1CLAQR5(1)           LAPACK auxiliary routine (version 3.2)           CLAQR5(1)
2
3
4

NAME

SYNOPSIS

7       SUBROUTINE CLAQR5( WANTT,  WANTZ,  KACC22, N, KTOP, KBOT, NSHFTS, S, H,
8                          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           COMPLEX        H( LDH, * ), S( * ), U( LDU, * ), V( LDV, *  ),  WH(
17                          LDWH, * ), WV( LDWV, * ), Z( LDZ, * )
18
19           COMPLEX        ZERO, ONE
20
21           PARAMETER      ( ZERO = ( 0.0e0, 0.0e0 ), ONE = ( 1.0e0, 0.0e0 ) )
22
23           REAL           RZERO, RONE
24
25           PARAMETER      ( RZERO = 0.0e0, RONE = 1.0e0 )
26
27           COMPLEX        ALPHA, BETA, CDUM, REFSUM
28
29           REAL           H11,  H12,  H21,  H22,  SAFMAX, SAFMIN, SCL, SMLNUM,
30                          TST1, TST2, ULP
31
32           INTEGER        I2, I4, INCOL, J, J2, J4, JBOT,  JCOL,  JLEN,  JROW,
33                          JTOP,  K,  K1,  KDU,  KMS,  KNZ, KRCOL, KZS, M, M22,
34                          MBOT, MEND, MSTART, MTOP, NBMPS, NDCOL, NS, NU
35
36           LOGICAL        ACCUM, BLK22, BMP22
37
38           REAL           SLAMCH
39
40           EXTERNAL       SLAMCH
41
42           INTRINSIC      ABS, AIMAG, CONJG, MAX, MIN, MOD, REAL
43
44           COMPLEX        VT( 3 )
45
46           EXTERNAL       CGEMM, CLACPY, CLAQR1, CLARFG, CLASET, CTRMM, SLABAD
47
48           REAL           CABS1
49
50           CABS1(         CDUM ) = ABS( REAL( CDUM ) ) + ABS( AIMAG( CDUM ) )
51
52           IF(            NSHFTS.LT.2 ) RETURN
53
54           IF(            KTOP.GE.KBOT ) RETURN
55
56           NS             = NSHFTS - MOD( NSHFTS, 2 )
57
58           SAFMIN         = SLAMCH( 'SAFE MINIMUM' )
59
60           SAFMAX         = RONE / SAFMIN
61
62           CALL           SLABAD( SAFMIN, SAFMAX )
63
64           ULP            = SLAMCH( 'PRECISION' )
65
66           SMLNUM         = SAFMIN*( REAL( N ) / ULP )
67
68           ACCUM          = ( KACC22.EQ.1 ) .OR. ( KACC22.EQ.2 )
69
70           BLK22          = ( NS.GT.2 ) .AND. ( KACC22.EQ.2 )
71
72           IF(            KTOP+2.LE.KBOT ) H( KTOP+2, KTOP ) = ZERO
73
74           NBMPS          = NS / 2
75
76           KDU            = 6*NBMPS - 3
77
78           DO             210 INCOL = 3*( 1-NBMPS ) + KTOP  -  1,  KBOT  -  2,
79                          3*NBMPS - 2
80
81           NDCOL          = INCOL + KDU
82
83           IF(            ACCUM  ) CALL CLASET( 'ALL', KDU, KDU, ZERO, ONE, U,
84                          LDU )
85
86           DO             140 KRCOL = INCOL, MIN( INCOL+3*NBMPS-3, KBOT-2 )
87
88           MTOP           = MAX( 1, ( ( KTOP-1 )-KRCOL+2 ) / 3+1 )
89
90           MBOT           = MIN( NBMPS, ( KBOT-KRCOL ) / 3 )
91
92           M22            = MBOT + 1
93
94           BMP22          = ( MBOT.LT.NBMPS ) .AND. ( KRCOL+3*( M22-1 )  ).EQ.
95                          ( KBOT-2 )
96
97           DO             10 M = MTOP, MBOT
98
99           K              = KRCOL + 3*( M-1 )
100
101           IF(            K.EQ.KTOP-1 ) THEN
102
103           CALL           CLAQR1(  3, H( KTOP, KTOP ), LDH, S( 2*M-1 ), S( 2*M
104                          ), V( 1, M ) )
105
106           ALPHA          = V( 1, M )
107
108           CALL           CLARFG( 3, ALPHA, V( 2, M ), 1, V( 1, M ) )
109
110           ELSE
111
112           BETA           = H( K+1, K )
113
