Struct GaussChebyshevSecondKind

pub struct GaussChebyshevSecondKind { /* private fields */ }

A Gauss-Chebyshev quadrature scheme of the second kind.

Used to integrate functions of the form f(x) * sqrt(1 - x^2) on finite intervals.

Example

let rule = GaussChebyshevSecondKind::new(2)?;

assert_relative_eq!(rule.integrate(-1.0, 1.0, |x| x * x), PI / 8.0);

Implementations

impl GaussChebyshevSecondKind

pub fn new(degree: usize) -> Result<Self, GaussChebyshevError>

Create a new GaussChebyshev rule that can integrate functions of the form f(x) * sqrt(1 - x^2).

Errors

Returns an error if degree is less than 2.

pub fn par_new(degree: usize) -> Result<Self, GaussChebyshevError>

Available on crate feature rayon only.

Same as new but runs in parallel.

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

where F: Fn(f64) -> f64,

Returns the value of the integral of the given integrand in the inverval [a, b].

Example

let rule = GaussChebyshevSecondKind::new(2)?;

assert_relative_eq!(rule.integrate(-1.0, 1.0, |x| 1.5 * x * x - 0.5), -PI / 16.0);

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.

impl GaussChebyshevSecondKind

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

Returns an iterator over the nodes of the quadrature rule.

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

Returns an iterator over the weights of the quadrature rule.

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

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 GaussChebyshevSecondKind

fn clone(&self) -> GaussChebyshevSecondKind

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for GaussChebyshevSecondKind

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for GaussChebyshevSecondKind

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

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl From<GaussChebyshevSecondKind> for GaussJacobi

Gauss-Chebyshev quadrature of the second kind is equivalent to Gauss-Jacobi quadrature with alpha = beta = 0.5.

fn from(value: GaussChebyshevSecondKind) -> Self

Converts to this type from the input type.

impl<'a> IntoIterator for &'a GaussChebyshevSecondKind

type IntoIter = GaussChebyshevSecondKindIter<'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 GaussChebyshevSecondKind

type IntoIter = GaussChebyshevSecondKindIntoIter

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 GaussChebyshevSecondKind

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

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 GaussChebyshevSecondKind