LAPACK - a library of linear algebra routines

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 shared-memory 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

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 ) ( 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.