Evaluate a 2-D Chebyshev series on the Cartesian product of x and y with 1d array of coefficient in Python

To evaluate a 2-D Chebyshev series on the Cartesian product of x and y, use the polynomial.chebgrid2d(x, y, c) method in Python. The method returns the values of the two dimensional Chebyshev series at points in the Cartesian product of x and y. If c has fewer than two dimensions, ones are implicitly appended to its shape to make it 2-D. The shape of the result will be c.shape[2:] + x.shape + y.shape.

The parameter, x and y are the two dimensional series is evaluated at the points in the Cartesian product of x and y. 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 parameter, c is an array of coefficients ordered so that the coefficient of the term of multi-degree 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 libraries −

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

Create a 1d array of coefficients −

c = np.array([3, 5]) 

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 2-D Chebyshev series on the Cartesian product of x and y, use the polynomial.chebgrid2d(x, y, c) method −

print("\nResult...\n",C.chebgrid2d([1,2],[1,2], c))

Example

import numpy as np from numpy.polynomial import chebyshev as C # Create a 1d array of coefficients c = np.array([3, 5]) # 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 2-D Chebyshev series on the Cartesian product of x and y, use the polynomial.chebgrid2d(x, y, c) method in Python print("\nResult...\n",C.chebgrid2d([1,2],[1,2], c))

Output

Our Array... [3 5] Dimensions of our Array... 1 Datatype of our Array object... int64 Shape of our Array object... (2,) Result... [21. 34.]