114           V(             2, M ) = H( K+2, K )
115
116           V(             3, M ) = H( K+3, K )
117
118           CALL           CLARFG( 3, BETA, V( 2, M ), 1, V( 1, M ) )
119
120           IF(            H( K+3, K ).NE.ZERO .OR. H(  K+3,  K+1  ).NE.   ZERO
121                          .OR. H( K+3, K+2 ).EQ.ZERO ) THEN
122
123           H(             K+1, K ) = BETA
124
125           H(             K+2, K ) = ZERO
126
127           H(             K+3, K ) = ZERO
128
129           ELSE
130
131           CALL           CLAQR1( 3, H( K+1, K+1 ), LDH, S( 2*M-1 ), S( 2*M ),
132                          VT )
133
134           ALPHA          = VT( 1 )
135
136           CALL           CLARFG( 3, ALPHA, VT( 2 ), 1, VT( 1 ) )
137
138           REFSUM         = CONJG( VT( 1 ) )* ( H( K+1, K )+CONJG( VT( 2 )  )*
139                          H( K+2, K ) )
140
141           IF(            CABS1(  H(  K+2,  K  )-REFSUM*VT( 2 ) )+ CABS1( REF‐
142                          SUM*VT( 3 ) ).GT.ULP* ( CABS1( H( K, K ) )+CABS1( H(
143                          K+1, K+1 ) )+CABS1( H( K+2, K+2 ) ) ) ) THEN
144
145           H(             K+1, K ) = BETA
146
147           H(             K+2, K ) = ZERO
148
149           H(             K+3, K ) = ZERO
150
151           ELSE
152
153           H(             K+1, K ) = H( K+1, K ) - REFSUM
154
155           H(             K+2, K ) = ZERO
156
157           H(             K+3, K ) = ZERO
158
159           V(             1, M ) = VT( 1 )
160
161           V(             2, M ) = VT( 2 )
162
163           V(             3, M ) = VT( 3 )
164
165           END            IF
166
167           END            IF
168
169           END            IF
170
171           10             CONTINUE
172
173           K              = KRCOL + 3*( M22-1 )
174
175           IF(            BMP22 ) THEN
176
177           IF(            K.EQ.KTOP-1 ) THEN
178
179           CALL           CLAQR1(  2,  H(  K+1,  K+1  ), LDH, S( 2*M22-1 ), S(
180                          2*M22 ), V( 1, M22 ) )
181
182           BETA           = V( 1, M22 )
183
184           CALL           CLARFG( 2, BETA, V( 2, M22 ), 1, V( 1, M22 ) )
185
186           ELSE
187
188           BETA           = H( K+1, K )
189
190           V(             2, M22 ) = H( K+2, K )
191
192           CALL           CLARFG( 2, BETA, V( 2, M22 ), 1, V( 1, M22 ) )
193
194           H(             K+1, K ) = BETA
195
196           H(             K+2, K ) = ZERO
197
198           END            IF
199
200           END            IF
201
202           IF(            ACCUM ) THEN
203
204           JBOT           = MIN( NDCOL, KBOT )
205
206           ELSE           IF( WANTT ) THEN
207
208           JBOT           = N
209
210           ELSE
211
212           JBOT           = KBOT
213
214           END            IF
215
216           DO             30 J = MAX( KTOP, KRCOL ), JBOT
217
218           MEND           = MIN( MBOT, ( J-KRCOL+2 ) / 3 )
219
220           DO             20 M = MTOP, MEND
221
222           K              = KRCOL + 3*( M-1 )
223
224           REFSUM         = CONJG( V( 1, M ) )* ( H( K+1, J )+CONJG( V( 2, M )
225                          )*H( K+2, J )+ CONJG( V( 3, M ) )*H( K+3, J ) )
226
227           H(             K+1, J ) = H( K+1, J ) - REFSUM
228
229           H(             K+2, J ) = H( K+2, J ) - REFSUM*V( 2, M )
230
231           H(             K+3, J ) = H( K+3, J ) - REFSUM*V( 3, M )
