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
|
*> \brief \b DCHKSY_ROOK
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DCHKSY_ROOK( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
* THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
* XACT, WORK, RWORK, IWORK, NOUT )
*
* .. Scalar Arguments ..
* LOGICAL TSTERR
* INTEGER NMAX, NN, NNB, NNS, NOUT
* DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
* LOGICAL DOTYPE( * )
* INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
* DOUBLE PRECISION A( * ), AFAC( * ), AINV( * ), B( * ),
* $ RWORK( * ), WORK( * ), X( * ), XACT( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DCHKSY_ROOK tests DSYTRF_ROOK, -TRI_ROOK, -TRS_ROOK,
*> and -CON_ROOK.
*> \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.
*> \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 dimension N.
*> \endverbatim
*>
*> \param[in] NNB
*> \verbatim
*> NNB is INTEGER
*> The number of values of NB contained in the vector NBVAL.
*> \endverbatim
*>
*> \param[in] NBVAL
*> \verbatim
*> NBVAL is INTEGER array, dimension (NBVAL)
*> The values of the blocksize NB.
*> \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 DOUBLE PRECISION
*> 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[in] NMAX
*> \verbatim
*> NMAX is INTEGER
*> The maximum value permitted for N, used in dimensioning the
*> work arrays.
*> \endverbatim
*>
*> \param[out] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
*> \endverbatim
*>
*> \param[out] AFAC
*> \verbatim
*> AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
*> \endverbatim
*>
*> \param[out] AINV
*> \verbatim
*> AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
*> \endverbatim
*>
*> \param[out] B
*> \verbatim
*> B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
*> where NSMAX is the largest entry in NSVAL.
*> \endverbatim
*>
*> \param[out] X
*> \verbatim
*> X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
*> \endverbatim
*>
*> \param[out] XACT
*> \verbatim
*> XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (NMAX*max(3,NSMAX))
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (max(NMAX,2*NSMAX))
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*> IWORK is INTEGER array, dimension (2*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 December 2016
*
*> \ingroup double_lin
*
* =====================================================================
SUBROUTINE DCHKSY_ROOK( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
$ THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
$ XACT, WORK, RWORK, IWORK, NOUT )
*
* -- LAPACK test 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 TSTERR
INTEGER NMAX, NN, NNB, NNS, NOUT
DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
LOGICAL DOTYPE( * )
INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
DOUBLE PRECISION A( * ), AFAC( * ), AINV( * ), B( * ),
$ RWORK( * ), WORK( * ), X( * ), XACT( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
DOUBLE PRECISION EIGHT, SEVTEN
PARAMETER ( EIGHT = 8.0D+0, SEVTEN = 17.0D+0 )
INTEGER NTYPES
PARAMETER ( NTYPES = 10 )
INTEGER NTESTS
PARAMETER ( NTESTS = 7 )
* ..
* .. Local Scalars ..
LOGICAL TRFCON, ZEROT
CHARACTER DIST, TYPE, UPLO, XTYPE
CHARACTER*3 PATH, MATPATH
INTEGER I, I1, I2, IMAT, IN, INB, INFO, IOFF, IRHS,
$ IUPLO, IZERO, J, K, KL, KU, LDA, LWORK, MODE,
$ N, NB, NERRS, NFAIL, NIMAT, NRHS, NRUN, NT
DOUBLE PRECISION ALPHA, ANORM, CNDNUM, CONST, DTEMP, SING_MAX,
$ SING_MIN, RCOND, RCONDC
* ..
* .. Local Arrays ..
CHARACTER UPLOS( 2 )
INTEGER ISEED( 4 ), ISEEDY( 4 )
DOUBLE PRECISION BLOCK( 2, 2 ), DDUMMY( 1 ), RESULT( NTESTS )
* ..
* .. External Functions ..
DOUBLE PRECISION DGET06, DLANGE, DLANSY
EXTERNAL DGET06, DLANGE, DLANSY
* ..
* .. External Subroutines ..
EXTERNAL ALAERH, ALAHD, ALASUM, DERRSY, DGET04, DLACPY,
$ DLARHS, DLATB4, DLATMS, DPOT02, DPOT03, DGESVD,
$ DSYCON_ROOK, DSYT01_ROOK, DSYTRF_ROOK,
$ DSYTRI_ROOK, DSYTRS_ROOK, XLAENV
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN, SQRT
* ..
