1DLAQR5(1)           LAPACK auxiliary routine (version 3.2)           DLAQR5(1)
2
3
4

NAME

SYNOPSIS

7       SUBROUTINE DLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, SR, SI,
8                          H, LDH, ILOZ, IHIZ, Z, LDZ, V, LDV, U, LDU, NV,  WV,
9                          LDWV, NH, WH, LDWH )
10
11           INTEGER        IHIZ, ILOZ, KACC22, KBOT, KTOP, LDH, LDU, LDV, LDWH,
12                          LDWV, LDZ, N, NH, NSHFTS, NV
13
14           LOGICAL        WANTT, WANTZ
15
16           DOUBLE         PRECISION H( LDH, * ), SI( * ), SR( * ), U(  LDU,  *
17                          ),  V(  LDV,  *  ), WH( LDWH, * ), WV( LDWV, * ), Z(
18                          LDZ, * )
19
20           DOUBLE         PRECISION ZERO, ONE
21
22           PARAMETER      ( ZERO = 0.0d0, ONE = 1.0d0 )
23
24           DOUBLE         PRECISION ALPHA, BETA, H11, H12, H21,  H22,  REFSUM,
25                          SAFMAX, SAFMIN, SCL, SMLNUM, SWAP, TST1, TST2, ULP
26
27           INTEGER        I, I2, I4, INCOL, J, J2, J4, JBOT, JCOL, JLEN, JROW,
28                          JTOP, K, K1, KDU, KMS,  KNZ,  KRCOL,  KZS,  M,  M22,
29                          MBOT, MEND, MSTART, MTOP, NBMPS, NDCOL, NS, NU
30
31           LOGICAL        ACCUM, BLK22, BMP22
32
33           DOUBLE         PRECISION DLAMCH
34
35           EXTERNAL       DLAMCH
36
37           INTRINSIC      ABS, DBLE, MAX, MIN, MOD
38
39           DOUBLE         PRECISION VT( 3 )
40
41           EXTERNAL       DGEMM, DLABAD, DLACPY, DLAQR1, DLARFG, DLASET, DTRMM
42
43           IF(            NSHFTS.LT.2 ) RETURN
44
45           IF(            KTOP.GE.KBOT ) RETURN
46
47           DO             10 I = 1, NSHFTS - 2, 2
48
49           IF(            SI( I ).NE.-SI( I+1 ) ) THEN
50
51           SWAP           = SR( I )
52
53           SR(            I ) = SR( I+1 )
54
55           SR(            I+1 ) = SR( I+2 )
56
57           SR(            I+2 ) = SWAP
58
59           SWAP           = SI( I )
60
61           SI(            I ) = SI( I+1 )
62
63           SI(            I+1 ) = SI( I+2 )
64
65           SI(            I+2 ) = SWAP
66
67           END            IF
68
69           10             CONTINUE
70
71           NS             = NSHFTS - MOD( NSHFTS, 2 )
72
73           SAFMIN         = DLAMCH( 'SAFE MINIMUM' )
74
75           SAFMAX         = ONE / SAFMIN
76
77           CALL           DLABAD( SAFMIN, SAFMAX )
78
79           ULP            = DLAMCH( 'PRECISION' )
80
81           SMLNUM         = SAFMIN*( DBLE( N ) / ULP )
82
83           ACCUM          = ( KACC22.EQ.1 ) .OR. ( KACC22.EQ.2 )
84
85           BLK22          = ( NS.GT.2 ) .AND. ( KACC22.EQ.2 )
86
87           IF(            KTOP+2.LE.KBOT ) H( KTOP+2, KTOP ) = ZERO
88
89           NBMPS          = NS / 2
90
91           KDU            = 6*NBMPS - 3
92
93           DO             220  INCOL  =  3*(  1-NBMPS  ) + KTOP - 1, KBOT - 2,
94                          3*NBMPS - 2
95
96           NDCOL          = INCOL + KDU
97
98           IF(            ACCUM ) CALL DLASET( 'ALL', KDU, KDU, ZERO, ONE,  U,
99                          LDU )
100
101           DO             150 KRCOL = INCOL, MIN( INCOL+3*NBMPS-3, KBOT-2 )
102
103           MTOP           = MAX( 1, ( ( KTOP-1 )-KRCOL+2 ) / 3+1 )
104
105           MBOT           = MIN( NBMPS, ( KBOT-KRCOL ) / 3 )
106
107           M22            = MBOT + 1
108
109           BMP22          =  ( MBOT.LT.NBMPS ) .AND. ( KRCOL+3*( M22-1 ) ).EQ.
