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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