* .. 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 UPLOS / 'U', 'L' /
* ..
* .. Executable Statements ..
*
* Initialize constants and the random number seed.
*
ALPHA = ( ONE+SQRT( SEVTEN ) ) / EIGHT
*
* Test path
*
PATH( 1: 1 ) = 'Double precision'
PATH( 2: 3 ) = 'SR'
*
* Path to generate matrices
*
MATPATH( 1: 1 ) = 'Double precision'
MATPATH( 2: 3 ) = 'SY'
*
NRUN = 0
NFAIL = 0
NERRS = 0
DO 10 I = 1, 4
ISEED( I ) = ISEEDY( I )
10 CONTINUE
*
* Test the error exits
*
IF( TSTERR )
$ CALL DERRSY( PATH, NOUT )
INFOT = 0
*
* Set the minimum block size for which the block routine should
* be used, which will be later returned by ILAENV
*
CALL XLAENV( 2, 2 )
*
* Do for each value of N in NVAL
*
DO 270 IN = 1, NN
N = NVAL( IN )
LDA = MAX( N, 1 )
XTYPE = 'N'
NIMAT = NTYPES
IF( N.LE.0 )
$ NIMAT = 1
*
IZERO = 0
*
* Do for each value of matrix type IMAT
*
DO 260 IMAT = 1, NIMAT
*
* Do the tests only if DOTYPE( IMAT ) is true.
*
IF( .NOT.DOTYPE( IMAT ) )
$ GO TO 260
*
* Skip types 3, 4, 5, or 6 if the matrix size is too small.
*
ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
IF( ZEROT .AND. N.LT.IMAT-2 )
$ GO TO 260
*
* Do first for UPLO = 'U', then for UPLO = 'L'
*
DO 250 IUPLO = 1, 2
UPLO = UPLOS( IUPLO )
*
* Begin generate the test matrix A.
*
* Set up parameters with DLATB4 for the matrix generator
* based on the type of matrix to be generated.
*
CALL DLATB4( MATPATH, IMAT, N, N, TYPE, KL, KU, ANORM,
$ MODE, CNDNUM, DIST )
*
* Generate a matrix with DLATMS.
*
SRNAMT = 'DLATMS'
CALL DLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
$ CNDNUM, ANORM, KL, KU, UPLO, A, LDA, WORK,
$ INFO )
*
* Check error code from DLATMS and handle error.
*
IF( INFO.NE.0 ) THEN
CALL ALAERH( PATH, 'DLATMS', INFO, 0, UPLO, N, N, -1,
$ -1, -1, IMAT, NFAIL, NERRS, NOUT )
*
* Skip all tests for this generated matrix
*
GO TO 250
END IF
*
* For matrix types 3-6, zero one or more rows and
* columns of the matrix to test that INFO is returned
* correctly.
*
IF( ZEROT ) THEN
IF( IMAT.EQ.3 ) THEN
IZERO = 1
ELSE IF( IMAT.EQ.4 ) THEN
IZERO = N
ELSE
IZERO = N / 2 + 1
END IF
*
IF( IMAT.LT.6 ) THEN
*
* Set row and column IZERO to zero.
*
IF( IUPLO.EQ.1 ) THEN
IOFF = ( IZERO-1 )*LDA
DO 20 I = 1, IZERO - 1
A( IOFF+I ) = ZERO
20 CONTINUE
IOFF = IOFF + IZERO
DO 30 I = IZERO, N
A( IOFF ) = ZERO
IOFF = IOFF + LDA
30 CONTINUE
ELSE
IOFF = IZERO
DO 40 I = 1, IZERO - 1
A( IOFF ) = ZERO
IOFF = IOFF + LDA
40 CONTINUE
IOFF = IOFF - IZERO
DO 50 I = IZERO, N
A( IOFF+I ) = ZERO
50 CONTINUE
END IF
ELSE
IF( IUPLO.EQ.1 ) THEN
*
* Set the first IZERO rows and columns to zero.
*
IOFF = 0
DO 70 J = 1, N
I2 = MIN( J, IZERO )
DO 60 I = 1, I2
A( IOFF+I ) = ZERO
60 CONTINUE
IOFF = IOFF + LDA
70 CONTINUE
ELSE
*
* Set the last IZERO rows and columns to zero.
