-
Notifications
You must be signed in to change notification settings - Fork 18
/
Copy pathdstebz_dev.f90
788 lines (785 loc) · 24.2 KB
/
dstebz_dev.f90
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
!> \brief \b DSTEBZ
!
! =========== DOCUMENTATION ===========
!
! Online html documentation available at
! http://www.netlib.org/lapack/explore-html/
!
!> \htmlonly
!> Download DSTEBZ + dependencies
!> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dstebz.f">
!> [TGZ]</a>
!> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dstebz.f">
!> [ZIP]</a>
!> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dstebz.f">
!> [TXT]</a>
!> \endhtmlonly
!
! Definition:
! ===========
!
! SUBROUTINE DSTEBZ( RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL, D, E,
! M, NSPLIT, W, IBLOCK, ISPLIT, WORK, IWORK,
! INFO )
!
! .. Scalar Arguments ..
! CHARACTER ORDER, RANGE
! INTEGER IL, INFO, IU, M, N, NSPLIT
! DOUBLE PRECISION ABSTOL, VL, VU
! ..
! .. Array Arguments ..
! INTEGER IBLOCK( * ), ISPLIT( * ), IWORK( * )
! DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * )
! ..
!
!
!> \par Purpose:
! =============
!>
!> \verbatim
!>
!> DSTEBZ computes the eigenvalues of a symmetric tridiagonal
!> matrix T. The user may ask for all eigenvalues, all eigenvalues
!> in the half-open interval (VL, VU], or the IL-th through IU-th
!> eigenvalues.
!>
!> To avoid overflow, the matrix must be scaled so that its
!> largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value, and for greatest
!> accuracy, it should not be much smaller than that.
!>
!> See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal
!> Matrix", Report CS41, Computer Science Dept., Stanford
!> University, July 21, 1966.
!> \endverbatim
!
! Arguments:
! ==========
!
!> \param[in] RANGE
!> \verbatim
!> RANGE is CHARACTER*1
!> = 'A': ("All") all eigenvalues will be found.
!> = 'V': ("Value") all eigenvalues in the half-open interval
!> (VL, VU] will be found.
!> = 'I': ("Index") the IL-th through IU-th eigenvalues (of the
!> entire matrix) will be found.
!> \endverbatim
!>
!> \param[in] ORDER
!> \verbatim
!> ORDER is CHARACTER*1
!> = 'B': ("By Block") the eigenvalues will be grouped by
!> split-off block (see IBLOCK, ISPLIT) and
!> ordered from smallest to largest within
!> the block.
!> = 'E': ("Entire matrix")
!> the eigenvalues for the entire matrix
!> will be ordered from smallest to
!> largest.
!> \endverbatim
!>
!> \param[in] N
!> \verbatim
!> N is INTEGER
!> The order of the tridiagonal matrix T. N >= 0.
!> \endverbatim
!>
!> \param[in] VL
!> \verbatim
!> VL is DOUBLE PRECISION
!>
!> If RANGE='V', the lower bound of the interval to
!> be searched for eigenvalues. Eigenvalues less than or equal
!> to VL, or greater than VU, will not be returned. VL < VU.
!> Not referenced if RANGE = 'A' or 'I'.
!> \endverbatim
!>
!> \param[in] VU
!> \verbatim
!> VU is DOUBLE PRECISION
!>
!> If RANGE='V', the upper bound of the interval to
!> be searched for eigenvalues. Eigenvalues less than or equal
!> to VL, or greater than VU, will not be returned. VL < VU.
!> Not referenced if RANGE = 'A' or 'I'.
!> \endverbatim
!>
!> \param[in] IL
!> \verbatim
!> IL is INTEGER
!>
!> If RANGE='I', the index of the
!> smallest eigenvalue to be returned.
!> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
!> Not referenced if RANGE = 'A' or 'V'.
!> \endverbatim
!>
!> \param[in] IU
!> \verbatim
!> IU is INTEGER
!>
!> If RANGE='I', the index of the
!> largest eigenvalue to be returned.
!> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
!> Not referenced if RANGE = 'A' or 'V'.
!> \endverbatim
!>
!> \param[in] ABSTOL
!> \verbatim
!> ABSTOL is DOUBLE PRECISION
!> The absolute tolerance for the eigenvalues. An eigenvalue
!> (or cluster) is considered to be located if it has been
!> determined to lie in an interval whose width is ABSTOL or
!> less. If ABSTOL is less than or equal to zero, then ULP*|T|
!> will be used, where |T| means the 1-norm of T.
!>
!> Eigenvalues will be computed most accurately when ABSTOL is
!> set to twice the underflow threshold 2*DLAMCH('S'), not zero.
!> \endverbatim
!>
!> \param[in] D
!> \verbatim
!> D is DOUBLE PRECISION array, dimension (N)
!> The n diagonal elements of the tridiagonal matrix T.
!> \endverbatim
!>
!> \param[in] E
!> \verbatim
!> E is DOUBLE PRECISION array, dimension (N-1)
!> The (n-1) off-diagonal elements of the tridiagonal matrix T.
!> \endverbatim
!>
!> \param[out] M
!> \verbatim
!> M is INTEGER
!> The actual number of eigenvalues found. 0 <= M <= N.
!> (See also the description of INFO=2,3.)
!> \endverbatim
!>
!> \param[out] NSPLIT
!> \verbatim
!> NSPLIT is INTEGER
!> The number of diagonal blocks in the matrix T.
!> 1 <= NSPLIT <= N.
!> \endverbatim
!>
!> \param[out] W
!> \verbatim
!> W is DOUBLE PRECISION array, dimension (N)
!> On exit, the first M elements of W will contain the
!> eigenvalues. (DSTEBZ may use the remaining N-M elements as
!> workspace.)
!> \endverbatim
!>
!> \param[out] IBLOCK
!> \verbatim
!> IBLOCK is INTEGER array, dimension (N)
!> At each row/column j where E(j) is zero or small, the
!> matrix T is considered to split into a block diagonal
!> matrix. On exit, if INFO = 0, IBLOCK(i) specifies to which
!> block (from 1 to the number of blocks) the eigenvalue W(i)
!> belongs. (DSTEBZ may use the remaining N-M elements as
!> workspace.)
!> \endverbatim
!>
!> \param[out] ISPLIT
!> \verbatim
!> ISPLIT is INTEGER array, dimension (N)
!> The splitting points, at which T breaks up into submatrices.
!> The first submatrix consists of rows/columns 1 to ISPLIT(1),
!> the second of rows/columns ISPLIT(1)+1 through ISPLIT(2),
!> etc., and the NSPLIT-th consists of rows/columns
!> ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N.
!> (Only the first NSPLIT elements will actually be used, but
!> since the user cannot know a priori what value NSPLIT will
!> have, N words must be reserved for ISPLIT.)
!> \endverbatim
!>
!> \param[out] WORK
!> \verbatim
!> WORK is DOUBLE PRECISION array, dimension (4*N)
!> \endverbatim
!>
!> \param[out] IWORK
!> \verbatim
!> IWORK is INTEGER array, dimension (3*N)
!> \endverbatim
!>
!> \param[out] INFO
!> \verbatim
!> INFO is INTEGER
!> = 0: successful exit
!> < 0: if INFO = -i, the i-th argument had an illegal value
!> > 0: some or all of the eigenvalues failed to converge or
!> were not computed:
!> =1 or 3: Bisection failed to converge for some
!> eigenvalues; these eigenvalues are flagged by a
!> negative block number. The effect is that the
!> eigenvalues may not be as accurate as the
!> absolute and relative tolerances. This is
!> generally caused by unexpectedly inaccurate
!> arithmetic.
!> =2 or 3: RANGE='I' only: Not all of the eigenvalues
!> IL:IU were found.
