Annotation of rpl/lapack/lapack/zgges.f, revision 1.19
1.8 bertrand 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: *
1.16 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.8 bertrand 7: *
8: *> \htmlonly
1.16 bertrand 9: *> Download ZGGES + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgges.f">
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">
1.8 bertrand 15: *> [TXT]</a>
1.16 bertrand 16: *> \endhtmlonly
1.8 bertrand 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 )
1.16 bertrand 24: *
1.8 bertrand 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: * ..
1.16 bertrand 40: *
1.8 bertrand 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
1.10 bertrand 103: *> SELCTG is a LOGICAL FUNCTION of two COMPLEX*16 arguments
1.8 bertrand 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.
1.14 bertrand 253: *> =N+3: reordering failed in ZTGSEN.
1.8 bertrand 254: *> \endverbatim
255: *
256: * Authors:
257: * ========
258: *
1.16 bertrand 259: *> \author Univ. of Tennessee
260: *> \author Univ. of California Berkeley
261: *> \author Univ. of Colorado Denver
262: *> \author NAG Ltd.
1.8 bertrand 263: *
264: *> \ingroup complex16GEeigen
265: *
266: * =====================================================================
1.1 bertrand 267: SUBROUTINE ZGGES( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, LDB,
268: $ SDIM, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK,
269: $ LWORK, RWORK, BWORK, INFO )
270: *
1.19 ! bertrand 271: * -- LAPACK driver routine --
1.1 bertrand 272: * -- LAPACK is a software package provided by Univ. of Tennessee, --
273: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
274: *
275: * .. Scalar Arguments ..
276: CHARACTER JOBVSL, JOBVSR, SORT
277: INTEGER INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N, SDIM
278: * ..
279: * .. Array Arguments ..
280: LOGICAL BWORK( * )
281: DOUBLE PRECISION RWORK( * )
282: COMPLEX*16 A( LDA, * ), ALPHA( * ), B( LDB, * ),
283: $ BETA( * ), VSL( LDVSL, * ), VSR( LDVSR, * ),
284: $ WORK( * )
285: * ..
286: * .. Function Arguments ..
287: LOGICAL SELCTG
288: EXTERNAL SELCTG
289: * ..
290: *
291: * =====================================================================
292: *
293: * .. Parameters ..
294: DOUBLE PRECISION ZERO, ONE
295: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
296: COMPLEX*16 CZERO, CONE
297: PARAMETER ( CZERO = ( 0.0D0, 0.0D0 ),
298: $ CONE = ( 1.0D0, 0.0D0 ) )
299: * ..
300: * .. Local Scalars ..
301: LOGICAL CURSL, ILASCL, ILBSCL, ILVSL, ILVSR, LASTSL,
302: $ LQUERY, WANTST
303: INTEGER I, ICOLS, IERR, IHI, IJOBVL, IJOBVR, ILEFT,
304: $ ILO, IRIGHT, IROWS, IRWRK, ITAU, IWRK, LWKMIN,
305: $ LWKOPT
306: DOUBLE PRECISION ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS, PVSL,
307: $ PVSR, SMLNUM
308: * ..
309: * .. Local Arrays ..
310: INTEGER IDUM( 1 )
311: DOUBLE PRECISION DIF( 2 )
312: * ..
313: * .. External Subroutines ..
314: EXTERNAL DLABAD, XERBLA, ZGEQRF, ZGGBAK, ZGGBAL, ZGGHRD,
315: $ ZHGEQZ, ZLACPY, ZLASCL, ZLASET, ZTGSEN, ZUNGQR,
316: $ ZUNMQR
317: * ..
318: * .. External Functions ..
319: LOGICAL LSAME
320: INTEGER ILAENV
321: DOUBLE PRECISION DLAMCH, ZLANGE
322: EXTERNAL LSAME, ILAENV, DLAMCH, ZLANGE
323: * ..
324: * .. Intrinsic Functions ..
325: INTRINSIC MAX, SQRT
326: * ..
327: * .. Executable Statements ..
328: *
329: * Decode the input arguments
330: *
331: IF( LSAME( JOBVSL, 'N' ) ) THEN
332: IJOBVL = 1
333: ILVSL = .FALSE.
334: ELSE IF( LSAME( JOBVSL, 'V' ) ) THEN
335: IJOBVL = 2
336: ILVSL = .TRUE.
337: ELSE
338: IJOBVL = -1
339: ILVSL = .FALSE.
340: END IF
341: *
342: IF( LSAME( JOBVSR, 'N' ) ) THEN
343: IJOBVR = 1
344: ILVSR = .FALSE.
345: ELSE IF( LSAME( JOBVSR, 'V' ) ) THEN
346: IJOBVR = 2
347: ILVSR = .TRUE.
348: ELSE
349: IJOBVR = -1
350: ILVSR = .FALSE.
