LibBi is used for state-space modelling and Bayesian inference on high-performance computer hardware, including multi-core CPUs, many-core GPUs (graphics processing units), and distributed-memory clusters. The staple methods of LibBi are based on sequential Monte Carlo (SMC), also known as particle filtering. These methods include particle Markov chain Monte Carlo (PMCMC) and SMC2. Other methods include the extended Kalman filter and some parameter optimization routines. LibBi consists of a C++ template library and a parser and compiler, written in Perl, for its own modelling language.
PyParticles is a particle simulation toolbox entirely written in Python. It simulates a particle-by-particle model with the most popular integrations methods, including Euler, Runge Kutta, and Midpoint. It represents the results on an OpenGL or Matplotlib plot, and offers an easy-to-use API.
GenFoo is a general Fokker-Planck solver for models of arbitrary dimensionality. It contains three backend solvers, a delta-f Monte Carlo, a standard Monte Carlo, and a Finite Element solver. The key property of the GenFoo package is that physics are separated from numerics by runtime loading of the Fokker-Planck coefficients, which enable solutions of a large class of Fokker-Planck models.
SHTns is a high-performance Spherical Harmonic Transform library. It was designed for numerical simulation (fluid flows, mhd, etc.) in spherical geometries, but can be used for any kind of problem involving scalar or vector spherical harmonics. It is very fast, thanks to careful vectorization and runtime tuning. It supports multi-threaded transforms via OpenMP. It features scalar and vector transforms, synthesis and analysis, and flexible truncation and normalization. A Python interface is included.
FEniCS is a collection of free software for automated, efficient solution of differential equations. It has an extensive list of features, including automated solution of variational problems, automated error control and adaptivity, a comprehensive library of finite elements, high performance linear algebra, and many more. It is organized as a collection of interoperable components, including the problem-solving environment DOLFIN, the form compiler FFC, the finite element tabulator FIAT, the just-in-time compiler Instant, the code generation interface UFC, the form language UFL, and a range of additional components.
Chebfun is a collection of algorithms and a software system in object-oriented MATLAB that extends familiar powerful methods of numerical computation involving numbers to continuous or piecewise-continuous functions. It also implements continuous analogues of linear algebra notions like the QR decomposition and the SVD, and solves ordinary differential equations. The mathematical basis of the system combines tools of Chebyshev expansions, fast Fourier transform, barycentric interpolation, recursive zerofinding, and automatic differentiation.
sparseLM is a software package for efficiently solving arbitrarily sparse non-linear least squares problems. It offers a generic implementation of the Levenberg - Marquardt optimization algorithm on top of a variety of sparse direct solvers, thus being applicable to problems with arbitrary sparseness. sparseLM accepts sparse Jacobians encoded in either compressed row storage (CRS) or compressed column storage (CCS, aka Harwell-Boeing) format. It is also possible to supply it just with the Jacobian's sparsity pattern and have its values be numerically approximated using finite differences, or even instruct it to attempt the automatic detection of the sparsity pattern corresponding to the Jacobian of the function to be minimized. Note that for dense non-linear least squares problems, project levmar is more appropriate.
Fuzzy machine learning framework is a library and a GUI front-end for machine learning using intuitionistic fuzzy data. The approach is based on the intuitionistic fuzzy sets and the possibility theory. Further characteristics are fuzzy features and classes; numeric, enumeration features and features based on linguistic variables; user-defined features; derived and evaluated features; classifiers as features for building hierarchical systems; automatic refinement in case of dependent features; incremental learning; fuzzy control language support; object-oriented software design with extensible objects and automatic garbage collection; generic data base support through ODBC; text I/O and HTML output; an advanced graphical user interface based on GTK+; and examples of use.