LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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clarfb.f
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1*> \brief \b CLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix.
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download CLARFB + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clarfb.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clarfb.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clarfb.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE CLARFB( 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 C( LDC, * ), T( LDT, * ), V( LDV, * ),
30* $ WORK( LDWORK, * )
31* ..
32*
33*
34*> \par Purpose:
35* =============
36*>
37*> \verbatim
38*>
39*> CLARFB 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*> If SIDE = 'L', M >= K >= 0;
96*> if SIDE = 'R', N >= K >= 0.
97*> \endverbatim
98*>
99*> \param[in] V
100*> \verbatim
101*> V is COMPLEX array, dimension
102*> (LDV,K) if STOREV = 'C'
103*> (LDV,M) if STOREV = 'R' and SIDE = 'L'
104*> (LDV,N) if STOREV = 'R' and SIDE = 'R'
105*> The matrix V. See Further Details.
106*> \endverbatim
107*>
108*> \param[in] LDV
109*> \verbatim
110*> LDV is INTEGER
111*> The leading dimension of the array V.
112*> If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M);
113*> if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);
114*> if STOREV = 'R', LDV >= K.
115*> \endverbatim
116*>
117*> \param[in] T
118*> \verbatim
119*> T is COMPLEX array, dimension (LDT,K)
120*> The triangular K-by-K matrix T in the representation of the
121*> block reflector.
122*> \endverbatim
123*>
124*> \param[in] LDT
125*> \verbatim
126*> LDT is INTEGER
127*> The leading dimension of the array T. LDT >= K.
128*> \endverbatim
129*>
130*> \param[in,out] C
131*> \verbatim
132*> C is COMPLEX array, dimension (LDC,N)
133*> On entry, the M-by-N matrix C.
134*> On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H.
135*> \endverbatim
136*>
137*> \param[in] LDC
138*> \verbatim
139*> LDC is INTEGER
140*> The leading dimension of the array C. LDC >= max(1,M).
141*> \endverbatim
142*>
143*> \param[out] WORK
144*> \verbatim
145*> WORK is COMPLEX array, dimension (LDWORK,K)
146*> \endverbatim
147*>
148*> \param[in] LDWORK
149*> \verbatim
150*> LDWORK is INTEGER
151*> The leading dimension of the array WORK.
152*> If SIDE = 'L', LDWORK >= max(1,N);
153*> if SIDE = 'R', LDWORK >= max(1,M).
154*> \endverbatim
155*
156* Authors:
157* ========
158*
159*> \author Univ. of Tennessee
160*> \author Univ. of California Berkeley
161*> \author Univ. of Colorado Denver
162*> \author NAG Ltd.
163*
164*> \ingroup complexOTHERauxiliary
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 clarfb( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV,
196 $ T, LDT, C, LDC, WORK, LDWORK )
197*
198* -- LAPACK auxiliary routine --
199* -- LAPACK is a software package provided by Univ. of Tennessee, --
200* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
201*
202* .. Scalar Arguments ..
203 CHARACTER DIRECT, SIDE, STOREV, TRANS
204 INTEGER K, LDC, LDT, LDV, LDWORK, M, N
205* ..
206* .. Array Arguments ..
207 COMPLEX C( LDC, * ), T( LDT, * ), V( LDV, * ),
208 $ work( ldwork, * )
209* ..
210*
211* =====================================================================
212*
213* .. Parameters ..
214 COMPLEX ONE
215 parameter( one = ( 1.0e+0, 0.0e+0 ) )
216* ..
217* .. Local Scalars ..
218 CHARACTER TRANST
219 INTEGER I, J
220* ..
221* .. External Functions ..
222 LOGICAL LSAME
223 EXTERNAL lsame
224* ..
225* .. External Subroutines ..
226 EXTERNAL ccopy, cgemm, clacgv, ctrmm
227* ..
228* .. Intrinsic Functions ..
229 INTRINSIC conjg
230* ..
231* .. Executable Statements ..
232*
233* Quick return if possible
234*
235 IF( m.LE.0 .OR. n.LE.0 )
236 $ RETURN
237*
238 IF( lsame( trans, 'N' ) ) THEN
239 transt = 'C'
240 ELSE
241 transt = 'N'
242 END IF
243*
244 IF( lsame( storev, 'C' ) ) THEN
245*
246 IF( lsame( direct, 'F' ) ) THEN
247*
248* Let V = ( V1 ) (first K rows)
249* ( V2 )
250* where V1 is unit lower triangular.
