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