Struct CircularGaussianFit2d 

pub struct CircularGaussianFit2d { /* private fields */ }

Maximum-likelihood fit of a Gaussian-blurred circle in two dimensions.

The generative model is

X = center + radius * U + epsilon,

where U is uniform on the unit circle and epsilon ~ N(0, noise_variance * I_2). Integrating out U gives the proper Cartesian density

p(x) = exp(-(r^2 + R^2)/(2s)) I0(Rr/s) / (2 pi s).

Unlike a Gaussian density assigned directly to the nonnegative radius, this density is normalized on the plane, remains finite at the center, and has no artificial 1/r singularity. The center is fitted jointly with (R, s) by latent-angle EM instead of being frozen at the coordinate mean.

Implementations

impl CircularGaussianFit2d

pub const NUM_FREE_PARAMETERS: usize = 4

Two center coordinates, one radius, and one isotropic noise variance.

pub fn from_parameters( center: [f64; 2], radius: f64, noise_variance: f64, ) -> Result<Self, String>

Construct a circular Gaussian from validated model parameters.

pub fn fit(coords: ArrayView2<'_, f64>, rows: &[usize]) -> Result<Self, String>

Fit selected rows of a finite two-column coordinate matrix.

pub const fn center(self) -> [f64; 2]

Fitted circle center.

pub const fn radius(self) -> f64

Fitted latent-circle radius.

pub const fn noise_variance(self) -> f64

Fitted isotropic Cartesian noise variance per coordinate.

pub fn log_density(self, x: f64, y: f64) -> f64

Proper Cartesian log density at (x, y).

pub fn log_likelihood( self, coords: ArrayView2<'_, f64>, rows: &[usize], ) -> Result<f64, String>

Sum the fitted log density over selected rows.

pub fn fit_with_bic( coords: ArrayView2<'_, f64>, rows: &[usize], ) -> Result<(Self, f64), String>

Fit selected rows and return both the fit and its BIC/2 (lower is better). Keeping fitting and evidence evaluation in one operation makes it impossible to label a likelihood on unrelated data as fitted BIC.

Trait Implementations

impl Clone for CircularGaussianFit2d

fn clone(&self) -> CircularGaussianFit2d

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copy for CircularGaussianFit2d

impl Debug for CircularGaussianFit2d

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

Formats the value using the given formatter.