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
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
|
SUBROUTINE CDRVGB( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, LA,
$ AFB, LAFB, ASAV, B, BSAV, X, XACT, S, WORK,
$ RWORK, IWORK, NOUT )
*
* -- LAPACK test routine (version 3.2) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
LOGICAL TSTERR
INTEGER LA, LAFB, NN, NOUT, NRHS
REAL THRESH
* ..
* .. Array Arguments ..
LOGICAL DOTYPE( * )
INTEGER IWORK( * ), NVAL( * )
REAL RWORK( * ), S( * )
COMPLEX A( * ), AFB( * ), ASAV( * ), B( * ), BSAV( * ),
$ WORK( * ), X( * ), XACT( * )
* ..
*
* Purpose
* =======
*
* CDRVGB tests the driver routines CGBSV, -SVX, and -SVXX.
*
* Note that this file is used only when the XBLAS are available,
* otherwise cdrvgb.f defines this subroutine.
*
* Arguments
* =========
*
* DOTYPE (input) LOGICAL array, dimension (NTYPES)
* The matrix types to be used for testing. Matrices of type j
* (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
* .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
*
* NN (input) INTEGER
* The number of values of N contained in the vector NVAL.
*
* NVAL (input) INTEGER array, dimension (NN)
* The values of the matrix column dimension N.
*
* NRHS (input) INTEGER
* The number of right hand side vectors to be generated for
* each linear system.
*
* THRESH (input) REAL
* The threshold value for the test ratios. A result is
* included in the output file if RESULT >= THRESH. To have
* every test ratio printed, use THRESH = 0.
*
* TSTERR (input) LOGICAL
* Flag that indicates whether error exits are to be tested.
*
* A (workspace) COMPLEX array, dimension (LA)
*
* LA (input) INTEGER
* The length of the array A. LA >= (2*NMAX-1)*NMAX
* where NMAX is the largest entry in NVAL.
*
* AFB (workspace) COMPLEX array, dimension (LAFB)
*
* LAFB (input) INTEGER
* The length of the array AFB. LAFB >= (3*NMAX-2)*NMAX
* where NMAX is the largest entry in NVAL.
*
* ASAV (workspace) COMPLEX array, dimension (LA)
*
* B (workspace) COMPLEX array, dimension (NMAX*NRHS)
*
* BSAV (workspace) COMPLEX array, dimension (NMAX*NRHS)
*
* X (workspace) COMPLEX array, dimension (NMAX*NRHS)
*
* XACT (workspace) COMPLEX array, dimension (NMAX*NRHS)
*
* S (workspace) REAL array, dimension (2*NMAX)
*
* WORK (workspace) COMPLEX array, dimension
* (NMAX*max(3,NRHS,NMAX))
*
* RWORK (workspace) REAL array, dimension
* (max(NMAX,2*NRHS))
*
* IWORK (workspace) INTEGER array, dimension (NMAX)
*
* NOUT (input) INTEGER
* The unit number for output.
*
* =====================================================================
*
* .. Parameters ..
REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
INTEGER NTYPES
PARAMETER ( NTYPES = 8 )
INTEGER NTESTS
PARAMETER ( NTESTS = 7 )
INTEGER NTRAN
PARAMETER ( NTRAN = 3 )
* ..
* .. Local Scalars ..
LOGICAL EQUIL, NOFACT, PREFAC, TRFCON, ZEROT
CHARACTER DIST, EQUED, FACT, TRANS, TYPE, XTYPE
CHARACTER*3 PATH
INTEGER I, I1, I2, IEQUED, IFACT, IKL, IKU, IMAT, IN,
$ INFO, IOFF, ITRAN, IZERO, J, K, K1, KL, KU,
$ LDA, LDAFB, LDB, MODE, N, NB, NBMIN, NERRS,
$ NFACT, NFAIL, NIMAT, NKL, NKU, NRUN, NT,
$ N_ERR_BNDS
REAL AINVNM, AMAX, ANORM, ANORMI, ANORMO, ANRMPV,
$ CNDNUM, COLCND, RCOND, RCONDC, RCONDI, RCONDO,
$ ROLDC, ROLDI, ROLDO, ROWCND, RPVGRW,
$ RPVGRW_SVXX
* ..