351: END IF
352: *
353: WANTST = LSAME( SORT, 'S' )
354: *
355: * Test the input arguments
356: *
357: INFO = 0
358: LQUERY = ( LWORK.EQ.-1 )
359: IF( IJOBVL.LE.0 ) THEN
360: INFO = -1
361: ELSE IF( IJOBVR.LE.0 ) THEN
362: INFO = -2
363: ELSE IF( ( .NOT.WANTST ) .AND. ( .NOT.LSAME( SORT, 'N' ) ) ) THEN
364: INFO = -3
365: ELSE IF( N.LT.0 ) THEN
366: INFO = -5
367: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
368: INFO = -7
369: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
370: INFO = -9
371: ELSE IF( LDVSL.LT.1 .OR. ( ILVSL .AND. LDVSL.LT.N ) ) THEN
372: INFO = -14
373: ELSE IF( LDVSR.LT.1 .OR. ( ILVSR .AND. LDVSR.LT.N ) ) THEN
374: INFO = -16
375: END IF
376: *
377: * Compute workspace
378: * (Note: Comments in the code beginning "Workspace:" describe the
379: * minimal amount of workspace needed at that point in the code,
380: * as well as the preferred amount for good performance.
381: * NB refers to the optimal block size for the immediately
382: * following subroutine, as returned by ILAENV.)
383: *
384: IF( INFO.EQ.0 ) THEN
385: LWKMIN = MAX( 1, 2*N )
386: LWKOPT = MAX( 1, N + N*ILAENV( 1, 'ZGEQRF', ' ', N, 1, N, 0 ) )
387: LWKOPT = MAX( LWKOPT, N +
388: $ N*ILAENV( 1, 'ZUNMQR', ' ', N, 1, N, -1 ) )
389: IF( ILVSL ) THEN
390: LWKOPT = MAX( LWKOPT, N +
391: $ N*ILAENV( 1, 'ZUNGQR', ' ', N, 1, N, -1 ) )
392: END IF
393: WORK( 1 ) = LWKOPT
394: *
395: IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY )
396: $ INFO = -18
397: END IF
398: *
399: IF( INFO.NE.0 ) THEN
400: CALL XERBLA( 'ZGGES ', -INFO )
401: RETURN
402: ELSE IF( LQUERY ) THEN
403: RETURN
404: END IF
405: *
406: * Quick return if possible
407: *
408: IF( N.EQ.0 ) THEN
409: SDIM = 0
410: RETURN
411: END IF
412: *
413: * Get machine constants
414: *
415: EPS = DLAMCH( 'P' )
416: SMLNUM = DLAMCH( 'S' )
417: BIGNUM = ONE / SMLNUM
418: CALL DLABAD( SMLNUM, BIGNUM )
419: SMLNUM = SQRT( SMLNUM ) / EPS
420: BIGNUM = ONE / SMLNUM
421: *
422: * Scale A if max element outside range [SMLNUM,BIGNUM]
423: *
424: ANRM = ZLANGE( 'M', N, N, A, LDA, RWORK )
425: ILASCL = .FALSE.
426: IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
427: ANRMTO = SMLNUM
428: ILASCL = .TRUE.
429: ELSE IF( ANRM.GT.BIGNUM ) THEN
430: ANRMTO = BIGNUM
431: ILASCL = .TRUE.
432: END IF
433: *
434: IF( ILASCL )
435: $ CALL ZLASCL( 'G', 0, 0, ANRM, ANRMTO, N, N, A, LDA, IERR )
436: *
437: * Scale B if max element outside range [SMLNUM,BIGNUM]
438: *
439: BNRM = ZLANGE( 'M', N, N, B, LDB, RWORK )
440: ILBSCL = .FALSE.
441: IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN
442: BNRMTO = SMLNUM
443: ILBSCL = .TRUE.
444: ELSE IF( BNRM.GT.BIGNUM ) THEN
445: BNRMTO = BIGNUM
446: ILBSCL = .TRUE.
