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.
POSNUMCON is a command-line (or console mode) program for converting between positional numeral systems written in C++. It is able to convert between any positional numeral system (e.g. decimal, octal, binary and hexadecimal) with base (radix) between 2-36 (there is the possibility for extension). It offers full support for big length, negative, and floating-point (fractional) numbers, saving calculation results to a text file. It is fully and easily customizable.
NLopt is a library for nonlinear optimization that allows one to select from a wide variety of optimization algorithms by changing a single parameter. Its features include both local and global optimization, unconstrained, bound-constrained, or nonlinear-inequality constrained problems, and optimization using function values only or using derivatives if they are available. It was initially begun as a wrapper around several existing optimization packages, but it now also includes original implementations of several algorithms for which no free code was available. It provides interfaces callable from C/C++, Fortran, Matlab, GNU Octave, Python, and GNU Guile.
wgms3d is a full-vectorial electromagnetic waveguide mode solver. It computes the modes of dielectric waveguides at a specified wavelength using a second-order finite-difference method. The waveguide cross section may consist of several adjacent regions of constant refractive index (i.e., step-index profiles). Dielectric interfaces do not have to be aligned with the discretization grid; they may be arbitrarily slanted or curved. The entire waveguide may be curved along the propagation direction. Leakage and curvature losses can be computed using Perfectly Matched Layers as absorbing boundaries.
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.