forked from Reference-LAPACK/lapack
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathdtgsyl.f
682 lines (682 loc) · 22.2 KB
/
dtgsyl.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
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
*> \brief \b DTGSYL
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DTGSYL + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtgsyl.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtgsyl.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtgsyl.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DTGSYL( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D,
* LDD, E, LDE, F, LDF, SCALE, DIF, WORK, LWORK,
* IWORK, INFO )
*
* .. Scalar Arguments ..
* CHARACTER TRANS
* INTEGER IJOB, INFO, LDA, LDB, LDC, LDD, LDE, LDF,
* $ LWORK, M, N
* DOUBLE PRECISION DIF, SCALE
* ..
* .. Array Arguments ..
* INTEGER IWORK( * )
* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * ),
* $ D( LDD, * ), E( LDE, * ), F( LDF, * ),
* $ WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DTGSYL solves the generalized Sylvester equation:
*>
*> A * R - L * B = scale * C (1)
*> D * R - L * E = scale * F
*>
*> where R and L are unknown m-by-n matrices, (A, D), (B, E) and
*> (C, F) are given matrix pairs of size m-by-m, n-by-n and m-by-n,
*> respectively, with real entries. (A, D) and (B, E) must be in
*> generalized (real) Schur canonical form, i.e. A, B are upper quasi
*> triangular and D, E are upper triangular.
*>
*> The solution (R, L) overwrites (C, F). 0 <= SCALE <= 1 is an output
*> scaling factor chosen to avoid overflow.
*>
*> In matrix notation (1) is equivalent to solve Zx = scale b, where
*> Z is defined as
*>
*> Z = [ kron(In, A) -kron(B**T, Im) ] (2)
*> [ kron(In, D) -kron(E**T, Im) ].
*>
*> Here Ik is the identity matrix of size k and X**T is the transpose of
*> X. kron(X, Y) is the Kronecker product between the matrices X and Y.
*>
*> If TRANS = 'T', DTGSYL solves the transposed system Z**T*y = scale*b,
*> which is equivalent to solve for R and L in
*>
*> A**T * R + D**T * L = scale * C (3)
*> R * B**T + L * E**T = scale * -F
*>
*> This case (TRANS = 'T') is used to compute an one-norm-based estimate
*> of Dif[(A,D), (B,E)], the separation between the matrix pairs (A,D)
*> and (B,E), using DLACON.
*>
*> If IJOB >= 1, DTGSYL computes a Frobenius norm-based estimate
*> of Dif[(A,D),(B,E)]. That is, the reciprocal of a lower bound on the
*> reciprocal of the smallest singular value of Z. See [1-2] for more
*> information.
*>
*> This is a level 3 BLAS algorithm.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] TRANS
*> \verbatim
*> TRANS is CHARACTER*1
*> = 'N': solve the generalized Sylvester equation (1).
*> = 'T': solve the 'transposed' system (3).
*> \endverbatim
*>
*> \param[in] IJOB
*> \verbatim
*> IJOB is INTEGER
*> Specifies what kind of functionality to be performed.
*> = 0: solve (1) only.
*> = 1: The functionality of 0 and 3.
*> = 2: The functionality of 0 and 4.
*> = 3: Only an estimate of Dif[(A,D), (B,E)] is computed.
*> (look ahead strategy IJOB = 1 is used).
*> = 4: Only an estimate of Dif[(A,D), (B,E)] is computed.
*> ( DGECON on sub-systems is used ).
*> Not referenced if TRANS = 'T'.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The order of the matrices A and D, and the row dimension of
*> the matrices C, F, R and L.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrices B and E, and the column dimension
*> of the matrices C, F, R and L.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension (LDA, M)
*> The upper quasi triangular matrix A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1, M).
*> \endverbatim
*>
*> \param[in] B
*> \verbatim
*> B is DOUBLE PRECISION array, dimension (LDB, N)
*> The upper quasi triangular matrix B.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1, N).
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*> C is DOUBLE PRECISION array, dimension (LDC, N)
*> On entry, C contains the right-hand-side of the first matrix
*> equation in (1) or (3).
*> On exit, if IJOB = 0, 1 or 2, C has been overwritten by
*> the solution R. If IJOB = 3 or 4 and TRANS = 'N', C holds R,
*> the solution achieved during the computation of the
*> Dif-estimate.
*> \endverbatim
*>
*> \param[in] LDC
*> \verbatim
*> LDC is INTEGER
*> The leading dimension of the array C. LDC >= max(1, M).
