summaryrefslogtreecommitdiff
path: root/TESTING/EIG/schksb2stg.f
blob: 637a018829244909bd35ef052d0f22f79048ae78 (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
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
*> \brief \b SCHKSBSTG
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE SCHKSB2STG( NSIZES, NN, NWDTHS, KK, NTYPES, DOTYPE,
*                          ISEED, THRESH, NOUNIT, A, LDA, SD, SE, D1,
*                          D2, D3, U, LDU, WORK, LWORK, RESULT, INFO )
*
*       .. Scalar Arguments ..
*       INTEGER            INFO, LDA, LDU, LWORK, NOUNIT, NSIZES, NTYPES,
*      $                   NWDTHS
*       REAL               THRESH
*       ..
*       .. Array Arguments ..
*       LOGICAL            DOTYPE( * )
*       INTEGER            ISEED( 4 ), KK( * ), NN( * )
*       REAL               A( LDA, * ), RESULT( * ), SD( * ), SE( * ),
*      $                   U( LDU, * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> SCHKSBSTG tests the reduction of a symmetric band matrix to tridiagonal
*> form, used with the symmetric eigenvalue problem.
*>
*> SSBTRD factors a symmetric band matrix A as  U S U' , where ' means
*> transpose, S is symmetric tridiagonal, and U is orthogonal.
*> SSBTRD can use either just the lower or just the upper triangle
*> of A; SCHKSBSTG checks both cases.
*>
*> SSYTRD_SB2ST factors a symmetric band matrix A as  U S U' , 
*> where ' means transpose, S is symmetric tridiagonal, and U is
*> orthogonal. SSYTRD_SB2ST can use either just the lower or just
*> the upper triangle of A; SCHKSBSTG checks both cases.
*>
*> SSTEQR factors S as  Z D1 Z'.  
*> D1 is the matrix of eigenvalues computed when Z is not computed
*> and from the S resulting of SSBTRD "U" (used as reference for SSYTRD_SB2ST)
*> D2 is the matrix of eigenvalues computed when Z is not computed
*> and from the S resulting of SSYTRD_SB2ST "U".
*> D3 is the matrix of eigenvalues computed when Z is not computed
*> and from the S resulting of SSYTRD_SB2ST "L".
*>
*> When SCHKSBSTG is called, a number of matrix "sizes" ("n's"), a number
*> of bandwidths ("k's"), and a number of matrix "types" are
*> specified.  For each size ("n"), each bandwidth ("k") less than or
*> equal to "n", and each type of matrix, one matrix will be generated
*> and used to test the symmetric banded reduction routine.  For each
*> matrix, a number of tests will be performed:
*>
*> (1)     | A - V S V' | / ( |A| n ulp )  computed by SSBTRD with
*>                                         UPLO='U'
*>
*> (2)     | I - UU' | / ( n ulp )
*>
*> (3)     | A - V S V' | / ( |A| n ulp )  computed by SSBTRD with
*>                                         UPLO='L'
*>
*> (4)     | I - UU' | / ( n ulp )
*>
*> (5)     | D1 - D2 | / ( |D1| ulp )      where D1 is computed by
*>                                         SSBTRD with UPLO='U' and
*>                                         D2 is computed by
*>                                         SSYTRD_SB2ST with UPLO='U'
*>
*> (6)     | D1 - D3 | / ( |D1| ulp )      where D1 is computed by
*>                                         SSBTRD with UPLO='U' and
*>                                         D3 is computed by
*>                                         SSYTRD_SB2ST with UPLO='L'
*>
*> The "sizes" are specified by an array NN(1:NSIZES); the value of
*> each element NN(j) specifies one size.
*> The "types" are specified by a logical array DOTYPE( 1:NTYPES );
*> if DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
*> Currently, the list of possible types is:
*>
*> (1)  The zero matrix.
*> (2)  The identity matrix.
*>
*> (3)  A diagonal matrix with evenly spaced entries
*>      1, ..., ULP  and random signs.
*>      (ULP = (first number larger than 1) - 1 )
*> (4)  A diagonal matrix with geometrically spaced entries
*>      1, ..., ULP  and random signs.
