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dlarfb.f
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1*> \brief \b DLARFB applies a block reflector or its 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 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*> 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDC,N)
133*> On entry, the m by n matrix C.
134*> On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T.
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 DOUBLE PRECISION 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 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 --
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 DOUBLE PRECISION C( LDC, * ), T( LDT, * ), V( LDV, * ),
208 $ work( ldwork, * )
209* ..
210*
211* =====================================================================
212*
213* .. Parameters ..
214 DOUBLE PRECISION ONE
215 parameter( one = 1.0d+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 dcopy, dgemm, dtrmm
227* ..
228* .. Executable Statements ..
229*
230* Quick return if possible
231*
232 IF( m.LE.0 .OR. n.LE.0 )
233 $ RETURN
234*
235 IF( lsame( trans, 'N' ) ) THEN
236 transt = 'T'
237 ELSE
238 transt = 'N'
239 END IF
240*
241 IF( lsame( storev, 'C' ) ) THEN
242*
243 IF( lsame( direct, 'F' ) ) THEN
244*
245* Let V = ( V1 ) (first K rows)
246* ( V2 )
247* where V1 is unit lower triangular.
248*
249 IF( lsame( side, 'L' ) ) THEN
250*
251* Form H * C or H**T * C where C = ( C1 )
252* ( C2 )
253*
254* W := C**T * V = (C1**T * V1 + C2**T * V2) (stored in WORK)
255*
256* W := C1**T
257*
258 DO 10 j = 1, k
259 CALL dcopy( n, c( j, 1 ), ldc, work( 1, j ), 1 )
260 10 CONTINUE
261*
262* W := W * V1
263*
264 CALL dtrmm( 'Right', 'Lower', 'No transpose', 'Unit', n,
265 $ k, one, v, ldv, work, ldwork )
266 IF( m.GT.k ) THEN
267*
268* W := W + C2**T * V2
269*
270 CALL dgemm( 'Transpose', 'No transpose', n, k, m-k,
271 $ one, c( k+1, 1 ), ldc, v( k+1, 1 ), ldv,
272 $ one, work, ldwork )
273 END IF
274*
275* W := W * T**T or W * T
276*
277 CALL dtrmm( 'Right', 'Upper', transt, 'Non-unit', n, k,
278 $ one, t, ldt, work, ldwork )
279*
280* C := C - V * W**T
281*
282 IF( m.GT.k ) THEN
283*
284* C2 := C2 - V2 * W**T
285*
286 CALL dgemm( 'No transpose', 'Transpose', m-k, n, k,
287 $ -one, v( k+1, 1 ), ldv, work, ldwork, one,
288 $ c( k+1, 1 ), ldc )
289 END IF
290*
291* W := W * V1**T
292*
293 CALL dtrmm( 'Right', 'Lower', 'Transpose', 'Unit', n, k,
294 $ one, v, ldv, work, ldwork )
295*
296* C1 := C1 - W**T
297*
298 DO 30 j = 1, k
299 DO 20 i = 1, n
300 c( j, i ) = c( j, i ) - work( i, j )
301 20 CONTINUE
302 30 CONTINUE
303*
304 ELSE IF( lsame( side, 'r' ) ) THEN
305*
306* Form C * H or C * H**T where C = ( C1 C2 )
307*
308* W := C * V = (C1*V1 + C2*V2) (stored in WORK)
309*
310* W := C1
311*
312 DO 40 J = 1, K
313 CALL DCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 )
314 40 CONTINUE
315*
316* W := W * V1
317*
318 CALL DTRMM( 'right', 'lower', 'no transpose', 'unit', M,
319 $ K, ONE, V, LDV, WORK, LDWORK )
320.GT. IF( NK ) THEN
321*
322* W := W + C2 * V2
323*
324 CALL DGEMM( 'no transpose', 'no transpose', M, K, N-K,
325 $ ONE, C( 1, K+1 ), LDC, V( K+1, 1 ), LDV,
326 $ ONE, WORK, LDWORK )
327 END IF
328*
329* W := W * T or W * T**T
330*
331 CALL DTRMM( 'right', 'upper', TRANS, 'non-unit', M, K,
332 $ ONE, T, LDT, WORK, LDWORK )
333*
334* C := C - W * V**T
335*
336.GT. IF( NK ) THEN
337*
338* C2 := C2 - W * V2**T
339*
340 CALL DGEMM( 'no transpose', 'transpose', M, N-K, K,
341 $ -ONE, WORK, LDWORK, V( K+1, 1 ), LDV, ONE,
342 $ C( 1, K+1 ), LDC )
343 END IF
344*
345* W := W * V1**T
346*
347 CALL DTRMM( 'right', 'lower', 'transpose', 'unit', M, K,
348 $ ONE, V, LDV, WORK, LDWORK )
349*
350* C1 := C1 - W
351*
352 DO 60 J = 1, K
353 DO 50 I = 1, M
354 C( I, J ) = C( I, J ) - WORK( I, J )
355 50 CONTINUE
356 60 CONTINUE
357 END IF
358*
359 ELSE
360*
361* Let V = ( V1 )
362* ( V2 ) (last K rows)
363* where V2 is unit upper triangular.
