Evaluate a Hermite_e series at points x broadcast over the columns of the coefficient in Python

In this article, we will cover how to evaluate a Hermite_e series at points x broadcast over the columns of the coefficient in Python using NumPy.

Example

Input: [1 2 3 4 5]
Output: [  -3. 1077.]
Explanation: Hermite_e series at input points.

hermite_e.hermeval method

To evaluate a Hermite_e series at points x with a multidimensional coefficient array, NumPy provides a function called hermite_e.hermeval(). It takes two parameters x and c. whereas x is a tuple or list and c is an array of coefficients and, it returns a Hermite_e series at the given input points. i.e – If an array has an element like [1,2,3,4,5], then the Hermite_e series will be 1*P_0 + 2*P_1 + 3*P_2 + 4*P_3 + 5*P_4. Below is the syntax of the hermeval method.

Syntax: hermite_e.hermeval(x, c, tensor)

Parameter:

• x: a list or tuple
• c: an array of coefficients ordered
• tensor: boolean, optional

Return: Hermite_e series at points x

Example 1:

In this example, we are creating a coefficient NumPy array with 5 elements and displaying the shape and dimensions.  After that, we  are evaluating the Hermite_e series at points – [2,4]

Python3

# import the numpy module
import numpy

# import hermite_se
from numpy.polynomial import hermite_e

# create array of coefficients with 5 elements
coefficients_data = numpy.array([1, 2, 3, 4, 5])

# Display the coefficients
print(coefficients_data)

# get the shape
print(f"\nShape of an array: {coefficients_data.shape}")

# get the dimensions
print(f"Dimension: {coefficients_data.ndim}")

# Evaluate a Hermite_e series at points - [2,4]
print("\nHermite_e series", hermite_e.hermeval(
    [2, 4], coefficients_data, tensor=False))

Output:

[1 2 3 4 5]

Shape of an array: (5,)
Dimension: 1

Hermite_e series [  -3. 1077.]

Example 2:

In this example, we are creating a coefficient NumPy array with 5 elements and displaying the shape and dimensions .  After that, we  are evaluating the Hermite_e series at points – [4,1]

Python3

# import the numpy module
import numpy

# import hermite_se
from numpy.polynomial import hermite_e

# create array of coefficients with 5 elements
coefficients_data = numpy.array([1, 2, 3, 4, 5])

# Display the coefficients
print(coefficients_data)

# get the shape
print(f"\nShape of an array: {coefficients_data.shape}")

# get the dimensions
print(f"Dimension: {coefficients_data.ndim}")

# Evaluate a Hermite_e series at points - [4,1]
print("\nHermite_e series", hermite_e.hermeval(
    [4, 1], coefficients_data, tensor=False))

Output:

[1 2 3 4 5]

Shape of an array: (5,)
Dimension: 1

Hermite_e series [1077.  -15.]