summaryrefslogtreecommitdiff
path: root/TESTING/LIN/cdrvls.f
blob: ededde5ac99407b9af141b87c0491fd3970713be (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
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
*> \brief \b CDRVLS
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE CDRVLS( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL, NNB,
*                          NBVAL, NXVAL, THRESH, TSTERR, A, COPYA, B,
*                          COPYB, C, S, COPYS, WORK, RWORK, IWORK,
*                          NOUT )
*
*       .. Scalar Arguments ..
*       LOGICAL            TSTERR
*       INTEGER            NM, NN, NNB, NNS, NOUT
*       REAL               THRESH
*       ..
*       .. Array Arguments ..
*       LOGICAL            DOTYPE( * )
*       INTEGER            IWORK( * ), MVAL( * ), NBVAL( * ), NSVAL( * ),
*      $                   NVAL( * ), NXVAL( * )
*       REAL               COPYS( * ), RWORK( * ), S( * )
*       COMPLEX            A( * ), B( * ), C( * ), COPYA( * ), COPYB( * ),
*      $                   WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> CDRVLS tests the least squares driver routines CGELS, CGELSS, CGELSY
*> and CGELSD.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] DOTYPE
*> \verbatim
*>          DOTYPE is 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.
*>          The matrix of type j is generated as follows:
*>          j=1: A = U*D*V where U and V are random unitary matrices
*>               and D has random entries (> 0.1) taken from a uniform
*>               distribution (0,1). A is full rank.
*>          j=2: The same of 1, but A is scaled up.
*>          j=3: The same of 1, but A is scaled down.
*>          j=4: A = U*D*V where U and V are random unitary matrices
*>               and D has 3*min(M,N)/4 random entries (> 0.1) taken
*>               from a uniform distribution (0,1) and the remaining
*>               entries set to 0. A is rank-deficient.
*>          j=5: The same of 4, but A is scaled up.
*>          j=6: The same of 5, but A is scaled down.
*> \endverbatim
*>
*> \param[in] NM
*> \verbatim
*>          NM is INTEGER
*>          The number of values of M contained in the vector MVAL.
*> \endverbatim
*>
*> \param[in] MVAL
*> \verbatim
*>          MVAL is INTEGER array, dimension (NM)
*>          The values of the matrix row dimension M.
*> \endverbatim
*>
*> \param[in] NN
*> \verbatim
*>          NN is INTEGER
*>          The number of values of N contained in the vector NVAL.
*> \endverbatim
*>
*> \param[in] NVAL
*> \verbatim
*>          NVAL is INTEGER array, dimension (NN)
*>          The values of the matrix column dimension N.
*> \endverbatim
*>
*> \param[in] NNB
*> \verbatim
*>          NNB is INTEGER
*>          The number of values of NB and NX contained in the
*>          vectors NBVAL and NXVAL.  The blocking parameters are used
*>          in pairs (NB,NX).
*> \endverbatim
*>
*> \param[in] NBVAL
*> \verbatim
*>          NBVAL is INTEGER array, dimension (NNB)
*>          The values of the blocksize NB.
*> \endverbatim
*>
*> \param[in] NXVAL
*> \verbatim
*>          NXVAL is INTEGER array, dimension (NNB)
*>          The values of the crossover point NX.
*> \endverbatim
*>
*> \param[in] NNS
*> \verbatim
*>          NNS is INTEGER
*>          The number of values of NRHS contained in the vector NSVAL.
*> \endverbatim
*>
*> \param[in] NSVAL
*> \verbatim
*>          NSVAL is INTEGER array, dimension (NNS)
*>          The values of the number of right hand sides NRHS.
*> \endverbatim
*>
*> \param[in] THRESH
*> \verbatim
*>          THRESH is 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.
*> \endverbatim
*>
*> \param[in] TSTERR
*> \verbatim
*>          TSTERR is LOGICAL
*>          Flag that indicates whether error exits are to be tested.
*> \endverbatim
*>
*> \param[out] A
*> \verbatim
*>          A is COMPLEX array, dimension (MMAX*NMAX)
*>          where MMAX is the maximum value of M in MVAL and NMAX is the
*>          maximum value of N in NVAL.
