NativeMinuit.jl

A native-Julia port of CERN ROOT Minuit2, the workhorse function-minimization library used throughout high-energy physics for χ² and likelihood fits.

Why?

iminuit (Python) wraps the upstream C++ Minuit2 library, and IMinuit.jl (Julia, by the same lead author) in turn wraps iminuit through PyCall — so it carries both a Python and a C++ dependency. NativeMinuit.jl is a clean-room Julia port of the same algorithms, with no C++ or Python dependency and no PyCall / FFI — plus full access to Julia tooling (ForwardDiff, threads, broadcasted FCN evaluation). On the benchmark corpus it runs in the 0.15–0.89× C++ wall-time range, i.e. comparable to or faster than C++ Minuit2 — see benchmark/.

Quick example

using NativeMinuit

# χ² with a 4-parameter quadratic
cf = CostFunction(x -> sum(abs2, x .- [1.0, 2.0, 3.0, 4.0]))

# Initial parameter values + step sizes
fm = migrad(cf, [0.0, 0.0, 0.0, 0.0], [0.1, 0.1, 0.1, 0.1])   # a FunctionMinimum

show(stdout, MIME"text/plain"(), fm)

┌───────────────────────────────────────────────────────────────────────┐
│                                Migrad                                 │
├───────────────────────────────────┬───────────────────────────────────┤
│ FCN = 2.257e-18                   │             Nfcn = 26             │
│ EDM = 2.257e-18 (Goal: 0.002)     │                                   │
├───────────────────────────────────┼───────────────────────────────────┤
│           Valid Minimum           │  Below EDM threshold (goal x 10)  │
├───────────────────────────────────┼───────────────────────────────────┤
│      No parameters at limit       │         Below call limit          │
├───────────────────────────────────┼───────────────────────────────────┤
│             Hesse OK              │        Covariance accurate        │
└───────────────────────────────────┴───────────────────────────────────┘

Or the iminuit / IMinuit.jl-style front end, with named parameters, limits, and asymmetric MINOS errors:

m = Minuit(x -> sum(abs2, x .- [1.0, 2.0, 3.0, 4.0]), zeros(4);
           names = ["a", "b", "c", "d"])
migrad!(m)
minos!(m)
m.values        # ≈ [1, 2, 3, 4]
m.merrors       # asymmetric ±σ per parameter (name-keyed Dict)

What's included

Minuit2 algorithms — MIGRAD, HESSE, MINOS, MnContours, Simplex and Scan; bounds, fixed parameters, and Strategy levels 0/1/2, ported against upstream C++ Minuit2 with iminuit-matching defaults.
iminuit / IMinuit.jl-compatible front end — m.values, m.errors, migrad!, minos!, mncontour, named-parameter access, per-parameter fix!/set_limits!, and Jupyter-first rich output. Fit/ArrayFit are exported aliases of Minuit.
Cost functions — a Julia-native family (LeastSquares, UnbinnedNLL, BinnedNLL, …) composable with CostSum.
Error analysis beyond HESSE/MINOS — derived-quantity intervals & profile bands (extremize/profile_band), Monte-Carlo Δχ² regions, likelihood-ensemble MCMC, a non-mutating Bayesian posterior bridge (bayesian/posterior_sample — priors, credible intervals & limits), bootstrap, jackknife, and multi-modal solution detection, for the flat or strongly non-Gaussian likelihoods where MINOS struggles.
AD & threaded gradients — a ForwardDiff extension and an opt-in threaded numerical gradient — plus an Optim.jl alternative-minimizer bridge (optim).

Tutorials & reference

Tutorials

Quickstart — a hands-on first fit.
Bounded parameters — parameter limits and fixed parameters.
MINOS errors & contours — asymmetric error bars and 2-D confidence contours.

Guides

Cost functions — the Julia-native cost family.
Gradients: AD & threading — ForwardDiff gradients and the threaded / :auto numerical gradient.
Alternative minimizers — the Optim.jl bridge (optim).
Error analysis — which uncertainty method to use, when.
Plotting & rich output — plot recipes, draw_* helpers, and LaTeX / ASCII tables.
Migrating from iminuit / IMinuit.jl — the drop-in mapping.

Full API reference and internals.

Citation & references

If you use NativeMinuit.jl in a publication, please cite both NativeMinuit.jl and the upstream Minuit algorithms it ports:

F.-K. Guo, NativeMinuit.jl: a native-Julia port of Minuit2, https://github.com/fkguo/NativeMinuit.jl (2026). A CITATION.cff is provided (GitHub's "Cite this repository" → APA / BibTeX).

F. James and M. Roos, "MINUIT: A system for function minimization and analysis of the parameter errors and correlations", Comput. Phys. Commun. 10 (1975) 343–367. doi:10.1016/0010-4655(75)90039-9

Further Minuit documentation:

F. James, MINUIT function minimization and error analysis: Reference manual version 94.1, CERN-D-506 (1994).
F. James and M. Winkler, MINUIT user's guide, CERN (2004).

License

LGPL-2.1-or-later — matches upstream Minuit2 (the same algorithms, ported to Julia). See docs/UPSTREAM.md for provenance and attribution.