slarra()

subroutine slarra	(	integer	N,
		real, dimension( * )	D,
		real, dimension( * )	E,
		real, dimension( * )	E2,
		real	SPLTOL,
		real	TNRM,
		integer	NSPLIT,
		integer, dimension( * )	ISPLIT,
		integer	INFO
	)

SLARRA computes the splitting points with the specified threshold.

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Purpose:

 Compute the splitting points with threshold SPLTOL.
 SLARRA sets any "small" off-diagonal elements to zero.

Parameters

[in]	N	N is INTEGER The order of the matrix. N > 0.
[in]	D	D is REAL array, dimension (N) On entry, the N diagonal elements of the tridiagonal matrix T.
[in,out]	E	E is REAL 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.
[in,out]	E2	E2 is REAL 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
[in]	SPLTOL	SPLTOL is REAL 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
[in]	TNRM	TNRM is REAL The norm of the matrix.
[out]	NSPLIT	NSPLIT is INTEGER The number of blocks T splits into. 1 <= NSPLIT <= N.
[out]	ISPLIT	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.
[out]	INFO	INFO is INTEGER = 0: successful exit

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date

June 2017

Contributors:

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

Definition at line 138 of file slarra.f.

*
*  -- LAPACK auxiliary routine (version 3.7.1) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     June 2017
*
*     .. Scalar Arguments ..
      INTEGER            INFO, N, NSPLIT
      REAL                SPLTOL, TNRM
*     ..
*     .. Array Arguments ..
      INTEGER            ISPLIT( * )
      REAL               D( * ), E( * ), E2( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO
      parameter( zero = 0.0e0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I
      REAL               EABS, TMP1
 
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs
*     ..
*     .. Executable Statements ..
*
      info = 0
*
*     Quick return if possible
*
      IF( n.LE.0 ) THEN
         RETURN
      END IF
*
*     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 SLARRA
*

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