110                          ( KBOT-2 )
111
112           DO             20 M = MTOP, MBOT
113
114           K              = KRCOL + 3*( M-1 )
115
116           IF(            K.EQ.KTOP-1 ) THEN
117
118           CALL           DLAQR1( 3, H( KTOP, KTOP ), LDH, SR(  2*M-1  ),  SI(
119                          2*M-1 ), SR( 2*M ), SI( 2*M ), V( 1, M ) )
120
121           ALPHA          = V( 1, M )
122
123           CALL           DLARFG( 3, ALPHA, V( 2, M ), 1, V( 1, M ) )
124
125           ELSE
126
127           BETA           = H( K+1, K )
128
129           V(             2, M ) = H( K+2, K )
130
131           V(             3, M ) = H( K+3, K )
132
133           CALL           DLARFG( 3, BETA, V( 2, M ), 1, V( 1, M ) )
134
135           IF(            H(  K+3,  K  ).NE.ZERO  .OR. H( K+3, K+1 ).NE.  ZERO
136                          .OR. H( K+3, K+2 ).EQ.ZERO ) THEN
137
138           H(             K+1, K ) = BETA
139
140           H(             K+2, K ) = ZERO
141
142           H(             K+3, K ) = ZERO
143
144           ELSE
145
146           CALL           DLAQR1( 3, H( K+1, K+1 ),  LDH,  SR(  2*M-1  ),  SI(
147                          2*M-1 ), SR( 2*M ), SI( 2*M ), VT )
148
149           ALPHA          = VT( 1 )
150
151           CALL           DLARFG( 3, ALPHA, VT( 2 ), 1, VT( 1 ) )
152
153           REFSUM         = VT( 1 )*( H( K+1, K )+VT( 2 )* H( K+2, K ) )
154
155           IF(            ABS( H( K+2, K )-REFSUM*VT( 2 ) )+ ABS( REFSUM*VT( 3
156                          ) ).GT.ULP* ( ABS( H( K, K ) )+ABS( H(  K+1,  K+1  )
157                          )+ABS( H( K+2, K+2 ) ) ) ) THEN
158
159           H(             K+1, K ) = BETA
160
161           H(             K+2, K ) = ZERO
162
163           H(             K+3, K ) = ZERO
164
165           ELSE
166
167           H(             K+1, K ) = H( K+1, K ) - REFSUM
168
169           H(             K+2, K ) = ZERO
170
171           H(             K+3, K ) = ZERO
172
173           V(             1, M ) = VT( 1 )
174
175           V(             2, M ) = VT( 2 )
176
177           V(             3, M ) = VT( 3 )
178
179           END            IF
180
181           END            IF
182
183           END            IF
184
185           20             CONTINUE
186
187           K              = KRCOL + 3*( M22-1 )
188
189           IF(            BMP22 ) THEN
190
191           IF(            K.EQ.KTOP-1 ) THEN
192
193           CALL           DLAQR1(  2,  H(  K+1, K+1 ), LDH, SR( 2*M22-1 ), SI(
194                          2*M22-1 ), SR( 2*M22 ), SI( 2*M22 ), V( 1, M22 ) )
195
196           BETA           = V( 1, M22 )
197
198           CALL           DLARFG( 2, BETA, V( 2, M22 ), 1, V( 1, M22 ) )
199
200           ELSE
201
202           BETA           = H( K+1, K )
203
204           V(             2, M22 ) = H( K+2, K )
205
206           CALL           DLARFG( 2, BETA, V( 2, M22 ), 1, V( 1, M22 ) )
207
208           H(             K+1, K ) = BETA
209
210           H(             K+2, K ) = ZERO
211
212           END            IF
213
214           END            IF
215
216           IF(            ACCUM ) THEN
217
218           JBOT           = MIN( NDCOL, KBOT )
219
220           ELSE           IF( WANTT ) THEN
221
222           JBOT           = N
223
224           ELSE
225
226           JBOT           = KBOT
227
228           END            IF
229
230           DO             40 J = MAX( KTOP, KRCOL ), JBOT