364*
365 IF( LSAME( SIDE, 'l' ) ) THEN
366*
367* Form H * C or H**T * C where C = ( C1 )
368* ( C2 )
369*
370* W := C**T * V = (C1**T * V1 + C2**T * V2) (stored in WORK)
371*
372* W := C2**T
373*
374 DO 70 J = 1, K
375 CALL DCOPY( N, C( M-K+J, 1 ), LDC, WORK( 1, J ), 1 )
376 70 CONTINUE
377*
378* W := W * V2
379*
380 CALL DTRMM( 'right', 'Upper', 'No transpose', 'Unit', n,
381 $ k, one, v( m-k+1, 1 ), ldv, work, ldwork )
382 IF( m.GT.k ) THEN
383*
384* W := W + C1**T * V1
385*
386 CALL dgemm( 'Transpose', 'No transpose', n, k, m-k,
387 $ one, c, ldc, v, ldv, one, work, ldwork )
388 END IF
389*
390* W := W * T**T or W * T
391*
392 CALL dtrmm( 'Right', 'Lower', transt, 'Non-unit', n, k,
393 $ one, t, ldt, work, ldwork )
394*
395* C := C - V * W**T
396*
397 IF( m.GT.k ) THEN
398*
399* C1 := C1 - V1 * W**T
400*
401 CALL dgemm( 'No transpose', 'Transpose', m-k, n, k,
402 $ -one, v, ldv, work, ldwork, one, c, ldc )
403 END IF
404*
405* W := W * V2**T
406*
407 CALL dtrmm( 'Right', 'Upper', 'Transpose', 'Unit', n, k,
408 $ one, v( m-k+1, 1 ), ldv, work, ldwork )
409*
410* C2 := C2 - W**T
411*
412 DO 90 j = 1, k
413 DO 80 i = 1, n
414 c( m-k+j, i ) = c( m-k+j, i ) - work( i, j )
415 80 CONTINUE
416 90 CONTINUE
417*
418 ELSE IF( lsame( side, 'r' ) ) THEN
419*
420* Form C * H or C * H**T where C = ( C1 C2 )
421*
422* W := C * V = (C1*V1 + C2*V2) (stored in WORK)
423*
424* W := C2
425*
426 DO 100 J = 1, K
427 CALL DCOPY( M, C( 1, N-K+J ), 1, WORK( 1, J ), 1 )
428 100 CONTINUE
429*
430* W := W * V2
431*
432 CALL DTRMM( 'right', 'upper', 'no transpose', 'unit', M,
433 $ K, ONE, V( N-K+1, 1 ), LDV, WORK, LDWORK )
434.GT. IF( NK ) THEN
435*
436* W := W + C1 * V1
437*
438 CALL DGEMM( 'no transpose', 'no transpose', M, K, N-K,
439 $ ONE, C, LDC, V, LDV, ONE, WORK, LDWORK )
440 END IF
441*
442* W := W * T or W * T**T
443*
444 CALL DTRMM( 'right', 'lower', trans, 'Non-unit', m, k,
445 $ one, t, ldt, work, ldwork )
446*
447* C := C - W * V**T
448*
449 IF( n.GT.k ) THEN
450*
451* C1 := C1 - W * V1**T
452*
453 CALL dgemm( 'No transpose', 'Transpose', m, n-k, k,
454 $ -one, work, ldwork, v, ldv, one, c, ldc )
455 END IF
456*
457* W := W * V2**T
458*
459 CALL dtrmm( 'Right', 'Upper', 'Transpose', 'Unit', m, k,
460 $ one, v( n-k+1, 1 ), ldv, work, ldwork )
461*
462* C2 := C2 - W
463*
464 DO 120 j = 1, k
465 DO 110 i = 1, m
466 c( i, n-k+j ) = c( i, n-k+j ) - work( i, j )
467 110 CONTINUE
468 120 CONTINUE
469 END IF
470 END IF
471*
472 ELSE IF( lsame( storev, 'R' ) ) THEN
473*
474 IF( lsame( direct, 'F' ) ) THEN
475*
476* Let V = ( V1 V2 ) (V1: first K columns)
477* where V1 is unit upper triangular.
