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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。

LAPACKLINPACKEISPACK 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。


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 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

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


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

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 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 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 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:


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.


姓名 <email>



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2 April 1993 LAPACK Version 1.1