Struct Rule 

pub struct Rule<T> { /* private fields */ }

Quadrature rule for numerical integration.

Represents an approximation of an integral by a weighted sum over discrete points. The rule contains quadrature points x, weights w, and auxiliary arrays x_forward and x_backward for efficient computation.

Implementations

impl<T> Rule<T>

where T: Copy,

pub fn x(&self) -> &[T]

Quadrature points, in non-decreasing order

pub fn w(&self) -> &[T]

Quadrature weights, one per point

pub fn x_forward(&self) -> &[T]

Distance of each point from the left endpoint: x - a

pub fn x_backward(&self) -> &[T]

Distance of each point from the right endpoint: b - x

pub fn a(&self) -> T

Left endpoint of the integration interval

pub fn b(&self) -> T

Right endpoint of the integration interval

impl<T> Rule<T>

where T: CustomNumeric,

pub fn new(x: Vec<T>, w: Vec<T>, a: T, b: T) -> Result<Rule<T>, Error>

Create a new quadrature rule from points and weights.

Arguments

• x - Quadrature points
• w - Quadrature weights
• a - Left endpoint (default: -1.0)
• b - Right endpoint (default: 1.0)

The points are not checked for order or for lying in [a, b]; Self::validate does that.

Errors

Error::InvalidParameter if x and w have different lengths.

pub fn from_vectors(x: Vec<T>, w: Vec<T>, a: T, b: T) -> Result<Rule<T>, Error>

Create a new quadrature rule from vectors.

Errors

The errors of Self::new.

pub fn empty() -> Rule<T>

Create a default rule with empty arrays.

pub fn reseat(&self, a: T, b: T) -> Rule<T>

Reseat the rule to a new interval [a, b].

Scales and translates the quadrature points and weights to the new interval.

pub fn scale(&self, factor: T) -> Rule<T>

Scale the weights by a factor.

pub fn piecewise(&self, edges: &[T]) -> Result<Rule<T>, Error>

Create a piecewise rule over multiple segments.

Arguments

• edges - Segment boundaries: at least 2, finite and strictly increasing, with finite segment lengths and a finite sum of the ends of each segment (the midpoint of the segment is computed from it)

Errors

Error::InvalidParameter if edges does not meet these conditions

pub fn join(rules: &[Rule<T>]) -> Rule<T>

Join multiple rules into a single rule.

Arguments

• rules - Vector of rules to join (must be contiguous and sorted)

Panics

Panics if rules are empty, not contiguous, or not sorted.

pub fn convert<U>(&self) -> Rule<U>

where U: CustomNumeric + Copy + Debug + Display,

Convert the rule to a different numeric type.

pub fn validate(&self) -> bool

Validate the rule for consistency.

Returns

true if the rule is valid, false otherwise.

impl<T> Rule<T>

where T: CustomNumeric,

CustomNumeric-based implementation for f64 and Df64 support

pub fn new_custom(x: Vec<T>, w: Vec<T>, a: T, b: T) -> Result<Rule<T>, Error>

Create a new quadrature rule from points and weights (CustomNumeric version).

Errors

Error::InvalidParameter if x and w have different lengths.

pub fn from_vectors_custom( x: Vec<T>, w: Vec<T>, a: T, b: T, ) -> Result<Rule<T>, Error>

Create a new quadrature rule from vectors (CustomNumeric version).

Errors

The errors of Self::new_custom.

pub fn reseat_custom(&self, a: T, b: T) -> Rule<T>

Reseat the rule to a new interval [a, b] (CustomNumeric version).

pub fn scale_custom(&self, factor: T) -> Rule<T>

Scale the weights by a factor (CustomNumeric version).

pub fn validate_custom(&self) -> bool

Validate the rule for consistency (CustomNumeric version).

impl Rule<Compensated<f64, f64>>

Df64-specific implementation without ScalarOperand requirement

pub fn new_twofloat( x: Vec<Compensated<f64, f64>>, w: Vec<Compensated<f64, f64>>, a: Compensated<f64, f64>, b: Compensated<f64, f64>, ) -> Result<Rule<Compensated<f64, f64>>, Error>

Create a new quadrature rule from points and weights (Df64 version).

Errors

Error::InvalidParameter if x and w have different lengths.

pub fn from_vectors_twofloat( x: Vec<Compensated<f64, f64>>, w: Vec<Compensated<f64, f64>>, a: Compensated<f64, f64>, b: Compensated<f64, f64>, ) -> Result<Rule<Compensated<f64, f64>>, Error>

Create a new quadrature rule from vectors (Df64 version).

Errors

The errors of Self::new_twofloat.

pub fn reseat_twofloat( &self, a: Compensated<f64, f64>, b: Compensated<f64, f64>, ) -> Rule<Compensated<f64, f64>>

Reseat the rule to a new interval [a, b] (Df64 version).

pub fn scale_twofloat( &self, factor: Compensated<f64, f64>, ) -> Rule<Compensated<f64, f64>>

Scale the weights by a factor (Df64 version).

pub fn validate_twofloat(&self) -> bool

Validate the rule for consistency (Df64 version).

Trait Implementations

impl<T> Clone for Rule<T>

where T: Clone,

fn clone(&self) -> Rule<T>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<T> Debug for Rule<T>

where T: Debug,

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

Formats the value using the given formatter.