Struct L2Function 

pub struct L2Function<const P: usize, const Q: usize, const R: usize> { /* private fields */ }

A square-integrable multivector-valued function.

This represents an element of L²(Ω, Cl(P,Q,R)) - a function from domain Ω to the Clifford algebra that is square-integrable.

Implementations

impl<const P: usize, const Q: usize, const R: usize> L2Function<P, Q, R>

pub fn new<F>(f: F) -> Self

where F: Fn(&[f64]) -> Multivector<P, Q, R> + Send + Sync + 'static,

Create a new L² function from a closure.

pub fn eval(&self, point: &[f64]) -> Multivector<P, Q, R>

Evaluate the function at a point.

pub fn zero_function() -> Self

Create the zero function.

pub fn constant(value: Multivector<P, Q, R>) -> Self

Create a constant function.

Trait Implementations

impl<const P: usize, const Q: usize, const R: usize> BanachSpace<L2Function<P, Q, R>> for MultivectorL2<P, Q, R>

fn is_cauchy_sequence( &self, sequence: &[L2Function<P, Q, R>], tolerance: f64, ) -> bool

Check if a sequence appears to be Cauchy.

fn sequence_limit( &self, sequence: &[L2Function<P, Q, R>], tolerance: f64, ) -> Result<L2Function<P, Q, R>>

Compute the limit of a Cauchy sequence if it exists.

impl<const P: usize, const Q: usize, const R: usize> Clone for L2Function<P, Q, R>

fn clone(&self) -> L2Function<P, Q, R>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<const P: usize, const Q: usize, const R: usize> Debug for L2Function<P, Q, R>

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

Formats the value using the given formatter.

impl<const P: usize, const Q: usize, const R: usize> HilbertSpace<L2Function<P, Q, R>> for MultivectorL2<P, Q, R>

fn riesz_representative<F>(&self, _functional: F) -> Result<L2Function<P, Q, R>>

where F: Fn(&L2Function<P, Q, R>) -> f64,

Apply the Riesz representation theorem.

fn orthogonal_complement_projection(&self, x: &V, subspace_basis: &[V]) -> V

where S: Into<f64> + From<f64>, V: Clone,

Compute the orthogonal complement projection.

fn best_approximation(&self, x: &V, subspace_basis: &[V]) -> V

where S: Into<f64> + From<f64>, V: Clone,

Compute the best approximation to x from a subspace.

fn is_orthonormal(&self, vectors: &[V], tolerance: f64) -> bool

where S: Into<f64>,

Check if a set of vectors forms an orthonormal system.

impl<const P: usize, const Q: usize, const R: usize> InnerProductSpace<L2Function<P, Q, R>> for MultivectorL2<P, Q, R>

fn inner_product(&self, f: &L2Function<P, Q, R>, g: &L2Function<P, Q, R>) -> f64

Compute the inner product of two vectors.

fn project( &self, f: &L2Function<P, Q, R>, g: &L2Function<P, Q, R>, ) -> L2Function<P, Q, R>

Project x onto y.

fn gram_schmidt( &self, functions: &[L2Function<P, Q, R>], ) -> Vec<L2Function<P, Q, R>>

Gram-Schmidt orthogonalization of a set of vectors.

fn are_orthogonal(&self, x: &V, y: &V, tolerance: f64) -> bool

where S: Into<f64>,

Check if two vectors are orthogonal.

impl<const P: usize, const Q: usize, const R: usize> NormedSpace<L2Function<P, Q, R>> for MultivectorL2<P, Q, R>

fn norm(&self, f: &L2Function<P, Q, R>) -> f64

Compute the norm of a vector.

fn normalize(&self, f: &L2Function<P, Q, R>) -> Option<L2Function<P, Q, R>>

Normalize a vector to unit length.

fn distance(&self, x: &V, y: &V) -> f64

Compute the distance between two vectors.

impl<const P: usize, const Q: usize, const R: usize> VectorSpace<L2Function<P, Q, R>> for MultivectorL2<P, Q, R>

fn add( &self, f: &L2Function<P, Q, R>, g: &L2Function<P, Q, R>, ) -> L2Function<P, Q, R>

Add two vectors.

fn sub( &self, f: &L2Function<P, Q, R>, g: &L2Function<P, Q, R>, ) -> L2Function<P, Q, R>

Subtract two vectors.

fn scale(&self, scalar: f64, f: &L2Function<P, Q, R>) -> L2Function<P, Q, R>

Multiply a vector by a scalar.

fn zero(&self) -> L2Function<P, Q, R>

Return the zero vector.

fn dimension(&self) -> Option<usize>

Return the dimension of the space (may be infinite).