Evaluate a 3-D Laguerre series on the Cartesian product of x, y and z in Python

To evaluate a 3-D Laguerre series on the Cartesian product of x, y and z, use the polynomial.laguerre.laggrid3d() method in Python. The method returns the values of the three dimensional Laguerre series at points in the Cartesian product of x, y and z.

If c has fewer than three dimensions, ones are implicitly appended to its shape to make it 3-D. The shape of the result will be c.shape[3:] + x.shape + y.shape + z.shape. The 1st parameter,x, y, z are the three dimensional series is evaluated at the points in the Cartesian product of x, y, and z. If x,`y`, or z is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and, if it isn’t an ndarray, it is treated as a scalar.

The 2nd parameter, c is an array of coefficients ordered so that the coefficients for terms of degree i,j are contained in c[i,j]. If c has dimension greater than two the remaining indices enumerate multiple sets of coefficients.

Steps

At first, import the required library −

import numpy as np
from numpy.polynomial import laguerre as L

Create a 3D array of coefficients −

c = np.arange(16).reshape(2,2,4)

Display the array −

print("Our Array...\n",c)

Check the Dimensions −

print("\nDimensions of our Array...\n",c.ndim)

Get the Datatype −

print("\nDatatype of our Array object...\n",c.dtype)

Get the Shape −

print("\nShape of our Array object...\n",c.shape)

To evaluate a 3-D Laguerre series on the Cartesian product of x, y and z, use the polynomial.laguerre.laggrid3d() method in Python −

print("\nResult...\n",L.laggrid3d([1,2], [1,2],[1,2], c))

Example

import numpy as np
from numpy.polynomial import laguerre as L

# Create a 3D array of coefficients
c = np.arange(16).reshape(2,2,4)

# Display the array
print("Our Array...\n",c)

# Check the Dimensions
print("\nDimensions of our Array...\n",c.ndim)

# Get the Datatype
print("\nDatatype of our Array object...\n",c.dtype)

# Get the Shape
print("\nShape of our Array object...\n",c.shape)

# To evaluate a 3-D Laguerre series on the Cartesian product of x, y and z, use the polynomial.laguerre.laggrid3d() method in Python
print("\nResult...\n",L.laggrid3d([1,2], [1,2],[1,2], c))

Output

Our Array...
   [[[ 0 1 2 3]
   [ 4 5 6 7]]

   [[ 8 9 10 11]
   [12 13 14 15]]]

Dimensions of our Array...
3

Datatype of our Array object...
int64

Shape of our Array object...
(2, 2, 4)

Result...
   [[[-3. -4. ]
   [ 0.66666667 5.33333333]]

   [[ 1.33333333 10.66666667]
   [ 0. 0. ]]]