1*> \brief \b DLARFB
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download DLARFB + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarfb.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarfb.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarfb.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE DLARFB( 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*       DOUBLE PRECISION   C( LDC, * ), T( LDT, * ), V( LDV, * ),
30*      $                   WORK( LDWORK, * )
31*       ..
32*
33*
34*> \par Purpose:
35*  =============
36*>
37*> \verbatim
38*>
39*> DLARFB applies a real block reflector H or its transpose H**T to a
40*> real 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**T from the Left
50*>          = 'R': apply H or H**T from the Right
51*> \endverbatim
52*>
53*> \param[in] TRANS
54*> \verbatim
55*>          TRANS is CHARACTER*1
56*>          = 'N': apply H (No transpose)
57*>          = 'T': apply H**T (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 DOUBLE PRECISION 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*>          The matrix V. 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDC,N)
131*>          On entry, the m by n matrix C.
132*>          On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T.
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 DOUBLE PRECISION 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 doubleOTHERauxiliary
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 DLARFB( 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      DOUBLE PRECISION   C( LDC, * ), T( LDT, * ), V( LDV, * ),
209     $                   WORK( LDWORK, * )
210*     ..
211*
212*  =====================================================================
213*
214*     .. Parameters ..
215      DOUBLE PRECISION   ONE
216      PARAMETER          ( ONE = 1.0D+0 )
217*     ..
218*     .. Local Scalars ..
219      CHARACTER          TRANST
220      INTEGER            I, J, LASTV, LASTC
221*     ..
222*     .. External Functions ..
223      LOGICAL            LSAME
224      INTEGER            ILADLR, ILADLC
225      EXTERNAL           LSAME, ILADLR, ILADLC
226*     ..
227*     .. External Subroutines ..
228      EXTERNAL           DCOPY, DGEMM, DTRMM
229*     ..
230*     .. Executable Statements ..
231*
232*     Quick return if possible
233*
234      IF( M.LE.0 .OR. N.LE.0 )
235     $   RETURN
236*
237      IF( LSAME( TRANS, 'N' ) ) THEN
238         TRANST = 'T'
239      ELSE
240         TRANST = 'N'
241      END IF
242*
243      IF( LSAME( STOREV, 'C' ) ) THEN
244*
245         IF( LSAME( DIRECT, 'F' ) ) THEN
246*
247*           Let  V =  ( V1 )    (first K rows)
248*                     ( V2 )
249*           where  V1  is unit lower triangular.
250*
251            IF( LSAME( SIDE, 'L' ) ) THEN
252*
253*              Form  H * C  or  H**T * C  where  C = ( C1 )
254*                                                    ( C2 )
255*
256               LASTV = MAX( K, ILADLR( M, K, V, LDV ) )
257               LASTC = ILADLC( LASTV, N, C, LDC )
258*
259*              W := C**T * V  =  (C1**T * V1 + C2**T * V2)  (stored in WORK)
260*
261*              W := C1**T
262*
263               DO 10 J = 1, K
264                  CALL DCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 )
265   10          CONTINUE
266*
267*              W := W * V1
268*
269               CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit',
270     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
271               IF( LASTV.GT.K ) THEN
272*
273*                 W := W + C2**T *V2
274*
275                  CALL DGEMM( 'Transpose', 'No transpose',
276     $                 LASTC, K, LASTV-K,
277     $                 ONE, C( K+1, 1 ), LDC, V( K+1, 1 ), LDV,
278     $                 ONE, WORK, LDWORK )
279               END IF
280*
281*              W := W * T**T  or  W * T
282*
283               CALL DTRMM( 'Right', 'Upper', TRANST, 'Non-unit',
284     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
285*
286*              C := C - V * W**T
287*
288               IF( LASTV.GT.K ) THEN
289*
290*                 C2 := C2 - V2 * W**T
291*
292                  CALL DGEMM( 'No transpose', 'Transpose',
293     $                 LASTV-K, LASTC, K,
294     $                 -ONE, V( K+1, 1 ), LDV, WORK, LDWORK, ONE,
295     $                 C( K+1, 1 ), LDC )
296               END IF
297*
298*              W := W * V1**T
299*
300               CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit',
301     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
302*
303*              C1 := C1 - W**T
304*
305               DO 30 J = 1, K
306                  DO 20 I = 1, LASTC
307                     C( J, I ) = C( J, I ) - WORK( I, J )
308   20             CONTINUE
309   30          CONTINUE
310*
311            ELSE IF( LSAME( SIDE, 'R' ) ) THEN
312*
313*              Form  C * H  or  C * H**T  where  C = ( C1  C2 )
314*
315               LASTV = MAX( K, ILADLR( N, K, V, LDV ) )
316               LASTC = ILADLR( M, LASTV, C, LDC )
317*
318*              W := C * V  =  (C1*V1 + C2*V2)  (stored in WORK)
319*
320*              W := C1
321*
322               DO 40 J = 1, K
323                  CALL DCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 )
324   40          CONTINUE
325*
326*              W := W * V1
327*
328               CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit',
329     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
330               IF( LASTV.GT.K ) THEN
331*
332*                 W := W + C2 * V2
333*
334                  CALL DGEMM( 'No transpose', 'No transpose',
335     $                 LASTC, K, LASTV-K,