*> (5)  A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
*>      and random signs.
*>
*> (6)  Same as (4), but multiplied by SQRT( overflow threshold )
*> (7)  Same as (4), but multiplied by SQRT( underflow threshold )
*>
*> (8)  A matrix of the form  U' D U, where U is orthogonal and
*>      D has evenly spaced entries 1, ..., ULP with random signs
*>      on the diagonal.
*>
*> (9)  A matrix of the form  U' D U, where U is orthogonal and
*>      D has geometrically spaced entries 1, ..., ULP with random
*>      signs on the diagonal.
*>
*> (10) A matrix of the form  U' D U, where U is orthogonal and
*>      D has "clustered" entries 1, ULP,..., ULP with random
*>      signs on the diagonal.
*>
*> (11) Same as (8), but multiplied by SQRT( overflow threshold )
*> (12) Same as (8), but multiplied by SQRT( underflow threshold )
*>
*> (13) Symmetric matrix with random entries chosen from (-1,1).
*> (14) Same as (13), but multiplied by SQRT( overflow threshold )
*> (15) Same as (13), but multiplied by SQRT( underflow threshold )
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] NSIZES
*> \verbatim
*>          NSIZES is INTEGER
*>          The number of sizes of matrices to use.  If it is zero,
*>          SCHKSBSTG does nothing.  It must be at least zero.
*> \endverbatim
*>
*> \param[in] NN
*> \verbatim
*>          NN is INTEGER array, dimension (NSIZES)
*>          An array containing the sizes to be used for the matrices.
*>          Zero values will be skipped.  The values must be at least
*>          zero.
*> \endverbatim
*>
*> \param[in] NWDTHS
*> \verbatim
*>          NWDTHS is INTEGER
*>          The number of bandwidths to use.  If it is zero,
*>          SCHKSBSTG does nothing.  It must be at least zero.
*> \endverbatim
*>
*> \param[in] KK
*> \verbatim
*>          KK is INTEGER array, dimension (NWDTHS)
*>          An array containing the bandwidths to be used for the band
*>          matrices.  The values must be at least zero.
*> \endverbatim
*>
*> \param[in] NTYPES
*> \verbatim
*>          NTYPES is INTEGER
*>          The number of elements in DOTYPE.   If it is zero, SCHKSBSTG
*>          does nothing.  It must be at least zero.  If it is MAXTYP+1
*>          and NSIZES is 1, then an additional type, MAXTYP+1 is
*>          defined, which is to use whatever matrix is in A.  This
*>          is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
*>          DOTYPE(MAXTYP+1) is .TRUE. .
*> \endverbatim
*>
*> \param[in] DOTYPE
*> \verbatim
*>          DOTYPE is LOGICAL array, dimension (NTYPES)
*>          If DOTYPE(j) is .TRUE., then for each size in NN a
*>          matrix of that size and of type j will be generated.
*>          If NTYPES is smaller than the maximum number of types
*>          defined (PARAMETER MAXTYP), then types NTYPES+1 through
*>          MAXTYP will not be generated.  If NTYPES is larger
*>          than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
*>          will be ignored.
*> \endverbatim
*>
*> \param[in,out] ISEED
*> \verbatim
*>          ISEED is INTEGER array, dimension (4)
*>          On entry ISEED specifies the seed of the random number
*>          generator. The array elements should be between 0 and 4095;
*>          if not they will be reduced mod 4096.  Also, ISEED(4) must
*>          be odd.  The random number generator uses a linear
*>          congruential sequence limited to small integers, and so
*>          should produce machine independent random numbers. The
*>          values of ISEED are changed on exit, and can be used in the
*>          next call to SCHKSBSTG to continue the same random number
*>          sequence.
*> \endverbatim
*>
*> \param[in] THRESH
*> \verbatim
*>          THRESH is REAL
*>          A test will count as "failed" if the "error", computed as
*>          described above, exceeds THRESH.  Note that the error
*>          is scaled to be O(1), so THRESH should be a reasonably
*>          small multiple of 1, e.g., 10 or 100.  In particular,
*>          it should not depend on the precision (single vs. double)
*>          or the size of the matrix.  It must be at least zero.
