Validation¶

The test suite (pytest, plus cargo test) checks the Rust implementation against independent references. The same tests run on the pure-numpy reference port and on the compiled package.

Check	Limit	Observed
Analytic \(\delta\) against an FFT Hilbert transform of \(\beta\), all four lineshapes	< 5e-6	about 2e-6
Rust against the numpy reference	rtol 1e-12	machine precision
Voigt with \(\gamma\to0\) against the Gaussian, \(\sigma\to0\) against the Lorentzian	< 1e-6, < 1e-5	5e-7, 3e-6
Thompson-Cox-Hastings pseudo-Voigt against the exact Voigt	< 2.5e-2	1.8e-2
Cu L-edge full model against kkcalc2 on the total \(\beta\)	< 2.5e-2 of max, < 2.5e-6 abs	2.0e-2, about 1e-6
Random models (peaks, scale, shift), 30 per size	1e-12	passes

Analytic \(\delta\) against the numerical Hilbert transform¶

Amplitude 1. Residual rows are analytic minus FFT; the slow linear drift is the finite window of the numerical transform.

Analytic delta against the FFT Hilbert transform for each lineshape

Full Cu L-edge model against kkcalc2¶

Gaussian peaks with analytic \(\delta\), on a kkcalc2 continuum table, against kkcalc2 applied to the total \(\beta\). The remainder is a near-constant offset of about 1e-6 against a \(\delta\) of order 1e-4.

Cu L-edge model against kkcalc2 with residual

The kkcalc2 version is pinned to one commit for the tests. Its output scales with the density argument, so tests use density=1.0 (see Concepts).

Speed¶

Speed tests require the Rust package to be no slower than the numpy reference, timed in the same run. Typical single-core results on 4001 points: Gaussian 2.7×, Lorentzian 1.9×, Voigt 1.6×, pseudo-Voigt 4.2×, a Cu model with 11 peaks and two steps 2.9× (170 µs). python -m benchmarks.bench reproduces the table.