Struct gauss_quad::GaussJacobi

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

A Gauss-Jacobi quadrature scheme.

These rules can approximate integrals with singularities at the end points of the domain, [a, b].

Examples

// initialize the quadrature rule.
let quad = GaussJacobi::init(10, -0.5, 0.0);

// numerically integrate e^-x / sqrt(1 + x).
let integral = quad.integrate(-1.0, 1.0, |x| (-x).exp());

let dawson_function_of_sqrt_2 = 0.4525399074037225;
assert_abs_diff_eq!(integral, 2.0 * E * dawson_function_of_sqrt_2, epsilon = 1e-14);

Fields

nodes: Vec<f64>

weights: Vec<f64>

Implementations

impl GaussJacobi

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

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

Panics

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

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

Apply Golub-Welsch algorithm to determine Gauss-Jacobi nodes & weights see Gil, Segura, Temme - Numerical Methods for Special Functions

Panics

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

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

Perform quadrature of integrand from a to b. This will integrate
(1 - x)^alpha * (1 + x)^beta * integrand
where alpha and beta were given in the call to init.

Trait Implementations

impl Clone for GaussJacobi

fn clone(&self) -> GaussJacobi

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for GaussJacobi

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

Formats the value using the given formatter.

impl PartialEq for GaussJacobi

fn eq(&self, other: &GaussJacobi) -> 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 GaussJacobi