Differentiate a Chebyshev series with multidimensional coefficients in Python
In this article, we will cover how to differentiate the Chebyshev series with multidimensional coefficients in Python using NumPy.
Example
Input: [[1 2 3 4 5]
[3 4 2 6 7]]
Output: [[3. 4. 2. 6. 7.]]
Explanation: Chebyshev series of the derivative.
chebyshev.chebder method
To evaluate a Chebyshev series at points x with a multidimensional coefficient array, NumPy provides a function called chebyshev.chebder(). This method is used to generate the Chebyshev series and this method is available in the NumPy module in python, it returns a multi-dimensional coefficient array, Below is the syntax of the Chebyshev method.
Syntax: chebyshev.chebder(x, m, axis)
Parameter:
- x: array
- m: Number of derivatives taken, must be non-negative. (Default: 1)
- axis: Axis over which the derivative is taken. (Default: 1).
Return: Chebyshev series.
Example 1:
In this example, we are creating a coefficient multi-dimensional array of 5 x 2 and, displaying the shape and dimensions of an array. Also, we are using chebyshev.chebder() method to differentiate a Chebyshev series.
Python3
# import the numpy module import numpy # import chebyshev from numpy.polynomial import chebyshev # create array of coefficients with 5 elements each coefficients_data = numpy.array([[ 1 , 2 , 3 , 4 , 5 ], [ 3 , 4 , 2 , 6 , 7 ]]) # Display the coefficients print (coefficients_data) # get the shape print (f "\nShape of an array: {coefficients_data.shape}" ) # get the dimensions print (f "Dimension: {coefficients_data.ndim}" ) # using chebyshev.chebder() method to differentiate # a chebyshev series. print ( "\nChebyshev series" , chebyshev.chebder(coefficients_data)) |
Output:
[[1 2 3 4 5] [3 4 2 6 7]] Shape of an array: (2, 5) Dimension: 2 Chebyshev series [[3. 4. 2. 6. 7.]]
Example 2:
In this example, we are creating a coefficient multi-dimensional array of 5 x 3 and, displaying the shape and dimensions of an array. Also, we are using the number of derivatives=2, and the axis over which the derivative is taken is 1.
Python3
# import the numpy module import numpy # import chebyshev from numpy.polynomial import chebyshev # create array of coefficients with 5 elements each coefficients_data = numpy.array( [[ 1 , 2 , 3 , 4 , 5 ], [ 3 , 4 , 2 , 6 , 7 ], [ 43 , 45 , 2 , 6 , 7 ]]) # Display the coefficients print (coefficients_data) # get the shape print (f "\nShape of an array: {coefficients_data.shape}" ) # get the dimensions print (f "Dimension: {coefficients_data.ndim}" ) # using chebyshev.chebder() method to differentiate a # chebyshev series. print ( "\nChebyshev series" , chebyshev.chebder(coefficients_data, m = 2 , axis = 1 )) |
Output:
[[ 1 2 3 4 5] [ 3 4 2 6 7] [43 45 2 6 7]] Shape of an array: (3, 5) Dimension: 2 Chebyshev series [[172. 96. 240.] [232. 144. 336.] [232. 144. 336.]]
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