*
IOFF = 0
DO 90 J = 1, N
I1 = MAX( J, IZERO )
DO 80 I = I1, N
A( IOFF+I ) = ZERO
80 CONTINUE
IOFF = IOFF + LDA
90 CONTINUE
END IF
END IF
ELSE
IZERO = 0
END IF
*
* End generate the test matrix A.
*
*
* Do for each value of NB in NBVAL
*
DO 240 INB = 1, NNB
*
* Set the optimal blocksize, which will be later
* returned by ILAENV.
*
NB = NBVAL( INB )
CALL XLAENV( 1, NB )
*
* Copy the test matrix A into matrix AFAC which
* will be factorized in place. This is needed to
* preserve the test matrix A for subsequent tests.
*
CALL DLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
*
* Compute the L*D*L**T or U*D*U**T factorization of the
* matrix. IWORK stores details of the interchanges and
* the block structure of D. AINV is a work array for
* block factorization, LWORK is the length of AINV.
*
LWORK = MAX( 2, NB )*LDA
SRNAMT = 'DSYTRF_ROOK'
CALL DSYTRF_ROOK( UPLO, N, AFAC, LDA, IWORK, AINV,
$ LWORK, INFO )
*
* Adjust the expected value of INFO to account for
* pivoting.
*
K = IZERO
IF( K.GT.0 ) THEN
100 CONTINUE
IF( IWORK( K ).LT.0 ) THEN
IF( IWORK( K ).NE.-K ) THEN
K = -IWORK( K )
GO TO 100
END IF
ELSE IF( IWORK( K ).NE.K ) THEN
K = IWORK( K )
GO TO 100
END IF
END IF
*
* Check error code from DSYTRF_ROOK and handle error.
*
IF( INFO.NE.K)
$ CALL ALAERH( PATH, 'DSYTRF_ROOK', INFO, K,
$ UPLO, N, N, -1, -1, NB, IMAT,
$ NFAIL, NERRS, NOUT )
*
* Set the condition estimate flag if the INFO is not 0.
*
IF( INFO.NE.0 ) THEN
TRFCON = .TRUE.
ELSE
TRFCON = .FALSE.
END IF
*
*+ TEST 1
* Reconstruct matrix from factors and compute residual.
*
CALL DSYT01_ROOK( UPLO, N, A, LDA, AFAC, LDA, IWORK,
$ AINV, LDA, RWORK, RESULT( 1 ) )
NT = 1
*
*+ TEST 2
* Form the inverse and compute the residual,
* if the factorization was competed without INFO > 0
* (i.e. there is no zero rows and columns).
* Do it only for the first block size.
*
IF( INB.EQ.1 .AND. .NOT.TRFCON ) THEN
CALL DLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA )
SRNAMT = 'DSYTRI_ROOK'
CALL DSYTRI_ROOK( UPLO, N, AINV, LDA, IWORK, WORK,
$ INFO )
*
* Check error code from DSYTRI_ROOK and handle error.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'DSYTRI_ROOK', INFO, -1,
$ UPLO, N, N, -1, -1, -1, IMAT,
$ NFAIL, NERRS, NOUT )
*
* Compute the residual for a symmetric matrix times
* its inverse.
*
CALL DPOT03( UPLO, N, A, LDA, AINV, LDA, WORK, LDA,
$ RWORK, RCONDC, RESULT( 2 ) )
NT = 2
END IF
*
* Print information about the tests that did not pass
* the threshold.
