Differentiate a Hermite series with multidimensional coefficients in Python
Last Updated :
22 Apr, 2022
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 numpy
from numpy.polynomial import hermite
coefficients_data = numpy.array([[ 1 , 2 , 3 , 4 , 5 ],
[ 3 , 4 , 2 , 6 , 7 ]])
print (coefficients_data)
print (f "\nShape of an array: {coefficients_data.shape}" )
print (f "Dimension: {coefficients_data.ndim}" )
print ( "\nHermite series" , hermite.hermder(coefficients_data))
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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 numpy
from numpy.polynomial import hermite
coefficients_data = numpy.array(
[[ 1 , 2 , 3 , 4 , 5 ], [ 3 , 4 , 2 , 6 , 7 ], [ 43 , 45 , 2 , 6 , 7 ]])
print (coefficients_data)
print (f "\nShape of an array: {coefficients_data.shape}" )
print (f "Dimension: {coefficients_data.ndim}" )
print ( "\nHermite series" , hermite.hermder(coefficients_data, m = 2 , axis = 1 ))
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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.]]
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