1SLAQR5(1)           LAPACK auxiliary routine (version 3.1)           SLAQR5(1)
2
3
4

NAME

SYNOPSIS

7       SUBROUTINE SLAQR5( 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           REAL           H( LDH, * ), SI( * ), SR( * ), U( LDU, * ), V(  LDV,
17                          * ), WH( LDWH, * ), WV( LDWV, * ), Z( LDZ, * )
18
19           REAL           ZERO, ONE
20
21           PARAMETER      ( ZERO = 0.0e0, ONE = 1.0e0 )
22
23           REAL           ALPHA,  BETA,  H11,  H12,  H21, H22, REFSUM, SAFMAX,
24                          SAFMIN, SCL, SMLNUM, SWAP, TST1, TST2, ULP
25
26           INTEGER        I, I2, I4, INCOL, J, J2, J4, JBOT, JCOL, JLEN, JROW,
27                          JTOP,  K,  K1,  KDU,  KMS,  KNZ, KRCOL, KZS, M, M22,
28                          MBOT, MEND, MSTART, MTOP, NBMPS, NDCOL, NS, NU
29
30           LOGICAL        ACCUM, BLK22, BMP22
31
32           REAL           SLAMCH
33
34           EXTERNAL       SLAMCH
35
36           INTRINSIC      ABS, MAX, MIN, MOD, REAL
37
38           REAL           VT( 3 )
39
40           EXTERNAL       SGEMM, SLABAD, SLACPY, SLAQR1, SLARFG, SLASET, STRMM
41
42           IF(            NSHFTS.LT.2 ) RETURN
43
44           IF(            KTOP.GE.KBOT ) RETURN
45
46           DO             10 I = 1, NSHFTS - 2, 2
47
48           IF(            SI( I ).NE.-SI( I+1 ) ) THEN
49
50           SWAP           = SR( I )
51
52           SR(            I ) = SR( I+1 )
53
54           SR(            I+1 ) = SR( I+2 )
55
56           SR(            I+2 ) = SWAP
57
58           SWAP           = SI( I )
59
60           SI(            I ) = SI( I+1 )
61
62           SI(            I+1 ) = SI( I+2 )
63
64           SI(            I+2 ) = SWAP
65
66           END            IF
67
68           10             CONTINUE
69
70           NS             = NSHFTS - MOD( NSHFTS, 2 )
71
72           SAFMIN         = SLAMCH( 'SAFE MINIMUM' )
73
74           SAFMAX         = ONE / SAFMIN
75
76           CALL           SLABAD( SAFMIN, SAFMAX )
77
78           ULP            = SLAMCH( 'PRECISION' )
79
80           SMLNUM         = SAFMIN*( REAL( N ) / ULP )
81
82           ACCUM          = ( KACC22.EQ.1 ) .OR. ( KACC22.EQ.2 )
83
84           BLK22          = ( NS.GT.2 ) .AND. ( KACC22.EQ.2 )
85
86           IF(            KTOP+2.LE.KBOT ) H( KTOP+2, KTOP ) = ZERO
87
88           NBMPS          = NS / 2
89
90           KDU            = 6*NBMPS - 3
91
92           DO             220 INCOL = 3*( 1-NBMPS ) + KTOP  -  1,  KBOT  -  2,
93                          3*NBMPS - 2
94
95           NDCOL          = INCOL + KDU
96
97           IF(            ACCUM  ) CALL SLASET( 'ALL', KDU, KDU, ZERO, ONE, U,
98                          LDU )
99
100           DO             150 KRCOL = INCOL, MIN( INCOL+3*NBMPS-3, KBOT-2 )
101
102           MTOP           = MAX( 1, ( ( KTOP-1 )-KRCOL+2 ) / 3+1 )
103
104           MBOT           = MIN( NBMPS, ( KBOT-KRCOL ) / 3 )
105
106           M22            = MBOT + 1
107
108           BMP22          = ( MBOT.LT.NBMPS ) .AND. ( KRCOL+3*( M22-1 )  ).EQ.
109                          ( KBOT-2 )
110
111           DO             20 M = MTOP, MBOT
112
113           K              = KRCOL + 3*( M-1 )
114
115           IF(            K.EQ.KTOP-1 ) THEN
116
117           CALL           SLAQR1(  3,  H(  KTOP, KTOP ), LDH, SR( 2*M-1 ), SI(
118                          2*M-1 ), SR( 2*M ), SI( 2*M ), V( 1, M ) )
119
120           ALPHA          = V( 1, M )
