Armadillo is a C++ linear algebra library (matrix maths) aiming towards a good balance between speed and ease of use. The API is deliberately similar to Matlab's. 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 numerics 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.
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.
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.
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.