*> \endverbatim
*>
*> \param[out] COPYA
*> \verbatim
*>          COPYA is COMPLEX array, dimension (MMAX*NMAX)
*> \endverbatim
*>
*> \param[out] B
*> \verbatim
*>          B is COMPLEX array, dimension (MMAX*NSMAX)
*>          where MMAX is the maximum value of M in MVAL and NSMAX is the
*>          maximum value of NRHS in NSVAL.
*> \endverbatim
*>
*> \param[out] COPYB
*> \verbatim
*>          COPYB is COMPLEX array, dimension (MMAX*NSMAX)
*> \endverbatim
*>
*> \param[out] C
*> \verbatim
*>          C is COMPLEX array, dimension (MMAX*NSMAX)
*> \endverbatim
*>
*> \param[out] S
*> \verbatim
*>          S is REAL array, dimension
*>                      (min(MMAX,NMAX))
*> \endverbatim
*>
*> \param[out] COPYS
*> \verbatim
*>          COPYS is REAL array, dimension
*>                      (min(MMAX,NMAX))
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is COMPLEX array, dimension
*>                      (MMAX*NMAX + 4*NMAX + MMAX).
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*>          RWORK is REAL array, dimension (5*NMAX-1)
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*>          IWORK is INTEGER array, dimension (15*NMAX)
*> \endverbatim
*>
*> \param[in] NOUT
*> \verbatim
*>          NOUT is INTEGER
*>          The unit number for output.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2015
*
*> \ingroup complex_lin
*
*  =====================================================================
      SUBROUTINE CDRVLS( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL, NNB,
     $                   NBVAL, NXVAL, THRESH, TSTERR, A, COPYA, B,
     $                   COPYB, C, S, COPYS, WORK, RWORK, IWORK,
     $                   NOUT )
*
*  -- LAPACK test routine (version 3.6.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2015
*
*     .. Scalar Arguments ..
      LOGICAL            TSTERR
      INTEGER            NM, NN, NNB, NNS, NOUT
      REAL               THRESH
*     ..
*     .. Array Arguments ..
      LOGICAL            DOTYPE( * )
      INTEGER            IWORK( * ), MVAL( * ), NBVAL( * ), NSVAL( * ),
     $                   NVAL( * ), NXVAL( * )
      REAL               COPYS( * ), RWORK( * ), S( * )
      COMPLEX            A( * ), B( * ), C( * ), COPYA( * ), COPYB( * ),
     $                   WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      INTEGER            NTESTS
      PARAMETER          ( NTESTS = 16 )
      INTEGER            SMLSIZ
      PARAMETER          ( SMLSIZ = 25 )
      REAL               ONE, ZERO
      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
      COMPLEX            CONE, CZERO
      PARAMETER          ( CONE = ( 1.0E+0, 0.0E+0 ),
     $                   CZERO = ( 0.0E+0, 0.0E+0 ) )
*     ..
*     .. Local Scalars ..
      CHARACTER          TRANS
      CHARACTER*3        PATH
      INTEGER            CRANK, I, IM, IMB, IN, INB, INFO, INS, IRANK,
     $                   ISCALE, ITRAN, ITYPE, J, K, LDA, LDB, LDWORK,
     $                   LWLSY, LWORK, M, MNMIN, N, NB, NCOLS, NERRS,
     $                   NFAIL, NRHS, NROWS, NRUN, RANK, MB, LWTS
      REAL               EPS, NORMA, NORMB, RCOND
*     ..
*     .. Local Arrays ..
      INTEGER            ISEED( 4 ), ISEEDY( 4 )
      REAL               RESULT( NTESTS )
*     ..
*     .. External Functions ..
      REAL               CQRT12, CQRT14, CQRT17, SASUM, SLAMCH
      EXTERNAL           CQRT12, CQRT14, CQRT17, SASUM, SLAMCH
*     ..
*     .. External Subroutines ..
      EXTERNAL           ALAERH, ALAHD, ALASVM, CERRLS, CGELS, CGELSD,
     $                   CGELSS, CGELSY, CGEMM, CGETSLS, CLACPY,
     $                   CLARNV, CQRT13, CQRT15, CQRT16, CSSCAL,
     $                   SAXPY, XLAENV
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, MIN, REAL, SQRT
*     ..
*     .. Scalars in Common ..
