1: *> \brief <b> ZGGES3 computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors for GE matrices (blocked algorithm)</b>
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZGGES3 + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgges3.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgges3.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgges3.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZGGES3( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B,
22: * $ LDB, SDIM, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR,
23: * $ WORK, 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: *> ZGGES3 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 ZGGES3. 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.
219: *>
220: *> If LWORK = -1, then a workspace query is assumed; the routine
221: *> only calculates the optimal size of the WORK array, returns
222: *> this value as the first entry of the WORK array, and no error
223: *> message related to LWORK is issued by XERBLA.
224: *> \endverbatim
225: *>
226: *> \param[out] RWORK
227: *> \verbatim
228: *> RWORK is DOUBLE PRECISION array, dimension (8*N)
229: *> \endverbatim
230: *>
231: *> \param[out] BWORK
232: *> \verbatim
233: *> BWORK is LOGICAL array, dimension (N)
234: *> Not referenced if SORT = 'N'.
235: *> \endverbatim
236: *>
237: *> \param[out] INFO
238: *> \verbatim
239: *> INFO is INTEGER
240: *> = 0: successful exit
241: *> < 0: if INFO = -i, the i-th argument had an illegal value.
242: *> =1,...,N:
243: *> The QZ iteration failed. (A,B) are not in Schur
244: *> form, but ALPHA(j) and BETA(j) should be correct for
245: *> j=INFO+1,...,N.
246: *> > N: =N+1: other than QZ iteration failed in ZLAQZ0
247: *> =N+2: after reordering, roundoff changed values of
248: *> some complex eigenvalues so that leading
249: *> eigenvalues in the Generalized Schur form no
250: *> longer satisfy SELCTG=.TRUE. This could also
251: *> be caused due to scaling.
252: *> =N+3: reordering failed in ZTGSEN.
253: *> \endverbatim
254: *
255: * Authors:
256: * ========
257: *
258: *> \author Univ. of Tennessee
259: *> \author Univ. of California Berkeley
260: *> \author Univ. of Colorado Denver
261: *> \author NAG Ltd.
262: *
263: *> \ingroup complex16GEeigen
264: *
265: * =====================================================================
266: SUBROUTINE ZGGES3( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B,
267: $ LDB, SDIM, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR,
268: $ WORK, LWORK, RWORK, BWORK, INFO )
269: *
270: * -- LAPACK driver routine --
271: * -- LAPACK is a software package provided by Univ. of Tennessee, --
272: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
273: *
274: * .. Scalar Arguments ..
275: CHARACTER JOBVSL, JOBVSR, SORT
276: INTEGER INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N, SDIM
277: * ..
278: * .. Array Arguments ..
279: LOGICAL BWORK( * )
280: DOUBLE PRECISION RWORK( * )
281: COMPLEX*16 A( LDA, * ), ALPHA( * ), B( LDB, * ),
282: $ BETA( * ), VSL( LDVSL, * ), VSR( LDVSR, * ),
283: $ WORK( * )
284: * ..
285: * .. Function Arguments ..
286: LOGICAL SELCTG
287: EXTERNAL SELCTG
288: * ..
289: *
290: * =====================================================================
291: *
292: * .. Parameters ..
293: DOUBLE PRECISION ZERO, ONE
294: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
295: COMPLEX*16 CZERO, CONE
296: PARAMETER ( CZERO = ( 0.0D0, 0.0D0 ),
297: $ CONE = ( 1.0D0, 0.0D0 ) )
298: * ..
299: * .. Local Scalars ..
300: LOGICAL CURSL, ILASCL, ILBSCL, ILVSL, ILVSR, LASTSL,
301: $ LQUERY, WANTST
302: INTEGER I, ICOLS, IERR, IHI, IJOBVL, IJOBVR, ILEFT,
303: $ ILO, IRIGHT, IROWS, IRWRK, ITAU, IWRK, LWKOPT
304: DOUBLE PRECISION ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS, PVSL,
305: $ PVSR, SMLNUM
306: * ..
307: * .. Local Arrays ..
