Struct ThinPlateSplineBasis 

pub struct ThinPlateSplineBasis {
    pub basis: Array2<f64>,
    pub penalty_bending: Array2<f64>,
    pub penalty_ridge: Array2<f64>,
    pub num_kernel_basis: usize,
    pub num_polynomial_basis: usize,
    pub dimension: usize,
    pub radial_reparam: Array2<f64>,
}

Thin-plate regression spline basis and penalty (order m=2).

The returned basis has columns [K_c | P] where:

• K_c is the constrained radial basis block (K * Z) with P(knots)^T * α = 0 enforced via nullspace projection
• P is the TPS polynomial null-space block containing all monomials of total degree < m, where m = thin_plate_penalty_order(d) (so P is just [1, x_1, ..., x_d] for d <= 3)

The returned penalty matrix is block-diagonal with:

• upper-left Omega_c = Z^T Omega Z for the constrained radial block
• zero lower-right block for unpenalized polynomial terms.

For double-penalty GAMs, a second ridge penalty I is also returned so the caller can optimize (lambda_bending, lambdaridge) jointly.

Fields

basis: Array2<f64>

penalty_bending: Array2<f64>

penalty_ridge: Array2<f64>

num_kernel_basis: usize

num_polynomial_basis: usize

dimension: usize

radial_reparam: Array2<f64>

Wood-TPRS radial reparameterization matrix V.

Rows live in the side-constrained radial coefficient space. Columns are the retained positive bending eigendirections of Z' Ω Z; numerically near-null radial directions are dropped before the basis is exposed. Therefore V can be rectangular: design columns are Φ Z V, and the radial penalty is diag(Λ_retained).

Trait Implementations

impl Clone for ThinPlateSplineBasis

fn clone(&self) -> ThinPlateSplineBasis

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for ThinPlateSplineBasis

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

Formats the value using the given formatter.