forked from Reference-LAPACK/lapack
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathctgsja.f
663 lines (663 loc) · 19.5 KB
/
ctgsja.f
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
*> \brief \b CTGSJA
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CTGSJA + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ctgsja.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ctgsja.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ctgsja.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CTGSJA( JOBU, JOBV, JOBQ, M, P, N, K, L, A, LDA, B,
* LDB, TOLA, TOLB, ALPHA, BETA, U, LDU, V, LDV,
* Q, LDQ, WORK, NCYCLE, INFO )
*
* .. Scalar Arguments ..
* CHARACTER JOBQ, JOBU, JOBV
* INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N,
* $ NCYCLE, P
* REAL TOLA, TOLB
* ..
* .. Array Arguments ..
* REAL ALPHA( * ), BETA( * )
* COMPLEX A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
* $ U( LDU, * ), V( LDV, * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CTGSJA computes the generalized singular value decomposition (GSVD)
*> of two complex upper triangular (or trapezoidal) matrices A and B.
*>
*> On entry, it is assumed that matrices A and B have the following
*> forms, which may be obtained by the preprocessing subroutine CGGSVP
*> from a general M-by-N matrix A and P-by-N matrix B:
*>
*> N-K-L K L
*> A = K ( 0 A12 A13 ) if M-K-L >= 0;
*> L ( 0 0 A23 )
*> M-K-L ( 0 0 0 )
*>
*> N-K-L K L
*> A = K ( 0 A12 A13 ) if M-K-L < 0;
*> M-K ( 0 0 A23 )
*>
*> N-K-L K L
*> B = L ( 0 0 B13 )
*> P-L ( 0 0 0 )
*>
*> where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular
*> upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,
*> otherwise A23 is (M-K)-by-L upper trapezoidal.
*>
*> On exit,
*>
*> U**H *A*Q = D1*( 0 R ), V**H *B*Q = D2*( 0 R ),
*>
*> where U, V and Q are unitary matrices.
*> R is a nonsingular upper triangular matrix, and D1
*> and D2 are ``diagonal'' matrices, which are of the following
*> structures:
*>
*> If M-K-L >= 0,
*>
*> K L
*> D1 = K ( I 0 )
*> L ( 0 C )
*> M-K-L ( 0 0 )
*>
*> K L
*> D2 = L ( 0 S )
*> P-L ( 0 0 )
*>
*> N-K-L K L
*> ( 0 R ) = K ( 0 R11 R12 ) K
*> L ( 0 0 R22 ) L
*>
*> where
*>
*> C = diag( ALPHA(K+1), ... , ALPHA(K+L) ),
*> S = diag( BETA(K+1), ... , BETA(K+L) ),
*> C**2 + S**2 = I.
*>
*> R is stored in A(1:K+L,N-K-L+1:N) on exit.
*>
*> If M-K-L < 0,
*>
*> K M-K K+L-M
*> D1 = K ( I 0 0 )
*> M-K ( 0 C 0 )
*>
*> K M-K K+L-M
*> D2 = M-K ( 0 S 0 )
*> K+L-M ( 0 0 I )
*> P-L ( 0 0 0 )
*>
*> N-K-L K M-K K+L-M
*> ( 0 R ) = K ( 0 R11 R12 R13 )
*> M-K ( 0 0 R22 R23 )
*> K+L-M ( 0 0 0 R33 )
*>
*> where
*> C = diag( ALPHA(K+1), ... , ALPHA(M) ),
*> S = diag( BETA(K+1), ... , BETA(M) ),
*> C**2 + S**2 = I.
*>
*> R = ( R11 R12 R13 ) is stored in A(1:M, N-K-L+1:N) and R33 is stored
*> ( 0 R22 R23 )
*> in B(M-K+1:L,N+M-K-L+1:N) on exit.
*>
*> The computation of the unitary transformation matrices U, V or Q
*> is optional. These matrices may either be formed explicitly, or they
*> may be postmultiplied into input matrices U1, V1, or Q1.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] JOBU
*> \verbatim
*> JOBU is CHARACTER*1
*> = 'U': U must contain a unitary matrix U1 on entry, and
*> the product U1*U is returned;
*> = 'I': U is initialized to the unit matrix, and the
*> unitary matrix U is returned;
*> = 'N': U is not computed.
