Struct GraphUncertaintyPrinciple 

pub struct GraphUncertaintyPrinciple {
    pub spatial_distances_sq: Array1<f64>,
    pub ref_frequency: f64,
}

Graph uncertainty principle: spatial spread vs. spectral spread tradeoff.

Analogous to Heisenberg’s uncertainty principle, signals on graphs cannot be simultaneously concentrated in both the vertex domain and the spectral domain.

Spatial spread of signal x about reference node v₀: Δ_V²(x) = Σ_i d(i, v₀)² x_i² / ‖x‖²

Spectral spread about reference frequency λ₀: Δ_S²(x) = Σ_k (λ_k − λ₀)² x̂_k² / ‖x‖²

The product Δ_V Δ_S ≥ C for some graph-dependent constant.

Fields

spatial_distances_sq: Array1<f64>

Squared pairwise distances from each node to node v₀.

ref_frequency: f64

Reference frequency λ₀ (usually the DC frequency = 0).

Implementations

impl GraphUncertaintyPrinciple

pub fn new(adj: &Array2<f64>, v0: usize, ref_frequency: f64) -> Result<Self>

Build from BFS shortest-path distances from reference node v0.

Arguments

• adj — weighted adjacency matrix.
• v0 — reference node index (typically the “centre” of the signal).
• ref_frequency — spectral reference point (default: 0 for DC).

pub fn spatial_spread(&self, signal: &Array1<f64>) -> Result<f64>

Compute the spatial spread Δ_V(x) for signal x.

pub fn spectral_spread( &self, gft: &GraphFourierTransform, signal: &Array1<f64>, ) -> Result<f64>

Compute the spectral spread Δ_S(x) for signal x using the GFT.

pub fn uncertainty( &self, gft: &GraphFourierTransform, signal: &Array1<f64>, ) -> Result<(f64, f64, f64)>

Compute both spatial and spectral spreads and their product.

Returns (spatial_spread, spectral_spread, product).

Trait Implementations

impl Clone for GraphUncertaintyPrinciple

fn clone(&self) -> GraphUncertaintyPrinciple

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for GraphUncertaintyPrinciple

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

Formats the value using the given formatter.