Interior Point Methods for Massive Support Vector Machines

We investigate the use of interior point methods for solving quadratic programming problems with a small number of linear constraints where the quadratic term consists of a low-rank update to a positive semi-de nite matrix. Several formulations of the support vector machine t into this category. An interesting feature of these particular problems is the vol- ume of data, which can lead to quadratic programs with between 10 and 100 million variables and a dense Q matrix. We use OOQP, an object- oriented interior point code, to solve these problem because it allows us to easily tailor the required linear algebra to the application. Our linear algebra implementation uses a proximal point modi cation to the under- lying algorithm, and exploits the Sherman-Morrison-Woodbury formula and the Schur complement to facilitate e cient linear system solution. Since we target massive problems, the data is stored out-of-core and we overlap computation and I/O to reduce overhead. Results are reported for several linear support vector machine formulations demonstrating the reliability and scalability of the method

Polymorphic Matrices in Paladin

International audienceScientific programmers are eager to take advantage of the computational power offered by Distributed Computing Systems (DCSs), but are generally reluctant to undertake the porting of their application programs onto such machines. The DCS commercially available today are indeed widely believed to be difficult to use, which should not be a surprise since they are traditionally programmed with software tools dating back to the days of punch cards and paper tape. We claim that provided modern object oriented technologies are used, these computers can be programmed easily and efficiently. In EPEE, our Eiffel Parallel Execution Environment, we propose to use a kind of parallelism known as data-parallelism, encapsulated within classes of the Eiffel sequential object-oriented language, using the SPMD (Single Program Multiple Data) programming model. We describe our method for designing with this environment Paladin, an object-oriented linear algebra library for DCSs. We show how dynamic binding and polymorphism can be used to solve the problems set by the dynamic aspects of the distribution of linear algebra objects such as matrices and vectors

An object-oriented programming of an explicit dynamics code: application to impact simulation

During the last fifty years, the development of better numerical methods and more powerful computers has been a major enterprise for the scientific community. Recent advances in computational softwares have lead to the possibility of solving more physical and complex problems (coupled problems, nonlinearities, high strain and high strain rate problems, etc.). The development of object-oriented programming leads to better structured codes for the finite element method and facilitates the development, the maintainability and the expandability of such codes. This paper presents an implementation in C++ of an explicit finite element program dedicated to the simulation of impacts. We first present a brief overview of the kinematics, the conservative and constitutive laws related to large deformation inelasticity. Then we present the design and the numerical implementation of some aspects developed with an emphasis on the object-oriented programming adopted. Finally, the efficiency and accuracy of the program are investigated through some benchmark tests

Object oriented design of a thermo-mechanical FEM code

An object oriented design is presented for a computer program that can perform\ud thermo-mechanically coupled analyzes. The target of the design is a \ud exible and robust\ud computer program. It should be easy to adapt and extend, re-using existing code, without\ud interfering with already established algorithms.\ud The program uses publicly available toolkits that are currently emerging as C++ pack-\ud ages. First of all the Standard C++ Library (formerly Standard Template Library) is\ud used for packing items in container classes. Secondly the matrix and vector operations\ud are derived from the Template Numerical Toolkit (TNT) and �nally (not essentially for\ud the numerical part) a graphical user interface is made, based on the wxWindows package,\ud that can generate a GUI for Motif and MS-Windows with the same code.\ud Attention is given to the design of classes such as speci�c elements and material classes\ud based on more general classes. A hierarchy of classes is constructed where general behavior\ud is put high in the hierarchy and speci�c behavior low. The choice between inheritance and\ud aggregation is made at several levels

Development of an object-oriented finite element program: application to metal-forming and impact simulations

During the last 50 years, the development of better numerical methods and more powerful computers has been a major enterprise for the scientific community. In the same time, the finite element method has become a widely used tool for researchers and engineers. Recent advances in computational software have made possible to solve more physical and complex problems such as coupled problems, nonlinearities, high strain and high-strain rate problems. In this field, an accurate analysis of large deformation inelastic problems occurring in metal-forming or impact simulations is extremely important as a consequence of high amount of plastic flow. In this presentation, the object-oriented implementation, using the C++ language, of an explicit finite element code called DynELA is presented. The object-oriented programming (OOP) leads to better-structured codes for the finite element method and facilitates the development, the maintainability and the expandability of such codes. The most significant advantage of OOP is in the modeling of complex physical systems such as deformation processing where the overall complex problem is partitioned in individual sub-problems based on physical, mathematical or geometric reasoning. We first focus on the advantages of OOP for the development of scientific programs. Specific aspects of OOP, such as the inheritance mechanism, the operators overload procedure or the use of template classes are detailed. Then we present the approach used for the development of our finite element code through the presentation of the kinematics, conservative and constitutive laws and their respective implementation in C++. Finally, the efficiency and accuracy of our finite element program are investigated using a number of benchmark tests relative to metal forming and impact simulations

Large Scale Parallel Computations in R through Elemental

Even though in recent years the scale of statistical analysis problems has increased tremendously, many statistical software tools are still limited to single-node computations. However, statistical analyses are largely based on dense linear algebra operations, which have been deeply studied, optimized and parallelized in the high-performance-computing community. To make high-performance distributed computations available for statistical analysis, and thus enable large scale statistical computations, we introduce RElem, an open source package that integrates the distributed dense linear algebra library Elemental into R. While on the one hand, RElem provides direct wrappers of Elemental's routines, on the other hand, it overloads various operators and functions to provide an entirely native R experience for distributed computations. We showcase how simple it is to port existing R programs to Relem and demonstrate that Relem indeed allows to scale beyond the single-node limitation of R with the full performance of Elemental without any overhead.Comment: 16 pages, 5 figure

Abstract State Machines 1988-1998: Commented ASM Bibliography

An annotated bibliography of papers which deal with or use Abstract State Machines (ASMs), as of January 1998.Comment: Also maintained as a BibTeX file at http://www.eecs.umich.edu/gasm