Annotation of rpl/lapack/lapack/zlarfb.f, revision 1.11
1.9 bertrand 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: * =====================================================================
1.1 bertrand 195: SUBROUTINE ZLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV,
196: $ T, LDT, C, LDC, WORK, LDWORK )
197: *
1.9 bertrand 198: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 199: * -- LAPACK is a software package provided by Univ. of Tennessee, --
200: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 bertrand 201: * November 2011
1.1 bertrand 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: *
1.8 bertrand 256: * Form H * C or H**H * C where C = ( C1 )
257: * ( C2 )
1.1 bertrand 258: *
259: LASTV = MAX( K, ILAZLR( M, K, V, LDV ) )
260: LASTC = ILAZLC( LASTV, N, C, LDC )
261: *
1.8 bertrand 262: * W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK)
1.1 bertrand 263: *
1.8 bertrand 264: * W := C1**H
1.1 bertrand 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: *
1.8 bertrand 277: * W := W + C2**H *V2
1.1 bertrand 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: *
1.8 bertrand 284: * W := W * T**H or W * T
1.1 bertrand 285: *
286: CALL ZTRMM( 'Right', 'Upper', TRANST, 'Non-unit',
287: $ LASTC, K, ONE, T, LDT, WORK, LDWORK )
288: *
1.8 bertrand 289: * C := C - V * W**H
1.1 bertrand 290: *
291: IF( M.GT.K ) THEN
292: *
1.8 bertrand 293: * C2 := C2 - V2 * W**H
1.1 bertrand 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: *
1.8 bertrand 301: * W := W * V1**H
1.1 bertrand 302: *
303: CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose',
304: $ 'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )
305: *
1.8 bertrand 306: * C1 := C1 - W**H
1.1 bertrand 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: *
1.8 bertrand 316: * Form C * H or C * H**H where C = ( C1 C2 )
1.1 bertrand 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: *
1.8 bertrand 343: * W := W * T or W * T**H
1.1 bertrand 344: *
345: CALL ZTRMM( 'Right', 'Upper', TRANS, 'Non-unit',
346: $ LASTC, K, ONE, T, LDT, WORK, LDWORK )
347: *
1.8 bertrand 348: * C := C - W * V**H
1.1 bertrand 349: *
350: IF( LASTV.GT.K ) THEN
351: *
1.8 bertrand 352: * C2 := C2 - W * V2**H
1.1 bertrand 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: *
1.8 bertrand 360: * W := W * V1**H
1.1 bertrand 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: *
1.8 bertrand 382: * Form H * C or H**H * C where C = ( C1 )
383: * ( C2 )
1.1 bertrand 384: *
385: LASTV = MAX( K, ILAZLR( M, K, V, LDV ) )
386: LASTC = ILAZLC( LASTV, N, C, LDC )
387: *
1.8 bertrand 388: * W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK)
1.1 bertrand 389: *
1.8 bertrand 390: * W := C2**H
1.1 bertrand 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: *
1.8 bertrand 405: * W := W + C1**H*V1
1.1 bertrand 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: *
1.8 bertrand 413: * W := W * T**H or W * T
1.1 bertrand 414: *
415: CALL ZTRMM( 'Right', 'Lower', TRANST, 'Non-unit',
416: $ LASTC, K, ONE, T, LDT, WORK, LDWORK )
417: *
1.8 bertrand 418: * C := C - V * W**H
1.1 bertrand 419: *
420: IF( LASTV.GT.K ) THEN
421: *
1.8 bertrand 422: * C1 := C1 - V1 * W**H
1.1 bertrand 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: *
1.8 bertrand 430: * W := W * V2**H
1.1 bertrand 431: *
432: CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose',
433: $ 'Unit', LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,
434: $ WORK, LDWORK )
435: *
1.8 bertrand 436: * C2 := C2 - W**H
1.1 bertrand 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: *
1.8 bertrand 447: * Form C * H or C * H**H where C = ( C1 C2 )
1.1 bertrand 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: *
1.8 bertrand 475: * W := W * T or W * T**H
1.1 bertrand 476: *
477: CALL ZTRMM( 'Right', 'Lower', TRANS, 'Non-unit',
478: $ LASTC, K, ONE, T, LDT, WORK, LDWORK )
479: *
1.8 bertrand 480: * C := C - W * V**H
1.1 bertrand 481: *
482: IF( LASTV.GT.K ) THEN
