libensemble is a complete toolkit for dynamic ensembles of calculations. It connects deciders to experiments or simulations.

Open CASCADE is a set of libraries for the development of applications dealing with 3D CAD data or requiring industrial 3D capabilities. It includes C++ class libraries providing services for 3D surface and solid modeling, CAD data exchange, and visualization. It is used for development of specialized software dealing with 3D models in design (CAD), manufacturing (CAM), numerical simulation (CAE), measurement equipment (CMM), and quality control (CAQ) domains.

This is the certified version of the Open Cascade Technology (OCCT) library.

This is a header-only C++ library for calculating analytical derivatives and taylor expansions of composite functions.

SCOTCH is a set of programs and libraries which implement the static mapping and sparse matrix reordering algorithms developed within the SCOTCH project. Its purpose is to apply graph theory, with a divide and conquer approach, to scientific computing problems such as graph and mesh partitioning, static mapping, and sparse matrix ordering, in application domains ranging from structural mechanics to operating systems or bio-chemistry.

Armadillo is a C++ linear algebra library, aiming towards a good balance between speed and ease of use. It is useful for algorithm development directly in C++, or quick conversion of research code into production environments. It can be used for machine learning, pattern recognition, signal processing, bioinformatics, statistics, econometrics, etc. The library provides efficient classes for vectors, matrices and cubes, as well as 150+ associated functions (e.g., contiguous and non-contiguous submatrix views).

MiniZinc is a high-level modeling language for constraint satisfaction and optimization problems. Models are compiled to FlatZinc, a language understood by many solvers.

ScaLAPACK is a Fortran 90 library of high-performance linear algebra routines on parallel distributed memory machines. ScaLAPACK solves dense and banded linear systems, least squares problems, eigenvalue problems, and singular value problems.

The GNU Scientific Library is a library for numerical analysis in C and C++. It includes a wide range of mathematical routines, with over 1000 functions in total. Subject areas covered by the library include: differential equations, linear algebra, Fast Fourier Transforms and random numbers.

This package provides the C library of RBio. It can be used for reading and writing sparse matrices in the Rutherford/Boeing format.

Gmsh is a 3D finite element grid generator with a built-in CAD engine and post-processor. Its design goal is to provide a fast, light and user-friendly meshing tool with parametric input and advanced visualization capabilities. Gmsh is built around four modules: geometry, mesh, solver and post-processing. The specification of any input to these modules is done either interactively using the graphical user interface or in ASCII text files using Gmsh's own scripting language.

4ti2 implements algorithms for solving algebraic, geometric and combinatorial problems on linear spaces. Among others, it solves systems of linear equations, computes extreme rays of polyhedral cones, solves integer programming problems and computes Markov bases for statistics.

An implementation of the maxflow algorithm described in An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Computer Vision.

Yuri Boykov and Vladimir Kolmogorov.

In IEEE Transactions on Pattern Analysis and Machine Intelligence,

September 2004

muParser is an extensible high performance math parser library. It is based on transforming an expression into a bytecode and precalculating constant parts of it.

SUNDIALS is a family of software packages implemented with the goal of providing robust time integrators and nonlinear solvers that can easily be incorporated into existing simulation codes.

CVXOPT is a package for convex optimization based on the Python programming language. Its main purpose is to make the development of software for convex optimization applications straightforward by building on Python’s extensive standard library and on the strengths of Python as a high-level programming language.

This package provides a range of SAT solvers, including the sequential lingeling and its parallel variants plingeling and treengeling. A bounded model checker is also included.

This package provides a SAT solver based on conflict-driven clause learning.

lp_solve is a mixed integer linear programming solver based on the revised simplex and the branch-and-bound methods.

The dune-functions module provides an abstraction layer for global finite element functions. Its two main concepts are functions implemented as callable objects, and bases of finite element spaces.

wxMaxima is a graphical user interface for the Maxima computer algebra system. It eases the use of Maxima by making most of its commands available through a menu system and by providing input dialogs for commands that require more than one argument. It also implements its own display engine that outputs mathematical symbols directly instead of depicting them with ASCII characters.

wxMaxima also features 2D and 3D inline plots, simple animations, mixing of text and mathematical calculations to create documents, exporting of input and output to TeX, and a browser for Maxima's manual including command index and full text searching.

Openspecfun provides AMOS and Faddeeva. AMOS (from Netlib) is a portable package for Bessel Functions of a Complex Argument and Nonnegative Order; it contains subroutines for computing Bessel functions and Airy functions. Faddeeva allows computing the various error functions of arbitrary complex arguments (Faddeeva function, error function, complementary error function, scaled complementary error function, imaginary error function, and Dawson function); given these, one can also easily compute Voigt functions, Fresnel integrals, and similar related functions as well.

HDF4 is a library and multi-object file format for storing and managing data between machines. HDF4 is an older hierarchical data format, incompatible with HDF5.

Vinci implements a number of volume computation algorithms for convex polytopes in arbitrary dimension. The polytopes can be given by their V-representation (as the convex hull of a finite number of vertices), by their H-representation (as the bounded intersection of a finite number of halfspaces) or by their double description with both representations.

CyLP is a Python interface to COIN-OR’s Linear and mixed-integer program solvers (CLP, CBC, and CGL). CyLP’s unique feature is that you can use it to alter the solution process of the solvers from within Python. For example, you may define cut generators, branch-and-bound strategies, and primal/dual Simplex pivot rules completely in Python.