In this article, we will discuss how to integrate a Chebyshev Series and set the integration constant
To perform Chebyshev integration, NumPy provides a function called chebyshev.chebint which can be used to integrate Chebyshev series.
Syntax: chebyshev.chebint(c, m=1, k=[], lbnd=0, scl=1, axis=0)
Parameters:
- c – Array of Chebyshev series coefficients.
- m – (integer) Order of integration, must be positive
- k – Integration constant. The value of the first integral at zero is the first value in the list, the value of the second integral at zero is the second value, etc
- lbnd – The lower bound of the integral. (Default: 0)
- scl – Following each integration the result is multiplied by scl before the integration constant is added. (Default: 1)
- axis – Axis over which the integral is taken.
Example 1:
In the first example. let us consider a 1D array with a first-order integration and 3 as an integration constant. Import the necessary packages as shown and pass the appropriate parameters as shown below.
Python3
import numpy as np from numpy.polynomial import chebyshev # co.efficient array c = np.array([11, 12, 13, 14, 15]) 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}') res = chebyshev.chebint(c, m=1, k=3) # integrated chebyshev series # with integration constant of 1 print(f'Resultant series ---> {res}') |
Output:
Example 2:
In the second example. let us consider a 2D array with a first-order integration and 5 as an integration constant. Import the necessary packages as shown and pass the appropriate parameters as shown below.
Python3
import numpy as np from numpy.polynomial import chebyshev # co.efficient array c = np.array([[11, 12, 13, 14, 15], [3, 4, 5, 6, 7]]) 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}') res = chebyshev.chebint(c, m=1, k=5) # integrated chebyshev series # with integration constant of 5 print(f'Resultant series ---> {res}') |
Output:
Example 3:
In the third example. let us consider a 3D array with a fifth-order integration and 7 as an integration constant. Import the necessary packages as shown and pass the appropriate parameters as shown below.
Python3
import numpy as np from numpy.polynomial import chebyshev # co.efficient array c = np.array([[[11, 12, 13, 14, 15], [3, 4, 5, 6, 7], [21, 22, 23, 24, 25]]]) 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}') res = chebyshev.chebint(c, m=5, k=7) # integrated chebyshev series # with integration constant of 7 print(f'Resultant series ---> {res}') |
Output:
