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
|
*> \brief \b ZHBTRD
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download ZHBTRD + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhbtrd.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhbtrd.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhbtrd.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE ZHBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ,
* WORK, INFO )
*
* .. Scalar Arguments ..
* CHARACTER UPLO, VECT
* INTEGER INFO, KD, LDAB, LDQ, N
* ..
* .. Array Arguments ..
* DOUBLE PRECISION D( * ), E( * )
* COMPLEX*16 AB( LDAB, * ), Q( LDQ, * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZHBTRD reduces a complex Hermitian band matrix A to real symmetric
*> tridiagonal form T by a unitary similarity transformation:
*> Q**H * A * Q = T.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] VECT
*> \verbatim
*> VECT is CHARACTER*1
*> = 'N': do not form Q;
*> = 'V': form Q;
*> = 'U': update a matrix X, by forming X*Q.
*> \endverbatim
*>
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> = 'U': Upper triangle of A is stored;
*> = 'L': Lower triangle of A is stored.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] KD
*> \verbatim
*> KD is INTEGER
*> The number of superdiagonals of the matrix A if UPLO = 'U',
*> or the number of subdiagonals if UPLO = 'L'. KD >= 0.
*> \endverbatim
*>
*> \param[in,out] AB
*> \verbatim
*> AB is COMPLEX*16 array, dimension (LDAB,N)
*> On entry, the upper or lower triangle of the Hermitian band
*> matrix A, stored in the first KD+1 rows of the array. The
*> j-th column of A is stored in the j-th column of the array AB
*> as follows:
*> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
*> On exit, the diagonal elements of AB are overwritten by the
*> diagonal elements of the tridiagonal matrix T; if KD > 0, the
*> elements on the first superdiagonal (if UPLO = 'U') or the
*> first subdiagonal (if UPLO = 'L') are overwritten by the
*> off-diagonal elements of T; the rest of AB is overwritten by
*> values generated during the reduction.
*> \endverbatim
*>
*> \param[in] LDAB
*> \verbatim
*> LDAB is INTEGER
*> The leading dimension of the array AB. LDAB >= KD+1.
*> \endverbatim
*>
*> \param[out] D
*> \verbatim
*> D is DOUBLE PRECISION array, dimension (N)
*> The diagonal elements of the tridiagonal matrix T.
*> \endverbatim
*>
*> \param[out] E
*> \verbatim
*> E is DOUBLE PRECISION array, dimension (N-1)
*> The off-diagonal elements of the tridiagonal matrix T:
*> E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'.
*> \endverbatim
*>
*> \param[in,out] Q
*> \verbatim
*> Q is COMPLEX*16 array, dimension (LDQ,N)
*> On entry, if VECT = 'U', then Q must contain an N-by-N
*> matrix X; if VECT = 'N' or 'V', then Q need not be set.
*>
*> On exit:
*> if VECT = 'V', Q contains the N-by-N unitary matrix Q;
*> if VECT = 'U', Q contains the product X*Q;
*> if VECT = 'N', the array Q is not referenced.
*> \endverbatim
*>
*> \param[in] LDQ
*> \verbatim
*> LDQ is INTEGER
*> The leading dimension of the array Q.
*> LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX*16 array, dimension (N)
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup complex16OTHERcomputational
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> Modified by Linda Kaufman, Bell Labs.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZHBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ,
$ WORK, INFO )
*
* -- LAPACK computational 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 ..
CHARACTER UPLO, VECT
INTEGER INFO, KD, LDAB, LDQ, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION D( * ), E( * )
COMPLEX*16 AB( LDAB, * ), Q( LDQ, * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D+0 )
COMPLEX*16 CZERO, CONE
PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
$ CONE = ( 1.0D+0, 0.0D+0 ) )
* ..
* .. Local Scalars ..
LOGICAL INITQ, UPPER, WANTQ
INTEGER I, I2, IBL, INCA, INCX, IQAEND, IQB, IQEND, J,
$ J1, J1END, J1INC, J2, JEND, JIN, JINC, K, KD1,
$ KDM1, KDN, L, LAST, LEND, NQ, NR, NRT
DOUBLE PRECISION ABST
COMPLEX*16 T, TEMP
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, ZLACGV, ZLAR2V, ZLARGV, ZLARTG, ZLARTV,
$ ZLASET, ZROT, ZSCAL
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, DCONJG, MAX, MIN
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. Executable Statements ..
