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1*> \brief \b ZLARFB
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download ZLARFB + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlarfb.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlarfb.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlarfb.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE ZLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV,
22*                          T, LDT, C, LDC, WORK, LDWORK )
23*
24*       .. Scalar Arguments ..
25*       CHARACTER          DIRECT, SIDE, STOREV, TRANS
26*       INTEGER            K, LDC, LDT, LDV, LDWORK, M, N
27*       ..
28*       .. Array Arguments ..
29*       COMPLEX*16         C( LDC, * ), T( LDT, * ), V( LDV, * ),
30*      $                   WORK( LDWORK, * )
31*       ..
32*
33*
34*> \par Purpose:
35*  =============
36*>
37*> \verbatim
38*>
39*> ZLARFB applies a complex block reflector H or its transpose H**H to a
40*> complex M-by-N matrix C, from either the left or the right.
41*> \endverbatim
42*
43*  Arguments:
44*  ==========
45*
46*> \param[in] SIDE
47*> \verbatim
48*>          SIDE is CHARACTER*1
49*>          = 'L': apply H or H**H from the Left
50*>          = 'R': apply H or H**H from the Right
51*> \endverbatim
52*>
53*> \param[in] TRANS
54*> \verbatim
55*>          TRANS is CHARACTER*1
56*>          = 'N': apply H (No transpose)
57*>          = 'C': apply H**H (Conjugate transpose)
58*> \endverbatim
59*>
60*> \param[in] DIRECT
61*> \verbatim
62*>          DIRECT is CHARACTER*1
63*>          Indicates how H is formed from a product of elementary
64*>          reflectors
65*>          = 'F': H = H(1) H(2) . . . H(k) (Forward)
66*>          = 'B': H = H(k) . . . H(2) H(1) (Backward)
67*> \endverbatim
68*>
69*> \param[in] STOREV
70*> \verbatim
71*>          STOREV is CHARACTER*1
72*>          Indicates how the vectors which define the elementary
73*>          reflectors are stored:
74*>          = 'C': Columnwise
75*>          = 'R': Rowwise
76*> \endverbatim
77*>
78*> \param[in] M
79*> \verbatim
80*>          M is INTEGER
81*>          The number of rows of the matrix C.
82*> \endverbatim
83*>
84*> \param[in] N
85*> \verbatim
86*>          N is INTEGER
87*>          The number of columns of the matrix C.
88*> \endverbatim
89*>
90*> \param[in] K
91*> \verbatim
92*>          K is INTEGER
93*>          The order of the matrix T (= the number of elementary
94*>          reflectors whose product defines the block reflector).
95*> \endverbatim
96*>
97*> \param[in] V
98*> \verbatim
99*>          V is COMPLEX*16 array, dimension
100*>                                (LDV,K) if STOREV = 'C'
101*>                                (LDV,M) if STOREV = 'R' and SIDE = 'L'
102*>                                (LDV,N) if STOREV = 'R' and SIDE = 'R'
103*>          See Further Details.
104*> \endverbatim
105*>
106*> \param[in] LDV
107*> \verbatim
108*>          LDV is INTEGER
109*>          The leading dimension of the array V.
110*>          If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M);
111*>          if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);
112*>          if STOREV = 'R', LDV >= K.
113*> \endverbatim
114*>
115*> \param[in] T
116*> \verbatim
117*>          T is COMPLEX*16 array, dimension (LDT,K)
118*>          The triangular K-by-K matrix T in the representation of the
119*>          block reflector.
120*> \endverbatim
121*>
122*> \param[in] LDT
123*> \verbatim
124*>          LDT is INTEGER
125*>          The leading dimension of the array T. LDT >= K.
126*> \endverbatim
127*>
128*> \param[in,out] C
129*> \verbatim
130*>          C is COMPLEX*16 array, dimension (LDC,N)
131*>          On entry, the M-by-N matrix C.
132*>          On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H.
133*> \endverbatim
134*>
135*> \param[in] LDC
136*> \verbatim
137*>          LDC is INTEGER
138*>          The leading dimension of the array C. LDC >= max(1,M).
139*> \endverbatim
140*>
141*> \param[out] WORK
142*> \verbatim
143*>          WORK is COMPLEX*16 array, dimension (LDWORK,K)
144*> \endverbatim
145*>
146*> \param[in] LDWORK
147*> \verbatim
148*>          LDWORK is INTEGER
149*>          The leading dimension of the array WORK.