*> \endverbatim
*>
*> \param[in] D
*> \verbatim
*> D is DOUBLE PRECISION array, dimension (LDD, M)
*> The upper triangular matrix D.
*> \endverbatim
*>
*> \param[in] LDD
*> \verbatim
*> LDD is INTEGER
*> The leading dimension of the array D. LDD >= max(1, M).
*> \endverbatim
*>
*> \param[in] E
*> \verbatim
*> E is DOUBLE PRECISION array, dimension (LDE, N)
*> The upper triangular matrix E.
*> \endverbatim
*>
*> \param[in] LDE
*> \verbatim
*> LDE is INTEGER
*> The leading dimension of the array E. LDE >= max(1, N).
*> \endverbatim
*>
*> \param[in,out] F
*> \verbatim
*> F is DOUBLE PRECISION array, dimension (LDF, N)
*> On entry, F contains the right-hand-side of the second matrix
*> equation in (1) or (3).
*> On exit, if IJOB = 0, 1 or 2, F has been overwritten by
*> the solution L. If IJOB = 3 or 4 and TRANS = 'N', F holds L,
*> the solution achieved during the computation of the
*> Dif-estimate.
*> \endverbatim
*>
*> \param[in] LDF
*> \verbatim
*> LDF is INTEGER
*> The leading dimension of the array F. LDF >= max(1, M).
*> \endverbatim
*>
*> \param[out] DIF
*> \verbatim
*> DIF is DOUBLE PRECISION
*> On exit DIF is the reciprocal of a lower bound of the
*> reciprocal of the Dif-function, i.e. DIF is an upper bound of
*> Dif[(A,D), (B,E)] = sigma_min(Z), where Z as in (2).
*> IF IJOB = 0 or TRANS = 'T', DIF is not touched.
*> \endverbatim
*>
*> \param[out] SCALE
*> \verbatim
*> SCALE is DOUBLE PRECISION
*> On exit SCALE is the scaling factor in (1) or (3).
*> If 0 < SCALE < 1, C and F hold the solutions R and L, resp.,
*> to a slightly perturbed system but the input matrices A, B, D
*> and E have not been changed. If SCALE = 0, C and F hold the
*> solutions R and L, respectively, to the homogeneous system
*> with C = F = 0. Normally, SCALE = 1.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION 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.
*> If IJOB = 1 or 2 and TRANS = 'N', LWORK >= max(1,2*M*N).
*>
*> 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] IWORK
*> \verbatim
*> IWORK is INTEGER array, dimension (M+N+6)
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> =0: successful exit
*> <0: If INFO = -i, the i-th argument had an illegal value.
*> >0: (A, D) and (B, E) have common or close eigenvalues.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup doubleSYcomputational
*
*> \par Contributors:
* ==================
*>
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
*
*> \par References:
* ================
*>
*> \verbatim
*>
*> [1] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software
*> for Solving the Generalized Sylvester Equation and Estimating the
*> Separation between Regular Matrix Pairs, Report UMINF - 93.23,
*> Department of Computing Science, Umea University, S-901 87 Umea,
*> Sweden, December 1993, Revised April 1994, Also as LAPACK Working
*> Note 75. To appear in ACM Trans. on Math. Software, Vol 22,
*> No 1, 1996.
*>
*> [2] B. Kagstrom, A Perturbation Analysis of the Generalized Sylvester
*> Equation (AR - LB, DR - LE ) = (C, F), SIAM J. Matrix Anal.
*> Appl., 15(4):1045-1060, 1994
*>
*> [3] B. Kagstrom and L. Westin, Generalized Schur Methods with
*> Condition Estimators for Solving the Generalized Sylvester
*> Equation, IEEE Transactions on Automatic Control, Vol. 34, No. 7,
*> July 1989, pp 745-751.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE DTGSYL( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D,
$ LDD, E, LDE, F, LDF, SCALE, DIF, WORK, LWORK,
$ IWORK, 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 ..
CHARACTER TRANS
INTEGER IJOB, INFO, LDA, LDB, LDC, LDD, LDE, LDF,
$ LWORK, M, N
DOUBLE PRECISION DIF, SCALE
* ..
* .. Array Arguments ..
INTEGER IWORK( * )
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * ),
$ D( LDD, * ), E( LDE, * ), F( LDF, * ),
$ WORK( * )
* ..
*
* =====================================================================
* Replaced various illegal calls to DCOPY by calls to DLASET.
* Sven Hammarling, 1/5/02.