232
233           20             CONTINUE
234
235           30             CONTINUE
236
237           IF(            BMP22 ) THEN
238
239           K              = KRCOL + 3*( M22-1 )
240
241           DO             40 J = MAX( K+1, KTOP ), JBOT
242
243           REFSUM         =  CONJG(  V( 1, M22 ) )* ( H( K+1, J )+CONJG( V( 2,
244                          M22 ) )* H( K+2, J ) )
245
246           H(             K+1, J ) = H( K+1, J ) - REFSUM
247
248           H(             K+2, J ) = H( K+2, J ) - REFSUM*V( 2, M22 )
249
250           40             CONTINUE
251
252           END            IF
253
254           IF(            ACCUM ) THEN
255
256           JTOP           = MAX( KTOP, INCOL )
257
258           ELSE           IF( WANTT ) THEN
259
260           JTOP           = 1
261
262           ELSE
263
264           JTOP           = KTOP
265
266           END            IF
267
268           DO             80 M = MTOP, MBOT
269
270           IF(            V( 1, M ).NE.ZERO ) THEN
271
272           K              = KRCOL + 3*( M-1 )
273
274           DO             50 J = JTOP, MIN( KBOT, K+3 )
275
276           REFSUM         = V( 1, M )*( H( J, K+1 )+V( 2, M )* H( J, K+2  )+V(
277                          3, M )*H( J, K+3 ) )
278
279           H(             J, K+1 ) = H( J, K+1 ) - REFSUM
280
281           H(             J, K+2 ) = H( J, K+2 ) - REFSUM*CONJG( V( 2, M ) )
282
283           H(             J, K+3 ) = H( J, K+3 ) - REFSUM*CONJG( V( 3, M ) )
284
285           50             CONTINUE
286
287           IF(            ACCUM ) THEN
288
289           KMS            = K - INCOL
290
291           DO             60 J = MAX( 1, KTOP-INCOL ), KDU
292
293           REFSUM         =  V(  1, M )*( U( J, KMS+1 )+V( 2, M )* U( J, KMS+2
294                          )+V( 3, M )*U( J, KMS+3 ) )
295
296           U(             J, KMS+1 ) = U( J, KMS+1 ) - REFSUM
297
298           U(             J, KMS+2 ) = U( J, KMS+2 ) - REFSUM*CONJG( V( 2, M )
299                          )
300
301           U(             J, KMS+3 ) = U( J, KMS+3 ) - REFSUM*CONJG( V( 3, M )
302                          )
303
304           60             CONTINUE
305
306           ELSE           IF( WANTZ ) THEN
307
308           DO             70 J = ILOZ, IHIZ
309
310           REFSUM         = V( 1, M )*( Z( J, K+1 )+V( 2, M )* Z( J, K+2  )+V(
311                          3, M )*Z( J, K+3 ) )
312
313           Z(             J, K+1 ) = Z( J, K+1 ) - REFSUM
314
315           Z(             J, K+2 ) = Z( J, K+2 ) - REFSUM*CONJG( V( 2, M ) )
316
317           Z(             J, K+3 ) = Z( J, K+3 ) - REFSUM*CONJG( V( 3, M ) )
318
319           70             CONTINUE
320
321           END            IF
322
323           END            IF
324
325           80             CONTINUE
326
327           K              = KRCOL + 3*( M22-1 )
328
329           IF(            BMP22 .AND. ( V( 1, M22 ).NE.ZERO ) ) THEN
330
331           DO             90 J = JTOP, MIN( KBOT, K+3 )
332
333           REFSUM         = V( 1, M22 )*( H( J, K+1 )+V( 2, M22 )* H( J, K+2 )
334                          )
335
336           H(             J, K+1 ) = H( J, K+1 ) - REFSUM
337
338           H(             J, K+2 ) = H( J, K+2 ) - REFSUM*CONJG( V( 2, M22 ) )
339
340           90             CONTINUE
341
342           IF(            ACCUM ) THEN
343