*> \endverbatim
*>
*> \param[in] NOUNIT
*> \verbatim
*>          NOUNIT is INTEGER
*>          The FORTRAN unit number for printing out error messages
*>          (e.g., if a routine returns IINFO not equal to 0.)
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          A is REAL array, dimension
*>                            (LDA, max(NN))
*>          Used to hold the matrix whose eigenvalues are to be
*>          computed.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of A.  It must be at least 2 (not 1!)
*>          and at least max( KK )+1.
*> \endverbatim
*>
*> \param[out] SD
*> \verbatim
*>          SD is REAL array, dimension (max(NN))
*>          Used to hold the diagonal of the tridiagonal matrix computed
*>          by SSBTRD.
*> \endverbatim
*>
*> \param[out] SE
*> \verbatim
*>          SE is REAL array, dimension (max(NN))
*>          Used to hold the off-diagonal of the tridiagonal matrix
*>          computed by SSBTRD.
*> \endverbatim
*>
*> \param[out] U
*> \verbatim
*>          U is REAL array, dimension (LDU, max(NN))
*>          Used to hold the orthogonal matrix computed by SSBTRD.
*> \endverbatim
*>
*> \param[in] LDU
*> \verbatim
*>          LDU is INTEGER
*>          The leading dimension of U.  It must be at least 1
*>          and at least max( NN ).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is REAL array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*>          LWORK is INTEGER
*>          The number of entries in WORK.  This must be at least
*>          max( LDA+1, max(NN)+1 )*max(NN).
*> \endverbatim
*>
*> \param[out] RESULT
*> \verbatim
*>          RESULT is REAL array, dimension (4)
*>          The values computed by the tests described above.
*>          The values are currently limited to 1/ulp, to avoid
*>          overflow.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          If 0, then everything ran OK.
*>
*>-----------------------------------------------------------------------
*>
*>       Some Local Variables and Parameters:
*>       ---- ----- --------- --- ----------
*>       ZERO, ONE       Real 0 and 1.
*>       MAXTYP          The number of types defined.
*>       NTEST           The number of tests performed, or which can
*>                       be performed so far, for the current matrix.
*>       NTESTT          The total number of tests performed so far.
*>       NMAX            Largest value in NN.
*>       NMATS           The number of matrices generated so far.
*>       NERRS           The number of tests which have exceeded THRESH
*>                       so far.
*>       COND, IMODE     Values to be passed to the matrix generators.
*>       ANORM           Norm of A; passed to matrix generators.
*>
*>       OVFL, UNFL      Overflow and underflow thresholds.
*>       ULP, ULPINV     Finest relative precision and its inverse.
*>       RTOVFL, RTUNFL  Square roots of the previous 2 values.
*>               The following four arrays decode JTYPE:
*>       KTYPE(j)        The general type (1-10) for type "j".
*>       KMODE(j)        The MODE value to be passed to the matrix
*>                       generator for type "j".
*>       KMAGN(j)        The order of magnitude ( O(1),
*>                       O(overflow^(1/2) ), O(underflow^(1/2) )
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup single_eig
*
*  =====================================================================
      SUBROUTINE SCHKSB2STG( NSIZES, NN, NWDTHS, KK, NTYPES, DOTYPE,
     $                   ISEED, THRESH, NOUNIT, A, LDA, SD, SE, D1,
     $                   D2, D3, U, LDU, WORK, LWORK, RESULT, INFO )
*
*  -- 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 ..
      INTEGER            INFO, LDA, LDU, LWORK, NOUNIT, NSIZES, NTYPES,
     $                   NWDTHS
      REAL               THRESH
*     ..
*     .. Array Arguments ..
      LOGICAL            DOTYPE( * )
      INTEGER            ISEED( 4 ), KK( * ), NN( * )
      REAL               A( LDA, * ), RESULT( * ), SD( * ), SE( * ),
     $                   D1( * ), D2( * ), D3( * ),
     $                   U( LDU, * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO, ONE, TWO, TEN
      PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0, TWO = 2.0E0,
     $                   TEN = 10.0E0 )
      REAL               HALF
      PARAMETER          ( HALF = ONE / TWO )
      INTEGER            MAXTYP
      PARAMETER          ( MAXTYP = 15 )
*     ..
