Struct ChebyshevExpansion 

pub struct ChebyshevExpansion {
    pub coefficients: Vec<f64>,
}

Chebyshev expansion of a function f(x) ≈ Σ c_k T_k(x)

Fields

coefficients: Vec<f64>

Chebyshev coefficients c_k

Implementations

impl ChebyshevExpansion

pub fn new(coefficients: Vec<f64>) -> Self

Create from coefficients

pub fn from_function<F: Fn(f64) -> f64>(f: F, degree: usize) -> Self

Approximate function on [-1, 1] using n+1 Chebyshev nodes

pub fn heat_kernel(t: f64, degree: usize) -> Self

Approximate exp(-t*x) for heat kernel (x in [0, 2]) Maps [0, 2] to [-1, 1] via x’ = x - 1

pub fn low_pass(cutoff: f64, degree: usize) -> Self

Approximate low-pass filter: 1 if λ < cutoff, 0 otherwise Smooth transition via sigmoid-like function

pub fn eval(&self, x: f64) -> f64

Evaluate expansion at point x using Clenshaw recurrence More numerically stable than direct summation

pub fn eval_vector(&self, x: &[f64]) -> Vec<f64>

Evaluate expansion on vector: apply filter to each component

pub fn degree(&self) -> usize

Degree of expansion

pub fn truncate(&self, new_degree: usize) -> Self

Truncate to lower degree

pub fn add(&self, other: &Self) -> Self

Add two expansions

pub fn scale(&self, s: f64) -> Self

Scale by constant

pub fn derivative(&self) -> Self

Derivative expansion d/dx Σ c_k T_k(x) = Σ c’_k T_k(x)

Trait Implementations

impl Clone for ChebyshevExpansion

fn clone(&self) -> ChebyshevExpansion

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for ChebyshevExpansion

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.