251*
252 IF( lsame( side, 'L' ) ) THEN
253*
254* Form H * C or H**H * C where C = ( C1 )
255* ( C2 )
256*
257* W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK)
258*
259* W := C1**H
260*
261 DO 10 j = 1, k
262 CALL ccopy( n, c( j, 1 ), ldc, work( 1, j ), 1 )
263 CALL clacgv( n, work( 1, j ), 1 )
264 10 CONTINUE
265*
266* W := W * V1
267*
268 CALL ctrmm( 'Right', 'Lower', 'No transpose', 'Unit', n,
269 $ k, one, v, ldv, work, ldwork )
270 IF( m.GT.k ) THEN
271*
272* W := W + C2**H *V2
273*
274 CALL cgemm( 'Conjugate transpose', 'No transpose', n,
275 $ k, m-k, one, c( k+1, 1 ), ldc,
276 $ v( k+1, 1 ), ldv, one, work, ldwork )
277 END IF
278*
279* W := W * T**H or W * T
280*
281 CALL ctrmm( 'Right', 'Upper', transt, 'Non-unit', n, k,
282 $ one, t, ldt, work, ldwork )
283*
284* C := C - V * W**H
285*
286 IF( m.GT.k ) THEN
287*
288* C2 := C2 - V2 * W**H
289*
290 CALL cgemm( 'No transpose', 'Conjugate transpose',
291 $ m-k, n, k, -one, v( k+1, 1 ), ldv, work,
292 $ ldwork, one, c( k+1, 1 ), ldc )
293 END IF
294*
295* W := W * V1**H
296*
297 CALL ctrmm( 'Right', 'Lower', 'Conjugate transpose',
298 $ 'Unit', n, k, one, v, ldv, work, ldwork )
299*
300* C1 := C1 - W**H
301*
302 DO 30 j = 1, k
303 DO 20 i = 1, n
304 c( j, i ) = c( j, i ) - conjg( work( i, j ) )
305 20 CONTINUE
306 30 CONTINUE
307*
308 ELSE IF( lsame( side, 'R' ) ) THEN
309*
310* Form C * H or C * H**H where C = ( C1 C2 )
311*
312* W := C * V = (C1*V1 + C2*V2) (stored in WORK)
313*
314* W := C1
315*
316 DO 40 j = 1, k
317 CALL ccopy( m, c( 1, j ), 1, work( 1, j ), 1 )
318 40 CONTINUE
319*
320* W := W * V1
321*
322 CALL ctrmm( 'Right', 'Lower', 'No transpose', 'Unit', m,
323 $ k, one, v, ldv, work, ldwork )
324 IF( n.GT.k ) THEN
325*
326* W := W + C2 * V2
327*
328 CALL cgemm( 'No transpose', 'No transpose', m, k, n-k,
329 $ one, c( 1, k+1 ), ldc, v( k+1, 1 ), ldv,
330 $ one, work, ldwork )
331 END IF
332*
333* W := W * T or W * T**H
334*
335 CALL ctrmm( 'Right', 'Upper', trans, 'Non-unit', m, k,
336 $ one, t, ldt, work, ldwork )
337*
338* C := C - W * V**H
339*
340 IF( n.GT.k ) THEN
341*
342* C2 := C2 - W * V2**H
343*
344 CALL cgemm( 'No transpose', 'Conjugate transpose', m,
345 $ n-k, k, -one, work, ldwork, v( k+1, 1 ),
346 $ ldv, one, c( 1, k+1 ), ldc )
347 END IF
348*
349* W := W * V1**H
350*
351 CALL ctrmm( 'Right', 'Lower', 'Conjugate transpose',
352 $ 'Unit', m, k, one, v, ldv, work, ldwork )
353*
354* C1 := C1 - W
355*
356 DO 60 j = 1, k
357 DO 50 i = 1, m
358 c( i, j ) = c( i, j ) - work( i, j )
359 50 CONTINUE
360 60 CONTINUE
361 END IF
362*
363 ELSE
364*
365* Let V = ( V1 )
366* ( V2 ) (last K rows)
367* where V2 is unit upper triangular.
