In this article, we will discuss how to evaluate a 2D Laguerre series at points (x,y) using NumPy in Python.
Example
Input: [[[ 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]]] Output: [[[1920. 522.] [ 414. 108.]] [[2020. 552.] [ 444. 117.]] [[2120. 582.] [ 474. 126.]]] Explanation: Two dimensional Laguerre series.
NumPy.polynomial.laguerre.lagval2d method
To perform Laguerre differentiation, NumPy provides a function called laguerre.lagval2d which can be used to evaluate the cartesian product of the 2D Laguerre series. This function converts the parameters x and y to arrays only if they are tuples or a list and of the same shape, otherwise, it is left unchanged and, if it is not an array, it is treated as a scalar. If c has a dimension greater than 2 the remaining indices enumerate multiple sets of coefficients.
Syntax: laguerre.lagval2d(x,y, c)
Parameters:
- x,y: Input array.
- c: Array of coefficients ordered
Returns: Two dimensional Laguerre series at points in the Cartesian product of x and y.
Example 1:
In the first example. let us consider a 3D array c of size 27 and a series of [2,2],[2,2] to evaluate against the 2D array.
Python3
import numpy as np from numpy.polynomial import laguerre # co.efficient array c = np.arange(27).reshape(3, 3, 3) print(f'The co.efficient 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}') # evaluating coeff array with a laguerre series res = laguerre.lagval2d([2, 2], [2, 2], c) # resultant array print(f'Resultant series ---> {res}') |
Output:
The co.efficient 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 int64 Resultant series ---> [[36. 36.] [37. 37.] [38. 38.]]
Example 2:
In the second example. let us consider a 2D array c of size 10 and a series of [2,2],[2,2] to evaluate against the 2D array.
Python3
import numpy as np from numpy.polynomial import laguerre # co.efficient array c = np.array([[1,2,3,4,5],[45,56,65,55,55]]) print(f'The co.efficient 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}') # evaluating coeff array with a laguerre series res = laguerre.lagval2d([2, 2], [2, 2], c) # resultant array print(f'Resultant series ---> {res}') |
Output:
The co.efficient array is [[ 1 2 3 4 5] [45 56 65 55 55]] The shape of the array is (2, 5) The dimension of the array is 2D The datatype of the array is int64 Resultant series ---> [72.33333333 72.33333333]
