1LAPACK(l) LAPACK FORTRAN LIBRARY ROUTINES LAPACK(l)
2
6 LAPACK is a transportable library of Fortran 77 subroutines for solving
7 the most common problems in numerical linear algebra: systems of linear
8 equations, linear least squares problems, eigenvalue problems, and singu‐
9 lar value problems. It has been designed to be efficient on a wide range
10 of modern high-performance computers.
11 LAPACK is intended to be the successor to LINPACK and EISPACK. It extends
13 the functionality of these packages by including equilibration, iterative
14 refinement, error bounds, and driver routines for linear systems, routines
15 for computing and re-ordering the Schur factorization, and condition esti‐
16 mation routines for eigenvalue problems. LAPACK improves on the accuracy
17 of the standard algorithms in EISPACK by including high accuracy algo‐
18 rithms for finding singular values and eigenvalues of bidiagonal and
19 tridiagonal matrices respectively that arise in SVD and symmetric eigen‐
20 value problems. The algorithms and software have been restructured to
21 achieve high efficiency on vector processors, high-performance ``super‐
22 scalar'' workstations, and shared-memory multiprocessors. A comprehensive
23 testing and timing suite is provided along with the LAPACK software.
24
27 The entire LAPACK package is available via xnetlib and NAG, or specific
28 routines can be obtained via netlib. To see a description of the contents
29 of LAPACK, send email to netlib@ornl.gov and in the mail message type:
30 send index from lapack.
31 Xnetlib is an X-version of netlib recently developed at the University of
33 Tennessee and Oak Ridge National Laboratory. Unlike netlib, which uses
34 electronic mail to process requests for software and other text, xnetlib
35 uses an X Window graphical user interface and a socket-based connection
36 between the user's machine and the xnetlib server machine to process soft‐
37 ware requests. The complete contents of LAPACK is available in tar/com‐
38 press format from xnetlib.
39 To receive a copy of xnetlib send the message "send xnetlib.shar from
41 xnetlib" to netlib@ornl.gov.
42 When you receive the shar file, remove the mail header, save it to a file,
44 type 'sh filename' and follow the instructions in the README file.
45 Alternatively, the complete LAPACK package can be obtained from NAG on
47 magnetic media for a handling charge. For further details contact NAG at
48 one of the following addresses:
49 NAG Inc NAG Ltd NAG GmbH
51 1400 Opus Place Wilkinson House Schleissheimerstrasse 5
52 Suite 200 Jordan Hill Road W-8046 Garching bei Munchen
53 Downers Grove, IL 60515-5702 Oxford OX2 8DR Germany
54 USA England
55 Tel: +1 708 971 2337 Tel: +44 865 511245 Tel: +49 89 3207395
56 Fax: +1 708 971 2706 Fax: +44 865 310139 Fax: +49 89 3207396
57 LAPACK has been thoroughly tested, on many different types of computers.
59 The LAPACK project supports the package in the sense that reports of
60 errors or poor performance will gain immediate attention from the develop‐
61 ers. Such reports, descriptions of interesting applications, and other
62 comments should be sent by electronic mail to lapack@cs.utk.edu.
63
66 The LAPACK Users' Guide is published by SIAM and was made available May,
67 1992. LAPACK Users' Guide gives an informal introduction to the design of
68 the algorithms and software, summarizes the contents of the package, and
69 describes the conventions used in the software and documentation, and
70 includes complete specifications for calling the routines. The LAPACK
71 Users' Guide can be purchased from: SIAM; 3600 University City Science
72 Center; Philadelphia, PA 19104-2688; 215-382-9800, FAX 215-386-7999. It
73 will also be available from booksellers. The Guide costs $15.60 for SIAM
74 members, and $19.50 for non-members. Please specify order code OT31 when
75 ordering. To order by email, send email to service@siam.org.
76 A list of known problems, bugs, and compiler errors for LAPACK, as well as
78 errata for the LAPACK Users' Guide and the LAPACK code itself, is main‐
79 tained on netlib. For a copy of this report, send email to
80 netlib@ornl.gov with a message of the form: send release_notes from
81 lapack.
82
85 A number of working notes were written during the development of LAPACK
86 and published as LAPACK Working Notes, initially by Argonne National Labo‐
87 ratory and later by the University of Tennessee. Many of these reports
88 have subsequently appeared as journal articles. Most of these working
89 notes are available in postscript form from netlib. To receive a list of
90 available reports, send email to netlib@ornl.gov with a message of the
91 form: send index from lapack/lawns. Otherwise, requests for copies of
92 these working notes can be sent to the following address.
93 LAPACK Project c/o J.J. Dongarra Computer Science Department University of
95 Tennessee Knoxville, Tennessee 37996-1301 USA Email: lapack@cs.utk.edu
96
99 LAPACK has been funded in part by NSF, DOE, and DARPA, with developmental
100 support from NAG Ltd., Cray Research, and many friends and colleagues
101 around the world.
102 Ed Anderson, Zhao-jun Bai, Chris Bischof, Jim Demmel, Jack Dongarra,
105 Jeremy Du Croz, Anne Greenbaum, Sven Hammarling, Alan McKenney, Susan
106 Ostrouchov, and Danny Sorensen
107 ( l l l l )
109 ( a -a a -a )
110 1/4 * ( p p -p -p )
111 ( a -a -a a )
112 ( c c -c -c )
113 ( k -k -k k )
114
118 The name of each LAPACK routine is a coded specification of its function
119 (within the very tight limits of standard Fortran 77 6-character names).
120 All driver and computational routines have names of the form XYYZZZ, where
122 for some driver routines the 6th character is blank.
123 The first letter, X, indicates the data type as follows:
125 S REAL
127 D DOUBLE PRECISION
128 C COMPLEX
129 Z COMPLEX*16 or DOUBLE COMPLEX
130 The next two letters, YY, indicate the type of matrix (or of the most sig‐
132 nificant matrix). Most of these two-letter codes apply to both real and
133 complex matrices; a few apply specifically to one or the other.
134 The last three letters ZZZ indicate the computation performed. For exam‐
136 ple, SGEBRD is a single precision routine that performs a bidiagonal
137 reduction (BRD) of a real general matrix.
138LAPACK Version 1.1 2 April 1993 LAPACK(l)