1*> \brief <b> ZGGES computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors for GE matrices</b>
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download ZGGES + dependencies
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11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgges.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgges.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE ZGGES( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, LDB,
22*                         SDIM, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK,
23*                         LWORK, RWORK, BWORK, INFO )
24*
25*       .. Scalar Arguments ..
26*       CHARACTER          JOBVSL, JOBVSR, SORT
27*       INTEGER            INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N, SDIM
28*       ..
29*       .. Array Arguments ..
30*       LOGICAL            BWORK( * )
31*       DOUBLE PRECISION   RWORK( * )
32*       COMPLEX*16         A( LDA, * ), ALPHA( * ), B( LDB, * ),
33*      $                   BETA( * ), VSL( LDVSL, * ), VSR( LDVSR, * ),
34*      $                   WORK( * )
35*       ..
36*       .. Function Arguments ..
37*       LOGICAL            SELCTG
38*       EXTERNAL           SELCTG
39*       ..
40*
41*
42*> \par Purpose:
43*  =============
44*>
45*> \verbatim
46*>
47*> ZGGES computes for a pair of N-by-N complex nonsymmetric matrices
48*> (A,B), the generalized eigenvalues, the generalized complex Schur
49*> form (S, T), and optionally left and/or right Schur vectors (VSL
50*> and VSR). This gives the generalized Schur factorization
51*>
52*>         (A,B) = ( (VSL)*S*(VSR)**H, (VSL)*T*(VSR)**H )
53*>
54*> where (VSR)**H is the conjugate-transpose of VSR.
55*>
56*> Optionally, it also orders the eigenvalues so that a selected cluster
57*> of eigenvalues appears in the leading diagonal blocks of the upper
58*> triangular matrix S and the upper triangular matrix T. The leading
59*> columns of VSL and VSR then form an unitary basis for the
60*> corresponding left and right eigenspaces (deflating subspaces).
61*>
62*> (If only the generalized eigenvalues are needed, use the driver
63*> ZGGEV instead, which is faster.)
64*>
65*> A generalized eigenvalue for a pair of matrices (A,B) is a scalar w
66*> or a ratio alpha/beta = w, such that  A - w*B is singular.  It is
67*> usually represented as the pair (alpha,beta), as there is a
68*> reasonable interpretation for beta=0, and even for both being zero.
69*>
70*> A pair of matrices (S,T) is in generalized complex Schur form if S
71*> and T are upper triangular and, in addition, the diagonal elements
72*> of T are non-negative real numbers.
73*> \endverbatim
74*
75*  Arguments:
76*  ==========
77*
78*> \param[in] JOBVSL
79*> \verbatim
80*>          JOBVSL is CHARACTER*1
81*>          = 'N':  do not compute the left Schur vectors;
82*>          = 'V':  compute the left Schur vectors.
83*> \endverbatim
84*>
85*> \param[in] JOBVSR
86*> \verbatim
87*>          JOBVSR is CHARACTER*1
88*>          = 'N':  do not compute the right Schur vectors;
89*>          = 'V':  compute the right Schur vectors.
90*> \endverbatim
91*>
92*> \param[in] SORT
93*> \verbatim
94*>          SORT is CHARACTER*1
95*>          Specifies whether or not to order the eigenvalues on the
96*>          diagonal of the generalized Schur form.
97*>          = 'N':  Eigenvalues are not ordered;
98*>          = 'S':  Eigenvalues are ordered (see SELCTG).
99*> \endverbatim
100*>
101*> \param[in] SELCTG
102*> \verbatim
103*>          SELCTG is a LOGICAL FUNCTION of two COMPLEX*16 arguments
104*>          SELCTG must be declared EXTERNAL in the calling subroutine.
105*>          If SORT = 'N', SELCTG is not referenced.
106*>          If SORT = 'S', SELCTG is used to select eigenvalues to sort
107*>          to the top left of the Schur form.
108*>          An eigenvalue ALPHA(j)/BETA(j) is selected if
109*>          SELCTG(ALPHA(j),BETA(j)) is true.