478*
479 IF( lsame( side, 'L' ) ) THEN
480*
481* Form H * C or H**T * C where C = ( C1 )
482* ( C2 )
483*
484* W := C**T * V**T = (C1**T * V1**T + C2**T * V2**T) (stored in WORK)
485*
486* W := C1**T
487*
488 DO 130 j = 1, k
489 CALL dcopy( n, c( j, 1 ), ldc, work( 1, j ), 1 )
490 130 CONTINUE
491*
492* W := W * V1**T
493*
494 CALL dtrmm( 'Right', 'Upper', 'Transpose', 'Unit', n, k,
495 $ one, v, ldv, work, ldwork )
496 IF( m.GT.k ) THEN
497*
498* W := W + C2**T * V2**T
499*
500 CALL dgemm( 'Transpose', 'Transpose', n, k, m-k, one,
501 $ c( k+1, 1 ), ldc, v( 1, k+1 ), ldv, one,
502 $ work, ldwork )
503 END IF
504*
505* W := W * T**T or W * T
506*
507 CALL dtrmm( 'Right', 'Upper', transt, 'Non-unit', n, k,
508 $ one, t, ldt, work, ldwork )
509*
510* C := C - V**T * W**T
511*
512 IF( m.GT.k ) THEN
513*
514* C2 := C2 - V2**T * W**T
515*
516 CALL dgemm( 'Transpose', 'Transpose', m-k, n, k, -one,
517 $ v( 1, k+1 ), ldv, work, ldwork, one,
518 $ c( k+1, 1 ), ldc )
519 END IF
520*
521* W := W * V1
522*
523 CALL dtrmm( 'Right', 'Upper', 'No transpose', 'Unit', n,
524 $ k, one, v, ldv, work, ldwork )
525*
526* C1 := C1 - W**T
527*
528 DO 150 j = 1, k
529 DO 140 i = 1, n
530 c( j, i ) = c( j, i ) - work( i, j )
531 140 CONTINUE
532 150 CONTINUE
533*
534 ELSE IF( lsame( side, 'R' ) ) THEN
535*
536* Form C * H or C * H**T where C = ( C1 C2 )
537*
538* W := C * V**T = (C1*V1**T + C2*V2**T) (stored in WORK)
539*
540* W := C1
541*
542 DO 160 j = 1, k
543 CALL dcopy( m, c( 1, j ), 1, work( 1, j ), 1 )
544 160 CONTINUE
545*
546* W := W * V1**T
547*
548 CALL dtrmm( 'Right', 'Upper', 'Transpose', 'Unit', m, k,
549 $ one, v, ldv, work, ldwork )
550 IF( n.GT.k ) THEN
551*
552* W := W + C2 * V2**T
553*
554 CALL dgemm( 'No transpose', 'Transpose', m, k, n-k,
555 $ one, c( 1, k+1 ), ldc, v( 1, k+1 ), ldv,
556 $ one, work, ldwork )
557 END IF
558*
559* W := W * T or W * T**T
560*
561 CALL dtrmm( 'Right', 'Upper', trans, 'Non-unit', m, k,
562 $ one, t, ldt, work, ldwork )
563*
564* C := C - W * V
565*
566 IF( n.GT.k ) THEN
567*
568* C2 := C2 - W * V2
569*
570 CALL dgemm( 'No transpose', 'No transpose', m, n-k, k,
571 $ -one, work, ldwork, v( 1, k+1 ), ldv, one,
572 $ c( 1, k+1 ), ldc )
573 END IF
574*
575* W := W * V1
576*
577 CALL dtrmm( 'Right', 'Upper', 'No transpose', 'Unit', m,
578 $ k, one, v, ldv, work, ldwork )
579*
580* C1 := C1 - W
581*
582 DO 180 j = 1, k
583 DO 170 i = 1, m
584 c( i, j ) = c( i, j ) - work( i, j )
585 170 CONTINUE
586 180 CONTINUE
587*
588 END IF
589*
590 ELSE
591*
592* Let V = ( V1 V2 ) (V2: last K columns)
593* where V2 is unit lower triangular.
