💡 Problem Formulation: When working with Hermite polynomials in Python, especially in computational physics or mathematics, it is common to encounter a polynomial with trailing coefficients that are negligibly small and effectively zero. For the sake of simplicity and efficiency, it is often preferable to remove these small coefficients. Suppose we have a Hermite polynomial represented as [2, -5e-15, 1e-12, 7], where the small trailing coefficients (-5e-15 and 1e-12) should be removed, resulting in a cleaner polynomial [2, 7].
Method 1: Manual Threshold Trimming
This method involves setting a manual threshold to strip off coefficients smaller than the threshold value. It’s simple to implement and can be adjusted based on the required precision. The threshold should be set considering the context of the problem and the level of precision required.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] trimmed_poly = list(filter(lambda coef: abs(coef) > 1e-14, coefficients)) print(trimmed_poly)
Output: [2, 7]
This functional approach passes a lambda function to filter, which retains values that have an absolute magnitude greater than the defined threshold. The result of filter is a filter object, which is then converted into a list to get the final array of significant coefficients.
Summary/Discussion
- Method 1: Manual Threshold Trimming. Straightforward, manually controllable precision. May require adjustment of the threshold based on context.
- Method 2: Using NumPy’s isclose Function. Utilizes a scientific library for numerical comparisons, reliable for a range of floating-point comparisons. Requires NumPy installation.
- Method 3: Truncate Small Coefficients Magnitude. Simple use of native Python functions. Precision level must be carefully chosen to avoid discarding significant digits.
- Method 4: Using SciPy’s Polynomial Class. Provides a professional and practical approach within the context of polynomial manipulation. Involves familiarity with SciPy and its API.
- Method 5: Python’s Filter Function. Offers a functional and elegant one-liner. Might be less intuitive for beginners and less flexible in terms of adjusting the tolerance inline.
from scipy.polynomial import Polynomial coefficients = [2, -5e-15, 1e-12, 7] p = Polynomial(coefficients) trimmed_poly = p.trim(tol=1e-14) print(trimmed_poly)
Output: Polynomial([2., 7.], domain=[-1, 1], window=[-1, 1])
This snippet uses SciPy’s Polynomial class to instantiate a polynomial object from the coefficients. The trim method is called, specifying a tolerance level to trim away small coefficients. The result is a Polynomial object with clean coefficients, from which the array of coefficients can be easily accessed if needed.
Bonus One-Liner Method 5: Python’s Filter Function
With Python’s filter function, one can easily create a one-liner to remove small coefficients by defining a filtering function that encapsulates the tolerance level, enabling concise and functional code.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] trimmed_poly = list(filter(lambda coef: abs(coef) > 1e-14, coefficients)) print(trimmed_poly)
Output: [2, 7]
This functional approach passes a lambda function to filter, which retains values that have an absolute magnitude greater than the defined threshold. The result of filter is a filter object, which is then converted into a list to get the final array of significant coefficients.
Summary/Discussion
- Method 1: Manual Threshold Trimming. Straightforward, manually controllable precision. May require adjustment of the threshold based on context.
- Method 2: Using NumPy’s isclose Function. Utilizes a scientific library for numerical comparisons, reliable for a range of floating-point comparisons. Requires NumPy installation.
- Method 3: Truncate Small Coefficients Magnitude. Simple use of native Python functions. Precision level must be carefully chosen to avoid discarding significant digits.
- Method 4: Using SciPy’s Polynomial Class. Provides a professional and practical approach within the context of polynomial manipulation. Involves familiarity with SciPy and its API.
- Method 5: Python’s Filter Function. Offers a functional and elegant one-liner. Might be less intuitive for beginners and less flexible in terms of adjusting the tolerance inline.
coefficients = [2, -5e-15, 1e-12, 7] precision = 14 trimmed_poly = [coef if round(abs(coef), precision) != 0 else 0 for coef in coefficients] print(trimmed_poly)
Output: [2, 0, 0, 7]
The snippet rounds the absolute value of each coefficient to a defined precision and checks if the result is non-zero. If not, it replaces the coefficient with zero in the list. It highlights the importance of specifying the correct level of precision for the particular problem domain.
Method 4: Using SciPy’s Polynomial Class
The SciPy library provides a Polynomial class with a method to clean small coefficients. This method is particularly useful when working with polynomials, as it is designed for such operations and can be more expressive and purpose-driven.
Here’s an example:
from scipy.polynomial import Polynomial coefficients = [2, -5e-15, 1e-12, 7] p = Polynomial(coefficients) trimmed_poly = p.trim(tol=1e-14) print(trimmed_poly)
Output: Polynomial([2., 7.], domain=[-1, 1], window=[-1, 1])
This snippet uses SciPy’s Polynomial class to instantiate a polynomial object from the coefficients. The trim method is called, specifying a tolerance level to trim away small coefficients. The result is a Polynomial object with clean coefficients, from which the array of coefficients can be easily accessed if needed.
Bonus One-Liner Method 5: Python’s Filter Function
With Python’s filter function, one can easily create a one-liner to remove small coefficients by defining a filtering function that encapsulates the tolerance level, enabling concise and functional code.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] trimmed_poly = list(filter(lambda coef: abs(coef) > 1e-14, coefficients)) print(trimmed_poly)
Output: [2, 7]
This functional approach passes a lambda function to filter, which retains values that have an absolute magnitude greater than the defined threshold. The result of filter is a filter object, which is then converted into a list to get the final array of significant coefficients.
Summary/Discussion
- Method 1: Manual Threshold Trimming. Straightforward, manually controllable precision. May require adjustment of the threshold based on context.
- Method 2: Using NumPy’s isclose Function. Utilizes a scientific library for numerical comparisons, reliable for a range of floating-point comparisons. Requires NumPy installation.
- Method 3: Truncate Small Coefficients Magnitude. Simple use of native Python functions. Precision level must be carefully chosen to avoid discarding significant digits.
- Method 4: Using SciPy’s Polynomial Class. Provides a professional and practical approach within the context of polynomial manipulation. Involves familiarity with SciPy and its API.
- Method 5: Python’s Filter Function. Offers a functional and elegant one-liner. Might be less intuitive for beginners and less flexible in terms of adjusting the tolerance inline.
import numpy as np coefficients = [2, -5e-15, 1e-12, 7] tolerance = 1e-14 trimmed_poly = [coef for coef in coefficients if not np.isclose(coef, 0, atol=tolerance)] print(trimmed_poly)
Output: [2, 7]
This approach utilizes the isclose function from the NumPy library to iteratively filter out the coefficients that are ‘close’ to zero within a certain absolute tolerance. The resulting list includes only the coefficients discernible from zero, effectively removing the small and negligible ones.
Method 3: Truncate Small Coefficients Magnitude
By truncating the magnitude of small coefficients using Python’s built-in round function, one can clear out coefficients that are insignificant when rounded to a certain number of decimal places.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] precision = 14 trimmed_poly = [coef if round(abs(coef), precision) != 0 else 0 for coef in coefficients] print(trimmed_poly)
Output: [2, 0, 0, 7]
The snippet rounds the absolute value of each coefficient to a defined precision and checks if the result is non-zero. If not, it replaces the coefficient with zero in the list. It highlights the importance of specifying the correct level of precision for the particular problem domain.
Method 4: Using SciPy’s Polynomial Class
The SciPy library provides a Polynomial class with a method to clean small coefficients. This method is particularly useful when working with polynomials, as it is designed for such operations and can be more expressive and purpose-driven.
Here’s an example:
from scipy.polynomial import Polynomial coefficients = [2, -5e-15, 1e-12, 7] p = Polynomial(coefficients) trimmed_poly = p.trim(tol=1e-14) print(trimmed_poly)
Output: Polynomial([2., 7.], domain=[-1, 1], window=[-1, 1])
This snippet uses SciPy’s Polynomial class to instantiate a polynomial object from the coefficients. The trim method is called, specifying a tolerance level to trim away small coefficients. The result is a Polynomial object with clean coefficients, from which the array of coefficients can be easily accessed if needed.