*> \endverbatim
*>
*> \param[in] JOBV
*> \verbatim
*> JOBV is CHARACTER*1
*> = 'V': V must contain a unitary matrix V1 on entry, and
*> the product V1*V is returned;
*> = 'I': V is initialized to the unit matrix, and the
*> unitary matrix V is returned;
*> = 'N': V is not computed.
*> \endverbatim
*>
*> \param[in] JOBQ
*> \verbatim
*> JOBQ is CHARACTER*1
*> = 'Q': Q must contain a unitary matrix Q1 on entry, and
*> the product Q1*Q is returned;
*> = 'I': Q is initialized to the unit matrix, and the
*> unitary matrix Q is returned;
*> = 'N': Q is not computed.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix A. M >= 0.
*> \endverbatim
*>
*> \param[in] P
*> \verbatim
*> P is INTEGER
*> The number of rows of the matrix B. P >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrices A and B. N >= 0.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*> K is INTEGER
*> \endverbatim
*>
*> \param[in] L
*> \verbatim
*> L is INTEGER
*>
*> K and L specify the subblocks in the input matrices A and B:
*> A23 = A(K+1:MIN(K+L,M),N-L+1:N) and B13 = B(1:L,,N-L+1:N)
*> of A and B, whose GSVD is going to be computed by CTGSJA.
*> See Further Details.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> A is COMPLEX array, dimension (LDA,N)
*> On entry, the M-by-N matrix A.
*> On exit, A(N-K+1:N,1:MIN(K+L,M) ) contains the triangular
*> matrix R or part of R. See Purpose for details.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,M).
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is COMPLEX array, dimension (LDB,N)
*> On entry, the P-by-N matrix B.
*> On exit, if necessary, B(M-K+1:L,N+M-K-L+1:N) contains
*> a part of R. See Purpose for details.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,P).
*> \endverbatim
*>
*> \param[in] TOLA
*> \verbatim
*> TOLA is REAL
*> \endverbatim
*>
*> \param[in] TOLB
*> \verbatim
*> TOLB is REAL
*>
*> TOLA and TOLB are the convergence criteria for the Jacobi-
*> Kogbetliantz iteration procedure. Generally, they are the
*> same as used in the preprocessing step, say
*> TOLA = MAX(M,N)*norm(A)*MACHEPS,
*> TOLB = MAX(P,N)*norm(B)*MACHEPS.
*> \endverbatim
*>
*> \param[out] ALPHA
*> \verbatim
*> ALPHA is REAL array, dimension (N)
*> \endverbatim
*>
*> \param[out] BETA
*> \verbatim
*> BETA is REAL array, dimension (N)
*>
*> On exit, ALPHA and BETA contain the generalized singular
*> value pairs of A and B;
*> ALPHA(1:K) = 1,
*> BETA(1:K) = 0,
*> and if M-K-L >= 0,
*> ALPHA(K+1:K+L) = diag(C),
*> BETA(K+1:K+L) = diag(S),
*> or if M-K-L < 0,
*> ALPHA(K+1:M)= C, ALPHA(M+1:K+L)= 0
*> BETA(K+1:M) = S, BETA(M+1:K+L) = 1.
*> Furthermore, if K+L < N,
*> ALPHA(K+L+1:N) = 0
*> BETA(K+L+1:N) = 0.
*> \endverbatim
*>
*> \param[in,out] U
*> \verbatim
*> U is COMPLEX array, dimension (LDU,M)
*> On entry, if JOBU = 'U', U must contain a matrix U1 (usually
*> the unitary matrix returned by CGGSVP).
*> On exit,
*> if JOBU = 'I', U contains the unitary matrix U;
*> if JOBU = 'U', U contains the product U1*U.
*> If JOBU = 'N', U is not referenced.
*> \endverbatim
*>
*> \param[in] LDU
*> \verbatim
*> LDU is INTEGER
*> The leading dimension of the array U. LDU >= max(1,M) if
*> JOBU = 'U'; LDU >= 1 otherwise.
