LAPACK(3F) LAPACK(3F)
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 designed to be efficient on a wide range of modern
high-performance computers.
LAPACK is intended to be the successor to LINPACK and EISPACK. It extends the
functionality of these packages by including equilibration, iterative
refinement, error bounds, and driver routines for linear systems, routines for
computing 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 values and eigenvalues of bidiagonal and tridiagonal matrices
respectively that arise in SVD and symmetric eigenvalue problems. The
algorithms and software have been restructured to achieve high efficiency on
vector processors, high-performance ``superscalar'' workstations, and sharedmemory multiprocessors. A comprehensive testing and timing suite is provided
along with the LAPACK software.
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 graphical 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 available 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 further details contact NAG at one
of the following addresses:
NAG Inc NAG Ltd NAG GmbH
1400 Opus Place Wilkinson House Schleissheimerstrasse 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
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LAPACK(3F) LAPACK(3F)
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 service@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.
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
available in postscript form from netlib. To receive a list of available
reports, 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
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 )
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LAPACK(3F) LAPACK(3F)
( a -a -a a )
( c c -c -c )
( k -k -k k )
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 apply to both real and
complex matrices; a few apply specifically to one or the other.
The last three letters ZZZ indicate the computation performed. For example,
SGEBRD is a single precision routine that performs a bidiagonal reduction
(BRD) of a real general matrix.
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