LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ 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

Download DGEBAK + dependencies [TGZ] [ZIP] [TXT]

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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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 = int( 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 = int( 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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