1: SUBROUTINE ZGGESX( JOBVSL, JOBVSR, SORT, SELCTG, SENSE, N, A, LDA,
2: $ B, LDB, SDIM, ALPHA, BETA, VSL, LDVSL, VSR,
3: $ LDVSR, RCONDE, RCONDV, WORK, LWORK, RWORK,
4: $ IWORK, LIWORK, BWORK, INFO )
5: *
6: * -- LAPACK driver routine (version 3.2) --
7: * -- LAPACK is a software package provided by Univ. of Tennessee, --
8: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
9: * November 2006
10: *
11: * .. Scalar Arguments ..
12: CHARACTER JOBVSL, JOBVSR, SENSE, SORT
13: INTEGER INFO, LDA, LDB, LDVSL, LDVSR, LIWORK, LWORK, N,
14: $ SDIM
15: * ..
16: * .. Array Arguments ..
17: LOGICAL BWORK( * )
18: INTEGER IWORK( * )
19: DOUBLE PRECISION RCONDE( 2 ), RCONDV( 2 ), RWORK( * )
20: COMPLEX*16 A( LDA, * ), ALPHA( * ), B( LDB, * ),
21: $ BETA( * ), VSL( LDVSL, * ), VSR( LDVSR, * ),
22: $ WORK( * )
23: * ..
24: * .. Function Arguments ..
25: LOGICAL SELCTG
26: EXTERNAL SELCTG
27: * ..
28: *
29: * Purpose
30: * =======
31: *
32: * ZGGESX computes for a pair of N-by-N complex nonsymmetric matrices
33: * (A,B), the generalized eigenvalues, the complex Schur form (S,T),
34: * and, optionally, the left and/or right matrices of Schur vectors (VSL
35: * and VSR). This gives the generalized Schur factorization
36: *
37: * (A,B) = ( (VSL) S (VSR)**H, (VSL) T (VSR)**H )
38: *
39: * where (VSR)**H is the conjugate-transpose of VSR.
40: *
41: * Optionally, it also orders the eigenvalues so that a selected cluster
42: * of eigenvalues appears in the leading diagonal blocks of the upper
43: * triangular matrix S and the upper triangular matrix T; computes
44: * a reciprocal condition number for the average of the selected
45: * eigenvalues (RCONDE); and computes a reciprocal condition number for
46: * the right and left deflating subspaces corresponding to the selected
47: * eigenvalues (RCONDV). The leading columns of VSL and VSR then form
48: * an orthonormal basis for the corresponding left and right eigenspaces
49: * (deflating subspaces).
50: *
51: * A generalized eigenvalue for a pair of matrices (A,B) is a scalar w
52: * or a ratio alpha/beta = w, such that A - w*B is singular. It is
53: * usually represented as the pair (alpha,beta), as there is a
54: * reasonable interpretation for beta=0 or for both being zero.
55: *
56: * A pair of matrices (S,T) is in generalized complex Schur form if T is
57: * upper triangular with non-negative diagonal and S is upper
58: * triangular.
59: *
60: * Arguments
61: * =========
62: *
63: * JOBVSL (input) CHARACTER*1
64: * = 'N': do not compute the left Schur vectors;
65: * = 'V': compute the left Schur vectors.
66: *
67: * JOBVSR (input) CHARACTER*1
68: * = 'N': do not compute the right Schur vectors;
69: * = 'V': compute the right Schur vectors.
70: *
71: * SORT (input) CHARACTER*1
72: * Specifies whether or not to order the eigenvalues on the
73: * diagonal of the generalized Schur form.
74: * = 'N': Eigenvalues are not ordered;
75: * = 'S': Eigenvalues are ordered (see SELCTG).
76: *
77: * SELCTG (external procedure) LOGICAL FUNCTION of two COMPLEX*16 arguments
78: * SELCTG must be declared EXTERNAL in the calling subroutine.
79: * If SORT = 'N', SELCTG is not referenced.
80: * If SORT = 'S', SELCTG is used to select eigenvalues to sort
81: * to the top left of the Schur form.
82: * Note that a selected complex eigenvalue may no longer satisfy
83: * SELCTG(ALPHA(j),BETA(j)) = .TRUE. after ordering, since
84: * ordering may change the value of complex eigenvalues
85: * (especially if the eigenvalue is ill-conditioned), in this
86: * case INFO is set to N+3 see INFO below).
