ALGLIB

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

The most actively developed parts of ALGLIB are:


 * Linear algebra, offering a comprehensive set of both dense and sparse linear solvers and factorizations
 * Interpolation, featuring standard algorithms like polynomials and 1D/2D splines, as well as several unique large-scale interpolation/fitting algorithms. These include penalized 1D/2D splines, fast thin plate splines and fast polyharmonic splines, all scalable to hundreds of thousands of points.
 * Least squares solvers, including linear/nonlinear unconstrained and constrained least squares and curve fitting solvers
 * Optimization, with LP, QP and NLP solvers, derivative-free global solvers and multiobjective optimization algorithms.
 * Data analysis, with various algorithms being implemented

The other functions in the library include:
 * Fast Fourier transforms
 * Numerical integration
 * Ordinary differential equations
 * Special functions
 * Statistics (descriptive statistics, hypothesis testing)
 * Multiple precision versions of linear algebra, interpolation and optimization algorithms (using MPFR for floating point computations)