121
122           CALL           SLARFG( 3, ALPHA, V( 2, M ), 1, V( 1, M ) )
123
124           ELSE
125
126           BETA           = H( K+1, K )
127
128           V(             2, M ) = H( K+2, K )
129
130           V(             3, M ) = H( K+3, K )
131
132           CALL           SLARFG( 3, BETA, V( 2, M ), 1, V( 1, M ) )
133
134           IF(            V( 1, M ).NE.ZERO .AND.  ( V( 3, M ).NE.ZERO .OR.  (
135                          H(  K+3, K+1 ).EQ.ZERO .AND. H( K+3, K+2 ).EQ.ZERO )
136                          ) ) 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           SLAQR1( 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           SCL            = ABS( VT( 1 ) ) + ABS( VT( 2 ) ) + ABS( VT( 3 ) )
150
151           IF(            SCL.NE.ZERO ) THEN
152
153           VT(            1 ) = VT( 1 ) / SCL
154
155           VT(            2 ) = VT( 2 ) / SCL
156
157           VT(            3 ) = VT( 3 ) / SCL
158
159           END            IF
160
161           IF(            ABS(  H( K+1, K ) )*( ABS( VT( 2 ) )+ ABS( VT( 3 ) )
162                          ).GT.ULP*ABS( VT( 1 ) )* ( ABS( H( K, K ) )+ABS(  H(
163                          K+1, K+1 ) )+ABS( H( K+2, K+2 ) ) ) ) THEN
164
165           IF(            V( 2, M ).EQ.ZERO .AND. V( 3, M ).EQ.ZERO ) THEN
166
167           V(             1, M ) = ZERO
168
169           ELSE
170
171           H(             K+1, K ) = BETA
172
173           H(             K+2, K ) = ZERO
174
175           H(             K+3, K ) = ZERO
176
177           END            IF
178
179           ELSE
180
181           ALPHA          = VT( 1 )
182
183           CALL           SLARFG( 3, ALPHA, VT( 2 ), 1, VT( 1 ) )
184
185           REFSUM         =  H(  K+1,  K  )  + H( K+2, K )*VT( 2 ) + H( K+3, K
186                          )*VT( 3 )
187
188           H(             K+1, K ) = H( K+1, K ) - VT( 1 )*REFSUM
189
190           H(             K+2, K ) = ZERO
191
192           H(             K+3, K ) = ZERO
193
194           V(             1, M ) = VT( 1 )
195
196           V(             2, M ) = VT( 2 )
197
198           V(             3, M ) = VT( 3 )
199
200           END            IF
201
202           END            IF
203
204           END            IF
205
206           20             CONTINUE
207
208           K              = KRCOL + 3*( M22-1 )
209
210           IF(            BMP22 ) THEN
211
212           IF(            K.EQ.KTOP-1 ) THEN
213
214           CALL           SLAQR1( 2, H( K+1, K+1 ), LDH, SR(  2*M22-1  ),  SI(
215                          2*M22-1 ), SR( 2*M22 ), SI( 2*M22 ), V( 1, M22 ) )
216
217           BETA           = V( 1, M22 )
218
219           CALL           SLARFG( 2, BETA, V( 2, M22 ), 1, V( 1, M22 ) )
220
221           ELSE
222
223           BETA           = H( K+1, K )
224
225           V(             2, M22 ) = H( K+2, K )
226
227           CALL           SLARFG( 2, BETA, V( 2, M22 ), 1, V( 1, M22 ) )
228
229           H(             K+1, K ) = BETA
230
231           H(             K+2, K ) = ZERO
232
233           END            IF
234
235           ELSE
236
237           V(             1, M22 ) = ZERO
238
239           END            IF
240
241           IF(            ACCUM ) THEN
242
243           JBOT           = MIN( NDCOL, KBOT )
244
245           ELSE           IF( WANTT ) THEN
246
247           JBOT           = N
248
249           ELSE
250
251           JBOT           = KBOT
252
253           END            IF
