 LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 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.

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```
Date
September 2012
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.

138 *
139 * -- LAPACK auxiliary routine (version 3.4.2) --
140 * -- LAPACK is a software package provided by Univ. of Tennessee, --
141 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
142 * September 2012
143 *
144 * .. Scalar Arguments ..
145  INTEGER info, n, nsplit
146  REAL spltol, tnrm
147 * ..
148 * .. Array Arguments ..
149  INTEGER isplit( * )
150  REAL d( * ), e( * ), e2( * )
151 * ..
152 *
153 * =====================================================================
154 *
155 * .. Parameters ..
156  REAL zero
157  parameter ( zero = 0.0e0 )
158 * ..
159 * .. Local Scalars ..
160  INTEGER i
161  REAL eabs, tmp1
162
163 * ..
164 * .. Intrinsic Functions ..
165  INTRINSIC abs
166 * ..
167 * .. Executable Statements ..
168 *
169  info = 0
170
171 * Compute splitting points
172  nsplit = 1
173  IF(spltol.LT.zero) THEN
174 * Criterion based on absolute off-diagonal value
175  tmp1 = abs(spltol)* tnrm
176  DO 9 i = 1, n-1
177  eabs = abs( e(i) )
178  IF( eabs .LE. tmp1) THEN
179  e(i) = zero
180  e2(i) = zero
181  isplit( nsplit ) = i
182  nsplit = nsplit + 1
183  END IF
184  9 CONTINUE
185  ELSE
186 * Criterion that guarantees relative accuracy
187  DO 10 i = 1, n-1
188  eabs = abs( e(i) )
189  IF( eabs .LE. spltol * sqrt(abs(d(i)))*sqrt(abs(d(i+1))) )
190  \$ THEN
191  e(i) = zero
192  e2(i) = zero
193  isplit( nsplit ) = i
194  nsplit = nsplit + 1
195  END IF
196  10 CONTINUE
197  ENDIF
198  isplit( nsplit ) = n
199
200  RETURN
201 *
202 * End of SLARRA
203 *

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