252 lines
6.4 KiB
Fortran
252 lines
6.4 KiB
Fortran
*> \brief \b DLARRC computes the number of eigenvalues of the symmetric tridiagonal matrix.
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download DLARRC + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarrc.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarrc.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarrc.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE DLARRC( JOBT, N, VL, VU, D, E, PIVMIN,
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* EIGCNT, LCNT, RCNT, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER JOBT
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* INTEGER EIGCNT, INFO, LCNT, N, RCNT
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* DOUBLE PRECISION PIVMIN, VL, VU
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION D( * ), E( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> Find the number of eigenvalues of the symmetric tridiagonal matrix T
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*> that are in the interval (VL,VU] if JOBT = 'T', and of L D L^T
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*> if JOBT = 'L'.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] JOBT
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*> \verbatim
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*> JOBT is CHARACTER*1
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*> = 'T': Compute Sturm count for matrix T.
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*> = 'L': Compute Sturm count for matrix L D L^T.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The order of the matrix. N > 0.
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*> \endverbatim
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*>
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*> \param[in] VL
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*> \verbatim
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*> VL is DOUBLE PRECISION
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*> The lower bound for the eigenvalues.
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*> \endverbatim
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*>
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*> \param[in] VU
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*> \verbatim
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*> VU is DOUBLE PRECISION
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*> The upper bound for the eigenvalues.
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*> \endverbatim
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*>
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*> \param[in] D
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*> \verbatim
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*> D is DOUBLE PRECISION array, dimension (N)
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*> JOBT = 'T': The N diagonal elements of the tridiagonal matrix T.
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*> JOBT = 'L': The N diagonal elements of the diagonal matrix D.
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*> \endverbatim
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*>
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*> \param[in] E
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*> \verbatim
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*> E is DOUBLE PRECISION array, dimension (N)
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*> JOBT = 'T': The N-1 offdiagonal elements of the matrix T.
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*> JOBT = 'L': The N-1 offdiagonal elements of the matrix L.
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*> \endverbatim
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*>
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*> \param[in] PIVMIN
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*> \verbatim
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*> PIVMIN is DOUBLE PRECISION
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*> The minimum pivot in the Sturm sequence for T.
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*> \endverbatim
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*>
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*> \param[out] EIGCNT
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*> \verbatim
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*> EIGCNT is INTEGER
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*> The number of eigenvalues of the symmetric tridiagonal matrix T
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*> that are in the interval (VL,VU]
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*> \endverbatim
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*>
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*> \param[out] LCNT
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*> \verbatim
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*> LCNT is INTEGER
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*> \endverbatim
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*>
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*> \param[out] RCNT
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*> \verbatim
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*> RCNT is INTEGER
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*> The left and right negcounts of the interval.
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date June 2016
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*
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*> \ingroup OTHERauxiliary
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*
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*> \par Contributors:
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* ==================
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*>
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*> Beresford Parlett, University of California, Berkeley, USA \n
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*> Jim Demmel, University of California, Berkeley, USA \n
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*> Inderjit Dhillon, University of Texas, Austin, USA \n
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*> Osni Marques, LBNL/NERSC, USA \n
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*> Christof Voemel, University of California, Berkeley, USA
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*
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* =====================================================================
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SUBROUTINE DLARRC( JOBT, N, VL, VU, D, E, PIVMIN,
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$ EIGCNT, LCNT, RCNT, INFO )
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*
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* -- LAPACK auxiliary routine (version 3.7.1) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* June 2016
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*
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* .. Scalar Arguments ..
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CHARACTER JOBT
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INTEGER EIGCNT, INFO, LCNT, N, RCNT
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DOUBLE PRECISION PIVMIN, VL, VU
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION D( * ), E( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ZERO
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PARAMETER ( ZERO = 0.0D0 )
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* ..
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* .. Local Scalars ..
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INTEGER I
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LOGICAL MATT
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DOUBLE PRECISION LPIVOT, RPIVOT, SL, SU, TMP, TMP2
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. Executable Statements ..
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*
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INFO = 0
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*
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* Quick return if possible
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*
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IF( N.LE.0 ) THEN
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RETURN
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END IF
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*
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LCNT = 0
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RCNT = 0
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EIGCNT = 0
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MATT = LSAME( JOBT, 'T' )
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IF (MATT) THEN
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* Sturm sequence count on T
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LPIVOT = D( 1 ) - VL
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RPIVOT = D( 1 ) - VU
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IF( LPIVOT.LE.ZERO ) THEN
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LCNT = LCNT + 1
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ENDIF
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IF( RPIVOT.LE.ZERO ) THEN
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RCNT = RCNT + 1
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ENDIF
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DO 10 I = 1, N-1
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TMP = E(I)**2
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LPIVOT = ( D( I+1 )-VL ) - TMP/LPIVOT
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RPIVOT = ( D( I+1 )-VU ) - TMP/RPIVOT
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IF( LPIVOT.LE.ZERO ) THEN
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LCNT = LCNT + 1
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ENDIF
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IF( RPIVOT.LE.ZERO ) THEN
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RCNT = RCNT + 1
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ENDIF
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10 CONTINUE
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ELSE
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* Sturm sequence count on L D L^T
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SL = -VL
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SU = -VU
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DO 20 I = 1, N - 1
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LPIVOT = D( I ) + SL
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RPIVOT = D( I ) + SU
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IF( LPIVOT.LE.ZERO ) THEN
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LCNT = LCNT + 1
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ENDIF
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IF( RPIVOT.LE.ZERO ) THEN
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RCNT = RCNT + 1
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ENDIF
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TMP = E(I) * D(I) * E(I)
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*
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TMP2 = TMP / LPIVOT
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IF( TMP2.EQ.ZERO ) THEN
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SL = TMP - VL
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ELSE
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SL = SL*TMP2 - VL
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END IF
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*
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TMP2 = TMP / RPIVOT
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IF( TMP2.EQ.ZERO ) THEN
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SU = TMP - VU
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ELSE
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SU = SU*TMP2 - VU
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END IF
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20 CONTINUE
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LPIVOT = D( N ) + SL
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RPIVOT = D( N ) + SU
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IF( LPIVOT.LE.ZERO ) THEN
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LCNT = LCNT + 1
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ENDIF
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IF( RPIVOT.LE.ZERO ) THEN
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RCNT = RCNT + 1
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ENDIF
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ENDIF
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EIGCNT = RCNT - LCNT
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RETURN
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*
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* end of DLARRC
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*
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END
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