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
LOGICAL LQUERY, NOTRAN
INTEGER I, IE, IFUNC, IROUND, IS, ISOLVE, J, JE, JS, K,
$ LINFO, LWMIN, MB, NB, P, PPQQ, PQ, Q
DOUBLE PRECISION DSCALE, DSUM, SCALE2, SCALOC
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ILAENV
EXTERNAL LSAME, ILAENV
* ..
* .. External Subroutines ..
EXTERNAL DGEMM, DLACPY, DLASET, DSCAL, DTGSY2, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, MAX, SQRT
* ..
* .. Executable Statements ..
*
* Decode and test input parameters
*
INFO = 0
NOTRAN = LSAME( TRANS, 'N' )
LQUERY = ( LWORK.EQ.-1 )
*
IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
INFO = -1
ELSE IF( NOTRAN ) THEN
IF( ( IJOB.LT.0 ) .OR. ( IJOB.GT.4 ) ) THEN
INFO = -2
END IF
END IF
IF( INFO.EQ.0 ) THEN
IF( M.LE.0 ) THEN
INFO = -3
ELSE IF( N.LE.0 ) THEN
INFO = -4
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
INFO = -6
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -8
ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
INFO = -10
ELSE IF( LDD.LT.MAX( 1, M ) ) THEN
INFO = -12
ELSE IF( LDE.LT.MAX( 1, N ) ) THEN
INFO = -14
ELSE IF( LDF.LT.MAX( 1, M ) ) THEN
INFO = -16
END IF
END IF
*
IF( INFO.EQ.0 ) THEN
IF( NOTRAN ) THEN
IF( IJOB.EQ.1 .OR. IJOB.EQ.2 ) THEN
LWMIN = MAX( 1, 2*M*N )
ELSE
LWMIN = 1
END IF
ELSE
LWMIN = 1
END IF
WORK( 1 ) = LWMIN
*
IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
INFO = -20
END IF
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DTGSYL', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
* Quick return if possible
*
IF( M.EQ.0 .OR. N.EQ.0 ) THEN
SCALE = 1
IF( NOTRAN ) THEN
IF( IJOB.NE.0 ) THEN
DIF = 0
END IF
END IF
RETURN
END IF
*
* Determine optimal block sizes MB and NB
*
MB = ILAENV( 2, 'DTGSYL', TRANS, M, N, -1, -1 )
NB = ILAENV( 5, 'DTGSYL', TRANS, M, N, -1, -1 )
*
ISOLVE = 1
IFUNC = 0
IF( NOTRAN ) THEN
IF( IJOB.GE.3 ) THEN
IFUNC = IJOB - 2
CALL DLASET( 'F', M, N, ZERO, ZERO, C, LDC )
CALL DLASET( 'F', M, N, ZERO, ZERO, F, LDF )
ELSE IF( IJOB.GE.1 ) THEN
ISOLVE = 2
END IF
END IF
*
IF( ( MB.LE.1 .AND. NB.LE.1 ) .OR. ( MB.GE.M .AND. NB.GE.N ) )
$ THEN
*
DO 30 IROUND = 1, ISOLVE
*
* Use unblocked Level 2 solver
*
DSCALE = ZERO
DSUM = ONE
PQ = 0
CALL DTGSY2( TRANS, IFUNC, M, N, A, LDA, B, LDB, C, LDC, D,
$ LDD, E, LDE, F, LDF, SCALE, DSUM, DSCALE,
$ IWORK, PQ, INFO )
IF( DSCALE.NE.ZERO ) THEN
IF( IJOB.EQ.1 .OR. IJOB.EQ.3 ) THEN
