dlarrc.f

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*> \brief \b DLARRC computes the number of eigenvalues of the symmetric tridiagonal matrix.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
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*> [TXT]</a>
*> \endhtmlonly 
*
*  Definition:
*  ===========
*
*       SUBROUTINE DLARRC( JOBT, N, VL, VU, D, E, PIVMIN,
*                                   EIGCNT, LCNT, RCNT, INFO )
* 
*       .. Scalar Arguments ..
*       CHARACTER          JOBT
*       INTEGER            EIGCNT, INFO, LCNT, N, RCNT
*       DOUBLE PRECISION   PIVMIN, VL, VU
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   D( * ), E( * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> Find the number of eigenvalues of the symmetric tridiagonal matrix T
*> that are in the interval (VL,VU] if JOBT = 'T', and of L D L^T
*> if JOBT = 'L'.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] JOBT
*> \verbatim
*>          JOBT is CHARACTER*1
*>          = 'T':  Compute Sturm count for matrix T.
*>          = 'L':  Compute Sturm count for matrix L D L^T.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix. N > 0.
*> \endverbatim
*>
*> \param[in] VL
*> \verbatim
*>          VL is DOUBLE PRECISION
*>          The lower bound for the eigenvalues.
*> \endverbatim
*>
*> \param[in] VU
*> \verbatim
*>          VU is DOUBLE PRECISION
*>          The upper bound for the eigenvalues.
*> \endverbatim
*>
*> \param[in] D
*> \verbatim
*>          D is DOUBLE PRECISION array, dimension (N)
*>          JOBT = 'T': The N diagonal elements of the tridiagonal matrix T.
*>          JOBT = 'L': The N diagonal elements of the diagonal matrix D.
*> \endverbatim
*>
*> \param[in] E
*> \verbatim
*>          E is DOUBLE PRECISION array, dimension (N)
*>          JOBT = 'T': The N-1 offdiagonal elements of the matrix T.
*>          JOBT = 'L': The N-1 offdiagonal elements of the matrix L.
*> \endverbatim
*>
*> \param[in] PIVMIN
*> \verbatim
*>          PIVMIN is DOUBLE PRECISION
*>          The minimum pivot in the Sturm sequence for T.
*> \endverbatim
*>
*> \param[out] EIGCNT
*> \verbatim
*>          EIGCNT is INTEGER
*>          The number of eigenvalues of the symmetric tridiagonal matrix T
*>          that are in the interval (VL,VU]
*> \endverbatim
*>
*> \param[out] LCNT
*> \verbatim
*>          LCNT is INTEGER
*> \endverbatim
*>
*> \param[out] RCNT
*> \verbatim
*>          RCNT is INTEGER
*>          The left and right negcounts of the interval.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date June 2016
*
*> \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 dlarrc( JOBT, N, VL, VU, D, E, PIVMIN,
     $                            eigcnt, lcnt, rcnt, info )
*
*  -- LAPACK auxiliary routine (version 3.6.1) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     June 2016
*
*     .. Scalar Arguments ..
      CHARACTER          JOBT
      INTEGER            EIGCNT, INFO, LCNT, N, RCNT
      DOUBLE PRECISION   PIVMIN, VL, VU
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   D( * ), E( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO
      parameter                ( zero = 0.0d0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I
      LOGICAL            MATT
      DOUBLE PRECISION   LPIVOT, RPIVOT, SL, SU, TMP, TMP2

*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. Executable Statements ..
*
      info = 0
      lcnt = 0
      rcnt = 0
      eigcnt = 0
      matt = lsame( jobt, 'T' )


      IF (matt) THEN
*        Sturm sequence count on T
         lpivot = d( 1 ) - vl
         rpivot = d( 1 ) - vu
         IF( lpivot.LE.zero ) THEN
            lcnt = lcnt + 1
         ENDIF
         IF( rpivot.LE.zero ) THEN
            rcnt = rcnt + 1
         ENDIF
         DO 10 i = 1, n-1
            tmp = e(i)**2
            lpivot = ( d( i+1 )-vl ) - tmp/lpivot
            rpivot = ( d( i+1 )-vu ) - tmp/rpivot
            IF( lpivot.LE.zero ) THEN
               lcnt = lcnt + 1
            ENDIF
            IF( rpivot.LE.zero ) THEN
               rcnt = rcnt + 1
            ENDIF
 10      CONTINUE
      ELSE
*        Sturm sequence count on L D L^T
         sl = -vl
         su = -vu
         DO 20 i = 1, n - 1
            lpivot = d( i ) + sl
            rpivot = d( i ) + su
            IF( lpivot.LE.zero ) THEN
               lcnt = lcnt + 1
            ENDIF
            IF( rpivot.LE.zero ) THEN
               rcnt = rcnt + 1
            ENDIF
            tmp = e(i) * d(i) * e(i)
*
            tmp2 = tmp / lpivot
            IF( tmp2.EQ.zero ) THEN
               sl =  tmp - vl
            ELSE
               sl = sl*tmp2 - vl
            END IF
*
            tmp2 = tmp / rpivot
            IF( tmp2.EQ.zero ) THEN
               su =  tmp - vu
            ELSE
               su = su*tmp2 - vu
            END IF
 20      CONTINUE
         lpivot = d( n ) + sl
         rpivot = d( n ) + su
         IF( lpivot.LE.zero ) THEN
            lcnt = lcnt + 1
         ENDIF
         IF( rpivot.LE.zero ) THEN
            rcnt = rcnt + 1
         ENDIF
      ENDIF
      eigcnt = rcnt - lcnt

      RETURN
*
*     end of DLARRC
*
      END