Remove small trailing coefficients from Laguerre polynomial in Python

To remove small trailing coefficients from Laguerre polynomial, use the laguerre.lagtrim() 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. The 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.laguerre.lagtrim(c, tol=0)

Parameters

The parameters are ?

• 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: 0)

Example

Let's create a Laguerre polynomial coefficient array and remove trailing zeros ?

import numpy as np
from numpy.polynomial import laguerre as L

# Create an array of coefficients
c = np.array([0, 5, 0, 0, 9, 0])

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

# Check the Dimensions
print("\nDimensions of our Array...\n", c.ndim)

# Get the Datatype
print("\nDatatype of our Array object...\n", c.dtype)

# Get the Shape
print("\nShape of our Array object...\n", c.shape)

# Remove small trailing coefficients from Laguerre polynomial
print("\nResult...\n", L.lagtrim(c))

Our Array...
 [0 5 0 0 9 0]

Dimensions of our Array...
 1

Datatype of our Array object...
 int64

Shape of our Array object...
 (6,)

Result...
 [0. 5. 0. 0. 9.]

Using Custom Tolerance

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

import numpy as np
from numpy.polynomial import laguerre as L

# Array with small trailing values
c = np.array([1, 2, 3, 0.001, 0.0005])

print("Original array:", c)
print("After trimming with default tol:", L.lagtrim(c))
print("After trimming with tol=0.01:", L.lagtrim(c, tol=0.01))

Original array: [1.     2.     3.     0.001  0.0005]
After trimming with default tol: [1.     2.     3.     0.001  0.0005]
After trimming with tol=0.01: [1. 2. 3.]

Conclusion

The lagtrim() method efficiently removes trailing coefficients from Laguerre polynomials. Use the tol parameter to control which coefficients are considered "small" and should be removed.