Struct gauss_quad::GaussLegendre

pub struct GaussLegendre { /* private fields */ }

A Gauss-Legendre quadrature scheme.

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

Examples

Basic usage:

// initialize a Gauss-Legendre rule with 2 nodes
let quad = GaussLegendre::new(2)?;

// 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::new(1_000_000)?;

let integral = quad.integrate(-3.0, 3.0, |x| x.sin());

assert_abs_diff_eq!(integral, 0.0);

Implementations

impl GaussLegendre

pub fn new(deg: usize) -> Result<Self, GaussLegendreError>

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

Uses the algorithm by Ignace Bogaert, which has linear time complexity.

Errors

Returns an error if deg is smaller than 2.

pub fn par_new(deg: usize) -> Result<Self, GaussLegendreError>

Available on crate feature rayon only.

Same as new but runs in parallel.

Errors

Returns an error if deg is smaller than 2.

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

where F: Fn(f64) -> f64,

Perform quadrature integration of given integrand from a to b.

Example

Basic usage

let glq_rule = GaussLegendre::new(3)?;

assert_abs_diff_eq!(glq_rule.integrate(-1.0, 1.0, |x| x.powi(5)), 0.0);

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

where F: Fn(f64) -> f64 + Sync,

Available on crate feature rayon only.

Same as integrate but runs in parallel.

Example

let glq_rule = GaussLegendre::par_new(1_000_000)?;

assert_abs_diff_eq!(glq_rule.par_integrate(0.0, 1.0, |x| x.ln()), -1.0, epsilon = 1e-12);

impl GaussLegendre

pub fn nodes(&self) -> GaussLegendreNodes<'_>

Returns an iterator over the nodes of the quadrature rule.

pub fn weights(&self) -> GaussLegendreWeights<'_>

Returns an iterator over the weights of the quadrature rule.

pub fn iter(&self) -> GaussLegendreIter<'_>

Returns an iterator over the node-weight pairs of the quadrature rule.

pub fn as_node_weight_pairs(&self) -> &[(Node, Weight)]

Returns a slice of all the node-weight pairs of the quadrature rule.

pub fn into_node_weight_pairs(self) -> Vec<(Node, Weight)>

Converts the quadrature rule into a vector of node-weight pairs.

This function just returns the underlying vector without any computation or cloning.

pub fn degree(&self) -> usize

Returns the degree of the quadrature rule.

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<'de> Deserialize<'de> for GaussLegendre

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<'a> IntoIterator for &'a GaussLegendre

type IntoIter = GaussLegendreIter<'a>

Which kind of iterator are we turning this into?

type Item = &'a (f64, f64)

The type of the elements being iterated over.

fn into_iter(self) -> Self::IntoIter

Creates an iterator from a value.

impl IntoIterator for GaussLegendre

type IntoIter = GaussLegendreIntoIter

Which kind of iterator are we turning this into?

type Item = (f64, f64)

The type of the elements being iterated over.

fn into_iter(self) -> Self::IntoIter

Creates an iterator from a value.

impl PartialEq for GaussLegendre

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

Tests for self and other values to be equal, and is used by ==.

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

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

impl Serialize for GaussLegendre

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl StructuralPartialEq for GaussLegendre