NAME¶
LAPACK - library of linear algebra routines
什麼是 LAPACK ?¶
LAPACK 是一個
Fortran 77
子程式的 transportable library ，
用來解決多數數字線性代數中共同的問題：
systems of linear equations, linear least squares problems, eigenvalue
problems, 還有 singular value problems.
它在大部分現代的高性能電腦中可以高效地運作。
LAPACK 是
LINPACK 和
EISPACK
的後繼者。
它擴展了這些庫的功能，包含了線性系統的
equilibration, iterative refinement, error bounds, 和 driver
routines， routines for computing and re-ordering the Schur
factorization， 還有 condition estimation routines for
eigenvalue problems.
LAPACK 通過包含 finding
singular values and eigenvalues of bidiagonal and tridiagonal matrices
respectively that arise in SVD and symmetric eigenvalue problems
的高精度算法提高了
EISPACK
中標準算法的精度。
這些算法和軟體被重新編寫，在向量處理器上，高性能
``superscalar'' 工作站上和
共享記憶體的多處理器上都可以獲得高效率。
LAPACK
軟體還附帶了一個復雜的測試和時間測算套件。
如何得到 LAPACK¶
完整的
LAPACK 套件可以從
xnetlib 和 NAG 得到，也可以從
netlib 獲得特定的庫。
要查看
LAPACK
內容的描述，向 netlib@ornl.gov
發一封消息類型為：
send index from lapack 的電子郵件。
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
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.
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
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
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 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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