Bonus One-Liner Method 5: Python’s Filter Function
With Python’s filter function, one can easily create a one-liner to remove small coefficients by defining a filtering function that encapsulates the tolerance level, enabling concise and functional code.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] trimmed_poly = list(filter(lambda coef: abs(coef) > 1e-14, coefficients)) print(trimmed_poly)
Output: [2, 7]
This functional approach passes a lambda function to filter, which retains values that have an absolute magnitude greater than the defined threshold. The result of filter is a filter object, which is then converted into a list to get the final array of significant coefficients.
Summary/Discussion
- Method 1: Manual Threshold Trimming. Straightforward, manually controllable precision. May require adjustment of the threshold based on context.
- Method 2: Using NumPy’s isclose Function. Utilizes a scientific library for numerical comparisons, reliable for a range of floating-point comparisons. Requires NumPy installation.
- Method 3: Truncate Small Coefficients Magnitude. Simple use of native Python functions. Precision level must be carefully chosen to avoid discarding significant digits.
- Method 4: Using SciPy’s Polynomial Class. Provides a professional and practical approach within the context of polynomial manipulation. Involves familiarity with SciPy and its API.
- Method 5: Python’s Filter Function. Offers a functional and elegant one-liner. Might be less intuitive for beginners and less flexible in terms of adjusting the tolerance inline.
coefficients = [2, -5e-15, 1e-12, 7] threshold = 1e-14 trimmed_poly = [coef for coef in coefficients if abs(coef) > threshold] print(trimmed_poly)
Output: [2, 7]
This code snippet creates a list comprehension that iterates through each coefficient in the Hermite polynomial. It checks if the absolute value of the coefficient is greater than the manually defined threshold. If so, it includes the coefficient in the output list, effectively removing small trailing coefficients.
Method 2: Using NumPy’s isclose Function
NumPy’s isclose function allows to compare each coefficient against zero within a specified tolerance, handling floating-point arithmetic issues. It’s a robust and concise solution when working with numerical data in Python.
Here’s an example:
import numpy as np coefficients = [2, -5e-15, 1e-12, 7] tolerance = 1e-14 trimmed_poly = [coef for coef in coefficients if not np.isclose(coef, 0, atol=tolerance)] print(trimmed_poly)
Output: [2, 7]
This approach utilizes the isclose function from the NumPy library to iteratively filter out the coefficients that are ‘close’ to zero within a certain absolute tolerance. The resulting list includes only the coefficients discernible from zero, effectively removing the small and negligible ones.
Method 3: Truncate Small Coefficients Magnitude
By truncating the magnitude of small coefficients using Python’s built-in round function, one can clear out coefficients that are insignificant when rounded to a certain number of decimal places.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] precision = 14 trimmed_poly = [coef if round(abs(coef), precision) != 0 else 0 for coef in coefficients] print(trimmed_poly)
Output: [2, 0, 0, 7]
The snippet rounds the absolute value of each coefficient to a defined precision and checks if the result is non-zero. If not, it replaces the coefficient with zero in the list. It highlights the importance of specifying the correct level of precision for the particular problem domain.
Method 4: Using SciPy’s Polynomial Class
The SciPy library provides a Polynomial class with a method to clean small coefficients. This method is particularly useful when working with polynomials, as it is designed for such operations and can be more expressive and purpose-driven.
Here’s an example:
from scipy.polynomial import Polynomial coefficients = [2, -5e-15, 1e-12, 7] p = Polynomial(coefficients) trimmed_poly = p.trim(tol=1e-14) print(trimmed_poly)
Output: Polynomial([2., 7.], domain=[-1, 1], window=[-1, 1])
This snippet uses SciPy’s Polynomial class to instantiate a polynomial object from the coefficients. The trim method is called, specifying a tolerance level to trim away small coefficients. The result is a Polynomial object with clean coefficients, from which the array of coefficients can be easily accessed if needed.
Bonus One-Liner Method 5: Python’s Filter Function
With Python’s filter function, one can easily create a one-liner to remove small coefficients by defining a filtering function that encapsulates the tolerance level, enabling concise and functional code.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] trimmed_poly = list(filter(lambda coef: abs(coef) > 1e-14, coefficients)) print(trimmed_poly)
Output: [2, 7]
This functional approach passes a lambda function to filter, which retains values that have an absolute magnitude greater than the defined threshold. The result of filter is a filter object, which is then converted into a list to get the final array of significant coefficients.
Summary/Discussion
- Method 1: Manual Threshold Trimming. Straightforward, manually controllable precision. May require adjustment of the threshold based on context.
- Method 2: Using NumPy’s isclose Function. Utilizes a scientific library for numerical comparisons, reliable for a range of floating-point comparisons. Requires NumPy installation.
- Method 3: Truncate Small Coefficients Magnitude. Simple use of native Python functions. Precision level must be carefully chosen to avoid discarding significant digits.
- Method 4: Using SciPy’s Polynomial Class. Provides a professional and practical approach within the context of polynomial manipulation. Involves familiarity with SciPy and its API.
- Method 5: Python’s Filter Function. Offers a functional and elegant one-liner. Might be less intuitive for beginners and less flexible in terms of adjusting the tolerance inline.
from scipy.polynomial import Polynomial coefficients = [2, -5e-15, 1e-12, 7] p = Polynomial(coefficients) trimmed_poly = p.trim(tol=1e-14) print(trimmed_poly)
Output: Polynomial([2., 7.], domain=[-1, 1], window=[-1, 1])
This snippet uses SciPy’s Polynomial class to instantiate a polynomial object from the coefficients. The trim method is called, specifying a tolerance level to trim away small coefficients. The result is a Polynomial object with clean coefficients, from which the array of coefficients can be easily accessed if needed.
Bonus One-Liner Method 5: Python’s Filter Function
With Python’s filter function, one can easily create a one-liner to remove small coefficients by defining a filtering function that encapsulates the tolerance level, enabling concise and functional code.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] trimmed_poly = list(filter(lambda coef: abs(coef) > 1e-14, coefficients)) print(trimmed_poly)
Output: [2, 7]
This functional approach passes a lambda function to filter, which retains values that have an absolute magnitude greater than the defined threshold. The result of filter is a filter object, which is then converted into a list to get the final array of significant coefficients.
Summary/Discussion
- Method 1: Manual Threshold Trimming. Straightforward, manually controllable precision. May require adjustment of the threshold based on context.
- Method 2: Using NumPy’s isclose Function. Utilizes a scientific library for numerical comparisons, reliable for a range of floating-point comparisons. Requires NumPy installation.
- Method 3: Truncate Small Coefficients Magnitude. Simple use of native Python functions. Precision level must be carefully chosen to avoid discarding significant digits.
- Method 4: Using SciPy’s Polynomial Class. Provides a professional and practical approach within the context of polynomial manipulation. Involves familiarity with SciPy and its API.
- Method 5: Python’s Filter Function. Offers a functional and elegant one-liner. Might be less intuitive for beginners and less flexible in terms of adjusting the tolerance inline.
coefficients = [2, -5e-15, 1e-12, 7] threshold = 1e-14 trimmed_poly = [coef for coef in coefficients if abs(coef) > threshold] print(trimmed_poly)
Output: [2, 7]
This code snippet creates a list comprehension that iterates through each coefficient in the Hermite polynomial. It checks if the absolute value of the coefficient is greater than the manually defined threshold. If so, it includes the coefficient in the output list, effectively removing small trailing coefficients.
