Struct MultivectorL2 

pub struct MultivectorL2<const P: usize, const Q: usize, const R: usize> { /* private fields */ }

The L² space of multivector-valued functions.

This is a Hilbert space with the L² inner product.

Type Parameters

• P - Number of positive signature basis vectors
• Q - Number of negative signature basis vectors
• R - Number of zero signature basis vectors

Implementations

impl<const P: usize, const Q: usize, const R: usize> MultivectorL2<P, Q, R>

pub const CODOMAIN_DIM: usize

The dimension of the Clifford algebra codomain.

pub fn new(domain: Domain<f64>) -> Self

Create a new L² space over a domain.

pub fn unit_interval() -> Self

Create an L² space over the unit interval [0, 1].

pub fn interval(a: f64, b: f64) -> Self

Create an L² space over [a, b].

pub fn with_quadrature_points(self, n: usize) -> Self

Set the number of quadrature points for numerical integration.

pub fn domain(&self) -> &Domain<f64>

Get the domain of the space.

pub fn signature(&self) -> (usize, usize, usize)

Get the signature of the Clifford algebra.

pub fn l2_inner_product( &self, f: &L2Function<P, Q, R>, g: &L2Function<P, Q, R>, ) -> f64

Compute the L² inner product of two functions.

pub fn l2_norm(&self, f: &L2Function<P, Q, R>) -> f64

Compute the L² norm of a 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 MultivectorL2<P, Q, R>

fn clone(&self) -> MultivectorL2<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 MultivectorL2<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).