!> Effect: M < IU+1-IL
!> Cause: non-monotonic arithmetic, causing the
!> Sturm sequence to be non-monotonic.
!> Cure: recalculate, using RANGE='A', and pick
!> out eigenvalues IL:IU. In some cases,
!> increasing the PARAMETER "FUDGE" may
!> make things work.
!> = 4: RANGE='I', and the Gershgorin interval
!> initially used was too small. No eigenvalues
!> were computed.
!> Probable cause: your machine has sloppy
!> floating-point arithmetic.
!> Cure: Increase the PARAMETER "FUDGE",
!> recompile, and try again.
!> \endverbatim
!
!> \par Internal Parameters:
! =========================
!>
!> \verbatim
!> RELFAC DOUBLE PRECISION, default = 2.0e0
!> The relative tolerance. An interval (a,b] lies within
!> "relative tolerance" if b-a < RELFAC*ulp*max(|a|,|b|),
!> where "ulp" is the machine precision (distance from 1 to
!> the next larger floating point number.)
!>
!> FUDGE DOUBLE PRECISION, default = 2
!> A "fudge factor" to widen the Gershgorin intervals. Ideally,
!> a value of 1 should work, but on machines with sloppy
!> arithmetic, this needs to be larger. The default for
!> publicly released versions should be large enough to handle
!> the worst machine around. Note that this has no effect
!> on accuracy of the solution.
!> \endverbatim
!
! Authors:
! ========
!
!> \author Univ. of Tennessee
!> \author Univ. of California Berkeley
!> \author Univ. of Colorado Denver
!> \author NAG Ltd.
!
!> \ingroup auxOTHERcomputational
!
! =====================================================================
#if defined(__CUDA)
ATTRIBUTES(DEVICE) SUBROUTINE DSTEBZ_XG( RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL, D, E, &
M, NSPLIT, W, IBLOCK, ISPLIT, WORK, IWORK, &
INFO )
#else
SUBROUTINE DSTEBZ_XG( RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL, D, E, &
M, NSPLIT, W, IBLOCK, ISPLIT, WORK, IWORK, &
INFO )
#endif
#include<lsame_interf.f90>
#include<dlamch_interf.f90>
#include<ilaenv_interf.f90>
#include<dlaebz_interf.f90>
#include<xerbla_interf.f90>
!
! -- LAPACK computational routine --
! -- LAPACK is a software package provided by Univ. of Tennessee, --
! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
!
! .. Scalar Arguments ..
CHARACTER ORDER, RANGE
INTEGER IL, INFO, IU, M, N, NSPLIT
DOUBLE PRECISION ABSTOL, VL, VU
! ..
! .. Array Arguments ..
INTEGER IBLOCK( * ), ISPLIT( * ), IWORK( * )
DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * )
! ..
!
! =====================================================================
!
! .. Parameters ..
DOUBLE PRECISION ZERO, ONE, TWO, HALF
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0, &
HALF = 1.0D0 / TWO )
DOUBLE PRECISION FUDGE, RELFAC
PARAMETER ( FUDGE = 2.1D0, RELFAC = 2.0D0 )
! ..
! .. Local Scalars ..
LOGICAL NCNVRG, TOOFEW
INTEGER IB, IBEGIN, IDISCL, IDISCU, IE, IEND, IINFO, &
IM, IN, IOFF, IORDER, IOUT, IRANGE, ITMAX, &
ITMP1, IW, IWOFF, J, JB, JDISC, JE, NB, NWL, &
NWU
DOUBLE PRECISION ATOLI, BNORM, GL, GU, PIVMIN, RTOLI, SAFEMN, &
TMP1, TMP2, TNORM, ULP, WKILL, WL, WLU, WU, WUL
! ..
! .. Local Arrays ..
INTEGER IDUMMA( 1 )
! ..
! .. External Functions ..
! LOGICAL LSAME
! INTEGER ILAENV
! DOUBLE PRECISION DLAMCH
! EXTERNAL LSAME, ILAENV, DLAMCH
! ..