87: *
88: * SENSE (input) CHARACTER*1
89: * Determines which reciprocal condition numbers are computed.
90: * = 'N' : None are computed;
91: * = 'E' : Computed for average of selected eigenvalues only;
92: * = 'V' : Computed for selected deflating subspaces only;
93: * = 'B' : Computed for both.
94: * If SENSE = 'E', 'V', or 'B', SORT must equal 'S'.
95: *
96: * N (input) INTEGER
97: * The order of the matrices A, B, VSL, and VSR. N >= 0.
98: *
99: * A (input/output) COMPLEX*16 array, dimension (LDA, N)
100: * On entry, the first of the pair of matrices.
101: * On exit, A has been overwritten by its generalized Schur
102: * form S.
103: *
104: * LDA (input) INTEGER
105: * The leading dimension of A. LDA >= max(1,N).
106: *
107: * B (input/output) COMPLEX*16 array, dimension (LDB, N)
108: * On entry, the second of the pair of matrices.
109: * On exit, B has been overwritten by its generalized Schur
110: * form T.
111: *
112: * LDB (input) INTEGER
113: * The leading dimension of B. LDB >= max(1,N).
114: *
115: * SDIM (output) INTEGER
116: * If SORT = 'N', SDIM = 0.
117: * If SORT = 'S', SDIM = number of eigenvalues (after sorting)
118: * for which SELCTG is true.
119: *
120: * ALPHA (output) COMPLEX*16 array, dimension (N)
121: * BETA (output) COMPLEX*16 array, dimension (N)
122: * On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the
123: * generalized eigenvalues. ALPHA(j) and BETA(j),j=1,...,N are
124: * the diagonals of the complex Schur form (S,T). BETA(j) will
125: * be non-negative real.
126: *
127: * Note: the quotients ALPHA(j)/BETA(j) may easily over- or
128: * underflow, and BETA(j) may even be zero. Thus, the user
129: * should avoid naively computing the ratio alpha/beta.
130: * However, ALPHA will be always less than and usually
131: * comparable with norm(A) in magnitude, and BETA always less
132: * than and usually comparable with norm(B).
133: *
134: * VSL (output) COMPLEX*16 array, dimension (LDVSL,N)
135: * If JOBVSL = 'V', VSL will contain the left Schur vectors.
136: * Not referenced if JOBVSL = 'N'.
137: *
138: * LDVSL (input) INTEGER
139: * The leading dimension of the matrix VSL. LDVSL >=1, and
140: * if JOBVSL = 'V', LDVSL >= N.
141: *
142: * VSR (output) COMPLEX*16 array, dimension (LDVSR,N)
143: * If JOBVSR = 'V', VSR will contain the right Schur vectors.
144: * Not referenced if JOBVSR = 'N'.
145: *
146: * LDVSR (input) INTEGER
147: * The leading dimension of the matrix VSR. LDVSR >= 1, and
148: * if JOBVSR = 'V', LDVSR >= N.
149: *
150: * RCONDE (output) DOUBLE PRECISION array, dimension ( 2 )
151: * If SENSE = 'E' or 'B', RCONDE(1) and RCONDE(2) contain the
152: * reciprocal condition numbers for the average of the selected
153: * eigenvalues.
154: * Not referenced if SENSE = 'N' or 'V'.
155: *
156: * RCONDV (output) DOUBLE PRECISION array, dimension ( 2 )
157: * If SENSE = 'V' or 'B', RCONDV(1) and RCONDV(2) contain the
158: * reciprocal condition number for the selected deflating
159: * subspaces.
160: * Not referenced if SENSE = 'N' or 'E'.
161: *
162: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
163: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
164: *
165: * LWORK (input) INTEGER
166: * The dimension of the array WORK.
167: * If N = 0, LWORK >= 1, else if SENSE = 'E', 'V', or 'B',
168: * LWORK >= MAX(1,2*N,2*SDIM*(N-SDIM)), else
169: * LWORK >= MAX(1,2*N). Note that 2*SDIM*(N-SDIM) <= N*N/2.
