Evaluate a 2-D Hermite series at points (x,y) in using NumPy Python

In this article, we will Evaluate a 2D Hermite series at points (x,y) in Numpy using python.

hermite.hermval2d method

In Python, To evaluate a Hermite series at points x with a multidimensional coefficient array, NumPy provides a function called hermite.hermval(), But to evaluate  2D Hermite series, hermite.hermval2d() is used to evaluate a 2D Hermite series at points (x,y). where coefficient_array is the input NumPy array with coefficients and points referred to as x and y. The first parameter can be a list of points. So we have to provide two lists such that each list has an x-point and y-point. The second parameter is a NumPy array of coefficients ordered.

Syntax: hermite.hermval2d(x,y,c)

Parameters:

• x,y: array_like, compatible objects
• c: Array of coefficients.

Return: The values of the two dimensional polynomial at points.

Example 1:

In this example, we are creating a NumPy array with 5 coefficients to evaluate Hermite Series at points [3,4],[1,2]. By using ndim, we are getting a total number of dimensions, and using shape, we are returning the shape of an array.

Python3

# import numpy module
import numpy

# import hermite
from numpy.polynomial import hermite

# Create 1d array of 5 elements
coefficient_array = numpy.array([45, 67, 54, 53, 15])

# Display
print(coefficient_array)

# display the Dimensions
print(coefficient_array.ndim)

# display Shape
print(coefficient_array.shape)

# Evaluate a 2D hermite series at points
# (x,y) - [3,4],[1,2]
print(hermite.hermval2d([3, 4], [1, 2], coefficient_array))

Output:

[45 67 54 53 15]
1
(5,)
[182205. 339447.]

Example 2:

In this example, we are creating a NumPy array with 6 coefficients and evaluating Hermite Series at points [1,4],[1,2]. By using ndim, we are getting a total number of dimensions, and using shape, we are returning the shape of an array.

Python3

# import numpy module
import numpy

# import hermite
from numpy.polynomial import hermite

# Create 1d array of 6 elements
coefficient_array = numpy.array([45, 67, 54, 53, 67, 15])

# Display
print(coefficient_array)

# display the Dimensions
print(coefficient_array.ndim)

# display Shape
print(coefficient_array.shape)

# Evaluate a 2D hermite series at points
# (x,y) - [1,4],[1,2]
print(hermite.hermval2d([1, 4], [1, 2], coefficient_array))

Output:

[45 67 54 53 67 15]
1
(6,)
[1193457. 2388299.]

Example 3:

In this example, we are creating a 2 D NumPy array with 3 coefficients each and evaluating Hermite Series at points [1,4],[1,2]. By using ndim, we are getting a total number of dimensions, and using shape, we are returning the shape of an array.

Python3

# import numpy module
import numpy

# import hermite
from numpy.polynomial import hermite

# Create 2d array of 3 elements each
coefficient_array = numpy.array([[45, 67, 54],
                                 [53, 67, 15]])

# Display
print(coefficient_array)

# display the Dimensions
print(coefficient_array.ndim)

# display Shape
print(coefficient_array.shape)

# Evaluate a 2D hermite series at points
# (x,y) - [1,4],[1,2]
print(hermite.hermval2d([1, 4], [1, 2], coefficient_array))

Output:

[[45 67 54]
 [53 67 15]]
2
(2, 3)
[ 721. 5317.]