! .. External Subroutines ..
! EXTERNAL DLAEBZ, XERBLA
! ..
! .. Intrinsic Functions ..
INTRINSIC ABS, INT, LOG, MAX, MIN, SQRT
#if defined(__CUDA)
ATTRIBUTES(VALUE) :: RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL
ATTRIBUTES(DEVICE) :: IBLOCK, ISPLIT, IWORK, D, E, W, WORK, M, INFO, NSPLIT
#endif
! ..
! .. Executable Statements ..
!
INFO = 0
!
! Decode RANGE
!
IF( LSAME_XG( RANGE, 'A' ) ) THEN
IRANGE = 1
ELSE IF( LSAME_XG( RANGE, 'V' ) ) THEN
IRANGE = 2
ELSE IF( LSAME_XG( RANGE, 'I' ) ) THEN
IRANGE = 3
ELSE
IRANGE = 0
END IF
!
! Decode ORDER
!
IF( LSAME_XG( ORDER, 'B' ) ) THEN
IORDER = 2
ELSE IF( LSAME_XG( ORDER, 'E' ) ) THEN
IORDER = 1
ELSE
IORDER = 0
END IF
!
! Check for Errors
!
IF( IRANGE.LE.0 ) THEN
INFO = -1
ELSE IF( IORDER.LE.0 ) THEN
INFO = -2
ELSE IF( N.LT.0 ) THEN
INFO = -3
ELSE IF( IRANGE.EQ.2 ) THEN
IF( VL.GE.VU ) &
INFO = -5
ELSE IF( IRANGE.EQ.3 .AND. ( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) ) &
THEN
INFO = -6
ELSE IF( IRANGE.EQ.3 .AND. ( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) ) &
THEN
INFO = -7
END IF
!
IF( INFO.NE.0 ) THEN
! CALL XERBLA( 'DSTEBZ', -INFO )
CALL XERBLA_XG( '#', -INFO )
RETURN
END IF
!
! Initialize error flags
!
INFO = 0
NCNVRG = .FALSE.
TOOFEW = .FALSE.
!
! Quick return if possible
!
M = 0
IF( N.EQ.0 ) &
RETURN
!
! Simplifications:
!
IF( IRANGE.EQ.3 .AND. IL.EQ.1 .AND. IU.EQ.N ) &
IRANGE = 1
!
! Get machine constants
! NB is the minimum vector length for vector bisection, or 0
! if only scalar is to be done.
!
SAFEMN = DLAMCH_XG( 'S' )
ULP = DLAMCH_XG( 'P' )
RTOLI = ULP*RELFAC
! NB = ILAENV_XG( 1, 'DSTEBZ', ' ', N, -1, -1, -1 )
NB = ILAENV_XG( 1, 'I', ' ', N, -1, -1, -1 )
IF( NB.LE.1 ) &
NB = 0
!
! Special Case when N=1
!
IF( N.EQ.1 ) THEN
NSPLIT = 1
ISPLIT( 1 ) = 1
IF( IRANGE.EQ.2 .AND. ( VL.GE.D( 1 ) .OR. VU.LT.D( 1 ) ) ) THEN
M = 0
ELSE
W( 1 ) = D( 1 )
IBLOCK( 1 ) = 1
M = 1
END IF
RETURN
END IF
!
! Compute Splitting Points
!
NSPLIT = 1
WORK( N ) = ZERO
PIVMIN = ONE
!
DO 10 J = 2, N
TMP1 = E( J-1 )**2
IF( ABS( D( J )*D( J-1 ) )*ULP**2+SAFEMN.GT.TMP1 ) THEN
ISPLIT( NSPLIT ) = J - 1
NSPLIT = NSPLIT + 1
WORK( J-1 ) = ZERO
ELSE
WORK( J-1 ) = TMP1
PIVMIN = MAX( PIVMIN, TMP1 )
END IF
10 CONTINUE
ISPLIT( NSPLIT ) = N
PIVMIN = PIVMIN*SAFEMN
!