170: * Note also that an error is only returned if
171: * LWORK < MAX(1,2*N), but if SENSE = 'E' or 'V' or 'B' this may
172: * not be large enough.
173: *
174: * If LWORK = -1, then a workspace query is assumed; the routine
175: * only calculates the bound on the optimal size of the WORK
176: * array and the minimum size of the IWORK array, returns these
177: * values as the first entries of the WORK and IWORK arrays, and
178: * no error message related to LWORK or LIWORK is issued by
179: * XERBLA.
180: *
181: * RWORK (workspace) DOUBLE PRECISION array, dimension ( 8*N )
182: * Real workspace.
183: *
184: * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
185: * On exit, if INFO = 0, IWORK(1) returns the minimum LIWORK.
186: *
187: * LIWORK (input) INTEGER
188: * The dimension of the array IWORK.
189: * If SENSE = 'N' or N = 0, LIWORK >= 1, otherwise
190: * LIWORK >= N+2.
191: *
192: * If LIWORK = -1, then a workspace query is assumed; the
193: * routine only calculates the bound on the optimal size of the
194: * WORK array and the minimum size of the IWORK array, returns
195: * these values as the first entries of the WORK and IWORK
196: * arrays, and no error message related to LWORK or LIWORK is
197: * issued by XERBLA.
198: *
199: * BWORK (workspace) LOGICAL array, dimension (N)
200: * Not referenced if SORT = 'N'.
201: *
202: * INFO (output) INTEGER
203: * = 0: successful exit
204: * < 0: if INFO = -i, the i-th argument had an illegal value.
205: * = 1,...,N:
206: * The QZ iteration failed. (A,B) are not in Schur
207: * form, but ALPHA(j) and BETA(j) should be correct for
208: * j=INFO+1,...,N.
209: * > N: =N+1: other than QZ iteration failed in ZHGEQZ
210: * =N+2: after reordering, roundoff changed values of
211: * some complex eigenvalues so that leading
212: * eigenvalues in the Generalized Schur form no
213: * longer satisfy SELCTG=.TRUE. This could also
214: * be caused due to scaling.
215: * =N+3: reordering failed in ZTGSEN.
216: *
217: * =====================================================================
218: *
219: * .. Parameters ..
220: DOUBLE PRECISION ZERO, ONE
221: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
222: COMPLEX*16 CZERO, CONE
223: PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
224: $ CONE = ( 1.0D+0, 0.0D+0 ) )
225: * ..
226: * .. Local Scalars ..
227: LOGICAL CURSL, ILASCL, ILBSCL, ILVSL, ILVSR, LASTSL,
228: $ LQUERY, WANTSB, WANTSE, WANTSN, WANTST, WANTSV
229: INTEGER I, ICOLS, IERR, IHI, IJOB, IJOBVL, IJOBVR,
230: $ ILEFT, ILO, IRIGHT, IROWS, IRWRK, ITAU, IWRK,
231: $ LIWMIN, LWRK, MAXWRK, MINWRK
232: DOUBLE PRECISION ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS, PL,
233: $ PR, SMLNUM
234: * ..
235: * .. Local Arrays ..
236: DOUBLE PRECISION DIF( 2 )
237: * ..
238: * .. External Subroutines ..
239: EXTERNAL DLABAD, XERBLA, ZGEQRF, ZGGBAK, ZGGBAL, ZGGHRD,
240: $ ZHGEQZ, ZLACPY, ZLASCL, ZLASET, ZTGSEN, ZUNGQR,
241: $ ZUNMQR
242: * ..
243: * .. External Functions ..
244: LOGICAL LSAME
245: INTEGER ILAENV
246: DOUBLE PRECISION DLAMCH, ZLANGE
247: EXTERNAL LSAME, ILAENV, DLAMCH, ZLANGE
248: * ..
249: * .. Intrinsic Functions ..
250: INTRINSIC MAX, SQRT
251: * ..
252: * .. Executable Statements ..
253: *
254: * Decode the input arguments
255: *
256: IF( LSAME( JOBVSL, 'N' ) ) THEN
257: IJOBVL = 1
258: ILVSL = .FALSE.
259: ELSE IF( LSAME( JOBVSL, 'V' ) ) THEN
260: IJOBVL = 2
261: ILVSL = .TRUE.
262: ELSE
263: IJOBVL = -1
264: ILVSL = .FALSE.
