LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ zggbak()

subroutine zggbak ( character job,
character side,
integer n,
integer ilo,
integer ihi,
double precision, dimension( * ) lscale,
double precision, dimension( * ) rscale,
integer m,
complex*16, dimension( ldv, * ) v,
integer ldv,
integer info )

ZGGBAK

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Purpose:
!>
!> ZGGBAK forms the right or left eigenvectors of a complex generalized
!> eigenvalue problem A*x = lambda*B*x, by backward transformation on
!> the computed eigenvectors of the balanced pair of matrices output by
!> ZGGBAL.
!>
Parameters
[in]JOB
!>          JOB is CHARACTER*1
!>          Specifies the type of backward transformation required:
!>          = 'N':  do nothing, return immediately;
!>          = 'P':  do backward transformation for permutation only;
!>          = 'S':  do backward transformation for scaling only;
!>          = 'B':  do backward transformations for both permutation and
!>                  scaling.
!>          JOB must be the same as the argument JOB supplied to ZGGBAL.
!>
[in]SIDE
!>          SIDE is CHARACTER*1
!>          = 'R':  V contains right eigenvectors;
!>          = 'L':  V contains left eigenvectors.
!>
[in]N
!>          N is INTEGER
!>          The number of rows of the matrix V.  N >= 0.
!>
[in]ILO
!>          ILO is INTEGER
!>
[in]IHI
!>          IHI is INTEGER
!>          The integers ILO and IHI determined by ZGGBAL.
!>          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
!>
[in]LSCALE
!>          LSCALE is DOUBLE PRECISION array, dimension (N)
!>          Details of the permutations and/or scaling factors applied
!>          to the left side of A and B, as returned by ZGGBAL.
!>
[in]RSCALE
!>          RSCALE is DOUBLE PRECISION array, dimension (N)
!>          Details of the permutations and/or scaling factors applied
!>          to the right side of A and B, as returned by ZGGBAL.
!>
[in]M
!>          M is INTEGER
!>          The number of columns of the matrix V.  M >= 0.
!>
[in,out]V
!>          V is COMPLEX*16 array, dimension (LDV,M)
!>          On entry, the matrix of right or left eigenvectors to be
!>          transformed, as returned by ZTGEVC.
!>          On exit, V is overwritten by the transformed eigenvectors.
!>
[in]LDV
!>          LDV is INTEGER
!>          The leading dimension of the matrix V. LDV >= max(1,N).
!>
[out]INFO
!>          INFO is INTEGER
!>          = 0:  successful exit.
!>          < 0:  if INFO = -i, the i-th argument had an illegal value.
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
!>
!>  See R.C. Ward, Balancing the generalized eigenvalue problem,
!>                 SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.
!>

Definition at line 144 of file zggbak.f.

