Struct gauss_quad::GaussLaguerre

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

A Gauss-Laguerre quadrature scheme.

These rules can perform integrals with integrands of the form x^alpha * e^(-x) * f(x) over the domain [0, ∞).

Example

Compute the factorial of 5:

// initialize a Gauss-Laguerre rule with 10 nodes
let quad = GaussLaguerre::init(10, 0.0);

// numerically evaluate this integral,
// which is a definition of the gamma function
let fact_5 = quad.integrate(|x| x.powi(5));

assert_abs_diff_eq!(fact_5, 1.0 * 2.0 * 3.0 * 4.0 * 5.0, epsilon = 1e-11);

Fields

nodes: Vec<f64>

weights: Vec<f64>

Implementations

impl GaussLaguerre

pub fn init(deg: usize, alpha: f64) -> GaussLaguerre

Initializes Gauss-Laguerre quadrature rule of the given degree by computing the nodes and weights needed for the given alpha parameter.

Panics

Panics if degree of quadrature is smaller than 2, or if alpha is smaller than -1

pub fn nodes_and_weights(deg: usize, alpha: f64) -> (Vec<f64>, Vec<f64>)

Apply Golub-Welsch algorithm to determine Gauss-Laguerre nodes & weights construct companion matrix A for the Laguerre Polynomial using the relation: -n L_{n-1} + (2n+1) L_{n} -(n+1) L_{n+1} = x L_n The constructed matrix is symmetric and tridiagonal with (2n+1) on the diagonal & -(n+1) on the off-diagonal (n = row number). Root & weight finding are equivalent to eigenvalue problem. see Gil, Segura, Temme - Numerical Methods for Special Functions

Panics

Panics if degree of quadrature is smaller than 2, or if alpha is smaller than -1

pub fn integrate<F>(&self, integrand: F) -> f64where F: Fn(f64) -> f64,

Perform quadrature of
x^alpha * e^(-x) * integrand
over the domain [0, ∞), where alpha was given in the call to init.

Trait Implementations

impl Clone for GaussLaguerre

fn clone(&self) -> GaussLaguerre

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for GaussLaguerre

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

Formats the value using the given formatter.

impl PartialEq for GaussLaguerre

fn eq(&self, other: &GaussLaguerre) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl StructuralPartialEq for GaussLaguerre