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 designed to be efficient on a wide range of mod
ern high-performance computers.
LAPACK is intended to be the successor to LINPACK and EIS
PACK. It extends the functionality of these packages by
including equilibration, iterative refinement, error bounds,
and driver routines for linear systems, routines for comput
ing and re-ordering 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 algorithms for finding singular val
ues and eigenvalues of bidiagonal and tridiagonal matrices
respectively that arise in SVD and symmetric eigenvalue prob
lems. The algorithms and software have been restructured to
achieve high efficiency on vector processors, high-perfor
mance ``superscalar'' workstations, and shared-memory multi
processors. A comprehensive testing and timing suite is pro
vided 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
description of the contents of LAPACK, send email to
netlib@ornl.gov and in the mail message type: send index from
lapack.
Xnetlib is an X-version of netlib recently developed at the
University of Tennessee and Oak Ridge National Laboratory.
Unlike netlib, which uses electronic mail to process requests
for software and other text, xnetlib uses an X Window graphi
cal user interface and a socket-based connection between the
user's machine and the xnetlib server machine to process
software requests. The complete contents of LAPACK is avail
able in tar/compress 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 fur
ther details contact NAG at one of the following addresses:
NAG Inc NAG Ltd NAG GmbH
1400 Opus Place Wilkinson House Schleissheimerstrasse 5
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 interesting 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
introduction to the design of the algorithms and software,
summarizes 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 order code OT31
when ordering. To order by email, send email to ser
vice@siam.org.
A list of known problems, bugs, and compiler errors for
LAPACK, as well as errata for the LAPACK Users' Guide and the
LAPACK 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
Argonne National Laboratory and later by the University of
Tennessee. Many of these reports have subsequently appeared
as journal articles. Most of these working notes are avail
able in postscript form from netlib. To receive a list of
available reports, send email to netlib@ornl.gov with a mes
sage 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
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 For
tran 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
apply to both real and complex matrices; a few apply specifi
cally 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.
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