Remove small trailing coefficients from Hermite polynomial in Python

To remove small trailing coefficients from Hermite polynomial, use the hermite.hermtrim() method in Python NumPy. The method returns a 1-d array with trailing zeros removed. If the resulting series would be empty, a series containing a single zero is returned.

The "Small" means "small in absolute value" and is controlled by the parameter tol; "trailing" means highest order coefficient(s), e.g., in [0, 1, 1, 0, 0] (which represents 0 + x + x**2 + 0*x**3 + 0*x**4) both the 3rd and 4th order coefficients would be "trimmed."

Syntax

numpy.polynomial.hermite.hermtrim(c, tol=0)

Parameters

c − A 1-d array of coefficients, ordered from lowest order to highest.

tol − Trailing elements with absolute value less than or equal to tol are removed. Default is 0.

Basic Example

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

# Create an array with trailing zeros
c = np.array([0, 5, 0, 0, 9, 0])
print("Original array:", c)

# Remove trailing coefficients
result = H.hermtrim(c)
print("After trimming:", result)

Original array: [0 5 0 0 9 0]
After trimming: [0. 5. 0. 0. 9.]

Using Tolerance Parameter

You can specify a tolerance value to remove coefficients that are small but not exactly zero ?

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

# Array with small coefficients at the end
c = np.array([1.0, 2.0, 3.0, 0.001, 0.0001])
print("Original array:", c)

# Remove coefficients smaller than 0.01
result = H.hermtrim(c, tol=0.01)
print("After trimming (tol=0.01):", result)

Original array: [1.0000e+00 2.0000e+00 3.0000e+00 1.0000e-03 1.0000e-04]
After trimming (tol=0.01): [1. 2. 3.]

Edge Cases

If all coefficients are removed, the function returns a single zero ?

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

# Array of only small values
c = np.array([0.001, 0.002, 0.0005])
print("Original array:", c)

# Remove all coefficients with tol=0.01
result = H.hermtrim(c, tol=0.01)
print("After trimming:", result)
print("Length:", len(result))

Original array: [0.001  0.002  0.0005]
After trimming: [0.]
Length: 1

Conclusion

The hermite.hermtrim() method efficiently removes trailing coefficients from Hermite polynomials. Use the tol parameter to control the threshold for "small" coefficients, making it useful for cleaning up numerical approximations.