*
* Test the input parameters
*
INITQ = LSAME( VECT, 'V' )
WANTQ = INITQ .OR. LSAME( VECT, 'U' )
UPPER = LSAME( UPLO, 'U' )
KD1 = KD + 1
KDM1 = KD - 1
INCX = LDAB - 1
IQEND = 1
*
INFO = 0
IF( .NOT.WANTQ .AND. .NOT.LSAME( VECT, 'N' ) ) THEN
INFO = -1
ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -2
ELSE IF( N.LT.0 ) THEN
INFO = -3
ELSE IF( KD.LT.0 ) THEN
INFO = -4
ELSE IF( LDAB.LT.KD1 ) THEN
INFO = -6
ELSE IF( LDQ.LT.MAX( 1, N ) .AND. WANTQ ) THEN
INFO = -10
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZHBTRD', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Initialize Q to the unit matrix, if needed
*
IF( INITQ )
$ CALL ZLASET( 'Full', N, N, CZERO, CONE, Q, LDQ )
*
* Wherever possible, plane rotations are generated and applied in
* vector operations of length NR over the index set J1:J2:KD1.
*
* The real cosines and complex sines of the plane rotations are
* stored in the arrays D and WORK.
*
INCA = KD1*LDAB
KDN = MIN( N-1, KD )
IF( UPPER ) THEN
*
IF( KD.GT.1 ) THEN
*
* Reduce to complex Hermitian tridiagonal form, working with
* the upper triangle
*
NR = 0
J1 = KDN + 2
J2 = 1
*
AB( KD1, 1 ) = DBLE( AB( KD1, 1 ) )
DO 90 I = 1, N - 2
*
* Reduce i-th row of matrix to tridiagonal form
*
DO 80 K = KDN + 1, 2, -1
J1 = J1 + KDN
J2 = J2 + KDN
*
IF( NR.GT.0 ) THEN
*
* generate plane rotations to annihilate nonzero
* elements which have been created outside the band
*
CALL ZLARGV( NR, AB( 1, J1-1 ), INCA, WORK( J1 ),
$ KD1, D( J1 ), KD1 )
*
* apply rotations from the right
*
*
* Dependent on the the number of diagonals either
* ZLARTV or ZROT is used
*
IF( NR.GE.2*KD-1 ) THEN
DO 10 L = 1, KD - 1
CALL ZLARTV( NR, AB( L+1, J1-1 ), INCA,
$ AB( L, J1 ), INCA, D( J1 ),
$ WORK( J1 ), KD1 )
10 CONTINUE
*
ELSE
JEND = J1 + ( NR-1 )*KD1
DO 20 JINC = J1, JEND, KD1
CALL ZROT( KDM1, AB( 2, JINC-1 ), 1,
$ AB( 1, JINC ), 1, D( JINC ),
$ WORK( JINC ) )
20 CONTINUE
END IF
END IF
*
*
IF( K.GT.2 ) THEN
IF( K.LE.N-I+1 ) THEN
*
* generate plane rotation to annihilate a(i,i+k-1)
* within the band
*
CALL ZLARTG( AB( KD-K+3, I+K-2 ),
$ AB( KD-K+2, I+K-1 ), D( I+K-1 ),
$ WORK( I+K-1 ), TEMP )
AB( KD-K+3, I+K-2 ) = TEMP
*
* apply rotation from the right
*
CALL ZROT( K-3, AB( KD-K+4, I+K-2 ), 1,
$ AB( KD-K+3, I+K-1 ), 1, D( I+K-1 ),
$ WORK( I+K-1 ) )
END IF
NR = NR + 1
J1 = J1 - KDN - 1
END IF
*
* apply plane rotations from both sides to diagonal
* blocks
*
IF( NR.GT.0 )
$ CALL ZLAR2V( NR, AB( KD1, J1-1 ), AB( KD1, J1 ),
$ AB( KD, J1 ), INCA, D( J1 ),
$ WORK( J1 ), KD1 )
*
* apply plane rotations from the left
*
IF( NR.GT.0 ) THEN
CALL ZLACGV( NR, WORK( J1 ), KD1 )
IF( 2*KD-1.LT.NR ) THEN
*
* Dependent on the the number of diagonals either
* ZLARTV or ZROT is used
*
DO 30 L = 1, KD - 1
IF( J2+L.GT.N ) THEN
NRT = NR - 1
ELSE
NRT = NR
END IF
IF( NRT.GT.0 )
$ CALL ZLARTV( NRT, AB( KD-L, J1+L ), INCA,
$ AB( KD-L+1, J1+L ), INCA,
$ D( J1 ), WORK( J1 ), KD1 )
