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

Last Updated : 21 Apr, 2022

In this article, we will be looking toward the approach to evaluating a Hermite series at points x broadcast over the columns of the coefficient in Python and NumPy.

Example:

Array: [1,2,3,4,5],[6,7,8,9,10]]

Result: [ 73. 100. 131. 166. 205.]

Explanation: Hermite series at points x broadcast over the columns

Numpy np.hermeval() method

To evaluate a Hermite series at a tuple of points x broadcast over the columns of the coefficient, the user needs to call the hermite.hermval() method of the Numpy library in Python. Further, the user needs to pass the first parameter to the function which is the x, where x is a list or tuple, the 2nd parameter is C, which is an array of coefficients, and the 3rd parameter tensor, if True, the shape of the coefficient array is extended with ones on the right, one for each dimension of x.

Syntax : np.hermeval(x, series,tensor)

Parameter:

x: list or tuple

series: array of coefficient

tensor, if True, the shape of the coefficient array is extended with ones on the right, one for each dimension of x. Scalars have dimension 0 for this action.

Return : Return the evaluated hermite series.

Example:

In this example, we created a 2-D array of 10 data points and further created a tuple name x., then with the use of the hermite.hermeval() method we pass the required parameters with tensor set to false to evaluate the Hermite series at points x broadcast over the columns in Python.

Python3

import numpy as np 
from numpy.polynomial import hermite 
  
a = np.array([[1, 2, 3, 4, 5], [6, 7, 8, 9, 10]]) 
  
# Dimensions of Array 
print("\nDimensions of Array:\n", a.ndim) 
  
# Shape of the array 
print("\nShape of Array:\n", a.shape) 
  
# Tuple 
x = [6, 7, 8, 9, 10] 
  
# To evaluate a Hermite series at  
# points x broadcast over the columns 
hermite.hermval(x, a, tensor=False) 

Output:

Dimensions of Array:
 2

Shape of Array:
 (2, 5)

array([ 73., 100., 131., 166., 205.])

Example:

In this example, we created a 2-D array of 10 data points and further created a tuple name x., then with the use of the hermite.hermeval() method we pass the required parameters with tensor set to true to evaluate the Hermite series at points x broadcast over the columns in Python.

Python3

import numpy as np 
from numpy.polynomial import hermite  
  
a = np.array([[1,2,3,4,5],[6,7,8,9,10]]) 
  
# Dimensions of Array 
print("\nDimensions of Array:\n",a.ndim) 
  
# Shape of the array 
print("\nShape of Array:\n",a.shape) 
  
# Tuple 
x = [6,7,8,9,10] 
  
# To evaluate a Hermite series at 
# points x broadcast over the columns 
hermite.hermval(x,a,tensor=True)

Output:

Dimensions of Array:
 2

Shape of Array:
 (2, 5)

array([[ 73.,  85.,  97., 109., 121.],
       [ 86., 100., 114., 128., 142.],
       [ 99., 115., 131., 147., 163.],
       [112., 130., 148., 166., 184.],
       [125., 145., 165., 185., 205.]])