LAPACK  3.6.1
LAPACK: Linear Algebra PACKage
subroutine dlarra ( integer  N,
double precision, dimension( * )  D,
double precision, dimension( * )  E,
double precision, dimension( * )  E2,
double precision  SPLTOL,
double precision  TNRM,
integer  NSPLIT,
integer, dimension( * )  ISPLIT,
integer  INFO 
)

DLARRA computes the splitting points with the specified threshold.

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Purpose: 
 Compute the splitting points with threshold SPLTOL.
 DLARRA 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 DOUBLE PRECISION array, dimension (N)
          On entry, the N diagonal elements of the tridiagonal
          matrix T.
[in,out]E
          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.
[in,out]E2
          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
[in]SPLTOL
          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
[in]TNRM
          TNRM is DOUBLE PRECISION
          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
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 dlarra.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  DOUBLE PRECISION spltol, tnrm
147 * ..
148 * .. Array Arguments ..
149  INTEGER isplit( * )
150  DOUBLE PRECISION d( * ), e( * ), e2( * )
151 * ..
152 *
153 * =====================================================================
154 *
155 * .. Parameters ..
156  DOUBLE PRECISION zero
157  parameter ( zero = 0.0d0 )
158 * ..
159 * .. Local Scalars ..
160  INTEGER i
161  DOUBLE PRECISION 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 DLARRA
203 *

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