      LOGICAL            LERR, OK
      CHARACTER*32       SRNAMT
      INTEGER            INFOT, IOUNIT
*     ..
*     .. Common blocks ..
      COMMON             / INFOC / INFOT, IOUNIT, OK, LERR
      COMMON             / SRNAMC / SRNAMT
*     ..
*     .. Data statements ..
      DATA               ISEEDY / 1988, 1989, 1990, 1991 /
*     ..
*     .. Executable Statements ..
*
*     Initialize constants and the random number seed.
*
      PATH( 1: 1 ) = 'Complex precision'
      PATH( 2: 3 ) = 'LS'
      NRUN = 0
      NFAIL = 0
      NERRS = 0
      DO 10 I = 1, 4
         ISEED( I ) = ISEEDY( I )
   10 CONTINUE
      EPS = SLAMCH( 'Epsilon' )
*
*     Threshold for rank estimation
*
      RCOND = SQRT( EPS ) - ( SQRT( EPS )-EPS ) / 2
*
*     Test the error exits
*
      CALL XLAENV( 9, SMLSIZ )
      IF( TSTERR )
     $   CALL CERRLS( PATH, NOUT )
*
*     Print the header if NM = 0 or NN = 0 and THRESH = 0.
*
      IF( ( NM.EQ.0 .OR. NN.EQ.0 ) .AND. THRESH.EQ.ZERO )
     $   CALL ALAHD( NOUT, PATH )
      INFOT = 0
*
      DO 140 IM = 1, NM
         M = MVAL( IM )
         LDA = MAX( 1, M )
*
         DO 130 IN = 1, NN
            N = NVAL( IN )
            MNMIN = MAX(MIN( M, N ),1)
            LDB = MAX( 1, M, N )
            MB = (MNMIN+1)
            IF(MNMIN.NE.MB) THEN
              LWTS = (((LDB-MB)/(MB-MNMIN))*MNMIN+MNMIN*2)*MB+5
            ELSE
              LWTS = 2*MNMIN+5
            END IF
*
            DO 120 INS = 1, NNS
               NRHS = NSVAL( INS )
               LWORK = MAX( 1, ( M+NRHS )*( N+2 ), ( N+NRHS )*( M+2 ),
     $                 M*N+4*MNMIN+MAX( M, N ), 2*N+M, LWTS )
*
               DO 110 IRANK = 1, 2
                  DO 100 ISCALE = 1, 3
                     ITYPE = ( IRANK-1 )*3 + ISCALE
                     IF( .NOT.DOTYPE( ITYPE ) )
     $                  GO TO 100
*
                     IF( IRANK.EQ.1 ) THEN
*
*                       Test CGELS
*
*                       Generate a matrix of scaling type ISCALE
*
                        CALL CQRT13( ISCALE, M, N, COPYA, LDA, NORMA,
     $                               ISEED )
                        DO 40 INB = 1, NNB
                           NB = NBVAL( INB )
                           CALL XLAENV( 1, NB )
                           CALL XLAENV( 3, NXVAL( INB ) )
*
                           DO 30 ITRAN = 1, 2
                              IF( ITRAN.EQ.1 ) THEN
                                 TRANS = 'N'
                                 NROWS = M
                                 NCOLS = N
                              ELSE
                                 TRANS = 'C'
                                 NROWS = N
                                 NCOLS = M
                              END IF
                              LDWORK = MAX( 1, NCOLS )
*
*                             Set up a consistent rhs
*
                              IF( NCOLS.GT.0 ) THEN
                                 CALL CLARNV( 2, ISEED, NCOLS*NRHS,
     $                                        WORK )
                                 CALL CSSCAL( NCOLS*NRHS,
     $                                        ONE / REAL( NCOLS ), WORK,
     $                                        1 )
                              END IF
                              CALL CGEMM( TRANS, 'No transpose', NROWS,
     $                                    NRHS, NCOLS, CONE, COPYA, LDA,
     $                                    WORK, LDWORK, CZERO, B, LDB )
                              CALL CLACPY( 'Full', NROWS, NRHS, B, LDB,
     $                                     COPYB, LDB )
*
*                             Solve LS or overdetermined system
*
                              IF( M.GT.0 .AND. N.GT.0 ) THEN
                                 CALL CLACPY( 'Full', M, N, COPYA, LDA,
     $                                        A, LDA )
                                 CALL CLACPY( 'Full', NROWS, NRHS,
     $                                        COPYB, LDB, B, LDB )
                              END IF
                              SRNAMT = 'CGELS '
                              CALL CGELS( TRANS, M, N, NRHS, A, LDA, B,
     $                                    LDB, WORK, LWORK, INFO )
*
                              IF( INFO.NE.0 )
     $                           CALL ALAERH( PATH, 'CGELS ', INFO, 0,
     $                                        TRANS, M, N, NRHS, -1, NB,
     $                                        ITYPE, NFAIL, NERRS,
     $                                        NOUT )
*
*                             Check correctness of results
*
                              LDWORK = MAX( 1, NROWS )
                              IF( NROWS.GT.0 .AND. NRHS.GT.0 )
     $                           CALL CLACPY( 'Full', NROWS, NRHS,
     $                                        COPYB, LDB, C, LDB )
                              CALL CQRT16( TRANS, M, N, NRHS, COPYA,
     $                                     LDA, B, LDB, C, LDB, RWORK,
