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hetorch.utils.polynomial

Polynomial approximation utilities for non-linear functions

Provides Chebyshev and least-squares polynomial approximations for common activation functions used in neural networks.

Functions​

approximate_activation(activation: str, degree: int = 8, method: str = 'chebyshev', range_override: Optional[Tuple[float, float]] = None) -\> numpy.ndarray​

Approximate an activation function with a polynomial

Args: activation: Activation function name (relu, gelu, sigmoid, etc.) degree: Polynomial degree method: Approximation method ("chebyshev" or "least_squares") range_override: Optional custom range (min, max)

Returns: Polynomial coefficients (from constant to highest degree)

chebyshev_approximation(func: Callable[[numpy.ndarray], numpy.ndarray], degree: int, a: float, b: float) -\> numpy.ndarray​

Compute Chebyshev polynomial approximation coefficients

Uses Chebyshev interpolation to approximate a function over [a, b]

Args: func: Function to approximate degree: Polynomial degree a: Left endpoint of approximation range b: Right endpoint of approximation range

Returns: Polynomial coefficients (from constant to highest degree)

chebyshev_nodes(n: int, a: float, b: float) -\> numpy.ndarray​

Generate Chebyshev nodes in interval [a, b]

Args: n: Number of nodes (degree + 1) a: Left endpoint b: Right endpoint

Returns: Array of Chebyshev nodes

chebyshev_to_polynomial(cheb_coeffs: numpy.ndarray, a: float, b: float) -\> numpy.ndarray​

Convert Chebyshev coefficients to standard polynomial coefficients

Args: cheb_coeffs: Chebyshev coefficients a: Left endpoint of interval b: Right endpoint of interval

Returns: Standard polynomial coefficients

evaluate_polynomial(x: torch.Tensor, coeffs: numpy.ndarray) -\> torch.Tensor​

Evaluate polynomial with given coefficients using Horner's method

Args: x: Input tensor coeffs: Polynomial coefficients (from constant to highest degree)

Returns: Polynomial evaluation result

get_activation_function(activation: str) -\> Callable[[numpy.ndarray], numpy.ndarray]​

Get numpy implementation of activation function

Args: activation: Activation function name

Returns: Numpy function implementing the activation

get_activation_range(activation: str) -\> Tuple[float, float]​

Get default approximation range for common activation functions

Args: activation: Activation function name

Returns: Tuple of (min, max) for approximation range

least_squares_approximation(func: Callable[[numpy.ndarray], numpy.ndarray], degree: int, a: float, b: float, n_points: int = 1000) -\> numpy.ndarray​

Compute least-squares polynomial approximation

Args: func: Function to approximate degree: Polynomial degree a: Left endpoint b: Right endpoint n_points: Number of sample points

Returns: Polynomial coefficients (from constant to highest degree)

polynomial_to_string(coeffs: numpy.ndarray, var: str = 'x') -\> str​

Convert polynomial coefficients to human-readable string

Args: coeffs: Polynomial coefficients var: Variable name

Returns: String representation of polynomial