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lineshapes

Fast, composable optical constants for soft X-ray work. A model is a sum of analytic peaks (Gaussian, Lorentzian, Voigt, pseudo-Voigt) on top of a fixed continuum, and evaluating it returns the complex optical constant \(\delta + i\beta\) on any energy grid.

The point of the design: every peak carries its exact Kramers-Kronig partner. When a fit changes a peak's position, width or height, \(\delta\) updates in closed form. No numerical KK transform runs inside the fitting loop.

  • Composable. Build a model by chaining gaussian, voigt, step, ... calls.
  • Fast. A Rust core: about 0.2 ms for a dozen peaks plus continuum on 4000 energies, single core, with an optional multi-core path.
  • Made for fitting. A flat parameter vector and a grid-bound Evaluator that recomputes only the peaks that changed, so finite-difference Jacobians are cheap.
  • Validated. Checked against a numpy reference, numerical Hilbert transforms and kkcalc2. See Validation.
  • Two packages, one version. A pure-Rust crate (lineshapes) and a Python package (lineshapes) built on it.

Install

Python (3.12+):

pip install lineshapes

The example scripts also need scipy and matplotlib: pip install "lineshapes[examples]".

Rust:

cargo add lineshapes

A first model

The package ships ZnPc and Alq3 carbon K-edge spectra, with each material's fixed continuum (Concepts). Add peaks on top of it and evaluate:

import numpy as np
from lineshapes import datasets

E = np.linspace(280, 300, 2001)

model = (
    datasets.continuum_model("znpc")        # fixed continuum: beta and its delta table
    .gaussian(e0=285.2, width=0.45, amp=1.4e-3)   # a pi* resonance
    .gaussian(e0=293.0, width=3.0, amp=0.8e-3)    # a broad sigma* resonance
)

n = model(E)                    # complex128: delta + 1j*beta
delta, beta = n.real, n.imag

Then see the worked examples: ZnPc NEXAFS and Alq3 optical constants, which fit real spectra and reproduce an independent \(\delta\) table from a \(\beta\) fit alone.

Concepts