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 2d array of coefficients −
c = np.arange(4).reshape(2,2)
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 2d array of coefficients c = np.arange(4).reshape(2,2) # 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]] Dimensions of our Array... 2 Datatype of our Array object... int64 Shape of our Array object... (2, 2) Result... [[17. 28.] [28. 46.]]