Struct OperatorSpectrum 

pub struct OperatorSpectrum {
    pub matrix: Vec<Vec<f64>>,
    pub n: usize,
}

Spectral analysis of compact operators represented as finite matrices.

Provides eigenvalue computation via power iteration, spectral radius estimation, and resolvent norm.

Fields

matrix: Vec<Vec<f64>>

Matrix representation of the operator (row-major, square).

n: usize

Size of the square matrix.

Implementations

impl OperatorSpectrum

pub fn new(matrix: Vec<Vec<f64>>) -> Self

Create an OperatorSpectrum from a square matrix.

Panics if the matrix is not square.

pub fn spectral_radius(&self, max_iter: usize) -> f64

Estimate the largest eigenvalue (spectral radius) via the power method.

Returns the dominant eigenvalue after max_iter iterations.

pub fn smallest_eigenvalue(&self, shift: f64, max_iter: usize) -> f64

Estimate the smallest eigenvalue via inverse power iteration with shift.

Uses Rayleigh quotient shift mu (default 0.0 ≈ smallest eigenvalue).

pub fn trace(&self) -> f64

Compute the trace of the matrix (sum of diagonal elements).

pub fn frobenius_norm(&self) -> f64

Compute the Frobenius norm ‖A‖_F = √(Σ aᵢⱼ²).

pub fn resolvent_norm(&self, lambda: f64) -> f64

Estimate the resolvent norm ‖(A - λI)⁻¹‖ at a regular point lambda.

Uses power iteration on the shifted operator (A - λI). Returns 1 / smallest_singular_value, approximated via the Frobenius norm of the shifted matrix.

pub fn apply(&self, v: &[f64]) -> Vec<f64>

Apply the operator (matrix-vector multiplication) to v.

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

Compute all diagonal elements (approximate eigenvalues of a diagonal operator).

Trait Implementations

impl Clone for OperatorSpectrum

fn clone(&self) -> OperatorSpectrum

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for OperatorSpectrum

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

Formats the value using the given formatter.