231
232           MEND           = MIN( MBOT, ( J-KRCOL+2 ) / 3 )
233
234           DO             30 M = MTOP, MEND
235
236           K              = KRCOL + 3*( M-1 )
237
238           REFSUM         = V( 1, M )*( H( K+1, J )+V( 2, M )* H( K+2, J  )+V(
239                          3, M )*H( K+3, J ) )
240
241           H(             K+1, J ) = H( K+1, J ) - REFSUM
242
243           H(             K+2, J ) = H( K+2, J ) - REFSUM*V( 2, M )
244
245           H(             K+3, J ) = H( K+3, J ) - REFSUM*V( 3, M )
246
247           30             CONTINUE
248
249           40             CONTINUE
250
251           IF(            BMP22 ) THEN
252
253           K              = KRCOL + 3*( M22-1 )
254
255           DO             50 J = MAX( K+1, KTOP ), JBOT
256
257           REFSUM         = V( 1, M22 )*( H( K+1, J )+V( 2, M22 )* H( K+2, J )
258                          )
259
260           H(             K+1, J ) = H( K+1, J ) - REFSUM
261
262           H(             K+2, J ) = H( K+2, J ) - REFSUM*V( 2, M22 )
263
264           50             CONTINUE
265
266           END            IF
267
268           IF(            ACCUM ) THEN
269
270           JTOP           = MAX( KTOP, INCOL )
271
272           ELSE           IF( WANTT ) THEN
273
274           JTOP           = 1
275
276           ELSE
277
278           JTOP           = KTOP
279
280           END            IF
281
282           DO             90 M = MTOP, MBOT
283
284           IF(            V( 1, M ).NE.ZERO ) THEN
285
286           K              = KRCOL + 3*( M-1 )
287
288           DO             60 J = JTOP, MIN( KBOT, K+3 )
289
290           REFSUM         = V( 1, M )*( H( J, K+1 )+V( 2, M )* H( J, K+2  )+V(
291                          3, M )*H( J, K+3 ) )
292
293           H(             J, K+1 ) = H( J, K+1 ) - REFSUM
294
295           H(             J, K+2 ) = H( J, K+2 ) - REFSUM*V( 2, M )
296
297           H(             J, K+3 ) = H( J, K+3 ) - REFSUM*V( 3, M )
298
299           60             CONTINUE
300
301           IF(            ACCUM ) THEN
302
303           KMS            = K - INCOL
304
305           DO             70 J = MAX( 1, KTOP-INCOL ), KDU
306
307           REFSUM         =  V(  1, M )*( U( J, KMS+1 )+V( 2, M )* U( J, KMS+2
308                          )+V( 3, M )*U( J, KMS+3 ) )
309
310           U(             J, KMS+1 ) = U( J, KMS+1 ) - REFSUM
311
312           U(             J, KMS+2 ) = U( J, KMS+2 ) - REFSUM*V( 2, M )
313
314           U(             J, KMS+3 ) = U( J, KMS+3 ) - REFSUM*V( 3, M )
315
316           70             CONTINUE
317
318           ELSE           IF( WANTZ ) THEN
319
320           DO             80 J = ILOZ, IHIZ
321
322           REFSUM         = V( 1, M )*( Z( J, K+1 )+V( 2, M )* Z( J, K+2  )+V(
323                          3, M )*Z( J, K+3 ) )
324
325           Z(             J, K+1 ) = Z( J, K+1 ) - REFSUM
326
327           Z(             J, K+2 ) = Z( J, K+2 ) - REFSUM*V( 2, M )
328
329           Z(             J, K+3 ) = Z( J, K+3 ) - REFSUM*V( 3, M )
330
331           80             CONTINUE
332
333           END            IF
334
335           END            IF
336
337           90             CONTINUE
338
339           K              = KRCOL + 3*( M22-1 )
340
341           IF(            BMP22 .AND. ( V( 1, M22 ).NE.ZERO ) ) THEN
342
343           DO             100 J = JTOP, MIN( KBOT, K+3 )
344
345           REFSUM         = V( 1, M22 )*( H( J, K+1 )+V( 2, M22 )* H( J, K+2 )