*     .. Local Scalars ..
      LOGICAL            BADNN, BADNNB
      INTEGER            I, IINFO, IMODE, ITYPE, J, JC, JCOL, JR, JSIZE,
     $                   JTYPE, JWIDTH, K, KMAX, LH, LW, MTYPES, N,
     $                   NERRS, NMATS, NMAX, NTEST, NTESTT
      REAL               ANINV, ANORM, COND, OVFL, RTOVFL, RTUNFL,
     $                   TEMP1, TEMP2, TEMP3, TEMP4, ULP, ULPINV, UNFL
*     ..
*     .. Local Arrays ..
      INTEGER            IDUMMA( 1 ), IOLDSD( 4 ), KMAGN( MAXTYP ),
     $                   KMODE( MAXTYP ), KTYPE( MAXTYP )
*     ..
*     .. External Functions ..
      REAL               SLAMCH
      EXTERNAL           SLAMCH
*     ..
*     .. External Subroutines ..
      EXTERNAL           SLACPY, SLASET, SLASUM, SLATMR, SLATMS, SSBT21,
     $                   SSBTRD, XERBLA, SSYTRD_SB2ST, SSTEQR
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, REAL, MAX, MIN, SQRT
*     ..
*     .. Data statements ..
      DATA               KTYPE / 1, 2, 5*4, 5*5, 3*8 /
      DATA               KMAGN / 2*1, 1, 1, 1, 2, 3, 1, 1, 1, 2, 3, 1,
     $                   2, 3 /
      DATA               KMODE / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
     $                   0, 0 /
*     ..
*     .. Executable Statements ..
*
*     Check for errors
*
      NTESTT = 0
      INFO = 0
*
*     Important constants
*
      BADNN = .FALSE.
      NMAX = 1
      DO 10 J = 1, NSIZES
         NMAX = MAX( NMAX, NN( J ) )
         IF( NN( J ).LT.0 )
     $      BADNN = .TRUE.
   10 CONTINUE
*
      BADNNB = .FALSE.
      KMAX = 0
      DO 20 J = 1, NSIZES
         KMAX = MAX( KMAX, KK( J ) )
         IF( KK( J ).LT.0 )
     $      BADNNB = .TRUE.
   20 CONTINUE
      KMAX = MIN( NMAX-1, KMAX )
*
*     Check for errors
*
      IF( NSIZES.LT.0 ) THEN
         INFO = -1
      ELSE IF( BADNN ) THEN
         INFO = -2
      ELSE IF( NWDTHS.LT.0 ) THEN
         INFO = -3
      ELSE IF( BADNNB ) THEN
         INFO = -4
      ELSE IF( NTYPES.LT.0 ) THEN
         INFO = -5
      ELSE IF( LDA.LT.KMAX+1 ) THEN
         INFO = -11
      ELSE IF( LDU.LT.NMAX ) THEN
         INFO = -15
      ELSE IF( ( MAX( LDA, NMAX )+1 )*NMAX.GT.LWORK ) THEN
         INFO = -17
      END IF
*
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'SCHKSBSTG', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 .OR. NWDTHS.EQ.0 )
     $   RETURN
*
*     More Important constants
*
      UNFL = SLAMCH( 'Safe minimum' )
      OVFL = ONE / UNFL
      ULP = SLAMCH( 'Epsilon' )*SLAMCH( 'Base' )
      ULPINV = ONE / ULP
      RTUNFL = SQRT( UNFL )
      RTOVFL = SQRT( OVFL )
*
*     Loop over sizes, types
*
      NERRS = 0
      NMATS = 0
*
      DO 190 JSIZE = 1, NSIZES
         N = NN( JSIZE )
         ANINV = ONE / REAL( MAX( 1, N ) )
*
         DO 180 JWIDTH = 1, NWDTHS
            K = KK( JWIDTH )
            IF( K.GT.N )
     $         GO TO 180
            K = MAX( 0, MIN( N-1, K ) )
*
            IF( NSIZES.NE.1 ) THEN
               MTYPES = MIN( MAXTYP, NTYPES )
            ELSE
               MTYPES = MIN( MAXTYP+1, NTYPES )
            END IF
*
            DO 170 JTYPE = 1, MTYPES
               IF( .NOT.DOTYPE( JTYPE ) )
     $            GO TO 170
               NMATS = NMATS + 1
               NTEST = 0
*
               DO 30 J = 1, 4
                  IOLDSD( J ) = ISEED( J )
   30          CONTINUE
*
*              Compute "A".