* .. Local Arrays ..
CHARACTER EQUEDS( 4 ), FACTS( 3 ), TRANSS( NTRAN )
INTEGER ISEED( 4 ), ISEEDY( 4 )
REAL RDUM( 1 ), RESULT( NTESTS ), BERR( NRHS ),
$ ERRBNDS_N( NRHS,3 ), ERRBNDS_C( NRHS, 3 )
* ..
* .. External Functions ..
LOGICAL LSAME
REAL CLANGB, CLANGE, CLANTB, SGET06, SLAMCH,
$ CLA_GBRPVGRW
EXTERNAL LSAME, CLANGB, CLANGE, CLANTB, SGET06, SLAMCH,
$ CLA_GBRPVGRW
* ..
* .. External Subroutines ..
EXTERNAL ALADHD, ALAERH, ALASVM, CERRVX, CGBEQU, CGBSV,
$ CGBSVX, CGBT01, CGBT02, CGBT05, CGBTRF, CGBTRS,
$ CGET04, CLACPY, CLAQGB, CLARHS, CLASET, CLATB4,
$ CLATMS, XLAENV, CGBSVXX
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, CMPLX, MAX, MIN
* ..
* .. Scalars in Common ..
LOGICAL LERR, OK
CHARACTER*32 SRNAMT
INTEGER INFOT, NUNIT
* ..
* .. Common blocks ..
COMMON / INFOC / INFOT, NUNIT, OK, LERR
COMMON / SRNAMC / SRNAMT
* ..
* .. Data statements ..
DATA ISEEDY / 1988, 1989, 1990, 1991 /
DATA TRANSS / 'N', 'T', 'C' /
DATA FACTS / 'F', 'N', 'E' /
DATA EQUEDS / 'N', 'R', 'C', 'B' /
* ..
* .. Executable Statements ..
*
* Initialize constants and the random number seed.
*
PATH( 1: 1 ) = 'Complex precision'
PATH( 2: 3 ) = 'GB'
NRUN = 0
NFAIL = 0
NERRS = 0
DO 10 I = 1, 4
ISEED( I ) = ISEEDY( I )
10 CONTINUE
*
* Test the error exits
*
IF( TSTERR )
$ CALL CERRVX( PATH, NOUT )
INFOT = 0
*
* Set the block size and minimum block size for testing.
*
NB = 1
NBMIN = 2
CALL XLAENV( 1, NB )
CALL XLAENV( 2, NBMIN )
*
* Do for each value of N in NVAL
*
DO 150 IN = 1, NN
N = NVAL( IN )
LDB = MAX( N, 1 )
XTYPE = 'N'
*
* Set limits on the number of loop iterations.
*
NKL = MAX( 1, MIN( N, 4 ) )
IF( N.EQ.0 )
$ NKL = 1
NKU = NKL
NIMAT = NTYPES
IF( N.LE.0 )
$ NIMAT = 1
*
DO 140 IKL = 1, NKL
*
* Do for KL = 0, N-1, (3N-1)/4, and (N+1)/4. This order makes
* it easier to skip redundant values for small values of N.
*
IF( IKL.EQ.1 ) THEN
KL = 0
ELSE IF( IKL.EQ.2 ) THEN
KL = MAX( N-1, 0 )
ELSE IF( IKL.EQ.3 ) THEN
KL = ( 3*N-1 ) / 4
ELSE IF( IKL.EQ.4 ) THEN
KL = ( N+1 ) / 4
END IF
DO 130 IKU = 1, NKU
*
* Do for KU = 0, N-1, (3N-1)/4, and (N+1)/4. This order
* makes it easier to skip redundant values for small
* values of N.
*
IF( IKU.EQ.1 ) THEN
KU = 0
ELSE IF( IKU.EQ.2 ) THEN
KU = MAX( N-1, 0 )
ELSE IF( IKU.EQ.3 ) THEN
KU = ( 3*N-1 ) / 4
ELSE IF( IKU.EQ.4 ) THEN
KU = ( N+1 ) / 4
END IF
*
* Check that A and AFB are big enough to generate this
* matrix.
