Annotation of rpl/lapack/lapack/dlarfb.f, revision 1.12
1.12 ! bertrand 1: *> \brief \b DLARFB applies a block reflector or its transpose to a general rectangular matrix.
1.9 bertrand 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: *
1.12 ! bertrand 162: *> \date September 2012
1.9 bertrand 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: * =====================================================================
1.1 bertrand 195: SUBROUTINE DLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV,
196: $ T, LDT, C, LDC, WORK, LDWORK )
197: *
1.12 ! bertrand 198: * -- LAPACK auxiliary routine (version 3.4.2) --
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..--
1.12 ! bertrand 201: * September 2012
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: 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
1.12 ! bertrand 220: INTEGER I, J, LASTV, LASTC, lastv2
1.1 bertrand 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: *
1.8 bertrand 253: * Form H * C or H**T * C where C = ( C1 )
254: * ( C2 )
1.1 bertrand 255: *
256: LASTV = MAX( K, ILADLR( M, K, V, LDV ) )
257: LASTC = ILADLC( LASTV, N, C, LDC )
258: *
1.8 bertrand 259: * W := C**T * V = (C1**T * V1 + C2**T * V2) (stored in WORK)
1.1 bertrand 260: *
1.8 bertrand 261: * W := C1**T
1.1 bertrand 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: *
1.8 bertrand 273: * W := W + C2**T *V2
1.1 bertrand 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: *
1.8 bertrand 281: * W := W * T**T or W * T
1.1 bertrand 282: *
283: CALL DTRMM( 'Right', 'Upper', TRANST, 'Non-unit',
284: $ LASTC, K, ONE, T, LDT, WORK, LDWORK )
285: *
1.8 bertrand 286: * C := C - V * W**T
1.1 bertrand 287: *
288: IF( LASTV.GT.K ) THEN
289: *
1.8 bertrand 290: * C2 := C2 - V2 * W**T
1.1 bertrand 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: *
1.8 bertrand 298: * W := W * V1**T
1.1 bertrand 299: *
300: CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit',
301: $ LASTC, K, ONE, V, LDV, WORK, LDWORK )
302: *
1.8 bertrand 303: * C1 := C1 - W**T
1.1 bertrand 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: *
1.8 bertrand 313: * Form C * H or C * H**T where C = ( C1 C2 )
1.1 bertrand 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: *
1.8 bertrand 340: * W := W * T or W * T**T
1.1 bertrand 341: *
342: CALL DTRMM( 'Right', 'Upper', TRANS, 'Non-unit',
343: $ LASTC, K, ONE, T, LDT, WORK, LDWORK )
344: *
1.8 bertrand 345: * C := C - W * V**T
1.1 bertrand 346: *
347: IF( LASTV.GT.K ) THEN
348: *
1.8 bertrand 349: * C2 := C2 - W * V2**T
1.1 bertrand 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: *
1.8 bertrand 357: * W := W * V1**T
1.1 bertrand 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: *
1.8 bertrand 379: * Form H * C or H**T * C where C = ( C1 )
380: * ( C2 )
1.1 bertrand 381: *
1.12 ! bertrand 382: LASTC = ILADLC( M, N, C, LDC )
1.1 bertrand 383: *
1.8 bertrand 384: * W := C**T * V = (C1**T * V1 + C2**T * V2) (stored in WORK)
1.1 bertrand 385: *
1.8 bertrand 386: * W := C2**T
1.1 bertrand 387: *
388: DO 70 J = 1, K
1.12 ! bertrand 389: CALL DCOPY( LASTC, C( M-K+J, 1 ), LDC,
1.1 bertrand 390: $ WORK( 1, J ), 1 )