Method 2: Using NumPy’s isclose Function
NumPy’s isclose function allows to compare each coefficient against zero within a specified tolerance, handling floating-point arithmetic issues. It’s a robust and concise solution when working with numerical data in Python.
Here’s an example:
import numpy as np coefficients = [2, -5e-15, 1e-12, 7] tolerance = 1e-14 trimmed_poly = [coef for coef in coefficients if not np.isclose(coef, 0, atol=tolerance)] print(trimmed_poly)
Output: [2, 7]
This approach utilizes the isclose function from the NumPy library to iteratively filter out the coefficients that are ‘close’ to zero within a certain absolute tolerance. The resulting list includes only the coefficients discernible from zero, effectively removing the small and negligible ones.
Method 3: Truncate Small Coefficients Magnitude
By truncating the magnitude of small coefficients using Python’s built-in round function, one can clear out coefficients that are insignificant when rounded to a certain number of decimal places.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] precision = 14 trimmed_poly = [coef if round(abs(coef), precision) != 0 else 0 for coef in coefficients] print(trimmed_poly)
Output: [2, 0, 0, 7]
The snippet rounds the absolute value of each coefficient to a defined precision and checks if the result is non-zero. If not, it replaces the coefficient with zero in the list. It highlights the importance of specifying the correct level of precision for the particular problem domain.
Method 4: Using SciPy’s Polynomial Class
The SciPy library provides a Polynomial class with a method to clean small coefficients. This method is particularly useful when working with polynomials, as it is designed for such operations and can be more expressive and purpose-driven.
Here’s an example:
from scipy.polynomial import Polynomial coefficients = [2, -5e-15, 1e-12, 7] p = Polynomial(coefficients) trimmed_poly = p.trim(tol=1e-14) print(trimmed_poly)
Output: Polynomial([2., 7.], domain=[-1, 1], window=[-1, 1])
This snippet uses SciPy’s Polynomial class to instantiate a polynomial object from the coefficients. The trim method is called, specifying a tolerance level to trim away small coefficients. The result is a Polynomial object with clean coefficients, from which the array of coefficients can be easily accessed if needed.
Bonus One-Liner Method 5: Python’s Filter Function
With Python’s filter function, one can easily create a one-liner to remove small coefficients by defining a filtering function that encapsulates the tolerance level, enabling concise and functional code.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] trimmed_poly = list(filter(lambda coef: abs(coef) > 1e-14, coefficients)) print(trimmed_poly)
Output: [2, 7]
This functional approach passes a lambda function to filter, which retains values that have an absolute magnitude greater than the defined threshold. The result of filter is a filter object, which is then converted into a list to get the final array of significant coefficients.
Summary/Discussion
- Method 1: Manual Threshold Trimming. Straightforward, manually controllable precision. May require adjustment of the threshold based on context.
- Method 2: Using NumPy’s isclose Function. Utilizes a scientific library for numerical comparisons, reliable for a range of floating-point comparisons. Requires NumPy installation.
- Method 3: Truncate Small Coefficients Magnitude. Simple use of native Python functions. Precision level must be carefully chosen to avoid discarding significant digits.
- Method 4: Using SciPy’s Polynomial Class. Provides a professional and practical approach within the context of polynomial manipulation. Involves familiarity with SciPy and its API.
- Method 5: Python’s Filter Function. Offers a functional and elegant one-liner. Might be less intuitive for beginners and less flexible in terms of adjusting the tolerance inline.
coefficients = [2, -5e-15, 1e-12, 7] precision = 14 trimmed_poly = [coef if round(abs(coef), precision) != 0 else 0 for coef in coefficients] print(trimmed_poly)
Output: [2, 0, 0, 7]
The snippet rounds the absolute value of each coefficient to a defined precision and checks if the result is non-zero. If not, it replaces the coefficient with zero in the list. It highlights the importance of specifying the correct level of precision for the particular problem domain.
Method 4: Using SciPy’s Polynomial Class
The SciPy library provides a Polynomial class with a method to clean small coefficients. This method is particularly useful when working with polynomials, as it is designed for such operations and can be more expressive and purpose-driven.
Here’s an example:
from scipy.polynomial import Polynomial coefficients = [2, -5e-15, 1e-12, 7] p = Polynomial(coefficients) trimmed_poly = p.trim(tol=1e-14) print(trimmed_poly)
Output: Polynomial([2., 7.], domain=[-1, 1], window=[-1, 1])
This snippet uses SciPy’s Polynomial class to instantiate a polynomial object from the coefficients. The trim method is called, specifying a tolerance level to trim away small coefficients. The result is a Polynomial object with clean coefficients, from which the array of coefficients can be easily accessed if needed.
Bonus One-Liner Method 5: Python’s Filter Function
With Python’s filter function, one can easily create a one-liner to remove small coefficients by defining a filtering function that encapsulates the tolerance level, enabling concise and functional code.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] trimmed_poly = list(filter(lambda coef: abs(coef) > 1e-14, coefficients)) print(trimmed_poly)
Output: [2, 7]
This functional approach passes a lambda function to filter, which retains values that have an absolute magnitude greater than the defined threshold. The result of filter is a filter object, which is then converted into a list to get the final array of significant coefficients.
Summary/Discussion
- Method 1: Manual Threshold Trimming. Straightforward, manually controllable precision. May require adjustment of the threshold based on context.
- Method 2: Using NumPy’s isclose Function. Utilizes a scientific library for numerical comparisons, reliable for a range of floating-point comparisons. Requires NumPy installation.
- Method 3: Truncate Small Coefficients Magnitude. Simple use of native Python functions. Precision level must be carefully chosen to avoid discarding significant digits.
- Method 4: Using SciPy’s Polynomial Class. Provides a professional and practical approach within the context of polynomial manipulation. Involves familiarity with SciPy and its API.
- Method 5: Python’s Filter Function. Offers a functional and elegant one-liner. Might be less intuitive for beginners and less flexible in terms of adjusting the tolerance inline.
coefficients = [2, -5e-15, 1e-12, 7] threshold = 1e-14 trimmed_poly = [coef for coef in coefficients if abs(coef) > threshold] print(trimmed_poly)
Output: [2, 7]
This code snippet creates a list comprehension that iterates through each coefficient in the Hermite polynomial. It checks if the absolute value of the coefficient is greater than the manually defined threshold. If so, it includes the coefficient in the output list, effectively removing small trailing coefficients.
Method 2: Using NumPy’s isclose Function
NumPy’s isclose function allows to compare each coefficient against zero within a specified tolerance, handling floating-point arithmetic issues. It’s a robust and concise solution when working with numerical data in Python.
Here’s an example:
import numpy as np coefficients = [2, -5e-15, 1e-12, 7] tolerance = 1e-14 trimmed_poly = [coef for coef in coefficients if not np.isclose(coef, 0, atol=tolerance)] print(trimmed_poly)
Output: [2, 7]
This approach utilizes the isclose function from the NumPy library to iteratively filter out the coefficients that are ‘close’ to zero within a certain absolute tolerance. The resulting list includes only the coefficients discernible from zero, effectively removing the small and negligible ones.
Method 3: Truncate Small Coefficients Magnitude
By truncating the magnitude of small coefficients using Python’s built-in round function, one can clear out coefficients that are insignificant when rounded to a certain number of decimal places.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] precision = 14 trimmed_poly = [coef if round(abs(coef), precision) != 0 else 0 for coef in coefficients] print(trimmed_poly)
Output: [2, 0, 0, 7]
The snippet rounds the absolute value of each coefficient to a defined precision and checks if the result is non-zero. If not, it replaces the coefficient with zero in the list. It highlights the importance of specifying the correct level of precision for the particular problem domain.
Method 4: Using SciPy’s Polynomial Class
The SciPy library provides a Polynomial class with a method to clean small coefficients. This method is particularly useful when working with polynomials, as it is designed for such operations and can be more expressive and purpose-driven.