*
DO 110 K = 1, NT
IF( RESULT( K ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9999 )UPLO, N, NB, IMAT, K,
$ RESULT( K )
NFAIL = NFAIL + 1
END IF
110 CONTINUE
NRUN = NRUN + NT
*
*+ TEST 3
* Compute largest element in U or L
*
RESULT( 3 ) = ZERO
DTEMP = ZERO
*
CONST = ONE / ( ONE-ALPHA )
*
IF( IUPLO.EQ.1 ) THEN
*
* Compute largest element in U
*
K = N
120 CONTINUE
IF( K.LE.1 )
$ GO TO 130
*
IF( IWORK( K ).GT.ZERO ) THEN
*
* Get max absolute value from elements
* in column k in in U
*
DTEMP = DLANGE( 'M', K-1, 1,
$ AFAC( ( K-1 )*LDA+1 ), LDA, RWORK )
ELSE
*
* Get max absolute value from elements
* in columns k and k-1 in U
*
DTEMP = DLANGE( 'M', K-2, 2,
$ AFAC( ( K-2 )*LDA+1 ), LDA, RWORK )
K = K - 1
*
END IF
*
* DTEMP should be bounded by CONST
*
DTEMP = DTEMP - CONST + THRESH
IF( DTEMP.GT.RESULT( 3 ) )
$ RESULT( 3 ) = DTEMP
*
K = K - 1
*
GO TO 120
130 CONTINUE
*
ELSE
*
* Compute largest element in L
*
K = 1
140 CONTINUE
IF( K.GE.N )
$ GO TO 150
*
IF( IWORK( K ).GT.ZERO ) THEN
*
* Get max absolute value from elements
* in column k in in L
*
DTEMP = DLANGE( 'M', N-K, 1,
$ AFAC( ( K-1 )*LDA+K+1 ), LDA, RWORK )
ELSE
*
* Get max absolute value from elements
* in columns k and k+1 in L
*
DTEMP = DLANGE( 'M', N-K-1, 2,
$ AFAC( ( K-1 )*LDA+K+2 ), LDA, RWORK )
K = K + 1
*
END IF
*
* DTEMP should be bounded by CONST
*
DTEMP = DTEMP - CONST + THRESH
IF( DTEMP.GT.RESULT( 3 ) )
$ RESULT( 3 ) = DTEMP
*
K = K + 1
*
GO TO 140
150 CONTINUE
END IF
*
*
*+ TEST 4
* Compute largest 2-Norm (condition number)
* of 2-by-2 diag blocks
*
RESULT( 4 ) = ZERO
DTEMP = ZERO
*
CONST = ( ONE+ALPHA ) / ( ONE-ALPHA )
CALL DLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA )
*
IF( IUPLO.EQ.1 ) THEN
*
* Loop backward for UPLO = 'U'
*
K = N
160 CONTINUE
IF( K.LE.1 )
$ GO TO 170
*
IF( IWORK( K ).LT.ZERO ) THEN
*
* Get the two singular values
* (real and non-negative) of a 2-by-2 block,
* store them in RWORK array
*
BLOCK( 1, 1 ) = AFAC( ( K-2 )*LDA+K-1 )
BLOCK( 1, 2 ) = AFAC( (K-1)*LDA+K-1 )
BLOCK( 2, 1 ) = BLOCK( 1, 2 )
BLOCK( 2, 2 ) = AFAC( (K-1)*LDA+K )
*
CALL DGESVD( 'N', 'N', 2, 2, BLOCK, 2, RWORK,
$ DDUMMY, 1, DDUMMY, 1,
$ WORK, 10, INFO )
*
SING_MAX = RWORK( 1 )
SING_MIN = RWORK( 2 )
*
DTEMP = SING_MAX / SING_MIN
*
* DTEMP should be bounded by CONST
*
DTEMP = DTEMP - CONST + THRESH
IF( DTEMP.GT.RESULT( 4 ) )
$ RESULT( 4 ) = DTEMP
K = K - 1
*
END IF
*
K = K - 1
*
GO TO 160
170 CONTINUE
*
ELSE
*
* Loop forward for UPLO = 'L'
*
K = 1
180 CONTINUE
IF( K.GE.N )
$ GO TO 190
*
IF( IWORK( K ).LT.ZERO ) THEN
*
* Get the two singular values
* (real and non-negative) of a 2-by-2 block,
* store them in RWORK array
*
BLOCK( 1, 1 ) = AFAC( ( K-1 )*LDA+K )
BLOCK( 2, 1 ) = AFAC( ( K-1 )*LDA+K+1 )
BLOCK( 1, 2 ) = BLOCK( 2, 1 )
BLOCK( 2, 2 ) = AFAC( K*LDA+K+1 )
*
CALL DGESVD( 'N', 'N', 2, 2, BLOCK, 2, RWORK,
$ DDUMMY, 1, DDUMMY, 1,
$ WORK, 10, INFO )
*
*
SING_MAX = RWORK( 1 )
SING_MIN = RWORK( 2 )
*
DTEMP = SING_MAX / SING_MIN
*
* DTEMP should be bounded by CONST
*
DTEMP = DTEMP - CONST + THRESH
IF( DTEMP.GT.RESULT( 4 ) )
$ RESULT( 4 ) = DTEMP
K = K + 1
*
END IF
*
K = K + 1
*
GO TO 180
190 CONTINUE
END IF
*
* Print information about the tests that did not pass
* the threshold.
