Struct DenseSpectralOperator 

pub struct DenseSpectralOperator { /* private fields */ }

Dense spectral Hessian operator using eigendecomposition.

Computes logdet, trace, and solve from a single eigendecomposition, guaranteeing spectral consistency. Indefinite or near-singular eigenvalues are handled via smooth spectral regularization r_ε(σ) rather than hard clamping, ensuring that logdet and inverse use the same smooth mapping.

Implementations

impl DenseSpectralOperator

pub fn from_symmetric(h: &Array2<f64>) -> Result<Self, String>

Create from a symmetric matrix (may be indefinite or singular).

The eigendecomposition is computed once. Eigenvalues are smoothly regularized via r_ε(σ). All subsequent operations (logdet, trace, solve) use the regularized spectrum, ensuring mathematical consistency.

pub fn from_symmetric_with_mode( h: &Array2<f64>, mode: PseudoLogdetMode, ) -> Result<Self, String>

Variant of from_symmetric that selects the log-determinant convention.

See PseudoLogdetMode for the derivation and the exact set of kernels that differ between the two modes. At a high level: Smooth keeps every eigenpair in play with a soft floor, whereas HardPseudo masks out σ_j ≤ ε consistently across logdet, gradient traces, cross-traces, and the H⁻¹ kernels.

pub fn logdet_gradient_factor(&self) -> &Array2<f64>

Factor F satisfying trace(G_epsilon(H) A) = trace(F^T A F).

Structured row-local operators use this to contract the logdet-gradient trace directly in row space without forming A F in coefficient space.

Trait Implementations

impl HessianOperator for DenseSpectralOperator

fn logdet(&self) -> f64

log|H|₊ — pseudo-logdet using only active eigenvalues/pivots.

fn as_exact_dense_spectral(&self) -> Option<&DenseSpectralOperator>

Exact dense spectral representation, when this backend has one.

fn assemble_h_dense_for_tangent_projection(&self) -> Result<Array2<f64>, String>

Assemble the raw dense Hessian represented by this backend for active-constraint tangent projection.

fn trace_hinv_product(&self, a: &Array2<f64>) -> f64

tr(H₊⁻¹ A) — trace of pseudo-inverse times a symmetric matrix. Uses the SAME decomposition as logdet.

fn solve(&self, rhs: &Array1<f64>) -> Array1<f64>

H⁻¹ v — linear solve using the active decomposition.

fn solve_multi(&self, rhs: &Array2<f64>) -> Array2<f64>

H⁻¹ M — multi-column solve.

fn trace_hinv_product_cross(&self, a: &Array2<f64>, b: &Array2<f64>) -> f64

tr(H⁻¹ A H⁻¹ B) for dense symmetric Hessian drifts.

fn trace_hinv_operator(&self, op: &dyn HyperOperator) -> f64

tr(H₊⁻¹ B) for an operator-backed Hessian drift.

fn trace_hinv_matrix_operator_cross( &self, matrix: &Array2<f64>, op: &dyn HyperOperator, ) -> f64

tr(H⁻¹ A H⁻¹ B) for a dense drift A and an operator-backed drift B.

fn trace_hinv_operator_cross( &self, left: &dyn HyperOperator, right: &dyn HyperOperator, ) -> f64

tr(H⁻¹ A H⁻¹ B) for operator-backed Hessian drifts.

fn trace_logdet_gradient(&self, a: &Array2<f64>) -> f64

tr(G_ε(H) A) — trace for the logdet gradient ∂_i log|R_ε(H)|.

fn xt_logdet_kernel_x_diagonal(&self, x: &DesignMatrix) -> Array1<f64>

diag(X · G_ε(H) · Xᵀ) — the leverage corresponding to trace_logdet_gradient. trace_logdet_gradient(Xᵀ diag(w) X) = Σᵢ wᵢ · h^G[i].

fn trace_logdet_block_local( &self, block: &Array2<f64>, scale: f64, start: usize, end: usize, ) -> f64

tr(G_ε(H) · A_block) where A_block is a p_block × p_block matrix embedded at rows/columns [start..end].

fn trace_logdet_operator(&self, op: &dyn HyperOperator) -> f64

tr(G_ε(H) B) for an operator-backed Hessian drift.

fn trace_logdet_hessian_cross( &self, h_i: &Array2<f64>, h_j: &Array2<f64>, ) -> f64

Cross-trace for the logdet Hessian: ∂²_{ij} log|R_ε(H)| = tr(G_ε Ḧ_{ij}) + spectral_cross(Ḣ_i, Ḣ_j).

fn trace_logdet_hessian_cross_matrix_operator( &self, h_i: &Array2<f64>, h_j: &dyn HyperOperator, ) -> f64

Operator-backed mixed form of [trace_logdet_hessian_cross].

fn trace_logdet_hessian_cross_operator( &self, h_i: &dyn HyperOperator, h_j: &dyn HyperOperator, ) -> f64

Operator-backed form of [trace_logdet_hessian_cross].

fn active_rank(&self) -> usize

Number of active dimensions (rank of pseudo-inverse).

fn dim(&self) -> usize

Full dimension of H.

fn is_dense(&self) -> bool

Whether this operator is backed by a dense factorization.

fn prefers_stochastic_trace_estimation(&self) -> bool

Whether the unified evaluator should batch large trace computations through the stochastic Hutchinson path for this operator.

fn logdet_traces_match_hinv_kernel(&self) -> bool

Whether stochastic Hutchinson estimates based on H⁻¹ are valid for logdet-gradient / logdet-Hessian trace terms on this backend.

fn as_dense_spectral(&self) -> Option<&DenseSpectralOperator>

Access the dense spectral backend when this operator is powered by a single eigendecomposition.

fn stochastic_trace_solve(&self, rhs: &Array1<f64>, rel_tol: f64) -> Array1<f64>

H⁻¹ v for stochastic trace probes.

fn stochastic_trace_solve_for_probe( &self, rhs: &Array1<f64>, rel_tol: f64, probe_id: u64, state: Option<&Arc<Mutex<StochasticTraceState>>>, ) -> Array1<f64>

H⁻¹ v for a deterministic stochastic trace probe id.

fn stochastic_trace_solve_multi( &self, rhs: &Array2<f64>, rel_tol: f64, ) -> Array2<f64>

H⁻¹ M for stochastic trace probes.

fn has_matrix_free_trace_cg_operator(&self) -> bool

Whether this backend exposes a matrix-free operator usable by trace CG.

fn trace_logdet_h_k( &self, a_k: &Array2<f64>, third_deriv_correction: Option<&Array2<f64>>, ) -> f64

Efficient computation of tr(G_ε(H) Hₖ) for the logdet gradient.