Compute the Roots of a Hermite_e series with given Complex Roots using NumPy in Python

In this article, we are going to see how to compute the roots of a Hermite_e series with given complex roots in Python.

NumPy hermeroots() Methods

We use the hermite e.hermeroots() function in Python Numpy to get the roots of a Hermite e series. This function will return an array containing the series’ roots. If from all the roots present, all roots are real then the output is real as well else it will be complex.

A 1-D array of coefficients is used as the parameter c. The eigenvalues of the companion matrix are used to calculate the root estimations; nevertheless, roots far from the complex plane’s origin may have high inaccuracies due to the numerical instability of the series. Because the value of the series around such points is largely insensitive to mistakes in the roots, roots with multiplicity greater than 1 will display significant errors. A few repeats of Newton’s technique on isolated roots near the origin can help. Also, the outputs of the function may look contradictory since the HermiteE series basis polynomials are not powers of x.

Syntax : numpy.polynomial.hermite_e.hermeroots(arr)

Parameter : arr (1-D array_like structure)

Returns : ndarray

 (Array of the roots of the series.If from all the roots present, all roots are real then the output is real 

as well else it will be complex.

Example 1 :

Python3

# importing hermite_e library
from numpy.polynomial import hermite_e

# creating an array 'arr' of complex coefficient
a = complex(1,2)
b = complex(2,0)
arr = [a, b]

# Evaluating roots of a Hermite_e
# series using hermeroots() function
print(hermite_e.hermeroots(arr))

 Output :

[-0.5-1.j]

Example 2 :

Python3

# importing hermite_e library
from numpy.polynomial import hermite_e

# creating an array 'arr' of complex coefficient
a = complex(1,2)

# Evaluating roots of a Hermite_e
# series using hermeroots() function
print(hermite_e.hermeroots([a,-a]))

Output : 

[1.-0.j]