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LAPACK Users' Guide
S O F T W A R E• E N V I R O N M E N TS • T O O LS The series includes handbooks and software guides as well as monographs on practical implementation of computational methods, environments, and tools. The focus is on making recent developments available in a practical format to researchers and other users of these methods and tools. Editor-in-Chief Jack J. Dongarra University of Tennessee and Oak Ridge National Laboratory Editorial Board James W. Demmel, University of California, Berkeley Dennis Gannon, Indiana University Eric Grosse, /AT&T Bell Laboratories Ken Kennedy, Rice University Jorge J. More, Argonne National Laboratory Software, Environments, and Tools E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users' Guide, Third Edition Michael W. Berry and Murray Browne, Understanding Search Engines: Mathematical Modeling and Text Retrieval Jack J. Dongarra, lain S. Duff, Danny C. Sorensen, and Henk A. van der Vorst, Numerical Linear Algebra for High-Performance Computers R. B. Lehoucq, D. C. Sorensen, and C. Yang, ARPACK Users' Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods Randolph E. Bank, PLTMG: A Software Package for Solving Elliptic Partial Differential Equations, Users' Guide 8.0 L S. Blackford, J. Choi, A. Geary, E. D'Azevedo, J. Demmel, I. Dhillon, J. Dongarra, S. Hammarling, G. Henry, A. Petitet, K. Stanley, D. Walker, and R. C. Whaley, ScaLAPACK Users' Guide Greg Astfalk, editor, Applications on Advanced Architecture Computers Francoise Chaitin-Chatelin and Valerie Fraysse, Lectures on Finite Precision Computations Roger W. Hockney, The Science of Computer Benchmark/ng__ Richard Barrett, Michael Berry, Tony F. Chan,James Demmel, June Donato, Jack Dongarra, Victor Eijkhout, Roldan Pozo, Charles Romine, and Henk van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, and D. Sorensen, LAPACK Usersl Guide Second Edition Jack J. Dongarra, lain S. Duff, Danny C. Sorensen, and Hark Van Der Vorst, Solving Linear Systems on Vector and Shared Memory Computers J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. Stewart, UNPACK Users' Guide
LAPACK Users' Guide Third Edition E. Anderson Z. Bai C. Bischof S. Blackford J. Demmel J. Dongarra J. Du Croz A. Greenbaum S. Hammarling A. McKenney D. Sorensen SOFTWARE • ENVIRONMENTS • TOOLS siam. Society for Industrial and Applied Mathematics Philadelphia
© 1999 by the Society for Industrial and Applied Mathematics. 1 0 9 8 7 6 5 43 All rights reserved. Printed in the United States of America. No part of this book may be reproduced, stored, or transmitted in any manner without the written permission of the publisher. For information, write to the Society for Industrial and Applied Mathematics, 3600 University City Science Center, Philadelphia, PA 19104-2688. No warranties, express or implied, are made by the publisher, authors, and their employers that the programs contained in this volume are free of error. They should not be relied on as the sole basis to solve a problem whose incorrect solution could result in injury to person or property. If the programs are employed in such a manner, it is at the user's own risk and the publisher, authors, and their employ- ers disclaim all liability for such misuse. Library of Congress Cataloging-in-Publication Data LAPACK users' guide / E. Anderson... [et al.]. — 3rd ed. p.cm. — (Software, environments, tools) Includes bibliographical references and index. ISBN 0-89871-447-8 (pbk.) 1. FORTRAN (Computer program language) 2. C (Computer program language) 3. Subroutines (Computer programs) 4. LAPACK. I. Anderson, E., 1962- II. Series. QA76.73.F25L361999 512'.5'02855369--dc21 This book is also available in html form over the Internet. To view the html file use the following URL: http://www.netlib.org/lapack/lug/lapackjug.htrnl Royalties from the sale of this book are placed in a fund to help students attend SIAM meetings and other SIAM-related activities. This fund is administered by SIAM and qualified individuals are encouraged to write directly to SIAM for guidelines. siam.is a registered trademark.
Dedication This work is dedicated to Jim Wilkinson whose ideas and spirit have given us inspiration and influenced the project at every turn.
Authors' Affiliations: E. Anderson University of Tennessee, Knoxville Z. Bai University of Kentucky and University of California, Davis Institute of Scientific Computing, Technical University Aachen, Germany C. Bischof L. S. Blackford (formerly L. S. Ostrouchov) University of Tennessee, Knoxville J. Demmel University of California, Berkeley J. Dongarra University of Tennessee, Knoxville and Oak Ridge National Laboratory J. Du Croz Numerical Algorithms Group Ltd. (retired) A. Greenbaum University of Washington S. Hammarling Numerical Algorithms Group Ltd. A. McKenney D. Sorensen Rice University
Contents Preface to the Third Edition Preface to the Second Edition 1 Guide 1 Essentials 1.1 LAPACK 1.2 Problems that LAPACK can Solve 1.3 Computers for which LAPACK is Suitable 1.4 LAPACK Compared with LINPACK and EISPACK 1.5 LAPACK and the BLAS 1.6 Availability of LAPACK 1.7 Commercial Use of LAPACK 1.8 Installation of LAPACK 1.9 Documentation for LAPACK 1.10 Support for LAPACK 1.11 Errata in LAPACK 1.12 Other Related Software 2 Contents of LAPACK 2.1 What's new in version 3.0? 2.2 Structure of LAPACK vii xv xix 1 3 3 3 4 4 4 5 . 6 6 7 7 8 8 9 9 11
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