Struct SimdSpectral 

pub struct SimdSpectral;

SIMD-accelerated operations for spectral graph methods.

Provides optimized kernels for Laplacian construction, eigenvalue iteration helpers, and spectral embedding computations.

Implementations

impl SimdSpectral

pub fn standard_laplacian( adjacency: &Array2<f64>, degrees: &Array1<f64>, ) -> Result<Array2<f64>>

Construct the standard graph Laplacian L = D - A using SIMD.

The Laplacian is computed row-by-row: L[i,j] = degree[i] * delta(i,j) - A[i,j]. SIMD acceleration is applied to the row-level subtraction.

Arguments

• adjacency - The adjacency matrix (n x n)
• degrees - The degree vector (length n)

Returns

The standard Laplacian matrix.

pub fn normalized_laplacian( adjacency: &Array2<f64>, degrees: &Array1<f64>, ) -> Result<Array2<f64>>

Construct the normalized Laplacian L_norm = I - D^{-1/2} A D^{-1/2} using SIMD.

Arguments

• adjacency - The adjacency matrix (n x n)
• degrees - The degree vector (length n)

Returns

The normalized Laplacian matrix.

pub fn random_walk_laplacian( adjacency: &Array2<f64>, degrees: &Array1<f64>, ) -> Result<Array2<f64>>

Construct the random-walk Laplacian L_rw = I - D^{-1} A using SIMD.

Arguments

• adjacency - The adjacency matrix (n x n)
• degrees - The degree vector (length n)

Returns

The random-walk Laplacian matrix.

pub fn compute_degree_inv_sqrt(degrees: &Array1<f64>) -> Array1<f64>

Compute D^{-1/2} vector using SIMD acceleration.

For each degree d, computes 1/sqrt(d) if d > 0, else 0.

Arguments

• degrees - The degree vector

Returns

The D^{-1/2} diagonal vector.

pub fn power_iteration( matrix: &Array2<f64>, initial: &Array1<f64>, max_iterations: usize, tolerance: f64, ) -> Result<(f64, Array1<f64>, usize)>

SIMD-accelerated power iteration for finding the dominant eigenvector.

Used in spectral methods to find eigenvectors of the Laplacian.

Arguments

• matrix - Symmetric matrix (n x n)
• initial - Initial guess vector (length n)
• max_iterations - Maximum iterations
• tolerance - Convergence tolerance

Returns

A tuple of (eigenvalue, eigenvector, iterations used).

pub fn gram_schmidt_orthogonalize(vectors: &mut Array2<f64>)

SIMD-accelerated Gram-Schmidt orthogonalization.

Orthogonalizes a set of column vectors in-place.

Arguments

• vectors - Matrix whose columns are vectors to orthogonalize (n x k)

pub fn rayleigh_quotient( matrix: &Array2<f64>, vector: &ArrayView1<'_, f64>, ) -> Result<f64>

SIMD-accelerated Rayleigh quotient: v^T M v / (v^T v).

Arguments

• matrix - Symmetric matrix (n x n)
• vector - Input vector (length n)

Returns

The Rayleigh quotient value.