447: END IF
448: *
449: IF( ILBSCL )
450: $ CALL ZLASCL( 'G', 0, 0, BNRM, BNRMTO, N, N, B, LDB, IERR )
451: *
452: * Permute the matrix to make it more nearly triangular
453: * (Real Workspace: need 6*N)
454: *
455: ILEFT = 1
456: IRIGHT = N + 1
457: IRWRK = IRIGHT + N
458: CALL ZGGBAL( 'P', N, A, LDA, B, LDB, ILO, IHI, RWORK( ILEFT ),
459: $ RWORK( IRIGHT ), RWORK( IRWRK ), IERR )
460: *
461: * Reduce B to triangular form (QR decomposition of B)
462: * (Complex Workspace: need N, prefer N*NB)
463: *
464: IROWS = IHI + 1 - ILO
465: ICOLS = N + 1 - ILO
466: ITAU = 1
467: IWRK = ITAU + IROWS
468: CALL ZGEQRF( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ),
469: $ WORK( IWRK ), LWORK+1-IWRK, IERR )
470: *
471: * Apply the orthogonal transformation to matrix A
472: * (Complex Workspace: need N, prefer N*NB)
473: *
474: CALL ZUNMQR( 'L', 'C', IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB,
475: $ WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWRK ),
476: $ LWORK+1-IWRK, IERR )
477: *
478: * Initialize VSL
479: * (Complex Workspace: need N, prefer N*NB)
480: *
481: IF( ILVSL ) THEN
482: CALL ZLASET( 'Full', N, N, CZERO, CONE, VSL, LDVSL )
483: IF( IROWS.GT.1 ) THEN
484: CALL ZLACPY( 'L', IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB,
485: $ VSL( ILO+1, ILO ), LDVSL )
486: END IF
487: CALL ZUNGQR( IROWS, IROWS, IROWS, VSL( ILO, ILO ), LDVSL,
488: $ WORK( ITAU ), WORK( IWRK ), LWORK+1-IWRK, IERR )
489: END IF
490: *
491: * Initialize VSR
492: *
493: IF( ILVSR )
494: $ CALL ZLASET( 'Full', N, N, CZERO, CONE, VSR, LDVSR )
495: *
496: * Reduce to generalized Hessenberg form
497: * (Workspace: none needed)
498: *
499: CALL ZGGHRD( JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB, VSL,
500: $ LDVSL, VSR, LDVSR, IERR )
501: *
502: SDIM = 0
503: *
504: * Perform QZ algorithm, computing Schur vectors if desired
505: * (Complex Workspace: need N)
506: * (Real Workspace: need N)
507: *
508: IWRK = ITAU
509: CALL ZHGEQZ( 'S', JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB,
510: $ ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK( IWRK ),
511: $ LWORK+1-IWRK, RWORK( IRWRK ), IERR )
512: IF( IERR.NE.0 ) THEN
513: IF( IERR.GT.0 .AND. IERR.LE.N ) THEN
514: INFO = IERR
515: ELSE IF( IERR.GT.N .AND. IERR.LE.2*N ) THEN
516: INFO = IERR - N
517: ELSE
518: INFO = N + 1
519: END IF
520: GO TO 30
521: END IF
522: *
523: * Sort eigenvalues ALPHA/BETA if desired
524: * (Workspace: none needed)
525: *
526: IF( WANTST ) THEN
527: *
528: * Undo scaling on eigenvalues before selecting
529: *
530: IF( ILASCL )
531: $ CALL ZLASCL( 'G', 0, 0, ANRM, ANRMTO, N, 1, ALPHA, N, IERR )
532: IF( ILBSCL )
533: $ CALL ZLASCL( 'G', 0, 0, BNRM, BNRMTO, N, 1, BETA, N, IERR )
534: *
535: * Select eigenvalues
536: *
537: DO 10 I = 1, N
538: BWORK( I ) = SELCTG( ALPHA( I ), BETA( I ) )
539: 10 CONTINUE
540: *
541: CALL ZTGSEN( 0, ILVSL, ILVSR, BWORK, N, A, LDA, B, LDB, ALPHA,
542: $ BETA, VSL, LDVSL, VSR, LDVSR, SDIM, PVSL, PVSR,
543: $ DIF, WORK( IWRK ), LWORK-IWRK+1, IDUM, 1, IERR )
544: IF( IERR.EQ.1 )
545: $ INFO = N + 3
546: *
547: END IF
548: *
549: * Apply back-permutation to VSL and VSR
550: * (Workspace: none needed)
551: *
552: IF( ILVSL )
553: $ CALL ZGGBAK( 'P', 'L', N, ILO, IHI, RWORK( ILEFT ),
554: $ RWORK( IRIGHT ), N, VSL, LDVSL, IERR )
555: IF( ILVSR )
556: $ CALL ZGGBAK( 'P', 'R', N, ILO, IHI, RWORK( ILEFT ),
557: $ RWORK( IRIGHT ), N, VSR, LDVSR, IERR )
558: *
559: * Undo scaling
560: *
561: IF( ILASCL ) THEN
562: CALL ZLASCL( 'U', 0, 0, ANRMTO, ANRM, N, N, A, LDA, IERR )
563: CALL ZLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHA, N, IERR )
564: END IF
565: *
566: IF( ILBSCL ) THEN
567: CALL ZLASCL( 'U', 0, 0, BNRMTO, BNRM, N, N, B, LDB, IERR )
568: CALL ZLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR )
569: END IF
570: *
571: IF( WANTST ) THEN
572: *
573: * Check if reordering is correct
574: *
575: LASTSL = .TRUE.
576: SDIM = 0
577: DO 20 I = 1, N
578: CURSL = SELCTG( ALPHA( I ), BETA( I ) )
579: IF( CURSL )
580: $ SDIM = SDIM + 1
581: IF( CURSL .AND. .NOT.LASTSL )
582: $ INFO = N + 2
583: LASTSL = CURSL
584: 20 CONTINUE
585: *
586: END IF
587: *
588: 30 CONTINUE
589: *
590: WORK( 1 ) = LWKOPT
591: *
592: RETURN
593: *
594: * End of ZGGES
595: *
596: END
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