*> \endverbatim
*>
*> \param[in,out] V
*> \verbatim
*> V is COMPLEX array, dimension (LDV,P)
*> On entry, if JOBV = 'V', V must contain a matrix V1 (usually
*> the unitary matrix returned by CGGSVP).
*> On exit,
*> if JOBV = 'I', V contains the unitary matrix V;
*> if JOBV = 'V', V contains the product V1*V.
*> If JOBV = 'N', V is not referenced.
*> \endverbatim
*>
*> \param[in] LDV
*> \verbatim
*> LDV is INTEGER
*> The leading dimension of the array V. LDV >= max(1,P) if
*> JOBV = 'V'; LDV >= 1 otherwise.
*> \endverbatim
*>
*> \param[in,out] Q
*> \verbatim
*> Q is COMPLEX array, dimension (LDQ,N)
*> On entry, if JOBQ = 'Q', Q must contain a matrix Q1 (usually
*> the unitary matrix returned by CGGSVP).
*> On exit,
*> if JOBQ = 'I', Q contains the unitary matrix Q;
*> if JOBQ = 'Q', Q contains the product Q1*Q.
*> If JOBQ = 'N', Q is not referenced.
*> \endverbatim
*>
*> \param[in] LDQ
*> \verbatim
*> LDQ is INTEGER
*> The leading dimension of the array Q. LDQ >= max(1,N) if
*> JOBQ = 'Q'; LDQ >= 1 otherwise.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX array, dimension (2*N)
*> \endverbatim
*>
*> \param[out] NCYCLE
*> \verbatim
*> NCYCLE is INTEGER
*> The number of cycles required for convergence.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> = 1: the procedure does not converge after MAXIT cycles.
*> \endverbatim
*
*> \par Internal Parameters:
* =========================
*>
*> \verbatim
*> MAXIT INTEGER
*> MAXIT specifies the total loops that the iterative procedure
*> may take. If after MAXIT cycles, the routine fails to
*> converge, we return INFO = 1.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complexOTHERcomputational
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> CTGSJA essentially uses a variant of Kogbetliantz algorithm to reduce
*> min(L,M-K)-by-L triangular (or trapezoidal) matrix A23 and L-by-L
*> matrix B13 to the form:
*>
*> U1**H *A13*Q1 = C1*R1; V1**H *B13*Q1 = S1*R1,
*>
*> where U1, V1 and Q1 are unitary matrix.
*> C1 and S1 are diagonal matrices satisfying
*>
*> C1**2 + S1**2 = I,
*>
*> and R1 is an L-by-L nonsingular upper triangular matrix.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE CTGSJA( JOBU, JOBV, JOBQ, M, P, N, K, L, A, LDA, B,
$ LDB, TOLA, TOLB, ALPHA, BETA, U, LDU, V, LDV,
$ Q, LDQ, WORK, NCYCLE, INFO )
*
* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
CHARACTER JOBQ, JOBU, JOBV
INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N,
$ NCYCLE, P
REAL TOLA, TOLB
* ..
* .. Array Arguments ..
REAL ALPHA( * ), BETA( * )
COMPLEX A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
$ U( LDU, * ), V( LDV, * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
INTEGER MAXIT
PARAMETER ( MAXIT = 40 )
REAL ZERO, ONE, HUGENUM
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
COMPLEX CZERO, CONE
PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ),
$ CONE = ( 1.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
*
LOGICAL INITQ, INITU, INITV, UPPER, WANTQ, WANTU, WANTV
INTEGER I, J, KCYCLE
REAL A1, A3, B1, B3, CSQ, CSU, CSV, ERROR, GAMMA,
$ RWK, SSMIN
COMPLEX A2, B2, SNQ, SNU, SNV
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL CCOPY, CLAGS2, CLAPLL, CLASET, CROT, CSSCAL,
$ SLARTG, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, CONJG, MAX, MIN, REAL, HUGE
PARAMETER ( HUGENUM = HUGE(ZERO) )
* ..
* .. Executable Statements ..
