Enum DuchonPsiDirection 

pub enum DuchonPsiDirection {
    Global,
    Axis(usize),
}

The outer coordinate a Duchon ψ-derivative differentiates (gam#2735).

The anisotropic Duchon metric is u² = Σ_a exp(2 ψ_a) h_a², and the ψ coordinates the outer REML solve owns are the raw ψ_a: each one decodes simultaneously into the global scale κ = exp(mean ψ) and the centered contrast η_a = ψ_a − mean ψ, so

    ∂ log κ / ∂ψ_a = 1/d           ∂η_b / ∂ψ_a = δ_ab − 1/d

Global is the all-ones direction of that frame — moving every ψ_a by the same amount leaves every contrast fixed and multiplies κ. That is not a convention, it is an identity, and it is what duchon_axis_log_kappa_derivatives reproduces by construction: summing its first derivative over a, and its second over (a, b), gives scaled_log_kappa_derivatives exactly. The isotropic route is therefore a contraction of the anisotropic one rather than a parallel derivation that could drift from it.

Variants

Global

ψ = log κ. Every contrast — and therefore every metric weight w_a = exp(2η_a) appearing explicitly in the operator-penalty blocks — is constant along this direction.

Axis(usize)

The raw per-axis coordinate ψ_a.

Trait Implementations

impl Clone for DuchonPsiDirection

fn clone(&self) -> DuchonPsiDirection

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copy for DuchonPsiDirection

impl Debug for DuchonPsiDirection

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

Formats the value using the given formatter.

impl Eq for DuchonPsiDirection

impl PartialEq for DuchonPsiDirection

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

Equality operator ==.

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

Inequality operator !=.

impl StructuralPartialEq for DuchonPsiDirection