100 Fitting Functions — Catalog & Implementation Status¶

Authoritative target catalog for the benchmark: lineshapes, UV/VIS, IR, XAS K-/L-edge, time-resolved XAS, 2-D RIXS, noise models, and optimization benchmark functions. The optimization landscapes (Part 9) are attributed to primary literature and survey citations there; useful-math-functions is the implementation the Rust kernels are ported from, not the literature origin of the functions themselves.

See the Model Reference for the canonical formulas and parameter names of every currently-implemented (✅) model below — this page tracks the broader target catalog and what's still planned.

Status legend - ✅ implemented — a Rust kernel in MODEL_REGISTRY (or a LANDSCAPE_REGISTRY entry) - ◐ expressible — no new kernel; a CaseSpec/CaseFamily recipe of existing kernels - 🔲 kernel — needs a new 1-D Rust kernel via the multi-crate path (see below) - 🧩 engine — needs an engine feature (2-D fit subject / IRF convolution / \(\chi(k)\) class / noise knob) - — analysis — a post-fit derived quantity, not a fittable curve (out of scope)

The multi-crate path for a 🔲 kernel (one new shape): crates/spectrafit-models/src/<name>.rs (Model: eval + param_names + FD Jacobian) → ModelTypeStr variant + its match arm in ModelTypeStr::as_str() in crates/spectrafit-types (the single canonical wire-format string per model — callers in spectrafit-graph::compiler and spectrafit-varpro read this method; there are no longer duplicate per-crate model_type_to_str tables to update) → Python ModelType → bench register_model + a case recipe. The numpy oracle in oracles.models must be numerically identical to the Rust kernel (the test_kernel_parity gate). log_normal is the worked example.

Note on parallelization: every 🔲 kernel still edits several shared registration files (ModelTypeStr + its as_str() match arm, the spectrafit-builder exhaustiveness gate, the Python enum, the bench registry), so kernels are not independently mergeable — they serialize on those files. A codegen step that emits those tables from one manifest would unlock parallel kernel work; until then, add kernels in small sequenced waves on the main branch.

Part 1 — Lineshapes & simple peaks (1–12)¶

Part 2 — UV/VIS (13–22)¶

Part 3 — IR (23–30)¶

23 harmonic oscillator ✅ harmonic_ir · 24/29 multi-Lorentzian + bg ◐ · 25 Morse levels — · 26 Fermi doublet ◐ (two Lorentzians) · 27 Fano-IR ✅ (fano + bg) · 28 Kubo width — (scalar T-law) · 30 asymmetric IR (Gauss\(\times\)sigmoid) ✅ asym_ir.

Part 4 — XAS K-edge (31–42)¶

31 arctan ✅ arctan_step · 32 erf ✅ erfc_step · 33/34 ✅ (reality xas + lineshapes k_edge) · 35 double-step ◐ · 40 white-line+step ✅ (lineshapes) · 41 Doniach+step ✅. Extended X-ray Absorption Fine Structure (EXAFS) 36/37/38/39/42 (\(\chi(k)\) shells, Debye–Waller, splines, FT) 🧩 — a separate \(\chi(k)\) model class.

Part 5 — XAS L-edge (43–54)¶

43 double-step ✅ · 45 crystal-field ◐ · 47 spin-orbit ✅ (lineshapes l_edge) · 53 Fano exciton ✅. 46/54 lifetime/multiplet broadening 🧩 (convolution). 44/48/49/50/51 branching / XMCD / saturation / sum-rules — (analyses).

Part 6 — Time-resolved XAS (55–64)¶

🧩 needs the time-series engine path (multi-dataset GlobalFitGraph + instrument response function (IRF) convolution). 56 bi-exponential ◐ (double_exponential). 57 KWW ✅ kww (stretched exponential, positive-t). 60 global analysis ✅ — engine._global_fit() runs a real multi-dataset GlobalFitGraph joint fit (shared centers/widths across dataset slices, per-slice amplitudes). 64 SVD —.

Part 7 — 2-D RIXS (65–76)¶

65 2-D Gaussian ✅ gaussian2d — spectrafit-core's native 2-D (n_dims=2) kernel. (SP-2: engine._multidim() now fits a genuine 3-D problem with the parametric gaussian_nd kernel, source=spectrafit-core, not the scipy oracle.) 66 2-D Lorentzian 🔲 lorentzian2d · 67 2-D Voigt 🔲 voigt2d (separable products). 68–76 (elastic line, phonon sidebands, Kramers–Heisenberg, …) 🧩 as 2-D suite cases.

