slarrc.f.html

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      SUBROUTINE <a name="SLARRC.1"></a><a href="slarrc.f.html#SLARRC.1">SLARRC</a>( JOBT, N, VL, VU, D, E, PIVMIN,
     $                            EIGCNT, LCNT, RCNT, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          JOBT
      INTEGER            EIGCNT, INFO, LCNT, N, RCNT
      REAL               PIVMIN, VL, VU
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      REAL               D( * ), E( * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Find the number of eigenvalues of the symmetric tridiagonal matrix T
</span><span class="comment">*</span><span class="comment">  that are in the interval (VL,VU] if JOBT = 'T', and of L D L^T
</span><span class="comment">*</span><span class="comment">  if JOBT = 'L'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  JOBT    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'T':  Compute Sturm count for matrix T.
</span><span class="comment">*</span><span class="comment">          = 'L':  Compute Sturm count for matrix L D L^T.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the matrix. N &gt; 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  VL      (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment">  VU      (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment">          The lower and upper bounds for the eigenvalues.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  D       (input) DOUBLE PRECISION array, dimension (N)
</span><span class="comment">*</span><span class="comment">          JOBT = 'T': The N diagonal elements of the tridiagonal matrix T.
</span><span class="comment">*</span><span class="comment">          JOBT = 'L': The N diagonal elements of the diagonal matrix D.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  E       (input) DOUBLE PRECISION array, dimension (N)
</span><span class="comment">*</span><span class="comment">          JOBT = 'T': The N-1 offdiagonal elements of the matrix T.
</span><span class="comment">*</span><span class="comment">          JOBT = 'L': The N-1 offdiagonal elements of the matrix L.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  PIVMIN  (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment">          The minimum pivot in the Sturm sequence for T.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  EIGCNT  (output) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of eigenvalues of the symmetric tridiagonal matrix T
</span><span class="comment">*</span><span class="comment">          that are in the interval (VL,VU]
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LCNT    (output) INTEGER
</span><span class="comment">*</span><span class="comment">  RCNT    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          The left and right negcounts of the interval.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO    (output) INTEGER
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Further Details
</span><span class="comment">*</span><span class="comment">  ===============
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Based on contributions by
</span><span class="comment">*</span><span class="comment">     Beresford Parlett, University of California, Berkeley, USA
</span><span class="comment">*</span><span class="comment">     Jim Demmel, University of California, Berkeley, USA
</span><span class="comment">*</span><span class="comment">     Inderjit Dhillon, University of Texas, Austin, USA
</span><span class="comment">*</span><span class="comment">     Osni Marques, LBNL/NERSC, USA
</span><span class="comment">*</span><span class="comment">     Christof Voemel, University of California, Berkeley, USA
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      REAL               ZERO
      PARAMETER          ( ZERO = 0.0E0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            I
      LOGICAL            MATT
      REAL               LPIVOT, RPIVOT, SL, SU, TMP, TMP2

<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.82"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      EXTERNAL           <a name="LSAME.83"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      LCNT = 0
      RCNT = 0
      EIGCNT = 0
      MATT = <a name="LSAME.91"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBT, <span class="string">'T'</span> )


      IF (MATT) THEN
<span class="comment">*</span><span class="comment">        Sturm sequence count on T
</span>         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
<span class="comment">*</span><span class="comment">        Sturm sequence count on L D L^T
</span>         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)
<span class="comment">*</span><span class="comment">
</span>            TMP2 = TMP / LPIVOT
            IF( TMP2.EQ.ZERO ) THEN
               SL =  TMP - VL
            ELSE
               SL = SL*TMP2 - VL
            END IF
<span class="comment">*</span><span class="comment">
</span>            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
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     end of <a name="SLARRC.157"></a><a href="slarrc.f.html#SLARRC.1">SLARRC</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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