Differentiate a Hermite series in Python

To differentiate a Hermite series, use the hermite.hermder() method in Python. This function computes the derivative of a Hermite series represented by its coefficients.

Syntax

numpy.polynomial.hermite.hermder(c, m=1, scl=1, axis=0)

Parameters

The hermder() method accepts the following parameters ?

• c ? Array of Hermite series coefficients. If multidimensional, different axes correspond to different variables.
• m ? Number of derivatives taken, must be non-negative (Default: 1).
• scl ? Scalar multiplier for each differentiation. Final result is multiplied by scl**m (Default: 1).
• axis ? Axis over which the derivative is taken (Default: 0).

Basic Example

Let's differentiate a simple Hermite series ?

import numpy as np
from numpy.polynomial import hermite as H

# Create an array of coefficients
c = np.array([1, 2, 3, 4])

# Display the array
print("Our Array...")
print(c)

# Check the dimensions and properties
print("\nDimensions of our Array...")
print(c.ndim)

print("\nDatatype of our Array object...")
print(c.dtype)

print("\nShape of our Array object...")
print(c.shape)

# Differentiate the Hermite series
print("\nFirst derivative...")
print(H.hermder(c))

Our Array...
[1 2 3 4]

Dimensions of our Array...
1

Datatype of our Array object...
int64

Shape of our Array object...
(4,)

First derivative...
[ 4. 12. 24.]

Multiple Derivatives

You can compute higher-order derivatives by specifying the m parameter ?

import numpy as np
from numpy.polynomial import hermite as H

c = np.array([1, 2, 3, 4, 5])

print("Original coefficients:")
print(c)

print("\nFirst derivative (m=1):")
print(H.hermder(c, m=1))

print("\nSecond derivative (m=2):")
print(H.hermder(c, m=2))

print("\nThird derivative (m=3):")
print(H.hermder(c, m=3))

Original coefficients:
[1 2 3 4 5]

First derivative (m=1):
[ 4.  12.  24.  40.]

Second derivative (m=2):
[ 24.  96. 240.]

Third derivative (m=3):
[192. 960.]

Using Scale Factor

The scl parameter allows you to scale the derivative ?

import numpy as np
from numpy.polynomial import hermite as H

c = np.array([1, 2, 3, 4])

print("Original derivative:")
print(H.hermder(c))

print("\nDerivative with scale factor 2:")
print(H.hermder(c, scl=2))

print("\nSecond derivative with scale factor 0.5:")
print(H.hermder(c, m=2, scl=0.5))

Original derivative:
[ 4. 12. 24.]

Derivative with scale factor 2:
[ 8. 24. 48.]

Second derivative with scale factor 0.5:
[ 3.  12.]

Conclusion

The hermite.hermder() method efficiently computes derivatives of Hermite series. Use the m parameter for higher-order derivatives and scl for scaling transformations.