 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ dgebak()

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

DGEBAK

Purpose:
``` DGEBAK forms the right or left eigenvectors of a real general matrix
by backward transformation on the computed eigenvectors of the
balanced matrix output by DGEBAL.```
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 DGEBAL.``` [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 DGEBAL. 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 DGEBAL.``` [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 DHSEIN or DTREVC. 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 128 of file dgebak.f.

130 *
131 * -- LAPACK computational routine --
132 * -- LAPACK is a software package provided by Univ. of Tennessee, --
133 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
134 *
135 * .. Scalar Arguments ..
136  CHARACTER JOB, SIDE
137  INTEGER IHI, ILO, INFO, LDV, M, N
138 * ..
139 * .. Array Arguments ..
140  DOUBLE PRECISION SCALE( * ), V( LDV, * )
141 * ..
142 *
143 * =====================================================================
144 *
145 * .. Parameters ..
146  DOUBLE PRECISION ONE
147  parameter( one = 1.0d+0 )
148 * ..
149 * .. Local Scalars ..
150  LOGICAL LEFTV, RIGHTV
151  INTEGER I, II, K
152  DOUBLE PRECISION S
153 * ..
154 * .. External Functions ..
155  LOGICAL LSAME
156  EXTERNAL lsame
157 * ..
158 * .. External Subroutines ..
159  EXTERNAL dscal, dswap, xerbla
160 * ..
161 * .. Intrinsic Functions ..
162  INTRINSIC max, min
163 * ..
164 * .. Executable Statements ..
165 *
166 * Decode and Test the input parameters
167 *
168  rightv = lsame( side, 'R' )
169  leftv = lsame( side, 'L' )
170 *
171  info = 0
172  IF( .NOT.lsame( job, 'N' ) .AND. .NOT.lsame( job, 'P' ) .AND.
173  \$ .NOT.lsame( job, 'S' ) .AND. .NOT.lsame( job, 'B' ) ) THEN
174  info = -1
175  ELSE IF( .NOT.rightv .AND. .NOT.leftv ) THEN
176  info = -2
177  ELSE IF( n.LT.0 ) THEN
178  info = -3
179  ELSE IF( ilo.LT.1 .OR. ilo.GT.max( 1, n ) ) THEN
180  info = -4
181  ELSE IF( ihi.LT.min( ilo, n ) .OR. ihi.GT.n ) THEN
182  info = -5
183  ELSE IF( m.LT.0 ) THEN
184  info = -7
185  ELSE IF( ldv.LT.max( 1, n ) ) THEN
186  info = -9
187  END IF
188  IF( info.NE.0 ) THEN
189  CALL xerbla( 'DGEBAK', -info )
190  RETURN
191  END IF
192 *
193 * Quick return if possible
194 *
195  IF( n.EQ.0 )
196  \$ RETURN
197  IF( m.EQ.0 )
198  \$ RETURN
199  IF( lsame( job, 'N' ) )
200  \$ RETURN
201 *
202  IF( ilo.EQ.ihi )
203  \$ GO TO 30
204 *
205 * Backward balance
206 *
207  IF( lsame( job, 'S' ) .OR. lsame( job, 'B' ) ) THEN
208 *
209  IF( rightv ) THEN
210  DO 10 i = ilo, ihi
211  s = scale( i )
212  CALL dscal( m, s, v( i, 1 ), ldv )
213  10 CONTINUE
214  END IF
215 *
216  IF( leftv ) THEN
217  DO 20 i = ilo, ihi
218  s = one / scale( i )
219  CALL dscal( m, s, v( i, 1 ), ldv )
220  20 CONTINUE
221  END IF
222 *
223  END IF
224 *
225 * Backward permutation
226 *
227 * For I = ILO-1 step -1 until 1,
228 * IHI+1 step 1 until N do --
229 *
230  30 CONTINUE
231  IF( lsame( job, 'P' ) .OR. lsame( job, 'B' ) ) THEN
232  IF( rightv ) THEN
233  DO 40 ii = 1, n
234  i = ii
235  IF( i.GE.ilo .AND. i.LE.ihi )
236  \$ GO TO 40
237  IF( i.LT.ilo )
238  \$ i = ilo - ii
239  k = scale( i )
240  IF( k.EQ.i )
241  \$ GO TO 40
242  CALL dswap( m, v( i, 1 ), ldv, v( k, 1 ), ldv )
243  40 CONTINUE
244  END IF
245 *
246  IF( leftv ) THEN
247  DO 50 ii = 1, n
248  i = ii
249  IF( i.GE.ilo .AND. i.LE.ihi )
250  \$ GO TO 50
251  IF( i.LT.ilo )
252  \$ i = ilo - ii
253  k = scale( i )
254  IF( k.EQ.i )
255  \$ GO TO 50
256  CALL dswap( m, v( i, 1 ), ldv, v( k, 1 ), ldv )
257  50 CONTINUE
258  END IF
259  END IF
260 *
261  RETURN
262 *
263 * End of DGEBAK
264 *
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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