110*>
111*>          Note that a selected complex eigenvalue may no longer satisfy
112*>          SELCTG(ALPHA(j),BETA(j)) = .TRUE. after ordering, since
113*>          ordering may change the value of complex eigenvalues
114*>          (especially if the eigenvalue is ill-conditioned), in this
115*>          case INFO is set to N+2 (See INFO below).
116*> \endverbatim
117*>
118*> \param[in] N
119*> \verbatim
120*>          N is INTEGER
121*>          The order of the matrices A, B, VSL, and VSR.  N >= 0.
122*> \endverbatim
123*>
124*> \param[in,out] A
125*> \verbatim
126*>          A is COMPLEX*16 array, dimension (LDA, N)
127*>          On entry, the first of the pair of matrices.
128*>          On exit, A has been overwritten by its generalized Schur
129*>          form S.
130*> \endverbatim
131*>
132*> \param[in] LDA
133*> \verbatim
134*>          LDA is INTEGER
135*>          The leading dimension of A.  LDA >= max(1,N).
136*> \endverbatim
137*>
138*> \param[in,out] B
139*> \verbatim
140*>          B is COMPLEX*16 array, dimension (LDB, N)
141*>          On entry, the second of the pair of matrices.
142*>          On exit, B has been overwritten by its generalized Schur
143*>          form T.
144*> \endverbatim
145*>
146*> \param[in] LDB
147*> \verbatim
148*>          LDB is INTEGER
149*>          The leading dimension of B.  LDB >= max(1,N).
150*> \endverbatim
151*>
152*> \param[out] SDIM
153*> \verbatim
154*>          SDIM is INTEGER
155*>          If SORT = 'N', SDIM = 0.
156*>          If SORT = 'S', SDIM = number of eigenvalues (after sorting)
157*>          for which SELCTG is true.
158*> \endverbatim
159*>
160*> \param[out] ALPHA
161*> \verbatim
162*>          ALPHA is COMPLEX*16 array, dimension (N)
163*> \endverbatim
164*>
165*> \param[out] BETA
166*> \verbatim
167*>          BETA is COMPLEX*16 array, dimension (N)
168*>          On exit,  ALPHA(j)/BETA(j), j=1,...,N, will be the
169*>          generalized eigenvalues.  ALPHA(j), j=1,...,N  and  BETA(j),
170*>          j=1,...,N  are the diagonals of the complex Schur form (A,B)
171*>          output by ZGGES. The  BETA(j) will be non-negative real.
172*>
173*>          Note: the quotients ALPHA(j)/BETA(j) may easily over- or
174*>          underflow, and BETA(j) may even be zero.  Thus, the user
175*>          should avoid naively computing the ratio alpha/beta.
176*>          However, ALPHA will be always less than and usually
177*>          comparable with norm(A) in magnitude, and BETA always less
178*>          than and usually comparable with norm(B).
179*> \endverbatim
180*>
181*> \param[out] VSL
182*> \verbatim
183*>          VSL is COMPLEX*16 array, dimension (LDVSL,N)
184*>          If JOBVSL = 'V', VSL will contain the left Schur vectors.
185*>          Not referenced if JOBVSL = 'N'.
186*> \endverbatim
187*>
188*> \param[in] LDVSL
189*> \verbatim
190*>          LDVSL is INTEGER
191*>          The leading dimension of the matrix VSL. LDVSL >= 1, and
192*>          if JOBVSL = 'V', LDVSL >= N.
193*> \endverbatim
194*>
195*> \param[out] VSR
196*> \verbatim
197*>          VSR is COMPLEX*16 array, dimension (LDVSR,N)
198*>          If JOBVSR = 'V', VSR will contain the right Schur vectors.
199*>          Not referenced if JOBVSR = 'N'.
200*> \endverbatim
201*>
202*> \param[in] LDVSR
203*> \verbatim
204*>          LDVSR is INTEGER
205*>          The leading dimension of the matrix VSR. LDVSR >= 1, and
206*>          if JOBVSR = 'V', LDVSR >= N.