! Compute Interval and ATOLI
!
IF( IRANGE.EQ.3 ) THEN
!
! RANGE='I': Compute the interval containing eigenvalues
! IL through IU.
!
! Compute Gershgorin interval for entire (split) matrix
! and use it as the initial interval
!
GU = D( 1 )
GL = D( 1 )
TMP1 = ZERO
!
DO 20 J = 1, N - 1
TMP2 = SQRT( WORK( J ) )
GU = MAX( GU, D( J )+TMP1+TMP2 )
GL = MIN( GL, D( J )-TMP1-TMP2 )
TMP1 = TMP2
20 CONTINUE
!
GU = MAX( GU, D( N )+TMP1 )
GL = MIN( GL, D( N )-TMP1 )
TNORM = MAX( ABS( GL ), ABS( GU ) )
GL = GL - FUDGE*TNORM*ULP*N - FUDGE*TWO*PIVMIN
GU = GU + FUDGE*TNORM*ULP*N + FUDGE*PIVMIN
!
! Compute Iteration parameters
!
ITMAX = INT( ( LOG( TNORM+PIVMIN )-LOG( PIVMIN ) ) / &
LOG( TWO ) ) + 2
IF( ABSTOL.LE.ZERO ) THEN
ATOLI = ULP*TNORM
ELSE
ATOLI = ABSTOL
END IF
!
WORK( N+1 ) = GL
WORK( N+2 ) = GL
WORK( N+3 ) = GU
WORK( N+4 ) = GU
WORK( N+5 ) = GL
WORK( N+6 ) = GU
IWORK( 1 ) = -1
IWORK( 2 ) = -1
IWORK( 3 ) = N + 1
IWORK( 4 ) = N + 1
IWORK( 5 ) = IL - 1
IWORK( 6 ) = IU
!
CALL DLAEBZ_XG( 3, ITMAX, N, 2, 2, NB, ATOLI, RTOLI, PIVMIN, D, E, &
WORK, IWORK( 5 ), WORK( N+1 ), WORK( N+5 ), IOUT, &
IWORK, W, IBLOCK, IINFO )
!
IF( IWORK( 6 ).EQ.IU ) THEN
WL = WORK( N+1 )
WLU = WORK( N+3 )
NWL = IWORK( 1 )
WU = WORK( N+4 )
WUL = WORK( N+2 )
NWU = IWORK( 4 )
ELSE
WL = WORK( N+2 )
WLU = WORK( N+4 )
NWL = IWORK( 2 )
WU = WORK( N+3 )
WUL = WORK( N+1 )
NWU = IWORK( 3 )
END IF
!
IF( NWL.LT.0 .OR. NWL.GE.N .OR. NWU.LT.1 .OR. NWU.GT.N ) THEN
INFO = 4
RETURN
END IF
ELSE
!
! RANGE='A' or 'V' -- Set ATOLI
!
TNORM = MAX( ABS( D( 1 ) )+ABS( E( 1 ) ), &
ABS( D( N ) )+ABS( E( N-1 ) ) )
!
DO 30 J = 2, N - 1
TNORM = MAX( TNORM, ABS( D( J ) )+ABS( E( J-1 ) )+ &
ABS( E( J ) ) )
30 CONTINUE
!
IF( ABSTOL.LE.ZERO ) THEN
ATOLI = ULP*TNORM
ELSE
ATOLI = ABSTOL
END IF
!
IF( IRANGE.EQ.2 ) THEN
WL = VL
WU = VU
ELSE
WL = ZERO
WU = ZERO
END IF
END IF
!
! Find Eigenvalues -- Loop Over Blocks and recompute NWL and NWU.
! NWL accumulates the number of eigenvalues .le. WL,
! NWU accumulates the number of eigenvalues .le. WU
!
M = 0
IEND = 0
INFO = 0
NWL = 0
NWU = 0
!
DO 70 JB = 1, NSPLIT
IOFF = IEND
IBEGIN = IOFF + 1
IEND = ISPLIT( JB )
IN = IEND - IOFF
!
