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NAME

       LAPACK - library of linear algebra routines

 LAPACK ?
    LAPACK    是一个    Fortran   77   子程序的   transportable   library   ,
    用来解决多数数字线性代数中共同的问题: systems of linear equations, linear
    least squares problems, eigenvalue problems, 还有 singular value problems.
    它在大部分现代的高性能计算机中可以高效地运作。

    LAPACKLINPACKEISPACK        的后继者。
    它扩展了这些库的功能,包含了线性系统的       equilibration,      iterative
    refinement, error bounds, 和 driver routines, routines for computing  and
    re-ordering  the  Schur factorization, 还有 condition estimation routines
    for eigenvalue problems.  LAPACK  通过包含  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
    中标准算法的精度。        这些算法和软件被重新编写,在向量处理器上,高性能
    ``superscalar'' 工作站上和  共享内存的多处理器上都可以获得高效率。  LAPACK
    软件还附带了一个复杂的测试和时间测算套件。

 LAPACK
    完整的   LAPACK   软件包可以从   xnetlib   和  NAG  得到,也可以从  netlib
    获得特定的库。    要查看     LAPACK     内容的描述,向     netlib@ornl.gov
    发一封消息类型为: send index from lapack 的电子邮件。

    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

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           1/4 * ( p    p             -p   -p )
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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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