*
* Decode and test the input parameters
*
INITU = LSAME( JOBU, 'I' )
WANTU = INITU .OR. LSAME( JOBU, 'U' )
*
INITV = LSAME( JOBV, 'I' )
WANTV = INITV .OR. LSAME( JOBV, 'V' )
*
INITQ = LSAME( JOBQ, 'I' )
WANTQ = INITQ .OR. LSAME( JOBQ, 'Q' )
*
INFO = 0
IF( .NOT.( INITU .OR. WANTU .OR. LSAME( JOBU, 'N' ) ) ) THEN
INFO = -1
ELSE IF( .NOT.( INITV .OR. WANTV .OR. LSAME( JOBV, 'N' ) ) ) THEN
INFO = -2
ELSE IF( .NOT.( INITQ .OR. WANTQ .OR. LSAME( JOBQ, 'N' ) ) ) THEN
INFO = -3
ELSE IF( M.LT.0 ) THEN
INFO = -4
ELSE IF( P.LT.0 ) THEN
INFO = -5
ELSE IF( N.LT.0 ) THEN
INFO = -6
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
INFO = -10
ELSE IF( LDB.LT.MAX( 1, P ) ) THEN
INFO = -12
ELSE IF( LDU.LT.1 .OR. ( WANTU .AND. LDU.LT.M ) ) THEN
INFO = -18
ELSE IF( LDV.LT.1 .OR. ( WANTV .AND. LDV.LT.P ) ) THEN
INFO = -20
ELSE IF( LDQ.LT.1 .OR. ( WANTQ .AND. LDQ.LT.N ) ) THEN
INFO = -22
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CTGSJA', -INFO )
RETURN
END IF
*
* Initialize U, V and Q, if necessary
*
IF( INITU )
$ CALL CLASET( 'Full', M, M, CZERO, CONE, U, LDU )
IF( INITV )
$ CALL CLASET( 'Full', P, P, CZERO, CONE, V, LDV )
IF( INITQ )
$ CALL CLASET( 'Full', N, N, CZERO, CONE, Q, LDQ )
*
* Loop until convergence
*
UPPER = .FALSE.
DO 40 KCYCLE = 1, MAXIT
*
UPPER = .NOT.UPPER
*
DO 20 I = 1, L - 1
DO 10 J = I + 1, L
*
A1 = ZERO
A2 = CZERO
A3 = ZERO
IF( K+I.LE.M )
$ A1 = REAL( A( K+I, N-L+I ) )
IF( K+J.LE.M )
$ A3 = REAL( A( K+J, N-L+J ) )
*
B1 = REAL( B( I, N-L+I ) )
B3 = REAL( B( J, N-L+J ) )
*
IF( UPPER ) THEN
IF( K+I.LE.M )
$ A2 = A( K+I, N-L+J )
B2 = B( I, N-L+J )
ELSE
IF( K+J.LE.M )
$ A2 = A( K+J, N-L+I )
B2 = B( J, N-L+I )
END IF
*
CALL CLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU,
$ CSV, SNV, CSQ, SNQ )
*
* Update (K+I)-th and (K+J)-th rows of matrix A: U**H *A
*
IF( K+J.LE.M )
$ CALL CROT( L, A( K+J, N-L+1 ), LDA, A( K+I, N-L+1 ),
$ LDA, CSU, CONJG( SNU ) )
*
* Update I-th and J-th rows of matrix B: V**H *B
*
CALL CROT( L, B( J, N-L+1 ), LDB, B( I, N-L+1 ), LDB,
$ CSV, CONJG( SNV ) )
*
* Update (N-L+I)-th and (N-L+J)-th columns of matrices
* A and B: A*Q and B*Q
*
CALL CROT( MIN( K+L, M ), A( 1, N-L+J ), 1,
$ A( 1, N-L+I ), 1, CSQ, SNQ )
*
CALL CROT( L, B( 1, N-L+J ), 1, B( 1, N-L+I ), 1, CSQ,
$ SNQ )
*
IF( UPPER ) THEN
IF( K+I.LE.M )
$ A( K+I, N-L+J ) = CZERO
B( I, N-L+J ) = CZERO
ELSE
IF( K+J.LE.M )
$ A( K+J, N-L+I ) = CZERO
B( J, N-L+I ) = CZERO
END IF
*
* Ensure that the diagonal elements of A and B are real.