Here’s an example:
from scipy.polynomial import Polynomial coefficients = [2, -5e-15, 1e-12, 7] p = Polynomial(coefficients) trimmed_poly = p.trim(tol=1e-14) print(trimmed_poly)
Output: Polynomial([2., 7.], domain=[-1, 1], window=[-1, 1])
This snippet uses SciPy’s Polynomial class to instantiate a polynomial object from the coefficients. The trim method is called, specifying a tolerance level to trim away small coefficients. The result is a Polynomial object with clean coefficients, from which the array of coefficients can be easily accessed if needed.
Bonus One-Liner Method 5: Python’s Filter Function
With Python’s filter function, one can easily create a one-liner to remove small coefficients by defining a filtering function that encapsulates the tolerance level, enabling concise and functional code.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] trimmed_poly = list(filter(lambda coef: abs(coef) > 1e-14, coefficients)) print(trimmed_poly)
Output: [2, 7]
This functional approach passes a lambda function to filter, which retains values that have an absolute magnitude greater than the defined threshold. The result of filter is a filter object, which is then converted into a list to get the final array of significant coefficients.
Summary/Discussion
- Method 1: Manual Threshold Trimming. Straightforward, manually controllable precision. May require adjustment of the threshold based on context.
- Method 2: Using NumPy’s isclose Function. Utilizes a scientific library for numerical comparisons, reliable for a range of floating-point comparisons. Requires NumPy installation.
- Method 3: Truncate Small Coefficients Magnitude. Simple use of native Python functions. Precision level must be carefully chosen to avoid discarding significant digits.
- Method 4: Using SciPy’s Polynomial Class. Provides a professional and practical approach within the context of polynomial manipulation. Involves familiarity with SciPy and its API.
- Method 5: Python’s Filter Function. Offers a functional and elegant one-liner. Might be less intuitive for beginners and less flexible in terms of adjusting the tolerance inline.
import numpy as np coefficients = [2, -5e-15, 1e-12, 7] tolerance = 1e-14 trimmed_poly = [coef for coef in coefficients if not np.isclose(coef, 0, atol=tolerance)] print(trimmed_poly)
Output: [2, 7]
This approach utilizes the isclose function from the NumPy library to iteratively filter out the coefficients that are ‘close’ to zero within a certain absolute tolerance. The resulting list includes only the coefficients discernible from zero, effectively removing the small and negligible ones.
Method 3: Truncate Small Coefficients Magnitude
By truncating the magnitude of small coefficients using Python’s built-in round function, one can clear out coefficients that are insignificant when rounded to a certain number of decimal places.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] precision = 14 trimmed_poly = [coef if round(abs(coef), precision) != 0 else 0 for coef in coefficients] print(trimmed_poly)
Output: [2, 0, 0, 7]
The snippet rounds the absolute value of each coefficient to a defined precision and checks if the result is non-zero. If not, it replaces the coefficient with zero in the list. It highlights the importance of specifying the correct level of precision for the particular problem domain.
Method 4: Using SciPy’s Polynomial Class
The SciPy library provides a Polynomial class with a method to clean small coefficients. This method is particularly useful when working with polynomials, as it is designed for such operations and can be more expressive and purpose-driven.
Here’s an example:
from scipy.polynomial import Polynomial coefficients = [2, -5e-15, 1e-12, 7] p = Polynomial(coefficients) trimmed_poly = p.trim(tol=1e-14) print(trimmed_poly)
Output: Polynomial([2., 7.], domain=[-1, 1], window=[-1, 1])
This snippet uses SciPy’s Polynomial class to instantiate a polynomial object from the coefficients. The trim method is called, specifying a tolerance level to trim away small coefficients. The result is a Polynomial object with clean coefficients, from which the array of coefficients can be easily accessed if needed.
Bonus One-Liner Method 5: Python’s Filter Function
With Python’s filter function, one can easily create a one-liner to remove small coefficients by defining a filtering function that encapsulates the tolerance level, enabling concise and functional code.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] trimmed_poly = list(filter(lambda coef: abs(coef) > 1e-14, coefficients)) print(trimmed_poly)
Output: [2, 7]
This functional approach passes a lambda function to filter, which retains values that have an absolute magnitude greater than the defined threshold. The result of filter is a filter object, which is then converted into a list to get the final array of significant coefficients.
Summary/Discussion
- Method 1: Manual Threshold Trimming. Straightforward, manually controllable precision. May require adjustment of the threshold based on context.
- Method 2: Using NumPy’s isclose Function. Utilizes a scientific library for numerical comparisons, reliable for a range of floating-point comparisons. Requires NumPy installation.
- Method 3: Truncate Small Coefficients Magnitude. Simple use of native Python functions. Precision level must be carefully chosen to avoid discarding significant digits.
- Method 4: Using SciPy’s Polynomial Class. Provides a professional and practical approach within the context of polynomial manipulation. Involves familiarity with SciPy and its API.
- Method 5: Python’s Filter Function. Offers a functional and elegant one-liner. Might be less intuitive for beginners and less flexible in terms of adjusting the tolerance inline.
coefficients = [2, -5e-15, 1e-12, 7] threshold = 1e-14 trimmed_poly = [coef for coef in coefficients if abs(coef) > threshold] print(trimmed_poly)
Output: [2, 7]
This code snippet creates a list comprehension that iterates through each coefficient in the Hermite polynomial. It checks if the absolute value of the coefficient is greater than the manually defined threshold. If so, it includes the coefficient in the output list, effectively removing small trailing coefficients.
Method 2: Using NumPy’s isclose Function
NumPy’s isclose function allows to compare each coefficient against zero within a specified tolerance, handling floating-point arithmetic issues. It’s a robust and concise solution when working with numerical data in Python.
Here’s an example:
import numpy as np coefficients = [2, -5e-15, 1e-12, 7] tolerance = 1e-14 trimmed_poly = [coef for coef in coefficients if not np.isclose(coef, 0, atol=tolerance)] print(trimmed_poly)
Output: [2, 7]
This approach utilizes the isclose function from the NumPy library to iteratively filter out the coefficients that are ‘close’ to zero within a certain absolute tolerance. The resulting list includes only the coefficients discernible from zero, effectively removing the small and negligible ones.
Method 3: Truncate Small Coefficients Magnitude
By truncating the magnitude of small coefficients using Python’s built-in round function, one can clear out coefficients that are insignificant when rounded to a certain number of decimal places.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] precision = 14 trimmed_poly = [coef if round(abs(coef), precision) != 0 else 0 for coef in coefficients] print(trimmed_poly)
Output: [2, 0, 0, 7]
The snippet rounds the absolute value of each coefficient to a defined precision and checks if the result is non-zero. If not, it replaces the coefficient with zero in the list. It highlights the importance of specifying the correct level of precision for the particular problem domain.
Method 4: Using SciPy’s Polynomial Class
The SciPy library provides a Polynomial class with a method to clean small coefficients. This method is particularly useful when working with polynomials, as it is designed for such operations and can be more expressive and purpose-driven.
Here’s an example:
from scipy.polynomial import Polynomial coefficients = [2, -5e-15, 1e-12, 7] p = Polynomial(coefficients) trimmed_poly = p.trim(tol=1e-14) print(trimmed_poly)
Output: Polynomial([2., 7.], domain=[-1, 1], window=[-1, 1])
This snippet uses SciPy’s Polynomial class to instantiate a polynomial object from the coefficients. The trim method is called, specifying a tolerance level to trim away small coefficients. The result is a Polynomial object with clean coefficients, from which the array of coefficients can be easily accessed if needed.