265: END IF
266: *
267: IF( LSAME( JOBVSR, 'N' ) ) THEN
268: IJOBVR = 1
269: ILVSR = .FALSE.
270: ELSE IF( LSAME( JOBVSR, 'V' ) ) THEN
271: IJOBVR = 2
272: ILVSR = .TRUE.
273: ELSE
274: IJOBVR = -1
275: ILVSR = .FALSE.
276: END IF
277: *
278: WANTST = LSAME( SORT, 'S' )
279: WANTSN = LSAME( SENSE, 'N' )
280: WANTSE = LSAME( SENSE, 'E' )
281: WANTSV = LSAME( SENSE, 'V' )
282: WANTSB = LSAME( SENSE, 'B' )
283: LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
284: IF( WANTSN ) THEN
285: IJOB = 0
286: ELSE IF( WANTSE ) THEN
287: IJOB = 1
288: ELSE IF( WANTSV ) THEN
289: IJOB = 2
290: ELSE IF( WANTSB ) THEN
291: IJOB = 4
292: END IF
293: *
294: * Test the input arguments
295: *
296: INFO = 0
297: IF( IJOBVL.LE.0 ) THEN
298: INFO = -1
299: ELSE IF( IJOBVR.LE.0 ) THEN
300: INFO = -2
301: ELSE IF( ( .NOT.WANTST ) .AND. ( .NOT.LSAME( SORT, 'N' ) ) ) THEN
302: INFO = -3
303: ELSE IF( .NOT.( WANTSN .OR. WANTSE .OR. WANTSV .OR. WANTSB ) .OR.
304: $ ( .NOT.WANTST .AND. .NOT.WANTSN ) ) THEN
305: INFO = -5
306: ELSE IF( N.LT.0 ) THEN
307: INFO = -6
308: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
309: INFO = -8
310: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
311: INFO = -10
312: ELSE IF( LDVSL.LT.1 .OR. ( ILVSL .AND. LDVSL.LT.N ) ) THEN
313: INFO = -15
314: ELSE IF( LDVSR.LT.1 .OR. ( ILVSR .AND. LDVSR.LT.N ) ) THEN
315: INFO = -17
316: END IF
317: *
318: * Compute workspace
319: * (Note: Comments in the code beginning "Workspace:" describe the
320: * minimal amount of workspace needed at that point in the code,
321: * as well as the preferred amount for good performance.
322: * NB refers to the optimal block size for the immediately
323: * following subroutine, as returned by ILAENV.)
324: *
325: IF( INFO.EQ.0 ) THEN
326: IF( N.GT.0) THEN
327: MINWRK = 2*N
328: MAXWRK = N*(1 + ILAENV( 1, 'ZGEQRF', ' ', N, 1, N, 0 ) )
329: MAXWRK = MAX( MAXWRK, N*( 1 +
330: $ ILAENV( 1, 'ZUNMQR', ' ', N, 1, N, -1 ) ) )
331: IF( ILVSL ) THEN
332: MAXWRK = MAX( MAXWRK, N*( 1 +
333: $ ILAENV( 1, 'ZUNGQR', ' ', N, 1, N, -1 ) ) )
334: END IF
335: LWRK = MAXWRK
336: IF( IJOB.GE.1 )
337: $ LWRK = MAX( LWRK, N*N/2 )
338: ELSE
339: MINWRK = 1
340: MAXWRK = 1
341: LWRK = 1
342: END IF
343: WORK( 1 ) = LWRK
344: IF( WANTSN .OR. N.EQ.0 ) THEN
345: LIWMIN = 1
346: ELSE
347: LIWMIN = N + 2
348: END IF
349: IWORK( 1 ) = LIWMIN
350: *
351: IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
352: INFO = -21
353: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY) THEN
354: INFO = -24
355: END IF
356: END IF
357: *
358: IF( INFO.NE.0 ) THEN
359: CALL XERBLA( 'ZGGESX', -INFO )
360: RETURN
361: ELSE IF (LQUERY) THEN
362: RETURN
363: END IF
364: *
365: * Quick return if possible
366: *
367: IF( N.EQ.0 ) THEN
368: SDIM = 0
369: RETURN
370: END IF
371: *
372: * Get machine constants
373: *
374: EPS = DLAMCH( 'P' )
375: SMLNUM = DLAMCH( 'S' )
376: BIGNUM = ONE / SMLNUM
377: CALL DLABAD( SMLNUM, BIGNUM )
378: SMLNUM = SQRT( SMLNUM ) / EPS
379: BIGNUM = ONE / SMLNUM
380: *
381: * Scale A if max element outside range [SMLNUM,BIGNUM]
382: *
383: ANRM = ZLANGE( 'M', N, N, A, LDA, RWORK )
384: ILASCL = .FALSE.