150*>          If SIDE = 'L', LDWORK >= max(1,N);
151*>          if SIDE = 'R', LDWORK >= max(1,M).
152*> \endverbatim
153*
154*  Authors:
155*  ========
156*
157*> \author Univ. of Tennessee
158*> \author Univ. of California Berkeley
159*> \author Univ. of Colorado Denver
160*> \author NAG Ltd.
161*
162*> \date November 2011
163*
164*> \ingroup complex16OTHERauxiliary
165*
166*> \par Further Details:
167*  =====================
168*>
169*> \verbatim
170*>
171*>  The shape of the matrix V and the storage of the vectors which define
172*>  the H(i) is best illustrated by the following example with n = 5 and
173*>  k = 3. The elements equal to 1 are not stored; the corresponding
174*>  array elements are modified but restored on exit. The rest of the
175*>  array is not used.
176*>
177*>  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':
178*>
179*>               V = (  1       )                 V = (  1 v1 v1 v1 v1 )
180*>                   ( v1  1    )                     (     1 v2 v2 v2 )
181*>                   ( v1 v2  1 )                     (        1 v3 v3 )
182*>                   ( v1 v2 v3 )
183*>                   ( v1 v2 v3 )
184*>
185*>  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':
186*>
187*>               V = ( v1 v2 v3 )                 V = ( v1 v1  1       )
188*>                   ( v1 v2 v3 )                     ( v2 v2 v2  1    )
189*>                   (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )
190*>                   (     1 v3 )
191*>                   (        1 )
192*> \endverbatim
193*>
194*  =====================================================================
195      SUBROUTINE ZLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV,
196     $                   T, LDT, C, LDC, WORK, LDWORK )
197*
198*  -- LAPACK auxiliary routine (version 3.4.0) --
199*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
200*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
201*     November 2011
202*
203*     .. Scalar Arguments ..
204      CHARACTER          DIRECT, SIDE, STOREV, TRANS
205      INTEGER            K, LDC, LDT, LDV, LDWORK, M, N
206*     ..
207*     .. Array Arguments ..
208      COMPLEX*16         C( LDC, * ), T( LDT, * ), V( LDV, * ),
209     $                   WORK( LDWORK, * )
210*     ..
211*
212*  =====================================================================
213*
214*     .. Parameters ..
215      COMPLEX*16         ONE
216      PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ) )
217*     ..
218*     .. Local Scalars ..
219      CHARACTER          TRANST
220      INTEGER            I, J, LASTV, LASTC
221*     ..
222*     .. External Functions ..
223      LOGICAL            LSAME
224      INTEGER            ILAZLR, ILAZLC
225      EXTERNAL           LSAME, ILAZLR, ILAZLC
226*     ..
227*     .. External Subroutines ..
228      EXTERNAL           ZCOPY, ZGEMM, ZLACGV, ZTRMM
229*     ..
230*     .. Intrinsic Functions ..
231      INTRINSIC          DCONJG
232*     ..
233*     .. Executable Statements ..
234*
235*     Quick return if possible
236*
237      IF( M.LE.0 .OR. N.LE.0 )
238     $   RETURN
239*
240      IF( LSAME( TRANS, 'N' ) ) THEN
241         TRANST = 'C'
242      ELSE
243         TRANST = 'N'
244      END IF
245*
246      IF( LSAME( STOREV, 'C' ) ) THEN
247*
248         IF( LSAME( DIRECT, 'F' ) ) THEN
249*
250*           Let  V =  ( V1 )    (first K rows)
251*                     ( V2 )
252*           where  V1  is unit lower triangular.
