LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ cggbak()

subroutine cggbak ( character  JOB,
character  SIDE,
integer  N,
integer  ILO,
integer  IHI,
real, dimension( * )  LSCALE,
real, dimension( * )  RSCALE,
integer  M,
complex, dimension( ldv, * )  V,
integer  LDV,
integer  INFO 
)

CGGBAK

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Purpose:
 CGGBAK 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
 CGGBAL.
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 CGGBAL.
[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 CGGBAL.
          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
[in]LSCALE
          LSCALE is REAL array, dimension (N)
          Details of the permutations and/or scaling factors applied
          to the left side of A and B, as returned by CGGBAL.
[in]RSCALE
          RSCALE is REAL array, dimension (N)
          Details of the permutations and/or scaling factors applied
          to the right side of A and B, as returned by CGGBAL.
[in]M
          M is INTEGER
          The number of columns of the matrix V.  M >= 0.
[in,out]V
          V is COMPLEX array, dimension (LDV,M)
          On entry, the matrix of right or left eigenvectors to be
          transformed, as returned by CTGEVC.
          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.
Date
December 2016
Further Details:
  See R.C. Ward, Balancing the generalized eigenvalue problem,
                 SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.

Definition at line 150 of file cggbak.f.

150 *
151 * -- LAPACK computational routine (version 3.7.0) --
152 * -- LAPACK is a software package provided by Univ. of Tennessee, --
153 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
154 * December 2016
155 *
156 * .. Scalar Arguments ..
157  CHARACTER job, side
158  INTEGER ihi, ilo, info, ldv, m, n
159 * ..
160 * .. Array Arguments ..
161  REAL lscale( * ), rscale( * )
162  COMPLEX v( ldv, * )
163 * ..
164 *
165 * =====================================================================
166 *
167 * .. Local Scalars ..
168  LOGICAL leftv, rightv
169  INTEGER i, k
170 * ..
171 * .. External Functions ..
172  LOGICAL lsame
173  EXTERNAL lsame
174 * ..
175 * .. External Subroutines ..
176  EXTERNAL csscal, cswap, xerbla
177 * ..
178 * .. Intrinsic Functions ..
179  INTRINSIC max
180 * ..
181 * .. Executable Statements ..
182 *
183 * Test the input parameters
184 *
185  rightv = lsame( side, 'R' )
186  leftv = lsame( side, 'L' )
187 *
188  info = 0
189  IF( .NOT.lsame( job, 'N' ) .AND. .NOT.lsame( job, 'P' ) .AND.
190  $ .NOT.lsame( job, 'S' ) .AND. .NOT.lsame( job, 'B' ) ) THEN
191  info = -1
192  ELSE IF( .NOT.rightv .AND. .NOT.leftv ) THEN
193  info = -2
194  ELSE IF( n.LT.0 ) THEN
195  info = -3
196  ELSE IF( ilo.LT.1 ) THEN
197  info = -4
198  ELSE IF( n.EQ.0 .AND. ihi.EQ.0 .AND. ilo.NE.1 ) THEN
199  info = -4
200  ELSE IF( n.GT.0 .AND. ( ihi.LT.ilo .OR. ihi.GT.max( 1, n ) ) )
201  $ THEN
202  info = -5
203  ELSE IF( n.EQ.0 .AND. ilo.EQ.1 .AND. ihi.NE.0 ) THEN
204  info = -5
205  ELSE IF( m.LT.0 ) THEN
206  info = -8
207  ELSE IF( ldv.LT.max( 1, n ) ) THEN
208  info = -10
209  END IF
210  IF( info.NE.0 ) THEN
211  CALL xerbla( 'CGGBAK', -info )
212  RETURN
213  END IF
214 *
215 * Quick return if possible
216 *
217  IF( n.EQ.0 )
218  $ RETURN
219  IF( m.EQ.0 )
220  $ RETURN
221  IF( lsame( job, 'N' ) )
222  $ RETURN
223 *
224  IF( ilo.EQ.ihi )
225  $ GO TO 30
226 *
227 * Backward balance
228 *
229  IF( lsame( job, 'S' ) .OR. lsame( job, 'B' ) ) THEN
230 *
231 * Backward transformation on right eigenvectors
232 *
233  IF( rightv ) THEN
234  DO 10 i = ilo, ihi
235  CALL csscal( m, rscale( i ), v( i, 1 ), ldv )
236  10 CONTINUE
237  END IF
238 *
239 * Backward transformation on left eigenvectors
240 *
241  IF( leftv ) THEN
242  DO 20 i = ilo, ihi
243  CALL csscal( m, lscale( i ), v( i, 1 ), ldv )
244  20 CONTINUE
245  END IF
246  END IF
247 *
248 * Backward permutation
249 *
250  30 CONTINUE
251  IF( lsame( job, 'P' ) .OR. lsame( job, 'B' ) ) THEN
252 *
253 * Backward permutation on right eigenvectors
254 *
255  IF( rightv ) THEN
256  IF( ilo.EQ.1 )
257  $ GO TO 50
258  DO 40 i = ilo - 1, 1, -1
259  k = rscale( i )
260  IF( k.EQ.i )
261  $ GO TO 40
262  CALL cswap( m, v( i, 1 ), ldv, v( k, 1 ), ldv )
263  40 CONTINUE
264 *
265  50 CONTINUE
266  IF( ihi.EQ.n )
267  $ GO TO 70
268  DO 60 i = ihi + 1, n
269  k = rscale( i )
270  IF( k.EQ.i )
271  $ GO TO 60
272  CALL cswap( m, v( i, 1 ), ldv, v( k, 1 ), ldv )
273  60 CONTINUE
274  END IF
275 *
276 * Backward permutation on left eigenvectors
277 *
278  70 CONTINUE
279  IF( leftv ) THEN
280  IF( ilo.EQ.1 )
281  $ GO TO 90
282  DO 80 i = ilo - 1, 1, -1
283  k = lscale( i )
284  IF( k.EQ.i )
285  $ GO TO 80
286  CALL cswap( m, v( i, 1 ), ldv, v( k, 1 ), ldv )
287  80 CONTINUE
288 *
289  90 CONTINUE
290  IF( ihi.EQ.n )
291  $ GO TO 110
292  DO 100 i = ihi + 1, n
293  k = lscale( i )
294  IF( k.EQ.i )
295  $ GO TO 100
296  CALL cswap( m, v( i, 1 ), ldv, v( k, 1 ), ldv )
297  100 CONTINUE
298  END IF
299  END IF
300 *
301  110 CONTINUE
302 *
303  RETURN
304 *
305 * End of CGGBAK
306 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine cswap(N, CX, INCX, CY, INCY)
CSWAP
Definition: cswap.f:83
subroutine csscal(N, SA, CX, INCX)
CSSCAL
Definition: csscal.f:80
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