385: IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
386: ANRMTO = SMLNUM
387: ILASCL = .TRUE.
388: ELSE IF( ANRM.GT.BIGNUM ) THEN
389: ANRMTO = BIGNUM
390: ILASCL = .TRUE.
391: END IF
392: IF( ILASCL )
393: $ CALL ZLASCL( 'G', 0, 0, ANRM, ANRMTO, N, N, A, LDA, IERR )
394: *
395: * Scale B if max element outside range [SMLNUM,BIGNUM]
396: *
397: BNRM = ZLANGE( 'M', N, N, B, LDB, RWORK )
398: ILBSCL = .FALSE.
399: IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN
400: BNRMTO = SMLNUM
401: ILBSCL = .TRUE.
402: ELSE IF( BNRM.GT.BIGNUM ) THEN
403: BNRMTO = BIGNUM
404: ILBSCL = .TRUE.
405: END IF
406: IF( ILBSCL )
407: $ CALL ZLASCL( 'G', 0, 0, BNRM, BNRMTO, N, N, B, LDB, IERR )
408: *
409: * Permute the matrix to make it more nearly triangular
410: * (Real Workspace: need 6*N)
411: *
412: ILEFT = 1
413: IRIGHT = N + 1
414: IRWRK = IRIGHT + N
415: CALL ZGGBAL( 'P', N, A, LDA, B, LDB, ILO, IHI, RWORK( ILEFT ),
416: $ RWORK( IRIGHT ), RWORK( IRWRK ), IERR )
417: *
418: * Reduce B to triangular form (QR decomposition of B)
419: * (Complex Workspace: need N, prefer N*NB)
420: *
421: IROWS = IHI + 1 - ILO
422: ICOLS = N + 1 - ILO
423: ITAU = 1
424: IWRK = ITAU + IROWS
425: CALL ZGEQRF( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ),
426: $ WORK( IWRK ), LWORK+1-IWRK, IERR )
427: *
428: * Apply the unitary transformation to matrix A
429: * (Complex Workspace: need N, prefer N*NB)
430: *
431: CALL ZUNMQR( 'L', 'C', IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB,
432: $ WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWRK ),
433: $ LWORK+1-IWRK, IERR )
434: *
435: * Initialize VSL
436: * (Complex Workspace: need N, prefer N*NB)
437: *
438: IF( ILVSL ) THEN
439: CALL ZLASET( 'Full', N, N, CZERO, CONE, VSL, LDVSL )
440: IF( IROWS.GT.1 ) THEN
441: CALL ZLACPY( 'L', IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB,
442: $ VSL( ILO+1, ILO ), LDVSL )
443: END IF
444: CALL ZUNGQR( IROWS, IROWS, IROWS, VSL( ILO, ILO ), LDVSL,
445: $ WORK( ITAU ), WORK( IWRK ), LWORK+1-IWRK, IERR )
446: END IF
447: *
448: * Initialize VSR
449: *
450: IF( ILVSR )
451: $ CALL ZLASET( 'Full', N, N, CZERO, CONE, VSR, LDVSR )
452: *
453: * Reduce to generalized Hessenberg form
454: * (Workspace: none needed)
455: *
456: CALL ZGGHRD( JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB, VSL,
457: $ LDVSL, VSR, LDVSR, IERR )
458: *
459: SDIM = 0
460: *
461: * Perform QZ algorithm, computing Schur vectors if desired
462: * (Complex Workspace: need N)
463: * (Real Workspace: need N)
464: *
465: IWRK = ITAU
466: CALL ZHGEQZ( 'S', JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB,
467: $ ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK( IWRK ),
468: $ LWORK+1-IWRK, RWORK( IRWRK ), IERR )
469: IF( IERR.NE.0 ) THEN
470: IF( IERR.GT.0 .AND. IERR.LE.N ) THEN