336     $                 ONE, C( 1, K+1 ), LDC, V( K+1, 1 ), LDV,
337     $                 ONE, WORK, LDWORK )
338               END IF
339*
340*              W := W * T  or  W * T**T
341*
342               CALL DTRMM( 'Right', 'Upper', TRANS, 'Non-unit',
343     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
344*
345*              C := C - W * V**T
346*
347               IF( LASTV.GT.K ) THEN
348*
349*                 C2 := C2 - W * V2**T
350*
351                  CALL DGEMM( 'No transpose', 'Transpose',
352     $                 LASTC, LASTV-K, K,
353     $                 -ONE, WORK, LDWORK, V( K+1, 1 ), LDV, ONE,
354     $                 C( 1, K+1 ), LDC )
355               END IF
356*
357*              W := W * V1**T
358*
359               CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit',
360     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
361*
362*              C1 := C1 - W
363*
364               DO 60 J = 1, K
365                  DO 50 I = 1, LASTC
366                     C( I, J ) = C( I, J ) - WORK( I, J )
367   50             CONTINUE
368   60          CONTINUE
369            END IF
370*
371         ELSE
372*
373*           Let  V =  ( V1 )
374*                     ( V2 )    (last K rows)
375*           where  V2  is unit upper triangular.
376*
377            IF( LSAME( SIDE, 'L' ) ) THEN
378*
379*              Form  H * C  or  H**T * C  where  C = ( C1 )
380*                                                    ( C2 )
381*
382               LASTV = MAX( K, ILADLR( M, K, V, LDV ) )
383               LASTC = ILADLC( LASTV, N, C, LDC )
384*
385*              W := C**T * V  =  (C1**T * V1 + C2**T * V2)  (stored in WORK)
386*
387*              W := C2**T
388*
389               DO 70 J = 1, K
390                  CALL DCOPY( LASTC, C( LASTV-K+J, 1 ), LDC,
391     $                 WORK( 1, J ), 1 )
392   70          CONTINUE
393*
394*              W := W * V2
395*
396               CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
397     $              LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,
398     $              WORK, LDWORK )
399               IF( LASTV.GT.K ) THEN
400*
401*                 W := W + C1**T*V1
402*
403                  CALL DGEMM( 'Transpose', 'No transpose',
404     $                 LASTC, K, LASTV-K, ONE, C, LDC, V, LDV,
405     $                 ONE, WORK, LDWORK )
406               END IF
407*
408*              W := W * T**T  or  W * T
409*
410               CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit',
411     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
412*
413*              C := C - V * W**T
414*
415               IF( LASTV.GT.K ) THEN
416*
417*                 C1 := C1 - V1 * W**T
418*
419                  CALL DGEMM( 'No transpose', 'Transpose',
420     $                 LASTV-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK,
421     $                 ONE, C, LDC )
422               END IF
423*
424*              W := W * V2**T
425*
426               CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit',
427     $              LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,
428     $              WORK, LDWORK )
429*
430*              C2 := C2 - W**T
431*
432               DO 90 J = 1, K
433                  DO 80 I = 1, LASTC
434                     C( LASTV-K+J, I ) = C( LASTV-K+J, I ) - WORK(I, J)
435   80             CONTINUE
436   90          CONTINUE
437*
438            ELSE IF( LSAME( SIDE, 'R' ) ) THEN
439*
440*              Form  C * H  or  C * H**T  where  C = ( C1  C2 )
441*
442               LASTV = MAX( K, ILADLR( N, K, V, LDV ) )
443               LASTC = ILADLR( M, LASTV, C, LDC )
444*
445*              W := C * V  =  (C1*V1 + C2*V2)  (stored in WORK)
446*
447*              W := C2
448*
449               DO 100 J = 1, K
450                  CALL DCOPY( LASTC, C( 1, N-K+J ), 1, WORK( 1, J ), 1 )
451  100          CONTINUE
452*
453*              W := W * V2
454*
455               CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
456     $              LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,
457     $              WORK, LDWORK )
458               IF( LASTV.GT.K ) THEN
459*
460*                 W := W + C1 * V1
461*
462                  CALL DGEMM( 'No transpose', 'No transpose',
463     $                 LASTC, K, LASTV-K, ONE, C, LDC, V, LDV,
464     $                 ONE, WORK, LDWORK )
465               END IF
466*
467*              W := W * T  or  W * T**T
468*
469               CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit',
470     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
471*
472*              C := C - W * V**T
473*
474               IF( LASTV.GT.K ) THEN
475*
476*                 C1 := C1 - W * V1**T
477*
478                  CALL DGEMM( 'No transpose', 'Transpose',
479     $                 LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV,
480     $                 ONE, C, LDC )
481               END IF
482*
483*              W := W * V2**T
484*
485               CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit',
486     $              LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,
487     $              WORK, LDWORK )
488*
489*              C2 := C2 - W
490*
491               DO 120 J = 1, K
492                  DO 110 I = 1, LASTC
493                     C( I, LASTV-K+J ) = C( I, LASTV-K+J ) - WORK(I, J)
494  110             CONTINUE
495  120          CONTINUE
496            END IF
497         END IF
498*
499      ELSE IF( LSAME( STOREV, 'R' ) ) THEN
500*
501         IF( LSAME( DIRECT, 'F' ) ) THEN
502*
503*           Let  V =  ( V1  V2 )    (V1: first K columns)
504*           where  V1  is unit upper triangular.
