Glossary¶

Project-specific terms used across these docs. General numerical-fitting vocabulary (residual, Jacobian, covariance) is assumed; this page covers the terms that are specific to spectrafit-core's own architecture and benchmark harness. For lineshape-formula conventions (amplitude, \(\sigma\) vs. FWHM/HWHM, fraction), see Model Reference instead of duplicating them here.

AIC / BIC¶

Akaike / Bayesian Information Criterion. Derived from a proper Gaussian deviance term (neg2_log_l = N_points * ln(chi2 / N_points)), not raw chi2 directly. Only comparable between models fit to the same data, and not a substitute for choosing a component list from the physics first — see Solver — what these statistics assume for the ablation-not-selector caveat and a worked case where trusting BIC alone over a bad seed would have dropped a real spectral component.

DAG IR¶

The directed-acyclic-graph intermediate representation models are compiled to: defined in Python as ModelNodeSpec + ExprEdge, serialised to JSON, and evaluated entirely in Rust. See Model Composition — DAG IR.

DOF¶

Degrees of freedom, N_points - N_free. For multi-dataset global fits, DOF = sum_d(N_d) - N_free_shared. See Solver.

`ExprEdge`¶

A graph-level parameter tie: ExprEdge(target_node=…, target_param=…, expression=…) added to FitGraph.expr_edges. One of two equivalent surfaces for constraining a parameter to another's value or a formula — the other is Parameter.expr. See Model Composition — DAG IR and Model Reference.

Gate (regression gate)¶

The benchmark's pass/fail check on every run: spectrafit must not be slower than the baseline solver, and accuracy parity must hold on the LM-family cases. Enforced by oracles.cli run / gate; reported as gate_state in the benchmark manifest. See Benchmark engine.

Geomean speedup¶

The geometric mean of spectrafit's per-case speedup versus the baseline solver (lmfit), across the benchmark case catalog — the headline number on the Performance page and in the benchmark manifest's geomean_speedup_vs_baseline field.

`ModelNodeSpec`¶

A typed model instance node in the DAG IR: an id, a model_type (ModelType), a parameters dict, and an optional dataset_index for multi-dataset scoping. See Model Composition — DAG IR.

`ModelType`¶

The Python enum of model kinds (GAUSSIAN, LORENTZIAN, …), pinned at runtime to the Rust model_manifest! macro's 37 canonical wire strings via model_type_wire_strings(). See Model Reference and Rust ↔ Python binding audit.

Oracle (parity oracle)¶

An independent reference implementation (lmfit, jax/optimistix, or the numpy formulas in oracles.models.MODEL_REGISTRY) that spectrafit's Rust kernel is cross-verified against — any formula or numerical difference surfaces as a benchmark accuracy-gate failure rather than a crash. See Benchmark engine.

`Parameter.expr`¶

A per-parameter tie: set expr="source_node.param" directly on a Parameter. Equivalent to an ExprEdge — both compile through the same dependency-ordered, cycle-checked tied-plan evaluator, and vary is ignored whenever expr is set. See Parameter Model.

PyO3 binding¶

A Rust function exposed to Python via #[pyfunction] in crates/spectrafit-core/src/lib.rs (e.g. fit, evaluate, model_type_wire_strings) — the FFI boundary between the Rust kernel and the Python package. See Rust ↔ Python binding audit.

`Solver::Variant`¶

A Rust enum case in spectrafit-solver::dispatch (Solver::Lm, Solver::Trf, Solver::Varpro, …) that a Python FitOptions.solver string resolves to at the PyO3 boundary. See Rust ↔ Python binding audit and Choosing a Solver.

Tied parameter¶

A parameter whose value is derived from another parameter or an expression every solver iteration, via either ExprEdge or Parameter.expr, rather than being independently optimised. Not supported by the "varpro" solver. See Model Reference.

Trust region¶

Every solver here ("lm", "trf", "dogleg", "newton-cg", geodesic LM) runs on the same spectrafit-trust-region core and bounds its step rather than taking an unconstrained Gauss-Newton step — none of them ever solves (JᵀJ)p = -Jᵀr unregularised. They differ in how the bound is set, not in whether one exists:

Explicit radius — "trf", "dogleg" and "newton-cg" expose a tunable radius via delta0, max_delta and eta. "trf" additionally scales its step by Coleman–Li bound-reflection; "dogleg" / "newton-cg" do not, so those three knobs are read only on the "dogleg" / "newton-cg" dispatch arm, and setting them alongside solver="trf" is silently inert rather than an error.
Implicit radius — "lm" and its geodesic-accelerated variant bound the step through the Levenberg–Marquardt damping term λI in (JᵀJ + λI)p = -Jᵀr instead of a named radius; for every λ there is an equivalent explicit trust-region radius (Moré, 1978), so this is the same family of methods under a different parameterisation, not an unconstrained one.

See Choosing a Solver.

VarPro (Variable Projection)¶

A solver strategy (solver="varpro") for separable nonlinear least squares: linear amplitude coefficients are solved analytically at each step, leaving only the nonlinear shape parameters (center, sigma, …) for the outer optimisation. Fastest option when its preconditions hold — no tied parameters, no bounds on the nonlinear side. See Choosing a Solver.

Wire string¶

The canonical, serialised name for a model type (e.g. "gaussian", "pseudo_voigt") generated from the Rust model_manifest! macro — the single source of truth ModelType is pinned against. See Model Reference.

Win rate¶

The fraction of benchmark cases whose winner is spectrafit, where the winner is the backend maximising the composite score r² · speedup (oracles.engine) — a blend of accuracy and speed, not a count of cases where spectrafit was merely faster. Reported alongside geomean speedup on the Performance page, which explains how the multimodal optfn category pulls it down on quality rather than on timing.