207*> \endverbatim
208*>
209*> \param[out] WORK
210*> \verbatim
211*>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
212*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
213*> \endverbatim
214*>
215*> \param[in] LWORK
216*> \verbatim
217*>          LWORK is INTEGER
218*>          The dimension of the array WORK.  LWORK >= max(1,2*N).
219*>          For good performance, LWORK must generally be larger.
220*>
221*>          If LWORK = -1, then a workspace query is assumed; the routine
222*>          only calculates the optimal size of the WORK array, returns
223*>          this value as the first entry of the WORK array, and no error
224*>          message related to LWORK is issued by XERBLA.
225*> \endverbatim
226*>
227*> \param[out] RWORK
228*> \verbatim
229*>          RWORK is DOUBLE PRECISION array, dimension (8*N)
230*> \endverbatim
231*>
232*> \param[out] BWORK
233*> \verbatim
234*>          BWORK is LOGICAL array, dimension (N)
235*>          Not referenced if SORT = 'N'.
236*> \endverbatim
237*>
238*> \param[out] INFO
239*> \verbatim
240*>          INFO is INTEGER
241*>          = 0:  successful exit
242*>          < 0:  if INFO = -i, the i-th argument had an illegal value.
243*>          =1,...,N:
244*>                The QZ iteration failed.  (A,B) are not in Schur
245*>                form, but ALPHA(j) and BETA(j) should be correct for
246*>                j=INFO+1,...,N.
247*>          > N:  =N+1: other than QZ iteration failed in ZHGEQZ
248*>                =N+2: after reordering, roundoff changed values of
249*>                      some complex eigenvalues so that leading
250*>                      eigenvalues in the Generalized Schur form no
251*>                      longer satisfy SELCTG=.TRUE.  This could also
252*>                      be caused due to scaling.
253*>                =N+3: reordering failed in ZTGSEN.
254*> \endverbatim
255*
256*  Authors:
257*  ========
258*
259*> \author Univ. of Tennessee
260*> \author Univ. of California Berkeley
261*> \author Univ. of Colorado Denver
262*> \author NAG Ltd.
263*
264*> \date November 2015
265*
266*> \ingroup complex16GEeigen
267*
268*  =====================================================================
269      SUBROUTINE ZGGES( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, LDB,
270     $                  SDIM, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK,
271     $                  LWORK, RWORK, BWORK, INFO )
272*
273*  -- LAPACK driver routine (version 3.6.0) --
274*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
275*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
276*     November 2015
277*
278*     .. Scalar Arguments ..
279      CHARACTER          JOBVSL, JOBVSR, SORT
280      INTEGER            INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N, SDIM
281*     ..
282*     .. Array Arguments ..
283      LOGICAL            BWORK( * )
284      DOUBLE PRECISION   RWORK( * )
285      COMPLEX*16         A( LDA, * ), ALPHA( * ), B( LDB, * ),
286     $                   BETA( * ), VSL( LDVSL, * ), VSR( LDVSR, * ),
287     $                   WORK( * )
288*     ..
289*     .. Function Arguments ..
290      LOGICAL            SELCTG
291      EXTERNAL           SELCTG
292*     ..
293*
294*  =====================================================================
295*
296*     .. Parameters ..
297      DOUBLE PRECISION   ZERO, ONE
298      PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
299      COMPLEX*16         CZERO, CONE
300      PARAMETER          ( CZERO = ( 0.0D0, 0.0D0 ),
301     $                   CONE = ( 1.0D0, 0.0D0 ) )
302*     ..
303*     .. Local Scalars ..
304      LOGICAL            CURSL, ILASCL, ILBSCL, ILVSL, ILVSR, LASTSL,
305     $                   LQUERY, WANTST
306      INTEGER            I, ICOLS, IERR, IHI, IJOBVL, IJOBVR, ILEFT,
307     $                   ILO, IRIGHT, IROWS, IRWRK, ITAU, IWRK, LWKMIN,
308     $                   LWKOPT
309      DOUBLE PRECISION   ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS, PVSL,
310     $                   PVSR, SMLNUM
311*     ..
