CCruncher is a project for quantifying portfolio credit risk using the copula approach. It is a framework consisting of two elements: a technical document that explains the theory, and a software program that implements it. CCruncher evaluates the portfolio credit risk by sampling the portfolio loss distribution and computing the Expected Loss (EL), Value at Risk (VaR), and Expected Shortfall (ES) statistics. The portfolio losses are obtained simulating the default times of obligors and simulating the EADs and LGDs of their assets.
Armadillo is a C++ linear algebra library (matrix maths) aiming towards a good balance between speed and ease of use. The API is deliberately similar to Matlab's. 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 numerics 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.
Social Networks Visualizer (SocNetV) is a flexible and user-friendly tool for the analysis and visualization of Social Networks. It lets you construct mathematical graphs with a few clicks on a virtual canvas, load networks of various formats (GraphViz, GraphML, Adjacency, Pajek, UCINET, etc), or create a network by crawling all links in a Web page. The application can compute basic network properties, such as density, diameter, and distances (shortest path lengths), as well as more advanced structural statistics, such as node and network centralities (i.e. closeness, betweenness, graph), clustering coefficient, etc.
SHOGUN is a machine learning toolbox whose focus is on large scale kernel methods and especially on Support Vector Machines (SVM). It provides a generic SVM object interfacing to several different SVM implementations, all making use of the same underlying, efficient kernel implementations. Apart from SVMs and regression, SHOGUN also features a number of linear methods like Linear Discriminant Analysis (LDA), Linear Programming Machine (LPM), (Kernel) Perceptrons, and algorithms to train hidden Markov models. SHOGUN can be used from within C++, Matlab, R, Octave, and Python.
Gmsh is an automatic 3D finite element grid generator with built-in CAD and post-processing facilities. Its design goal is to provide a simple meshing tool with parametric input and advanced visualization capabilities. It 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 (based on FLTK and OpenGL) or in ASCII text files using Gmsh's own scripting language.
MLPACK is a C++ machine learning library with an emphasis on scalability, speed, and ease-of-use. Its aim is to make machine learning possible for novice users by means of a simple, consistent API, while simultaneously exploiting C++ language features to provide maximum performance and maximum flexibility for expert users. It contains algorithms such as k-means, Gaussian mixture models, hidden Markov models, density estimation trees, kernel PCA, locality-sensitive hashing, sparse coding, linear regression and least-angle regression.
GNU TeXmacs is a free wysiwyw (what you see is what you want) editing platform with special features for scientists. The software aims to provide a unified and user friendly framework for editing structured documents with different types of content: text, mathematics, graphics, interactive content. TeXmacs can also be used as an interface to many external systems for computer algebra, numerical analysis, and statistics. New presentation styles can be written by the user and new features can be added to the editor using Scheme.
TSPSG is intended to generate and solve "travelling salesman problem" (TSP) tasks. It uses the Branch and Bound method for solving. Its input is a number of cities and a matrix of city-to-city travel costs. The matrix can be populated with random values in a given range (which is useful for generating tasks). The result is an optimal route, its price, step-by-step matrices of solving, and a solving graph. The task can be saved in an internal binary format and opened later. The result can be printed or saved as PDF, HTML, or ODF. TSPSG may be useful for teachers to generate test tasks or just for regular users to solve TSPs. Also, it may be used as an example of using the Branch and Bound method to solve a particular task.
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).
TRIP is a general computer algebra system dedicated to celestial mechanics. It includes a numerical kernel and has interfaces to gnuplot and xmgrace. Computations can be performed with double, quadruple, or multi-precision. Users can dynamically load external libraries written in C, C++, or Fortran. Parallel computations on multivariate polynomials can be performed.