254
255           DO             40 J = MAX( KTOP, KRCOL ), JBOT
256
257           MEND           = MIN( MBOT, ( J-KRCOL+2 ) / 3 )
258
259           DO             30 M = MTOP, MEND
260
261           K              = KRCOL + 3*( M-1 )
262
263           REFSUM         =  V( 1, M )*( H( K+1, J )+V( 2, M )* H( K+2, J )+V(
264                          3, M )*H( K+3, J ) )
265
266           H(             K+1, J ) = H( K+1, J ) - REFSUM
267
268           H(             K+2, J ) = H( K+2, J ) - REFSUM*V( 2, M )
269
270           H(             K+3, J ) = H( K+3, J ) - REFSUM*V( 3, M )
271
272           30             CONTINUE
273
274           40             CONTINUE
275
276           IF(            BMP22 ) THEN
277
278           K              = KRCOL + 3*( M22-1 )
279
280           DO             50 J = MAX( K+1, KTOP ), JBOT
281
282           REFSUM         = V( 1, M22 )*( H( K+1, J )+V( 2, M22 )* H( K+2, J )
283                          )
284
285           H(             K+1, J ) = H( K+1, J ) - REFSUM
286
287           H(             K+2, J ) = H( K+2, J ) - REFSUM*V( 2, M22 )
288
289           50             CONTINUE
290
291           END            IF
292
293           IF(            ACCUM ) THEN
294
295           JTOP           = MAX( KTOP, INCOL )
296
297           ELSE           IF( WANTT ) THEN
298
299           JTOP           = 1
300
301           ELSE
302
303           JTOP           = KTOP
304
305           END            IF
306
307           DO             90 M = MTOP, MBOT
308
309           IF(            V( 1, M ).NE.ZERO ) THEN
310
311           K              = KRCOL + 3*( M-1 )
312
313           DO             60 J = JTOP, MIN( KBOT, K+3 )
314
315           REFSUM         =  V( 1, M )*( H( J, K+1 )+V( 2, M )* H( J, K+2 )+V(
316                          3, M )*H( J, K+3 ) )
317
318           H(             J, K+1 ) = H( J, K+1 ) - REFSUM
319
320           H(             J, K+2 ) = H( J, K+2 ) - REFSUM*V( 2, M )
321
322           H(             J, K+3 ) = H( J, K+3 ) - REFSUM*V( 3, M )
323
324           60             CONTINUE
325
326           IF(            ACCUM ) THEN
327
328           KMS            = K - INCOL
329
330           DO             70 J = MAX( 1, KTOP-INCOL ), KDU
331
332           REFSUM         = V( 1, M )*( U( J, KMS+1 )+V( 2, M )* U(  J,  KMS+2
333                          )+V( 3, M )*U( J, KMS+3 ) )
334
335           U(             J, KMS+1 ) = U( J, KMS+1 ) - REFSUM
336
337           U(             J, KMS+2 ) = U( J, KMS+2 ) - REFSUM*V( 2, M )
338
339           U(             J, KMS+3 ) = U( J, KMS+3 ) - REFSUM*V( 3, M )
340
341           70             CONTINUE
342
343           ELSE           IF( WANTZ ) THEN
344
345           DO             80 J = ILOZ, IHIZ
346
347           REFSUM         =  V( 1, M )*( Z( J, K+1 )+V( 2, M )* Z( J, K+2 )+V(
348                          3, M )*Z( J, K+3 ) )
349
350           Z(             J, K+1 ) = Z( J, K+1 ) - REFSUM
351
352           Z(             J, K+2 ) = Z( J, K+2 ) - REFSUM*V( 2, M )
353
354           Z(             J, K+3 ) = Z( J, K+3 ) - REFSUM*V( 3, M )
355
356           80             CONTINUE
357
358           END            IF
359
360           END            IF
361
362           90             CONTINUE
363
364           K              = KRCOL + 3*( M22-1 )
365
366           IF(            BMP22 .AND. ( V( 1, M22 ).NE.ZERO ) ) THEN
367
368           DO             100 J = JTOP, MIN( KBOT, K+3 )