346                          )
347
348           H(             J, K+1 ) = H( J, K+1 ) - REFSUM
349
350           H(             J, K+2 ) = H( J, K+2 ) - REFSUM*V( 2, M22 )
351
352           100            CONTINUE
353
354           IF(            ACCUM ) THEN
355
356           KMS            = K - INCOL
357
358           DO             110 J = MAX( 1, KTOP-INCOL ), KDU
359
360           REFSUM         = V( 1, M22 )*( U( J, KMS+1 )+V( 2,  M22  )*  U(  J,
361                          KMS+2 ) )
362
363           U(             J, KMS+1 ) = U( J, KMS+1 ) - REFSUM
364
365           U(             J, KMS+2 ) = U( J, KMS+2 ) - REFSUM*V( 2, M22 )
366
367           110            CONTINUE
368
369           ELSE           IF( WANTZ ) THEN
370
371           DO             120 J = ILOZ, IHIZ
372
373           REFSUM         = V( 1, M22 )*( Z( J, K+1 )+V( 2, M22 )* Z( J, K+2 )
374                          )
375
376           Z(             J, K+1 ) = Z( J, K+1 ) - REFSUM
377
378           Z(             J, K+2 ) = Z( J, K+2 ) - REFSUM*V( 2, M22 )
379
380           120            CONTINUE
381
382           END            IF
383
384           END            IF
385
386           MSTART         = MTOP
387
388           IF(            KRCOL+3*( MSTART-1 ).LT.KTOP ) MSTART = MSTART + 1
389
390           MEND           = MBOT
391
392           IF(            BMP22 ) MEND = MEND + 1
393
394           IF(            KRCOL.EQ.KBOT-2 ) MEND = MEND + 1
395
396           DO             130 M = MSTART, MEND
397
398           K              = MIN( KBOT-1, KRCOL+3*( M-1 ) )
399
400           IF(            H( K+1, K ).NE.ZERO ) THEN
401
402           TST1           = ABS( H( K, K ) ) + ABS( H( K+1, K+1 ) )
403
404           IF(            TST1.EQ.ZERO ) THEN
405
406           IF(            K.GE.KTOP+1 ) TST1 = TST1 + ABS( H( K, K-1 ) )
407
408           IF(            K.GE.KTOP+2 ) TST1 = TST1 + ABS( H( K, K-2 ) )
409
410           IF(            K.GE.KTOP+3 ) TST1 = TST1 + ABS( H( K, K-3 ) )
411
412           IF(            K.LE.KBOT-2 ) TST1 = TST1 + ABS( H( K+2, K+1 ) )
413
414           IF(            K.LE.KBOT-3 ) TST1 = TST1 + ABS( H( K+3, K+1 ) )
415
416           IF(            K.LE.KBOT-4 ) TST1 = TST1 + ABS( H( K+4, K+1 ) )
417
418           END            IF
419
420           IF(            ABS( H( K+1, K ) ).LE.MAX( SMLNUM, ULP*TST1 ) ) THEN
421
422           H12            = MAX( ABS( H( K+1, K ) ), ABS( H( K, K+1 ) ) )
423
424           H21            = MIN( ABS( H( K+1, K ) ), ABS( H( K, K+1 ) ) )
425
426           H11            = MAX( ABS( H( K+1, K+1 ) ), ABS( H( K, K )-H(  K+1,
427                          K+1 ) ) )
428
429           H22            =  MIN( ABS( H( K+1, K+1 ) ), ABS( H( K, K )-H( K+1,
430                          K+1 ) ) )
431
432           SCL            = H11 + H12
433
434           TST2           = H22*( H11 / SCL )
435
436           IF(            TST2.EQ.ZERO .OR. H21*( H12 / SCL ).LE.   MAX(  SML‐
437                          NUM, ULP*TST2 ) )H( K+1, K ) = ZERO
438
439           END            IF
440
441           END            IF
442
443           130            CONTINUE
444
445           MEND           = MIN( NBMPS, ( KBOT-KRCOL-1 ) / 3 )
446
447           DO             140 M = MTOP, MEND
448
449           K              = KRCOL + 3*( M-1 )
450
451           REFSUM         = V( 1, M )*V( 3, M )*H( K+4, K+3 )
452
