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.
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.
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.
GSL shell offers an interactive user interface that gives access to the GSL collection of mathematical functions. It is based on the powerful and elegant scripting language Lua. GSL shell is not just a wrapper over the C API of GSL, but offers a much more simple and expressive way to use GSL. The objective is to give the user the power to easily access GSL functions without having to write a complete C application. It also has a powerful module to produce plots or almost any kind of graphics based on data or functions.
TooN is a very efficient numerics library for C++. The main focus of the library is efficient and safe handling of large numbers of small vector matrices and providing as much compile time checking as is possible. The library also works with large vectors and matrices and integrates easily with existing code. In addition to elementary vector and matrix operations, the library also providers linear solvers, matrix decompositions, optimization, and wrappers around LAPACK.
jblas is a fast linear algebra library for Java. It is based on BLAS and LAPACK, the de-facto industry standard for matrix computations, and uses state-of-the-art implementations like ATLAS for all its computational routines, making it very fast. It is essentially a lightweight wrapper around the BLAS and LAPACK routines. These packages originated in the Fortran community, which explains their archaic API. On the other hand, modern implementations are hard to beat performance-wise. jblas aims to make this functionality available to Java programmers such that they do not have to worry about writing JNI interfaces and calling conventions of Fortran code.
REDUCE is a system for doing algebra by computer that also supports numerical approximation and interfaces to gnuplot to provide graphics. It has a long and distinguished place in the history of computer algebra systems. For comparison, other systems that address some of the same issues but sometimes with rather different emphases are Axiom, Derive, Macsyma (Maxima), Maple, Mathematica, and MuPAD.
Armadillo is a C++ linear algebra library (matrix maths) aiming towards a good balance between speed and ease of use. Integer, floating point, and complex numbers are supported, as well as a subset of trigonometric and statistics functions. Various matrix decompositions are provided through optional integration with LAPACK and ATLAS libraries. A delayed evaluation approach, based on template meta-programming, is used (during compile time) to combine several operations into one and reduce or eliminate the need for temporaries.