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go-numerics documentation

Numerical methods in pure Go (CGO=0): optimisation and root finding, quadrature and ODE solvers, special functions — on go-ndarray.

go-numerics is numerical computing in pure Go. Three libraries port reference algorithms statement by statement — MINPACK, L-BFGS-B, QUADPACK, the Runge–Kutta, Radau and BDF solvers, Cephes and Boost.Math — and test them against recorded answers: SciPy 1.18.1 runs for optimize and integrate, with the netlib Fortran as a second oracle, and mpmath at high precision for special, with SciPy measured on the same points. Where the Go code is slower than the reference, the pages say so.

Prey and predator populations from SolveIVP with RK45, one marker per accepted step

Every figure on these pages was computed by the library it illustrates and drawn by go-plot, from the code shown beside it.

The libraries

LibraryVersionWhat it does
optimizev0.1.0minimisation (Nelder–Mead, Powell, CG, BFGS, Newton-CG, L-BFGS-B), scalar and system roots, nonlinear least squares, curve fitting with covariance, linear programming
integratev0.1.0adaptive quadrature (QUADPACK), fixed and sample rules, multiple integrals, initial value problems (RK45, RK23, DOP853, Radau, BDF, stiffness switching)
specialv0.1.0gamma, beta, error and normal functions, incomplete gamma and beta and their inverses, Bessel, zeta, elliptic integrals; an element-wise layer over go-ndarray

Install 

go get github.com/go-numerics/optimize@v0.1.0
go get github.com/go-numerics/integrate@v0.1.0
go get github.com/go-numerics/special@v0.1.0

Each module needs Go 1.27.2 or later and is pure Go (CGO_ENABLED=0). Each one’s CI runs its tests on amd64 and arm64 and under emulation on riscv64, loong64, ppc64le and s390x; integrate and special add 386 and 32-bit arm.

What each library’s pages hold

LibraryPages
optimizeoverview · design · performance
integrateoverview · design · verification · quadrature table · ODE table · performance
specialoverview · accuracy · accuracy table · performance · performance table

Honest weak points

Where these libraries are slower than the reference, their own measurements say so, and so do these pages:

  • optimize: curve_fit on 10⁴ points is slower than SciPy’s (0.67× with LM, 0.77× with TRF); the gap is in the solver’s workspace handling (performance).
  • special: single-threaded, a Go loop is about 3× slower than SciPy’s C for the gamma and error-function families and 10–15× for the Bessel functions of real order and the incomplete beta function; the nd functions, spread over the cores, beat SciPy for 21 of 31 functions measured (performance).

Built on

go-ndarray (arrays: curve-fit data, covariances, LP matrices, ODE solutions and the element-wise special/nd layer). The figures are drawn by go-plot, and a go-notebook cell can use all of it.

Created on by tannevaled

Modified on by tannevaled