Bonus One-Liner Method 5: Python’s Filter Function
With Python’s filter function, one can easily create a one-liner to remove small coefficients by defining a filtering function that encapsulates the tolerance level, enabling concise and functional code.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] trimmed_poly = list(filter(lambda coef: abs(coef) > 1e-14, coefficients)) print(trimmed_poly)
Output: [2, 7]
This functional approach passes a lambda function to filter, which retains values that have an absolute magnitude greater than the defined threshold. The result of filter is a filter object, which is then converted into a list to get the final array of significant coefficients.
Summary/Discussion
- Method 1: Manual Threshold Trimming. Straightforward, manually controllable precision. May require adjustment of the threshold based on context.
- Method 2: Using NumPy’s isclose Function. Utilizes a scientific library for numerical comparisons, reliable for a range of floating-point comparisons. Requires NumPy installation.
- Method 3: Truncate Small Coefficients Magnitude. Simple use of native Python functions. Precision level must be carefully chosen to avoid discarding significant digits.
- Method 4: Using SciPy’s Polynomial Class. Provides a professional and practical approach within the context of polynomial manipulation. Involves familiarity with SciPy and its API.
- Method 5: Python’s Filter Function. Offers a functional and elegant one-liner. Might be less intuitive for beginners and less flexible in terms of adjusting the tolerance inline.
from scipy.polynomial import Polynomial coefficients = [2, -5e-15, 1e-12, 7] p = Polynomial(coefficients) trimmed_poly = p.trim(tol=1e-14) print(trimmed_poly)
Output: Polynomial([2., 7.], domain=[-1, 1], window=[-1, 1])
This snippet uses SciPy’s Polynomial class to instantiate a polynomial object from the coefficients. The trim method is called, specifying a tolerance level to trim away small coefficients. The result is a Polynomial object with clean coefficients, from which the array of coefficients can be easily accessed if needed.
Bonus One-Liner Method 5: Python’s Filter Function
With Python’s filter function, one can easily create a one-liner to remove small coefficients by defining a filtering function that encapsulates the tolerance level, enabling concise and functional code.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] trimmed_poly = list(filter(lambda coef: abs(coef) > 1e-14, coefficients)) print(trimmed_poly)
Output: [2, 7]
This functional approach passes a lambda function to filter, which retains values that have an absolute magnitude greater than the defined threshold. The result of filter is a filter object, which is then converted into a list to get the final array of significant coefficients.
Summary/Discussion
- Method 1: Manual Threshold Trimming. Straightforward, manually controllable precision. May require adjustment of the threshold based on context.
- Method 2: Using NumPy’s isclose Function. Utilizes a scientific library for numerical comparisons, reliable for a range of floating-point comparisons. Requires NumPy installation.
- Method 3: Truncate Small Coefficients Magnitude. Simple use of native Python functions. Precision level must be carefully chosen to avoid discarding significant digits.
- Method 4: Using SciPy’s Polynomial Class. Provides a professional and practical approach within the context of polynomial manipulation. Involves familiarity with SciPy and its API.
- Method 5: Python’s Filter Function. Offers a functional and elegant one-liner. Might be less intuitive for beginners and less flexible in terms of adjusting the tolerance inline.
import numpy as np coefficients = [2, -5e-15, 1e-12, 7] tolerance = 1e-14 trimmed_poly = [coef for coef in coefficients if not np.isclose(coef, 0, atol=tolerance)] print(trimmed_poly)
Output: [2, 7]
This approach utilizes the isclose function from the NumPy library to iteratively filter out the coefficients that are ‘close’ to zero within a certain absolute tolerance. The resulting list includes only the coefficients discernible from zero, effectively removing the small and negligible ones.
Method 3: Truncate Small Coefficients Magnitude
By truncating the magnitude of small coefficients using Python’s built-in round function, one can clear out coefficients that are insignificant when rounded to a certain number of decimal places.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] precision = 14 trimmed_poly = [coef if round(abs(coef), precision) != 0 else 0 for coef in coefficients] print(trimmed_poly)
Output: [2, 0, 0, 7]
The snippet rounds the absolute value of each coefficient to a defined precision and checks if the result is non-zero. If not, it replaces the coefficient with zero in the list. It highlights the importance of specifying the correct level of precision for the particular problem domain.
Method 4: Using SciPy’s Polynomial Class
The SciPy library provides a Polynomial class with a method to clean small coefficients. This method is particularly useful when working with polynomials, as it is designed for such operations and can be more expressive and purpose-driven.
Here’s an example:
from scipy.polynomial import Polynomial coefficients = [2, -5e-15, 1e-12, 7] p = Polynomial(coefficients) trimmed_poly = p.trim(tol=1e-14) print(trimmed_poly)
Output: Polynomial([2., 7.], domain=[-1, 1], window=[-1, 1])
This snippet uses SciPy’s Polynomial class to instantiate a polynomial object from the coefficients. The trim method is called, specifying a tolerance level to trim away small coefficients. The result is a Polynomial object with clean coefficients, from which the array of coefficients can be easily accessed if needed.
Bonus One-Liner Method 5: Python’s Filter Function
With Python’s filter function, one can easily create a one-liner to remove small coefficients by defining a filtering function that encapsulates the tolerance level, enabling concise and functional code.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] trimmed_poly = list(filter(lambda coef: abs(coef) > 1e-14, coefficients)) print(trimmed_poly)
Output: [2, 7]
This functional approach passes a lambda function to filter, which retains values that have an absolute magnitude greater than the defined threshold. The result of filter is a filter object, which is then converted into a list to get the final array of significant coefficients.
Summary/Discussion
- Method 1: Manual Threshold Trimming. Straightforward, manually controllable precision. May require adjustment of the threshold based on context.
- Method 2: Using NumPy’s isclose Function. Utilizes a scientific library for numerical comparisons, reliable for a range of floating-point comparisons. Requires NumPy installation.
- Method 3: Truncate Small Coefficients Magnitude. Simple use of native Python functions. Precision level must be carefully chosen to avoid discarding significant digits.
- Method 4: Using SciPy’s Polynomial Class. Provides a professional and practical approach within the context of polynomial manipulation. Involves familiarity with SciPy and its API.
- Method 5: Python’s Filter Function. Offers a functional and elegant one-liner. Might be less intuitive for beginners and less flexible in terms of adjusting the tolerance inline.
coefficients = [2, -5e-15, 1e-12, 7] threshold = 1e-14 trimmed_poly = [coef for coef in coefficients if abs(coef) > threshold] print(trimmed_poly)
Output: [2, 7]
This code snippet creates a list comprehension that iterates through each coefficient in the Hermite polynomial. It checks if the absolute value of the coefficient is greater than the manually defined threshold. If so, it includes the coefficient in the output list, effectively removing small trailing coefficients.
Method 2: Using NumPy’s isclose Function
NumPy’s isclose function allows to compare each coefficient against zero within a specified tolerance, handling floating-point arithmetic issues. It’s a robust and concise solution when working with numerical data in Python.
Here’s an example:
import numpy as np coefficients = [2, -5e-15, 1e-12, 7] tolerance = 1e-14 trimmed_poly = [coef for coef in coefficients if not np.isclose(coef, 0, atol=tolerance)] print(trimmed_poly)
Output: [2, 7]
This approach utilizes the isclose function from the NumPy library to iteratively filter out the coefficients that are ‘close’ to zero within a certain absolute tolerance. The resulting list includes only the coefficients discernible from zero, effectively removing the small and negligible ones.
Method 3: Truncate Small Coefficients Magnitude
By truncating the magnitude of small coefficients using Python’s built-in round function, one can clear out coefficients that are insignificant when rounded to a certain number of decimal places.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] precision = 14 trimmed_poly = [coef if round(abs(coef), precision) != 0 else 0 for coef in coefficients] print(trimmed_poly)
Output: [2, 0, 0, 7]
The snippet rounds the absolute value of each coefficient to a defined precision and checks if the result is non-zero. If not, it replaces the coefficient with zero in the list. It highlights the importance of specifying the correct level of precision for the particular problem domain.
