Evaluate a 3-D Chebyshev series on the Cartesian product of x, y and z with 2d array of coefficient in Python

To evaluate a 3-D Chebyshev series on the Cartesian product of x, y, z, use the polynomial.chebgrid3d(x, y, z) method in Python. 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 parameter, x, y and 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 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 libraries −

import numpy as np from numpy.polynomial import chebyshev as C

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 3-D Chebyshev series on the Cartesian product of x, y, z, use the polynomial.chebgrid3d(x, y, z) method −

print("\nResult...\n",C.chebgrid3d([1,2],[1,2], [1,2], c))

Example

import numpy as np from numpy.polynomial import chebyshev as C # 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 3-D Chebyshev series on the Cartesian product of x, y, z, use the polynomial.chebgrid3d(x, y, z) method in Python print("\nResult...\n",C.chebgrid3d([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.]]