Welcome to the LGSL documentation

LGSL is a collection of numerical algorithms and functions for Lua, based on the GNU Scientific Library (GSL). It allows matrix and vector manipulation, linear algebra operations, special functions, and much more. LGSL is based on the numerical modules of GSL Shell, and aims to be an easy-to-include Lua module with a focus on numerical algorithms.

LGSL offers an intuitive interface to the GSL functions, giving you easy access to a well-tested scientific toolbox from your favourite Lua application. The bindings to GSL were made with the FFI library of LuaJIT. Thanks to LuaJIT, a Just-In-Time compiler for Lua, scripts which use LGSL can run at speeds comparable to optimized C code. A selection of functions were reimplemented in Lua to get the most out of LuaJIT.

LGSL on GitHub

Contents:

• LGSL introduction
  • Real and complex numbers
  • Matrices
  • An Example
• Iterators
  • More complex iterators
• Complex Numbers
  • Complex Functions
• Matrices
  • Overview
  • Accessing Matrix Elements
  • Matrix methods
  • Matrix Functions
• Linear Algebra
  • Functions
• Eigensystems
  • Real Symmetric Matrices
  • Real Nonsymmetric Matrices
  • Complex Hermitian Matrices
  • Real Generalized Symmetric-Definite Eigensystems
  • Complex Generalized Hermitian-Definite Eigensystems
  • Real Generalized Nonsymmetric Eigensystems
• Random Numbers
  • General comments on random numbers
  • The Random Number Generator Interface
  • Examples
  • Random Number Generator Algorithms
• Random Number Distributions
• Probability Distribution Functions
  • Overview
• Linear Least Squares fit
  • Overview
  • Linear Fit Functions
  • Complete Example
• Nonlinear Least Squares fit
  • Overview
  • Performing a non-linear fit
  • Solver class definition
• Basis Splines
  • Overview
  • B-Splines functions
  • B-splines Example
• Fast Fourier Transform
  • Mathematical Definitions
  • LGSL interface
  • Fourier Transform of Real Data
  • FFT example
• Ordinary Differential Equations
  • Overview
  • Creating a ODE system solver
  • ODE solver usage example
  • A Slightly Improved Example
  • ODE Solver Class Definition
• Numerical Integration
  • Introduction
  • Functions
  • Usage Example
• Monte Carlo Integration
  • Description of the VEGAS algorithm
  • Errors and consistency
  • Functions
  • Usage example
• Special functions
  • Overview
• LGSL Examples
  • Home-made Bessel Functions
  • Zernike Polynomials
• GSL FFI interface
  • Introduction
  • GSL FFI interface
  • GSL FFI examples