Struct SpectralAnalysis 

pub struct SpectralAnalysis {
    pub eigenvalues: Vec<f64>,
    pub spectral_gap: f64,
    pub algebraic_connectivity: f64,
    pub mixing_time_bound: f64,
    pub components: usize,
}

Result of spectral analysis on the verification graph.

Fields

eigenvalues: Vec<f64>

Eigenvalues of the normalised Laplacian, sorted ascending.

spectral_gap: f64

Spectral gap: λ₁ (the smallest non-zero eigenvalue).

algebraic_connectivity: f64

Algebraic connectivity (= λ₁ of the Laplacian).

mixing_time_bound: f64

Upper bound on mixing time from the spectral gap.

components: usize

Number of connected components (count of zero eigenvalues).

Implementations

impl SpectralAnalysis

pub fn from_network(network: &FlowNetwork) -> Self

Perform spectral analysis on a flow network’s Laplacian.

pub fn from_adjacency(adj: &Array2<f64>) -> Self

Perform spectral analysis on an arbitrary adjacency matrix.

pub fn heat_kernel_trace(&self, t: f64) -> f64

Heat kernel: H(t) = exp(-tL). Approximated via eigendecomposition.

Returns the heat kernel trace at time t.

Trait Implementations

impl Clone for SpectralAnalysis

fn clone(&self) -> SpectralAnalysis

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for SpectralAnalysis

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for SpectralAnalysis

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Serialize for SpectralAnalysis

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.