     $                                     RESULT( 1 ) )
*
                              IF( ( ITRAN.EQ.1 .AND. M.GE.N ) .OR.
     $                            ( ITRAN.EQ.2 .AND. M.LT.N ) ) THEN
*
*                                Solving LS system
*
                                 RESULT( 2 ) = CQRT17( TRANS, 1, M, N,
     $                                         NRHS, COPYA, LDA, B, LDB,
     $                                         COPYB, LDB, C, WORK,
     $                                         LWORK )
                              ELSE
*
*                                Solving overdetermined system
*
                                 RESULT( 2 ) = CQRT14( TRANS, M, N,
     $                                         NRHS, COPYA, LDA, B, LDB,
     $                                         WORK, LWORK )
                              END IF
*
*                             Print information about the tests that
*                             did not pass the threshold.
*
                              DO 20 K = 1, 2
                                 IF( RESULT( K ).GE.THRESH ) THEN
                                    IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
     $                                 CALL ALAHD( NOUT, PATH )
                                    WRITE( NOUT, FMT = 9999 )TRANS, M,
     $                                 N, NRHS, NB, ITYPE, K,
     $                                 RESULT( K )
                                    NFAIL = NFAIL + 1
                                 END IF
   20                         CONTINUE
                              NRUN = NRUN + 2
   30                      CONTINUE
   40                   CONTINUE
*
*
*                       Test CGETSLS
*
*                       Generate a matrix of scaling type ISCALE
*
                        CALL CQRT13( ISCALE, M, N, COPYA, LDA, NORMA,
     $                               ISEED )
                        DO 65 INB = 1, NNB
                             MB = NBVAL( INB )
                             CALL XLAENV( 1, MB )
                             DO 62 IMB = 1, NNB
                              NB = NBVAL( IMB )
                              CALL XLAENV( 2, NB )
*
                           DO 60 ITRAN = 1, 2
                              IF( ITRAN.EQ.1 ) THEN
                                 TRANS = 'N'
                                 NROWS = M
                                 NCOLS = N
                              ELSE
                                 TRANS = 'C'
                                 NROWS = N
                                 NCOLS = M
                              END IF
                              LDWORK = MAX( 1, NCOLS )
*
*                             Set up a consistent rhs
*
                              IF( NCOLS.GT.0 ) THEN
                                 CALL CLARNV( 2, ISEED, NCOLS*NRHS,
     $                                        WORK )
                                 CALL CSCAL( NCOLS*NRHS,
     $                                       ONE / REAL( NCOLS ), WORK,
     $                                       1 )
                              END IF
                              CALL CGEMM( TRANS, 'No transpose', NROWS,
     $                                    NRHS, NCOLS, CONE, COPYA, LDA,
     $                                    WORK, LDWORK, CZERO, B, LDB )
                              CALL CLACPY( 'Full', NROWS, NRHS, B, LDB,
     $                                     COPYB, LDB )
*
*                             Solve LS or overdetermined system
*
                              IF( M.GT.0 .AND. N.GT.0 ) THEN
                                 CALL CLACPY( 'Full', M, N, COPYA, LDA,
     $                                        A, LDA )
                                 CALL CLACPY( 'Full', NROWS, NRHS,
     $                                        COPYB, LDB, B, LDB )
                              END IF
                              SRNAMT = 'CGETSLS '
                              CALL CGETSLS( TRANS, M, N, NRHS, A,
     $                                 LDA, B, LDB, WORK, LWORK, INFO )
                              IF( INFO.NE.0 )
     $                           CALL ALAERH( PATH, 'CGETSLS ', INFO, 0,
     $                                        TRANS, M, N, NRHS, -1, NB,
     $                                        ITYPE, NFAIL, NERRS,
     $                                        NOUT )
*
*                             Check correctness of results
*
                              LDWORK = MAX( 1, NROWS )
                              IF( NROWS.GT.0 .AND. NRHS.GT.0 )
     $                           CALL CLACPY( 'Full', NROWS, NRHS,
     $                                        COPYB, LDB, C, LDB )
                              CALL CQRT16( TRANS, M, N, NRHS, COPYA,
     $                                     LDA, B, LDB, C, LDB, WORK,
     $                                     RESULT( 15 ) )
*
                              IF( ( ITRAN.EQ.1 .AND. M.GE.N ) .OR.
