In this article, we will cover how to differentiate a Legendre series in Python using NumPy.
legendre.legder method
In python, the Legendre module provides many functions like legder to perform arithmetic, and calculus operations on the Legendre series. It is one of the functions provided by the Legendre class. This method is used to generate the Legendre 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 legder method.
Syntax: legendre.legder(x, m, axis)
Parameter:
- x: a list or tuple.
- m: Number of derivatives taken, must be non-negative. (Default: 1).
- axis: Axis over which the derivative is taken. (Default: 0).
Return: Legendre series
Example 1:
In this example, we are creating an array of 5 x 3 and, displaying the shape and dimensions of an array. Also, we are using legendre.legder() method to differentiate a Legendre series.
Python3
# import the numpy module import numpy # import legendre from numpy.polynomial import legendre # 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 legendre.legder() method to differentiate # a legendre series. print("\nDifferentiated legendre series", legendre.legder(coefficients_data)) |
Output:
[[ 1 2 3 4 5] [ 3 4 2 6 7] [43 45 2 6 7]] Shape of an array: (3, 5) Dimension: 2 Differentiated legendre series [[ 3. 4. 2. 6. 7.] [129. 135. 6. 18. 21.]]
Example 2:
In this example, we are creating an array of 5 x 2 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 legendre from numpy.polynomial import legendre # create array of coefficients with 5 elements each coefficients_data = numpy.array([[1, 2, 3, 4, 5], [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 legendre.legder() method to differentiate # a legendre series. print("\nDifferentiated legendre series", legendre.legder(coefficients_data, m=2, axis=1)) |
Output:
[[ 1 2 3 4 5] [43 45 2 6 7]] Shape of an array: (2, 5) Dimension: 2 Differentiated legendre series [[ 59. 60. 175.] [ 76. 90. 245.]]
