dlarrc.f

          SUBROUTINE DLARRC( JOBT, N, VL, VU, D, E, PIVMIN,
         $                            EIGCNT, LCNT, RCNT, INFO )
    *
    *  -- LAPACK auxiliary routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          JOBT
          INTEGER            EIGCNT, INFO, LCNT, N, RCNT
          DOUBLE PRECISION   PIVMIN, VL, VU
    *     ..
    *     .. Array Arguments ..
          DOUBLE PRECISION   D( * ), E( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  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'.
    *
    *  Arguments
    *  =========
    *
    *  JOBT    (input) CHARACTER*1
    *          = 'T':  Compute Sturm count for matrix T.
    *          = 'L':  Compute Sturm count for matrix L D L^T.
    *
    *  N       (input) INTEGER
    *          The order of the matrix. N > 0.
    *
    *  VL      (input) DOUBLE PRECISION
    *  VU      (input) DOUBLE PRECISION
    *          The lower and upper bounds for the eigenvalues.
    *
    *  D       (input) 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.
    *
    *  E       (input) 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.
    *
    *  PIVMIN  (input) DOUBLE PRECISION
    *          The minimum pivot in the Sturm sequence for T.
    *
    *  EIGCNT  (output) INTEGER
    *          The number of eigenvalues of the symmetric tridiagonal matrix T
    *          that are in the interval (VL,VU]
    *
    *  LCNT    (output) INTEGER
    *  RCNT    (output) INTEGER
    *          The left and right negcounts of the interval.
    *
    *  INFO    (output) INTEGER
    *
    *  Further Details
    *  ===============
    *
    *  Based on contributions by
    *     Beresford Parlett, University of California, Berkeley, USA
    *     Jim Demmel, University of California, Berkeley, USA
    *     Inderjit Dhillon, University of Texas, Austin, USA
    *     Osni Marques, LBNL/NERSC, USA
    *     Christof Voemel, University of California, Berkeley, USA
    *
    *  =====================================================================
    *
    *     .. 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