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*> \brief \b DLARRA computes the splitting points with the specified threshold.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DLARRA + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarra.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarra.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarra.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DLARRA( N, D, E, E2, SPLTOL, TNRM,
* NSPLIT, ISPLIT, INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, N, NSPLIT
* DOUBLE PRECISION SPLTOL, TNRM
* ..
* .. Array Arguments ..
* INTEGER ISPLIT( * )
* DOUBLE PRECISION D( * ), E( * ), E2( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> Compute the splitting points with threshold SPLTOL.
*> DLARRA sets any "small" off-diagonal elements to zero.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix. N > 0.
*> \endverbatim
*>
*> \param[in] D
*> \verbatim
*> D is DOUBLE PRECISION array, dimension (N)
*> On entry, the N diagonal elements of the tridiagonal
*> matrix T.
*> \endverbatim
*>
*> \param[in,out] E
*> \verbatim
*> E is 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.
*> \endverbatim
*>
*> \param[in,out] E2
*> \verbatim
*> E2 is 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
*> \endverbatim
*>
*> \param[in] SPLTOL
*> \verbatim
*> SPLTOL is 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
*> \endverbatim
*>
*> \param[in] TNRM
*> \verbatim
*> TNRM is DOUBLE PRECISION
*> The norm of the matrix.
*> \endverbatim
*>
*> \param[out] NSPLIT
*> \verbatim
*> NSPLIT is INTEGER
*> The number of blocks T splits into. 1 <= NSPLIT <= N.
*> \endverbatim
*>
*> \param[out] ISPLIT
*> \verbatim
*> ISPLIT is 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.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Contributors:
* ==================
*>
*> Beresford Parlett, University of California, Berkeley, USA \n
*> Jim Demmel, University of California, Berkeley, USA \n
*> Inderjit Dhillon, University of Texas, Austin, USA \n
*> Osni Marques, LBNL/NERSC, USA \n
*> Christof Voemel, University of California, Berkeley, USA
*
* =====================================================================
SUBROUTINE DLARRA( N, D, E, E2, SPLTOL, TNRM,
$ NSPLIT, ISPLIT, INFO )
*
* -- LAPACK auxiliary routine (version 3.4.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* September 2012
*
* .. Scalar Arguments ..
INTEGER INFO, N, NSPLIT
DOUBLE PRECISION SPLTOL, TNRM
* ..
* .. Array Arguments ..
INTEGER ISPLIT( * )
DOUBLE PRECISION D( * ), E( * ), E2( * )
* ..
*
* =====================================================================
*
* .. 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
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