     $                            ( ITRAN.EQ.2 .AND. M.LT.N ) ) THEN
*
*                                Solving LS system
*
                                 RESULT( 16 ) = CQRT17( TRANS, 1, M, N,
     $                                         NRHS, COPYA, LDA, B, LDB,
     $                                         COPYB, LDB, C, WORK,
     $                                         LWORK )
                              ELSE
*
*                                Solving overdetermined system
*
                                 RESULT( 16 ) = CQRT14( TRANS, M, N,
     $                                         NRHS, COPYA, LDA, B, LDB,
     $                                         WORK, LWORK )
                              END IF
*
*                             Print information about the tests that
*                             did not pass the threshold.
*
                              DO 50 K = 15, 16
                                 IF( RESULT( K ).GE.THRESH ) THEN
                                    IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
     $                                 CALL ALAHD( NOUT, PATH )
                                    WRITE( NOUT, FMT = 9997 )TRANS, M,
     $                                 N, NRHS, MB, NB, ITYPE, K,
     $                                 RESULT( K )
                                    NFAIL = NFAIL + 1
                                 END IF
   50                         CONTINUE
                              NRUN = NRUN + 2
   60                      CONTINUE
   62                      CONTINUE
   65                   CONTINUE
                     END IF
*
*                    Generate a matrix of scaling type ISCALE and rank
*                    type IRANK.
*
                     CALL CQRT15( ISCALE, IRANK, M, N, NRHS, COPYA, LDA,
     $                            COPYB, LDB, COPYS, RANK, NORMA, NORMB,
     $                            ISEED, WORK, LWORK )
*
*                    workspace used: MAX(M+MIN(M,N),NRHS*MIN(M,N),2*N+M)
*
                     LDWORK = MAX( 1, M )
*
*                    Loop for testing different block sizes.
*
                     DO 90 INB = 1, NNB
                        NB = NBVAL( INB )
                        CALL XLAENV( 1, NB )
                        CALL XLAENV( 3, NXVAL( INB ) )
*
*                       Test CGELSY
*
*                       CGELSY:  Compute the minimum-norm solution
*                       X to min( norm( A * X - B ) )
*                       using the rank-revealing orthogonal
*                       factorization.
*
                        CALL CLACPY( 'Full', M, N, COPYA, LDA, A, LDA )
                        CALL CLACPY( 'Full', M, NRHS, COPYB, LDB, B,
     $                               LDB )
*
*                       Initialize vector IWORK.
*
                        DO 70 J = 1, N
                           IWORK( J ) = 0
   70                   CONTINUE
*
*                       Set LWLSY to the adequate value.