*
IF( K+I.LE.M )
$ A( K+I, N-L+I ) = REAL( A( K+I, N-L+I ) )
IF( K+J.LE.M )
$ A( K+J, N-L+J ) = REAL( A( K+J, N-L+J ) )
B( I, N-L+I ) = REAL( B( I, N-L+I ) )
B( J, N-L+J ) = REAL( B( J, N-L+J ) )
*
* Update unitary matrices U, V, Q, if desired.
*
IF( WANTU .AND. K+J.LE.M )
$ CALL CROT( M, U( 1, K+J ), 1, U( 1, K+I ), 1, CSU,
$ SNU )
*
IF( WANTV )
$ CALL CROT( P, V( 1, J ), 1, V( 1, I ), 1, CSV, SNV )
*
IF( WANTQ )
$ CALL CROT( N, Q( 1, N-L+J ), 1, Q( 1, N-L+I ), 1, CSQ,
$ SNQ )
*
10 CONTINUE
20 CONTINUE
*
IF( .NOT.UPPER ) THEN
*
* The matrices A13 and B13 were lower triangular at the start
* of the cycle, and are now upper triangular.
*
* Convergence test: test the parallelism of the corresponding
* rows of A and B.
*
ERROR = ZERO
DO 30 I = 1, MIN( L, M-K )
CALL CCOPY( L-I+1, A( K+I, N-L+I ), LDA, WORK, 1 )
CALL CCOPY( L-I+1, B( I, N-L+I ), LDB, WORK( L+1 ), 1 )
CALL CLAPLL( L-I+1, WORK, 1, WORK( L+1 ), 1, SSMIN )
ERROR = MAX( ERROR, SSMIN )
30 CONTINUE
*
IF( ABS( ERROR ).LE.MIN( TOLA, TOLB ) )
$ GO TO 50
END IF
*
* End of cycle loop
*
40 CONTINUE
*
* The algorithm has not converged after MAXIT cycles.
*
INFO = 1
GO TO 100
*
50 CONTINUE
*
* If ERROR <= MIN(TOLA,TOLB), then the algorithm has converged.
* Compute the generalized singular value pairs (ALPHA, BETA), and
* set the triangular matrix R to array A.
*
DO 60 I = 1, K
ALPHA( I ) = ONE
BETA( I ) = ZERO
60 CONTINUE
*
DO 70 I = 1, MIN( L, M-K )
*
A1 = REAL( A( K+I, N-L+I ) )
B1 = REAL( B( I, N-L+I ) )
GAMMA = B1 / A1
*
IF( (GAMMA.LE.HUGENUM).AND.(GAMMA.GE.-HUGENUM) ) THEN
*
IF( GAMMA.LT.ZERO ) THEN
CALL CSSCAL( L-I+1, -ONE, B( I, N-L+I ), LDB )
IF( WANTV )
$ CALL CSSCAL( P, -ONE, V( 1, I ), 1 )
END IF
*
CALL SLARTG( ABS( GAMMA ), ONE, BETA( K+I ), ALPHA( K+I ),
$ RWK )
*
IF( ALPHA( K+I ).GE.BETA( K+I ) ) THEN
CALL CSSCAL( L-I+1, ONE / ALPHA( K+I ), A( K+I, N-L+I ),
$ LDA )
ELSE
CALL CSSCAL( L-I+1, ONE / BETA( K+I ), B( I, N-L+I ),
$ LDB )
CALL CCOPY( L-I+1, B( I, N-L+I ), LDB, A( K+I, N-L+I ),
$ LDA )
END IF
*
ELSE
ALPHA( K+I ) = ZERO
BETA( K+I ) = ONE
CALL CCOPY( L-I+1, B( I, N-L+I ), LDB, A( K+I, N-L+I ),
$ LDA )
END IF
70 CONTINUE
*
* Post-assignment
*
DO 80 I = M + 1, K + L
ALPHA( I ) = ZERO
BETA( I ) = ONE
80 CONTINUE
*
IF( K+L.LT.N ) THEN
DO 90 I = K + L + 1, N
ALPHA( I ) = ZERO
BETA( I ) = ZERO
90 CONTINUE
END IF
*
100 CONTINUE
NCYCLE = KCYCLE
*
RETURN
*
* End of CTGSJA
*
END