369
370           REFSUM         = V( 1, M22 )*( H( J, K+1 )+V( 2, M22 )* H( J, K+2 )
371                          )
372
373           H(             J, K+1 ) = H( J, K+1 ) - REFSUM
374
375           H(             J, K+2 ) = H( J, K+2 ) - REFSUM*V( 2, M22 )
376
377           100            CONTINUE
378
379           IF(            ACCUM ) THEN
380
381           KMS            = K - INCOL
382
383           DO             110 J = MAX( 1, KTOP-INCOL ), KDU
384
385           REFSUM         =  V(  1,  M22  )*( U( J, KMS+1 )+V( 2, M22 )* U( J,
386                          KMS+2 ) )
387
388           U(             J, KMS+1 ) = U( J, KMS+1 ) - REFSUM
389
390           U(             J, KMS+2 ) = U( J, KMS+2 ) - REFSUM*V( 2, M22 )
391
392           110            CONTINUE
393
394           ELSE           IF( WANTZ ) THEN
395
396           DO             120 J = ILOZ, IHIZ
397
398           REFSUM         = V( 1, M22 )*( Z( J, K+1 )+V( 2, M22 )* Z( J, K+2 )
399                          )
400
401           Z(             J, K+1 ) = Z( J, K+1 ) - REFSUM
402
403           Z(             J, K+2 ) = Z( J, K+2 ) - REFSUM*V( 2, M22 )
404
405           120            CONTINUE
406
407           END            IF
408
409           END            IF
410
411           MSTART         = MTOP
412
413           IF(            KRCOL+3*( MSTART-1 ).LT.KTOP ) MSTART = MSTART + 1
414
415           MEND           = MBOT
416
417           IF(            BMP22 ) MEND = MEND + 1
418
419           IF(            KRCOL.EQ.KBOT-2 ) MEND = MEND + 1
420
421           DO             130 M = MSTART, MEND
422
423           K              = MIN( KBOT-1, KRCOL+3*( M-1 ) )
424
425           IF(            H( K+1, K ).NE.ZERO ) THEN
426
427           TST1           = ABS( H( K, K ) ) + ABS( H( K+1, K+1 ) )
428
429           IF(            TST1.EQ.ZERO ) THEN
430
431           IF(            K.GE.KTOP+1 ) TST1 = TST1 + ABS( H( K, K-1 ) )
432
433           IF(            K.GE.KTOP+2 ) TST1 = TST1 + ABS( H( K, K-2 ) )
434
435           IF(            K.GE.KTOP+3 ) TST1 = TST1 + ABS( H( K, K-3 ) )
436
437           IF(            K.LE.KBOT-2 ) TST1 = TST1 + ABS( H( K+2, K+1 ) )
438
439           IF(            K.LE.KBOT-3 ) TST1 = TST1 + ABS( H( K+3, K+1 ) )
440
441           IF(            K.LE.KBOT-4 ) TST1 = TST1 + ABS( H( K+4, K+1 ) )
442
443           END            IF
444
445           IF(            ABS( H( K+1, K ) ).LE.MAX( SMLNUM, ULP*TST1 ) ) THEN
446
447           H12            = MAX( ABS( H( K+1, K ) ), ABS( H( K, K+1 ) ) )
448
449           H21            = MIN( ABS( H( K+1, K ) ), ABS( H( K, K+1 ) ) )
450
451           H11            =  MAX( ABS( H( K+1, K+1 ) ), ABS( H( K, K )-H( K+1,
452                          K+1 ) ) )
453
454           H22            = MIN( ABS( H( K+1, K+1 ) ), ABS( H( K, K )-H(  K+1,
455                          K+1 ) ) )
456
457           SCL            = H11 + H12
458
459           TST2           = H22*( H11 / SCL )
460
461           IF(            TST2.EQ.ZERO  .OR.  H21*( H12 / SCL ).LE.  MAX( SML‐
462                          NUM, ULP*TST2 ) )H( K+1, K ) = ZERO
463
464           END            IF
465
466           END            IF
467
468           130            CONTINUE
469
470           MEND           = MIN( NBMPS, ( KBOT-KRCOL-1 ) / 3 )
471
472           DO             140 M = MTOP, MEND
473
474           K              = KRCOL + 3*( M-1 )
475
476           REFSUM         = V( 1, M )*V( 3, M )*H( K+4, K+3 )
