Struct DuchonBasisSpec 

pub struct DuchonBasisSpec {
    pub center_strategy: CenterStrategy,
    pub periodic: Option<Vec<Option<f64>>>,
    pub length_scale: Option<f64>,
    pub power: f64,
    pub nullspace_order: DuchonNullspaceOrder,
    pub identifiability: SpatialIdentifiability,
    pub aniso_log_scales: Option<Vec<f64>>,
    pub operator_penalties: DuchonOperatorPenaltySpec,
    pub boundary: OneDimensionalBoundary,
    pub radial_reparam: Option<Array2<f64>>,
}

Duchon-like basis configuration with explicit low-frequency null-space control and explicit spectral power.

Fields

center_strategy: CenterStrategy

periodic: Option<Vec<Option<f64>>>

length_scale: Option<f64>

Optional hybrid Matérn width. None means pure scale-free Duchon with spectrum ||w||^(2p + 2s). Some(length_scale) enables the hybrid spectrum ||w||^(2p) * (kappa^2 + ||w||^2)^s, kappa = 1/length_scale.

power: f64

Literal Duchon spectral power s (f64, fractional values fully threaded end-to-end). The pure-Duchon kernel exponent is 2(p + s) − d, so this is the knob that sets φ(r): s = 0 is the integer-order Duchon kernel r^{2p−d} (its r²·log r log case in even d, ≡ the thin-plate kernel); s = (d − 1)/2 gives the cubic r³ in every dimension.

This field is taken LITERALLY by the basis builder — power = 0 means s = 0, NOT “use a default”. The magic cubic default (applied when the user gives no explicit power) is a request-layer choice resolved by the formula / CLI / pyffi front-ends via duchon_cubic_default; by the time a spec reaches the builder this value is the final intended s. The hybrid Duchon–Matérn path (length_scale = Some) still requires an integer s (read via spec.power_as_usize()).

nullspace_order: DuchonNullspaceOrder

identifiability: SpatialIdentifiability

aniso_log_scales: Option<Vec<f64>>

Per-axis anisotropy log-scales η_a.

For hybrid Duchon (length_scale=Some), these are centered contrasts in the decomposition Λ = κA with det(A)=1. For pure Duchon (length_scale=None), they parameterize shape-only axis warping on the public path and are centered before basis evaluation/writeback so no global length scale is introduced.

When Some, the distance is r = √(Σ_a exp(2η_a) · (x_a - c_a)²). When None, isotropic distance r = ‖x - c‖ is used.

operator_penalties: DuchonOperatorPenaltySpec

boundary: OneDimensionalBoundary

radial_reparam: Option<Array2<f64>>

Data-metric radial reparameterization V (#1355), mirroring the thin-plate Wood-TPRS reparam. When Some, the constrained kernel transform is folded to Z·V so the realized design columns rotate into the G_c-orthonormal generalized eigenbasis of Ω_c v = μ G_c v and the native penalty becomes the diagonal curvature-per-unit-data-variance spectrum (mgcv’s cliff), preventing the REML over-smoothing collapse to EDF = 1. Frozen at the cold dense build and replayed verbatim by the predict / κ-trial / ψ-derivative paths so they stay bit-consistent with the fit-time design. None on the lazy/streaming path (huge n), which retains the original constrained basis.

Implementations

impl DuchonBasisSpec

pub fn power_as_usize(&self) -> usize

Integer view of power for the existing integer-only downstream chain. Non-finite or non-integer values fall back to 0 (the integer-only validators downstream already reject this case with a clear message).

Trait Implementations

impl Clone for DuchonBasisSpec

fn clone(&self) -> DuchonBasisSpec

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for DuchonBasisSpec

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for DuchonBasisSpec

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Serialize for DuchonBasisSpec

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.