505*
506            IF( LSAME( SIDE, 'L' ) ) THEN
507*
508*              Form  H * C  or  H**T * C  where  C = ( C1 )
509*                                                    ( C2 )
510*
511               LASTV = MAX( K, ILADLC( K, M, V, LDV ) )
512               LASTC = ILADLC( LASTV, N, C, LDC )
513*
514*              W := C**T * V**T  =  (C1**T * V1**T + C2**T * V2**T) (stored in WORK)
515*
516*              W := C1**T
517*
518               DO 130 J = 1, K
519                  CALL DCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 )
520  130          CONTINUE
521*
522*              W := W * V1**T
523*
524               CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit',
525     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
526               IF( LASTV.GT.K ) THEN
527*
528*                 W := W + C2**T*V2**T
529*
530                  CALL DGEMM( 'Transpose', 'Transpose',
531     $                 LASTC, K, LASTV-K,
532     $                 ONE, C( K+1, 1 ), LDC, V( 1, K+1 ), LDV,
533     $                 ONE, WORK, LDWORK )
534               END IF
535*
536*              W := W * T**T  or  W * T
537*
538               CALL DTRMM( 'Right', 'Upper', TRANST, 'Non-unit',
539     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
540*
541*              C := C - V**T * W**T
542*
543               IF( LASTV.GT.K ) THEN
544*
545*                 C2 := C2 - V2**T * W**T
546*
547                  CALL DGEMM( 'Transpose', 'Transpose',
548     $                 LASTV-K, LASTC, K,
549     $                 -ONE, V( 1, K+1 ), LDV, WORK, LDWORK,
550     $                 ONE, C( K+1, 1 ), LDC )
551               END IF
552*
553*              W := W * V1
554*
555               CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
556     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
557*
558*              C1 := C1 - W**T
559*
560               DO 150 J = 1, K
561                  DO 140 I = 1, LASTC
562                     C( J, I ) = C( J, I ) - WORK( I, J )
563  140             CONTINUE
564  150          CONTINUE
565*
566            ELSE IF( LSAME( SIDE, 'R' ) ) THEN
567*
568*              Form  C * H  or  C * H**T  where  C = ( C1  C2 )
569*
570               LASTV = MAX( K, ILADLC( K, N, V, LDV ) )
571               LASTC = ILADLR( M, LASTV, C, LDC )
572*
573*              W := C * V**T  =  (C1*V1**T + C2*V2**T)  (stored in WORK)
574*
575*              W := C1
576*
577               DO 160 J = 1, K
578                  CALL DCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 )
579  160          CONTINUE
580*
581*              W := W * V1**T
582*
583               CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit',
584     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
585               IF( LASTV.GT.K ) THEN
586*
587*                 W := W + C2 * V2**T
588*
589                  CALL DGEMM( 'No transpose', 'Transpose',
590     $                 LASTC, K, LASTV-K,
591     $                 ONE, C( 1, K+1 ), LDC, V( 1, K+1 ), LDV,
592     $                 ONE, WORK, LDWORK )
593               END IF
594*
595*              W := W * T  or  W * T**T
596*
597               CALL DTRMM( 'Right', 'Upper', TRANS, 'Non-unit',
598     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
599*
600*              C := C - W * V
601*
602               IF( LASTV.GT.K ) THEN
603*
604*                 C2 := C2 - W * V2
605*
606                  CALL DGEMM( 'No transpose', 'No transpose',
607     $                 LASTC, LASTV-K, K,
608     $                 -ONE, WORK, LDWORK, V( 1, K+1 ), LDV,
609     $                 ONE, C( 1, K+1 ), LDC )
610               END IF
611*
612*              W := W * V1
613*
614               CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
615     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
616*
617*              C1 := C1 - W
618*
619               DO 180 J = 1, K
620                  DO 170 I = 1, LASTC
621                     C( I, J ) = C( I, J ) - WORK( I, J )
622  170             CONTINUE
623  180          CONTINUE
624*
625            END IF
626*
627         ELSE
628*
629*           Let  V =  ( V1  V2 )    (V2: last K columns)
630*           where  V2  is unit lower triangular.