477
478           H(             K+4, K+1 ) = -REFSUM
479
480           H(             K+4, K+2 ) = -REFSUM*V( 2, M )
481
482           H(             K+4, K+3 ) = H( K+4, K+3 ) - REFSUM*V( 3, M )
483
484           140            CONTINUE
485
486           150            CONTINUE
487
488           IF(            ACCUM ) THEN
489
490           IF(            WANTT ) THEN
491
492           JTOP           = 1
493
494           JBOT           = N
495
496           ELSE
497
498           JTOP           = KTOP
499
500           JBOT           = KBOT
501
502           END            IF
503
504           IF(            ( .NOT.BLK22  )  .OR.  (  INCOL.LT.KTOP  )  .OR.   (
505                          NDCOL.GT.KBOT ) .OR. ( NS.LE.2 ) ) THEN
506
507           K1             = MAX( 1, KTOP-INCOL )
508
509           NU             = ( KDU-MAX( 0, NDCOL-KBOT ) ) - K1 + 1
510
511           DO             160 JCOL = MIN( NDCOL, KBOT ) + 1, JBOT, NH
512
513           JLEN           = MIN( NH, JBOT-JCOL+1 )
514
515           CALL           SGEMM(  'C',  'N',  NU,  JLEN, NU, ONE, U( K1, K1 ),
516                          LDU, H( INCOL+K1, JCOL ), LDH, ZERO, WH, LDWH )
517
518           CALL           SLACPY( 'ALL', NU, JLEN, WH, LDWH, H( INCOL+K1, JCOL
519                          ), LDH )
520
521           160            CONTINUE
522
523           DO             170 JROW = JTOP, MAX( KTOP, INCOL ) - 1, NV
524
525           JLEN           = MIN( NV, MAX( KTOP, INCOL )-JROW )
526
527           CALL           SGEMM(  'N',  'N',  JLEN,  NU,  NU,  ONE,  H(  JROW,
528                          INCOL+K1 ), LDH, U( K1, K1 ), LDU, ZERO, WV, LDWV )
529
530           CALL           SLACPY( 'ALL', JLEN, NU, WV, LDWV, H( JROW, INCOL+K1
531                          ), LDH )
532
533           170            CONTINUE
534
535           IF(            WANTZ ) THEN
536
537           DO             180 JROW = ILOZ, IHIZ, NV
538
539           JLEN           = MIN( NV, IHIZ-JROW+1 )
540
541           CALL           SGEMM(  'N',  'N',  JLEN,  NU,  NU,  ONE,  Z(  JROW,
542                          INCOL+K1 ), LDZ, U( K1, K1 ), LDU, ZERO, WV, LDWV )
543
544           CALL           SLACPY( 'ALL', JLEN, NU, WV, LDWV, Z( JROW, INCOL+K1
545                          ), LDZ )
546
547           180            CONTINUE
548
549           END            IF
550
551           ELSE
552
553           I2             = ( KDU+1 ) / 2
554
555           I4             = KDU
556
557           J2             = I4 - I2
558
559           J4             = KDU
560
561           KZS            = ( J4-J2 ) - ( NS+1 )
562
563           KNZ            = NS + 1
564
565           DO             190 JCOL = MIN( NDCOL, KBOT ) + 1, JBOT, NH
566
567           JLEN           = MIN( NH, JBOT-JCOL+1 )
568
569           CALL           SLACPY(  'ALL',  KNZ,  JLEN,  H( INCOL+1+J2, JCOL ),
570                          LDH, WH( KZS+1, 1 ), LDWH )
571
572           CALL           SLASET( 'ALL', KZS, JLEN, ZERO, ZERO, WH, LDWH )
573
574           CALL           STRMM( 'L', 'U', 'C', 'N', KNZ, JLEN, ONE, U(  J2+1,
575                          1+KZS ), LDU, WH( KZS+1, 1 ), LDWH )
576
577           CALL           SGEMM(  'C',  'N',  I2,  JLEN,  J2,  ONE, U, LDU, H(
578                          INCOL+1, JCOL ), LDH, ONE, WH, LDWH )
579
580           CALL           SLACPY( 'ALL', J2, JLEN, H( INCOL+1,  JCOL  ),  LDH,
581                          WH( I2+1, 1 ), LDWH )
582