IF( IN.EQ.1 ) THEN
!
! Special Case -- IN=1
!
IF( IRANGE.EQ.1 .OR. WL.GE.D( IBEGIN )-PIVMIN ) &
NWL = NWL + 1
IF( IRANGE.EQ.1 .OR. WU.GE.D( IBEGIN )-PIVMIN ) &
NWU = NWU + 1
IF( IRANGE.EQ.1 .OR. ( WL.LT.D( IBEGIN )-PIVMIN .AND. WU.GE. &
D( IBEGIN )-PIVMIN ) ) THEN
M = M + 1
W( M ) = D( IBEGIN )
IBLOCK( M ) = JB
END IF
ELSE
!
! General Case -- IN > 1
!
! Compute Gershgorin Interval
! and use it as the initial interval
!
GU = D( IBEGIN )
GL = D( IBEGIN )
TMP1 = ZERO
!
DO 40 J = IBEGIN, IEND - 1
TMP2 = ABS( E( J ) )
GU = MAX( GU, D( J )+TMP1+TMP2 )
GL = MIN( GL, D( J )-TMP1-TMP2 )
TMP1 = TMP2
40 CONTINUE
!
GU = MAX( GU, D( IEND )+TMP1 )
GL = MIN( GL, D( IEND )-TMP1 )
BNORM = MAX( ABS( GL ), ABS( GU ) )
GL = GL - FUDGE*BNORM*ULP*IN - FUDGE*PIVMIN
GU = GU + FUDGE*BNORM*ULP*IN + FUDGE*PIVMIN
!
! Compute ATOLI for the current submatrix
!
IF( ABSTOL.LE.ZERO ) THEN
ATOLI = ULP*MAX( ABS( GL ), ABS( GU ) )
ELSE
ATOLI = ABSTOL
END IF
!
IF( IRANGE.GT.1 ) THEN
IF( GU.LT.WL ) THEN
NWL = NWL + IN
NWU = NWU + IN
GO TO 70
END IF
GL = MAX( GL, WL )
GU = MIN( GU, WU )
IF( GL.GE.GU ) &
GO TO 70
END IF
!
! Set Up Initial Interval
!
WORK( N+1 ) = GL
WORK( N+IN+1 ) = GU
CALL DLAEBZ_XG( 1, 0, IN, IN, 1, NB, ATOLI, RTOLI, PIVMIN, &
D( IBEGIN ), E( IBEGIN ), WORK( IBEGIN ), &
IDUMMA, WORK( N+1 ), WORK( N+2*IN+1 ), IM, &
IWORK, W( M+1 ), IBLOCK( M+1 ), IINFO )
!
NWL = NWL + IWORK( 1 )
NWU = NWU + IWORK( IN+1 )
IWOFF = M - IWORK( 1 )
!
! Compute Eigenvalues
!
ITMAX = INT( ( LOG( GU-GL+PIVMIN )-LOG( PIVMIN ) ) / &
LOG( TWO ) ) + 2
CALL DLAEBZ_XG( 2, ITMAX, IN, IN, 1, NB, ATOLI, RTOLI, PIVMIN, &
D( IBEGIN ), E( IBEGIN ), WORK( IBEGIN ), &
IDUMMA, WORK( N+1 ), WORK( N+2*IN+1 ), IOUT, &
IWORK, W( M+1 ), IBLOCK( M+1 ), IINFO )
!
! Copy Eigenvalues Into W and IBLOCK
! Use -JB for block number for unconverged eigenvalues.
!
DO 60 J = 1, IOUT
TMP1 = HALF*( WORK( J+N )+WORK( J+IN+N ) )
!
! Flag non-convergence.
!
IF( J.GT.IOUT-IINFO ) THEN
NCNVRG = .TRUE.
