A Proposal of a Mathematical Roadmap for Scilab DRAFT - Projects

The practical situation is that we have limited time, limited task force, limitedfeedback from the users about existing use cases and limited will to explore newuse cases. In this context, we suggest to focus on the following main numericalcomputing domains, already covered by existing features in Scilab:• elementary functions,• dense linear algebra,• control,• ordinary differential equations,• optimization,• statistics.We feel that Symbolic computations, Design of Experiments, Partial DifferentialEquations, Finite Elements, Neural Networks, Geometry, Sparse linear algebra shouldbe considered as secondary Scilab goals. This is highly questionable. We suggestthe following features updates and creations.• Elementary functions: test the accuracy of existing elementary and update theelementary functions by connecting the Fdlibm library.• Sparse iterative solvers: provide pre-conditioners for sparse matrices based onan update of the Scilin project.• Statistics: test existing distribution functions and create new PDFs, CDFs,inverse CDFs, RNGs and other statistics features (smoothing density estimateby kernel, maximum log-likelihood fitting functions, test statistics).• Ordinary Differential Equations : update the Odepack solvers and replacethem by Sundials solvers.• Design of Experiments: create full factorial, fractional factorial, D-optimal andLHS designs functions. This domain is not covered by existing features. Still,we forecast that the ratio between the technical difficulty and the practicalapplications favors this topic.Moreover, we feel that creating a technical report describing the current state ofdense linear algebra should be a secondary priority. Indeed, this is the core of Scilaband this primary goal cannot be ignored. In particular, we should provide a versionof Atlas for Gnu/Linux the same way that we provide the Intel MKL for Windows.Moreover, we should clarify specific points, such as the presence of the Eispacksources in Scilab and the future evolutions required to use multi-core architectures,including the analysis of the open-source projects candidates for parallel dense linearalgebra.22