LifeV is a finite element (FE) library providing implementations of state of the art mathematical and numerical methods. It serves both as a research and production library. It has already been used in medical and industrial contexts to simulate fluid structure interaction and mass transport. LifeV is the joint collaboration between four institutions: École Polytechnique Fédérale de Lausanne (CMCS) in Switzerland, Politecnico di Milano (MOX) in Italy, INRIA (REO, ESTIME) in France, and Emory University (Sc. Comp) in the U.S.A.
SHTns is a high-performance Spherical Harmonic Transform library. It was designed for numerical simulation (fluid flows, mhd, etc.) in spherical geometries, but can be used for any kind of problem involving scalar or vector spherical harmonics. It is very fast, thanks to careful vectorization and runtime tuning. It supports multi-threaded transforms via OpenMP. It features scalar and vector transforms, synthesis and analysis, and flexible truncation and normalization. A Python interface is included.
Date::Calc::XS is a Perl module that is the C/XS part which Date::Calc used to consist of. Date::Calc has become a (pure-Perl) wrapper which tries to load Date::Calc::XS, and failing that, loads Date::Calc::PP (a pure-Perl implementation which is now part of Date::Calc and used to be Date::Pcalc).
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.
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.
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.
Mathnetics is an API for creating advanced, interactive, Web-based mathematical applications. It defines various important mathematical objects that are inter-related and on which many numerical calculations can be done. It also features rendering of 3D objects onto an SVG canvas (to do so, it includes certain utilities such as browser sniffing, DOM node selection, and DOM readiness detection), which is quite robust. A few basic 3D objects are given (Line, Sphere, Cube), but the user can define any 3D object desired as per the specification.
Math::GSL is a Perl API to the GNU Scientific Library, which contains a large set of tools for writing scientific computing applications, like statistical distributions, special functions, random number generators, linear algebra, numeric integration/derivatives, FFTs, wavelets, and much more.