Python Program to Evaluate a Chebyshev Series at Points X When Coefficients are multi-dimensional

In this article, we will discuss how to evaluate a Chebyshev Series at points X when coefficients are multi-dimensional.

To evaluate the Chebyshev series at points, NumPy provides a function called chebyshev.chebval which can be used to integrate the Chebyshev series. 

Syntax: Chebyshev.chebval(x, c, tensor)

Parameters:

• x – array_like, compatible object. If x is a list or tuple, it is converted to an array, otherwise, it is left unchanged and treated as a scalar. In either case, x or its elements must support addition and multiplication with themselves and with the elements of c.
• c – array_like. An array of coefficients is ordered so that the coefficients for terms of degree n are contained in c[n]. If c is multidimensional the remaining indices enumerate multiple polynomials. In the two-dimensional case, the coefficients may be thought of as stored in the columns of c.
• tensor – boolean. If True, the shape of the coefficient array is extended with ones on the right, one for each dimension of x.

Example 1:

In the first example. let us consider a 2D array and evaluate it in the point [1,2]. Import the necessary packages as shown and pass the appropriate parameters as shown below.

Python3

import numpy as np
from numpy.polynomial import chebyshev

# multidimensional array of coefficients
c = np.arange(9).reshape(3, 3)

print(f'The shape of the array is {c.shape}')
print(f'The dimension of the array is {c.ndim}D')
print(f'The datatype of the array is {c.dtype}')

# pass the points to evaluate at x to the
# chebval function
res = chebyshev.chebval([1, 2], c, tensor=True)

# chebyshev series evaluated at point [1,2]
print(f'Resultant series ---> {res}')

Output:

Example 2:

In the first example. let us consider a 3D array and evaluate it in the point [11,12]. Import the necessary packages as shown and pass the appropriate parameters as shown below.

Python3

import numpy as np
from numpy.polynomial import chebyshev

# multidimensional array of coefficients
c = np.arange(9).reshape(3, 3, 1)

print(f'The shape of the array is {c.shape}')
print(f'The dimension of the array is {c.ndim}D')
print(f'The datatype of the array is {c.dtype}')

# pass the points to evaluate at x to the chebval function
res = chebyshev.chebval([11, 12], c, tensor=True)

# chebyshev series evaluated at point [1,2]
print(f'Resultant series ---> {res}')

Output:

Output

Example 3:

In the third example. let us consider a different 3D array of shape (3,3,3) and evaluate it in the point [33,56]. Import the necessary packages as shown and pass the appropriate parameters as shown below.

Python3

import numpy as np
from numpy.polynomial import chebyshev

# multidimensional array of coefficients
c = np.arange(27).reshape(3, 3, 3)

print(f'The shape of the array is {c.shape}')
print(f'The dimension of the array is {c.ndim}D')
print(f'The datatype of the array is {c.dtype}')

# pass the points to evaluate at x to the chebval function
res = chebyshev.chebval([33, 56], c, tensor=True)

# chebyshev series evaluated at point [33,56]
print(f'Resultant series ---> {res}')

Output: