

from scipy.special import expit

#calculate sigmoid function for x = 2.5
expit(2.5)

The following examples show how to use this function in practice.

Example 1: Calculate Sigmoid Function for One Value

The following code shows how to calculate the sigmoid function for the value x = 2.5:

from scipy.special import expit

#calculate sigmoid function for x = 2.5
expit(2.5)

0.9241418199787566

The value of the sigmoid function for x = 2.5 is 0.924.

We can confirm this by calculating the value manually:

  • F(x) = 1 / (1 + e-x)
  • F(x) = 1 / (1 + e-2.5)
  • F(x) = 1 / (1 + .082)
  • F(x) = 0.924

Example 2: Calculate Sigmoid Function for Multiple Values

The following code shows how to calculate the sigmoid function for multiple x values at once:

from scipy.special import expit

#define list of values
values = [-2, -1, 0, 1, 2]

#calculate sigmoid function for each value in list
expit(values)

array([0.11920292, 0.26894142, 0.5, 0.73105858, 0.88079708])

Example 3: Plot Sigmoid Function for Range of Values

The following code shows how to plot the values of a sigmoid function for a range of x values using matplotlib:

import matplotlib.pyplot as plt
from scipy.special import expit
import numpy as np

#define range of x-values
x = np.linspace(-10, 10, 100)

#calculate sigmoid function for each x-value
y = expit(x)
  
#create plot
plt.plot(x, y)
plt.xlabel('x')
plt.ylabel('F(x)')

#display plot
plt.show()

sigmoid function in Python

Notice that the plot exhibits the “S” shaped curve that is characteristic of a sigmoid function.

Additional Resources

The following tutorials explain how to perform other common operations in Python:

How to Perform Logistic Regression in Python
How to Plot a Logistic Regression Curve in Python

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