483: *
1.8 bertrand 484: * C1 := C1 - W * V1**H
1.1 bertrand 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: *
1.8 bertrand 491: * W := W * V2**H
1.1 bertrand 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: *
1.8 bertrand 517: * Form H * C or H**H * C where C = ( C1 )
518: * ( C2 )
1.1 bertrand 519: *
520: LASTV = MAX( K, ILAZLC( K, M, V, LDV ) )
521: LASTC = ILAZLC( LASTV, N, C, LDC )
522: *
1.8 bertrand 523: * W := C**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK)
1.1 bertrand 524: *
1.8 bertrand 525: * W := C1**H
1.1 bertrand 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: *
1.8 bertrand 532: * W := W * V1**H
1.1 bertrand 533: *
534: CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose',
535: $ 'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )
536: IF( LASTV.GT.K ) THEN
537: *
1.8 bertrand 538: * W := W + C2**H*V2**H
1.1 bertrand 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: *
1.8 bertrand 546: * W := W * T**H or W * T
1.1 bertrand 547: *
548: CALL ZTRMM( 'Right', 'Upper', TRANST, 'Non-unit',
549: $ LASTC, K, ONE, T, LDT, WORK, LDWORK )
550: *
1.8 bertrand 551: * C := C - V**H * W**H
1.1 bertrand 552: *
553: IF( LASTV.GT.K ) THEN
554: *
1.8 bertrand 555: * C2 := C2 - V2**H * W**H
1.1 bertrand 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: *
1.8 bertrand 568: * C1 := C1 - W**H
1.1 bertrand 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: *
1.8 bertrand 578: * Form C * H or C * H**H where C = ( C1 C2 )
1.1 bertrand 579: *
580: LASTV = MAX( K, ILAZLC( K, N, V, LDV ) )
581: LASTC = ILAZLR( M, LASTV, C, LDC )
582: *
1.8 bertrand 583: * W := C * V**H = (C1*V1**H + C2*V2**H) (stored in WORK)
1.1 bertrand 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: *
1.8 bertrand 591: * W := W * V1**H
1.1 bertrand 592: *
593: CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose',
594: $ 'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )
595: IF( LASTV.GT.K ) THEN
596: *
1.8 bertrand 597: * W := W + C2 * V2**H
1.1 bertrand 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: *
1.8 bertrand 604: * W := W * T or W * T**H
1.1 bertrand 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: *
1.8 bertrand 643: * Form H * C or H**H * C where C = ( C1 )
644: * ( C2 )
1.1 bertrand 645: *
646: LASTV = MAX( K, ILAZLC( K, M, V, LDV ) )
647: LASTC = ILAZLC( LASTV, N, C, LDC )
648: *
1.8 bertrand 649: * W := C**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK)
1.1 bertrand 650: *
1.8 bertrand 651: * W := C2**H
1.1 bertrand 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: *
1.8 bertrand 659: * W := W * V2**H
1.1 bertrand 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: *
1.8 bertrand 666: * W := W + C1**H * V1**H
1.1 bertrand 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: *
1.8 bertrand 673: * W := W * T**H or W * T
1.1 bertrand 674: *
675: CALL ZTRMM( 'Right', 'Lower', TRANST, 'Non-unit',
676: $ LASTC, K, ONE, T, LDT, WORK, LDWORK )
677: *
1.8 bertrand 678: * C := C - V**H * W**H
1.1 bertrand 679: *
680: IF( LASTV.GT.K ) THEN
681: *
1.8 bertrand 682: * C1 := C1 - V1**H * W**H
1.1 bertrand 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: *
1.8 bertrand 695: * C2 := C2 - W**H
1.1 bertrand 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: *
1.8 bertrand 706: * Form C * H or C * H**H where C = ( C1 C2 )
1.1 bertrand 707: *
708: LASTV = MAX( K, ILAZLC( K, N, V, LDV ) )
709: LASTC = ILAZLR( M, LASTV, C, LDC )
710: *
1.8 bertrand 711: * W := C * V**H = (C1*V1**H + C2*V2**H) (stored in WORK)
1.1 bertrand 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: *
1.8 bertrand 720: * W := W * V2**H
1.1 bertrand 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: *
1.8 bertrand 727: * W := W + C1 * V1**H
1.1 bertrand 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: *
1.8 bertrand 734: * W := W * T or W * T**H
1.1 bertrand 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
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