Struct PowerLawOffset 

pub struct PowerLawOffset;

Power-law with offset: amplitude · (offset + x)^(−1/shape)

Parameters (in order): [amplitude, offset, shape]

This is the NIST StRD Bennett5 model. It describes a power-law relationship of the form y = b1·(b2 + x)^(−1/b3) with the mapping:

• amplitude = b1 (≈ −2524 for Bennett5; may be negative)
• offset = b2 (≈ 46.7 for Bennett5; shifts x-origin)
• shape = b3 (≈ 0.932 for Bennett5; controls the exponent)

Domain guard: u = offset + x must be strictly positive so that ln(u) and u^p (with p = −1/shape) are finite. If u ≤ 0 the function returns f64::NAN (the LM solver will reject the step and backtrack).

Note: amplitude is the overall scale, NOT a peak-at-center value as in the spectral-peak convention documented in docs/reference/models/index.md. For Bennett5 the certified b1 is large and negative.

Analytic Jacobian (let u = offset + x, p = −1/shape):

• ∂y/∂amplitude = u^p
• ∂y/∂offset = amplitude · p · u^(p−1)
• ∂y/∂shape = amplitude · u^p · ln(u) · (1/shape²)

Trait Implementations

impl Model for PowerLawOffset

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.