Method 4: Using SciPy’s Polynomial Class
The SciPy library provides a Polynomial class with a method to clean small coefficients. This method is particularly useful when working with polynomials, as it is designed for such operations and can be more expressive and purpose-driven.
Here’s an example:
from scipy.polynomial import Polynomial coefficients = [2, -5e-15, 1e-12, 7] p = Polynomial(coefficients) trimmed_poly = p.trim(tol=1e-14) print(trimmed_poly)
Output: Polynomial([2., 7.], domain=[-1, 1], window=[-1, 1])
This snippet uses SciPy’s Polynomial class to instantiate a polynomial object from the coefficients. The trim method is called, specifying a tolerance level to trim away small coefficients. The result is a Polynomial object with clean coefficients, from which the array of coefficients can be easily accessed if needed.
Bonus One-Liner Method 5: Python’s Filter Function
With Python’s filter function, one can easily create a one-liner to remove small coefficients by defining a filtering function that encapsulates the tolerance level, enabling concise and functional code.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] trimmed_poly = list(filter(lambda coef: abs(coef) > 1e-14, coefficients)) print(trimmed_poly)
Output: [2, 7]
This functional approach passes a lambda function to filter, which retains values that have an absolute magnitude greater than the defined threshold. The result of filter is a filter object, which is then converted into a list to get the final array of significant coefficients.
Summary/Discussion
- Method 1: Manual Threshold Trimming. Straightforward, manually controllable precision. May require adjustment of the threshold based on context.
- Method 2: Using NumPy’s isclose Function. Utilizes a scientific library for numerical comparisons, reliable for a range of floating-point comparisons. Requires NumPy installation.
- Method 3: Truncate Small Coefficients Magnitude. Simple use of native Python functions. Precision level must be carefully chosen to avoid discarding significant digits.
- Method 4: Using SciPy’s Polynomial Class. Provides a professional and practical approach within the context of polynomial manipulation. Involves familiarity with SciPy and its API.
- Method 5: Python’s Filter Function. Offers a functional and elegant one-liner. Might be less intuitive for beginners and less flexible in terms of adjusting the tolerance inline.
coefficients = [2, -5e-15, 1e-12, 7] precision = 14 trimmed_poly = [coef if round(abs(coef), precision) != 0 else 0 for coef in coefficients] print(trimmed_poly)
Output: [2, 0, 0, 7]
The snippet rounds the absolute value of each coefficient to a defined precision and checks if the result is non-zero. If not, it replaces the coefficient with zero in the list. It highlights the importance of specifying the correct level of precision for the particular problem domain.
Method 4: Using SciPy’s Polynomial Class
The SciPy library provides a Polynomial class with a method to clean small coefficients. This method is particularly useful when working with polynomials, as it is designed for such operations and can be more expressive and purpose-driven.
Here’s an example:
from scipy.polynomial import Polynomial coefficients = [2, -5e-15, 1e-12, 7] p = Polynomial(coefficients) trimmed_poly = p.trim(tol=1e-14) print(trimmed_poly)
Output: Polynomial([2., 7.], domain=[-1, 1], window=[-1, 1])
This snippet uses SciPy’s Polynomial class to instantiate a polynomial object from the coefficients. The trim method is called, specifying a tolerance level to trim away small coefficients. The result is a Polynomial object with clean coefficients, from which the array of coefficients can be easily accessed if needed.
Bonus One-Liner Method 5: Python’s Filter Function
With Python’s filter function, one can easily create a one-liner to remove small coefficients by defining a filtering function that encapsulates the tolerance level, enabling concise and functional code.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] trimmed_poly = list(filter(lambda coef: abs(coef) > 1e-14, coefficients)) print(trimmed_poly)
Output: [2, 7]
This functional approach passes a lambda function to filter, which retains values that have an absolute magnitude greater than the defined threshold. The result of filter is a filter object, which is then converted into a list to get the final array of significant coefficients.
Summary/Discussion
- Method 1: Manual Threshold Trimming. Straightforward, manually controllable precision. May require adjustment of the threshold based on context.
- Method 2: Using NumPy’s isclose Function. Utilizes a scientific library for numerical comparisons, reliable for a range of floating-point comparisons. Requires NumPy installation.
- Method 3: Truncate Small Coefficients Magnitude. Simple use of native Python functions. Precision level must be carefully chosen to avoid discarding significant digits.
- Method 4: Using SciPy’s Polynomial Class. Provides a professional and practical approach within the context of polynomial manipulation. Involves familiarity with SciPy and its API.
- Method 5: Python’s Filter Function. Offers a functional and elegant one-liner. Might be less intuitive for beginners and less flexible in terms of adjusting the tolerance inline.
import numpy as np coefficients = [2, -5e-15, 1e-12, 7] tolerance = 1e-14 trimmed_poly = [coef for coef in coefficients if not np.isclose(coef, 0, atol=tolerance)] print(trimmed_poly)
Output: [2, 7]
This approach utilizes the isclose function from the NumPy library to iteratively filter out the coefficients that are ‘close’ to zero within a certain absolute tolerance. The resulting list includes only the coefficients discernible from zero, effectively removing the small and negligible ones.
Method 3: Truncate Small Coefficients Magnitude
By truncating the magnitude of small coefficients using Python’s built-in round function, one can clear out coefficients that are insignificant when rounded to a certain number of decimal places.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] precision = 14 trimmed_poly = [coef if round(abs(coef), precision) != 0 else 0 for coef in coefficients] print(trimmed_poly)
Output: [2, 0, 0, 7]
The snippet rounds the absolute value of each coefficient to a defined precision and checks if the result is non-zero. If not, it replaces the coefficient with zero in the list. It highlights the importance of specifying the correct level of precision for the particular problem domain.
Method 4: Using SciPy’s Polynomial Class
The SciPy library provides a Polynomial class with a method to clean small coefficients. This method is particularly useful when working with polynomials, as it is designed for such operations and can be more expressive and purpose-driven.
Here’s an example:
from scipy.polynomial import Polynomial coefficients = [2, -5e-15, 1e-12, 7] p = Polynomial(coefficients) trimmed_poly = p.trim(tol=1e-14) print(trimmed_poly)
Output: Polynomial([2., 7.], domain=[-1, 1], window=[-1, 1])
This snippet uses SciPy’s Polynomial class to instantiate a polynomial object from the coefficients. The trim method is called, specifying a tolerance level to trim away small coefficients. The result is a Polynomial object with clean coefficients, from which the array of coefficients can be easily accessed if needed.
Bonus One-Liner Method 5: Python’s Filter Function
With Python’s filter function, one can easily create a one-liner to remove small coefficients by defining a filtering function that encapsulates the tolerance level, enabling concise and functional code.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] trimmed_poly = list(filter(lambda coef: abs(coef) > 1e-14, coefficients)) print(trimmed_poly)
Output: [2, 7]
This functional approach passes a lambda function to filter, which retains values that have an absolute magnitude greater than the defined threshold. The result of filter is a filter object, which is then converted into a list to get the final array of significant coefficients.
Summary/Discussion
- Method 1: Manual Threshold Trimming. Straightforward, manually controllable precision. May require adjustment of the threshold based on context.
- Method 2: Using NumPy’s isclose Function. Utilizes a scientific library for numerical comparisons, reliable for a range of floating-point comparisons. Requires NumPy installation.
- Method 3: Truncate Small Coefficients Magnitude. Simple use of native Python functions. Precision level must be carefully chosen to avoid discarding significant digits.
- Method 4: Using SciPy’s Polynomial Class. Provides a professional and practical approach within the context of polynomial manipulation. Involves familiarity with SciPy and its API.