631*
632            IF( LSAME( SIDE, 'L' ) ) THEN
633*
634*              Form  H * C  or  H**T * C  where  C = ( C1 )
635*                                                    ( C2 )
636*
637               LASTV = MAX( K, ILADLC( K, M, V, LDV ) )
638               LASTC = ILADLC( LASTV, N, C, LDC )
639*
640*              W := C**T * V**T  =  (C1**T * V1**T + C2**T * V2**T) (stored in WORK)
641*
642*              W := C2**T
643*
644               DO 190 J = 1, K
645                  CALL DCOPY( LASTC, C( LASTV-K+J, 1 ), LDC,
646     $                 WORK( 1, J ), 1 )
647  190          CONTINUE
648*
649*              W := W * V2**T
650*
651               CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit',
652     $              LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
653     $              WORK, LDWORK )
654               IF( LASTV.GT.K ) THEN
655*
656*                 W := W + C1**T * V1**T
657*
658                  CALL DGEMM( 'Transpose', 'Transpose',
659     $                 LASTC, K, LASTV-K, ONE, C, LDC, V, LDV,
660     $                 ONE, WORK, LDWORK )
661               END IF
662*
663*              W := W * T**T  or  W * T
664*
665               CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit',
666     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
667*
668*              C := C - V**T * W**T
669*
670               IF( LASTV.GT.K ) THEN
671*
672*                 C1 := C1 - V1**T * W**T
673*
674                  CALL DGEMM( 'Transpose', 'Transpose',
675     $                 LASTV-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK,
676     $                 ONE, C, LDC )
677               END IF
678*
679*              W := W * V2
680*
681               CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit',
682     $              LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
683     $              WORK, LDWORK )
684*
685*              C2 := C2 - W**T
686*
687               DO 210 J = 1, K
688                  DO 200 I = 1, LASTC
689                     C( LASTV-K+J, I ) = C( LASTV-K+J, I ) - WORK(I, J)
690  200             CONTINUE
691  210          CONTINUE
692*
693            ELSE IF( LSAME( SIDE, 'R' ) ) THEN
694*
695*              Form  C * H  or  C * H**T  where  C = ( C1  C2 )
696*
697               LASTV = MAX( K, ILADLC( K, N, V, LDV ) )
698               LASTC = ILADLR( M, LASTV, C, LDC )
699*
700*              W := C * V**T  =  (C1*V1**T + C2*V2**T)  (stored in WORK)
701*
702*              W := C2
703*
704               DO 220 J = 1, K
705                  CALL DCOPY( LASTC, C( 1, LASTV-K+J ), 1,
706     $                 WORK( 1, J ), 1 )
707  220          CONTINUE
708*
709*              W := W * V2**T
710*
711               CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit',
712     $              LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
713     $              WORK, LDWORK )
714               IF( LASTV.GT.K ) THEN
715*
716*                 W := W + C1 * V1**T
717*
718                  CALL DGEMM( 'No transpose', 'Transpose',
719     $                 LASTC, K, LASTV-K, ONE, C, LDC, V, LDV,
720     $                 ONE, WORK, LDWORK )
721               END IF
722*
723*              W := W * T  or  W * T**T
724*
725               CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit',
726     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
727*
728*              C := C - W * V
729*
730               IF( LASTV.GT.K ) THEN
731*
732*                 C1 := C1 - W * V1
733*
734                  CALL DGEMM( 'No transpose', 'No transpose',
735     $                 LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV,
736     $                 ONE, C, LDC )
737               END IF
738*
739*              W := W * V2
740*
741               CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit',
742     $              LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
743     $              WORK, LDWORK )
744*
745*              C1 := C1 - W
746*
747               DO 240 J = 1, K
748                  DO 230 I = 1, LASTC
749                     C( I, LASTV-K+J ) = C( I, LASTV-K+J ) - WORK(I, J)
750  230             CONTINUE
751  240          CONTINUE
752*
753            END IF
754*
755         END IF
756      END IF
757*
758      RETURN
759*
760*     End of DLARFB
761*
762      END
763