253*
254            IF( LSAME( SIDE, 'L' ) ) THEN
255*
256*              Form  H * C  or  H**H * C  where  C = ( C1 )
257*                                                    ( C2 )
258*
259               LASTV = MAX( K, ILAZLR( M, K, V, LDV ) )
260               LASTC = ILAZLC( LASTV, N, C, LDC )
261*
262*              W := C**H * V  =  (C1**H * V1 + C2**H * V2)  (stored in WORK)
263*
264*              W := C1**H
265*
266               DO 10 J = 1, K
267                  CALL ZCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 )
268                  CALL ZLACGV( LASTC, WORK( 1, J ), 1 )
269   10          CONTINUE
270*
271*              W := W * V1
272*
273               CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit',
274     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
275               IF( LASTV.GT.K ) THEN
276*
277*                 W := W + C2**H *V2
278*
279                  CALL ZGEMM( 'Conjugate transpose', 'No transpose',
280     $                 LASTC, K, LASTV-K, ONE, C( K+1, 1 ), LDC,
281     $                 V( K+1, 1 ), LDV, ONE, WORK, LDWORK )
282               END IF
283*
284*              W := W * T**H  or  W * T
285*
286               CALL ZTRMM( 'Right', 'Upper', TRANST, 'Non-unit',
287     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
288*
289*              C := C - V * W**H
290*
291               IF( M.GT.K ) THEN
292*
293*                 C2 := C2 - V2 * W**H
294*
295                  CALL ZGEMM( 'No transpose', 'Conjugate transpose',
296     $                 LASTV-K, LASTC, K,
297     $                 -ONE, V( K+1, 1 ), LDV, WORK, LDWORK,
298     $                 ONE, C( K+1, 1 ), LDC )
299               END IF
300*
301*              W := W * V1**H
302*
303               CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose',
304     $              'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )
305*
306*              C1 := C1 - W**H
307*
308               DO 30 J = 1, K
309                  DO 20 I = 1, LASTC
310                     C( J, I ) = C( J, I ) - DCONJG( WORK( I, J ) )
311   20             CONTINUE
312   30          CONTINUE
313*
314            ELSE IF( LSAME( SIDE, 'R' ) ) THEN
315*
316*              Form  C * H  or  C * H**H  where  C = ( C1  C2 )
317*
318               LASTV = MAX( K, ILAZLR( N, K, V, LDV ) )
319               LASTC = ILAZLR( M, LASTV, C, LDC )
320*
321*              W := C * V  =  (C1*V1 + C2*V2)  (stored in WORK)
322*
323*              W := C1
324*
325               DO 40 J = 1, K
326                  CALL ZCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 )
327   40          CONTINUE
328*
329*              W := W * V1
330*
331               CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit',
332     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
333               IF( LASTV.GT.K ) THEN
334*
335*                 W := W + C2 * V2
336*
337                  CALL ZGEMM( 'No transpose', 'No transpose',
338     $                 LASTC, K, LASTV-K,
339     $                 ONE, C( 1, K+1 ), LDC, V( K+1, 1 ), LDV,
340     $                 ONE, WORK, LDWORK )
341               END IF
342*
343*              W := W * T  or  W * T**H
344*
345               CALL ZTRMM( 'Right', 'Upper', TRANS, 'Non-unit',
346     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
347*
348*              C := C - W * V**H
349*
350               IF( LASTV.GT.K ) THEN
351*
352*                 C2 := C2 - W * V2**H
353*
354                  CALL ZGEMM( 'No transpose', 'Conjugate transpose',
355     $                 LASTC, LASTV-K, K,
356     $                 -ONE, WORK, LDWORK, V( K+1, 1 ), LDV,
357     $                 ONE, C( 1, K+1 ), LDC )
358               END IF
359*
360*              W := W * V1**H
361*
362               CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose',
363     $              'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )
364*
365*              C1 := C1 - W
366*
367               DO 60 J = 1, K
368                  DO 50 I = 1, LASTC
369                     C( I, J ) = C( I, J ) - WORK( I, J )
370   50             CONTINUE
371   60          CONTINUE
372            END IF
373*
374         ELSE
375*
376*           Let  V =  ( V1 )
377*                     ( V2 )    (last K rows)
378*           where  V2  is unit upper triangular.