30 CONTINUE
ELSE
J1END = J1 + KD1*( NR-2 )
IF( J1END.GE.J1 ) THEN
DO 40 JIN = J1, J1END, KD1
CALL ZROT( KD-1, AB( KD-1, JIN+1 ), INCX,
$ AB( KD, JIN+1 ), INCX,
$ D( JIN ), WORK( JIN ) )
40 CONTINUE
END IF
LEND = MIN( KDM1, N-J2 )
LAST = J1END + KD1
IF( LEND.GT.0 )
$ CALL ZROT( LEND, AB( KD-1, LAST+1 ), INCX,
$ AB( KD, LAST+1 ), INCX, D( LAST ),
$ WORK( LAST ) )
END IF
END IF
*
IF( WANTQ ) THEN
*
* accumulate product of plane rotations in Q
*
IF( INITQ ) THEN
*
* take advantage of the fact that Q was
* initially the Identity matrix
*
IQEND = MAX( IQEND, J2 )
I2 = MAX( 0, K-3 )
IQAEND = 1 + I*KD
IF( K.EQ.2 )
$ IQAEND = IQAEND + KD
IQAEND = MIN( IQAEND, IQEND )
DO 50 J = J1, J2, KD1
IBL = I - I2 / KDM1
I2 = I2 + 1
IQB = MAX( 1, J-IBL )
NQ = 1 + IQAEND - IQB
IQAEND = MIN( IQAEND+KD, IQEND )
CALL ZROT( NQ, Q( IQB, J-1 ), 1, Q( IQB, J ),
$ 1, D( J ), DCONJG( WORK( J ) ) )
50 CONTINUE
ELSE
*
DO 60 J = J1, J2, KD1
CALL ZROT( N, Q( 1, J-1 ), 1, Q( 1, J ), 1,
$ D( J ), DCONJG( WORK( J ) ) )
60 CONTINUE
END IF
*
END IF
*
IF( J2+KDN.GT.N ) THEN
*
* adjust J2 to keep within the bounds of the matrix
*
NR = NR - 1
J2 = J2 - KDN - 1
END IF
*
DO 70 J = J1, J2, KD1
*
* create nonzero element a(j-1,j+kd) outside the band
* and store it in WORK
*
WORK( J+KD ) = WORK( J )*AB( 1, J+KD )
AB( 1, J+KD ) = D( J )*AB( 1, J+KD )
70 CONTINUE
80 CONTINUE
90 CONTINUE
END IF
*
IF( KD.GT.0 ) THEN
*
* make off-diagonal elements real and copy them to E
*
DO 100 I = 1, N - 1
T = AB( KD, I+1 )
ABST = ABS( T )
AB( KD, I+1 ) = ABST
E( I ) = ABST
IF( ABST.NE.ZERO ) THEN
T = T / ABST
ELSE
T = CONE
END IF
IF( I.LT.N-1 )
$ AB( KD, I+2 ) = AB( KD, I+2 )*T
IF( WANTQ ) THEN
CALL ZSCAL( N, DCONJG( T ), Q( 1, I+1 ), 1 )
END IF
100 CONTINUE
ELSE
*
* set E to zero if original matrix was diagonal
*
DO 110 I = 1, N - 1
E( I ) = ZERO
110 CONTINUE
END IF
*
* copy diagonal elements to D
*
DO 120 I = 1, N
D( I ) = AB( KD1, I )
120 CONTINUE
*
ELSE
*
IF( KD.GT.1 ) THEN
*
* Reduce to complex Hermitian tridiagonal form, working with
* the lower triangle
*
NR = 0
J1 = KDN + 2
J2 = 1
*
AB( 1, 1 ) = DBLE( AB( 1, 1 ) )
DO 210 I = 1, N - 2
*
* Reduce i-th column of matrix to tridiagonal form
*
DO 200 K = KDN + 1, 2, -1
J1 = J1 + KDN
J2 = J2 + KDN
*
IF( NR.GT.0 ) THEN
*
* generate plane rotations to annihilate nonzero
* elements which have been created outside the band
*
CALL ZLARGV( NR, AB( KD1, J1-KD1 ), INCA,
$ WORK( J1 ), KD1, D( J1 ), KD1 )
*
* apply plane rotations from one side
*
*
* Dependent on the the number of diagonals either
* ZLARTV or ZROT is used
*
IF( NR.GT.2*KD-1 ) THEN
DO 130 L = 1, KD - 1
CALL ZLARTV( NR, AB( KD1-L, J1-KD1+L ), INCA,
$ AB( KD1-L+1, J1-KD1+L ), INCA,
$ D( J1 ), WORK( J1 ), KD1 )
130 CONTINUE
ELSE
JEND = J1 + KD1*( NR-1 )
DO 140 JINC = J1, JEND, KD1
CALL ZROT( KDM1, AB( KD, JINC-KD ), INCX,
$ AB( KD1, JINC-KD ), INCX,
$ D( JINC ), WORK( JINC ) )
140 CONTINUE
