ALGLIB is a cross-platform open source numerical analysis and data processing library. It can be used from several programming languages (C++, C#, VB.NET, Python, Delphi, Java).
ALGLIB started in 1999 and has a long history of steady development with roughly 1-3 releases per year. It is used by several open source projects, commercial libraries, and applications (e.g. TOL project, Math.NET Numerics, SpaceClaim).
Features
Distinctive features of the library are: Support for several programming languages with identical APIs (as of 2023, it supports C++, C#, FreePascal/Delphi, VB.NET, Python, and Java) Self-contained code with no mandatory external dependencies and easy installation Portability (it was tested under x86/x86-64/ARM, Windows and Linux) Two independent backends (pure C# implementation, native C implementation) with automatically generated APIs (C++, C#, ...) Same functionality of commercial and GPL versions, with enhancements for speed and parallelism provided in the commercial version
ALGLIB provides functions for: Linear algebra (direct algorithms, solvers, EVD/SVD) Fast Fourier transforms Numerical integration Interpolation Linear and nonlinear least-squares fitting Optimization (linear and non-linear, both convex and non-convex) Ordinary differential equations Special functions Statistics (descriptive statistics, hypothesis testing) Data analysis (classification/regression, including neural networks) Multiple precision versions of linear algebra, interpolation and optimization algorithms (using MPFR for floating point computations)