Struct TrueVoigt 

pub struct TrueVoigt;

True Voigt profile (Gaussian ⊗ Lorentzian) via the Faddeeva function.

A · Re[w(z)] / Re[w(z₀)], with z = ((x−c) + iγ)/(σ√2) and z₀ = iγ/(σ√2), so amplitude is the peak height (A at x=c).

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

• sigma is the Gaussian standard deviation, gamma the Lorentzian HWHM. γ→0 ⇒ Gaussian; σ→0 ⇒ Lorentzian. Distinct from the voigt/pseudo_voigt key, which is the linear pseudo-Voigt approximation.

Trait Implementations

impl Model for TrueVoigt

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

Analytical Jacobian of the true Voigt profile.

Uses the Faddeeva derivative identity: dw(z)/dz = −2z·w(z) + 2i/√π, which gives (treating z_r and z_i as independent real parameters):

∂Re[w]/∂z_r = Re[dw/dz] = −2(z_r·w_r − z_i·w_i) ∂Re[w]/∂z_i = −Im[dw/dz] = 2(z_r·w_i + z_i·w_r) − 2/√π

where (w_r, w_i) = faddeeva_complex(z_r, z_i).

For the profile f = A·w_r / peak0 (with peak0 = Re[w(0, z_i)]):

∂f/∂A = w_r / peak0 ∂f/∂c = A / peak0 · dwr_dzr · (−inv) [∂z_r/∂c = −inv] ∂f/∂σ and ∂f/∂γ use the quotient rule because peak0 also changes.

Accuracy note

The HAW approximation has ≈1e-6 accuracy; the Jacobian inherits that floor, so the self-consistency test uses tolerance 1e-5 (10× the default analytic budget). This is a justified relaxation, not a correctness gap.

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.