lapack(3)

NAME

LAPACK - a library of linear algebra routines

WHAT IS LAPACK?

LAPACK is a transportable library of Fortran 77 subroutines

for solving the most common problems in numerical linear algebra:

systems of linear equations, linear least squares problems,

eigenvalue problems, and singular value problems. It has been de

signed to be efficient on a wide range of modern high-performance

computers.

LAPACK is intended to be the successor to LINPACK and EIS

PACK. It extends the functionality of these packages by includ

ing equilibration, iterative refinement, error bounds, and driver

routines for linear systems, routines for computing and re-order

ing the Schur factorization, and condition estimation routines

for eigenvalue problems. LAPACK improves on the accuracy of the

standard algorithms in EISPACK by including high accuracy algo

rithms for finding singular values and eigenvalues of bidiagonal

and tridiagonal matrices respectively that arise in SVD and sym

metric eigenvalue problems. The algorithms and software have

been restructured to achieve high efficiency on vector proces

sors, high-performance ``superscalar'' workstations, and shared

memory multiprocessors. A comprehensive testing and timing suite

is provided along with the LAPACK software.

HOW TO GET LAPACK

The entire LAPACK package is available via xnetlib and NAG,

or specific routines can be obtained via netlib. To see a de

scription of the contents of LAPACK, send email to

netlib@ornl.gov and in the mail message type: send index from la

pack.

Xnetlib is an X-version of netlib recently developed at the

University of Tennessee and Oak Ridge National Laboratory. Un

like netlib, which uses electronic mail to process requests for

software and other text, xnetlib uses an X Window graphical user

interface and a socket-based connection between the user's ma

chine and the xnetlib server machine to process software re

quests. The complete contents of LAPACK is available in tar/com

press format from xnetlib.

To receive a copy of xnetlib send the message "send

xnetlib.shar from xnetlib" to netlib@ornl.gov.

When you receive the shar file, remove the mail header, save

it to a file, type 'sh filename' and follow the instructions in

the README file.

Alternatively, the complete LAPACK package can be obtained

from NAG on magnetic media for a handling charge. For further

details contact NAG at one of the following addresses:

NAG Inc NAG Ltd NAG GmbH
1400 Opus Place Wilkinson House Schleis

sheimerstrasse 5
Suite 200 Jordan Hill Road W-8046

Garching bei Munchen
Downers Grove, IL 60515-5702 Oxford OX2 8DR Germany
USA England
Tel: +1 708 971 2337 Tel: +44 865 511245 Tel: +49

89 3207395
Fax: +1 708 971 2706 Fax: +44 865 310139 Fax: +49

89 3207396

LAPACK has been thoroughly tested, on many different types of

computers. The LAPACK project supports the package in the sense

that reports of errors or poor performance will gain immediate

attention from the developers. Such reports, descriptions of in

teresting applications, and other comments should be sent by

electronic mail to lapack@cs.utk.edu.

LAPACK USERS' GUIDE

The LAPACK Users' Guide is published by SIAM and was made

available May, 1992. LAPACK Users' Guide gives an informal in

troduction to the design of the algorithms and software, summa

rizes the contents of the package, and describes the conventions

used in the software and documentation, and includes complete

specifications for calling the routines. The LAPACK Users' Guide

can be purchased from: SIAM; 3600 University City Science Center;

Philadelphia, PA 19104-2688; 215-382-9800, FAX 215-386-7999. It

will also be available from booksellers. The Guide costs $15.60

for SIAM members, and $19.50 for non-members. Please specify or

der code OT31 when ordering. To order by email, send email to

service@siam.org.

A list of known problems, bugs, and compiler errors for LA

PACK, as well as errata for the LAPACK Users' Guide and the LA

PACK code itself, is maintained on netlib. For a copy of this

report, send email to netlib@ornl.gov with a message of the form:

send release_notes from lapack.

LAPACK WORKING NOTES

A number of working notes were written during the development

of LAPACK and published as LAPACK Working Notes, initially by Ar

gonne National Laboratory and later by the University of Ten

nessee. Many of these reports have subsequently appeared as

journal articles. Most of these working notes are available in

postscript form from netlib. To receive a list of available re

ports, send email to netlib@ornl.gov with a message of the form:

send index from lapack/lawns. Otherwise, requests for copies of

these working notes can be sent to the following address.

LAPACK Project c/o J.J. Dongarra Computer Science Department

University of Tennessee Knoxville, Tennessee 37996-1301 USA

Email: lapack@cs.utk.edu

ACKNOWLEDGEMENTS

LAPACK has been funded in part by NSF, DOE, and DARPA, with

developmental support from NAG Ltd., Cray Research, and many

friends and colleagues around the world.

Ed Anderson, Zhao-jun Bai, Chris Bischof, Jim Demmel, Jack

Dongarra, Jeremy Du Croz, Anne Greenbaum, Sven Hammarling, Alan

McKenney, Susan Ostrouchov, and Danny Sorensen

( l l l l )
( a -a a -a )

1/4 * ( p p -p -p )

( a -a -a a )
( c c -c -c )
( k -k -k k )

NAMING SCHEME

The name of each LAPACK routine is a coded specification of

its function (within the very tight limits of standard Fortran 77

6-character names).

All driver and computational routines have names of the form

XYYZZZ, where for some driver routines the 6th character is

blank.

The first letter, X, indicates the data type as follows:

S REAL
D DOUBLE PRECISION
C COMPLEX
Z COMPLEX*16 or DOUBLE COMPLEX

The next two letters, YY, indicate the type of matrix (or of

the most significant matrix). Most of these two-letter codes ap

ply to both real and complex matrices; a few apply specifically

to one or the other.

The last three letters ZZZ indicate the computation per

formed. For example, SGEBRD is a single precision routine that

performs a bidiagonal reduction (BRD) of a real general matrix.

LAPACK Version 1.1 2 April 1993

LAPACK(3)