Struct EvaluationDomain

pub struct EvaluationDomain<F: Field> { /* private fields */ }

A domain that univariate polynomials may be evaluated on.

An evaluation domain of size d + 1 together with polynomial values on that domain uniquely defines a degree <= d polynomial.

Implementations

impl<F: Field> EvaluationDomain<F>

pub fn from_points(points: Vec<F>) -> Self

Create a new evaluation domain from a set of points.

Arguments

• points - The points that define the domain

Panics

• If any points are repeated (not distinct)

pub fn size(&self) -> usize

pub fn points(&self) -> &[F]

pub fn lagrange_evals(&self, x: F) -> Vec<F>

Compute a vector of Lagrange polynomial evaluations in $O(N)$ at a given point x.

For an evaluation domain consisting of points $x_i$ Lagrange polynomials $L_i(x)$ are defined by

$$L_i(x) = \prod_{j \neq i}\frac{x - \pi_j}{\pi_i - \pi_j}$$

pub fn extrapolate(&self, values: &[F], x: F) -> F

Evaluate the unique interpolated polynomial at any point x.

Computational complexity is $O(n)$, for a domain of size $n$.

Trait Implementations

impl<F: Clone + Field> Clone for EvaluationDomain<F>

fn clone(&self) -> EvaluationDomain<F>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<F: Debug + Field> Debug for EvaluationDomain<F>

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

Formats the value using the given formatter.