*
LDA = KL + KU + 1
LDAFB = 2*KL + KU + 1
IF( LDA*N.GT.LA .OR. LDAFB*N.GT.LAFB ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALADHD( NOUT, PATH )
IF( LDA*N.GT.LA ) THEN
WRITE( NOUT, FMT = 9999 )LA, N, KL, KU,
$ N*( KL+KU+1 )
NERRS = NERRS + 1
END IF
IF( LDAFB*N.GT.LAFB ) THEN
WRITE( NOUT, FMT = 9998 )LAFB, N, KL, KU,
$ N*( 2*KL+KU+1 )
NERRS = NERRS + 1
END IF
GO TO 130
END IF
*
DO 120 IMAT = 1, NIMAT
*
* Do the tests only if DOTYPE( IMAT ) is true.
*
IF( .NOT.DOTYPE( IMAT ) )
$ GO TO 120
*
* Skip types 2, 3, or 4 if the matrix is too small.
*
ZEROT = IMAT.GE.2 .AND. IMAT.LE.4
IF( ZEROT .AND. N.LT.IMAT-1 )
$ GO TO 120
*
* Set up parameters with CLATB4 and generate a
* test matrix with CLATMS.
*
CALL CLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM,
$ MODE, CNDNUM, DIST )
RCONDC = ONE / CNDNUM
*
SRNAMT = 'CLATMS'
CALL CLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
$ CNDNUM, ANORM, KL, KU, 'Z', A, LDA, WORK,
$ INFO )
*
* Check the error code from CLATMS.
*
IF( INFO.NE.0 ) THEN
CALL ALAERH( PATH, 'CLATMS', INFO, 0, ' ', N, N,
$ KL, KU, -1, IMAT, NFAIL, NERRS, NOUT )
GO TO 120
END IF
*
* For types 2, 3, and 4, zero one or more columns of
* the matrix to test that INFO is returned correctly.
*
IZERO = 0
IF( ZEROT ) THEN
IF( IMAT.EQ.2 ) THEN
IZERO = 1
ELSE IF( IMAT.EQ.3 ) THEN
IZERO = N
ELSE
IZERO = N / 2 + 1
END IF
IOFF = ( IZERO-1 )*LDA
IF( IMAT.LT.4 ) THEN
I1 = MAX( 1, KU+2-IZERO )
I2 = MIN( KL+KU+1, KU+1+( N-IZERO ) )
DO 20 I = I1, I2
A( IOFF+I ) = ZERO
20 CONTINUE
ELSE
DO 40 J = IZERO, N
DO 30 I = MAX( 1, KU+2-J ),
$ MIN( KL+KU+1, KU+1+( N-J ) )
A( IOFF+I ) = ZERO
30 CONTINUE
IOFF = IOFF + LDA
40 CONTINUE
END IF
END IF
*
* Save a copy of the matrix A in ASAV.
*
CALL CLACPY( 'Full', KL+KU+1, N, A, LDA, ASAV, LDA )
*
DO 110 IEQUED = 1, 4
EQUED = EQUEDS( IEQUED )
IF( IEQUED.EQ.1 ) THEN
NFACT = 3
ELSE
NFACT = 1
END IF
*
DO 100 IFACT = 1, NFACT
FACT = FACTS( IFACT )
PREFAC = LSAME( FACT, 'F' )
NOFACT = LSAME( FACT, 'N' )
EQUIL = LSAME( FACT, 'E' )
*
IF( ZEROT ) THEN
IF( PREFAC )
$ GO TO 100
RCONDO = ZERO
RCONDI = ZERO
*
ELSE IF( .NOT.NOFACT ) THEN
*
* Compute the condition number for comparison
* with the value returned by SGESVX (FACT =
* 'N' reuses the condition number from the
* previous iteration with FACT = 'F').
*
CALL CLACPY( 'Full', KL+KU+1, N, ASAV, LDA,
$ AFB( KL+1 ), LDAFB )
IF( EQUIL .OR. IEQUED.GT.1 ) THEN
*
* Compute row and column scale factors to
* equilibrate the matrix A.
