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SUBROUTINE DLARRC( JOBT, N, VL, VU, D, E, PIVMIN,
$ EIGCNT, LCNT, RCNT, INFO )
*
* -- LAPACK auxiliary routine (version 3.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver 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
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