312*     .. Local Arrays ..
313      INTEGER            IDUM( 1 )
314      DOUBLE PRECISION   DIF( 2 )
315*     ..
316*     .. External Subroutines ..
317      EXTERNAL           DLABAD, XERBLA, ZGEQRF, ZGGBAK, ZGGBAL, ZGGHRD,
318     $                   ZHGEQZ, ZLACPY, ZLASCL, ZLASET, ZTGSEN, ZUNGQR,
319     $                   ZUNMQR
320*     ..
321*     .. External Functions ..
322      LOGICAL            LSAME
323      INTEGER            ILAENV
324      DOUBLE PRECISION   DLAMCH, ZLANGE
325      EXTERNAL           LSAME, ILAENV, DLAMCH, ZLANGE
326*     ..
327*     .. Intrinsic Functions ..
328      INTRINSIC          MAX, SQRT
329*     ..
330*     .. Executable Statements ..
331*
332*     Decode the input arguments
333*
334      IF( LSAME( JOBVSL, 'N' ) ) THEN
335         IJOBVL = 1
336         ILVSL = .FALSE.
337      ELSE IF( LSAME( JOBVSL, 'V' ) ) THEN
338         IJOBVL = 2
339         ILVSL = .TRUE.
340      ELSE
341         IJOBVL = -1
342         ILVSL = .FALSE.
343      END IF
344*
345      IF( LSAME( JOBVSR, 'N' ) ) THEN
346         IJOBVR = 1
347         ILVSR = .FALSE.
348      ELSE IF( LSAME( JOBVSR, 'V' ) ) THEN
349         IJOBVR = 2
350         ILVSR = .TRUE.
351      ELSE
352         IJOBVR = -1
353         ILVSR = .FALSE.
354      END IF
355*
356      WANTST = LSAME( SORT, 'S' )
357*
358*     Test the input arguments
359*
360      INFO = 0
361      LQUERY = ( LWORK.EQ.-1 )
362      IF( IJOBVL.LE.0 ) THEN
363         INFO = -1
364      ELSE IF( IJOBVR.LE.0 ) THEN
365         INFO = -2
366      ELSE IF( ( .NOT.WANTST ) .AND. ( .NOT.LSAME( SORT, 'N' ) ) ) THEN
367         INFO = -3
368      ELSE IF( N.LT.0 ) THEN
369         INFO = -5
370      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
371         INFO = -7
372      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
373         INFO = -9
374      ELSE IF( LDVSL.LT.1 .OR. ( ILVSL .AND. LDVSL.LT.N ) ) THEN
375         INFO = -14
376      ELSE IF( LDVSR.LT.1 .OR. ( ILVSR .AND. LDVSR.LT.N ) ) THEN
377         INFO = -16
378      END IF
379*
380*     Compute workspace
381*      (Note: Comments in the code beginning "Workspace:" describe the
382*       minimal amount of workspace needed at that point in the code,
383*       as well as the preferred amount for good performance.
384*       NB refers to the optimal block size for the immediately
385*       following subroutine, as returned by ILAENV.)