594*
595 IF( lsame( side, 'L' ) ) THEN
596*
597* Form H * C or H**T * C where C = ( C1 )
598* ( C2 )
599*
600* W := C**T * V**T = (C1**T * V1**T + C2**T * V2**T) (stored in WORK)
601*
602* W := C2**T
603*
604 DO 190 j = 1, k
605 CALL dcopy( n, c( m-k+j, 1 ), ldc, work( 1, j ), 1 )
606 190 CONTINUE
607*
608* W := W * V2**T
609*
610 CALL dtrmm( 'Right', 'Lower', 'Transpose', 'Unit', n, k,
611 $ one, v( 1, m-k+1 ), ldv, work, ldwork )
612 IF( m.GT.k ) THEN
613*
614* W := W + C1**T * V1**T
615*
616 CALL dgemm( 'Transpose', 'Transpose', n, k, m-k, one,
617 $ c, ldc, v, ldv, one, work, ldwork )
618 END IF
619*
620* W := W * T**T or W * T
621*
622 CALL dtrmm( 'Right', 'lower', TRANST, 'non-unit', N, K,
623 $ ONE, T, LDT, WORK, LDWORK )
624*
625* C := C - V**T * W**T
626*
627.GT. IF( MK ) THEN
628*
629* C1 := C1 - V1**T * W**T
630*
631 CALL DGEMM( 'transpose', 'transpose', M-K, N, K, -ONE,
632 $ V, LDV, WORK, LDWORK, ONE, C, LDC )
633 END IF
634*
635* W := W * V2
636*
637 CALL DTRMM( 'right', 'lower', 'no transpose', 'unit', N,
638 $ K, ONE, V( 1, M-K+1 ), LDV, WORK, LDWORK )
639*
640* C2 := C2 - W**T
641*
642 DO 210 J = 1, K
643 DO 200 I = 1, N
644 C( M-K+J, I ) = C( M-K+J, I ) - WORK( I, J )
645 200 CONTINUE
646 210 CONTINUE
647*
648 ELSE IF( LSAME( SIDE, 'r' ) ) THEN
649*
650* Form C * H or C * H' where C = ( C1 C2 )
651*
652* W := C * V**T = (C1*V1**T + C2*V2**T) (stored in WORK)
653*
654* W := C2
655*
656 DO 220 J = 1, K
657 CALL DCOPY( M, C( 1, N-K+J ), 1, WORK( 1, J ), 1 )
658 220 CONTINUE
659*
660* W := W * V2**T
661*
662 CALL DTRMM( 'right', 'lower', 'transpose', 'unit', M, K,
663 $ ONE, V( 1, N-K+1 ), LDV, WORK, LDWORK )
664.GT. IF( NK ) THEN
665*
666* W := W + C1 * V1**T
667*
668 CALL DGEMM( 'no transpose', 'transpose', M, K, N-K,
669 $ ONE, C, LDC, V, LDV, ONE, WORK, LDWORK )
670 END IF
671*
672* W := W * T or W * T**T
673*
674 CALL DTRMM( 'right', 'lower', trans, 'Non-unit', m, k,
675 $ one, t, ldt, work, ldwork )
676*
677* C := C - W * V
678*
679 IF( n.GT.k ) THEN
680*
681* C1 := C1 - W * V1
682*
683 CALL dgemm( 'No transpose', 'No transpose', m, n-k, k,
684 $ -one, work, ldwork, v, ldv, one, c, ldc )
685 END IF
686*
687* W := W * V2
688*
689 CALL dtrmm( 'Right', 'Lower', 'No transpose', 'Unit', m,
690 $ k, one, v( 1, n-k+1 ), ldv, work, ldwork )
691*
692* C1 := C1 - W
693*
694 DO 240 j = 1, k
695 DO 230 i = 1, m
696 c( i, n-k+j ) = c( i, n-k+j ) - work( i, j )
697 230 CONTINUE
698 240 CONTINUE
699*
700 END IF
701*
702 END IF
703 END IF
704*
705 RETURN
706*
707* End of DLARFB
708*
709 END
dlarfb
subroutine dlarfb(side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork)
DLARFB applies a block reflector or its transpose to a general rectangular matrix.
Definition dlarfb.f:197
dcopy
subroutine dcopy(n, dx, incx, dy, incy)
DCOPY
Definition dcopy.f:82
dgemm
subroutine dgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
DGEMM
Definition dgemm.f:187
dtrmm
subroutine dtrmm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
DTRMM
Definition dtrmm.f:177