Part 8 — Noise models (77–84)¶

🧩 a per-case noise_model knob on CaseSpec/materialize (these GENERATE data, they are not fittable kernels). 77 additive Gaussian ✅ (the engine adds Gaussian noise per case). 78 Poisson / 79 Cauchy / 80 pink / 81 heteroscedastic / 82 mixed / 83 AR(1) 🧩. 84 detector bg ◐.

Part 9 — Optimization landscapes (85–100)¶

Fit a 2-Gaussian surrogate to a multimodal 1-D slice (optfn category, LANDSCAPE_REGISTRY). The suite as a whole follows the benchmark-function compendium of Jamil & Yang¹; the Rust kernels are ported from useful-math-functions, which is the implementation source, not the literature origin of the functions.

Implemented (✅) — all 20: sphere(85), sum_squares(86), trid(87), zirilli(88), bohachevsky(89)⁷, perm_beta(90), ackley(91)³, rastrigin(92), schwefel(93)⁵, griewank(94)⁴, levy(95)⁶, drop_wave(96), egg_holder(97), cross_in_tray(98), shubert(99)⁸, cosine_mixture(100), plus rosenbrock², styblinski_tang⁹, salomon¹⁰, alpine. (cross_in_tray's exp(100…) is clamped to avoid overflow.)

Nine of the twenty trace to a verifiable primary paper (footnoted above). For the remaining eleven — sphere, sum_squares, trid, perm_beta, drop_wave, egg_holder, cross_in_tray, cosine_mixture, alpine, rastrigin, and zirilli — no primary source could be established: the first nine of those are standard benchmark-suite functions with no identifiable originating paper, and Rastrigin's and Zirilli's namesakes could not be independently verified (the monograph Rastrigin's function is usually traced to is unindexed in the sources checked, and no record was found for Zirilli). All twenty are covered by the Jamil & Yang compendium above; the eleven get no per-function citation beyond that.

Current implementation snapshot¶

Counts are exact: the test_catalog_drift guard fails CI if these lines drift from len(MODEL_REGISTRY) / len(LANDSCAPE_REGISTRY), or if any registry key is unnamed below.

• 35 peak/background kernels (MODEL_REGISTRY): gaussian, lorentzian, pseudo_voigt, voigt, fano, constant, linear, quadratic, arctan_step, tanh_step, erfc_step, double_exponential, true_voigt, skewed_gaussian, exp_gaussian, doniach_sunjic, log_normal, pearson7, split_gaussian, moffat, students_t, split_pearson7, breit_wigner, asym_ir, harmonic_ir, tauc, cauchy_dispersion, kww, saturating_exponential, power_saturation, power_law_offset, mgh09_rational, rational_cubic, generalised_logistic, exp_over_linear. voigt is a frozen alias of pseudo_voigt.

The last three are deliberately families rather than one-dataset kernels, and each covers several NIST StRD problems at once: rational_cubic fits Kirby2 (quadratic/quadratic, with the cubic coefficients held at zero), Hahn1 and Thurber, and subsumes mgh09_rational; generalised_logistic fits Rat43 and, with its shape exponent fixed at 1, Rat42; exp_over_linear fits Chwirut1 and Chwirut2. Together with five datasets that needed no new kernel at all — Lanczos2 and Lanczos3 reuse Lanczos1's builder, Eckerle4 is a Gaussian whose amplitude is projected from its width, Roszman1 is a line plus an arctan step, and DanWood is a power law with the offset fixed — NIST StRD coverage is 22 of 27. - 20 optimization landscapes (LANDSCAPE_REGISTRY, see Part 9): ackley, rastrigin, griewank, rosenbrock, schwefel, levy, bohachevsky, drop_wave, shubert, styblinski_tang, salomon, alpine, sphere, trid, zirilli, cosine_mixture, egg_holder, sum_squares, cross_in_tray, perm_beta. - Catalog: 160 diversity-driven cases (no count padding) across ten categories: easy / complex (asymmetric & true-Voigt & Fano blends) / reality / optfn / scaling / edge / lineshapes / fixed / tied / robust (IRLS on outlier-contaminated spectra).

Next kernels (highest diversity per unit of multi-crate work)¶

1. vibronic/Franck–Condon (21) — Poisson-weighted Gaussian progression.
2. lorentzian2d (66) / voigt2d (67) — separable 2-D RIXS products (gaussian2d pattern).
3. A \(\chi(k)\) EXAFS model class (Part 4) and the IRF-convolution time-series path (Part 6).

Then the 🧩 engine features as separate efforts: a noise_model knob (Part 8), a 2-D fit subject (Part 7), IRF convolution + multi-dataset (Part 6), and a \(\chi(k)\) EXAFS class (Part 4).

Next steps¶

• Implement one of the kernels above — Adding a model walks the same multi-crate path (Rust kernel → ModelTypeStr → Python ModelType → bench registry) step by step.