Struct GaussLaguerre

pub struct GaussLaguerre { /* private fields */ }

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 4 nodes
let quad = GaussLaguerre::new(4, 0.0)?;

// numerically evaluate the integral x^5*e^(-x),
// which is a definition of the gamma function of six
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-12);

Implementations

impl GaussLaguerre

pub fn new(deg: usize, alpha: f64) -> Result<Self, GaussLaguerreError>

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

A rule of degree n can integrate polynomials of degree 2n-1 exactly.

Applies the Golub-Welsch algorithm to determine Gauss-Laguerre nodes & weights. Constructs the 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

Errors

Returns an error if deg is smaller than 2, or if alpha is smaller than -1.

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

where F: Fn(f64) -> f64,

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

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

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

Available on crate feature rayon only.

Same as integrate but runs in parallel.

pub const fn alpha(&self) -> f64

Returns the value of the alpha parameter of the rule.

impl GaussLaguerre

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

Returns an iterator over the nodes of the quadrature rule.

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

Returns an iterator over the weights of the quadrature rule.

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

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 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<'de> Deserialize<'de> for GaussLaguerre

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 GaussLaguerre

type IntoIter = GaussLaguerreIter<'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 GaussLaguerre

type IntoIter = GaussLaguerreIntoIter

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 GaussLaguerre

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

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 GaussLaguerre