Struct ChebyshevPolynomial 

pub struct ChebyshevPolynomial;

Chebyshev polynomials of the first kind: T_n(x).

Provides evaluation via the three-term recurrence, Chebyshev nodes on [-1, 1], differentiation matrix for spectral differentiation, and interpolation coefficients from function values at Chebyshev nodes.

Implementations

impl ChebyshevPolynomial

pub fn eval(n: usize, x: f64) -> f64

Evaluate T_n(x) using the recurrence T_0=1, T_1=x, T_{n+1}=2x T_n - T_{n-1}.

pub fn eval_all(n: usize, x: f64) -> Vec<f64>

Evaluate all Chebyshev polynomials T_0(x), …, T_n(x).

pub fn nodes(n: usize) -> Vec<f64>

Return the n+1 Chebyshev-Gauss-Lobatto nodes on [-1, 1]: x_j = cos(j*pi/n), j = 0, …, n.

pub fn gauss_nodes(n: usize) -> Vec<f64>

Return the n interior Chebyshev-Gauss nodes on (-1, 1): x_j = cos((2j+1)*pi / (2n)), j = 0, …, n-1.

pub fn diff_matrix(n: usize) -> Vec<Vec<f64>>

Compute the (n+1) x (n+1) spectral differentiation matrix at Chebyshev-Gauss-Lobatto nodes.

The entry D[i][j] approximates the derivative of the j-th basis function at node x_i.

pub fn interpolation_coeffs(vals: &[f64]) -> Vec<f64>

Compute Chebyshev expansion coefficients from function values at Chebyshev-Gauss-Lobatto nodes using the DCT-I formula.

Returns coefficients a_k such that f(x) ≈ Σ a_k T_k(x).

pub fn eval_series(coeffs: &[f64], x: f64) -> f64

Evaluate the Chebyshev series with coefficients coeffs at point x.