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

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]