*              Store as "Upper"; later, we will copy to other format.
*
*              Control parameters:
*
*                  KMAGN  KMODE        KTYPE
*              =1  O(1)   clustered 1  zero
*              =2  large  clustered 2  identity
*              =3  small  exponential  (none)
*              =4         arithmetic   diagonal, (w/ eigenvalues)
*              =5         random log   symmetric, w/ eigenvalues
*              =6         random       (none)
*              =7                      random diagonal
*              =8                      random symmetric
*              =9                      positive definite
*              =10                     diagonally dominant tridiagonal
*
               IF( MTYPES.GT.MAXTYP )
     $            GO TO 100
*
               ITYPE = KTYPE( JTYPE )
               IMODE = KMODE( JTYPE )
*
*              Compute norm
*
               GO TO ( 40, 50, 60 )KMAGN( JTYPE )
*
   40          CONTINUE
               ANORM = ONE
               GO TO 70
*
   50          CONTINUE
               ANORM = ( RTOVFL*ULP )*ANINV
               GO TO 70
*
   60          CONTINUE
               ANORM = RTUNFL*N*ULPINV
               GO TO 70
*
   70          CONTINUE
*
               CALL SLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA )
               IINFO = 0
               IF( JTYPE.LE.15 ) THEN
                  COND = ULPINV
               ELSE
                  COND = ULPINV*ANINV / TEN
               END IF
*
*              Special Matrices -- Identity & Jordan block
*
*                 Zero
*
               IF( ITYPE.EQ.1 ) THEN
                  IINFO = 0
*
               ELSE IF( ITYPE.EQ.2 ) THEN
*
*                 Identity
*
                  DO 80 JCOL = 1, N
                     A( K+1, JCOL ) = ANORM
   80             CONTINUE
*
               ELSE IF( ITYPE.EQ.4 ) THEN
*
*                 Diagonal Matrix, [Eigen]values Specified
*
                  CALL SLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
     $                         ANORM, 0, 0, 'Q', A( K+1, 1 ), LDA,
     $                         WORK( N+1 ), IINFO )
*
               ELSE IF( ITYPE.EQ.5 ) THEN
*
*                 Symmetric, eigenvalues specified
*
                  CALL SLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
     $                         ANORM, K, K, 'Q', A, LDA, WORK( N+1 ),
     $                         IINFO )
*
               ELSE IF( ITYPE.EQ.7 ) THEN
*
*                 Diagonal, random eigenvalues
*
                  CALL SLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE,
     $                         'T', 'N', WORK( N+1 ), 1, ONE,
     $                         WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, 0, 0,
     $                         ZERO, ANORM, 'Q', A( K+1, 1 ), LDA,
     $                         IDUMMA, IINFO )
*
               ELSE IF( ITYPE.EQ.8 ) THEN
*
*                 Symmetric, random eigenvalues
*
                  CALL SLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE,
     $                         'T', 'N', WORK( N+1 ), 1, ONE,
     $                         WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, K, K,
     $                         ZERO, ANORM, 'Q', A, LDA, IDUMMA, IINFO )
*
               ELSE IF( ITYPE.EQ.9 ) THEN
*
*                 Positive definite, eigenvalues specified.
*
                  CALL SLATMS( N, N, 'S', ISEED, 'P', WORK, IMODE, COND,
     $                         ANORM, K, K, 'Q', A, LDA, WORK( N+1 ),
     $                         IINFO )
*
               ELSE IF( ITYPE.EQ.10 ) THEN
*
*                 Positive definite tridiagonal, eigenvalues specified.
