Struct FiniteRankOperator 

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

A finite-rank operator represented as a sum of rank-1 operators.

T = Σᵢ |vᵢ⟩⟨wᵢ|

where |vᵢ⟩⟨wᵢ| maps x to ⟨wᵢ, x⟩vᵢ.

Implementations

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

pub fn new( left_vectors: Vec<Multivector<P, Q, R>>, right_vectors: Vec<Multivector<P, Q, R>>, ) -> Result<Self>

Create a new finite-rank operator from left and right vectors.

pub fn rank_one(v: Multivector<P, Q, R>, w: Multivector<P, Q, R>) -> Self

Create a rank-1 operator |v⟩⟨w|.

pub fn get_rank(&self) -> usize

Get the rank of the operator.

pub fn to_matrix(&self) -> Result<MatrixOperator<P, Q, R>>

Convert to a matrix representation.

Trait Implementations

impl<const P: usize, const Q: usize, const R: usize> BoundedOperator<Multivector<P, Q, R>> for FiniteRankOperator<P, Q, R>

fn operator_norm(&self) -> f64

Compute or estimate the operator norm ||T||.

fn is_bounded_by(&self, bound: f64) -> bool

Check if the operator is bounded by a given constant.

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

fn clone(&self) -> FiniteRankOperator<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> CompactOperator<Multivector<P, Q, R>> for FiniteRankOperator<P, Q, R>

fn is_finite_rank(&self) -> bool

Check if the operator has finite rank.

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

Get the rank (dimension of range) if finite.

fn singular_values(&self) -> Result<Vec<f64>>

Get the singular values (if computable).

impl<const P: usize, const Q: usize, const R: usize> Debug for FiniteRankOperator<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> FredholmOperator<Multivector<P, Q, R>> for FiniteRankOperator<P, Q, R>

fn kernel_dimension(&self) -> usize

Compute the dimension of the kernel.

fn cokernel_dimension(&self) -> usize

Compute the dimension of the cokernel.

fn index(&self) -> i64

Compute the Fredholm index: dim(ker T) - dim(coker T).

fn is_isomorphism(&self) -> bool

Check if the operator is an isomorphism (index 0, trivial kernel).

impl<const P: usize, const Q: usize, const R: usize> LinearOperator<Multivector<P, Q, R>> for FiniteRankOperator<P, Q, R>

fn apply(&self, x: &Multivector<P, Q, R>) -> Result<Multivector<P, Q, R>>

Apply the operator to an element.

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

Get the domain dimension (None if infinite).

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

Get the codomain dimension (None if infinite).