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 npfrom numpy.polynomial import chebyshev# multidimensional array of coefficientsc = 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 functionres = 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 npfrom numpy.polynomial import chebyshev# multidimensional array of coefficientsc = 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 functionres = 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 npfrom numpy.polynomial import chebyshev# multidimensional array of coefficientsc = 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 functionres = chebyshev.chebval([33, 56], c, tensor=True)# chebyshev series evaluated at point [33,56]print(f'Resultant series ---> {res}') |
Output:
