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version 1.8, 2010/12/21 13:53:30 version 1.9, 2011/11/21 20:42:55
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   *> \brief \b DLANEG
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DLANEG + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaneg.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaneg.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaneg.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       INTEGER FUNCTION DLANEG( N, D, LLD, SIGMA, PIVMIN, R )
   * 
   *       .. Scalar Arguments ..
   *       INTEGER            N, R
   *       DOUBLE PRECISION   PIVMIN, SIGMA
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   D( * ), LLD( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DLANEG computes the Sturm count, the number of negative pivots
   *> encountered while factoring tridiagonal T - sigma I = L D L^T.
   *> This implementation works directly on the factors without forming
   *> the tridiagonal matrix T.  The Sturm count is also the number of
   *> eigenvalues of T less than sigma.
   *>
   *> This routine is called from DLARRB.
   *>
   *> The current routine does not use the PIVMIN parameter but rather
   *> requires IEEE-754 propagation of Infinities and NaNs.  This
   *> routine also has no input range restrictions but does require
   *> default exception handling such that x/0 produces Inf when x is
   *> non-zero, and Inf/Inf produces NaN.  For more information, see:
   *>
   *>   Marques, Riedy, and Voemel, "Benefits of IEEE-754 Features in
   *>   Modern Symmetric Tridiagonal Eigensolvers," SIAM Journal on
   *>   Scientific Computing, v28, n5, 2006.  DOI 10.1137/050641624
   *>   (Tech report version in LAWN 172 with the same title.)
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrix.
   *> \endverbatim
   *>
   *> \param[in] D
   *> \verbatim
   *>          D is DOUBLE PRECISION array, dimension (N)
   *>          The N diagonal elements of the diagonal matrix D.
   *> \endverbatim
   *>
   *> \param[in] LLD
   *> \verbatim
   *>          LLD is DOUBLE PRECISION array, dimension (N-1)
   *>          The (N-1) elements L(i)*L(i)*D(i).
   *> \endverbatim
   *>
   *> \param[in] SIGMA
   *> \verbatim
   *>          SIGMA is DOUBLE PRECISION
   *>          Shift amount in T - sigma I = L D L^T.
   *> \endverbatim
   *>
   *> \param[in] PIVMIN
   *> \verbatim
   *>          PIVMIN is DOUBLE PRECISION
   *>          The minimum pivot in the Sturm sequence.  May be used
   *>          when zero pivots are encountered on non-IEEE-754
   *>          architectures.
   *> \endverbatim
   *>
   *> \param[in] R
   *> \verbatim
   *>          R is INTEGER
   *>          The twist index for the twisted factorization that is used
   *>          for the negcount.
   *> \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:
   *  ==================
   *>
   *>     Osni Marques, LBNL/NERSC, USA \n
   *>     Christof Voemel, University of California, Berkeley, USA \n
   *>     Jason Riedy, University of California, Berkeley, USA \n
   *>
   *  =====================================================================
       INTEGER FUNCTION DLANEG( N, D, LLD, SIGMA, PIVMIN, R )        INTEGER FUNCTION DLANEG( N, D, LLD, SIGMA, PIVMIN, R )
       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            N, R        INTEGER            N, R
Line 14 Line 131
       DOUBLE PRECISION   D( * ), LLD( * )        DOUBLE PRECISION   D( * ), LLD( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DLANEG computes the Sturm count, the number of negative pivots  
 *  encountered while factoring tridiagonal T - sigma I = L D L^T.  
 *  This implementation works directly on the factors without forming  
 *  the tridiagonal matrix T.  The Sturm count is also the number of  
 *  eigenvalues of T less than sigma.  
 *  
 *  This routine is called from DLARRB.  
 *  
 *  The current routine does not use the PIVMIN parameter but rather  
 *  requires IEEE-754 propagation of Infinities and NaNs.  This  
 *  routine also has no input range restrictions but does require  
 *  default exception handling such that x/0 produces Inf when x is  
 *  non-zero, and Inf/Inf produces NaN.  For more information, see:  
 *  
 *    Marques, Riedy, and Voemel, "Benefits of IEEE-754 Features in  
 *    Modern Symmetric Tridiagonal Eigensolvers," SIAM Journal on  
 *    Scientific Computing, v28, n5, 2006.  DOI 10.1137/050641624  
 *    (Tech report version in LAWN 172 with the same title.)  
 *  
 *  Arguments  
 *  =========  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrix.  
 *  
 *  D       (input) DOUBLE PRECISION array, dimension (N)  
 *          The N diagonal elements of the diagonal matrix D.  
 *  
 *  LLD     (input) DOUBLE PRECISION array, dimension (N-1)  
 *          The (N-1) elements L(i)*L(i)*D(i).  
 *  
 *  SIGMA   (input) DOUBLE PRECISION  
 *          Shift amount in T - sigma I = L D L^T.  
 *  
 *  PIVMIN  (input) DOUBLE PRECISION  
 *          The minimum pivot in the Sturm sequence.  May be used  
 *          when zero pivots are encountered on non-IEEE-754  
 *          architectures.  
 *  
 *  R       (input) INTEGER  
 *          The twist index for the twisted factorization that is used  
 *          for the negcount.  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  Based on contributions by  
 *     Osni Marques, LBNL/NERSC, USA  
 *     Christof Voemel, University of California, Berkeley, USA  
 *     Jason Riedy, University of California, Berkeley, USA  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.8  
changed lines
  Added in v.1.9

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