379*
380            IF( LSAME( SIDE, 'L' ) ) THEN
381*
382*              Form  H * C  or  H**H * C  where  C = ( C1 )
383*                                                    ( C2 )
384*
385               LASTV = MAX( K, ILAZLR( M, K, V, LDV ) )
386               LASTC = ILAZLC( LASTV, N, C, LDC )
387*
388*              W := C**H * V  =  (C1**H * V1 + C2**H * V2)  (stored in WORK)
389*
390*              W := C2**H
391*
392               DO 70 J = 1, K
393                  CALL ZCOPY( LASTC, C( LASTV-K+J, 1 ), LDC,
394     $                 WORK( 1, J ), 1 )
395                  CALL ZLACGV( LASTC, WORK( 1, J ), 1 )
396   70          CONTINUE
397*
398*              W := W * V2
399*
400               CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
401     $              LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,
402     $              WORK, LDWORK )
403               IF( LASTV.GT.K ) THEN
404*
405*                 W := W + C1**H*V1
406*
407                  CALL ZGEMM( 'Conjugate transpose', 'No transpose',
408     $                 LASTC, K, LASTV-K,
409     $                 ONE, C, LDC, V, LDV,
410     $                 ONE, WORK, LDWORK )
411               END IF
412*
413*              W := W * T**H  or  W * T
414*
415               CALL ZTRMM( 'Right', 'Lower', TRANST, 'Non-unit',
416     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
417*
418*              C := C - V * W**H
419*
420               IF( LASTV.GT.K ) THEN
421*
422*                 C1 := C1 - V1 * W**H
423*
424                  CALL ZGEMM( 'No transpose', 'Conjugate transpose',
425     $                 LASTV-K, LASTC, K,
426     $                 -ONE, V, LDV, WORK, LDWORK,
427     $                 ONE, C, LDC )
428               END IF
429*
430*              W := W * V2**H
431*
432               CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose',
433     $              'Unit', LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,
434     $              WORK, LDWORK )
435*
436*              C2 := C2 - W**H
437*
438               DO 90 J = 1, K
439                  DO 80 I = 1, LASTC
440                     C( LASTV-K+J, I ) = C( LASTV-K+J, I ) -
441     $                               DCONJG( WORK( I, J ) )
442   80             CONTINUE
443   90          CONTINUE
444*
445            ELSE IF( LSAME( SIDE, 'R' ) ) THEN
446*
447*              Form  C * H  or  C * H**H  where  C = ( C1  C2 )
448*
449               LASTV = MAX( K, ILAZLR( N, K, V, LDV ) )
450               LASTC = ILAZLR( M, LASTV, C, LDC )
451*
452*              W := C * V  =  (C1*V1 + C2*V2)  (stored in WORK)
453*
454*              W := C2
455*
456               DO 100 J = 1, K
457                  CALL ZCOPY( LASTC, C( 1, LASTV-K+J ), 1,
458     $                 WORK( 1, J ), 1 )
459  100          CONTINUE
460*
461*              W := W * V2
462*
463               CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
464     $              LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,
465     $              WORK, LDWORK )
466               IF( LASTV.GT.K ) THEN
467*
468*                 W := W + C1 * V1
469*
470                  CALL ZGEMM( 'No transpose', 'No transpose',
471     $                 LASTC, K, LASTV-K,
472     $                 ONE, C, LDC, V, LDV, ONE, WORK, LDWORK )
473               END IF
474*
475*              W := W * T  or  W * T**H
476*
477               CALL ZTRMM( 'Right', 'Lower', TRANS, 'Non-unit',
478     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
479*
480*              C := C - W * V**H
481*
482               IF( LASTV.GT.K ) THEN
483*
484*                 C1 := C1 - W * V1**H
485*
486                  CALL ZGEMM( 'No transpose', 'Conjugate transpose',
487     $                 LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV,
488     $                 ONE, C, LDC )
489               END IF
490*
491*              W := W * V2**H
492*
493               CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose',
494     $              'Unit', LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,
495     $              WORK, LDWORK )
496*
497*              C2 := C2 - W
498*
499               DO 120 J = 1, K
500                  DO 110 I = 1, LASTC
501                     C( I, LASTV-K+J ) = C( I, LASTV-K+J )
502     $                    - WORK( I, J )
503  110             CONTINUE
504  120          CONTINUE
505            END IF
506         END IF
507*
508      ELSE IF( LSAME( STOREV, 'R' ) ) THEN
509*
510         IF( LSAME( DIRECT, 'F' ) ) THEN
511*
512*           Let  V =  ( V1  V2 )    (V1: first K columns)
513*           where  V1  is unit upper triangular.
