Struct GraphFourierTransform 

pub struct GraphFourierTransform {
    pub eigenvalues: Array1<f64>,
    pub eigenvectors: Array2<f64>,
}

Graph Fourier Transform (GFT) based on the graph Laplacian eigenvectors.

The GFT projects a graph signal onto the frequency basis defined by the eigenvectors of the graph Laplacian L = D − A. Low-frequency components correspond to smooth signals (slowly varying across edges); high-frequency components to rapidly oscillating signals.

Fields

• eigenvalues — sorted Laplacian spectrum (graph frequencies) λ₀ ≤ λ₁ ≤ …
• eigenvectors — columns are eigenvectors (basis functions); shape (n, n)

Fields

eigenvalues: Array1<f64>

Graph frequencies (Laplacian eigenvalues), sorted ascending.

eigenvectors: Array2<f64>

Frequency basis: eigenvectors as columns, shape (n, n).

Implementations

impl GraphFourierTransform

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

Build a GFT from a weighted adjacency matrix.

Computes L = D − A and its full eigendecomposition.

pub fn from_laplacian(laplacian: &Array2<f64>) -> Result<Self>

Build a GFT directly from a precomputed Laplacian matrix.

pub fn num_nodes(&self) -> usize

Number of nodes (= size of frequency basis).

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

Forward GFT: x̂ = Uᵀ x.

Arguments

• signal — graph signal of length n (one value per node).

Returns

Spectral coefficients x̂ of length n.

pub fn inverse(&self, freq_signal: &Array1<f64>) -> Result<Array1<f64>>

Inverse GFT: x = U x̂.

Arguments

• freq_signal — spectral coefficients x̂ of length n.

Returns

Reconstructed graph signal x of length n.

Trait Implementations

impl Clone for GraphFourierTransform

fn clone(&self) -> GraphFourierTransform

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for GraphFourierTransform

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

Formats the value using the given formatter.