Evaluate Hermite_e series at array of points x in Python

In this article, we will be looking at the approach to evaluate a Hermite_e series at an array of points x in Python.

We are using the hermite.hermeval() function in Python Numpy to evaluate a Hermite e series at point x. The first parameter, x, is transformed to an array if it is a list or tuple; otherwise, it is kept unmodified and handled as a scalar. In any scenario, x or its elements must be able to add and multiply with itself as well as with the elements of c. The second parameter ‘C’ is a coefficient array that is sorted in such a way that the coefficients for the terms of degree n are all stored in ‘c[n]’. The remaining indices enumerate distinct polynomials if c is multidimensional. The coefficients in the two-dimensional situation can be thought of as being stored in the columns of c.

Syntax : np.hermeval(x, series)
Return : Return the evaluated hermite series.

Steps to evaluate the Hermite_e series :

Step 1: Import Numpy and hermite_e libraries :

import numpy as np
from numpy.polynomial import hermite_e as H

Step 2: Use the hermite.hermeval() function in Python Numpy to evaluate a Hermite_e series at point x as shown below :

x = np.array([[1,2],[3,4]])
print("Result : ",H.hermeval(x,c))

Example 1 : 

In this example, we are creating a coefficient array of 3 data points and a 2-d array assigned to x and further, we are evaluating a Hermite_e series at points x, using the hermite.hermeval() method in Python.

Python3

# importing necessary libraries
import numpy as np
from numpy.polynomial import hermite_e as H

# Create an array of coefficients
c = np.array([3, 5, 7])

# To evaluate a Hermite_e series at points x,
# use the hermite.hermeval() method in Python Numpy
x = np.array([[2, 3], [5, 6]])
print("Result : \n", H.hermeval(x, c))

Output : 

Result : 
[[ 34.  74.]
 [196. 278.]]

Example 2 : 

In this example, an array of coefficients is made of 3 points and are evaluating a Hermite_e series at point 1, with the x assigned using the hermite.hermeval() method in Python.

Python3

from numpy.polynomial import hermite_e as H

coef = [3, 5, 7]
print("Result 1 : \n",H.hermeval(1, coef))

x = [[2, 3], [5, 6]]
print("Result 2 : \n",H.hermeval(x, coef))

Output :

Result 1 : 
 8.0
Result 2 : 
[[ 34.  74.]
 [196. 278.]]