344           KMS            = K - INCOL
345
346           DO             100 J = MAX( 1, KTOP-INCOL ), KDU
347
348           REFSUM         = V( 1, M22 )*( U( J, KMS+1 )+V( 2,  M22  )*  U(  J,
349                          KMS+2 ) )
350
351           U(             J, KMS+1 ) = U( J, KMS+1 ) - REFSUM
352
353           U(             J, KMS+2 ) = U( J, KMS+2 ) - REFSUM*CONJG( V( 2, M22
354                          ) )
355
356           100            CONTINUE
357
358           ELSE           IF( WANTZ ) THEN
359
360           DO             110 J = ILOZ, IHIZ
361
362           REFSUM         = V( 1, M22 )*( Z( J, K+1 )+V( 2, M22 )* Z( J, K+2 )
363                          )
364
365           Z(             J, K+1 ) = Z( J, K+1 ) - REFSUM
366
367           Z(             J, K+2 ) = Z( J, K+2 ) - REFSUM*CONJG( V( 2, M22 ) )
368
369           110            CONTINUE
370
371           END            IF
372
373           END            IF
374
375           MSTART         = MTOP
376
377           IF(            KRCOL+3*( MSTART-1 ).LT.KTOP ) MSTART = MSTART + 1
378
379           MEND           = MBOT
380
381           IF(            BMP22 ) MEND = MEND + 1
382
383           IF(            KRCOL.EQ.KBOT-2 ) MEND = MEND + 1
384
385           DO             120 M = MSTART, MEND
386
387           K              = MIN( KBOT-1, KRCOL+3*( M-1 ) )
388
389           IF(            H( K+1, K ).NE.ZERO ) THEN
390
391           TST1           = CABS1( H( K, K ) ) + CABS1( H( K+1, K+1 ) )
392
393           IF(            TST1.EQ.RZERO ) THEN
394
395           IF(            K.GE.KTOP+1 ) TST1 = TST1 + CABS1( H( K, K-1 ) )
396
397           IF(            K.GE.KTOP+2 ) TST1 = TST1 + CABS1( H( K, K-2 ) )
398
399           IF(            K.GE.KTOP+3 ) TST1 = TST1 + CABS1( H( K, K-3 ) )
400
401           IF(            K.LE.KBOT-2 ) TST1 = TST1 + CABS1( H( K+2, K+1 ) )
402
403           IF(            K.LE.KBOT-3 ) TST1 = TST1 + CABS1( H( K+3, K+1 ) )
404
405           IF(            K.LE.KBOT-4 ) TST1 = TST1 + CABS1( H( K+4, K+1 ) )
406
407           END            IF
408
409           IF(            CABS1(  H(  K+1,  K ) ).LE.MAX( SMLNUM, ULP*TST1 ) )
410                          THEN
411
412           H12            = MAX( CABS1( H( K+1, K ) ), CABS1( H( K, K+1 ) ) )
413
414           H21            = MIN( CABS1( H( K+1, K ) ), CABS1( H( K, K+1 ) ) )
415
416           H11            = MAX( CABS1( H( K+1, K+1 ) ), CABS1( H( K,  K  )-H(
417                          K+1, K+1 ) ) )
418
419           H22            =  MIN(  CABS1( H( K+1, K+1 ) ), CABS1( H( K, K )-H(
420                          K+1, K+1 ) ) )
421
422           SCL            = H11 + H12
423
424           TST2           = H22*( H11 / SCL )
425
426           IF(            TST2.EQ.RZERO .OR. H21*( H12 / SCL ).LE.  MAX(  SML‐
427                          NUM, ULP*TST2 ) )H( K+1, K ) = ZERO
428
429           END            IF
430
431           END            IF
432
433           120            CONTINUE
434
435           MEND           = MIN( NBMPS, ( KBOT-KRCOL-1 ) / 3 )
436
437           DO             130 M = MTOP, MEND
438
439           K              = KRCOL + 3*( M-1 )
440
441           REFSUM         = V( 1, M )*V( 3, M )*H( K+4, K+3 )
442
443           H(             K+4, K+1 ) = -REFSUM
444
445           H(             K+4, K+2 ) = -REFSUM*CONJG( V( 2, M ) )
446