*
CALL CGBEQU( N, N, KL, KU, AFB( KL+1 ),
$ LDAFB, S, S( N+1 ), ROWCND,
$ COLCND, AMAX, INFO )
IF( INFO.EQ.0 .AND. N.GT.0 ) THEN
IF( LSAME( EQUED, 'R' ) ) THEN
ROWCND = ZERO
COLCND = ONE
ELSE IF( LSAME( EQUED, 'C' ) ) THEN
ROWCND = ONE
COLCND = ZERO
ELSE IF( LSAME( EQUED, 'B' ) ) THEN
ROWCND = ZERO
COLCND = ZERO
END IF
*
* Equilibrate the matrix.
*
CALL CLAQGB( N, N, KL, KU, AFB( KL+1 ),
$ LDAFB, S, S( N+1 ),
$ ROWCND, COLCND, AMAX,
$ EQUED )
END IF
END IF
*
* Save the condition number of the
* non-equilibrated system for use in CGET04.
*
IF( EQUIL ) THEN
ROLDO = RCONDO
ROLDI = RCONDI
END IF
*
* Compute the 1-norm and infinity-norm of A.
*
ANORMO = CLANGB( '1', N, KL, KU, AFB( KL+1 ),
$ LDAFB, RWORK )
ANORMI = CLANGB( 'I', N, KL, KU, AFB( KL+1 ),
$ LDAFB, RWORK )
*
* Factor the matrix A.
*
CALL CGBTRF( N, N, KL, KU, AFB, LDAFB, IWORK,
$ INFO )
*
* Form the inverse of A.
*
CALL CLASET( 'Full', N, N, CMPLX( ZERO ),
$ CMPLX( ONE ), WORK, LDB )
SRNAMT = 'CGBTRS'
CALL CGBTRS( 'No transpose', N, KL, KU, N,
$ AFB, LDAFB, IWORK, WORK, LDB,
$ INFO )
*
* Compute the 1-norm condition number of A.
*
AINVNM = CLANGE( '1', N, N, WORK, LDB,
$ RWORK )
IF( ANORMO.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
RCONDO = ONE
ELSE
RCONDO = ( ONE / ANORMO ) / AINVNM
END IF
*
* Compute the infinity-norm condition number
* of A.
*
AINVNM = CLANGE( 'I', N, N, WORK, LDB,
$ RWORK )
IF( ANORMI.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
RCONDI = ONE
ELSE
RCONDI = ( ONE / ANORMI ) / AINVNM
END IF
END IF
*
DO 90 ITRAN = 1, NTRAN
*
* Do for each value of TRANS.
*
TRANS = TRANSS( ITRAN )
IF( ITRAN.EQ.1 ) THEN
RCONDC = RCONDO
ELSE
RCONDC = RCONDI
END IF
*
* Restore the matrix A.
*
CALL CLACPY( 'Full', KL+KU+1, N, ASAV, LDA,
$ A, LDA )
*
* Form an exact solution and set the right hand
* side.
*
SRNAMT = 'CLARHS'
CALL CLARHS( PATH, XTYPE, 'Full', TRANS, N,
$ N, KL, KU, NRHS, A, LDA, XACT,
$ LDB, B, LDB, ISEED, INFO )
XTYPE = 'C'
CALL CLACPY( 'Full', N, NRHS, B, LDB, BSAV,
$ LDB )
*
IF( NOFACT .AND. ITRAN.EQ.1 ) THEN
*
* --- Test CGBSV ---
*
* Compute the LU factorization of the matrix
* and solve the system.
*
CALL CLACPY( 'Full', KL+KU+1, N, A, LDA,
$ AFB( KL+1 ), LDAFB )
CALL CLACPY( 'Full', N, NRHS, B, LDB, X,
$ LDB )
*
SRNAMT = 'CGBSV '
CALL CGBSV( N, KL, KU, NRHS, AFB, LDAFB,
$ IWORK, X, LDB, INFO )
*
* Check error code from CGBSV .
*
IF( INFO.NE.IZERO )
$ CALL ALAERH( PATH, 'CGBSV ', INFO,
$ IZERO, ' ', N, N, KL, KU,
$ NRHS, IMAT, NFAIL, NERRS,
$ NOUT )
*
* Reconstruct matrix from factors and
* compute residual.