*
                        LWLSY = MNMIN + MAX( 2*MNMIN, NB*( N+1 ),
     $                          MNMIN+NB*NRHS )
                        LWLSY = MAX( 1, LWLSY )
*
                        SRNAMT = 'CGELSY'
                        CALL CGELSY( M, N, NRHS, A, LDA, B, LDB, IWORK,
     $                               RCOND, CRANK, WORK, LWLSY, RWORK,
     $                               INFO )
                        IF( INFO.NE.0 )
     $                     CALL ALAERH( PATH, 'CGELSY', INFO, 0, ' ', M,
     $                                  N, NRHS, -1, NB, ITYPE, NFAIL,
     $                                  NERRS, NOUT )
*
*                       workspace used: 2*MNMIN+NB*NB+NB*MAX(N,NRHS)
*
*                       Test 3:  Compute relative error in svd
*                                workspace: M*N + 4*MIN(M,N) + MAX(M,N)
*
                        RESULT( 3 ) = CQRT12( CRANK, CRANK, A, LDA,
     $                                COPYS, WORK, LWORK, RWORK )
*
*                       Test 4:  Compute error in solution
*                                workspace:  M*NRHS + M
*
                        CALL CLACPY( 'Full', M, NRHS, COPYB, LDB, WORK,
     $                               LDWORK )
                        CALL CQRT16( 'No transpose', M, N, NRHS, COPYA,
     $                               LDA, B, LDB, WORK, LDWORK, RWORK,
     $                               RESULT( 4 ) )
*
*                       Test 5:  Check norm of r'*A
*                                workspace: NRHS*(M+N)
*
                        RESULT( 5 ) = ZERO
                        IF( M.GT.CRANK )
     $                     RESULT( 5 ) = CQRT17( 'No transpose', 1, M,
     $                                   N, NRHS, COPYA, LDA, B, LDB,
     $                                   COPYB, LDB, C, WORK, LWORK )
*
*                       Test 6:  Check if x is in the rowspace of A
*                                workspace: (M+NRHS)*(N+2)
*
                        RESULT( 6 ) = ZERO
*
                        IF( N.GT.CRANK )
     $                     RESULT( 6 ) = CQRT14( 'No transpose', M, N,
     $                                   NRHS, COPYA, LDA, B, LDB,
     $                                   WORK, LWORK )
*
*                       Test CGELSS
*
*                       CGELSS:  Compute the minimum-norm solution
*                       X to min( norm( A * X - B ) )
*                       using the SVD.
*
                        CALL CLACPY( 'Full', M, N, COPYA, LDA, A, LDA )
                        CALL CLACPY( 'Full', M, NRHS, COPYB, LDB, B,
     $                               LDB )
                        SRNAMT = 'CGELSS'
                        CALL CGELSS( M, N, NRHS, A, LDA, B, LDB, S,
     $                               RCOND, CRANK, WORK, LWORK, RWORK,
     $                               INFO )
*
                        IF( INFO.NE.0 )
     $                     CALL ALAERH( PATH, 'CGELSS', INFO, 0, ' ', M,
     $                                  N, NRHS, -1, NB, ITYPE, NFAIL,
     $                                  NERRS, NOUT )
*
*                       workspace used: 3*min(m,n) +
*                                       max(2*min(m,n),nrhs,max(m,n))
*
*                       Test 7:  Compute relative error in svd
*
                        IF( RANK.GT.0 ) THEN
                           CALL SAXPY( MNMIN, -ONE, COPYS, 1, S, 1 )
                           RESULT( 7 ) = SASUM( MNMIN, S, 1 ) /
     $                                    SASUM( MNMIN, COPYS, 1 ) /
     $                                    ( EPS*REAL( MNMIN ) )
                        ELSE
                           RESULT( 7 ) = ZERO
                        END IF
*
*                       Test 8:  Compute error in solution
*
                        CALL CLACPY( 'Full', M, NRHS, COPYB, LDB, WORK,
     $                               LDWORK )
                        CALL CQRT16( 'No transpose', M, N, NRHS, COPYA,
     $                               LDA, B, LDB, WORK, LDWORK, RWORK,
     $                               RESULT( 8 ) )
*
*                       Test 9:  Check norm of r'*A
*
                        RESULT( 9 ) = ZERO
                        IF( M.GT.CRANK )
     $                     RESULT( 9 ) = CQRT17( 'No transpose', 1, M,
     $                                    N, NRHS, COPYA, LDA, B, LDB,
     $                                    COPYB, LDB, C, WORK, LWORK )
*
*                       Test 10:  Check if x is in the rowspace of A
*
                        RESULT( 10 ) = ZERO
                        IF( N.GT.CRANK )
     $                     RESULT( 10 ) = CQRT14( 'No transpose', M, N,
     $                                    NRHS, COPYA, LDA, B, LDB,
     $                                    WORK, LWORK )
*
*                       Test CGELSD
*
*                       CGELSD:  Compute the minimum-norm solution X
*                       to min( norm( A * X - B ) ) using a
*                       divide and conquer SVD.