386*
387      IF( INFO.EQ.0 ) THEN
388         LWKMIN = MAX( 1, 2*N )
389         LWKOPT = MAX( 1, N + N*ILAENV( 1, 'ZGEQRF', ' ', N, 1, N, 0 ) )
390         LWKOPT = MAX( LWKOPT, N +
391     $                 N*ILAENV( 1, 'ZUNMQR', ' ', N, 1, N, -1 ) )
392         IF( ILVSL ) THEN
393            LWKOPT = MAX( LWKOPT, N +
394     $                    N*ILAENV( 1, 'ZUNGQR', ' ', N, 1, N, -1 ) )
395         END IF
396         WORK( 1 ) = LWKOPT
397*
398         IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY )
399     $      INFO = -18
400      END IF
401*
402      IF( INFO.NE.0 ) THEN
403         CALL XERBLA( 'ZGGES ', -INFO )
404         RETURN
405      ELSE IF( LQUERY ) THEN
406         RETURN
407      END IF
408*
409*     Quick return if possible
410*
411      IF( N.EQ.0 ) THEN
412         SDIM = 0
413         RETURN
414      END IF
415*
416*     Get machine constants
417*
418      EPS = DLAMCH( 'P' )
419      SMLNUM = DLAMCH( 'S' )
420      BIGNUM = ONE / SMLNUM
421      CALL DLABAD( SMLNUM, BIGNUM )
422      SMLNUM = SQRT( SMLNUM ) / EPS
423      BIGNUM = ONE / SMLNUM
424*
425*     Scale A if max element outside range [SMLNUM,BIGNUM]
426*
427      ANRM = ZLANGE( 'M', N, N, A, LDA, RWORK )
428      ILASCL = .FALSE.
429      IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
430         ANRMTO = SMLNUM
431         ILASCL = .TRUE.
432      ELSE IF( ANRM.GT.BIGNUM ) THEN
433         ANRMTO = BIGNUM
434         ILASCL = .TRUE.
435      END IF
436*
437      IF( ILASCL )
438     $   CALL ZLASCL( 'G', 0, 0, ANRM, ANRMTO, N, N, A, LDA, IERR )
439*
440*     Scale B if max element outside range [SMLNUM,BIGNUM]
441*
442      BNRM = ZLANGE( 'M', N, N, B, LDB, RWORK )
443      ILBSCL = .FALSE.
444      IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN
445         BNRMTO = SMLNUM
446         ILBSCL = .TRUE.
447      ELSE IF( BNRM.GT.BIGNUM ) THEN
448         BNRMTO = BIGNUM
449         ILBSCL = .TRUE.
450      END IF
451*
452      IF( ILBSCL )
453     $   CALL ZLASCL( 'G', 0, 0, BNRM, BNRMTO, N, N, B, LDB, IERR )
454*
455*     Permute the matrix to make it more nearly triangular
456*     (Real Workspace: need 6*N)
457*
458      ILEFT = 1
459      IRIGHT = N + 1
460      IRWRK = IRIGHT + N
461      CALL ZGGBAL( 'P', N, A, LDA, B, LDB, ILO, IHI, RWORK( ILEFT ),
462     $             RWORK( IRIGHT ), RWORK( IRWRK ), IERR )
463*
464*     Reduce B to triangular form (QR decomposition of B)
465*     (Complex Workspace: need N, prefer N*NB)
466*
467      IROWS = IHI + 1 - ILO
468      ICOLS = N + 1 - ILO
469      ITAU = 1
470      IWRK = ITAU + IROWS
471      CALL ZGEQRF( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ),
472     $             WORK( IWRK ), LWORK+1-IWRK, IERR )
473*
474*     Apply the orthogonal transformation to matrix A
475*     (Complex Workspace: need N, prefer N*NB)
476*
477      CALL ZUNMQR( 'L', 'C', IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB,
478     $             WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWRK ),
479     $             LWORK+1-IWRK, IERR )
480*
481*     Initialize VSL
482*     (Complex Workspace: need N, prefer N*NB)
483*
484      IF( ILVSL ) THEN
485         CALL ZLASET( 'Full', N, N, CZERO, CONE, VSL, LDVSL )
486         IF( IROWS.GT.1 ) THEN
487            CALL ZLACPY( 'L', IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB,
488     $                   VSL( ILO+1, ILO ), LDVSL )
489         END IF