*
                  IF( N.GT.1 )
     $               K = MAX( 1, K )
                  CALL SLATMS( N, N, 'S', ISEED, 'P', WORK, IMODE, COND,
     $                         ANORM, 1, 1, 'Q', A( K, 1 ), LDA,
     $                         WORK( N+1 ), IINFO )
                  DO 90 I = 2, N
                     TEMP1 = ABS( A( K, I ) ) /
     $                       SQRT( ABS( A( K+1, I-1 )*A( K+1, I ) ) )
                     IF( TEMP1.GT.HALF ) THEN
                        A( K, I ) = HALF*SQRT( ABS( A( K+1,
     $                              I-1 )*A( K+1, I ) ) )
                     END IF
   90             CONTINUE
*
               ELSE
*
                  IINFO = 1
               END IF
*
               IF( IINFO.NE.0 ) THEN
                  WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N,
     $               JTYPE, IOLDSD
                  INFO = ABS( IINFO )
                  RETURN
               END IF
*
  100          CONTINUE
*
*              Call SSBTRD to compute S and U from upper triangle.
*
               CALL SLACPY( ' ', K+1, N, A, LDA, WORK, LDA )
*
               NTEST = 1
               CALL SSBTRD( 'V', 'U', N, K, WORK, LDA, SD, SE, U, LDU,
     $                      WORK( LDA*N+1 ), IINFO )
*
               IF( IINFO.NE.0 ) THEN
                  WRITE( NOUNIT, FMT = 9999 )'SSBTRD(U)', IINFO, N,
     $               JTYPE, IOLDSD
                  INFO = ABS( IINFO )
                  IF( IINFO.LT.0 ) THEN
                     RETURN
                  ELSE
                     RESULT( 1 ) = ULPINV
                     GO TO 150
                  END IF
               END IF
*
*              Do tests 1 and 2
*
               CALL SSBT21( 'Upper', N, K, 1, A, LDA, SD, SE, U, LDU,
     $                      WORK, RESULT( 1 ) )
*
*              Before converting A into lower for SSBTRD, run SSYTRD_SB2ST 
*              otherwise matrix A will be converted to lower and then need
*              to be converted back to upper in order to run the upper case 
*              ofSSYTRD_SB2ST
*            
*              Compute D1 the eigenvalues resulting from the tridiagonal
*              form using the SSBTRD and used as reference to compare
*              with the SSYTRD_SB2ST routine
*            
*              Compute D1 from the SSBTRD and used as reference for the
*              SSYTRD_SB2ST
*            
               CALL SCOPY( N, SD, 1, D1, 1 )
               IF( N.GT.0 )
     $            CALL SCOPY( N-1, SE, 1, WORK, 1 )
*            
               CALL SSTEQR( 'N', N, D1, WORK, WORK( N+1 ), LDU,
     $                      WORK( N+1 ), IINFO )
               IF( IINFO.NE.0 ) THEN
                  WRITE( NOUNIT, FMT = 9999 )'SSTEQR(N)', IINFO, N,
     $               JTYPE, IOLDSD
                  INFO = ABS( IINFO )
                  IF( IINFO.LT.0 ) THEN
                     RETURN
                  ELSE
                     RESULT( 5 ) = ULPINV
                     GO TO 150
                  END IF
               END IF
*            
*              SSYTRD_SB2ST Upper case is used to compute D2.
*              Note to set SD and SE to zero to be sure not reusing 
*              the one from above. Compare it with D1 computed 
*              using the SSBTRD.
*            
               CALL SLASET( 'Full', N, 1, ZERO, ZERO, SD, 1 )
               CALL SLASET( 'Full', N, 1, ZERO, ZERO, SE, 1 )
               CALL SLACPY( ' ', K+1, N, A, LDA, U, LDU )
               LH = MAX(1, 4*N)
               LW = LWORK - LH
               CALL SSYTRD_SB2ST( 'N', 'N', "U", N, K, U, LDU, SD, SE, 
     $                      WORK, LH, WORK( LH+1 ), LW, IINFO )
*            
*              Compute D2 from the SSYTRD_SB2ST Upper case
*            
               CALL SCOPY( N, SD, 1, D2, 1 )
               IF( N.GT.0 )
     $            CALL SCOPY( N-1, SE, 1, WORK, 1 )
*            
               CALL SSTEQR( 'N', N, D2, WORK, WORK( N+1 ), LDU,
     $                      WORK( N+1 ), IINFO )
               IF( IINFO.NE.0 ) THEN
                  WRITE( NOUNIT, FMT = 9999 )'SSTEQR(N)', IINFO, N,
     $               JTYPE, IOLDSD
                  INFO = ABS( IINFO )
                  IF( IINFO.LT.0 ) THEN
                     RETURN
                  ELSE
                     RESULT( 5 ) = ULPINV
                     GO TO 150
                  END IF
               END IF
*
*              Convert A from Upper-Triangle-Only storage to
*              Lower-Triangle-Only storage.
