Struct DuchonOperatorPenaltySpec 

pub struct DuchonOperatorPenaltySpec {
    pub mass: OperatorPenaltySpec,
    pub tension: OperatorPenaltySpec,
    pub stiffness: OperatorPenaltySpec,
}

Fields

mass: OperatorPenaltySpec

tension: OperatorPenaltySpec

stiffness: OperatorPenaltySpec

Implementations

impl DuchonOperatorPenaltySpec

pub fn all_disabled() -> Self

pub fn all_active() -> Self

All three operator dials active — used by the Matérn collocation overlay.

pub fn matern_for_smoothness(nu: MaternNu, d: usize) -> Self

Operator-penalty dials appropriate for a Matérn-ν kernel in dimension d.

The Matérn-ν RKHS is the Sobolev space H^m with m = ν + d/2: its squared norm controls the order-j derivative in L2 exactly when j ≤ m. The collocation overlay penalizes the squared L2 norms of the value (mass, D0, j=0), gradient (tension, D1, j=1) and Hessian (stiffness, D2, j=2). Activating a penalty whose derivative order exceeds the RKHS smoothness (j > m) imposes a roughness constraint the true kernel does NOT — it over-smooths the reduced-rank fit relative to the exact GP (mgcv bs="gp", GpGp).

Concretely the roughest Matérn, ν=1/2 in d=1 (m = 1), is the Ornstein–Uhlenbeck/exponential kernel: an H¹ process whose sample paths are continuous but non-differentiable. Although ∫(f')² is finite on its RKHS, the kernel itself already encodes the H¹ control; layering an extra tension dial on top biases the reduced-rank fit toward the smooth C¹ functions the kernel does not favour (and stiffness D2 toward C²), collapsing held-out oscillation (#707). We therefore gate each operator on j < m STRICTLY: mass (j=0) is always on, tension (j=1) is on for m > 1, stiffness (j=2) is on for m > 2. For ν ≥ 3/2 (or any d ≥ 2) every dial is active, recovering all_active; only the genuinely rough ν=1/2 (d=1) kernel — where the Sobolev order sits exactly on a derivative boundary — drops the higher operators.

Trait Implementations

impl Clone for DuchonOperatorPenaltySpec

fn clone(&self) -> DuchonOperatorPenaltySpec

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for DuchonOperatorPenaltySpec

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

Formats the value using the given formatter.

impl Default for DuchonOperatorPenaltySpec

fn default() -> Self

Returns the “default value” for a type.

impl<'de> Deserialize<'de> for DuchonOperatorPenaltySpec

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

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Serialize for DuchonOperatorPenaltySpec

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

where __S: Serializer,

Serialize this value into the given Serde serializer.