IB = -JB
ELSE
IB = JB
END IF
DO 50 JE = IWORK( J ) + 1 + IWOFF, &
IWORK( J+IN ) + IWOFF
W( JE ) = TMP1
IBLOCK( JE ) = IB
50 CONTINUE
60 CONTINUE
!
M = M + IM
END IF
70 CONTINUE
!
! If RANGE='I', then (WL,WU) contains eigenvalues NWL+1,...,NWU
! If NWL+1 < IL or NWU > IU, discard extra eigenvalues.
!
IF( IRANGE.EQ.3 ) THEN
IM = 0
IDISCL = IL - 1 - NWL
IDISCU = NWU - IU
!
IF( IDISCL.GT.0 .OR. IDISCU.GT.0 ) THEN
DO 80 JE = 1, M
IF( W( JE ).LE.WLU .AND. IDISCL.GT.0 ) THEN
IDISCL = IDISCL - 1
ELSE IF( W( JE ).GE.WUL .AND. IDISCU.GT.0 ) THEN
IDISCU = IDISCU - 1
ELSE
IM = IM + 1
W( IM ) = W( JE )
IBLOCK( IM ) = IBLOCK( JE )
END IF
80 CONTINUE
M = IM
END IF
IF( IDISCL.GT.0 .OR. IDISCU.GT.0 ) THEN
!
! Code to deal with effects of bad arithmetic:
! Some low eigenvalues to be discarded are not in (WL,WLU],
! or high eigenvalues to be discarded are not in (WUL,WU]
! so just kill off the smallest IDISCL/largest IDISCU
! eigenvalues, by simply finding the smallest/largest
! eigenvalue(s).
!
! (If N(w) is monotone non-decreasing, this should never
! happen.)
!
IF( IDISCL.GT.0 ) THEN
WKILL = WU
DO 100 JDISC = 1, IDISCL
IW = 0
DO 90 JE = 1, M
IF( IBLOCK( JE ).NE.0 .AND. &
( W( JE ).LT.WKILL .OR. IW.EQ.0 ) ) THEN
IW = JE
WKILL = W( JE )
END IF
90 CONTINUE
IBLOCK( IW ) = 0
100 CONTINUE
END IF
IF( IDISCU.GT.0 ) THEN
!
WKILL = WL
DO 120 JDISC = 1, IDISCU
IW = 0
DO 110 JE = 1, M
IF( IBLOCK( JE ).NE.0 .AND. &
( W( JE ).GT.WKILL .OR. IW.EQ.0 ) ) THEN
IW = JE
WKILL = W( JE )
END IF
110 CONTINUE
IBLOCK( IW ) = 0
120 CONTINUE
END IF
IM = 0
DO 130 JE = 1, M
IF( IBLOCK( JE ).NE.0 ) THEN
IM = IM + 1
W( IM ) = W( JE )
IBLOCK( IM ) = IBLOCK( JE )
END IF
130 CONTINUE
M = IM
END IF
IF( IDISCL.LT.0 .OR. IDISCU.LT.0 ) THEN
TOOFEW = .TRUE.
END IF
END IF
!
! If ORDER='B', do nothing -- the eigenvalues are already sorted
! by block.
! If ORDER='E', sort the eigenvalues from smallest to largest
!
IF( IORDER.EQ.1 .AND. NSPLIT.GT.1 ) THEN
DO 150 JE = 1, M - 1
IE = 0
TMP1 = W( JE )
DO 140 J = JE + 1, M
IF( W( J ).LT.TMP1 ) THEN
IE = J
TMP1 = W( J )
END IF
140 CONTINUE
!
IF( IE.NE.0 ) THEN
ITMP1 = IBLOCK( IE )
W( IE ) = W( JE )
IBLOCK( IE ) = IBLOCK( JE )
W( JE ) = TMP1
IBLOCK( JE ) = ITMP1
END IF
150 CONTINUE
END IF
!
INFO = 0
IF( NCNVRG ) &
INFO = INFO + 1
IF( TOOFEW ) &
INFO = INFO + 2
RETURN
!
! End of DSTEBZ
!
END