Struct DoniachSunjic 

pub struct DoniachSunjic;

Doniach–Šunjić asymmetric lineshape (XPS core-level peaks).

A · cos[πγ/2 + (1−γ)·atan((x−c)/σ)] / (1 + ((x−c)/σ)²)^((1−γ)/2)

Parameters (in order): [amplitude, center, sigma, gamma]

• gamma is the asymmetry index (0 ⇒ symmetric Lorentzian-like; larger ⇒ stronger high-binding-energy tail). amplitude scales the curve.

The area-normalising 1/σ^(1−γ) prefactor of the textbook form is folded into amplitude so the parameter set matches the other height-amplitude kernels; the numpy benchmark formula is identical, so numpy↔Rust parity is exact.

Trait Implementations

impl Model for DoniachSunjic

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

Analytical Jacobian of the Doniach–Šunjić lineshape.

Let u = (x−c)/σ, φ = πγ/2 + (1−γ)·atan(u), D = (1+u²)^((1−γ)/2), so f = A·cos(φ)/D.

∂f/∂A = cos(φ)/D

Shared factor for center/sigma (via ∂f/∂u): ∂f/∂u = A·(1−γ)·[−sin(φ)−cos(φ)·u] / ((1+u²)·D)

∂u/∂c = −1/σ ⟹ ∂f/∂c = ∂f/∂u · (−1/σ) ∂u/∂σ = −u/σ ⟹ ∂f/∂σ = ∂f/∂u · (−u/σ)

For gamma: ∂φ/∂γ = π/2 − atan(u), ∂D/∂γ = −½·ln(1+u²)·D ∂f/∂γ = A·[−sin(φ)·(π/2−atan(u)) + ½·cos(φ)·ln(1+u²)] / D

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

Evaluate the model at coordinate x with the given params.

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

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

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.