spectral.h file

Dense spectral primitives: matvec, symmetric eigensolve, graph Laplacian.

Functions

void vm_matvec(vm_float_t* y, const vm_mat* A, const vm_float_t* x): Dense matrix-vector product y = A x.
void vm_symv(vm_float_t* y, const vm_mat* A, const vm_float_t* x): Symmetric matrix-vector product.
auto vm_syev(vm_mat* A, vm_float_t* eigenvalues, vm_mat* V) -> bool: Symmetric real eigenvalue decomposition (Jacobi).
auto vm_laplacian(vm_mat* L, const vm_mat* A) -> bool: Unnormalized graph Laplacian L = D − A.
auto vm_syev_topk(const vm_mat* A, int k, vm_float_t* eigenvalues, vm_mat* eigenvectors) -> bool: Top-k eigenvectors of a symmetric matrix.

Function documentation

void vm_matvec(vm_float_t* y, const vm_mat* A, const vm_float_t* x)

Dense matrix-vector product y = A x.

Parameters
y	Output vector.
A	Input matrix.
x	Input vector.

A is rows × cols. x has length cols, y has length rows.

void vm_symv(vm_float_t* y, const vm_mat* A, const vm_float_t* x)

Symmetric matrix-vector product.

Parameters
y	Output vector.
A	Symmetric matrix (lower triangle used).
x	Input vector.

Only the lower triangle of A is read. A must be square.

bool vm_syev(vm_mat* A, vm_float_t* eigenvalues, vm_mat* V)

Symmetric real eigenvalue decomposition (Jacobi).

Parameters
A	Symmetric matrix, overwritten on success.
eigenvalues	Output eigenvalues (length `n`), descending.
V	Optional `n × n` eigenvector matrix (columns).
Returns	true on success.

On success, eigenvalues are written in descending order. Eigenvector columns are written to V if non-NULL (V must be n × n). A is overwritten. Returns false on non-square, bad sizes, or numerical failure.

bool vm_laplacian(vm_mat* L, const vm_mat* A)

Unnormalized graph Laplacian L = D − A.

Parameters
L	Output Laplacian.
A	Symmetric adjacency (non-negative entries expected).
Returns	true on success.

From a dense symmetric adjacency matrix A. L is allocated or resized as needed.

bool vm_syev_topk(const vm_mat* A, int k, vm_float_t* eigenvalues, vm_mat* eigenvectors)

Top-k eigenvectors of a symmetric matrix.

Parameters
A	Symmetric matrix (not overwritten).
k	Number of leading eigenpairs (`1 ≤ k ≤ n`).
eigenvalues	Output eigenvalues (length `k`).
eigenvectors	Output `n × k` eigenvectors (columns).
Returns	true on success.

Thin wrapper around vm_syev. Eigenvalues descending. eigenvectors is n × k on success.