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version 1.8, 2010/12/21 13:53:31 version 1.9, 2011/11/21 20:42:57
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   *> \brief \b DLARRA
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DLARRA + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarra.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarra.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarra.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DLARRA( N, D, E, E2, SPLTOL, TNRM,
   *                           NSPLIT, ISPLIT, INFO )
   * 
   *       .. Scalar Arguments ..
   *       INTEGER            INFO, N, NSPLIT
   *       DOUBLE PRECISION    SPLTOL, TNRM
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            ISPLIT( * )
   *       DOUBLE PRECISION   D( * ), E( * ), E2( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> Compute the splitting points with threshold SPLTOL.
   *> DLARRA sets any "small" off-diagonal elements to zero.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrix. N > 0.
   *> \endverbatim
   *>
   *> \param[in] D
   *> \verbatim
   *>          D is DOUBLE PRECISION array, dimension (N)
   *>          On entry, the N diagonal elements of the tridiagonal
   *>          matrix T.
   *> \endverbatim
   *>
   *> \param[in,out] E
   *> \verbatim
   *>          E is DOUBLE PRECISION array, dimension (N)
   *>          On entry, the first (N-1) entries contain the subdiagonal
   *>          elements of the tridiagonal matrix T; E(N) need not be set.
   *>          On exit, the entries E( ISPLIT( I ) ), 1 <= I <= NSPLIT,
   *>          are set to zero, the other entries of E are untouched.
   *> \endverbatim
   *>
   *> \param[in,out] E2
   *> \verbatim
   *>          E2 is DOUBLE PRECISION array, dimension (N)
   *>          On entry, the first (N-1) entries contain the SQUARES of the
   *>          subdiagonal elements of the tridiagonal matrix T;
   *>          E2(N) need not be set.
   *>          On exit, the entries E2( ISPLIT( I ) ),
   *>          1 <= I <= NSPLIT, have been set to zero
   *> \endverbatim
   *>
   *> \param[in] SPLTOL
   *> \verbatim
   *>          SPLTOL is DOUBLE PRECISION
   *>          The threshold for splitting. Two criteria can be used:
   *>          SPLTOL<0 : criterion based on absolute off-diagonal value
   *>          SPLTOL>0 : criterion that preserves relative accuracy
   *> \endverbatim
   *>
   *> \param[in] TNRM
   *> \verbatim
   *>          TNRM is DOUBLE PRECISION
   *>          The norm of the matrix.
   *> \endverbatim
   *>
   *> \param[out] NSPLIT
   *> \verbatim
   *>          NSPLIT is INTEGER
   *>          The number of blocks T splits into. 1 <= NSPLIT <= N.
   *> \endverbatim
   *>
   *> \param[out] ISPLIT
   *> \verbatim
   *>          ISPLIT is INTEGER array, dimension (N)
   *>          The splitting points, at which T breaks up into blocks.
   *>          The first block consists of rows/columns 1 to ISPLIT(1),
   *>          the second of rows/columns ISPLIT(1)+1 through ISPLIT(2),
   *>          etc., and the NSPLIT-th consists of rows/columns
   *>          ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N.
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>          = 0:  successful exit
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup auxOTHERauxiliary
   *
   *> \par Contributors:
   *  ==================
   *>
   *> Beresford Parlett, University of California, Berkeley, USA \n
   *> Jim Demmel, University of California, Berkeley, USA \n
   *> Inderjit Dhillon, University of Texas, Austin, USA \n
   *> Osni Marques, LBNL/NERSC, USA \n
   *> Christof Voemel, University of California, Berkeley, USA
   *
   *  =====================================================================
       SUBROUTINE DLARRA( N, D, E, E2, SPLTOL, TNRM,        SUBROUTINE DLARRA( N, D, E, E2, SPLTOL, TNRM,
      $                    NSPLIT, ISPLIT, INFO )       $                    NSPLIT, ISPLIT, INFO )
       IMPLICIT NONE  
 *  *
 *  -- LAPACK auxiliary routine (version 3.2.2) --  *  -- LAPACK auxiliary routine (version 3.4.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     June 2010  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       INTEGER            INFO, N, NSPLIT        INTEGER            INFO, N, NSPLIT
Line 16 Line 150
       DOUBLE PRECISION   D( * ), E( * ), E2( * )        DOUBLE PRECISION   D( * ), E( * ), E2( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  Compute the splitting points with threshold SPLTOL.  
 *  DLARRA sets any "small" off-diagonal elements to zero.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrix. N > 0.  
 *  
 *  D       (input) DOUBLE PRECISION array, dimension (N)  
 *          On entry, the N diagonal elements of the tridiagonal  
 *          matrix T.  
 *  
 *  E       (input/output) DOUBLE PRECISION array, dimension (N)  
 *          On entry, the first (N-1) entries contain the subdiagonal  
 *          elements of the tridiagonal matrix T; E(N) need not be set.  
 *          On exit, the entries E( ISPLIT( I ) ), 1 <= I <= NSPLIT,  
 *          are set to zero, the other entries of E are untouched.  
 *  
 *  E2      (input/output) DOUBLE PRECISION array, dimension (N)  
 *          On entry, the first (N-1) entries contain the SQUARES of the  
 *          subdiagonal elements of the tridiagonal matrix T;  
 *          E2(N) need not be set.  
 *          On exit, the entries E2( ISPLIT( I ) ),  
 *          1 <= I <= NSPLIT, have been set to zero  
 *  
 *  SPLTOL  (input) DOUBLE PRECISION  
 *          The threshold for splitting. Two criteria can be used:  
 *          SPLTOL<0 : criterion based on absolute off-diagonal value  
 *          SPLTOL>0 : criterion that preserves relative accuracy  
 *  
 *  TNRM    (input) DOUBLE PRECISION  
 *          The norm of the matrix.  
 *  
 *  NSPLIT  (output) INTEGER  
 *          The number of blocks T splits into. 1 <= NSPLIT <= N.  
 *  
 *  ISPLIT  (output) INTEGER array, dimension (N)  
 *          The splitting points, at which T breaks up into blocks.  
 *          The first block consists of rows/columns 1 to ISPLIT(1),  
 *          the second of rows/columns ISPLIT(1)+1 through ISPLIT(2),  
 *          etc., and the NSPLIT-th consists of rows/columns  
 *          ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N.  
 *  
 *  
 *  INFO    (output) INTEGER  
 *          = 0:  successful exit  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  Based on contributions by  
 *     Beresford Parlett, University of California, Berkeley, USA  
 *     Jim Demmel, University of California, Berkeley, USA  
 *     Inderjit Dhillon, University of Texas, Austin, USA  
 *     Osni Marques, LBNL/NERSC, USA  
 *     Christof Voemel, University of California, Berkeley, USA  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.8  
changed lines
  Added in v.1.9

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