Struct Tauc 

pub struct Tauc;

Tauc optical band-gap edge: A · ((x − e_gap) · H(x − e_gap))^p.

Parameters (in order): [amplitude, e_gap, exponent]

• amplitude (A) scales the absorption above the gap.
• e_gap is the optical band-gap energy: the edge onset. Below it the model is exactly 0 (Heaviside H(x − e_gap)); at and above it the absorption rises as a power law in the excess energy (x − e_gap).
• exponent (p) is the Tauc power (p = 2 for an allowed indirect transition, p = 1/2 for an allowed direct one). The classic Tauc plot fits (α·hν)^{1/p} linearly in hν; here we expose the forward edge A·(hν − E_g)^p directly.

The kernel is 0 for x ≤ e_gap (where the base (x − e_gap) is non-positive and a fractional exponent would otherwise be NaN). The numpy benchmark formula is identical — np.where(x > e_gap, A·(x − e_gap)^p, 0) — so numpy↔Rust parity is exact.

Trait Implementations

impl Model for Tauc

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

Central finite-difference Jacobian. The Heaviside cut-off makes the closed-form derivative piecewise (and the power law’s ∂/∂e_gap diverges as x → e_gap⁺ for exponent < 1), so a numerical Jacobian is used — matching log_normal.

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

Evaluate the model at coordinate x with the given params.

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

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

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

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

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.