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    LAPACK is a transportable library of Fortran 77 subroutines for solving the most common prob-
    lems 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 modern high-performance computers.

    LAPACK is intended to be the successor to LINPACK and EISPACK.  It extends the  functionality
    of	these packages by including equilibration, iterative refinement, error bounds, and driver
    routines for linear systems, routines for computing 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  sin-
    gular  values  and eigenvalues of bidiagonal and tridiagonal matrices respectively that arise
    in SVD and symmetric eigenvalue problems.  The algorithms and software have been restructured
    to	achieve  high  efficiency on vector processors, high-performance ``superscalar'' worksta-
    tions, and shared-memory multiprocessors.  A comprehensive testing and timing suite  is  pro-
    vided along with the LAPACK software.

    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 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 imme-
    diate attention from the developers. Such reports, descriptions of interesting  applications,
    and other comments should be sent by electronic mail to lapack@cs.utk.edu.

    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 documen-
    tation, 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

    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  fol-
    lowing 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	      )

    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

    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 performed.  For example, SGEBRD is a sin-
    gle precision routine that performs a bidiagonal reduction (BRD) of a real general matrix.

LAPACK Version 1.1			   2 April 1993 				LAPACK(l)
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