Struct MeasureState 

pub struct MeasureState<F: SemiflowFloat, const D: usize> { /* private fields */ }

Sparse signed-measure state on M(ℝ^D) for adjoint Fokker-Planck Chernoff. Representation: finite weighted-Dirac sum + optional Gaussian background. Lemma A.1 pushes each Dirac at x to four children x±h, x+k, x with weights (1/4, 1/4, 1/2, τc). The 4^n blow-up is resolved by gridless.rs.

Implementations

impl<F: SemiflowFloat, const D: usize> MeasureState<F, D>

pub fn dirac(position: [F; D], weight: F) -> Self

Construct a single Dirac δ_position with signed weight.

pub fn gaussian( mean: [F; D], variance: F, weight: F, ) -> Result<Self, SemiflowError>

Construct a Gaussian-smoothed measure (isotropic variance).

Errors

SemiflowError::DomainViolation if variance ≤ 0 or weight non-finite.

pub fn from_particles(particles: &[([F; D], F)]) -> Self

Construct from (position, weight) pairs; no validity checks.

pub fn total_variation(&self) -> F

Total-variation norm ‖ρ‖_TV — rate modulator in Theorem A.2 (§38.4).

pub fn second_moment(&self) -> F

Second moment ⟨x², ρ⟩ — tightness monitor per Lemma A.3 (§38.5).

pub fn pair<G: Fn(&[F; D]) -> F>(&self, f: G) -> F

Dual pairing ⟨f, ρ⟩ for a test function f ∈ C_b. Gaussians use point evaluation at the mean.

pub fn n_diracs(&self) -> usize

Number of Dirac components (diagnostic).

pub fn first_moment(&self) -> [F; D]

Mass-weighted centre of mass (first moment), per axis (§38.12).

Returns E[x_d] = (Σ_diracs w·pos[d] + Σ_gauss w·mean[d]) / mass for each axis d, where mass = total_variation().

If mass = 0, returns all-zeros (undefined mean for the zero measure).

pub fn variance(&self) -> F

Total scalar variance Var = E[|x|²] − |E[x]|² (§38.12).

Uses mass-normalised second moment: E[|x|²] = second_moment() / mass. Returns 0 if mass = 0.

pub fn variance_per_axis(&self) -> [F; D]

Per-axis variance Var_d = E[x_d²] − (E[x_d])² (§38.12).

Returns all-zeros if mass = 0.

pub fn to_flat_buffers_d1(&self) -> (Vec<F>, Vec<F>)

where [F; 1]: Sized, F: Copy,

Extract Dirac positions and weights as (positions, weights) (D=1 binding ABI). Gaussians are not included; use on pure-Dirac states from apply_into. Used by G_BINDING_ADJOINT_FP_PARITY integration tests.

Trait Implementations

impl<F: Clone + SemiflowFloat, const D: usize> Clone for MeasureState<F, D>

fn clone(&self) -> Self

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<F: SemiflowFloat, const D: usize> State<F> for MeasureState<F, D>

State<F> impl for MeasureState<F, D> (dynamic-length signed measure).

len() = atom count (grows after axpy_into). axpy_into APPENDS atoms; norm_sup() returns ‖ρ‖_TV. Fixed-length invariants from GridFn1D do NOT apply here.

fn norm_sup(&self) -> F

Returns ‖ρ‖_TV as a surrogate (TV-norm is the natural measure norm).

fn len(&self) -> usize

Number of degrees of freedom (grid nodes, graph nodes, etc.).

fn axpy_into(&mut self, alpha: F, src: &Self)

In-place AXPY: self ← self + alpha · src. No allocation.

fn copy_from(&mut self, src: &Self)

Node-wise copy: self ← src. No allocation.

fn zero_into(&mut self)

Zero all nodes: self[i] ← 0 for all i. len() unchanged.

fn scale_into(&mut self, k: F)

In-place scale: self ← k · self.

fn is_empty(&self) -> bool

Returns true if this state has no nodes.