490         CALL ZUNGQR( IROWS, IROWS, IROWS, VSL( ILO, ILO ), LDVSL,
491     $                WORK( ITAU ), WORK( IWRK ), LWORK+1-IWRK, IERR )
492      END IF
493*
494*     Initialize VSR
495*
496      IF( ILVSR )
497     $   CALL ZLASET( 'Full', N, N, CZERO, CONE, VSR, LDVSR )
498*
499*     Reduce to generalized Hessenberg form
500*     (Workspace: none needed)
501*
502      CALL ZGGHRD( JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB, VSL,
503     $             LDVSL, VSR, LDVSR, IERR )
504*
505      SDIM = 0
506*
507*     Perform QZ algorithm, computing Schur vectors if desired
508*     (Complex Workspace: need N)
509*     (Real Workspace: need N)
510*
511      IWRK = ITAU
512      CALL ZHGEQZ( 'S', JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB,
513     $             ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK( IWRK ),
514     $             LWORK+1-IWRK, RWORK( IRWRK ), IERR )
515      IF( IERR.NE.0 ) THEN
516         IF( IERR.GT.0 .AND. IERR.LE.N ) THEN
517            INFO = IERR
518         ELSE IF( IERR.GT.N .AND. IERR.LE.2*N ) THEN
519            INFO = IERR - N
520         ELSE
521            INFO = N + 1
522         END IF
523         GO TO 30
524      END IF
525*
526*     Sort eigenvalues ALPHA/BETA if desired
527*     (Workspace: none needed)
528*
529      IF( WANTST ) THEN
530*
531*        Undo scaling on eigenvalues before selecting
532*
533         IF( ILASCL )
534     $      CALL ZLASCL( 'G', 0, 0, ANRM, ANRMTO, N, 1, ALPHA, N, IERR )
535         IF( ILBSCL )
536     $      CALL ZLASCL( 'G', 0, 0, BNRM, BNRMTO, N, 1, BETA, N, IERR )
537*
538*        Select eigenvalues
539*
540         DO 10 I = 1, N
541            BWORK( I ) = SELCTG( ALPHA( I ), BETA( I ) )
542   10    CONTINUE
543*
544         CALL ZTGSEN( 0, ILVSL, ILVSR, BWORK, N, A, LDA, B, LDB, ALPHA,
545     $                BETA, VSL, LDVSL, VSR, LDVSR, SDIM, PVSL, PVSR,
546     $                DIF, WORK( IWRK ), LWORK-IWRK+1, IDUM, 1, IERR )
547         IF( IERR.EQ.1 )
548     $      INFO = N + 3
549*
550      END IF
551*
552*     Apply back-permutation to VSL and VSR
553*     (Workspace: none needed)
554*
555      IF( ILVSL )
556     $   CALL ZGGBAK( 'P', 'L', N, ILO, IHI, RWORK( ILEFT ),
557     $                RWORK( IRIGHT ), N, VSL, LDVSL, IERR )
558      IF( ILVSR )
559     $   CALL ZGGBAK( 'P', 'R', N, ILO, IHI, RWORK( ILEFT ),
560     $                RWORK( IRIGHT ), N, VSR, LDVSR, IERR )
561*
562*     Undo scaling
563*
564      IF( ILASCL ) THEN
565         CALL ZLASCL( 'U', 0, 0, ANRMTO, ANRM, N, N, A, LDA, IERR )
566         CALL ZLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHA, N, IERR )
567      END IF
568*
569      IF( ILBSCL ) THEN
570         CALL ZLASCL( 'U', 0, 0, BNRMTO, BNRM, N, N, B, LDB, IERR )
571         CALL ZLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR )
572      END IF
573*
574      IF( WANTST ) THEN
575*
576*        Check if reordering is correct
577*
578         LASTSL = .TRUE.
579         SDIM = 0
580         DO 20 I = 1, N
581            CURSL = SELCTG( ALPHA( I ), BETA( I ) )
582            IF( CURSL )
583     $         SDIM = SDIM + 1
584            IF( CURSL .AND. .NOT.LASTSL )
585     $         INFO = N + 2
586            LASTSL = CURSL
587   20    CONTINUE
588*
589      END IF
590*
591   30 CONTINUE
592*
593      WORK( 1 ) = LWKOPT
594*
595      RETURN
596*
597*     End of ZGGES
598*
599      END
600