DIF = SQRT( DBLE( 2*M*N ) ) / ( DSCALE*SQRT( DSUM ) )
ELSE
DIF = SQRT( DBLE( PQ ) ) / ( DSCALE*SQRT( DSUM ) )
END IF
END IF
*
IF( ISOLVE.EQ.2 .AND. IROUND.EQ.1 ) THEN
IF( NOTRAN ) THEN
IFUNC = IJOB
END IF
SCALE2 = SCALE
CALL DLACPY( 'F', M, N, C, LDC, WORK, M )
CALL DLACPY( 'F', M, N, F, LDF, WORK( M*N+1 ), M )
CALL DLASET( 'F', M, N, ZERO, ZERO, C, LDC )
CALL DLASET( 'F', M, N, ZERO, ZERO, F, LDF )
ELSE IF( ISOLVE.EQ.2 .AND. IROUND.EQ.2 ) THEN
CALL DLACPY( 'F', M, N, WORK, M, C, LDC )
CALL DLACPY( 'F', M, N, WORK( M*N+1 ), M, F, LDF )
SCALE = SCALE2
END IF
30 CONTINUE
*
RETURN
END IF
*
* Determine block structure of A
*
P = 0
I = 1
40 CONTINUE
IF( I.GT.M )
$ GO TO 50
P = P + 1
IWORK( P ) = I
I = I + MB
IF( I.GE.M )
$ GO TO 50
IF( A( I, I-1 ).NE.ZERO )
$ I = I + 1
GO TO 40
50 CONTINUE
*
IWORK( P+1 ) = M + 1
IF( IWORK( P ).EQ.IWORK( P+1 ) )
$ P = P - 1
*
* Determine block structure of B
*
Q = P + 1
J = 1
60 CONTINUE
IF( J.GT.N )
$ GO TO 70
Q = Q + 1
IWORK( Q ) = J
J = J + NB
IF( J.GE.N )
$ GO TO 70
IF( B( J, J-1 ).NE.ZERO )
$ J = J + 1
GO TO 60
70 CONTINUE
*
IWORK( Q+1 ) = N + 1
IF( IWORK( Q ).EQ.IWORK( Q+1 ) )
$ Q = Q - 1
*
IF( NOTRAN ) THEN
*
DO 150 IROUND = 1, ISOLVE
*
* Solve (I, J)-subsystem
* A(I, I) * R(I, J) - L(I, J) * B(J, J) = C(I, J)
* D(I, I) * R(I, J) - L(I, J) * E(J, J) = F(I, J)
* for I = P, P - 1,..., 1; J = 1, 2,..., Q
*
DSCALE = ZERO
DSUM = ONE
PQ = 0
SCALE = ONE
DO 130 J = P + 2, Q
JS = IWORK( J )
JE = IWORK( J+1 ) - 1
NB = JE - JS + 1
DO 120 I = P, 1, -1
IS = IWORK( I )
IE = IWORK( I+1 ) - 1
MB = IE - IS + 1
PPQQ = 0
CALL DTGSY2( TRANS, IFUNC, MB, NB, A( IS, IS ), LDA,
$ B( JS, JS ), LDB, C( IS, JS ), LDC,
$ D( IS, IS ), LDD, E( JS, JS ), LDE,
$ F( IS, JS ), LDF, SCALOC, DSUM, DSCALE,
$ IWORK( Q+2 ), PPQQ, LINFO )
IF( LINFO.GT.0 )
$ INFO = LINFO
*
PQ = PQ + PPQQ
IF( SCALOC.NE.ONE ) THEN
DO 80 K = 1, JS - 1
CALL DSCAL( M, SCALOC, C( 1, K ), 1 )
CALL DSCAL( M, SCALOC, F( 1, K ), 1 )
80 CONTINUE
DO 90 K = JS, JE
CALL DSCAL( IS-1, SCALOC, C( 1, K ), 1 )
CALL DSCAL( IS-1, SCALOC, F( 1, K ), 1 )
90 CONTINUE
DO 100 K = JS, JE
CALL DSCAL( M-IE, SCALOC, C( IE+1, K ), 1 )
CALL DSCAL( M-IE, SCALOC, F( IE+1, K ), 1 )
100 CONTINUE
DO 110 K = JE + 1, N
CALL DSCAL( M, SCALOC, C( 1, K ), 1 )
CALL DSCAL( M, SCALOC, F( 1, K ), 1 )
110 CONTINUE
SCALE = SCALE*SCALOC
END IF
*
* Substitute R(I, J) and L(I, J) into remaining
* equation.