*
CALL CGBT01( N, N, KL, KU, A, LDA, AFB,
$ LDAFB, IWORK, WORK,
$ RESULT( 1 ) )
NT = 1
IF( IZERO.EQ.0 ) THEN
*
* Compute residual of the computed
* solution.
*
CALL CLACPY( 'Full', N, NRHS, B, LDB,
$ WORK, LDB )
CALL CGBT02( 'No transpose', N, N, KL,
$ KU, NRHS, A, LDA, X, LDB,
$ WORK, LDB, RESULT( 2 ) )
*
* Check solution from generated exact
* solution.
*
CALL CGET04( N, NRHS, X, LDB, XACT,
$ LDB, RCONDC, RESULT( 3 ) )
NT = 3
END IF
*
* Print information about the tests that did
* not pass the threshold.
*
DO 50 K = 1, NT
IF( RESULT( K ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALADHD( NOUT, PATH )
WRITE( NOUT, FMT = 9997 )'CGBSV ',
$ N, KL, KU, IMAT, K, RESULT( K )
NFAIL = NFAIL + 1
END IF
50 CONTINUE
NRUN = NRUN + NT
END IF
*
* --- Test CGBSVX ---
*
IF( .NOT.PREFAC )
$ CALL CLASET( 'Full', 2*KL+KU+1, N,
$ CMPLX( ZERO ), CMPLX( ZERO ),
$ AFB, LDAFB )
CALL CLASET( 'Full', N, NRHS, CMPLX( ZERO ),
$ CMPLX( ZERO ), X, LDB )
IF( IEQUED.GT.1 .AND. N.GT.0 ) THEN
*
* Equilibrate the matrix if FACT = 'F' and
* EQUED = 'R', 'C', or 'B'.
*
CALL CLAQGB( N, N, KL, KU, A, LDA, S,
$ S( N+1 ), ROWCND, COLCND,
$ AMAX, EQUED )
END IF
*
* Solve the system and compute the condition
* number and error bounds using CGBSVX.
*
SRNAMT = 'CGBSVX'
CALL CGBSVX( FACT, TRANS, N, KL, KU, NRHS, A,
$ LDA, AFB, LDAFB, IWORK, EQUED,
$ S, S( LDB+1 ), B, LDB, X, LDB,
$ RCOND, RWORK, RWORK( NRHS+1 ),
$ WORK, RWORK( 2*NRHS+1 ), INFO )
*
* Check the error code from CGBSVX.
*
IF( INFO.NE.IZERO )
$ CALL ALAERH( PATH, 'CGBSVX', INFO, IZERO,
$ FACT // TRANS, N, N, KL, KU,
$ NRHS, IMAT, NFAIL, NERRS,
$ NOUT )
*
* Compare RWORK(2*NRHS+1) from CGBSVX with the
* computed reciprocal pivot growth RPVGRW
*
IF( INFO.NE.0 ) THEN
ANRMPV = ZERO
DO 70 J = 1, INFO
DO 60 I = MAX( KU+2-J, 1 ),
$ MIN( N+KU+1-J, KL+KU+1 )
ANRMPV = MAX( ANRMPV,
$ ABS( A( I+( J-1 )*LDA ) ) )
60 CONTINUE
70 CONTINUE
RPVGRW = CLANTB( 'M', 'U', 'N', INFO,
$ MIN( INFO-1, KL+KU ),
$ AFB( MAX( 1, KL+KU+2-INFO ) ),
$ LDAFB, RDUM )
IF( RPVGRW.EQ.ZERO ) THEN
RPVGRW = ONE
ELSE
RPVGRW = ANRMPV / RPVGRW
END IF
ELSE
RPVGRW = CLANTB( 'M', 'U', 'N', N, KL+KU,
$ AFB, LDAFB, RDUM )
IF( RPVGRW.EQ.ZERO ) THEN
RPVGRW = ONE
ELSE
RPVGRW = CLANGB( 'M', N, KL, KU, A,
$ LDA, RDUM ) / RPVGRW
END IF
END IF
RESULT( 7 ) = ABS( RPVGRW-RWORK( 2*NRHS+1 ) )
$ / MAX( RWORK( 2*NRHS+1 ),
$ RPVGRW ) / SLAMCH( 'E' )
*
IF( .NOT.PREFAC ) THEN
*
* Reconstruct matrix from factors and
* compute residual.