447           H(             K+4, K+3 ) = H( K+4, K+3 ) - REFSUM*CONJG( V( 3, M )
448                          )
449
450           130            CONTINUE
451
452           140            CONTINUE
453
454           IF(            ACCUM ) THEN
455
456           IF(            WANTT ) THEN
457
458           JTOP           = 1
459
460           JBOT           = N
461
462           ELSE
463
464           JTOP           = KTOP
465
466           JBOT           = KBOT
467
468           END            IF
469
470           IF(            ( .NOT.BLK22  )  .OR.  (  INCOL.LT.KTOP  )  .OR.   (
471                          NDCOL.GT.KBOT ) .OR. ( NS.LE.2 ) ) THEN
472
473           K1             = MAX( 1, KTOP-INCOL )
474
475           NU             = ( KDU-MAX( 0, NDCOL-KBOT ) ) - K1 + 1
476
477           DO             150 JCOL = MIN( NDCOL, KBOT ) + 1, JBOT, NH
478
479           JLEN           = MIN( NH, JBOT-JCOL+1 )
480
481           CALL           CGEMM(  'C',  'N',  NU,  JLEN, NU, ONE, U( K1, K1 ),
482                          LDU, H( INCOL+K1, JCOL ), LDH, ZERO, WH, LDWH )
483
484           CALL           CLACPY( 'ALL', NU, JLEN, WH, LDWH, H( INCOL+K1, JCOL
485                          ), LDH )
486
487           150            CONTINUE
488
489           DO             160 JROW = JTOP, MAX( KTOP, INCOL ) - 1, NV
490
491           JLEN           = MIN( NV, MAX( KTOP, INCOL )-JROW )
492
493           CALL           CGEMM(  'N',  'N',  JLEN,  NU,  NU,  ONE,  H(  JROW,
494                          INCOL+K1 ), LDH, U( K1, K1 ), LDU, ZERO, WV, LDWV )
495
496           CALL           CLACPY( 'ALL', JLEN, NU, WV, LDWV, H( JROW, INCOL+K1
497                          ), LDH )
498
499           160            CONTINUE
500
501           IF(            WANTZ ) THEN
502
503           DO             170 JROW = ILOZ, IHIZ, NV
504
505           JLEN           = MIN( NV, IHIZ-JROW+1 )
506
507           CALL           CGEMM(  'N',  'N',  JLEN,  NU,  NU,  ONE,  Z(  JROW,
508                          INCOL+K1 ), LDZ, U( K1, K1 ), LDU, ZERO, WV, LDWV )
509
510           CALL           CLACPY( 'ALL', JLEN, NU, WV, LDWV, Z( JROW, INCOL+K1
511                          ), LDZ )
512
513           170            CONTINUE
514
515           END            IF
516
517           ELSE
518
519           I2             = ( KDU+1 ) / 2
520
521           I4             = KDU
522
523           J2             = I4 - I2
524
525           J4             = KDU
526
527           KZS            = ( J4-J2 ) - ( NS+1 )
528
529           KNZ            = NS + 1
530
531           DO             180 JCOL = MIN( NDCOL, KBOT ) + 1, JBOT, NH
532
533           JLEN           = MIN( NH, JBOT-JCOL+1 )
534
535           CALL           CLACPY(  'ALL',  KNZ,  JLEN,  H( INCOL+1+J2, JCOL ),
536                          LDH, WH( KZS+1, 1 ), LDWH )
537
538           CALL           CLASET( 'ALL', KZS, JLEN, ZERO, ZERO, WH, LDWH )
539
540           CALL           CTRMM( 'L', 'U', 'C', 'N', KNZ, JLEN, ONE, U(  J2+1,
541                          1+KZS ), LDU, WH( KZS+1, 1 ), LDWH )
542
543           CALL           CGEMM(  'C',  'N',  I2,  JLEN,  J2,  ONE, U, LDU, H(
544                          INCOL+1, JCOL ), LDH, ONE, WH, LDWH )
545
546           CALL           CLACPY( 'ALL', J2, JLEN, H( INCOL+1,  JCOL  ),  LDH,
547                          WH( I2+1, 1 ), LDWH )
548
549           CALL           CTRMM( 'L', 'L', 'C', 'N', J2, JLEN, ONE, U( 1, I2+1