*
IF( I.GT.1 ) THEN
CALL DGEMM( 'N', 'N', IS-1, NB, MB, -ONE,
$ A( 1, IS ), LDA, C( IS, JS ), LDC, ONE,
$ C( 1, JS ), LDC )
CALL DGEMM( 'N', 'N', IS-1, NB, MB, -ONE,
$ D( 1, IS ), LDD, C( IS, JS ), LDC, ONE,
$ F( 1, JS ), LDF )
END IF
IF( J.LT.Q ) THEN
CALL DGEMM( 'N', 'N', MB, N-JE, NB, ONE,
$ F( IS, JS ), LDF, B( JS, JE+1 ), LDB,
$ ONE, C( IS, JE+1 ), LDC )
CALL DGEMM( 'N', 'N', MB, N-JE, NB, ONE,
$ F( IS, JS ), LDF, E( JS, JE+1 ), LDE,
$ ONE, F( IS, JE+1 ), LDF )
END IF
120 CONTINUE
130 CONTINUE
IF( DSCALE.NE.ZERO ) THEN
IF( IJOB.EQ.1 .OR. IJOB.EQ.3 ) THEN
DIF = SQRT( DBLE( 2*M*N ) ) / ( DSCALE*SQRT( DSUM ) )
ELSE
DIF = SQRT( DBLE( PQ ) ) / ( DSCALE*SQRT( DSUM ) )
END IF
END IF
IF( ISOLVE.EQ.2 .AND. IROUND.EQ.1 ) THEN
IF( NOTRAN ) THEN
IFUNC = IJOB
END IF
SCALE2 = SCALE
CALL DLACPY( 'F', M, N, C, LDC, WORK, M )
CALL DLACPY( 'F', M, N, F, LDF, WORK( M*N+1 ), M )
CALL DLASET( 'F', M, N, ZERO, ZERO, C, LDC )
CALL DLASET( 'F', M, N, ZERO, ZERO, F, LDF )
ELSE IF( ISOLVE.EQ.2 .AND. IROUND.EQ.2 ) THEN
CALL DLACPY( 'F', M, N, WORK, M, C, LDC )
CALL DLACPY( 'F', M, N, WORK( M*N+1 ), M, F, LDF )
SCALE = SCALE2
END IF
150 CONTINUE
*
ELSE
*
* Solve transposed (I, J)-subsystem
* A(I, I)**T * R(I, J) + D(I, I)**T * L(I, J) = C(I, J)
* R(I, J) * B(J, J)**T + L(I, J) * E(J, J)**T = -F(I, J)
* for I = 1,2,..., P; J = Q, Q-1,..., 1
*
SCALE = ONE
DO 210 I = 1, P
IS = IWORK( I )
IE = IWORK( I+1 ) - 1
MB = IE - IS + 1
DO 200 J = Q, P + 2, -1
JS = IWORK( J )
JE = IWORK( J+1 ) - 1
NB = JE - JS + 1
CALL DTGSY2( TRANS, IFUNC, MB, NB, A( IS, IS ), LDA,
$ B( JS, JS ), LDB, C( IS, JS ), LDC,
$ D( IS, IS ), LDD, E( JS, JS ), LDE,
$ F( IS, JS ), LDF, SCALOC, DSUM, DSCALE,
$ IWORK( Q+2 ), PPQQ, LINFO )
IF( LINFO.GT.0 )
$ INFO = LINFO
IF( SCALOC.NE.ONE ) THEN
DO 160 K = 1, JS - 1
CALL DSCAL( M, SCALOC, C( 1, K ), 1 )
CALL DSCAL( M, SCALOC, F( 1, K ), 1 )
160 CONTINUE
DO 170 K = JS, JE
CALL DSCAL( IS-1, SCALOC, C( 1, K ), 1 )
CALL DSCAL( IS-1, SCALOC, F( 1, K ), 1 )
170 CONTINUE
DO 180 K = JS, JE
CALL DSCAL( M-IE, SCALOC, C( IE+1, K ), 1 )
CALL DSCAL( M-IE, SCALOC, F( IE+1, K ), 1 )
180 CONTINUE
DO 190 K = JE + 1, N
CALL DSCAL( M, SCALOC, C( 1, K ), 1 )
CALL DSCAL( M, SCALOC, F( 1, K ), 1 )
190 CONTINUE
SCALE = SCALE*SCALOC
END IF
*
* Substitute R(I, J) and L(I, J) into remaining equation.
*
IF( J.GT.P+2 ) THEN
CALL DGEMM( 'N', 'T', MB, JS-1, NB, ONE, C( IS, JS ),
$ LDC, B( 1, JS ), LDB, ONE, F( IS, 1 ),
$ LDF )
CALL DGEMM( 'N', 'T', MB, JS-1, NB, ONE, F( IS, JS ),
$ LDF, E( 1, JS ), LDE, ONE, F( IS, 1 ),
$ LDF )
END IF
IF( I.LT.P ) THEN
CALL DGEMM( 'T', 'N', M-IE, NB, MB, -ONE,
$ A( IS, IE+1 ), LDA, C( IS, JS ), LDC, ONE,
$ C( IE+1, JS ), LDC )
CALL DGEMM( 'T', 'N', M-IE, NB, MB, -ONE,
$ D( IS, IE+1 ), LDD, F( IS, JS ), LDF, ONE,
$ C( IE+1, JS ), LDC )
END IF
200 CONTINUE
210 CONTINUE
*
END IF
*
WORK( 1 ) = LWMIN
*
RETURN
*
* End of DTGSYL
*
END