 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ dggbak()

 subroutine dggbak ( character JOB, character SIDE, integer N, integer ILO, integer IHI, double precision, dimension( * ) LSCALE, double precision, dimension( * ) RSCALE, integer M, double precision, dimension( ldv, * ) V, integer LDV, integer INFO )

DGGBAK

Purpose:
``` DGGBAK forms the right or left eigenvectors of a real generalized
eigenvalue problem A*x = lambda*B*x, by backward transformation on
the computed eigenvectors of the balanced pair of matrices output by
DGGBAL.```
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 DGGBAL.``` [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 DGGBAL. 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 DGGBAL.``` [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 DGGBAL.``` [in] M ``` M is INTEGER The number of columns of the matrix V. M >= 0.``` [in,out] V ``` V is DOUBLE PRECISION array, dimension (LDV,M) On entry, the matrix of right or left eigenvectors to be transformed, as returned by DTGEVC. 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.```
Further Details:
```  See R.C. Ward, Balancing the generalized eigenvalue problem,
SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.```

Definition at line 145 of file dggbak.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( * ), V( LDV, * )
158 * ..
159 *
160 * =====================================================================
161 *
162 * .. Local Scalars ..
163  LOGICAL LEFTV, RIGHTV
164  INTEGER I, K
165 * ..
166 * .. External Functions ..
167  LOGICAL LSAME
168  EXTERNAL lsame
169 * ..
170 * .. External Subroutines ..
171  EXTERNAL dscal, dswap, xerbla
172 * ..
173 * .. Intrinsic Functions ..
174  INTRINSIC max, int
175 * ..
176 * .. Executable Statements ..
177 *
178 * Test the input parameters
179 *
180  rightv = lsame( side, 'R' )
181  leftv = lsame( side, 'L' )
182 *
183  info = 0
184  IF( .NOT.lsame( job, 'N' ) .AND. .NOT.lsame( job, 'P' ) .AND.
185  \$ .NOT.lsame( job, 'S' ) .AND. .NOT.lsame( job, 'B' ) ) THEN
186  info = -1
187  ELSE IF( .NOT.rightv .AND. .NOT.leftv ) THEN
188  info = -2
189  ELSE IF( n.LT.0 ) THEN
190  info = -3
191  ELSE IF( ilo.LT.1 ) THEN
192  info = -4
193  ELSE IF( n.EQ.0 .AND. ihi.EQ.0 .AND. ilo.NE.1 ) THEN
194  info = -4
195  ELSE IF( n.GT.0 .AND. ( ihi.LT.ilo .OR. ihi.GT.max( 1, n ) ) )
196  \$ THEN
197  info = -5
198  ELSE IF( n.EQ.0 .AND. ilo.EQ.1 .AND. ihi.NE.0 ) THEN
199  info = -5
200  ELSE IF( m.LT.0 ) THEN
201  info = -8
202  ELSE IF( ldv.LT.max( 1, n ) ) THEN
203  info = -10
204  END IF
205  IF( info.NE.0 ) THEN
206  CALL xerbla( 'DGGBAK', -info )
207  RETURN
208  END IF
209 *
210 * Quick return if possible
211 *
212  IF( n.EQ.0 )
213  \$ RETURN
214  IF( m.EQ.0 )
215  \$ RETURN
216  IF( lsame( job, 'N' ) )
217  \$ RETURN
218 *
219  IF( ilo.EQ.ihi )
220  \$ GO TO 30
221 *
222 * Backward balance
223 *
224  IF( lsame( job, 'S' ) .OR. lsame( job, 'B' ) ) THEN
225 *
226 * Backward transformation on right eigenvectors
227 *
228  IF( rightv ) THEN
229  DO 10 i = ilo, ihi
230  CALL dscal( m, rscale( i ), v( i, 1 ), ldv )
231  10 CONTINUE
232  END IF
233 *
234 * Backward transformation on left eigenvectors
235 *
236  IF( leftv ) THEN
237  DO 20 i = ilo, ihi
238  CALL dscal( m, lscale( i ), v( i, 1 ), ldv )
239  20 CONTINUE
240  END IF
241  END IF
242 *
243 * Backward permutation
244 *
245  30 CONTINUE
246  IF( lsame( job, 'P' ) .OR. lsame( job, 'B' ) ) THEN
247 *
248 * Backward permutation on right eigenvectors
249 *
250  IF( rightv ) THEN
251  IF( ilo.EQ.1 )
252  \$ GO TO 50
253 *
254  DO 40 i = ilo - 1, 1, -1
255  k = int(rscale( i ))
256  IF( k.EQ.i )
257  \$ GO TO 40
258  CALL dswap( m, v( i, 1 ), ldv, v( k, 1 ), ldv )
259  40 CONTINUE
260 *
261  50 CONTINUE
262  IF( ihi.EQ.n )
263  \$ GO TO 70
264  DO 60 i = ihi + 1, n
265  k = int(rscale( i ))
266  IF( k.EQ.i )
267  \$ GO TO 60
268  CALL dswap( m, v( i, 1 ), ldv, v( k, 1 ), ldv )
269  60 CONTINUE
270  END IF
271 *
272 * Backward permutation on left eigenvectors
273 *
274  70 CONTINUE
275  IF( leftv ) THEN
276  IF( ilo.EQ.1 )
277  \$ GO TO 90
278  DO 80 i = ilo - 1, 1, -1
279  k = int(lscale( i ))
280  IF( k.EQ.i )
281  \$ GO TO 80
282  CALL dswap( m, v( i, 1 ), ldv, v( k, 1 ), ldv )
283  80 CONTINUE
284 *
285  90 CONTINUE
286  IF( ihi.EQ.n )
287  \$ GO TO 110
288  DO 100 i = ihi + 1, n
289  k = int(lscale( i ))
290  IF( k.EQ.i )
291  \$ GO TO 100
292  CALL dswap( m, v( i, 1 ), ldv, v( k, 1 ), ldv )
293  100 CONTINUE
294  END IF
295  END IF
296 *
297  110 CONTINUE
298 *
299  RETURN
300 *
301 * End of DGGBAK
302 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dscal(N, DA, DX, INCX)
DSCAL
Definition: dscal.f:79
subroutine dswap(N, DX, INCX, DY, INCY)
DSWAP
Definition: dswap.f:82
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