LAPACK  is  a transportable library of Fortran 77 subroutines
    for solving the most  common  problems  in  numerical  linear
    algebra:  systems  of  linear equations, linear least squares
    problems, eigenvalue problems, and singular  value  problems.
    It  has been designed to be efficient on a wide range of mod­
    ern high-performance computers.

    LAPACK is intended to be the successor to  LINPACK  and  EIS­
    PACK.   It  extends  the  functionality  of these packages by
    including equilibration, iterative refinement, error  bounds,
    and  driver routines for linear systems, routines for comput­
    ing and re-ordering the Schur  factorization,  and  condition
    estimation routines for eigenvalue problems.  LAPACK improves
    on the accuracy of the  standard  algorithms  in  EISPACK  by
    including  high accuracy algorithms for finding singular val­
    ues and eigenvalues of bidiagonal  and  tridiagonal  matrices
    respectively that arise in SVD and symmetric eigenvalue prob­
    lems.  The algorithms and software have been restructured  to
    achieve  high  efficiency  on vector processors, high-perfor­
    mance ``superscalar'' workstations, and shared-memory  multi­
    processors.  A comprehensive testing and timing suite is pro­
    vided along with the LAPACK software.


HOW TO GET LAPACK

    The entire LAPACK package is available via xnetlib  and  NAG,
    or  specific  routines  can be obtained via netlib.  To see a
    description  of  the  contents  of  LAPACK,  send  email   to
    netlib@ornl.gov and in the mail message type: send index from
    lapack.

    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 graphi­
    cal 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  avail­
    able 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 fur­
    ther details contact NAG at one of the following addresses:

    NAG Inc                         NAG Ltd              NAG GmbH
    1400 Opus Place               Wilkinson House      Schleissheimerstrasse 5

    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  ser­
    vice@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 avail­
    able in postscript form from netlib.  To receive  a  list  of
    available  reports, send email to netlib@ornl.gov with a mes­
    sage 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

    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 For­
    tran 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 specifi­
    cally to one or the other.

    The  last  three  letters  ZZZ  indicate the computation per­
    formed.  For example, SGEBRD is a  single  precision  routine
    that  performs a bidiagonal reduction (BRD) of a real general
    matrix.


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