dlarra.f

          SUBROUTINE DLARRA( N, D, E, E2, SPLTOL, TNRM,
         $                    NSPLIT, ISPLIT, INFO )
          IMPLICIT NONE
    *
    *  -- LAPACK auxiliary routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          INTEGER            INFO, N, NSPLIT
          DOUBLE PRECISION    SPLTOL, TNRM
    *     ..
    *     .. Array Arguments ..
          INTEGER            ISPLIT( * )
          DOUBLE PRECISION   D( * ), E( * ), E2( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  Compute the splitting points with threshold SPLTOL.
    *  DLARRA sets any "small" off-diagonal elements to zero.
    *
    *  Arguments
    *  =========
    *
    *  N       (input) INTEGER
    *          The order of the matrix. N > 0.
    *
    *  D       (input) DOUBLE PRECISION array, dimension (N)
    *          On entry, the N diagonal elements of the tridiagonal
    *          matrix T.
    *
    *  E       (input/output) DOUBLE PRECISION array, dimension (N)
    *          On entry, the first (N-1) entries contain the subdiagonal
    *          elements of the tridiagonal matrix T; E(N) need not be set.
    *          On exit, the entries E( ISPLIT( I ) ), 1 <= I <= NSPLIT,
    *          are set to zero, the other entries of E are untouched.
    *
    *  E2      (input/output) DOUBLE PRECISION array, dimension (N)
    *          On entry, the first (N-1) entries contain the SQUARES of the
    *          subdiagonal elements of the tridiagonal matrix T;
    *          E2(N) need not be set.
    *          On exit, the entries E2( ISPLIT( I ) ),
    *          1 <= I <= NSPLIT, have been set to zero
    *
    *  SPLTOL (input) DOUBLE PRECISION
    *          The threshold for splitting. Two criteria can be used:
    *          SPLTOL<0 : criterion based on absolute off-diagonal value
    *          SPLTOL>0 : criterion that preserves relative accuracy
    *
    *  TNRM (input) DOUBLE PRECISION
    *          The norm of the matrix.
    *
    *  NSPLIT  (output) INTEGER
    *          The number of blocks T splits into. 1 <= NSPLIT <= N.
    *
    *  ISPLIT  (output) INTEGER array, dimension (N)
    *          The splitting points, at which T breaks up into blocks.
    *          The first block consists of rows/columns 1 to ISPLIT(1),
    *          the second of rows/columns ISPLIT(1)+1 through ISPLIT(2),
    *          etc., and the NSPLIT-th consists of rows/columns
    *          ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N.
    *
    *
    *  INFO    (output) INTEGER
    *          = 0:  successful exit
    *
    *  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
          DOUBLE PRECISION   EABS, TMP1

    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          ABS
    *     ..
    *     .. Executable Statements ..
    *
          INFO = 0

    *     Compute splitting points
          NSPLIT = 1
          IF(SPLTOL.LT.ZERO) THEN
    *        Criterion based on absolute off-diagonal value
             TMP1 = ABS(SPLTOL)* TNRM
             DO 9 I = 1, N-1
                EABS = ABS( E(I) )
                IF( EABS .LE. TMP1) THEN
                   E(I) = ZERO
                   E2(I) = ZERO
                   ISPLIT( NSPLIT ) = I
                   NSPLIT = NSPLIT + 1
                END IF
     9       CONTINUE
          ELSE
    *        Criterion that guarantees relative accuracy
             DO 10 I = 1, N-1
                EABS = ABS( E(I) )
                IF( EABS .LE. SPLTOL * SQRT(ABS(D(I)))*SQRT(ABS(D(I+1))) )
         $      THEN
                   E(I) = ZERO
                   E2(I) = ZERO
                   ISPLIT( NSPLIT ) = I
                   NSPLIT = NSPLIT + 1
                END IF
     10      CONTINUE
          ENDIF
          ISPLIT( NSPLIT ) = N

          RETURN
    *
    *     End of DLARRA
    *
          END