*
CALL CGBT01( N, N, KL, KU, A, LDA, AFB,
$ LDAFB, IWORK, WORK,
$ RESULT( 1 ) )
K1 = 1
ELSE
K1 = 2
END IF
*
IF( INFO.EQ.0 ) THEN
TRFCON = .FALSE.
*
* Compute residual of the computed solution.
*
CALL CLACPY( 'Full', N, NRHS, BSAV, LDB,
$ WORK, LDB )
CALL CGBT02( TRANS, N, N, KL, KU, NRHS,
$ ASAV, LDA, X, LDB, WORK, LDB,
$ RESULT( 2 ) )
*
* Check solution from generated exact
* solution.
*
IF( NOFACT .OR. ( PREFAC .AND.
$ LSAME( EQUED, 'N' ) ) ) THEN
CALL CGET04( N, NRHS, X, LDB, XACT,
$ LDB, RCONDC, RESULT( 3 ) )
ELSE
IF( ITRAN.EQ.1 ) THEN
ROLDC = ROLDO
ELSE
ROLDC = ROLDI
END IF
CALL CGET04( N, NRHS, X, LDB, XACT,
$ LDB, ROLDC, RESULT( 3 ) )
END IF
*
* Check the error bounds from iterative
* refinement.
*
CALL CGBT05( TRANS, N, KL, KU, NRHS, ASAV,
$ LDA, BSAV, LDB, X, LDB, XACT,
$ LDB, RWORK, RWORK( NRHS+1 ),
$ RESULT( 4 ) )
ELSE
TRFCON = .TRUE.
END IF
*
* Compare RCOND from CGBSVX with the computed
* value in RCONDC.
*
RESULT( 6 ) = SGET06( RCOND, RCONDC )
*
* Print information about the tests that did
* not pass the threshold.
*
IF( .NOT.TRFCON ) THEN
DO 80 K = K1, NTESTS
IF( RESULT( K ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALADHD( NOUT, PATH )
IF( PREFAC ) THEN
WRITE( NOUT, FMT = 9995 )
$ 'CGBSVX', FACT, TRANS, N, KL,
$ KU, EQUED, IMAT, K,
$ RESULT( K )
ELSE
WRITE( NOUT, FMT = 9996 )
$ 'CGBSVX', FACT, TRANS, N, KL,
$ KU, IMAT, K, RESULT( K )
END IF
NFAIL = NFAIL + 1
END IF
80 CONTINUE
NRUN = NRUN + 7 - K1
ELSE
IF( RESULT( 1 ).GE.THRESH .AND. .NOT.
$ PREFAC ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALADHD( NOUT, PATH )
IF( PREFAC ) THEN
WRITE( NOUT, FMT = 9995 )'CGBSVX',
$ FACT, TRANS, N, KL, KU, EQUED,
$ IMAT, 1, RESULT( 1 )
ELSE
WRITE( NOUT, FMT = 9996 )'CGBSVX',
$ FACT, TRANS, N, KL, KU, IMAT, 1,
$ RESULT( 1 )
END IF
NFAIL = NFAIL + 1
NRUN = NRUN + 1
END IF
IF( RESULT( 6 ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALADHD( NOUT, PATH )
IF( PREFAC ) THEN
WRITE( NOUT, FMT = 9995 )'CGBSVX',
$ FACT, TRANS, N, KL, KU, EQUED,
$ IMAT, 6, RESULT( 6 )
ELSE
WRITE( NOUT, FMT = 9996 )'CGBSVX',
$ FACT, TRANS, N, KL, KU, IMAT, 6,
$ RESULT( 6 )
END IF
NFAIL = NFAIL + 1
NRUN = NRUN + 1
END IF
IF( RESULT( 7 ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALADHD( NOUT, PATH )
IF( PREFAC ) THEN
WRITE( NOUT, FMT = 9995 )'CGBSVX',
$ FACT, TRANS, N, KL, KU, EQUED,
$ IMAT, 7, RESULT( 7 )
ELSE
WRITE( NOUT, FMT = 9996 )'CGBSVX',
$ FACT, TRANS, N, KL, KU, IMAT, 7,
$ RESULT( 7 )
END IF
NFAIL = NFAIL + 1
NRUN = NRUN + 1
END IF
END IF
* --- Test CGBSVXX ---
* Restore the matrices A and B.
