J. Du Croz

LAPACK: a portable linear algebra library for high-performance computers

The goal of the LAPACK project is to design and implement a portable linear algebra library for efficient use on a variety of high-performance computers. The library is based on the widely used LINPACK and EISPACK packages for solving linear equations, eigenvalue problems, and linear least-squares problems, but extends their functionality in a number of ways. The major methodology for making the algorithms run faster is to restructure them to perform block matrix operations (e.g., matrix-matrix multiplication) in their inner loops. These block operations may be optimized to exploit the memory hierarchy of a specific architecture. The LAPACK project is also working on new algorithms that yield higher relative accuracy for a variety of linear algebra problems. >

LAPACK95 users' guide

LAPACK95 is a Fortran 95 interface to the Fortran 77 LAPACK library. It is relevant for anyone who writes in the Fortran 95 language and needs reliable software for basic numerical linear algebra. It improves upon the original user-interface to the LAPACK package, taking advantage of the considerable simplifications that Fortran 95 allows.

The NAG library ‘machine’

If a reliable, high quality numerical algorithms library is to be developed then it is essential that we recognize the need for collaboration between different technical communities in the development of the library. This paper suggests an ultimate design for the library and describes the implications of that design for the people involved in the development of the library.

Performance of a subroutine library on vector-processing machines

Abstract We describe the strategy adopted to enable selected linear algebra routines in the NAG Library to achieve high levels of performance on vector-processing machines. The routines have been restructed so as to perform the bulk of their computation via calls to simple kernel routines, which have been implemented in different versions to suit specific vector-processing machines as well as scalar machines. We present performance measurements for some of the kernel routines and some of the routines which call them, for Cray-1, Cray-XMP, Cyber 205 and FPS-164.

Aids to Portability Within the NAG Project

We discuss the increasing relevance of portability aids to NAG in its efforts to develop a multi-machine mathematical software library. In particular we outline some of the utilities employed so far and give an informal guide to a FORTRAN transformer (APT) currently under development.

Preparing the NAG library

If a reliable, high quality numerical algorithm library is to be developed then it is essential that we recognise the need for collaboration between different technical communities in the development of the library. This paper suggests an ultimate design for the library and describes the implications of that design for the people involved in the development of the library.

The NAG Library in a Supercomputing Environment

In a supercomputing environment the role of a numerical subroutine library is even more important than in a more conventional computing environment. Not only should the library provide accuracy, reliability and robustness in performing standard numerical computations, but it should also — as far as possible — offer the high levels of performance which users of supercomputers may expect. Indeed, users may reasonably look to a subroutine library to relieve them of some of the burden of acquiring the specialised expertise — for example, knowledge of architectural details or of the capabilities of a vectorizing compiler — that may be necessary to use a supercomputer efficiently.