- Method 5: Python’s Filter Function. Offers a functional and elegant one-liner. Might be less intuitive for beginners and less flexible in terms of adjusting the tolerance inline.
coefficients = [2, -5e-15, 1e-12, 7] threshold = 1e-14 trimmed_poly = [coef for coef in coefficients if abs(coef) > threshold] print(trimmed_poly)
Output: [2, 7]
This code snippet creates a list comprehension that iterates through each coefficient in the Hermite polynomial. It checks if the absolute value of the coefficient is greater than the manually defined threshold. If so, it includes the coefficient in the output list, effectively removing small trailing coefficients.
Method 2: Using NumPy’s isclose Function
NumPy’s isclose function allows to compare each coefficient against zero within a specified tolerance, handling floating-point arithmetic issues. It’s a robust and concise solution when working with numerical data in Python.
Here’s an example:
import numpy as np coefficients = [2, -5e-15, 1e-12, 7] tolerance = 1e-14 trimmed_poly = [coef for coef in coefficients if not np.isclose(coef, 0, atol=tolerance)] print(trimmed_poly)
Output: [2, 7]
This approach utilizes the isclose function from the NumPy library to iteratively filter out the coefficients that are ‘close’ to zero within a certain absolute tolerance. The resulting list includes only the coefficients discernible from zero, effectively removing the small and negligible ones.
Method 3: Truncate Small Coefficients Magnitude
By truncating the magnitude of small coefficients using Python’s built-in round function, one can clear out coefficients that are insignificant when rounded to a certain number of decimal places.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] precision = 14 trimmed_poly = [coef if round(abs(coef), precision) != 0 else 0 for coef in coefficients] print(trimmed_poly)
Output: [2, 0, 0, 7]
The snippet rounds the absolute value of each coefficient to a defined precision and checks if the result is non-zero. If not, it replaces the coefficient with zero in the list. It highlights the importance of specifying the correct level of precision for the particular problem domain.
Method 4: Using SciPy’s Polynomial Class
The SciPy library provides a Polynomial class with a method to clean small coefficients. This method is particularly useful when working with polynomials, as it is designed for such operations and can be more expressive and purpose-driven.
Here’s an example:
from scipy.polynomial import Polynomial coefficients = [2, -5e-15, 1e-12, 7] p = Polynomial(coefficients) trimmed_poly = p.trim(tol=1e-14) print(trimmed_poly)
Output: Polynomial([2., 7.], domain=[-1, 1], window=[-1, 1])
This snippet uses SciPy’s Polynomial class to instantiate a polynomial object from the coefficients. The trim method is called, specifying a tolerance level to trim away small coefficients. The result is a Polynomial object with clean coefficients, from which the array of coefficients can be easily accessed if needed.
Bonus One-Liner Method 5: Python’s Filter Function
With Python’s filter function, one can easily create a one-liner to remove small coefficients by defining a filtering function that encapsulates the tolerance level, enabling concise and functional code.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] trimmed_poly = list(filter(lambda coef: abs(coef) > 1e-14, coefficients)) print(trimmed_poly)
Output: [2, 7]
This functional approach passes a lambda function to filter, which retains values that have an absolute magnitude greater than the defined threshold. The result of filter is a filter object, which is then converted into a list to get the final array of significant coefficients.
Summary/Discussion
- Method 1: Manual Threshold Trimming. Straightforward, manually controllable precision. May require adjustment of the threshold based on context.
- Method 2: Using NumPy’s isclose Function. Utilizes a scientific library for numerical comparisons, reliable for a range of floating-point comparisons. Requires NumPy installation.
- Method 3: Truncate Small Coefficients Magnitude. Simple use of native Python functions. Precision level must be carefully chosen to avoid discarding significant digits.
- Method 4: Using SciPy’s Polynomial Class. Provides a professional and practical approach within the context of polynomial manipulation. Involves familiarity with SciPy and its API.
- Method 5: Python’s Filter Function. Offers a functional and elegant one-liner. Might be less intuitive for beginners and less flexible in terms of adjusting the tolerance inline.
from scipy.polynomial import Polynomial coefficients = [2, -5e-15, 1e-12, 7] p = Polynomial(coefficients) trimmed_poly = p.trim(tol=1e-14) print(trimmed_poly)
Output: Polynomial([2., 7.], domain=[-1, 1], window=[-1, 1])
This snippet uses SciPy’s Polynomial class to instantiate a polynomial object from the coefficients. The trim method is called, specifying a tolerance level to trim away small coefficients. The result is a Polynomial object with clean coefficients, from which the array of coefficients can be easily accessed if needed.
Bonus One-Liner Method 5: Python’s Filter Function
With Python’s filter function, one can easily create a one-liner to remove small coefficients by defining a filtering function that encapsulates the tolerance level, enabling concise and functional code.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] trimmed_poly = list(filter(lambda coef: abs(coef) > 1e-14, coefficients)) print(trimmed_poly)
Output: [2, 7]
This functional approach passes a lambda function to filter, which retains values that have an absolute magnitude greater than the defined threshold. The result of filter is a filter object, which is then converted into a list to get the final array of significant coefficients.
Summary/Discussion
- Method 1: Manual Threshold Trimming. Straightforward, manually controllable precision. May require adjustment of the threshold based on context.
- Method 2: Using NumPy’s isclose Function. Utilizes a scientific library for numerical comparisons, reliable for a range of floating-point comparisons. Requires NumPy installation.
- Method 3: Truncate Small Coefficients Magnitude. Simple use of native Python functions. Precision level must be carefully chosen to avoid discarding significant digits.
- Method 4: Using SciPy’s Polynomial Class. Provides a professional and practical approach within the context of polynomial manipulation. Involves familiarity with SciPy and its API.
- Method 5: Python’s Filter Function. Offers a functional and elegant one-liner. Might be less intuitive for beginners and less flexible in terms of adjusting the tolerance inline.
coefficients = [2, -5e-15, 1e-12, 7] precision = 14 trimmed_poly = [coef if round(abs(coef), precision) != 0 else 0 for coef in coefficients] print(trimmed_poly)
Output: [2, 0, 0, 7]
The snippet rounds the absolute value of each coefficient to a defined precision and checks if the result is non-zero. If not, it replaces the coefficient with zero in the list. It highlights the importance of specifying the correct level of precision for the particular problem domain.
Method 4: Using SciPy’s Polynomial Class
The SciPy library provides a Polynomial class with a method to clean small coefficients. This method is particularly useful when working with polynomials, as it is designed for such operations and can be more expressive and purpose-driven.
Here’s an example:
from scipy.polynomial import Polynomial coefficients = [2, -5e-15, 1e-12, 7] p = Polynomial(coefficients) trimmed_poly = p.trim(tol=1e-14) print(trimmed_poly)
Output: Polynomial([2., 7.], domain=[-1, 1], window=[-1, 1])
This snippet uses SciPy’s Polynomial class to instantiate a polynomial object from the coefficients. The trim method is called, specifying a tolerance level to trim away small coefficients. The result is a Polynomial object with clean coefficients, from which the array of coefficients can be easily accessed if needed.
Bonus One-Liner Method 5: Python’s Filter Function
With Python’s filter function, one can easily create a one-liner to remove small coefficients by defining a filtering function that encapsulates the tolerance level, enabling concise and functional code.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] trimmed_poly = list(filter(lambda coef: abs(coef) > 1e-14, coefficients)) print(trimmed_poly)
Output: [2, 7]
This functional approach passes a lambda function to filter, which retains values that have an absolute magnitude greater than the defined threshold. The result of filter is a filter object, which is then converted into a list to get the final array of significant coefficients.
Summary/Discussion
- Method 1: Manual Threshold Trimming. Straightforward, manually controllable precision. May require adjustment of the threshold based on context.