368*
369 IF( lsame( side, 'L' ) ) THEN
370*
371* Form H * C or H**H * C where C = ( C1 )
372* ( C2 )
373*
374* W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK)
375*
376* W := C2**H
377*
378 DO 70 j = 1, k
379 CALL ccopy( n, c( m-k+j, 1 ), ldc, work( 1, j ), 1 )
380 CALL clacgv( n, work( 1, j ), 1 )
381 70 CONTINUE
382*
383* W := W * V2
384*
385 CALL ctrmm( 'Right', 'Upper', 'No transpose', 'Unit', n,
386 $ k, one, v( m-k+1, 1 ), ldv, work, ldwork )
387 IF( m.GT.k ) THEN
388*
389* W := W + C1**H * V1
390*
391 CALL cgemm( 'Conjugate transpose', 'No transpose', n,
392 $ k, m-k, one, c, ldc, v, ldv, one, work,
393 $ ldwork )
394 END IF
395*
396* W := W * T**H or W * T
397*
398 CALL ctrmm( 'Right', 'Lower', transt, 'Non-unit', n, k,
399 $ one, t, ldt, work, ldwork )
400*
401* C := C - V * W**H
402*
403 IF( m.GT.k ) THEN
404*
405* C1 := C1 - V1 * W**H
406*
407 CALL cgemm( 'No transpose', 'Conjugate transpose',
408 $ m-k, n, k, -one, v, ldv, work, ldwork,
409 $ one, c, ldc )
410 END IF
411*
412* W := W * V2**H
413*
414 CALL ctrmm( 'Right', 'Upper', 'Conjugate transpose',
415 $ 'Unit', n, k, one, v( m-k+1, 1 ), ldv, work,
416 $ ldwork )
417*
418* C2 := C2 - W**H
419*
420 DO 90 j = 1, k
421 DO 80 i = 1, n
422 c( m-k+j, i ) = c( m-k+j, i ) -
423 $ conjg( work( i, j ) )
424 80 CONTINUE
425 90 CONTINUE
426*
427 ELSE IF( lsame( side, 'R' ) ) THEN
428*
429* Form C * H or C * H**H where C = ( C1 C2 )
430*
431* W := C * V = (C1*V1 + C2*V2) (stored in WORK)
432*
433* W := C2
434*
435 DO 100 j = 1, k
436 CALL ccopy( m, c( 1, n-k+j ), 1, work( 1, j ), 1 )
437 100 CONTINUE
438*
439* W := W * V2
440*
441 CALL ctrmm( 'Right', 'Upper', 'No transpose', 'Unit', m,
442 $ k, one, v( n-k+1, 1 ), ldv, work, ldwork )
443 IF( n.GT.k ) THEN
444*
445* W := W + C1 * V1
446*
447 CALL cgemm( 'No transpose', 'No transpose', m, k, n-k,
448 $ one, c, ldc, v, ldv, one, work, ldwork )
449 END IF
450*
451* W := W * T or W * T**H
452*
453 CALL ctrmm( 'Right', 'Lower', trans, 'Non-unit', m, k,
454 $ one, t, ldt, work, ldwork )
455*
456* C := C - W * V**H
457*
458 IF( n.GT.k ) THEN
459*
460* C1 := C1 - W * V1**H
461*
462 CALL cgemm( 'No transpose', 'Conjugate transpose', m,
463 $ n-k, k, -one, work, ldwork, v, ldv, one,
464 $ c, ldc )
465 END IF
466*
467* W := W * V2**H
468*
469 CALL ctrmm( 'Right', 'Upper', 'Conjugate transpose',
470 $ 'Unit', m, k, one, v( n-k+1, 1 ), ldv, work,
471 $ ldwork )
472*
473* C2 := C2 - W
474*
475 DO 120 j = 1, k
476 DO 110 i = 1, m
477 c( i, n-k+j ) = c( i, n-k+j ) - work( i, j )
478 110 CONTINUE
479 120 CONTINUE
480 END IF
481 END IF
482*
483 ELSE IF( lsame( storev, 'R' ) ) THEN
484*
485 IF( lsame( direct, 'F' ) ) THEN
486*
487* Let V = ( V1 V2 ) (V1: first K columns)
488* where V1 is unit upper triangular.