308: INTEGER IDUM( 1 )
309: DOUBLE PRECISION DIF( 2 )
310: * ..
311: * .. External Subroutines ..
312: EXTERNAL DLABAD, XERBLA, ZGEQRF, ZGGBAK, ZGGBAL, ZGGHD3,
313: $ ZLAQZ0, ZLACPY, ZLASCL, ZLASET, ZTGSEN, ZUNGQR,
314: $ ZUNMQR
315: * ..
316: * .. External Functions ..
317: LOGICAL LSAME
318: DOUBLE PRECISION DLAMCH, ZLANGE
319: EXTERNAL LSAME, DLAMCH, ZLANGE
320: * ..
321: * .. Intrinsic Functions ..
322: INTRINSIC MAX, SQRT
323: * ..
324: * .. Executable Statements ..
325: *
326: * Decode the input arguments
327: *
328: IF( LSAME( JOBVSL, 'N' ) ) THEN
329: IJOBVL = 1
330: ILVSL = .FALSE.
331: ELSE IF( LSAME( JOBVSL, 'V' ) ) THEN
332: IJOBVL = 2
333: ILVSL = .TRUE.
334: ELSE
335: IJOBVL = -1
336: ILVSL = .FALSE.
337: END IF
338: *
339: IF( LSAME( JOBVSR, 'N' ) ) THEN
340: IJOBVR = 1
341: ILVSR = .FALSE.
342: ELSE IF( LSAME( JOBVSR, 'V' ) ) THEN
343: IJOBVR = 2
344: ILVSR = .TRUE.
345: ELSE
346: IJOBVR = -1
347: ILVSR = .FALSE.
348: END IF
349: *
350: WANTST = LSAME( SORT, 'S' )
351: *
352: * Test the input arguments
353: *
354: INFO = 0
355: LQUERY = ( LWORK.EQ.-1 )
356: IF( IJOBVL.LE.0 ) THEN
357: INFO = -1
358: ELSE IF( IJOBVR.LE.0 ) THEN
359: INFO = -2
360: ELSE IF( ( .NOT.WANTST ) .AND. ( .NOT.LSAME( SORT, 'N' ) ) ) THEN
361: INFO = -3
362: ELSE IF( N.LT.0 ) THEN
363: INFO = -5
364: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
365: INFO = -7
366: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
367: INFO = -9
368: ELSE IF( LDVSL.LT.1 .OR. ( ILVSL .AND. LDVSL.LT.N ) ) THEN
369: INFO = -14
370: ELSE IF( LDVSR.LT.1 .OR. ( ILVSR .AND. LDVSR.LT.N ) ) THEN
371: INFO = -16
372: ELSE IF( LWORK.LT.MAX( 1, 2*N ) .AND. .NOT.LQUERY ) THEN
373: INFO = -18
374: END IF
375: *
376: * Compute workspace
377: *
378: IF( INFO.EQ.0 ) THEN
379: CALL ZGEQRF( N, N, B, LDB, WORK, WORK, -1, IERR )
380: LWKOPT = MAX( 1, N + INT ( WORK( 1 ) ) )
381: CALL ZUNMQR( 'L', 'C', N, N, N, B, LDB, WORK, A, LDA, WORK,
382: $ -1, IERR )
383: LWKOPT = MAX( LWKOPT, N + INT ( WORK( 1 ) ) )
384: IF( ILVSL ) THEN
385: CALL ZUNGQR( N, N, N, VSL, LDVSL, WORK, WORK, -1, IERR )
386: LWKOPT = MAX( LWKOPT, N + INT ( WORK( 1 ) ) )
387: END IF
388: CALL ZGGHD3( JOBVSL, JOBVSR, N, 1, N, A, LDA, B, LDB, VSL,
389: $ LDVSL, VSR, LDVSR, WORK, -1, IERR )
390: LWKOPT = MAX( LWKOPT, N + INT ( WORK( 1 ) ) )
391: CALL ZLAQZ0( 'S', JOBVSL, JOBVSR, N, 1, N, A, LDA, B, LDB,
392: $ ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK, -1,
393: $ RWORK, 0, IERR )
394: LWKOPT = MAX( LWKOPT, INT ( WORK( 1 ) ) )
395: IF( WANTST ) THEN
396: CALL ZTGSEN( 0, ILVSL, ILVSR, BWORK, N, A, LDA, B, LDB,
