 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
Searching...
No Matches

## ◆ 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 = int( 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 = int( 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
Here is the call graph for this function:
Here is the caller graph for this function: