FLENS is short for Flexible Library for Efficient Numerical Solutions. This C++ can be used as a builing block for the implementation of other (higher-level) numerical libraries or numerical applications. It is a C++ library (requires a C++11 conform compiler). Easy install, as FLENS is headers only. It gives you Matrix/vector types for dense linear algebra; a generic (i.e. templated) implementation of BLAS; and a generic reimplementation of LAPACK. If high performance BLAS libraries like ATLAS, GotoBLAS, etc. are available, you simply can link against them and boost performance.

Thinknowlogy is grammar-based software, designed to utilize the Natural Laws of Intelligence in grammar, in order to create intelligence through natural language in software. This is demonstrated by programming in natural language, reasoning in natural language and drawing conclusions (more detailed than scientific solutions), making assumptions (with self-adjusting level of uncertainty), asking questions (about gaps in the knowledge), and detecting conflicts in the knowledge. It builds semantics autonomously (with no vocabularies or words lists), detecting some cases of semantic ambiguity. It is multi-grammar, proving that Natural Laws of Intelligence are universal.

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.

Meep is a free finite-difference time-domain (FDTD) simulation software package to model electromagnetic systems. It supports distributed-memory parallel simulations, nonlinear, anisotropic, and dispersive media, PML absorbing boundaries, and 1D/2D/3D and cylindrical problems. It is completely scriptable from either C++ or a Scheme (GNU Guile) interface.

Meta.Numerics is a Mono-compatible .NET library for scientific and numerical programming. It includes functionality for matrix algebra (including SVD, non-symmetric eigensystems, and sparse matrices), special functions of real and complex numbers (including Bessel functions and the complex error function), statistics and data analysis (including PCA, logistic and nonlinear regression, statistical tests, and nonuniform random deviates), and signal processing (including arbitrary-length FFTs).

Punto is a tool for plotting particles. It reads particle data from a file and displays them in a window in several ways, like dots, circles, squares, and spheres. It can also plot vectorial fields. The output can be in one, two, or three dimensions. It is possible to zoom in and out, rotate in three dimensions, draw periodic images, and more. It can produce animations easily from your data files.

Sally is a tool for mapping a set of strings to a set of vectors. This mapping is referred to as embedding and allows techniques of machine learning and data mining to be applied for the analysis of string data. It can be used with data such as text documents, DNA sequences, or log files. The vector space model or bag-of-words model is used. Strings are characterized by a set of features, where each feature is associated with one dimension of the vector space. Occurrences of the features in each string are counted. Alternatively, binary or TF-IDF values can be computed. Vectors can be output in plain text, LibSVM, or Matlab format.

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.