Struct SpectralDecomposition 

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

Spectral decomposition of a self-adjoint operator.

For a self-adjoint operator T, the spectral decomposition is: T = Σᵢ λᵢ Pᵢ

where λᵢ are eigenvalues and Pᵢ are orthogonal projections onto the corresponding eigenspaces.

Implementations

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

pub fn new(eigenpairs: Vec<Eigenpair<Multivector<P, Q, R>>>) -> Self

Create a new spectral decomposition from eigenpairs.

pub fn eigenpairs(&self) -> &[Eigenpair<Multivector<P, Q, R>>]

Get the eigenpairs.

pub fn eigenvalues(&self) -> Vec<Eigenvalue>

Get the eigenvalues.

pub fn eigenvectors(&self) -> Vec<&Multivector<P, Q, R>>

Get the eigenvectors.

pub fn is_complete(&self) -> bool

Check if the decomposition is complete.

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

Apply the operator T = Σᵢ λᵢ |vᵢ⟩⟨vᵢ| to a vector.

Computes Tx = Σᵢ λᵢ ⟨vᵢ, x⟩ vᵢ

pub fn apply_function<F>( &self, f: F, x: &Multivector<P, Q, R>, ) -> Multivector<P, Q, R>

where F: Fn(f64) -> f64,

Apply a function f to the operator: f(T) = Σᵢ f(λᵢ) |vᵢ⟩⟨vᵢ|.

This is the functional calculus for self-adjoint operators.

pub fn spectral_radius(&self) -> f64

Compute the spectral radius: max|λᵢ|.

pub fn condition_number(&self) -> Option<f64>

Compute the condition number (ratio of largest to smallest eigenvalue magnitudes).

pub fn is_positive_definite(&self) -> bool

Check if the operator is positive definite.

pub fn is_positive_semidefinite(&self) -> bool

Check if the operator is positive semi-definite.

Trait Implementations

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

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

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

Formats the value using the given formatter.