c write(*,*) 'begin cgbsvxx testing'
CALL CLACPY( 'Full', KL+KU+1, N, ASAV, LDA, A,
$ LDA )
CALL CLACPY( 'Full', N, NRHS, BSAV, LDB, B, LDB )
IF( .NOT.PREFAC )
$ CALL CLASET( 'Full', 2*KL+KU+1, N, ZERO, ZERO,
$ AFB, LDAFB )
CALL CLASET( 'Full', N, NRHS, ZERO, ZERO, X, LDB )
IF( IEQUED.GT.1 .AND. N.GT.0 ) THEN
*
* Equilibrate the matrix if FACT = 'F' and
* EQUED = 'R', 'C', or 'B'.
*
CALL CLAQGB( N, N, KL, KU, A, LDA, S,
$ S( N+1 ), ROWCND, COLCND, AMAX, EQUED )
END IF
*
* Solve the system and compute the condition number
* and error bounds using CGBSVXX.
*
SRNAMT = 'CGBSVXX'
n_err_bnds = 3
CALL CGBSVXX( FACT, TRANS, N, KL, KU, NRHS, A, LDA,
$ AFB, LDAFB, IWORK, EQUED, S, S( N+1 ), B, LDB,
$ X, LDB, rcond, rpvgrw_svxx, berr, n_err_bnds,
$ errbnds_n, errbnds_c, 0, ZERO, WORK,
$ RWORK, INFO )
*
* Check the error code from CGBSVXX.
*
IF( INFO.EQ.N+1 ) GOTO 90
IF( INFO.NE.IZERO ) THEN
CALL ALAERH( PATH, 'CGBSVXX', INFO, IZERO,
$ FACT // TRANS, N, N, -1, -1, NRHS,
$ IMAT, NFAIL, NERRS, NOUT )
GOTO 90
END IF
*
* Compare rpvgrw_svxx from CGESVXX with the computed
* reciprocal pivot growth factor RPVGRW
*
IF ( INFO .GT. 0 .AND. INFO .LT. N+1 ) THEN
RPVGRW = CLA_GBRPVGRW(N, KL, KU, INFO, A, LDA,
$ AFB, LDAFB)
ELSE
RPVGRW = CLA_GBRPVGRW(N, KL, KU, N, A, LDA,
$ AFB, LDAFB)
ENDIF
RESULT( 7 ) = ABS( RPVGRW-rpvgrw_svxx ) /
$ MAX( rpvgrw_svxx, RPVGRW ) /
$ SLAMCH( 'E' )
*
IF( .NOT.PREFAC ) THEN
*
* Reconstruct matrix from factors and compute
* residual.
*
CALL CGBT01( N, N, KL, KU, A, LDA, AFB, LDAFB,
$ IWORK, RWORK( 2*NRHS+1 ), RESULT( 1 ) )
K1 = 1
ELSE
K1 = 2
END IF
*
IF( INFO.EQ.0 ) THEN
TRFCON = .FALSE.
*
* Compute residual of the computed solution.
*
CALL CLACPY( 'Full', N, NRHS, BSAV, LDB, WORK,
$ LDB )
CALL CGBT02( TRANS, N, N, KL, KU, NRHS, ASAV,
$ LDA, X, LDB, WORK, LDB, RWORK( 2*NRHS+1 ),
$ RESULT( 2 ) )
*
* Check solution from generated exact solution.
*
IF( NOFACT .OR. ( PREFAC .AND. LSAME( EQUED,
$ 'N' ) ) ) THEN
CALL CGET04( N, NRHS, X, LDB, XACT, LDB,
$ RCONDC, RESULT( 3 ) )
ELSE
IF( ITRAN.EQ.1 ) THEN
ROLDC = ROLDO
ELSE
ROLDC = ROLDI
END IF
CALL CGET04( N, NRHS, X, LDB, XACT, LDB,
$ ROLDC, RESULT( 3 ) )
END IF
ELSE
TRFCON = .TRUE.
