Struct GaussianLocationScaleChannelHessian 

pub struct GaussianLocationScaleChannelHessian { /* private fields */ }

Per-subject 2×2 channel Hessian W_i for Gaussian location-scale.

The row negative log-likelihood (with per-row weight w_i, response y_i, mean predictor μ_i, log-scale predictor s_i = log σ_i) is

ρ_i(μ, s) = w_i [s + 0.5·(y_i − μ)²·exp(−2s)]

The 2×2 Hessian in (μ, s) coordinates:

W_i[0,0] = w_i · exp(−2 s_i)                        ∂²ρ/∂μ²
W_i[1,1] = w_i · 2·(y_i − μ_i)²·exp(−2 s_i)        ∂²ρ/∂s²
W_i[0,1] = W_i[1,0] = w_i · 2·(y_i − μ_i)·exp(−2 s_i)  ∂²ρ/∂μ∂s

The off-diagonal cross-channel term ∂²ρ/∂μ∂s is nonzero whenever the residual (y_i − μ_i) ≠ 0, i.e. away from the fitted mean.

Implementations

impl GaussianLocationScaleChannelHessian

pub fn from_pilot_observed_unclamped( y: &Array1<f64>, w: &Array1<f64>, eta_mu: &Array1<f64>, eta_log_sigma: &Array1<f64>, ) -> Result<Self, String>

Construct the raw (un-PSD-clamped) per-subject observed Hessian.

For Gaussian location-scale the 2×2 observed Hessian [[w·e^{-2s}, 2·w·r·e^{-2s}], [2·w·r·e^{-2s}, 2·w·r²·e^{-2s}]] has determinant -2·w²·r²·e^{-4s} which is non-positive whenever the residual r = y − μ ≠ 0. Tests that finite-difference the row NLL must compare against this raw observed Hessian — PSD clamping alters the eigenvalues and the FD-versus-closed-form match fails.

Production code that needs a PSD matrix (e.g. the canonicalize gate) must call Self::from_pilot which PSD-clamps via 2×2 eigendecomposition.

pub fn from_pilot( y: &Array1<f64>, w: &Array1<f64>, eta_mu: &Array1<f64>, eta_log_sigma: &Array1<f64>, ) -> Result<Self, String>

Construct from pilot predictors (μ and log σ at current β) and data, with PSD eigenvalue clamping applied per subject.

y is the response, w the per-row sample weights, eta_mu and eta_log_sigma the current linear predictors. Negative eigenvalues are projected to zero (PSD clamp) before storage so the resulting matrix is a valid metric for the W-Gram identifiability compile.

Trait Implementations

impl FamilyChannelHessian for GaussianLocationScaleChannelHessian

fn n_outputs(&self) -> usize

Number of output channels n_outputs (= K in the row Jacobian).

fn n_subjects(&self) -> usize

Number of subjects (rows).

fn fill_subject(&self, i: usize, out: &mut [f64])

Fill the n_outputs × n_outputs per-subject channel Hessian W_i into out (row-major, length n_outputs * n_outputs) for subject i. Negative eigenvalues must be clamped to zero (PSD projection) before or inside this call.

fn evaluate_full(&self) -> Array3<f64>

Materialise the full (n_subjects × n_outputs × n_outputs) tensor. Default implementation calls fill_subject for each row.

fn channel_hessian_at( &self, beta: &[f64], family_scalars: Option<&Arc<dyn Any + Sync + Send>>, ) -> Result<Arc<dyn FamilyChannelHessian>, String>

Return a refreshed W evaluated at beta using family_scalars when those scalars carry the per-row primary state at the current β.