489*
490 IF( lsame( side, 'L' ) ) THEN
491*
492* Form H * C or H**H * C where C = ( C1 )
493* ( C2 )
494*
495* W := C**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK)
496*
497* W := C1**H
498*
499 DO 130 j = 1, k
500 CALL ccopy( n, c( j, 1 ), ldc, work( 1, j ), 1 )
501 CALL clacgv( n, work( 1, j ), 1 )
502 130 CONTINUE
503*
504* W := W * V1**H
505*
506 CALL ctrmm( 'Right', 'Upper', 'Conjugate transpose',
507 $ 'Unit', n, k, one, v, ldv, work, ldwork )
508 IF( m.GT.k ) THEN
509*
510* W := W + C2**H * V2**H
511*
512 CALL cgemm( 'Conjugate transpose',
513 $ 'Conjugate transpose', n, k, m-k, one,
514 $ c( k+1, 1 ), ldc, v( 1, k+1 ), ldv, one,
515 $ work, ldwork )
516 END IF
517*
518* W := W * T**H or W * T
519*
520 CALL ctrmm( 'Right', 'Upper', transt, 'Non-unit', n, k,
521 $ one, t, ldt, work, ldwork )
522*
523* C := C - V**H * W**H
524*
525 IF( m.GT.k ) THEN
526*
527* C2 := C2 - V2**H * W**H
528*
529 CALL cgemm( 'Conjugate transpose',
530 $ 'Conjugate transpose', m-k, n, k, -one,
531 $ v( 1, k+1 ), ldv, work, ldwork, one,
532 $ c( k+1, 1 ), ldc )
533 END IF
534*
535* W := W * V1
536*
537 CALL ctrmm( 'Right', 'Upper', 'No transpose', 'Unit', n,
538 $ k, one, v, ldv, work, ldwork )
539*
540* C1 := C1 - W**H
541*
542 DO 150 j = 1, k
543 DO 140 i = 1, n
544 c( j, i ) = c( j, i ) - conjg( work( i, j ) )
545 140 CONTINUE
546 150 CONTINUE
547*
548 ELSE IF( lsame( side, 'R' ) ) THEN
549*
550* Form C * H or C * H**H where C = ( C1 C2 )
551*
552* W := C * V**H = (C1*V1**H + C2*V2**H) (stored in WORK)
553*
554* W := C1
555*
556 DO 160 j = 1, k
557 CALL ccopy( m, c( 1, j ), 1, work( 1, j ), 1 )
558 160 CONTINUE
559*
560* W := W * V1**H
561*
562 CALL ctrmm( 'Right', 'Upper', 'Conjugate transpose',
563 $ 'Unit', m, k, one, v, ldv, work, ldwork )
564 IF( n.GT.k ) THEN
565*
566* W := W + C2 * V2**H
567*
568 CALL cgemm( 'No transpose', 'Conjugate transpose', m,
569 $ k, n-k, one, c( 1, k+1 ), ldc,
570 $ v( 1, k+1 ), ldv, one, work, ldwork )
571 END IF
572*
573* W := W * T or W * T**H
574*
575 CALL ctrmm( 'Right', 'Upper', trans, 'Non-unit', m, k,
576 $ one, t, ldt, work, ldwork )
577*
578* C := C - W * V
579*
580 IF( n.GT.k ) THEN
581*
582* C2 := C2 - W * V2
583*
584 CALL cgemm( 'No transpose', 'No transpose', m, n-k, k,
585 $ -one, work, ldwork, v( 1, k+1 ), ldv, one,
586 $ c( 1, k+1 ), ldc )
587 END IF
588*
589* W := W * V1
590*
591 CALL ctrmm( 'Right', 'Upper', 'No transpose', 'Unit', m,
592 $ k, one, v, ldv, work, ldwork )
593*
594* C1 := C1 - W
595*
596 DO 180 j = 1, k
597 DO 170 i = 1, m
598 c( i, j ) = c( i, j ) - work( i, j )
599 170 CONTINUE
600 180 CONTINUE
601*
602 END IF
603*
604 ELSE
605*
606* Let V = ( V1 V2 ) (V2: last K columns)
607* where V2 is unit lower triangular.