583           CALL           STRMM( 'L', 'L', 'C', 'N', J2, JLEN, ONE, U( 1, I2+1
584                          ), LDU, WH( I2+1, 1 ), LDWH )
585
586           CALL           SGEMM( 'C', 'N', I4-I2, JLEN, J4-J2, ONE,  U(  J2+1,
587                          I2+1  ),  LDU,  H( INCOL+1+J2, JCOL ), LDH, ONE, WH(
588                          I2+1, 1 ), LDWH )
589
590           CALL           SLACPY( 'ALL', KDU, JLEN, WH, LDWH, H( INCOL+1, JCOL
591                          ), LDH )
592
593           190            CONTINUE
594
595           DO             200 JROW = JTOP, MAX( INCOL, KTOP ) - 1, NV
596
597           JLEN           = MIN( NV, MAX( INCOL, KTOP )-JROW )
598
599           CALL           SLACPY(  'ALL',  JLEN,  KNZ,  H( JROW, INCOL+1+J2 ),
600                          LDH, WV( 1, 1+KZS ), LDWV )
601
602           CALL           SLASET( 'ALL', JLEN, KZS, ZERO, ZERO, WV, LDWV )
603
604           CALL           STRMM( 'R', 'U', 'N', 'N', JLEN, KNZ, ONE, U(  J2+1,
605                          1+KZS ), LDU, WV( 1, 1+KZS ), LDWV )
606
607           CALL           SGEMM( 'N', 'N', JLEN, I2, J2, ONE, H( JROW, INCOL+1
608                          ), LDH, U, LDU, ONE, WV, LDWV )
609
610           CALL           SLACPY( 'ALL', JLEN, J2, H( JROW,  INCOL+1  ),  LDH,
611                          WV( 1, 1+I2 ), LDWV )
612
613           CALL           STRMM(  'R',  'L', 'N', 'N', JLEN, I4-I2, ONE, U( 1,
614                          I2+1 ), LDU, WV( 1, 1+I2 ), LDWV )
615
616           CALL           SGEMM( 'N', 'N', JLEN, I4-I2, J4-J2, ONE,  H(  JROW,
617                          INCOL+1+J2 ), LDH, U( J2+1, I2+1 ), LDU, ONE, WV( 1,
618                          1+I2 ), LDWV )
619
620           CALL           SLACPY( 'ALL', JLEN, KDU, WV, LDWV, H( JROW, INCOL+1
621                          ), LDH )
622
623           200            CONTINUE
624
625           IF(            WANTZ ) THEN
626
627           DO             210 JROW = ILOZ, IHIZ, NV
628
629           JLEN           = MIN( NV, IHIZ-JROW+1 )
630
631           CALL           SLACPY(  'ALL',  JLEN,  KNZ,  Z( JROW, INCOL+1+J2 ),
632                          LDZ, WV( 1, 1+KZS ), LDWV )
633
634           CALL           SLASET( 'ALL', JLEN, KZS, ZERO, ZERO, WV, LDWV )
635
636           CALL           STRMM( 'R', 'U', 'N', 'N', JLEN, KNZ, ONE, U(  J2+1,
637                          1+KZS ), LDU, WV( 1, 1+KZS ), LDWV )
638
639           CALL           SGEMM( 'N', 'N', JLEN, I2, J2, ONE, Z( JROW, INCOL+1
640                          ), LDZ, U, LDU, ONE, WV, LDWV )
641
642           CALL           SLACPY( 'ALL', JLEN, J2, Z( JROW,  INCOL+1  ),  LDZ,
643                          WV( 1, 1+I2 ), LDWV )
644
645           CALL           STRMM(  'R',  'L', 'N', 'N', JLEN, I4-I2, ONE, U( 1,
646                          I2+1 ), LDU, WV( 1, 1+I2 ), LDWV )
647
648           CALL           SGEMM( 'N', 'N', JLEN, I4-I2, J4-J2, ONE,  Z(  JROW,
649                          INCOL+1+J2 ), LDZ, U( J2+1, I2+1 ), LDU, ONE, WV( 1,
650                          1+I2 ), LDWV )
651
652           CALL           SLACPY( 'ALL', JLEN, KDU, WV, LDWV, Z( JROW, INCOL+1
653                          ), LDZ )
654
655           210            CONTINUE
656
657           END            IF
658
659           END            IF
660
661           END            IF
662
663           220            CONTINUE
664
665           END
666

PURPOSE

668 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       SLAQR5(1)