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