Enum BasisDesignScaleLaw 

pub enum BasisDesignScaleLaw {
    Invariant,
    NumericMultiplierDegreeOne,
    ReplicatedInner,
    TensorProductOfMarginals,
    RandomInterceptSlopeDegreesZeroAndOne,
    ChartSimilarityDegreeOne,
}

Transformation of the emitted design matrix.

Variants

Invariant

The declared joint coordinate/parameter action leaves every design entry invariant (up to floating-point roundoff).

NumericMultiplierDegreeOne

Scaling only the numeric multiplier by a sends X -> a*X; scaling an inner coordinate follows the child’s law.

ReplicatedInner

Wrapper design is a row gate/replication of its invariant inner design.

TensorProductOfMarginals

Tensor design is the row-wise product of invariant marginal designs.

RandomInterceptSlopeDegreesZeroAndOne

A random-intercept/slope block has alternating degree-zero and degree-one columns in each factor level: intercept columns are invariant and slope columns gain one power of the abscissa scale.

ChartSimilarityDegreeOne

Every design entry gains exactly one power of the chart scale a.

The constant-curvature smooth’s kernel is ℓ·(e^{−d_κ/ℓ} − 1), which is a LENGTH: the ℓ factor is what stops the realized design collapsing like 1/ℓ and dragging ρ̂ with it, and what makes the ℓ → ∞ face the finite geodesic-distance kernel rather than nothing (gam#2747, constant_curvature_kernel_matrix). Under x' = a·x, κ' = κ/a², ℓ' = a·ℓ the exponent d_κ/ℓ is invariant and the prefactor is not, so X' = a·X exactly.

This is equivariance, not a broken invariance: the design gains a power the penalty gains too, and a common positive factor on (X, S) is absorbed exactly by λ, so the fitted function is unchanged. A basis whose columns carry units is ordinary — a parametric x column does — and the alternative (a dimensionless kernel) is what confounded the range coordinate with the smoothing parameter.

Trait Implementations

impl Clone for BasisDesignScaleLaw

fn clone(&self) -> BasisDesignScaleLaw

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copy for BasisDesignScaleLaw

impl Debug for BasisDesignScaleLaw

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

Formats the value using the given formatter.

impl Eq for BasisDesignScaleLaw

impl PartialEq for BasisDesignScaleLaw

fn eq(&self, other: &BasisDesignScaleLaw) -> bool

Equality operator ==.

fn ne(&self, other: &Rhs) -> bool

Inequality operator !=.

impl StructuralPartialEq for BasisDesignScaleLaw