In this article, we will cover how to differentiate a Hermite series with multidimensional coefficients in Python using NumPy.
Example
Input: [[ 1 2 3 4 5]
[ 3 4 2 6 7]
[43 45 2 6 7]]
Output: [[ 3. 4. 2. 6. 7.]
[129. 135. 6. 18. 21.]]
Explanation: Hermite series of the derivative.
hermite.hermder method
To evaluate a Hermite series at points x with a multidimensional coefficient array, NumPy provides a function called hermite.hermder(). This method is used to generate the Hermite 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 Hermite method.
Syntax: hermite.hermder(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: Hermite 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 hermite.hermder() method to differentiate a hermite series.
Python3
# import the numpy module import numpy # import hermite from numpy.polynomial import hermite # 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 hermite.hermder() method to differentiate # a Hermite series. print("\nHermite series", hermite.hermder(coefficients_data)) |
Output:
[[1 2 3 4 5] [3 4 2 6 7]] Shape of an array: (2, 5) Dimension: 2 Hermite series [[ 6. 8. 4. 12. 14.]]
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 hermite from numpy.polynomial import hermite # 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 hermite.hermder() method to differentiate a Hermite series. print("\nHermite series", hermite.hermder(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 Hermite series [[ 24. 96. 240.] [ 16. 144. 336.] [ 16. 144. 336.]]
