summaryrefslogtreecommitdiff
path: root/SRC/stgexc.f
blob: a1d9dbb56e2f0c717b2e4463636ff81b2fe9dfce (plain)
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
*> \brief \b STGEXC
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download STGEXC + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/stgexc.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/stgexc.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/stgexc.f">
*> [TXT]</a>
*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE STGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
*                          LDZ, IFST, ILST, WORK, LWORK, INFO )
*
*       .. Scalar Arguments ..
*       LOGICAL            WANTQ, WANTZ
*       INTEGER            IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, LWORK, N
*       ..
*       .. Array Arguments ..
*       REAL               A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
*      $                   WORK( * ), Z( LDZ, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> STGEXC reorders the generalized real Schur decomposition of a real
*> matrix pair (A,B) using an orthogonal equivalence transformation
*>
*>                (A, B) = Q * (A, B) * Z**T,
*>
*> so that the diagonal block of (A, B) with row index IFST is moved
*> to row ILST.
*>
*> (A, B) must be in generalized real Schur canonical form (as returned
*> by SGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2
*> diagonal blocks. B is upper triangular.
*>
*> Optionally, the matrices Q and Z of generalized Schur vectors are
*> updated.
*>
*>        Q(in) * A(in) * Z(in)**T = Q(out) * A(out) * Z(out)**T
*>        Q(in) * B(in) * Z(in)**T = Q(out) * B(out) * Z(out)**T
*>
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] WANTQ
*> \verbatim
*>          WANTQ is LOGICAL
*>          .TRUE. : update the left transformation matrix Q;
*>          .FALSE.: do not update Q.
*> \endverbatim
*>
*> \param[in] WANTZ
*> \verbatim
*>          WANTZ is LOGICAL
*>          .TRUE. : update the right transformation matrix Z;
*>          .FALSE.: do not update Z.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrices A and B. N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          A is REAL array, dimension (LDA,N)
*>          On entry, the matrix A in generalized real Schur canonical
*>          form.
*>          On exit, the updated matrix A, again in generalized
*>          real Schur canonical form.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A. LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*>          B is REAL array, dimension (LDB,N)
*>          On entry, the matrix B in generalized real Schur canonical
*>          form (A,B).
*>          On exit, the updated matrix B, again in generalized
*>          real Schur canonical form (A,B).
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*>          LDB is INTEGER
*>          The leading dimension of the array B. LDB >= max(1,N).
*> \endverbatim
*>
*> \param[in,out] Q
*> \verbatim
*>          Q is REAL array, dimension (LDZ,N)
*>          On entry, if WANTQ = .TRUE., the orthogonal matrix Q.
*>          On exit, the updated matrix Q.
*>          If WANTQ = .FALSE., Q is not referenced.
*> \endverbatim
*>
*> \param[in] LDQ
*> \verbatim
*>          LDQ is INTEGER
*>          The leading dimension of the array Q. LDQ >= 1.
*>          If WANTQ = .TRUE., LDQ >= N.
*> \endverbatim
*>
*> \param[in,out] Z
*> \verbatim
*>          Z is REAL array, dimension (LDZ,N)
*>          On entry, if WANTZ = .TRUE., the orthogonal matrix Z.
*>          On exit, the updated matrix Z.
*>          If WANTZ = .FALSE., Z is not referenced.
*> \endverbatim
*>
*> \param[in] LDZ
*> \verbatim
*>          LDZ is INTEGER
*>          The leading dimension of the array Z. LDZ >= 1.
*>          If WANTZ = .TRUE., LDZ >= N.
*> \endverbatim
*>
*> \param[in,out] IFST
*> \verbatim
*>          IFST is INTEGER
*> \endverbatim
*>
*> \param[in,out] ILST
*> \verbatim
*>          ILST is INTEGER
*>          Specify the reordering of the diagonal blocks of (A, B).
*>          The block with row index IFST is moved to row ILST, by a
*>          sequence of swapping between adjacent blocks.
*>          On exit, if IFST pointed on entry to the second row of
*>          a 2-by-2 block, it is changed to point to the first row;
*>          ILST always points to the first row of the block in its
*>          final position (which may differ from its input value by
*>          +1 or -1). 1 <= IFST, ILST <= N.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is REAL array, dimension (MAX(1,LWORK))
*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*>          LWORK is INTEGER
*>          The dimension of the array WORK.
*>          LWORK >= 1 when N <= 1, otherwise LWORK >= 4*N + 16.
*>
*>          If LWORK = -1, then a workspace query is assumed; the routine
*>          only calculates the optimal size of the WORK array, returns
*>          this value as the first entry of the WORK array, and no error
*>          message related to LWORK is issued by XERBLA.
*> \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 transformed matrix pair (A, B) would be too far
*>                from generalized Schur form; the problem is ill-
*>                conditioned. (A, B) may have been partially reordered,
*>                and ILST points to the first row of the current
*>                position of the block being moved.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup realGEcomputational
*
*> \par Contributors:
*  ==================
*>
*>     Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*>     Umea University, S-901 87 Umea, Sweden.
