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.
Theano is a Python library that allows you to define, optimize, and evaluate mathematical expressions involving multi-dimensional arrays efficiently. Theano features tight integration with numpy, transparent use of a GPU, efficient symbolic differentiation, speed and stability optimizations, dynamic C code generation, and extensive unit-testing and self-verification. Theano has been powering large-scale computationally intensive scientific investigations since 2007. But it is also approachable enough to be used in the classroom (IFT6266 at the University of Montreal).
ODE is a high performance library for simulating rigid body dynamics. It is fully featured, stable, mature, and platform independent with an easy-to-use C/C++ API. It has advanced joint types and integrated collision detection with friction. ODE is useful for simulating vehicles, objects in virtual reality environments, and virtual creatures. It is currently used in many computer games, 3D authoring tools, and simulation tools.
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.
Evolving Games for Unnatural Intelligence is a Java package for unsupervised machine learning based on Evolutionary Game Theory on directed graphs. It is able to segment data without any previuos information on the number of segments. It has no GUI, but implements generalizations of the original method proposed by Li, Chen, He and Jiang in the arxiv paper "A Novel Clustering Algorithm Based Upon Games on Evolving Network", published on 30 Dec 2008.
dnAnalytics is a numerical library for the .NET Framework and Mono. The library is written in C# and is available as a fully managed library or with a wrapper around the Intel® Math Kernel Library (MKL). The MKL wrapped version provides significantly better performance when working with large data sets. dnAnalytics is compatible with .NET 2.0 or later and Mono. The managed version will run on Windows XP or newer and on any platform that supports Mono. The MKL wrapped version supports 32-bit and 64-bit versions of Windows XP or newer and 32-bit and 64-bit versions of Linux.
Hasard is a pseudo-random number generator (PRNG) library. It includes multiple engines (algorithms): Park-Miller, Mersenne Twister, Linux device (/dev/urandom or /dev/random), and more. It has a simple but powerful API. For example, a PRNG seed can be generated using strong entropy (using a hardware random number generator like /dev/random on Linux). The library is written in C, and a Python binding is available. The word "hasard" is the French word for "randomness" or "chance".
Ecere Fractals Explorer is a cross-platform explorer for the Mandelbrot and Julia set fractals. It supports smooth coloring, features a gradient editor, supports arbitrary powers, has an option to save with or without computed data, exports to a variety of image formats (with or without bilinear filtering), and comes with a few interesting presets.
Big Fraction is a Java class that represents an immutable fraction, as held in a numerator and denominator. Calculations may be performed on this fraction, but the value is always held as a numerator/denominator pair. Therefore, no precision is lost. The fraction may be top-heavy, but is reduced when printed. The value can be converted into floats if desired, although precision will invariably be lost, and some large fractions (such as calculations for pi) can not be converted if the values of BigInteger exceed the range capable of floats.