END IF
*
END IF
*
IF( K.GT.2 ) THEN
IF( K.LE.N-I+1 ) THEN
*
* generate plane rotation to annihilate a(i+k-1,i)
* within the band
*
CALL ZLARTG( AB( K-1, I ), AB( K, I ),
$ D( I+K-1 ), WORK( I+K-1 ), TEMP )
AB( K-1, I ) = TEMP
*
* apply rotation from the left
*
CALL ZROT( K-3, AB( K-2, I+1 ), LDAB-1,
$ AB( K-1, I+1 ), LDAB-1, D( I+K-1 ),
$ WORK( I+K-1 ) )
END IF
NR = NR + 1
J1 = J1 - KDN - 1
END IF
*
* apply plane rotations from both sides to diagonal
* blocks
*
IF( NR.GT.0 )
$ CALL ZLAR2V( NR, AB( 1, J1-1 ), AB( 1, J1 ),
$ AB( 2, J1-1 ), INCA, D( J1 ),
$ WORK( J1 ), KD1 )
*
* apply plane rotations from the right
*
*
* Dependent on the the number of diagonals either
* ZLARTV or ZROT is used
*
IF( NR.GT.0 ) THEN
CALL ZLACGV( NR, WORK( J1 ), KD1 )
IF( NR.GT.2*KD-1 ) THEN
DO 150 L = 1, KD - 1
IF( J2+L.GT.N ) THEN
NRT = NR - 1
ELSE
NRT = NR
END IF
IF( NRT.GT.0 )
$ CALL ZLARTV( NRT, AB( L+2, J1-1 ), INCA,
$ AB( L+1, J1 ), INCA, D( J1 ),
$ WORK( J1 ), KD1 )
150 CONTINUE
ELSE
J1END = J1 + KD1*( NR-2 )
IF( J1END.GE.J1 ) THEN
DO 160 J1INC = J1, J1END, KD1
CALL ZROT( KDM1, AB( 3, J1INC-1 ), 1,
$ AB( 2, J1INC ), 1, D( J1INC ),
$ WORK( J1INC ) )
160 CONTINUE
END IF
LEND = MIN( KDM1, N-J2 )
LAST = J1END + KD1
IF( LEND.GT.0 )
$ CALL ZROT( LEND, AB( 3, LAST-1 ), 1,
$ AB( 2, LAST ), 1, D( LAST ),
$ WORK( LAST ) )
END IF
END IF
*
*
*
IF( WANTQ ) THEN
*
* accumulate product of plane rotations in Q
*
IF( INITQ ) THEN
*
* take advantage of the fact that Q was
* initially the Identity matrix
*
IQEND = MAX( IQEND, J2 )
I2 = MAX( 0, K-3 )
IQAEND = 1 + I*KD
IF( K.EQ.2 )
$ IQAEND = IQAEND + KD
IQAEND = MIN( IQAEND, IQEND )
DO 170 J = J1, J2, KD1
IBL = I - I2 / KDM1
I2 = I2 + 1
IQB = MAX( 1, J-IBL )
NQ = 1 + IQAEND - IQB
IQAEND = MIN( IQAEND+KD, IQEND )
CALL ZROT( NQ, Q( IQB, J-1 ), 1, Q( IQB, J ),
$ 1, D( J ), WORK( J ) )
170 CONTINUE
ELSE
*
DO 180 J = J1, J2, KD1
CALL ZROT( N, Q( 1, J-1 ), 1, Q( 1, J ), 1,
$ D( J ), WORK( J ) )
180 CONTINUE
END IF
END IF
*
IF( J2+KDN.GT.N ) THEN
*
* adjust J2 to keep within the bounds of the matrix
*
NR = NR - 1
J2 = J2 - KDN - 1
END IF
*
DO 190 J = J1, J2, KD1
*
* create nonzero element a(j+kd,j-1) outside the
* band and store it in WORK
*
WORK( J+KD ) = WORK( J )*AB( KD1, J )
AB( KD1, J ) = D( J )*AB( KD1, J )
190 CONTINUE
200 CONTINUE
210 CONTINUE
END IF
*
IF( KD.GT.0 ) THEN
*
* make off-diagonal elements real and copy them to E
*
DO 220 I = 1, N - 1
T = AB( 2, I )
ABST = ABS( T )
AB( 2, I ) = ABST
E( I ) = ABST
IF( ABST.NE.ZERO ) THEN
T = T / ABST
ELSE
T = CONE
END IF
IF( I.LT.N-1 )
$ AB( 2, I+1 ) = AB( 2, I+1 )*T
IF( WANTQ ) THEN
CALL ZSCAL( N, T, Q( 1, I+1 ), 1 )
END IF
220 CONTINUE
ELSE
*
* set E to zero if original matrix was diagonal
*
DO 230 I = 1, N - 1
E( I ) = ZERO
230 CONTINUE
END IF
*
* copy diagonal elements to D
*
DO 240 I = 1, N
D( I ) = AB( 1, I )
240 CONTINUE
END IF
*
RETURN
*
* End of ZHBTRD
*
END
|