*
DO 200 K = 3, 4
IF( RESULT( K ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9999 )UPLO, N, NB, IMAT, K,
$ RESULT( K )
NFAIL = NFAIL + 1
END IF
200 CONTINUE
NRUN = NRUN + 2
*
* Skip the other tests if this is not the first block
* size.
*
IF( INB.GT.1 )
$ GO TO 240
*
* Do only the condition estimate if INFO is not 0.
*
IF( TRFCON ) THEN
RCONDC = ZERO
GO TO 230
END IF
*
* Do for each value of NRHS in NSVAL.
*
DO 220 IRHS = 1, NNS
NRHS = NSVAL( IRHS )
*
*+ TEST 5 ( Using TRS_ROOK)
* Solve and compute residual for A * X = B.
*
* Choose a set of NRHS random solution vectors
* stored in XACT and set up the right hand side B
*
SRNAMT = 'DLARHS'
CALL DLARHS( MATPATH, XTYPE, UPLO, ' ', N, N,
$ KL, KU, NRHS, A, LDA, XACT, LDA,
$ B, LDA, ISEED, INFO )
CALL DLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
*
SRNAMT = 'DSYTRS_ROOK'
CALL DSYTRS_ROOK( UPLO, N, NRHS, AFAC, LDA, IWORK,
$ X, LDA, INFO )
*
* Check error code from DSYTRS_ROOK and handle error.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'DSYTRS_ROOK', INFO, 0,
$ UPLO, N, N, -1, -1, NRHS, IMAT,
$ NFAIL, NERRS, NOUT )
*
CALL DLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
*
* Compute the residual for the solution
*
CALL DPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
$ LDA, RWORK, RESULT( 5 ) )
*
*+ TEST 6
* Check solution from generated exact solution.
*
CALL DGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
$ RESULT( 6 ) )
*
* Print information about the tests that did not pass
* the threshold.
*
DO 210 K = 5, 6
IF( RESULT( K ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9998 )UPLO, N, NRHS,
$ IMAT, K, RESULT( K )
NFAIL = NFAIL + 1
END IF
210 CONTINUE
NRUN = NRUN + 2
*
* End do for each value of NRHS in NSVAL.
*
220 CONTINUE
*
*+ TEST 7
* Get an estimate of RCOND = 1/CNDNUM.
*
230 CONTINUE
ANORM = DLANSY( '1', UPLO, N, A, LDA, RWORK )
SRNAMT = 'DSYCON_ROOK'
CALL DSYCON_ROOK( UPLO, N, AFAC, LDA, IWORK, ANORM,
$ RCOND, WORK, IWORK( N+1 ), INFO )
*
* Check error code from DSYCON_ROOK and handle error.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'DSYCON_ROOK', INFO, 0,
$ UPLO, N, N, -1, -1, -1, IMAT,
$ NFAIL, NERRS, NOUT )
*
* Compute the test ratio to compare to values of RCOND
*
RESULT( 7 ) = DGET06( RCOND, RCONDC )
*
* Print information about the tests that did not pass
* the threshold.
*
IF( RESULT( 7 ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9997 )UPLO, N, IMAT, 7,
$ RESULT( 7 )
NFAIL = NFAIL + 1
END IF
NRUN = NRUN + 1
240 CONTINUE
*
250 CONTINUE
260 CONTINUE
270 CONTINUE
*
* Print a summary of the results.
*
CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
*
9999 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', NB =', I4, ', type ',
$ I2, ', test ', I2, ', ratio =', G12.5 )
9998 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', NRHS=', I3, ', type ',
$ I2, ', test(', I2, ') =', G12.5 )
9997 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ',', 10X, ' type ', I2,
$ ', test(', I2, ') =', G12.5 )
RETURN
*
* End of DCHKSY_ROOK
*
END
|
