Struct gauss_quad::legendre::GaussLegendre

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

A Gauss-Legendre quadrature scheme.

These rules can integrate functions on the domain [a, b].

Examples

Basic usage:

// initialize a Gauss-Legendre rule with 3 nodes
let quad = GaussLegendre::init(3);

// numerically integrate x^2 - 1/3 over the domain [0, 1]
let integral = quad.integrate(0.0, 1.0, |x| x * x - 1.0 / 3.0);

assert_abs_diff_eq!(integral, 0.0);

The nodes and weights are computed in O(n) time, so large quadrature rules are feasible:

let quad = GaussLegendre::init(1_000_000);
let integral = quad.integrate(-3.0, 3.0, |x| x.sin());
assert_abs_diff_eq!(integral, 0.0);

Fields

nodes: Vec<f64>

weights: Vec<f64>

Implementations

impl GaussLegendre

pub fn init(deg: usize) -> Self

Initializes a Gauss-Legendre quadrature rule of the given degree by computing the needed nodes and weights.

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

Compute the nodes and weights of a Gauss-Legendre quadrature rule of degree deg with the algorithm by Ignace Bogaert.

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

Perform quadrature integration of given integrand from a to b.

Example

Basic usage

let glq_rule = GaussLegendre::init(3);
assert_abs_diff_eq!(glq_rule.integrate(-1.0, 1.0, |x| x.powi(5)), 0.0);

Trait Implementations

impl Clone for GaussLegendre

fn clone(&self) -> GaussLegendre

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for GaussLegendre

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

Formats the value using the given formatter.

impl PartialEq for GaussLegendre

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