147*
148* -- LAPACK computational routine --
149* -- LAPACK is a software package provided by Univ. of Tennessee, --
150* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
151*
152* .. Scalar Arguments ..
153 CHARACTER JOB, SIDE
154 INTEGER IHI, ILO, INFO, LDV, M, N
155* ..
156* .. Array Arguments ..
157 DOUBLE PRECISION LSCALE( * ), RSCALE( * )
158 COMPLEX*16 V( LDV, * )
159* ..
160*
161* =====================================================================
162*
163* .. Local Scalars ..
164 LOGICAL LEFTV, RIGHTV
165 INTEGER I, K
166* ..
167* .. External Functions ..
168 LOGICAL LSAME
169 EXTERNAL lsame
170* ..
171* .. External Subroutines ..
172 EXTERNAL xerbla, zdscal, zswap
173* ..
174* .. Intrinsic Functions ..
175 INTRINSIC max, int
176* ..
177* .. Executable Statements ..
178*
179* Test the input parameters
180*
181 rightv = lsame( side, 'R' )
182 leftv = lsame( side, 'L' )
183*
184 info = 0
185 IF( .NOT.lsame( job, 'N' ) .AND.
186 $ .NOT.lsame( job, 'P' ) .AND.
187 $ .NOT.lsame( job, 'S' ) .AND.
188 $ .NOT.lsame( job, 'B' ) ) THEN
189 info = -1
190 ELSE IF( .NOT.rightv .AND. .NOT.leftv ) THEN
191 info = -2
192 ELSE IF( n.LT.0 ) THEN
193 info = -3
194 ELSE IF( ilo.LT.1 ) THEN
195 info = -4
196 ELSE IF( n.EQ.0 .AND. ihi.EQ.0 .AND. ilo.NE.1 ) THEN
197 info = -4
198 ELSE IF( n.GT.0 .AND. ( ihi.LT.ilo .OR. ihi.GT.max( 1, n ) ) )
199 $ THEN
200 info = -5
201 ELSE IF( n.EQ.0 .AND. ilo.EQ.1 .AND. ihi.NE.0 ) THEN
202 info = -5
203 ELSE IF( m.LT.0 ) THEN
204 info = -8
205 ELSE IF( ldv.LT.max( 1, n ) ) THEN
206 info = -10
207 END IF
208 IF( info.NE.0 ) THEN
209 CALL xerbla( 'ZGGBAK', -info )
210 RETURN
211 END IF
212*
213* Quick return if possible
214*
215 IF( n.EQ.0 )
216 $ RETURN
217 IF( m.EQ.0 )
218 $ RETURN
219 IF( lsame( job, 'N' ) )
220 $ RETURN
221*
222 IF( ilo.EQ.ihi )
223 $ GO TO 30
224*
225* Backward balance
226*
227 IF( lsame( job, 'S' ) .OR. lsame( job, 'B' ) ) THEN
228*
229* Backward transformation on right eigenvectors
230*
231 IF( rightv ) THEN
232 DO 10 i = ilo, ihi
233 CALL zdscal( m, rscale( i ), v( i, 1 ), ldv )
234 10 CONTINUE
235 END IF
236*
237* Backward transformation on left eigenvectors
238*
239 IF( leftv ) THEN
240 DO 20 i = ilo, ihi
241 CALL zdscal( m, lscale( i ), v( i, 1 ), ldv )
242 20 CONTINUE
243 END IF
244 END IF
245*
246* Backward permutation
247*
248 30 CONTINUE
249 IF( lsame( job, 'P' ) .OR. lsame( job, 'B' ) ) THEN
250*
251* Backward permutation on right eigenvectors
252*
253 IF( rightv ) THEN
254 IF( ilo.EQ.1 )
255 $ GO TO 50
256 DO 40 i = ilo - 1, 1, -1
257 k = int(rscale( i ))
258 IF( k.EQ.i )
259 $ GO TO 40
260 CALL zswap( m, v( i, 1 ), ldv, v( k, 1 ), ldv )
261 40 CONTINUE
262*
263 50 CONTINUE
264 IF( ihi.EQ.n )
265 $ GO TO 70
266 DO 60 i = ihi + 1, n
267 k = int(rscale( i ))
268 IF( k.EQ.i )
269 $ GO TO 60
270 CALL zswap( m, v( i, 1 ), ldv, v( k, 1 ), ldv )
271 60 CONTINUE
272 END IF
273*
274* Backward permutation on left eigenvectors
275*
276 70 CONTINUE
277 IF( leftv ) THEN
278 IF( ilo.EQ.1 )
279 $ GO TO 90
280 DO 80 i = ilo - 1, 1, -1
281 k = int(lscale( i ))
282 IF( k.EQ.i )
283 $ GO TO 80
284 CALL zswap( m, v( i, 1 ), ldv, v( k, 1 ), ldv )
285 80 CONTINUE
286*
287 90 CONTINUE
288 IF( ihi.EQ.n )
289 $ GO TO 110
290 DO 100 i = ihi + 1, n
291 k = int(lscale( i ))
292 IF( k.EQ.i )
293 $ GO TO 100
294 CALL zswap( m, v( i, 1 ), ldv, v( k, 1 ), ldv )
295 100 CONTINUE
296 END IF
297 END IF
298*
299 110 CONTINUE
300*
301 RETURN
302*
303* End of ZGGBAK
304*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
zdscal
subroutine zdscal(n, da, zx, incx)
ZDSCAL
Definition zdscal.f:78
zswap
subroutine zswap(n, zx, incx, zy, incy)
ZSWAP
Definition zswap.f:81
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