Python Program to Integrate a Chebyshev Series and Set the Integration Constant
Last Updated :
21 Apr, 2022
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
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 )
print (f 'Resultant series ---> {res}' )
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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
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 )
print (f 'Resultant series ---> {res}' )
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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
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 )
print (f 'Resultant series ---> {res}' )
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Output:
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