514*
515            IF( LSAME( SIDE, 'L' ) ) THEN
516*
517*              Form  H * C  or  H**H * C  where  C = ( C1 )
518*                                                    ( C2 )
519*
520               LASTV = MAX( K, ILAZLC( K, M, V, LDV ) )
521               LASTC = ILAZLC( LASTV, N, C, LDC )
522*
523*              W := C**H * V**H  =  (C1**H * V1**H + C2**H * V2**H) (stored in WORK)
524*
525*              W := C1**H
526*
527               DO 130 J = 1, K
528                  CALL ZCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 )
529                  CALL ZLACGV( LASTC, WORK( 1, J ), 1 )
530  130          CONTINUE
531*
532*              W := W * V1**H
533*
534               CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose',
535     $                     'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )
536               IF( LASTV.GT.K ) THEN
537*
538*                 W := W + C2**H*V2**H
539*
540                  CALL ZGEMM( 'Conjugate transpose',
541     $                 'Conjugate transpose', LASTC, K, LASTV-K,
542     $                 ONE, C( K+1, 1 ), LDC, V( 1, K+1 ), LDV,
543     $                 ONE, WORK, LDWORK )
544               END IF
545*
546*              W := W * T**H  or  W * T
547*
548               CALL ZTRMM( 'Right', 'Upper', TRANST, 'Non-unit',
549     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
550*
551*              C := C - V**H * W**H
552*
553               IF( LASTV.GT.K ) THEN
554*
555*                 C2 := C2 - V2**H * W**H
556*
557                  CALL ZGEMM( 'Conjugate transpose',
558     $                 'Conjugate transpose', LASTV-K, LASTC, K,
559     $                 -ONE, V( 1, K+1 ), LDV, WORK, LDWORK,
560     $                 ONE, C( K+1, 1 ), LDC )
561               END IF
562*
563*              W := W * V1
564*
565               CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
566     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
567*
568*              C1 := C1 - W**H
569*
570               DO 150 J = 1, K
571                  DO 140 I = 1, LASTC
572                     C( J, I ) = C( J, I ) - DCONJG( WORK( I, J ) )
573  140             CONTINUE
574  150          CONTINUE
575*
576            ELSE IF( LSAME( SIDE, 'R' ) ) THEN
577*
578*              Form  C * H  or  C * H**H  where  C = ( C1  C2 )
579*
580               LASTV = MAX( K, ILAZLC( K, N, V, LDV ) )
581               LASTC = ILAZLR( M, LASTV, C, LDC )
582*
583*              W := C * V**H  =  (C1*V1**H + C2*V2**H)  (stored in WORK)
584*
585*              W := C1
586*
587               DO 160 J = 1, K
588                  CALL ZCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 )
589  160          CONTINUE
590*
591*              W := W * V1**H
592*
593               CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose',
594     $                     'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )
595               IF( LASTV.GT.K ) THEN
596*
597*                 W := W + C2 * V2**H
598*
599                  CALL ZGEMM( 'No transpose', 'Conjugate transpose',
600     $                 LASTC, K, LASTV-K, ONE, C( 1, K+1 ), LDC,
601     $                 V( 1, K+1 ), LDV, ONE, WORK, LDWORK )
602               END IF
603*
604*              W := W * T  or  W * T**H
605*
606               CALL ZTRMM( 'Right', 'Upper', TRANS, 'Non-unit',
607     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
608*
609*              C := C - W * V
610*
611               IF( LASTV.GT.K ) THEN
612*
613*                 C2 := C2 - W * V2
614*
615                  CALL ZGEMM( 'No transpose', 'No transpose',
616     $                 LASTC, LASTV-K, K,
617     $                 -ONE, WORK, LDWORK, V( 1, K+1 ), LDV,
618     $                 ONE, C( 1, K+1 ), LDC )
619               END IF
620*
621*              W := W * V1
622*
623               CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
624     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
625*
626*              C1 := C1 - W
627*
628               DO 180 J = 1, K
629                  DO 170 I = 1, LASTC
630                     C( I, J ) = C( I, J ) - WORK( I, J )
631  170             CONTINUE
632  180          CONTINUE
633*
634            END IF
635*
636         ELSE
637*
638*           Let  V =  ( V1  V2 )    (V2: last K columns)
639*           where  V2  is unit lower triangular.
