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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LAPACK Version 1.1                                2 April 1993                                         LAPACK(7)