- Method 2: Using NumPy’s isclose Function. Utilizes a scientific library for numerical comparisons, reliable for a range of floating-point comparisons. Requires NumPy installation.
- Method 3: Truncate Small Coefficients Magnitude. Simple use of native Python functions. Precision level must be carefully chosen to avoid discarding significant digits.
- Method 4: Using SciPy’s Polynomial Class. Provides a professional and practical approach within the context of polynomial manipulation. Involves familiarity with SciPy and its API.
- Method 5: Python’s Filter Function. Offers a functional and elegant one-liner. Might be less intuitive for beginners and less flexible in terms of adjusting the tolerance inline.
import numpy as np coefficients = [2, -5e-15, 1e-12, 7] tolerance = 1e-14 trimmed_poly = [coef for coef in coefficients if not np.isclose(coef, 0, atol=tolerance)] print(trimmed_poly)
Output: [2, 7]
This approach utilizes the isclose function from the NumPy library to iteratively filter out the coefficients that are ‘close’ to zero within a certain absolute tolerance. The resulting list includes only the coefficients discernible from zero, effectively removing the small and negligible ones.
Method 3: Truncate Small Coefficients Magnitude
By truncating the magnitude of small coefficients using Python’s built-in round function, one can clear out coefficients that are insignificant when rounded to a certain number of decimal places.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] precision = 14 trimmed_poly = [coef if round(abs(coef), precision) != 0 else 0 for coef in coefficients] print(trimmed_poly)
Output: [2, 0, 0, 7]
The snippet rounds the absolute value of each coefficient to a defined precision and checks if the result is non-zero. If not, it replaces the coefficient with zero in the list. It highlights the importance of specifying the correct level of precision for the particular problem domain.
Method 4: Using SciPy’s Polynomial Class
The SciPy library provides a Polynomial class with a method to clean small coefficients. This method is particularly useful when working with polynomials, as it is designed for such operations and can be more expressive and purpose-driven.
Here’s an example:
from scipy.polynomial import Polynomial coefficients = [2, -5e-15, 1e-12, 7] p = Polynomial(coefficients) trimmed_poly = p.trim(tol=1e-14) print(trimmed_poly)
Output: Polynomial([2., 7.], domain=[-1, 1], window=[-1, 1])
This snippet uses SciPy’s Polynomial class to instantiate a polynomial object from the coefficients. The trim method is called, specifying a tolerance level to trim away small coefficients. The result is a Polynomial object with clean coefficients, from which the array of coefficients can be easily accessed if needed.
Bonus One-Liner Method 5: Python’s Filter Function
With Python’s filter function, one can easily create a one-liner to remove small coefficients by defining a filtering function that encapsulates the tolerance level, enabling concise and functional code.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] trimmed_poly = list(filter(lambda coef: abs(coef) > 1e-14, coefficients)) print(trimmed_poly)
Output: [2, 7]
This functional approach passes a lambda function to filter, which retains values that have an absolute magnitude greater than the defined threshold. The result of filter is a filter object, which is then converted into a list to get the final array of significant coefficients.
Summary/Discussion
- Method 1: Manual Threshold Trimming. Straightforward, manually controllable precision. May require adjustment of the threshold based on context.
- Method 2: Using NumPy’s isclose Function. Utilizes a scientific library for numerical comparisons, reliable for a range of floating-point comparisons. Requires NumPy installation.
- Method 3: Truncate Small Coefficients Magnitude. Simple use of native Python functions. Precision level must be carefully chosen to avoid discarding significant digits.
- Method 4: Using SciPy’s Polynomial Class. Provides a professional and practical approach within the context of polynomial manipulation. Involves familiarity with SciPy and its API.
- Method 5: Python’s Filter Function. Offers a functional and elegant one-liner. Might be less intuitive for beginners and less flexible in terms of adjusting the tolerance inline.
coefficients = [2, -5e-15, 1e-12, 7] threshold = 1e-14 trimmed_poly = [coef for coef in coefficients if abs(coef) > threshold] print(trimmed_poly)
Output: [2, 7]
This code snippet creates a list comprehension that iterates through each coefficient in the Hermite polynomial. It checks if the absolute value of the coefficient is greater than the manually defined threshold. If so, it includes the coefficient in the output list, effectively removing small trailing coefficients.
Method 2: Using NumPy’s isclose Function
NumPy’s isclose function allows to compare each coefficient against zero within a specified tolerance, handling floating-point arithmetic issues. It’s a robust and concise solution when working with numerical data in Python.
Here’s an example:
import numpy as np coefficients = [2, -5e-15, 1e-12, 7] tolerance = 1e-14 trimmed_poly = [coef for coef in coefficients if not np.isclose(coef, 0, atol=tolerance)] print(trimmed_poly)
Output: [2, 7]
This approach utilizes the isclose function from the NumPy library to iteratively filter out the coefficients that are ‘close’ to zero within a certain absolute tolerance. The resulting list includes only the coefficients discernible from zero, effectively removing the small and negligible ones.
Method 3: Truncate Small Coefficients Magnitude
By truncating the magnitude of small coefficients using Python’s built-in round function, one can clear out coefficients that are insignificant when rounded to a certain number of decimal places.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] precision = 14 trimmed_poly = [coef if round(abs(coef), precision) != 0 else 0 for coef in coefficients] print(trimmed_poly)
Output: [2, 0, 0, 7]
The snippet rounds the absolute value of each coefficient to a defined precision and checks if the result is non-zero. If not, it replaces the coefficient with zero in the list. It highlights the importance of specifying the correct level of precision for the particular problem domain.
Method 4: Using SciPy’s Polynomial Class
The SciPy library provides a Polynomial class with a method to clean small coefficients. This method is particularly useful when working with polynomials, as it is designed for such operations and can be more expressive and purpose-driven.
Here’s an example:
from scipy.polynomial import Polynomial coefficients = [2, -5e-15, 1e-12, 7] p = Polynomial(coefficients) trimmed_poly = p.trim(tol=1e-14) print(trimmed_poly)
Output: Polynomial([2., 7.], domain=[-1, 1], window=[-1, 1])
This snippet uses SciPy’s Polynomial class to instantiate a polynomial object from the coefficients. The trim method is called, specifying a tolerance level to trim away small coefficients. The result is a Polynomial object with clean coefficients, from which the array of coefficients can be easily accessed if needed.
Bonus One-Liner Method 5: Python’s Filter Function
With Python’s filter function, one can easily create a one-liner to remove small coefficients by defining a filtering function that encapsulates the tolerance level, enabling concise and functional code.
Here’s an example:
coefficients = [2, -5e-15, 1e-12, 7] trimmed_poly = list(filter(lambda coef: abs(coef) > 1e-14, coefficients)) print(trimmed_poly)
Output: [2, 7]
This functional approach passes a lambda function to filter, which retains values that have an absolute magnitude greater than the defined threshold. The result of filter is a filter object, which is then converted into a list to get the final array of significant coefficients.
Summary/Discussion
- Method 1: Manual Threshold Trimming. Straightforward, manually controllable precision. May require adjustment of the threshold based on context.
- Method 2: Using NumPy’s isclose Function. Utilizes a scientific library for numerical comparisons, reliable for a range of floating-point comparisons. Requires NumPy installation.
- Method 3: Truncate Small Coefficients Magnitude. Simple use of native Python functions. Precision level must be carefully chosen to avoid discarding significant digits.
- Method 4: Using SciPy’s Polynomial Class. Provides a professional and practical approach within the context of polynomial manipulation. Involves familiarity with SciPy and its API.
- Method 5: Python’s Filter Function. Offers a functional and elegant one-liner. Might be less intuitive for beginners and less flexible in terms of adjusting the tolerance inline.