LINPACK

LINPACK
Name	LINPACK
Author	Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart
Released	0 1979
Programming language	Fortran
Operating system	Cross-platform
Genre	Numerical linear algebra

LINPACK. It is a seminal collection of Fortran subroutines for solving systems of linear equations and performing related matrix computations. Developed in the late 1970s, it became a foundational tool in scientific computing and engineering. Its most enduring contribution is the LINPACK Benchmark, which evolved into a standard for measuring the performance of the world's most powerful supercomputers.

Overview

The library was designed to provide robust, portable, and efficient routines for common problems in numerical linear algebra. Its primary functions include solving systems of linear equations using LU decomposition, computing matrix inversions, and estimating condition numbers. The software was intentionally written in a clear, well-documented style to serve as both a practical tool and an educational resource for the scientific community. This approach influenced subsequent numerical libraries, including its direct successor, LAPACK.

History and development

The project was initiated by Jack Dongarra, Jim Bunch, Cleve Moler, and Pete Stewart, with its first official release in 1979. The work was supported by grants from the National Science Foundation and the United States Department of Energy. Its creation was motivated by the need for reliable, machine-independent software following the proliferation of minicomputers and early vector processors like the Cray-1. The team drew upon earlier algorithmic work from projects such as the EISPACK library and the LINPACK Users' Guide became a widely used textbook.

LINPACK Benchmark

The most famous derivative is the LINPACK Benchmark, a specific test designed to solve a dense system of linear equations using routines from the library. In 1993, Jack Dongarra formalized the "Top500" list, which uses a version of this benchmark to rank the performance of supercomputers worldwide. The benchmark's high-performance variant, HPL, is the standard test for the TOP500 project. While influential, the benchmark has been critiqued for not representing all modern computational science workloads, leading to the development of alternative benchmarks like HPCG.

Mathematical foundation

The core algorithms are based on Gaussian elimination with partial pivoting, implemented via LU decomposition for general dense matrices. For positive-definite systems, it employs the more efficient Cholesky decomposition. Key numerical considerations addressed by the library include numerical stability and the estimation of round-off error through computed condition numbers. These methods are fundamental to many applications in computational physics, computational fluid dynamics, and circuit simulation.

Software and implementations

The original distribution was written in Fortran 66 and later updated to Fortran 77. Its design emphasized portability across different computer architectures, from mainframe computers to early supercomputers like those from Cray Research. The library's source code was freely distributed, fostering widespread adoption in academia and industry. Its architecture directly informed the design of LAPACK, which was optimized for cache memory hierarchies and later for parallel computing environments.

Impact and legacy

The library's influence is profound, having educated a generation of scientists and engineers in practical numerical analysis. Its benchmark created a standardized, competitive metric that drove innovation in high-performance computing for decades, tracked by the TOP500 list maintained by researchers at the University of Tennessee, University of Mannheim, and Lawrence Berkeley National Laboratory. The principles of its design—clarity, reliability, and portability—became hallmarks for subsequent projects like LAPACK, ScaLAPACK, and the BLAS standard.

Category:Numerical analysis Category:Fortran software Category:Computer benchmarks Category:1979 software