397: $ ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, SDIM,
398: $ PVSL, PVSR, DIF, WORK, -1, IDUM, 1, IERR )
399: LWKOPT = MAX( LWKOPT, INT ( WORK( 1 ) ) )
400: END IF
401: WORK( 1 ) = DCMPLX( LWKOPT )
402: END IF
403: *
404: IF( INFO.NE.0 ) THEN
405: CALL XERBLA( 'ZGGES3 ', -INFO )
406: RETURN
407: ELSE IF( LQUERY ) THEN
408: RETURN
409: END IF
410: *
411: * Quick return if possible
412: *
413: IF( N.EQ.0 ) THEN
414: SDIM = 0
415: RETURN
416: END IF
417: *
418: * Get machine constants
419: *
420: EPS = DLAMCH( 'P' )
421: SMLNUM = DLAMCH( 'S' )
422: BIGNUM = ONE / SMLNUM
423: CALL DLABAD( SMLNUM, BIGNUM )
424: SMLNUM = SQRT( SMLNUM ) / EPS
425: BIGNUM = ONE / SMLNUM
426: *
427: * Scale A if max element outside range [SMLNUM,BIGNUM]
428: *
429: ANRM = ZLANGE( 'M', N, N, A, LDA, RWORK )
430: ILASCL = .FALSE.
431: IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
432: ANRMTO = SMLNUM
433: ILASCL = .TRUE.
434: ELSE IF( ANRM.GT.BIGNUM ) THEN
435: ANRMTO = BIGNUM
436: ILASCL = .TRUE.
437: END IF
438: *
439: IF( ILASCL )
440: $ CALL ZLASCL( 'G', 0, 0, ANRM, ANRMTO, N, N, A, LDA, IERR )
441: *
442: * Scale B if max element outside range [SMLNUM,BIGNUM]
443: *
444: BNRM = ZLANGE( 'M', N, N, B, LDB, RWORK )
445: ILBSCL = .FALSE.
446: IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN
447: BNRMTO = SMLNUM
448: ILBSCL = .TRUE.
449: ELSE IF( BNRM.GT.BIGNUM ) THEN
450: BNRMTO = BIGNUM
451: ILBSCL = .TRUE.
452: END IF
453: *
454: IF( ILBSCL )
455: $ CALL ZLASCL( 'G', 0, 0, BNRM, BNRMTO, N, N, B, LDB, IERR )
456: *
457: * Permute the matrix to make it more nearly triangular
458: *
459: ILEFT = 1
460: IRIGHT = N + 1
461: IRWRK = IRIGHT + N
462: CALL ZGGBAL( 'P', N, A, LDA, B, LDB, ILO, IHI, RWORK( ILEFT ),
463: $ RWORK( IRIGHT ), RWORK( IRWRK ), IERR )
464: *
465: * Reduce B to triangular form (QR decomposition of B)
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: *
476: CALL ZUNMQR( 'L', 'C', IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB,
477: $ WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWRK ),
478: $ LWORK+1-IWRK, IERR )
479: *
480: * Initialize VSL
481: *
482: IF( ILVSL ) THEN
483: CALL ZLASET( 'Full', N, N, CZERO, CONE, VSL, LDVSL )
484: IF( IROWS.GT.1 ) THEN
485: CALL ZLACPY( 'L', IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB,
486: $ VSL( ILO+1, ILO ), LDVSL )
487: END IF
488: CALL ZUNGQR( IROWS, IROWS, IROWS, VSL( ILO, ILO ), LDVSL,
489: $ WORK( ITAU ), WORK( IWRK ), LWORK+1-IWRK, IERR )
490: END IF
491: *
492: * Initialize VSR
493: *
494: IF( ILVSR )
495: $ CALL ZLASET( 'Full', N, N, CZERO, CONE, VSR, LDVSR )
496: *
