*> \brief \b SLARRC 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 SLARRC + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE SLARRC( JOBT, N, VL, VU, D, E, PIVMIN, * EIGCNT, LCNT, RCNT, INFO ) * * .. Scalar Arguments .. * CHARACTER JOBT * INTEGER EIGCNT, INFO, LCNT, N, RCNT * REAL PIVMIN, VL, VU * .. * .. Array Arguments .. * REAL 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 REAL *> The lower bound for the eigenvalues. *> \endverbatim *> *> \param[in] VU *> \verbatim *> VU is REAL *> The upper bound for the eigenvalues. *> \endverbatim *> *> \param[in] D *> \verbatim *> D is REAL 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 REAL 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 REAL *> 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 SLARRC( JOBT, N, VL, VU, D, E, PIVMIN, \$ EIGCNT, LCNT, RCNT, INFO ) * * -- LAPACK auxiliary routine (version 3.7.1) -- * -- 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 REAL PIVMIN, VL, VU * .. * .. Array Arguments .. REAL D( * ), E( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E0 ) * .. * .. Local Scalars .. INTEGER I LOGICAL MATT REAL 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 SLARRC * END