160 lines
4.3 KiB
FortranFixed
160 lines
4.3 KiB
FortranFixed
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 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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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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* Purpose
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* =======
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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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*
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* Arguments
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* =========
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*
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* JOBT (input) 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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*
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* N (input) INTEGER
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* The order of the matrix. N > 0.
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*
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* VL (input) DOUBLE PRECISION
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* VU (input) DOUBLE PRECISION
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* The lower and upper bounds for the eigenvalues.
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*
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* D (input) 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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*
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* E (input) 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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*
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* PIVMIN (input) DOUBLE PRECISION
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* The minimum pivot in the Sturm sequence for T.
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*
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* EIGCNT (output) 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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*
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* LCNT (output) INTEGER
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* RCNT (output) INTEGER
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* The left and right negcounts of the interval.
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*
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* INFO (output) INTEGER
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*
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* Further Details
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* ===============
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*
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* Based on contributions by
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* Beresford Parlett, University of California, Berkeley, USA
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* Jim Demmel, University of California, Berkeley, USA
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* Inderjit Dhillon, University of Texas, Austin, USA
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* Osni Marques, LBNL/NERSC, USA
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* Christof Voemel, University of California, Berkeley, USA
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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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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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