Struct SpectralMeasure 

pub struct SpectralMeasure {
    pub eigenvalues: Vec<f64>,
    pub projector_vectors: Vec<Vec<f64>>,
    pub dim: usize,
}

A simplified spectral measure (discrete version for finite matrices).

Fields

eigenvalues: Vec<f64>

Eigenvalues (the support of the spectral measure).

projector_vectors: Vec<Vec<f64>>

Spectral projections as rank-1 projectors (encoded as outer products of eigenvectors).

dim: usize

Dimension of the space.

Implementations

impl SpectralMeasure

pub fn diagonal(eigenvalues: Vec<f64>) -> Self

Creates a spectral measure from eigenvalues (diagonal matrix case).

pub fn apply_function<F: Fn(f64) -> f64>(&self, f: F) -> Vec<f64>

Applies a Borel function f to the operator via functional calculus. Returns the eigenvalues of f(A).

pub fn trace_of_function<F: Fn(f64) -> f64>(&self, f: F) -> f64

Computes trace(f(A)) = sum f(λ_i).

pub fn spectral_radius(&self) -> f64

Computes the spectral radius.

pub fn operator_norm(&self) -> f64

Computes the operator norm (largest |λ|).

pub fn is_positive(&self) -> bool

Checks if the operator is positive (all eigenvalues >= 0).

pub fn is_positive_definite(&self) -> bool

Checks if the operator is positive definite (all eigenvalues > 0).

pub fn sqrt_eigenvalues(&self) -> Option<Vec<f64>>

Computes the square root of a positive operator.

pub fn exp_eigenvalues(&self) -> Vec<f64>

Computes the exponential exp(A) eigenvalues.

pub fn log_eigenvalues(&self) -> Option<Vec<f64>>

Computes the logarithm log(A) for positive definite A.

Trait Implementations

impl Clone for SpectralMeasure

fn clone(&self) -> SpectralMeasure

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for SpectralMeasure

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

Formats the value using the given formatter.