497: * Reduce to generalized Hessenberg form
498: *
499: CALL ZGGHD3( JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB, VSL,
500: $ LDVSL, VSR, LDVSR, WORK( IWRK ), LWORK+1-IWRK, IERR )
501: *
502: SDIM = 0
503: *
504: * Perform QZ algorithm, computing Schur vectors if desired
505: *
506: IWRK = ITAU
507: CALL ZLAQZ0( 'S', JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB,
508: $ ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK( IWRK ),
509: $ LWORK+1-IWRK, RWORK( IRWRK ), 0, IERR )
510: IF( IERR.NE.0 ) THEN
511: IF( IERR.GT.0 .AND. IERR.LE.N ) THEN
512: INFO = IERR
513: ELSE IF( IERR.GT.N .AND. IERR.LE.2*N ) THEN
514: INFO = IERR - N
515: ELSE
516: INFO = N + 1
517: END IF
518: GO TO 30
519: END IF
520: *
521: * Sort eigenvalues ALPHA/BETA if desired
522: *
523: IF( WANTST ) THEN
524: *
525: * Undo scaling on eigenvalues before selecting
526: *
527: IF( ILASCL )
528: $ CALL ZLASCL( 'G', 0, 0, ANRM, ANRMTO, N, 1, ALPHA, N, IERR )
529: IF( ILBSCL )
530: $ CALL ZLASCL( 'G', 0, 0, BNRM, BNRMTO, N, 1, BETA, N, IERR )
531: *
532: * Select eigenvalues
533: *
534: DO 10 I = 1, N
535: BWORK( I ) = SELCTG( ALPHA( I ), BETA( I ) )
536: 10 CONTINUE
537: *
538: CALL ZTGSEN( 0, ILVSL, ILVSR, BWORK, N, A, LDA, B, LDB, ALPHA,
539: $ BETA, VSL, LDVSL, VSR, LDVSR, SDIM, PVSL, PVSR,
540: $ DIF, WORK( IWRK ), LWORK-IWRK+1, IDUM, 1, IERR )
541: IF( IERR.EQ.1 )
542: $ INFO = N + 3
543: *
544: END IF
545: *
546: * Apply back-permutation to VSL and VSR
547: *
548: IF( ILVSL )
549: $ CALL ZGGBAK( 'P', 'L', N, ILO, IHI, RWORK( ILEFT ),
550: $ RWORK( IRIGHT ), N, VSL, LDVSL, IERR )
551: IF( ILVSR )
552: $ CALL ZGGBAK( 'P', 'R', N, ILO, IHI, RWORK( ILEFT ),
553: $ RWORK( IRIGHT ), N, VSR, LDVSR, IERR )
554: *
555: * Undo scaling
556: *
557: IF( ILASCL ) THEN
558: CALL ZLASCL( 'U', 0, 0, ANRMTO, ANRM, N, N, A, LDA, IERR )
559: CALL ZLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHA, N, IERR )
560: END IF
561: *
562: IF( ILBSCL ) THEN
563: CALL ZLASCL( 'U', 0, 0, BNRMTO, BNRM, N, N, B, LDB, IERR )
564: CALL ZLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR )
565: END IF
566: *
567: IF( WANTST ) THEN
568: *
569: * Check if reordering is correct
570: *
571: LASTSL = .TRUE.
572: SDIM = 0
573: DO 20 I = 1, N
574: CURSL = SELCTG( ALPHA( I ), BETA( I ) )
575: IF( CURSL )
576: $ SDIM = SDIM + 1
577: IF( CURSL .AND. .NOT.LASTSL )
578: $ INFO = N + 2
579: LASTSL = CURSL
580: 20 CONTINUE
581: *
582: END IF
583: *
584: 30 CONTINUE
585: *
586: WORK( 1 ) = DCMPLX( LWKOPT )
587: *
588: RETURN
589: *
590: * End of ZGGES3
591: *
592: END
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