sparseLM is a software package for efficiently solving arbitrarily sparse non-linear least squares problems. It offers a generic implementation of the Levenberg - Marquardt optimization algorithm on top of a variety of sparse direct solvers, thus being applicable to problems with arbitrary sparseness. sparseLM accepts sparse Jacobians encoded in either compressed row storage (CRS) or compressed column storage (CCS, aka Harwell-Boeing) format. It is also possible to supply it just with the Jacobian's sparsity pattern and have its values be numerically approximated using finite differences, or even instruct it to attempt the automatic detection of the sparsity pattern corresponding to the Jacobian of the function to be minimized. Note that for dense non-linear least squares problems, project levmar is more appropriate.
Deep Mandelbrot is a small command line utility to compute pretty pictures (or movies) of any size and depth of the famous Mandelbrot set and its surroundings. The most important features are: multi-threaded computation to support modern multi-core CPUs efficiently; arbitrary precision computations (using libgmp, so only your hardware is the limit); normalized iteration count to achieve continuous coloring (and to avoid color bands); image oversampling to enhance the quality of the resulting PNG image; many selected color tables and the ability to re-color an already computed data frame; an optional histogram as a table for further analysis (e. g. with Octave or Matlab) plus chosen 'color table vs histogram' as another PNG image; and support for easy movie creation.
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.
ShapeKit Suite is highly specialized software focused on data modeling. It helps engineers and researchers in creating a data model based on empirical data gathered from experiments. Data models are used in very different scientific domains and are sometimes called differently, depending on the field. ShapeKit Suite is composed of several programs, and uses a broad range of state-of-the-art algorithms and techniques to construct data models in the most effective manner.
FEniCS is a collection of free software for automated, efficient solution of differential equations. It has an extensive list of features, including automated solution of variational problems, automated error control and adaptivity, a comprehensive library of finite elements, high performance linear algebra, and many more. It is organized as a collection of interoperable components, including the problem-solving environment DOLFIN, the form compiler FFC, the finite element tabulator FIAT, the just-in-time compiler Instant, the code generation interface UFC, the form language UFL, and a range of additional components.
pyuds is a Python library for measuring uncertainty in the Dempster-Shafer theory of evidence. The functionals supported are the Generalized Hartley (GH) uncertainty functional, Generalized Shannon (GS) uncertainty functional, and Aggregate Uncertainty (AU) functional. The library can be utilized either through its API, or through a user-friendly Web interface.