453           H(             K+4, K+1 ) = -REFSUM
454
455           H(             K+4, K+2 ) = -REFSUM*V( 2, M )
456
457           H(             K+4, K+3 ) = H( K+4, K+3 ) - REFSUM*V( 3, M )
458
459           140            CONTINUE
460
461           150            CONTINUE
462
463           IF(            ACCUM ) THEN
464
465           IF(            WANTT ) THEN
466
467           JTOP           = 1
468
469           JBOT           = N
470
471           ELSE
472
473           JTOP           = KTOP
474
475           JBOT           = KBOT
476
477           END            IF
478
479           IF(            (  .NOT.BLK22  )  .OR.  (  INCOL.LT.KTOP  )  .OR.  (
480                          NDCOL.GT.KBOT ) .OR. ( NS.LE.2 ) ) THEN
481
482           K1             = MAX( 1, KTOP-INCOL )
483
484           NU             = ( KDU-MAX( 0, NDCOL-KBOT ) ) - K1 + 1
485
486           DO             160 JCOL = MIN( NDCOL, KBOT ) + 1, JBOT, NH
487
488           JLEN           = MIN( NH, JBOT-JCOL+1 )
489
490           CALL           DGEMM( 'C', 'N', NU, JLEN, NU, ONE,  U(  K1,  K1  ),
491                          LDU, H( INCOL+K1, JCOL ), LDH, ZERO, WH, LDWH )
492
493           CALL           DLACPY( 'ALL', NU, JLEN, WH, LDWH, H( INCOL+K1, JCOL
494                          ), LDH )
495
496           160            CONTINUE
497
498           DO             170 JROW = JTOP, MAX( KTOP, INCOL ) - 1, NV
499
500           JLEN           = MIN( NV, MAX( KTOP, INCOL )-JROW )
501
502           CALL           DGEMM(  'N',  'N',  JLEN,  NU,  NU,  ONE,  H(  JROW,
503                          INCOL+K1 ), LDH, U( K1, K1 ), LDU, ZERO, WV, LDWV )
504
505           CALL           DLACPY( 'ALL', JLEN, NU, WV, LDWV, H( JROW, INCOL+K1
506                          ), LDH )
507
508           170            CONTINUE
509
510           IF(            WANTZ ) THEN
511
512           DO             180 JROW = ILOZ, IHIZ, NV
513
514           JLEN           = MIN( NV, IHIZ-JROW+1 )
515
516           CALL           DGEMM(  'N',  'N',  JLEN,  NU,  NU,  ONE,  Z(  JROW,
517                          INCOL+K1 ), LDZ, U( K1, K1 ), LDU, ZERO, WV, LDWV )
518
519           CALL           DLACPY( 'ALL', JLEN, NU, WV, LDWV, Z( JROW, INCOL+K1
520                          ), LDZ )
521
522           180            CONTINUE
523
524           END            IF
525
526           ELSE
527
528           I2             = ( KDU+1 ) / 2
529
530           I4             = KDU
531
532           J2             = I4 - I2
533
534           J4             = KDU
535
536           KZS            = ( J4-J2 ) - ( NS+1 )
537
538           KNZ            = NS + 1
539
540           DO             190 JCOL = MIN( NDCOL, KBOT ) + 1, JBOT, NH
541
542           JLEN           = MIN( NH, JBOT-JCOL+1 )
543
544           CALL           DLACPY( 'ALL', KNZ, JLEN,  H(  INCOL+1+J2,  JCOL  ),
545                          LDH, WH( KZS+1, 1 ), LDWH )
546
547           CALL           DLASET( 'ALL', KZS, JLEN, ZERO, ZERO, WH, LDWH )
548
549           CALL           DTRMM(  'L', 'U', 'C', 'N', KNZ, JLEN, ONE, U( J2+1,
550                          1+KZS ), LDU, WH( KZS+1, 1 ), LDWH )
551
552           CALL           DGEMM( 'C', 'N', I2,  JLEN,  J2,  ONE,  U,  LDU,  H(
553                          INCOL+1, JCOL ), LDH, ONE, WH, LDWH )
554
555           CALL           DLACPY(  'ALL',  J2,  JLEN, H( INCOL+1, JCOL ), LDH,
556                          WH( I2+1, 1 ), LDWH )
557
