In this article, we will cover how to evaluate a Hermite series at points x with a multidimensional coefficient array in Python using NumPy.
Example
Input: [[11 12][13 14]] Output: [[37. 63.][40. 68.]] Explanation: Hermite series at points x.
NumPy.polynomial.hermite.hermval method
To evaluate a Hermite series at points x with a multidimensional coefficient array, NumPy provides a function called hermite.hermval(). It takes two parameters x and c. whereas x is a tuple or list. It is considered a scalar. But, the parameter x should support multiplication and addition within itself and with the elements of c. If c is a 1-D array, then it will have the same shape as x. If c is multidimensional, then the shape of the result depends on the value of the tensor.
Syntax: polynomial.hermite.hermval(x,c, tensor)
Parameter:
- x: array_like
- c: Array of coefficient
- tensor: boolean(optional).
Return: An Hermite series at points x.
Example 1:
In the first example, let us consider a 2D array and evaluate a Hermite series at point x. Import the necessary packages and pass the appropriate parameters as shown.
Python3
import numpy as npfrom numpy.polynomial import hermiteÂ
# coefficient arrayc = np.array([[11, 12], [13, 14]])Â
print(f'The coefficient array is {c}')print(f'The shape of the array is {c.shape}')print(f'The dimension of the array is {c.ndim}D')print(f'The datatype of the array is {c.dtype}')Â
# evaluating multidimensal array of hermiteseriesres = hermite.hermval([1, 2], c)Â
# resultant arrayprint(f'Resultant series ---> {res}') |
Output:
The coefficient array is [[11 12] [13 14]] The shape of the array is (2, 2) The dimension of the array is 2D The datatype of the array is int32 Resultant series ---> [[37. 63.] [40. 68.]]
Example 2:
In the second example, let us consider a 3D array and evaluate a Hermite series at point x. Import the necessary packages and pass the appropriate parameters as shown
Python3
import numpy as npfrom numpy.polynomial import hermiteÂ
# coefficient arrayc = np.arange(27).reshape(3, 3, 3)Â
print(f'The coefficient array is {c}')print(f'The shape of the array is {c.shape}')print(f'The dimension of the array is {c.ndim}D')print(f'The datatype of the array is {c.dtype}')Â
# evaluating multidimensal array of hermiteseriesres = hermite.hermval([17, 22], c)Â
# resultant arrayprint(f'Resultant series ---> {res}') |
Output:
The coefficient array is [[[ 0 1 2] [ 3 4 5] [ 6 7 8]] [[ 9 10 11] [12 13 14] [15 16 17]] [[18 19 20] [21 22 23] [24 25 26]]] The shape of the array is (3, 3, 3) The dimension of the array is 3D The datatype of the array is int32 Resultant series ---> [[[21078. 35208.] [22267. 37187.] [23456. 39166.]] [[24645. 41145.] [25834. 43124.] [27023. 45103.]] [[28212. 47082.] [29401. 49061.] [30590. 51040.]]]
