[−][src]Struct gauss_quad::legendre::GaussLegendre

pub struct GaussLegendre {
    pub nodes: Vec<f64>,
    pub weights: Vec<f64>,
}

Fields

nodes: Vec<f64>weights: Vec<f64>

Methods

impl GaussLegendre[src]

pub fn init(deg: usize) -> GaussLegendre[src]

pub fn nodes_and_weights(deg: usize) -> (Vec<f64>, Vec<f64>)[src]

Apply Golub-Welsch algorithm to determine Gauss-Legendre nodes & weights construct companion matrix A for the Hermite Polynomial using the relation: (n+1)/(2n+1) P_{n+1} + n/(2n+1) P_{n-1} = x P_n A similar matrix that is symmetrized is constructed by C = D A D^{-1} where D is a diagonal matrix and det(C-t1) = det(A-t1) Resulting in a symmetric tridiagonal matrix with 0 on the diagonal & n/sqrt(4n^2 - 1) on the off-diagonal. Root & weight finding are equivalent to eigenvalue problem. see Gil, Segura, Temme - Numerical Methods for Special Functions

pub fn integrate<F>(&self, a: f64, b: f64, integrand: F) -> f64 where
    F: Fn(f64) -> f64, [src]

Perform quadrature of integrand using given nodes x and weights w

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