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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/
*
*> \htmlonly
*> Download DLARRC + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarrc.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarrc.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarrc.f">
*> [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 OTHERauxiliary
*
*> \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 3.7.0) --
* -- 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
*
* Quick return if possible
*
IF( N.LE.0 ) THEN
RETURN
END IF
*
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
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