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BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE

IP.com Disclosure Number: IPCOM000128700D
Original Publication Date: 1977-Dec-31
Included in the Prior Art Database: 2005-Sep-16
Document File: 17 page(s) / 43K

Publishing Venue

Software Patent Institute

Related People

C., L. Lawson: AUTHOR [+6]

Abstract

A pac kage of low-level subprograms for many of the basic operations of numerical linear algebra is presented. The package is intended to be used with FORTRAN. The operations in the package are dot products, elementary vector operations, Givens transformations, vector copy and swap, vector norms, vector scaling, and the indices of largest component magnitude.

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THIS DOCUMENT IS AN APPROXIMATE REPRESENTATION OF THE ORIGINAL.

BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE

C., L. Lawson, Jet Propulsion Laboratory R. J. Hanson, Sandia Laboratories, Albuquerque D. R. Kincaid., University of Texas, Austin F. T. Krogh, Jet Propulsion Laboratory

July 1977 CNA-124 TR-72

This report is being produced jointly with the Department of Computer Sciences at UT Austin; also, it is a report distributed by Jet Propulsion Laboratory and Sandia Labora-tories.

Abstract

A pac kage of low-level subprograms for many of the basic operations of numerical linear algebra is presented. The package is intended to be used with FORTRAN. The operations in the package are dot products, elementary vector operations, Givens transformations, vector copy and swap, vector norms, vector scaling, and the indices of largest component magnitude.

The subprograms and a test driver are available in portable FORTRAN. Versions of the subprograms are provided in assembly language for the IBM 360-67, the CDC 6600 and CDC 7600, and the Univac 1108.

1. Introduction

This paper describes a package, called the BLAS, of thirty-eight FORTRAN-callable subprograms for basic operations of numerical linear algebra. This paper and the associated package of subprograms and testing program are the result of a collaborative voluntary project of the ACM-SIGNUM comnittee on basic linear alge~bra subprograms. This project was carried out during the period 1973-1977.

The initial version of the subprogram specifications app-red in Ref. [1]. Following distribution of Ref. [1] to persons active in t.he develop-ment of numerical linear algebra software, open meetings of the project were held at the Purdue Mathematical Software II Conference, May,, 1974, Ref. [2], and at the National Computer Conference, Anaheim, May, 1975. Extensive modifications of the specifications were made following the Purdue meeting which was attended by thirty people. A few additional changes resulted from the Anaheim meeting. Most of the further Fortran code changes resulted from an effort to improve the design and to make them more robust.

2. Reasons for Developingthe Package

Designers of computer programs involving linear algebraic operations have frequently chosen to implement certain low-level operations such as the dot product as separate subprograms. This may be observed both in many published codes and in codes written for specific applications at many computer installations. Following are some of the reasons for taking this approach:

University of Texas Page 1 Dec 31, 1977

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BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE

(1) It can serve as a conceptual aid in both the design and coding stages of a programming effort to regard an operation such as the dot product as a basic building block. This is consistent with the ideas of structured programming which encourage modularizing common code sequences.

(2) It imprcves ~~-he self-documenting quality of code to...