 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ zgebak()

 subroutine zgebak ( character JOB, character SIDE, integer N, integer ILO, integer IHI, double precision, dimension( * ) SCALE, integer M, complex*16, dimension( ldv, * ) V, integer LDV, integer INFO )

ZGEBAK

Purpose:
``` ZGEBAK forms the right or left eigenvectors of a complex general
matrix by backward transformation on the computed eigenvectors of the
balanced matrix output by ZGEBAL.```
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 ZGEBAL.``` [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 ZGEBAL. 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.``` [in] SCALE ``` SCALE is DOUBLE PRECISION array, dimension (N) Details of the permutation and scaling factors, as returned by ZGEBAL.``` [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 ZHSEIN or ZTREVC. On exit, V is overwritten by the transformed eigenvectors.``` [in] LDV ``` LDV is INTEGER The leading dimension of the array 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.```

Definition at line 129 of file zgebak.f.

131 *
132 * -- LAPACK computational routine --
133 * -- LAPACK is a software package provided by Univ. of Tennessee, --
134 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
135 *
136 * .. Scalar Arguments ..
137  CHARACTER JOB, SIDE
138  INTEGER IHI, ILO, INFO, LDV, M, N
139 * ..
140 * .. Array Arguments ..
141  DOUBLE PRECISION SCALE( * )
142  COMPLEX*16 V( LDV, * )
143 * ..
144 *
145 * =====================================================================
146 *
147 * .. Parameters ..
148  DOUBLE PRECISION ONE
149  parameter( one = 1.0d+0 )
150 * ..
151 * .. Local Scalars ..
152  LOGICAL LEFTV, RIGHTV
153  INTEGER I, II, K
154  DOUBLE PRECISION S
155 * ..
156 * .. External Functions ..
157  LOGICAL LSAME
158  EXTERNAL lsame
159 * ..
160 * .. External Subroutines ..
161  EXTERNAL xerbla, zdscal, zswap
162 * ..
163 * .. Intrinsic Functions ..
164  INTRINSIC max, min
165 * ..
166 * .. Executable Statements ..
167 *
168 * Decode and Test the input parameters
169 *
170  rightv = lsame( side, 'R' )
171  leftv = lsame( side, 'L' )
172 *
173  info = 0
174  IF( .NOT.lsame( job, 'N' ) .AND. .NOT.lsame( job, 'P' ) .AND.
175  \$ .NOT.lsame( job, 'S' ) .AND. .NOT.lsame( job, 'B' ) ) THEN
176  info = -1
177  ELSE IF( .NOT.rightv .AND. .NOT.leftv ) THEN
178  info = -2
179  ELSE IF( n.LT.0 ) THEN
180  info = -3
181  ELSE IF( ilo.LT.1 .OR. ilo.GT.max( 1, n ) ) THEN
182  info = -4
183  ELSE IF( ihi.LT.min( ilo, n ) .OR. ihi.GT.n ) THEN
184  info = -5
185  ELSE IF( m.LT.0 ) THEN
186  info = -7
187  ELSE IF( ldv.LT.max( 1, n ) ) THEN
188  info = -9
189  END IF
190  IF( info.NE.0 ) THEN
191  CALL xerbla( 'ZGEBAK', -info )
192  RETURN
193  END IF
194 *
195 * Quick return if possible
196 *
197  IF( n.EQ.0 )
198  \$ RETURN
199  IF( m.EQ.0 )
200  \$ RETURN
201  IF( lsame( job, 'N' ) )
202  \$ RETURN
203 *
204  IF( ilo.EQ.ihi )
205  \$ GO TO 30
206 *
207 * Backward balance
208 *
209  IF( lsame( job, 'S' ) .OR. lsame( job, 'B' ) ) THEN
210 *
211  IF( rightv ) THEN
212  DO 10 i = ilo, ihi
213  s = scale( i )
214  CALL zdscal( m, s, v( i, 1 ), ldv )
215  10 CONTINUE
216  END IF
217 *
218  IF( leftv ) THEN
219  DO 20 i = ilo, ihi
220  s = one / scale( i )
221  CALL zdscal( m, s, v( i, 1 ), ldv )
222  20 CONTINUE
223  END IF
224 *
225  END IF
226 *
227 * Backward permutation
228 *
229 * For I = ILO-1 step -1 until 1,
230 * IHI+1 step 1 until N do --
231 *
232  30 CONTINUE
233  IF( lsame( job, 'P' ) .OR. lsame( job, 'B' ) ) THEN
234  IF( rightv ) THEN
235  DO 40 ii = 1, n
236  i = ii
237  IF( i.GE.ilo .AND. i.LE.ihi )
238  \$ GO TO 40
239  IF( i.LT.ilo )
240  \$ i = ilo - ii
241  k = scale( i )
242  IF( k.EQ.i )
243  \$ GO TO 40
244  CALL zswap( m, v( i, 1 ), ldv, v( k, 1 ), ldv )
245  40 CONTINUE
246  END IF
247 *
248  IF( leftv ) THEN
249  DO 50 ii = 1, n
250  i = ii
251  IF( i.GE.ilo .AND. i.LE.ihi )
252  \$ GO TO 50
253  IF( i.LT.ilo )
254  \$ i = ilo - ii
255  k = scale( i )
256  IF( k.EQ.i )
257  \$ GO TO 50
258  CALL zswap( m, v( i, 1 ), ldv, v( k, 1 ), ldv )
259  50 CONTINUE
260  END IF
261  END IF
262 *
263  RETURN
264 *
265 * End of ZGEBAK
266 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zswap(N, ZX, INCX, ZY, INCY)
ZSWAP
Definition: zswap.f:81
subroutine zdscal(N, DA, ZX, INCX)
ZDSCAL
Definition: zdscal.f:78
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