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

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To evaluate a 3D Legendre series on the Cartesian product of x, y and z use the polynomial.legendre.leggrid3d() method in Python Numpy. The method returns the values of the three dimensional Chebyshev series at points in the Cartesian product of x, 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 is x, y, z. The three dimensional series is evaluated at the points in the Cartesian product of x,y and z. If x or y 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 is c. Array of coefficients ordered so that the coefficient of the term of multidegree i,j is 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 legendre 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 3D Legendre series on the Cartesian product of x, y and z use the polynomial.legendre.leggrid3d() method in Python −

print("\nResult...\n",L.leggrid3d([1,2],[1,2],[1,2],c))

Example

import numpy as np
from numpy.polynomial import legendre 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 3D Legendre series on the Cartesian product of x, y and z use the polynomial.legendre.leggrid3d() method in Python Numpy
print("\nResult...\n",L.leggrid3d([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...
   [[[ 120. 868.]
   [ 196. 1404.]]

   [[ 212. 1506.]
   [ 342. 2412.]]]
raja
Updated on 07-Mar-2022 07:11:23

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