471: INFO = IERR
472: ELSE IF( IERR.GT.N .AND. IERR.LE.2*N ) THEN
473: INFO = IERR - N
474: ELSE
475: INFO = N + 1
476: END IF
477: GO TO 40
478: END IF
479: *
480: * Sort eigenvalues ALPHA/BETA and compute the reciprocal of
481: * condition number(s)
482: *
483: IF( WANTST ) THEN
484: *
485: * Undo scaling on eigenvalues before SELCTGing
486: *
487: IF( ILASCL )
488: $ CALL ZLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHA, N, IERR )
489: IF( ILBSCL )
490: $ CALL ZLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR )
491: *
492: * Select eigenvalues
493: *
494: DO 10 I = 1, N
495: BWORK( I ) = SELCTG( ALPHA( I ), BETA( I ) )
496: 10 CONTINUE
497: *
498: * Reorder eigenvalues, transform Generalized Schur vectors, and
499: * compute reciprocal condition numbers
500: * (Complex Workspace: If IJOB >= 1, need MAX(1, 2*SDIM*(N-SDIM))
501: * otherwise, need 1 )
502: *
503: CALL ZTGSEN( IJOB, ILVSL, ILVSR, BWORK, N, A, LDA, B, LDB,
504: $ ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, SDIM, PL, PR,
505: $ DIF, WORK( IWRK ), LWORK-IWRK+1, IWORK, LIWORK,
506: $ IERR )
507: *
508: IF( IJOB.GE.1 )
509: $ MAXWRK = MAX( MAXWRK, 2*SDIM*( N-SDIM ) )
510: IF( IERR.EQ.-21 ) THEN
511: *
512: * not enough complex workspace
513: *
514: INFO = -21
515: ELSE
516: IF( IJOB.EQ.1 .OR. IJOB.EQ.4 ) THEN
517: RCONDE( 1 ) = PL
518: RCONDE( 2 ) = PR
519: END IF
520: IF( IJOB.EQ.2 .OR. IJOB.EQ.4 ) THEN
521: RCONDV( 1 ) = DIF( 1 )
522: RCONDV( 2 ) = DIF( 2 )
523: END IF
524: IF( IERR.EQ.1 )
525: $ INFO = N + 3
526: END IF
527: *
528: END IF
529: *
530: * Apply permutation to VSL and VSR
531: * (Workspace: none needed)
532: *
533: IF( ILVSL )
534: $ CALL ZGGBAK( 'P', 'L', N, ILO, IHI, RWORK( ILEFT ),
535: $ RWORK( IRIGHT ), N, VSL, LDVSL, IERR )
536: *
537: IF( ILVSR )
538: $ CALL ZGGBAK( 'P', 'R', N, ILO, IHI, RWORK( ILEFT ),
539: $ RWORK( IRIGHT ), N, VSR, LDVSR, IERR )
540: *
541: * Undo scaling
542: *
543: IF( ILASCL ) THEN
544: CALL ZLASCL( 'U', 0, 0, ANRMTO, ANRM, N, N, A, LDA, IERR )
545: CALL ZLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHA, N, IERR )
546: END IF
547: *
548: IF( ILBSCL ) THEN
549: CALL ZLASCL( 'U', 0, 0, BNRMTO, BNRM, N, N, B, LDB, IERR )
550: CALL ZLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR )
551: END IF
552: *
553: IF( WANTST ) THEN
554: *
555: * Check if reordering is correct
556: *
557: LASTSL = .TRUE.
558: SDIM = 0
559: DO 30 I = 1, N
560: CURSL = SELCTG( ALPHA( I ), BETA( I ) )
561: IF( CURSL )
562: $ SDIM = SDIM + 1
563: IF( CURSL .AND. .NOT.LASTSL )
564: $ INFO = N + 2
565: LASTSL = CURSL
566: 30 CONTINUE
567: *
568: END IF
569: *
570: 40 CONTINUE
571: *
572: WORK( 1 ) = MAXWRK
573: IWORK( 1 ) = LIWMIN
574: *
575: RETURN
576: *
577: * End of ZGGESX
578: *
579: END
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