608*
609 IF( lsame( side, 'L' ) ) THEN
610*
611* Form H * C or H**H * C where C = ( C1 )
612* ( C2 )
613*
614* W := C**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK)
615*
616* W := C2**H
617*
618 DO 190 j = 1, k
619 CALL ccopy( n, c( m-k+j, 1 ), ldc, work( 1, j ), 1 )
620 CALL clacgv( n, work( 1, j ), 1 )
621 190 CONTINUE
622*
623* W := W * V2**H
624*
625 CALL ctrmm( 'Right', 'Lower', 'Conjugate transpose',
626 $ 'Unit', n, k, one, v( 1, m-k+1 ), ldv, work,
627 $ ldwork )
628 IF( m.GT.k ) THEN
629*
630* W := W + C1**H * V1**H
631*
632 CALL cgemm( 'Conjugate transpose',
633 $ 'Conjugate transpose', n, k, m-k, one, c,
634 $ ldc, v, ldv, one, work, ldwork )
635 END IF
636*
637* W := W * T**H or W * T
638*
639 CALL ctrmm( 'Right', 'Lower', transt, 'Non-unit', n, k,
640 $ one, t, ldt, work, ldwork )
641*
642* C := C - V**H * W**H
643*
644 IF( m.GT.k ) THEN
645*
646* C1 := C1 - V1**H * W**H
647*
648 CALL cgemm( 'Conjugate transpose',
649 $ 'Conjugate transpose', m-k, n, k, -one, v,
650 $ ldv, work, ldwork, one, c, ldc )
651 END IF
652*
653* W := W * V2
654*
655 CALL ctrmm( 'Right', 'Lower', 'No transpose', 'Unit', n,
656 $ k, one, v( 1, m-k+1 ), ldv, work, ldwork )
657*
658* C2 := C2 - W**H
659*
660 DO 210 j = 1, k
661 DO 200 i = 1, n
662 c( m-k+j, i ) = c( m-k+j, i ) -
663 $ conjg( work( i, j ) )
664 200 CONTINUE
665 210 CONTINUE
666*
667 ELSE IF( lsame( side, 'R' ) ) THEN
668*
669* Form C * H or C * H**H where C = ( C1 C2 )
670*
671* W := C * V**H = (C1*V1**H + C2*V2**H) (stored in WORK)
672*
673* W := C2
674*
675 DO 220 j = 1, k
676 CALL ccopy( m, c( 1, n-k+j ), 1, work( 1, j ), 1 )
677 220 CONTINUE
678*
679* W := W * V2**H
680*
681 CALL ctrmm( 'Right', 'Lower', 'Conjugate transpose',
682 $ 'Unit', m, k, one, v( 1, n-k+1 ), ldv, work,
683 $ ldwork )
684 IF( n.GT.k ) THEN
685*
686* W := W + C1 * V1**H
687*
688 CALL cgemm( 'No transpose', 'Conjugate transpose', m,
689 $ k, n-k, one, c, ldc, v, ldv, one, work,
690 $ ldwork )
691 END IF
692*
693* W := W * T or W * T**H
694*
695 CALL ctrmm( 'Right', 'Lower', trans, 'Non-unit', m, k,
696 $ one, t, ldt, work, ldwork )
697*
698* C := C - W * V
699*
700 IF( n.GT.k ) THEN
701*
702* C1 := C1 - W * V1
703*
704 CALL cgemm( 'No transpose', 'No transpose', m, n-k, k,
705 $ -one, work, ldwork, v, ldv, one, c, ldc )
706 END IF
707*
708* W := W * V2
709*
710 CALL ctrmm( 'Right', 'Lower', 'No transpose', 'Unit', m,
711 $ k, one, v( 1, n-k+1 ), ldv, work, ldwork )
712*
713* C1 := C1 - W
714*
715 DO 240 j = 1, k
716 DO 230 i = 1, m
717 c( i, n-k+j ) = c( i, n-k+j ) - work( i, j )
718 230 CONTINUE
719 240 CONTINUE
720*
721 END IF
722*
723 END IF
724 END IF
725*
726 RETURN
727*
728* End of CLARFB
729*
730 END
ccopy
subroutine ccopy(N, CX, INCX, CY, INCY)
CCOPY
Definition: ccopy.f:81
cgemm
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:187
ctrmm
subroutine ctrmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
CTRMM
Definition: ctrmm.f:177
clacgv
subroutine clacgv(N, X, INCX)
CLACGV conjugates a complex vector.
Definition: clacgv.f:74
clarfb
subroutine clarfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
CLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix.
Definition: clarfb.f:197