In this article, we learn how to calculate the Heaviside step function using numpy.heaviside()
, a NumPy package function in python. We will get a stronger hold of this topic by implementing a few examples and understanding its syntax.
What is numpy.heaviside()?
numpy.heaviside()
is a mathematical function of the NumPy package in python. This function is utilized to calculate the Heaviside step function of an input array.
Mathematical representation and rules
We define the mathematical representation and rules to implement numpy.heaviside()
below :
- H(x1,x2) = 0 , if x1 < 0
- H(x1,x2) = x2 , if x1 = 0
- H(x1,x2) = 1 , if x1 > 0
Note :
– H is a notation used to represent the Heaviside function other notations like θ, and u are also used.
– The value of x2 is often assumed as 0.5 but 1 or 0 are also sometimes used.
Syntax of numpy.heaviside()
numpy.heaviside(x1, x2, /, out=None, *, where=True)
Parameters
Parameter | Description | Required/Optional |
x1 | The input array. | Required |
x2 | The input value/array of the function when the value of x1 is 0. If x1.shape != x2.shape , they must be broadcastable to a common shape | Required |
out | The location where the output is expected to be stored. | Optional |
where | The resulting array will be set to ufunc if the condition is set to True otherwise, it will retain its original value. | Optional |
**kwargs | Other keyword parameters. | Optional |
Return value
An array consisting of element-wise Heaviside step function of x1.
Examples of using Heaviside
Importing NumPy and displaying the input array.
import numpy as np
arr=np.array([-1.5,0,2,0.5,10.5,-20])
print("The input array : \n",arr)
Example 1: Basic usage of np.heaviside()
output=np.heaviside(arr,0.5)
print("The output array : \n",output)
arr[0] : -1.5 < 0 thus output[0]= 0
arr[1] : 0 = 0 thus output[1]=0.5
arr[2] : 2 > 0 thus output[2]=1
and so on
The input array :
[ -1.5 0. 2. 0.5 10.5 -20. ]
The output array :
[0. 0.5 1. 1. 1. 0. ]
Example 2: Assigning x2 = 1
x2 = np.zeros(4)
print("The output array : \n",np.heaviside([1.5,0.9,-4.5,1], x2))
Output
The output array :
[1. 1. 0. 1.]
Conclusion
We have implemented and understood the syntax and working of numpy.heaviside()
under various parameter values.
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Reference
https://numpy.org/doc/stable/reference/generated/numpy.heaviside.html