Add one Hermite series to another using NumPy in Python

In this article, we will cover how to add one Hermite series to another using NumPy in Python.

np.polynomial.hermite.hermadd method

The numpy.polynomial.hermite.hermadd() method from the NumPy library is used to add one Hermite series to another. The sum of two Hermite series (c1 + c2) is returned. The arguments are sequences of coefficients in ascending order from the lowest to the highest order term, for example, [4,3,1] denotes the series 4*P 0 + 3*P 1 + 1*P 2.

Syntax: polynomial.hermite.hermadd(c1, c2)

Parameters:

• c1,c2: array like objects: Hermite series coefficients are arranged from low to high in a 1-D array.

Return: array representing the Hermite series of their sum.

Example 1:

Here, the packages are imported and NumPy arrays of coefficients are created .numpy.polynomial.hermite_e.hermadd() is used to add one Hermite series to another. The shape of the array of coefficients is found by the .shape attribute, the dimension of the array is found by the .ndim attribute, and the data type of the array is .dtype attribute. The method takes arrays of coefficients as input and gives out the sum of the Hermite series as output.

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

# array1 coefficients
array1 = np.array([1,2,3,4,5])
print(array1)

# array2 coefficients
array2 = np.array([6,7,8,9,10])
print(array2)

# shape of the arrays are
print("Shape of array1 is: ", array1.shape)
print("Shape of array1 is: ", array2.shape)

# dimensions of the array
print("The dimension of array1 is: ", array1.ndim)
print("The dimension of array2 is: ", array2.ndim)

# adding two hermite series
print('addition of the two hermite series : ')
print(H.hermeadd(array1,array2))

Output:

[1 2 3 4 5]
[ 6  7  8  9 10]
Shape of array1 is:  (5,)
Shape of array1 is:  (5,)
The dimension of array1 is:  1
The dimension of array2 is:  1
addition of the two hermite series : 
[ 7.  9. 11. 13. 15.]

Example 2:

In the example, we give arrays of different shapes as input, the addition of two Hermite series doesn't need the shapes of arrays of coefficients to be similar.

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

# array1 coefficients
array1 = np.array([1,2,3,4,5])
print(array1)

# array2 coefficients
array2 = np.array([6,7,8,9])
print(array2)

# shape of the arrays are
print("Shape of array1 is: ", array1.shape)
print("Shape of array1 is: ", array2.shape)

# dimensions of the array
print("The dimension of array1 is: ", array1.ndim)
print("The dimension of array2 is: ", array2.ndim)

# adding two hermite series
print('addition of the two hermite series : ')
print(H.hermeadd(array1,array2))

Output:

[1 2 3 4 5]
[6 7 8 9]
Shape of array1 is:  (5,)
Shape of array1 is:  (4,)
The dimension of array1 is:  1
The dimension of array2 is:  1
addition of the two hermite series : 
[ 7.  9. 11. 13.  5.]