*
               DO 120 JC = 1, N
                  DO 110 JR = 0, MIN( K, N-JC )
                     A( JR+1, JC ) = A( K+1-JR, JC+JR )
  110             CONTINUE
  120          CONTINUE
               DO 140 JC = N + 1 - K, N
                  DO 130 JR = MIN( K, N-JC ) + 1, K
                     A( JR+1, JC ) = ZERO
  130             CONTINUE
  140          CONTINUE
*
*              Call SSBTRD to compute S and U from lower triangle
*
               CALL SLACPY( ' ', K+1, N, A, LDA, WORK, LDA )
*
               NTEST = 3
               CALL SSBTRD( 'V', 'L', N, K, WORK, LDA, SD, SE, U, LDU,
     $                      WORK( LDA*N+1 ), IINFO )
*
               IF( IINFO.NE.0 ) THEN
                  WRITE( NOUNIT, FMT = 9999 )'SSBTRD(L)', IINFO, N,
     $               JTYPE, IOLDSD
                  INFO = ABS( IINFO )
                  IF( IINFO.LT.0 ) THEN
                     RETURN
                  ELSE
                     RESULT( 3 ) = ULPINV
                     GO TO 150
                  END IF
               END IF
               NTEST = 4
*
*              Do tests 3 and 4
*
               CALL SSBT21( 'Lower', N, K, 1, A, LDA, SD, SE, U, LDU,
     $                      WORK, RESULT( 3 ) )
*
*              SSYTRD_SB2ST Lower case is used to compute D3.
*              Note to set SD and SE to zero to be sure not reusing 
*              the one from above. Compare it with D1 computed 
*              using the SSBTRD. 
*           
               CALL SLASET( 'Full', N, 1, ZERO, ZERO, SD, 1 )
               CALL SLASET( 'Full', N, 1, ZERO, ZERO, SE, 1 )
               CALL SLACPY( ' ', K+1, N, A, LDA, U, LDU )
               LH = MAX(1, 4*N)
               LW = LWORK - LH
               CALL SSYTRD_SB2ST( 'N', 'N', "L", N, K, U, LDU, SD, SE, 
     $                      WORK, LH, WORK( LH+1 ), LW, IINFO )
*           
*              Compute D3 from the 2-stage Upper case
*           
               CALL SCOPY( N, SD, 1, D3, 1 )
               IF( N.GT.0 )
     $            CALL SCOPY( N-1, SE, 1, WORK, 1 )
*           
               CALL SSTEQR( 'N', N, D3, WORK, WORK( N+1 ), LDU,
     $                      WORK( N+1 ), IINFO )
               IF( IINFO.NE.0 ) THEN
                  WRITE( NOUNIT, FMT = 9999 )'SSTEQR(N)', IINFO, N,
     $               JTYPE, IOLDSD
                  INFO = ABS( IINFO )
                  IF( IINFO.LT.0 ) THEN
                     RETURN
                  ELSE
                     RESULT( 6 ) = ULPINV
                     GO TO 150
                  END IF
               END IF
*           
*           
*              Do Tests 3 and 4 which are similar to 11 and 12 but with the
*              D1 computed using the standard 1-stage reduction as reference
*           
               NTEST = 6
               TEMP1 = ZERO
               TEMP2 = ZERO
               TEMP3 = ZERO
               TEMP4 = ZERO
*           
               DO 151 J = 1, N
                  TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D2( J ) ) )
                  TEMP2 = MAX( TEMP2, ABS( D1( J )-D2( J ) ) )
                  TEMP3 = MAX( TEMP3, ABS( D1( J ) ), ABS( D3( J ) ) )
                  TEMP4 = MAX( TEMP4, ABS( D1( J )-D3( J ) ) )
  151          CONTINUE
*           
               RESULT(5) = TEMP2 / MAX( UNFL, ULP*MAX( TEMP1, TEMP2 ) )
               RESULT(6) = TEMP4 / MAX( UNFL, ULP*MAX( TEMP3, TEMP4 ) )
*
*              End of Loop -- Check for RESULT(j) > THRESH
*
  150          CONTINUE
               NTESTT = NTESTT + NTEST
*
*              Print out tests which fail.