*
                        CALL XLAENV( 9, 25 )
*
                        CALL CLACPY( 'Full', M, N, COPYA, LDA, A, LDA )
                        CALL CLACPY( 'Full', M, NRHS, COPYB, LDB, B,
     $                               LDB )
*
                        SRNAMT = 'CGELSD'
                        CALL CGELSD( M, N, NRHS, A, LDA, B, LDB, S,
     $                               RCOND, CRANK, WORK, LWORK, RWORK,
     $                               IWORK, INFO )
                        IF( INFO.NE.0 )
     $                     CALL ALAERH( PATH, 'CGELSD', INFO, 0, ' ', M,
     $                                  N, NRHS, -1, NB, ITYPE, NFAIL,
     $                                  NERRS, NOUT )
*
*                       Test 11:  Compute relative error in svd
*
                        IF( RANK.GT.0 ) THEN
                           CALL SAXPY( MNMIN, -ONE, COPYS, 1, S, 1 )
                           RESULT( 11 ) = SASUM( MNMIN, S, 1 ) /
     $                                    SASUM( MNMIN, COPYS, 1 ) /
     $                                    ( EPS*REAL( MNMIN ) )
                        ELSE
                           RESULT( 11 ) = ZERO
                        END IF
*
*                       Test 12:  Compute error in solution
*
                        CALL CLACPY( 'Full', M, NRHS, COPYB, LDB, WORK,
     $                               LDWORK )
                        CALL CQRT16( 'No transpose', M, N, NRHS, COPYA,
     $                               LDA, B, LDB, WORK, LDWORK, RWORK,
     $                               RESULT( 12 ) )
*
*                       Test 13:  Check norm of r'*A
*
                        RESULT( 13 ) = ZERO
                        IF( M.GT.CRANK )
     $                     RESULT( 13 ) = CQRT17( 'No transpose', 1, M,
     $                                    N, NRHS, COPYA, LDA, B, LDB,
     $                                    COPYB, LDB, C, WORK, LWORK )
*
*                       Test 14:  Check if x is in the rowspace of A
*
                        RESULT( 14 ) = ZERO
                        IF( N.GT.CRANK )
     $                     RESULT( 14 ) = CQRT14( 'No transpose', M, N,
     $                                    NRHS, COPYA, LDA, B, LDB,
     $                                    WORK, LWORK )
*
*                       Print information about the tests that did not
*                       pass the threshold.
*
                        DO 80 K = 3, 14
                           IF( RESULT( K ).GE.THRESH ) THEN
                              IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
     $                           CALL ALAHD( NOUT, PATH )
                              WRITE( NOUT, FMT = 9998 )M, N, NRHS, NB,
     $                           ITYPE, K, RESULT( K )
                              NFAIL = NFAIL + 1
                           END IF
   80                   CONTINUE
                        NRUN = NRUN + 12
*
   90                CONTINUE
  100             CONTINUE
  110          CONTINUE
  120       CONTINUE
  130    CONTINUE
  140 CONTINUE
*
*     Print a summary of the results.
*
      CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
*
 9999 FORMAT( ' TRANS=''', A1, ''', M=', I5, ', N=', I5, ', NRHS=', I4,
     $      ', NB=', I4, ', type', I2, ', test(', I2, ')=', G12.5 )
 9998 FORMAT( ' M=', I5, ', N=', I5, ', NRHS=', I4, ', NB=', I4,
     $      ', type', I2, ', test(', I2, ')=', G12.5 )
 9997 FORMAT( ' TRANS=''', A1,' M=', I5, ', N=', I5, ', NRHS=', I4,
     $      ', MB=', I4,', NB=', I4,', type', I2,
     $      ', test(', I2, ')=', G12.5 )
      RETURN
*
*     End of CDRVLS
*
      END