640*
641            IF( LSAME( SIDE, 'L' ) ) THEN
642*
643*              Form  H * C  or  H**H * C  where  C = ( C1 )
644*                                                    ( C2 )
645*
646               LASTV = MAX( K, ILAZLC( K, M, V, LDV ) )
647               LASTC = ILAZLC( LASTV, N, C, LDC )
648*
649*              W := C**H * V**H  =  (C1**H * V1**H + C2**H * V2**H) (stored in WORK)
650*
651*              W := C2**H
652*
653               DO 190 J = 1, K
654                  CALL ZCOPY( LASTC, C( LASTV-K+J, 1 ), LDC,
655     $                 WORK( 1, J ), 1 )
656                  CALL ZLACGV( LASTC, WORK( 1, J ), 1 )
657  190          CONTINUE
658*
659*              W := W * V2**H
660*
661               CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose',
662     $              'Unit', LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
663     $              WORK, LDWORK )
664               IF( LASTV.GT.K ) THEN
665*
666*                 W := W + C1**H * V1**H
667*
668                  CALL ZGEMM( 'Conjugate transpose',
669     $                 'Conjugate transpose', LASTC, K, LASTV-K,
670     $                 ONE, C, LDC, V, LDV, ONE, WORK, LDWORK )
671               END IF
672*
673*              W := W * T**H  or  W * T
674*
675               CALL ZTRMM( 'Right', 'Lower', TRANST, 'Non-unit',
676     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
677*
678*              C := C - V**H * W**H
679*
680               IF( LASTV.GT.K ) THEN
681*
682*                 C1 := C1 - V1**H * W**H
683*
684                  CALL ZGEMM( 'Conjugate transpose',
685     $                 'Conjugate transpose', LASTV-K, LASTC, K,
686     $                 -ONE, V, LDV, WORK, LDWORK, ONE, C, LDC )
687               END IF
688*
689*              W := W * V2
690*
691               CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit',
692     $              LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
693     $              WORK, LDWORK )
694*
695*              C2 := C2 - W**H
696*
697               DO 210 J = 1, K
698                  DO 200 I = 1, LASTC
699                     C( LASTV-K+J, I ) = C( LASTV-K+J, I ) -
700     $                               DCONJG( WORK( I, J ) )
701  200             CONTINUE
702  210          CONTINUE
703*
704            ELSE IF( LSAME( SIDE, 'R' ) ) THEN
705*
706*              Form  C * H  or  C * H**H  where  C = ( C1  C2 )
707*
708               LASTV = MAX( K, ILAZLC( K, N, V, LDV ) )
709               LASTC = ILAZLR( M, LASTV, C, LDC )
710*
711*              W := C * V**H  =  (C1*V1**H + C2*V2**H)  (stored in WORK)
712*
713*              W := C2
714*
715               DO 220 J = 1, K
716                  CALL ZCOPY( LASTC, C( 1, LASTV-K+J ), 1,
717     $                 WORK( 1, J ), 1 )
718  220          CONTINUE
719*
720*              W := W * V2**H
721*
722               CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose',
723     $              'Unit', LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
724     $              WORK, LDWORK )
725               IF( LASTV.GT.K ) THEN
726*
727*                 W := W + C1 * V1**H
728*
729                  CALL ZGEMM( 'No transpose', 'Conjugate transpose',
730     $                 LASTC, K, LASTV-K, ONE, C, LDC, V, LDV, ONE,
731     $                 WORK, LDWORK )
732               END IF
733*
734*              W := W * T  or  W * T**H
735*
736               CALL ZTRMM( 'Right', 'Lower', TRANS, 'Non-unit',
737     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
738*
739*              C := C - W * V
740*
741               IF( LASTV.GT.K ) THEN
742*
743*                 C1 := C1 - W * V1
744*
745                  CALL ZGEMM( 'No transpose', 'No transpose',
746     $                 LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV,
747     $                 ONE, C, LDC )
748               END IF
749*
750*              W := W * V2
751*
752               CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit',
753     $              LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
754     $              WORK, LDWORK )
755*
756*              C1 := C1 - W
757*
758               DO 240 J = 1, K
759                  DO 230 I = 1, LASTC
760                     C( I, LASTV-K+J ) = C( I, LASTV-K+J )
761     $                    - WORK( I, J )
762  230             CONTINUE
763  240          CONTINUE
764*
765            END IF
766*
767         END IF
768      END IF
769*
770      RETURN
771*
772*     End of ZLARFB
773*
774      END
775