*
*> \par References:
*  ================
*>
*> \verbatim
*>
*>  [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
*>      Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
*>      M.S. Moonen et al (eds), Linear Algebra for Large Scale and
*>      Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE STGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
     $                   LDZ, IFST, ILST, WORK, LWORK, INFO )
*
*  -- LAPACK computational routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      LOGICAL            WANTQ, WANTZ
      INTEGER            IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, LWORK, N
*     ..
*     .. Array Arguments ..
      REAL               A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
     $                   WORK( * ), Z( LDZ, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO
      PARAMETER          ( ZERO = 0.0E+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            LQUERY
      INTEGER            HERE, LWMIN, NBF, NBL, NBNEXT
*     ..
*     .. External Subroutines ..
      EXTERNAL           STGEX2, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     ..
*     .. Executable Statements ..
*
*     Decode and test input arguments.
*
      INFO = 0
      LQUERY = ( LWORK.EQ.-1 )
      IF( N.LT.0 ) THEN
         INFO = -3
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -5
      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
         INFO = -7
      ELSE IF( LDQ.LT.1 .OR. WANTQ .AND. ( LDQ.LT.MAX( 1, N ) ) ) THEN
         INFO = -9
      ELSE IF( LDZ.LT.1 .OR. WANTZ .AND. ( LDZ.LT.MAX( 1, N ) ) ) THEN
         INFO = -11
      ELSE IF( IFST.LT.1 .OR. IFST.GT.N ) THEN
         INFO = -12
      ELSE IF( ILST.LT.1 .OR. ILST.GT.N ) THEN
         INFO = -13
      END IF
*
      IF( INFO.EQ.0 ) THEN
         IF( N.LE.1 ) THEN
            LWMIN = 1
         ELSE
            LWMIN = 4*N + 16
         END IF
         WORK(1) = LWMIN
*
         IF (LWORK.LT.LWMIN .AND. .NOT.LQUERY) THEN
            INFO = -15
         END IF
      END IF
*
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'STGEXC', -INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.LE.1 )
     $   RETURN
*
*     Determine the first row of the specified block and find out
*     if it is 1-by-1 or 2-by-2.
*
      IF( IFST.GT.1 ) THEN
         IF( A( IFST, IFST-1 ).NE.ZERO )
     $      IFST = IFST - 1
      END IF
      NBF = 1
      IF( IFST.LT.N ) THEN
         IF( A( IFST+1, IFST ).NE.ZERO )
     $      NBF = 2
      END IF
*
*     Determine the first row of the final block
*     and find out if it is 1-by-1 or 2-by-2.
*
      IF( ILST.GT.1 ) THEN
         IF( A( ILST, ILST-1 ).NE.ZERO )
     $      ILST = ILST - 1
      END IF
      NBL = 1
      IF( ILST.LT.N ) THEN
         IF( A( ILST+1, ILST ).NE.ZERO )
     $      NBL = 2
      END IF
      IF( IFST.EQ.ILST )
     $   RETURN
*
      IF( IFST.LT.ILST ) THEN
*
*        Update ILST.
*
         IF( NBF.EQ.2 .AND. NBL.EQ.1 )
     $      ILST = ILST - 1
         IF( NBF.EQ.1 .AND. NBL.EQ.2 )
     $      ILST = ILST + 1
*
         HERE = IFST
*
   10    CONTINUE
*
*        Swap with next one below.
*
         IF( NBF.EQ.1 .OR. NBF.EQ.2 ) THEN
*
*           Current block either 1-by-1 or 2-by-2.
*
            NBNEXT = 1
            IF( HERE+NBF+1.LE.N ) THEN
               IF( A( HERE+NBF+1, HERE+NBF ).NE.ZERO )
     $            NBNEXT = 2
            END IF
            CALL STGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
     $                   LDZ, HERE, NBF, NBNEXT, WORK, LWORK, INFO )
            IF( INFO.NE.0 ) THEN
               ILST = HERE
               RETURN
            END IF
            HERE = HERE + NBNEXT
*
*           Test if 2-by-2 block breaks into two 1-by-1 blocks.
*
            IF( NBF.EQ.2 ) THEN
               IF( A( HERE+1, HERE ).EQ.ZERO )
     $            NBF = 3
            END IF
*
         ELSE
*
*           Current block consists of two 1-by-1 blocks, each of which
*           must be swapped individually.
*
            NBNEXT = 1
            IF( HERE+3.LE.N ) THEN
               IF( A( HERE+3, HERE+2 ).NE.ZERO )
     $            NBNEXT = 2
            END IF
            CALL STGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
     $                   LDZ, HERE+1, 1, NBNEXT, WORK, LWORK, INFO )
            IF( INFO.NE.0 ) THEN
               ILST = HERE
               RETURN
            END IF
            IF( NBNEXT.EQ.1 ) THEN
*
*              Swap two 1-by-1 blocks.
