LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ sgebak()

 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.```

Definition at line 128 of file sgebak.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 REAL V( LDV, * ), SCALE( * )
141* ..
142*
143* =====================================================================
144*
145* .. Parameters ..
146 REAL ONE
147 parameter( one = 1.0e+0 )
148* ..
149* .. Local Scalars ..
150 LOGICAL LEFTV, RIGHTV
151 INTEGER I, II, K
152 REAL S
153* ..
154* .. External Functions ..
155 LOGICAL LSAME
156 EXTERNAL lsame
157* ..
158* .. External Subroutines ..
159 EXTERNAL sscal, sswap, 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( 'SGEBAK', -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 sscal( 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 sscal( 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 sswap( 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 sswap( 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 SGEBAK
264*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine sswap(N, SX, INCX, SY, INCY)
SSWAP
Definition: sswap.f:82
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:79
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