550                          ), LDU, WH( I2+1, 1 ), LDWH )
551
552           CALL           CGEMM( 'C', 'N', I4-I2, JLEN, J4-J2, ONE,  U(  J2+1,
553                          I2+1  ),  LDU,  H( INCOL+1+J2, JCOL ), LDH, ONE, WH(
554                          I2+1, 1 ), LDWH )
555
556           CALL           CLACPY( 'ALL', KDU, JLEN, WH, LDWH, H( INCOL+1, JCOL
557                          ), LDH )
558
559           180            CONTINUE
560
561           DO             190 JROW = JTOP, MAX( INCOL, KTOP ) - 1, NV
562
563           JLEN           = MIN( NV, MAX( INCOL, KTOP )-JROW )
564
565           CALL           CLACPY(  'ALL',  JLEN,  KNZ,  H( JROW, INCOL+1+J2 ),
566                          LDH, WV( 1, 1+KZS ), LDWV )
567
568           CALL           CLASET( 'ALL', JLEN, KZS, ZERO, ZERO, WV, LDWV )
569
570           CALL           CTRMM( 'R', 'U', 'N', 'N', JLEN, KNZ, ONE, U(  J2+1,
571                          1+KZS ), LDU, WV( 1, 1+KZS ), LDWV )
572
573           CALL           CGEMM( 'N', 'N', JLEN, I2, J2, ONE, H( JROW, INCOL+1
574                          ), LDH, U, LDU, ONE, WV, LDWV )
575
576           CALL           CLACPY( 'ALL', JLEN, J2, H( JROW,  INCOL+1  ),  LDH,
577                          WV( 1, 1+I2 ), LDWV )
578
579           CALL           CTRMM(  'R',  'L', 'N', 'N', JLEN, I4-I2, ONE, U( 1,
580                          I2+1 ), LDU, WV( 1, 1+I2 ), LDWV )
581
582           CALL           CGEMM( 'N', 'N', JLEN, I4-I2, J4-J2, ONE,  H(  JROW,
583                          INCOL+1+J2 ), LDH, U( J2+1, I2+1 ), LDU, ONE, WV( 1,
584                          1+I2 ), LDWV )
585
586           CALL           CLACPY( 'ALL', JLEN, KDU, WV, LDWV, H( JROW, INCOL+1
587                          ), LDH )
588
589           190            CONTINUE
590
591           IF(            WANTZ ) THEN
592
593           DO             200 JROW = ILOZ, IHIZ, NV
594
595           JLEN           = MIN( NV, IHIZ-JROW+1 )
596
597           CALL           CLACPY(  'ALL',  JLEN,  KNZ,  Z( JROW, INCOL+1+J2 ),
598                          LDZ, WV( 1, 1+KZS ), LDWV )
599
600           CALL           CLASET( 'ALL', JLEN, KZS, ZERO, ZERO, WV, LDWV )
601
602           CALL           CTRMM( 'R', 'U', 'N', 'N', JLEN, KNZ, ONE, U(  J2+1,
603                          1+KZS ), LDU, WV( 1, 1+KZS ), LDWV )
604
605           CALL           CGEMM( 'N', 'N', JLEN, I2, J2, ONE, Z( JROW, INCOL+1
606                          ), LDZ, U, LDU, ONE, WV, LDWV )
607
608           CALL           CLACPY( 'ALL', JLEN, J2, Z( JROW,  INCOL+1  ),  LDZ,
609                          WV( 1, 1+I2 ), LDWV )
610
611           CALL           CTRMM(  'R',  'L', 'N', 'N', JLEN, I4-I2, ONE, U( 1,
612                          I2+1 ), LDU, WV( 1, 1+I2 ), LDWV )
613
614           CALL           CGEMM( 'N', 'N', JLEN, I4-I2, J4-J2, ONE,  Z(  JROW,
615                          INCOL+1+J2 ), LDZ, U( J2+1, I2+1 ), LDU, ONE, WV( 1,
616                          1+I2 ), LDWV )
617
618           CALL           CLACPY( 'ALL', JLEN, KDU, WV, LDWV, Z( JROW, INCOL+1
619                          ), LDZ )
620
621           200            CONTINUE
622
623           END            IF
624
625           END            IF
626
627           END            IF
628
629           210            CONTINUE
630
631           END
632

PURPOSE

634 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       CLAQR5(1)