END IF
*
* Compare RCOND from CGBSVXX with the computed value
* in RCONDC.
*
RESULT( 6 ) = SGET06( RCOND, RCONDC )
*
* Print information about the tests that did not pass
* the threshold.
*
IF( .NOT.TRFCON ) THEN
DO 45 K = K1, NTESTS
IF( RESULT( K ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALADHD( NOUT, PATH )
IF( PREFAC ) THEN
WRITE( NOUT, FMT = 9997 )'CGBSVXX',
$ FACT, TRANS, N, KL, KU, EQUED,
$ IMAT, K, RESULT( K )
ELSE
WRITE( NOUT, FMT = 9998 )'CGBSVXX',
$ FACT, TRANS, N, KL, KU, IMAT, K,
$ RESULT( K )
END IF
NFAIL = NFAIL + 1
END IF
45 CONTINUE
NRUN = NRUN + 7 - K1
ELSE
IF( RESULT( 1 ).GE.THRESH .AND. .NOT.PREFAC )
$ THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALADHD( NOUT, PATH )
IF( PREFAC ) THEN
WRITE( NOUT, FMT = 9997 )'CGBSVXX', FACT,
$ TRANS, N, KL, KU, EQUED, IMAT, 1,
$ RESULT( 1 )
ELSE
WRITE( NOUT, FMT = 9998 )'CGBSVXX', FACT,
$ TRANS, N, KL, KU, IMAT, 1,
$ RESULT( 1 )
END IF
NFAIL = NFAIL + 1
NRUN = NRUN + 1
END IF
IF( RESULT( 6 ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALADHD( NOUT, PATH )
IF( PREFAC ) THEN
WRITE( NOUT, FMT = 9997 )'CGBSVXX', FACT,
$ TRANS, N, KL, KU, EQUED, IMAT, 6,
$ RESULT( 6 )
ELSE
WRITE( NOUT, FMT = 9998 )'CGBSVXX', FACT,
$ TRANS, N, KL, KU, IMAT, 6,
$ RESULT( 6 )
END IF
NFAIL = NFAIL + 1
NRUN = NRUN + 1
END IF
IF( RESULT( 7 ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALADHD( NOUT, PATH )
IF( PREFAC ) THEN
WRITE( NOUT, FMT = 9997 )'CGBSVXX', FACT,
$ TRANS, N, KL, KU, EQUED, IMAT, 7,
$ RESULT( 7 )
ELSE
WRITE( NOUT, FMT = 9998 )'CGBSVXX', FACT,
$ TRANS, N, KL, KU, IMAT, 7,
$ RESULT( 7 )
END IF
NFAIL = NFAIL + 1
NRUN = NRUN + 1
END IF
*
END IF
*
90 CONTINUE
100 CONTINUE
110 CONTINUE
120 CONTINUE
130 CONTINUE
140 CONTINUE
150 CONTINUE
*
* Print a summary of the results.
*
CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
*
* Test Error Bounds from CGBSVXX
CALL CEBCHVXX(THRESH, PATH)
9999 FORMAT( ' *** In CDRVGB, LA=', I5, ' is too small for N=', I5,
$ ', KU=', I5, ', KL=', I5, / ' ==> Increase LA to at least ',
$ I5 )
9998 FORMAT( ' *** In CDRVGB, LAFB=', I5, ' is too small for N=', I5,
$ ', KU=', I5, ', KL=', I5, /
$ ' ==> Increase LAFB to at least ', I5 )
9997 FORMAT( 1X, A, ', N=', I5, ', KL=', I5, ', KU=', I5, ', type ',
$ I1, ', test(', I1, ')=', G12.5 )
9996 FORMAT( 1X, A, '( ''', A1, ''',''', A1, ''',', I5, ',', I5, ',',
$ I5, ',...), type ', I1, ', test(', I1, ')=', G12.5 )
9995 FORMAT( 1X, A, '( ''', A1, ''',''', A1, ''',', I5, ',', I5, ',',
$ I5, ',...), EQUED=''', A1, ''', type ', I1, ', test(', I1,
$ ')=', G12.5 )
*
RETURN
*
* End of CDRVGB
*
END
|
