Reliable and Scalable Software for Linear Algebra Computations on High End Computers

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This project aims to address the issue of inadequate software support for High Performance Computing by improving two widely used standard libraries, LAPACK and ScaLAPCK, both of which provide numerical linear algebra kernels. By a combination of algorithmic research, an on-going user and vendor survey (at icl.cs.utk.edu/lapack-survey.html), and anticipation of the demands and opportunities of new architectures and modern programming languages, the following key improvements to the current versions have been identified. The use of novel, improved algorithms. Improved ease of use. Performance Tuning. Improved reliability and support. First, new state-of-the-art algorithms will improve speed, accuracy, and memory efficiency. Second, improved user interfaces that exploit features of modern programming languages are important for better ease of use and also hide some of the underlying complex, possibly distributed, data structures. Third, the performance of both libraries crucially depends on a number of machine-dependent parameters whose setting can benefit from automatic tuning techniques developed very successfully in the ATLAS project. Last, there is a huge demand for ongoing support and maintenance of both LAPACK and ScaLAPACK, and there is a need for installing a formal mechanism for user feedback, for tracking bugs, for version management, and facilitated installation. Broader Impacts: LAPACK and ScaLAPACK have been adopted by many vendors as the basis of their own libraries: SGI/Cray, IBM, HP-Convex, Fujitsu, NEC, NAG and IMSL, and the Mathworks (producers of Matlab). For this reason, the proposed changes will have a large impact. Furthermore, recent origin of most of the algorithms described in this proposal means that there are not yet any easily accessible descriptions suitable for education. As part of the project documentation, tutorial material will be developed that is suitable for classroom instruction and wide educational outreach. The development of LAPACK and ScaLAPACK is part of a long and successful history of collaboration between the PIs. In addition, for the current improvements, numerous outside collaborators have offered support ranging from software and ideas to help in programming and development.