*
               CALL STGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
     $                      LDZ, HERE, 1, 1, WORK, LWORK, INFO )
               IF( INFO.NE.0 ) THEN
                  ILST = HERE
                  RETURN
               END IF
               HERE = HERE + 1
*
            ELSE
*
*              Recompute NBNEXT in case of 2-by-2 split.
*
               IF( A( HERE+2, HERE+1 ).EQ.ZERO )
     $            NBNEXT = 1
               IF( NBNEXT.EQ.2 ) THEN
*
*                 2-by-2 block did not split.
*
                  CALL STGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ,
     $                         Z, LDZ, HERE, 1, NBNEXT, WORK, LWORK,
     $                         INFO )
                  IF( INFO.NE.0 ) THEN
                     ILST = HERE
                     RETURN
                  END IF
                  HERE = HERE + 2
               ELSE
*
*                 2-by-2 block did split.
*
                  CALL STGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ,
     $                         Z, LDZ, HERE, 1, 1, WORK, LWORK, INFO )
                  IF( INFO.NE.0 ) THEN
                     ILST = HERE
                     RETURN
                  END IF
                  HERE = HERE + 1
                  CALL STGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ,
     $                         Z, LDZ, HERE, 1, 1, WORK, LWORK, INFO )
                  IF( INFO.NE.0 ) THEN
                     ILST = HERE
                     RETURN
                  END IF
                  HERE = HERE + 1
               END IF
*
            END IF
         END IF
         IF( HERE.LT.ILST )
     $      GO TO 10
      ELSE
         HERE = IFST
*
   20    CONTINUE
*
*        Swap with next one below.
*
         IF( NBF.EQ.1 .OR. NBF.EQ.2 ) THEN
*
*           Current block either 1-by-1 or 2-by-2.
*
            NBNEXT = 1
            IF( HERE.GE.3 ) THEN
               IF( A( HERE-1, HERE-2 ).NE.ZERO )
     $            NBNEXT = 2
            END IF
            CALL STGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
     $                   LDZ, HERE-NBNEXT, NBNEXT, NBF, WORK, LWORK,
     $                   INFO )
            IF( INFO.NE.0 ) THEN
               ILST = HERE
               RETURN
            END IF
            HERE = HERE - NBNEXT
*
*           Test if 2-by-2 block breaks into two 1-by-1 blocks.
*
            IF( NBF.EQ.2 ) THEN
               IF( A( HERE+1, HERE ).EQ.ZERO )
     $            NBF = 3
            END IF
*
         ELSE
*
*           Current block consists of two 1-by-1 blocks, each of which
*           must be swapped individually.
*
            NBNEXT = 1
            IF( HERE.GE.3 ) THEN
               IF( A( HERE-1, HERE-2 ).NE.ZERO )
     $            NBNEXT = 2
            END IF
            CALL STGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
     $                   LDZ, HERE-NBNEXT, NBNEXT, 1, WORK, LWORK,
     $                   INFO )
            IF( INFO.NE.0 ) THEN
               ILST = HERE
               RETURN
            END IF
            IF( NBNEXT.EQ.1 ) THEN
*
*              Swap two 1-by-1 blocks.
*
               CALL STGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
     $                      LDZ, HERE, NBNEXT, 1, WORK, LWORK, INFO )
               IF( INFO.NE.0 ) THEN
                  ILST = HERE
                  RETURN
               END IF
               HERE = HERE - 1
            ELSE
*
*             Recompute NBNEXT in case of 2-by-2 split.
*
               IF( A( HERE, HERE-1 ).EQ.ZERO )
     $            NBNEXT = 1
               IF( NBNEXT.EQ.2 ) THEN
*
*                 2-by-2 block did not split.
*
                  CALL STGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ,
     $                         Z, LDZ, HERE-1, 2, 1, WORK, LWORK, INFO )
                  IF( INFO.NE.0 ) THEN
                     ILST = HERE
                     RETURN
                  END IF
                  HERE = HERE - 2
               ELSE
*
*                 2-by-2 block did split.
*
                  CALL STGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ,
     $                         Z, LDZ, HERE, 1, 1, WORK, LWORK, INFO )
                  IF( INFO.NE.0 ) THEN
                     ILST = HERE
                     RETURN
                  END IF
                  HERE = HERE - 1
                  CALL STGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ,
     $                         Z, LDZ, HERE, 1, 1, WORK, LWORK, INFO )
                  IF( INFO.NE.0 ) THEN
                     ILST = HERE
                     RETURN
                  END IF
                  HERE = HERE - 1
               END IF
            END IF
         END IF
         IF( HERE.GT.ILST )
     $      GO TO 20
      END IF
      ILST = HERE
      WORK( 1 ) = LWMIN
      RETURN
*
*     End of STGEXC
*
      END