Roldan Pozo

ScaLAPACK: a scalable linear algebra library for distributed memory concurrent computers

The authors describe ScaLAPACK, a distributed memory version of the LAPACK software package for dense and banded matrix computations. Key design features are the use of distributed versions of the Level 3 BLAS as building blocks, and an object-oriented interface to the library routines. The square block scattered decomposition is described. The implementation of a distributed memory version of the right-looking LU factorization algorithm on the Intel Delta multicomputer is discussed, and performance results are presented that demonstrate the scalability of the algorithm.<<ETX>>

LAPACK++: A design overview of object-oriented extensions for high performance linear algebra

LAPACK++ is an object-oriented C++ extension of the LAPACK (Linear Algebra PACKage) library for solving the common problems of numerical linear algebra: linear systems, linear least squares, and eigenvalue problems on high-performance computer architectures. The advantages of an object-oriented approach include the ability to encapsulate various matrix representations, hide their implementation details, reduce the number of subroutines, simplify their calling sequences, and provide an extendible software framework that can incorporate future extensions of LAPACK, such as ScaLAPACK++ for distributed memory architectures. The authors present an overview of the object-oriented design of the matrix and decomposition classes in C++ and discuss its impact on elegance, generality, and performance.

Template Numerical Toolkit for Linear Algebra: High Performance Programming With C++ and the Standard Template Library

We present a new C++ library design for linear algebra computations on high performance architectures. The template numerical toolkit (TNT) for linear algebra is a successor to the Lapack++, Sparselib++, and IM L++ pack ages, providing support for direct and iterative solvers. Its goal is to formally integrate these ideas into a generic algorithm library supporting user-defined data types and data neutrality. The design of the core library uses compo nents from the C++ standard template library (STL) and the basic parallel extensions defined in High Performance C++ (HPC++).

Crpc Research Into Linear Algebra Software for High Performance Computers

In this paper we look at a number of approaches being investigated in the Center for Research on Parallel Computation (CRPC) to develop linear algebra soft ware for high-performance computers. These ap proaches are exemplified by the LAPACK, templates, and ARPACK projects. LAPACK is a software library for performing dense and banded linear algebra computa tions, and was designed to run efficiently on high-per formance computers. We focus on the design of the distributed-memory version of LAPACK, and on an ob ject-oriented interface to LAPACK.

Performance Modeling of Sparse Matrix Methods for Distributed Memory Architectures

We present analytical performance models for the numerical factorization phase of the multifrontal method for sparse matrices. Using a concise characterization of parallel architectures, we provide upper-bound estimates for the speedups observed on actual test problems taken from scientific and engineering applications. Representative architectures include an iPSC/2, iPSC/860, various clusters of workstations, and supercomputers connected by HIPPI interfaces. Simulation results suggest that the effective parallelism of these problems is quite sensitive to the communication bandwidth of the underlying architecture and load imbalances in the computational graph due to irregular data patterns.

ScaLAPACK++: an object oriented linear algebra library for scalable systems

We describe the design of ScaLAPACK++, an object oriented CSS library for implementing linear algebra computations on distributed memory multicomputers. This package, when complete, will support distributed dense, banded, sparse matrix operations for symmetric, positive-definite, and non-symmetric cases. In ScaLAPACK++ we have employed object oriented design methods to enhance scalability, portability, flexibility, and ease-of-use. We illustrate some of these points by describing the implementation of a right-looking LU factorization for dense systems in ScaLAPACK++.<<ETX>>

Limited resource scheduling in multifrontal algorithms for sparse linear systems

We present analytic models and simulation techniques that describe the performance of the multifrontal method on distributed memory architectures. We focus on particular strategies for partitioning, clustering, and mapping of task nodes to processors in order to minimize the overall parallel execution time and minimize communication costs. The performance model has been used to obtain estimates for the speedups of various engineering and scientific problems, on several distributed architectures. The result is that the available speedup of these problems is strongly dependent on the sparsity structure and reordering of the input matrices.<<ETX>>

Constructing Numerical Software Libraries for High-Performance Computing Environments

In this paper we look at a number of approaches being investigated in the ScaLAPACK Project to develop linear algebra software for high-performance computers. The focus is on issues impacting the design of scalable libraries for performing dense and sparse linear algebra computations on multicomputers.