Struct GaussianFixedCache 

pub struct GaussianFixedCache {
    pub xtwx_orig: Array2<f64>,
    pub xtwy_orig: Array1<f64>,
    pub centered_weighted_y_sq: f64,
    pub row_prediction_is_stale: bool,
    pub xtwx_sparse_orig: Option<Arc<SparseXtwxPrecomputed>>,
}

Reusable XᵀWX and XᵀW(y − offset) for Gaussian + Identity REML fits.

The Gaussian-identity P-IRLS short-circuit solves a single linear system (XᵀWX + Σ λ_k S_k + ρ·I) β = XᵀW(y − offset). The right-hand-side matrix and vector are independent of the smoothing parameters λ, so when the outer REML loop evaluates the same problem at many (λ_1, …, λ_k) candidates we only need to assemble them once before the loop and reuse them inside every inner PIRLS call.

Stored in original coordinates (no Qs rotation applied). When the inner solver uses a WorkingReparamTransform, it conjugates / projects these matrices on the fly — that step is O(p³) / O(p²), independent of N.

Fields

xtwx_orig: Array2<f64>

XᵀWX in the original coefficient basis. Symmetric, p × p.

xtwy_orig: Array1<f64>

XᵀW(y − offset) in the original basis. Length p.

centered_weighted_y_sq: f64

(y − offset)ᵀW(y − offset).

Together with xtwx_orig and xtwy_orig, this is the last scalar sufficient statistic needed to evaluate the Gaussian penalized RSS exactly at any λ without re-streaming the rows.

row_prediction_is_stale: bool

When true, the caller is deliberately serving a design-moving trial from sufficient statistics and the DesignMatrix rows on the current REML surface may be a stale reference surface. Consumers must not apply those rows for fitted values, RSS, or likelihood summaries.

xtwx_sparse_orig: Option<Arc<SparseXtwxPrecomputed>>

XᵀWX precomputed for the sparse path, aligned with the symbolic pattern of SparseXtWxCache::new(x) on the original sparse design. None when the design has no sparse form (e.g. dense-only fits).

The sparse REML path rebuilds H = XᵀWX + Sλ + δI per outer evaluation. For Gaussian-Identity the weights never change, so the XᵀWX contribution is invariant across the outer loop and can be scattered from this cached values vector instead of re-doing the O(nnz²/n) SpGEMM each call.

Trait Implementations

impl Debug for GaussianFixedCache

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

Formats the value using the given formatter.