*
               DO 160 JR = 1, NTEST
                  IF( RESULT( JR ).GE.THRESH ) THEN
*
*                    If this is the first test to fail,
*                    print a header to the data file.
*
                     IF( NERRS.EQ.0 ) THEN
                        WRITE( NOUNIT, FMT = 9998 )'SSB'
                        WRITE( NOUNIT, FMT = 9997 )
                        WRITE( NOUNIT, FMT = 9996 )
                        WRITE( NOUNIT, FMT = 9995 )'Symmetric'
                        WRITE( NOUNIT, FMT = 9994 )'orthogonal', '''',
     $                     'transpose', ( '''', J = 1, 6 )
                     END IF
                     NERRS = NERRS + 1
                     WRITE( NOUNIT, FMT = 9993 )N, K, IOLDSD, JTYPE,
     $                  JR, RESULT( JR )
                  END IF
  160          CONTINUE
*
  170       CONTINUE
  180    CONTINUE
  190 CONTINUE
*
*     Summary
*
      CALL SLASUM( 'SSB', NOUNIT, NERRS, NTESTT )
      RETURN
*
 9999 FORMAT( ' SCHKSBSTG: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
     $      I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
*
 9998 FORMAT( / 1X, A3,
     $      ' -- Real Symmetric Banded Tridiagonal Reduction Routines' )
 9997 FORMAT( ' Matrix types (see SCHKSBSTG for details): ' )
*
 9996 FORMAT( / ' Special Matrices:',
     $      / '  1=Zero matrix.                        ',
     $      '  5=Diagonal: clustered entries.',
     $      / '  2=Identity matrix.                    ',
     $      '  6=Diagonal: large, evenly spaced.',
     $      / '  3=Diagonal: evenly spaced entries.    ',
     $      '  7=Diagonal: small, evenly spaced.',
     $      / '  4=Diagonal: geometr. spaced entries.' )
 9995 FORMAT( ' Dense ', A, ' Banded Matrices:',
     $      / '  8=Evenly spaced eigenvals.            ',
     $      ' 12=Small, evenly spaced eigenvals.',
     $      / '  9=Geometrically spaced eigenvals.     ',
     $      ' 13=Matrix with random O(1) entries.',
     $      / ' 10=Clustered eigenvalues.              ',
     $      ' 14=Matrix with large random entries.',
     $      / ' 11=Large, evenly spaced eigenvals.     ',
     $      ' 15=Matrix with small random entries.' )
*
 9994 FORMAT( / ' Tests performed:   (S is Tridiag,  U is ', A, ',',
     $      / 20X, A, ' means ', A, '.', / ' UPLO=''U'':',
     $      / '  1= | A - U S U', A1, ' | / ( |A| n ulp )     ',
     $      '  2= | I - U U', A1, ' | / ( n ulp )', / ' UPLO=''L'':',
     $      / '  3= | A - U S U', A1, ' | / ( |A| n ulp )     ',
     $      '  4= | I - U U', A1, ' | / ( n ulp )' / ' Eig check:',
     $      /'  5= | D1 - D2', '', ' | / ( |D1| ulp )         ',
     $      '  6= | D1 - D3', '', ' | / ( |D1| ulp )          ' )
 9993 FORMAT( ' N=', I5, ', K=', I4, ', seed=', 4( I4, ',' ), ' type ',
     $      I2, ', test(', I2, ')=', G10.3 )
*
*     End of SCHKSBSTG
*
      END