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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
部分現代的高效能計算機中可以高效地運作。
LAPACK 是 LINPACK 和 EISPACK 的後繼者。 它擴充套件了這些庫的功能，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 透過包含 finding
singular values and eigenvalues of bidiagonal and tridiagonal matrices respectively that arise in SVD and
symmetric eigenvalue problems 的高精度演算法提高了 EISPACK 中標準演算法的精度。 這些演算法和軟體被重新編
寫，在向量處理器上，高效能 ``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
附帶了一個複雜的測試和時間測算套件。
如何得到 LAPACK
完整的 LAPACK 軟體包可以從 xnetlib 和 NAG 得到，也可以從 netlib 獲得特定的庫。 要檢視 LAPACK 內容的描述，向
netlib@ornl.gov 發一封訊息型別為： 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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