LAPACK: A Linear Algebra Library for High-Performance Computers

Abstract

This talk outlines the computational package called LAPACK. LAPACK is a collection of Fortran 77 subroutines for the analysis and solution of various systems of simultaneous linear algebraic equations, linear least squares problems, and matrix eigenvalue problems. Such computations form the core of perhaps the majority of statistical methods. The library provides a uniform set of subroutines to solve the most common linear algebra problems and runs efficiently on a wide range of architectures. This library, which is freely accessible via computer network, not only eases code development, makes codes more portable among machines of different architectures, and increases efficiency, but also provides tools for evaluating computer performance. The library is based on the well-known and widely used LINPACK and EISPACK packages for linear equation solving, eigenvalue problems, and linear least squares. LINPACK and EISPACK have provided an important infrastructure for scientific computing on serial machines, but they were not designed to exploit the profusion of parallel and vector architectures now becoming available. This talk will describe the evolution of LAPACK and the naming scheme for the routines, as well as give listings for a few routines and notes on the structure of the routines and choice of algorithms. In addition, a discussion of the aspects of software design will be given.