558           CALL           DTRMM( 'L', 'L', 'C', 'N', J2, JLEN, ONE, U( 1, I2+1
559                          ), LDU, WH( I2+1, 1 ), LDWH )
560
561           CALL           DGEMM(  'C',  'N', I4-I2, JLEN, J4-J2, ONE, U( J2+1,
562                          I2+1 ), LDU, H( INCOL+1+J2, JCOL ),  LDH,  ONE,  WH(
563                          I2+1, 1 ), LDWH )
564
565           CALL           DLACPY( 'ALL', KDU, JLEN, WH, LDWH, H( INCOL+1, JCOL
566                          ), LDH )
567
568           190            CONTINUE
569
570           DO             200 JROW = JTOP, MAX( INCOL, KTOP ) - 1, NV
571
572           JLEN           = MIN( NV, MAX( INCOL, KTOP )-JROW )
573
574           CALL           DLACPY( 'ALL', JLEN, KNZ,  H(  JROW,  INCOL+1+J2  ),
575                          LDH, WV( 1, 1+KZS ), LDWV )
576
577           CALL           DLASET( 'ALL', JLEN, KZS, ZERO, ZERO, WV, LDWV )
578
579           CALL           DTRMM(  'R', 'U', 'N', 'N', JLEN, KNZ, ONE, U( J2+1,
580                          1+KZS ), LDU, WV( 1, 1+KZS ), LDWV )
581
582           CALL           DGEMM( 'N', 'N', JLEN, I2, J2, ONE, H( JROW, INCOL+1
583                          ), LDH, U, LDU, ONE, WV, LDWV )
584
585           CALL           DLACPY(  'ALL',  JLEN,  J2, H( JROW, INCOL+1 ), LDH,
586                          WV( 1, 1+I2 ), LDWV )
587
588           CALL           DTRMM( 'R', 'L', 'N', 'N', JLEN, I4-I2, ONE,  U(  1,
589                          I2+1 ), LDU, WV( 1, 1+I2 ), LDWV )
590
591           CALL           DGEMM(  'N',  'N', JLEN, I4-I2, J4-J2, ONE, H( JROW,
592                          INCOL+1+J2 ), LDH, U( J2+1, I2+1 ), LDU, ONE, WV( 1,
593                          1+I2 ), LDWV )
594
595           CALL           DLACPY( 'ALL', JLEN, KDU, WV, LDWV, H( JROW, INCOL+1
596                          ), LDH )
597
598           200            CONTINUE
599
600           IF(            WANTZ ) THEN
601
602           DO             210 JROW = ILOZ, IHIZ, NV
603
604           JLEN           = MIN( NV, IHIZ-JROW+1 )
605
606           CALL           DLACPY( 'ALL', JLEN, KNZ,  Z(  JROW,  INCOL+1+J2  ),
607                          LDZ, WV( 1, 1+KZS ), LDWV )
608
609           CALL           DLASET( 'ALL', JLEN, KZS, ZERO, ZERO, WV, LDWV )
610
611           CALL           DTRMM(  'R', 'U', 'N', 'N', JLEN, KNZ, ONE, U( J2+1,
612                          1+KZS ), LDU, WV( 1, 1+KZS ), LDWV )
613
614           CALL           DGEMM( 'N', 'N', JLEN, I2, J2, ONE, Z( JROW, INCOL+1
615                          ), LDZ, U, LDU, ONE, WV, LDWV )
616
617           CALL           DLACPY(  'ALL',  JLEN,  J2, Z( JROW, INCOL+1 ), LDZ,
618                          WV( 1, 1+I2 ), LDWV )
619
620           CALL           DTRMM( 'R', 'L', 'N', 'N', JLEN, I4-I2, ONE,  U(  1,
621                          I2+1 ), LDU, WV( 1, 1+I2 ), LDWV )
622
623           CALL           DGEMM(  'N',  'N', JLEN, I4-I2, J4-J2, ONE, Z( JROW,
624                          INCOL+1+J2 ), LDZ, U( J2+1, I2+1 ), LDU, ONE, WV( 1,
625                          1+I2 ), LDWV )
626
627           CALL           DLACPY( 'ALL', JLEN, KDU, WV, LDWV, Z( JROW, INCOL+1
628                          ), LDZ )
629
630           210            CONTINUE
631
632           END            IF
633
634           END            IF
635
636           END            IF
637
638           220            CONTINUE
639
640           END
641

PURPOSE

643 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       DLAQR5(1)