Struct Mgh09Rational 

pub struct Mgh09Rational;

Kowalik–Osborne rational function (NIST StRD MGH09 model).

y = amplitude · (x² + num_lin · x) / (x² + den_lin · x + den_const)

Parameters (in order): [amplitude, num_lin, den_lin, den_const]

Mapping from NIST MGH09 b-parameters:

• amplitude = b1 (≈ 0.1928)
• num_lin = b2 (≈ 0.1913; coefficient of x in the numerator)
• den_lin = b3 (≈ 0.1231; coefficient of x in the denominator)
• den_const = b4 (≈ 0.1361; constant term in the denominator)

Domain guard: D = x² + den_lin·x + den_const must be non-zero. The MGH09 certified parameters satisfy discriminant = den_lin² − 4·den_const < 0, which means D > 0 for all x. If D = 0 (or becomes zero during LM search), the function returns f64::NAN so the solver backs off.

Analytic Jacobian (let N = x² + num_lin·x, D = x² + den_lin·x + den_const):

• ∂y/∂amplitude = N/D
• ∂y/∂num_lin = amplitude · x / D
• ∂y/∂den_lin = −amplitude · N · x / D²
• ∂y/∂den_const = −amplitude · N / D²

Trait Implementations

impl Model for Mgh09Rational

fn eval(&self, x: &[f64], p: &[f64]) -> f64

Evaluate the model at coordinate x with the given params.

fn jacobian_into(&self, x: &[f64], p: &[f64], out: &mut [f64])

Fill a pre-allocated slice with Jacobian values (one entry per parameter).

fn jacobian(&self, x: &[f64], p: &[f64]) -> Vec<f64>

Jacobian — one derivative per parameter, in the same order as param_names().

fn param_names(&self) -> Vec<Cow<'static, str>>

Ordered parameter names, matching the layout expected by eval and jacobian.

fn eval_slice_into(&self, xs: &[f64], params: &[f64], out: &mut [f64])

Batch evaluation of a 1-D model: fill out[i] = eval([xs[i]], params).

fn jac_slice_into(&self, xs: &[f64], params: &[f64], out: &mut [f64])

Batch Jacobian for a 1-D model: fill out in row-major layout [i * params.len() + j] = d(model)/d(params[j]) at xs[i].

fn n_dims(&self) -> usize

Number of coordinate dimensions consumed from x. Defaults to 1.