LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine sgebak ( character JOB, character SIDE, integer N, integer ILO, integer IHI, real, dimension( * ) SCALE, integer M, real, dimension( ldv, * ) V, integer LDV, integer INFO )

SGEBAK

Purpose:
``` SGEBAK forms the right or left eigenvectors of a real general matrix
by backward transformation on the computed eigenvectors of the
balanced matrix output by SGEBAL.```
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 SGEBAL.``` [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 SGEBAL. 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.``` [in] SCALE ``` SCALE is REAL array, dimension (N) Details of the permutation and scaling factors, as returned by SGEBAL.``` [in] M ``` M is INTEGER The number of columns of the matrix V. M >= 0.``` [in,out] V ``` V is REAL array, dimension (LDV,M) On entry, the matrix of right or left eigenvectors to be transformed, as returned by SHSEIN or STREVC. 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.```
Date
November 2011

Definition at line 132 of file sgebak.f.

132 *
133 * -- LAPACK computational routine (version 3.4.0) --
134 * -- LAPACK is a software package provided by Univ. of Tennessee, --
135 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
136 * November 2011
137 *
138 * .. Scalar Arguments ..
139  CHARACTER job, side
140  INTEGER ihi, ilo, info, ldv, m, n
141 * ..
142 * .. Array Arguments ..
143  REAL v( ldv, * ), scale( * )
144 * ..
145 *
146 * =====================================================================
147 *
148 * .. Parameters ..
149  REAL one
150  parameter ( one = 1.0e+0 )
151 * ..
152 * .. Local Scalars ..
153  LOGICAL leftv, rightv
154  INTEGER i, ii, k
155  REAL s
156 * ..
157 * .. External Functions ..
158  LOGICAL lsame
159  EXTERNAL lsame
160 * ..
161 * .. External Subroutines ..
162  EXTERNAL sscal, sswap, xerbla
163 * ..
164 * .. Intrinsic Functions ..
165  INTRINSIC max, min
166 * ..
167 * .. Executable Statements ..
168 *
169 * Decode and Test the input parameters
170 *
171  rightv = lsame( side, 'R' )
172  leftv = lsame( side, 'L' )
173 *
174  info = 0
175  IF( .NOT.lsame( job, 'N' ) .AND. .NOT.lsame( job, 'P' ) .AND.
176  \$ .NOT.lsame( job, 'S' ) .AND. .NOT.lsame( job, 'B' ) ) THEN
177  info = -1
178  ELSE IF( .NOT.rightv .AND. .NOT.leftv ) THEN
179  info = -2
180  ELSE IF( n.LT.0 ) THEN
181  info = -3
182  ELSE IF( ilo.LT.1 .OR. ilo.GT.max( 1, n ) ) THEN
183  info = -4
184  ELSE IF( ihi.LT.min( ilo, n ) .OR. ihi.GT.n ) THEN
185  info = -5
186  ELSE IF( m.LT.0 ) THEN
187  info = -7
188  ELSE IF( ldv.LT.max( 1, n ) ) THEN
189  info = -9
190  END IF
191  IF( info.NE.0 ) THEN
192  CALL xerbla( 'SGEBAK', -info )
193  RETURN
194  END IF
195 *
196 * Quick return if possible
197 *
198  IF( n.EQ.0 )
199  \$ RETURN
200  IF( m.EQ.0 )
201  \$ RETURN
202  IF( lsame( job, 'N' ) )
203  \$ RETURN
204 *
205  IF( ilo.EQ.ihi )
206  \$ GO TO 30
207 *
208 * Backward balance
209 *
210  IF( lsame( job, 'S' ) .OR. lsame( job, 'B' ) ) THEN
211 *
212  IF( rightv ) THEN
213  DO 10 i = ilo, ihi
214  s = scale( i )
215  CALL sscal( m, s, v( i, 1 ), ldv )
216  10 CONTINUE
217  END IF
218 *
219  IF( leftv ) THEN
220  DO 20 i = ilo, ihi
221  s = one / scale( i )
222  CALL sscal( m, s, v( i, 1 ), ldv )
223  20 CONTINUE
224  END IF
225 *
226  END IF
227 *
228 * Backward permutation
229 *
230 * For I = ILO-1 step -1 until 1,
231 * IHI+1 step 1 until N do --
232 *
233  30 CONTINUE
234  IF( lsame( job, 'P' ) .OR. lsame( job, 'B' ) ) THEN
235  IF( rightv ) THEN
236  DO 40 ii = 1, n
237  i = ii
238  IF( i.GE.ilo .AND. i.LE.ihi )
239  \$ GO TO 40
240  IF( i.LT.ilo )
241  \$ i = ilo - ii
242  k = scale( i )
243  IF( k.EQ.i )
244  \$ GO TO 40
245  CALL sswap( m, v( i, 1 ), ldv, v( k, 1 ), ldv )
246  40 CONTINUE
247  END IF
248 *
249  IF( leftv ) THEN
250  DO 50 ii = 1, n
251  i = ii
252  IF( i.GE.ilo .AND. i.LE.ihi )
253  \$ GO TO 50
254  IF( i.LT.ilo )
255  \$ i = ilo - ii
256  k = scale( i )
257  IF( k.EQ.i )
258  \$ GO TO 50
259  CALL sswap( m, v( i, 1 ), ldv, v( k, 1 ), ldv )
260  50 CONTINUE
261  END IF
262  END IF
263 *
264  RETURN
265 *
266 * End of SGEBAK
267 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:55
subroutine sswap(N, SX, INCX, SY, INCY)
SSWAP
Definition: sswap.f:53
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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