391: 70 CONTINUE
392: *
393: * W := W * V2
394: *
395: CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
1.12 ! bertrand 396: $ LASTC, K, ONE, V( M-K+1, 1 ), LDV,
1.1 bertrand 397: $ WORK, LDWORK )
1.12 ! bertrand 398: IF( M.GT.K ) THEN
1.1 bertrand 399: *
1.8 bertrand 400: * W := W + C1**T*V1
1.1 bertrand 401: *
402: CALL DGEMM( 'Transpose', 'No transpose',
1.12 ! bertrand 403: $ LASTC, K, M-K, ONE, C, LDC, V, LDV,
1.1 bertrand 404: $ ONE, WORK, LDWORK )
405: END IF
406: *
1.8 bertrand 407: * W := W * T**T or W * T
1.1 bertrand 408: *
409: CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit',
410: $ LASTC, K, ONE, T, LDT, WORK, LDWORK )
411: *
1.8 bertrand 412: * C := C - V * W**T
1.1 bertrand 413: *
1.12 ! bertrand 414: IF( M.GT.K ) THEN
1.1 bertrand 415: *
1.8 bertrand 416: * C1 := C1 - V1 * W**T
1.1 bertrand 417: *
418: CALL DGEMM( 'No transpose', 'Transpose',
1.12 ! bertrand 419: $ M-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK,
1.1 bertrand 420: $ ONE, C, LDC )
421: END IF
422: *
1.8 bertrand 423: * W := W * V2**T
1.1 bertrand 424: *
425: CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit',
1.12 ! bertrand 426: $ LASTC, K, ONE, V( M-K+1, 1 ), LDV,
1.1 bertrand 427: $ WORK, LDWORK )
428: *
1.8 bertrand 429: * C2 := C2 - W**T
1.1 bertrand 430: *
431: DO 90 J = 1, K
432: DO 80 I = 1, LASTC
1.12 ! bertrand 433: C( M-K+J, I ) = C( M-K+J, I ) - WORK(I, J)
1.1 bertrand 434: 80 CONTINUE
435: 90 CONTINUE
436: *
437: ELSE IF( LSAME( SIDE, 'R' ) ) THEN
438: *
1.8 bertrand 439: * Form C * H or C * H**T where C = ( C1 C2 )
1.1 bertrand 440: *
1.12 ! bertrand 441: LASTC = ILADLR( M, N, C, LDC )
1.1 bertrand 442: *
443: * W := C * V = (C1*V1 + C2*V2) (stored in WORK)
444: *
445: * W := C2
446: *
447: DO 100 J = 1, K
448: CALL DCOPY( LASTC, C( 1, N-K+J ), 1, WORK( 1, J ), 1 )
449: 100 CONTINUE
450: *
451: * W := W * V2
452: *
453: CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
1.12 ! bertrand 454: $ LASTC, K, ONE, V( N-K+1, 1 ), LDV,
1.1 bertrand 455: $ WORK, LDWORK )
1.12 ! bertrand 456: IF( N.GT.K ) THEN
1.1 bertrand 457: *
458: * W := W + C1 * V1
459: *
460: CALL DGEMM( 'No transpose', 'No transpose',
1.12 ! bertrand 461: $ LASTC, K, N-K, ONE, C, LDC, V, LDV,
1.1 bertrand 462: $ ONE, WORK, LDWORK )
463: END IF
464: *
1.8 bertrand 465: * W := W * T or W * T**T
1.1 bertrand 466: *
467: CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit',
468: $ LASTC, K, ONE, T, LDT, WORK, LDWORK )
469: *
1.8 bertrand 470: * C := C - W * V**T
1.1 bertrand 471: *
1.12 ! bertrand 472: IF( N.GT.K ) THEN
1.1 bertrand 473: *
1.8 bertrand 474: * C1 := C1 - W * V1**T
1.1 bertrand 475: *
476: CALL DGEMM( 'No transpose', 'Transpose',
1.12 ! bertrand 477: $ LASTC, N-K, K, -ONE, WORK, LDWORK, V, LDV,
1.1 bertrand 478: $ ONE, C, LDC )
479: END IF
480: *
1.8 bertrand 481: * W := W * V2**T
1.1 bertrand 482: *
483: CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit',
1.12 ! bertrand 484: $ LASTC, K, ONE, V( N-K+1, 1 ), LDV,
1.1 bertrand 485: $ WORK, LDWORK )
486: *
487: * C2 := C2 - W
488: *
489: DO 120 J = 1, K
490: DO 110 I = 1, LASTC
1.12 ! bertrand 491: C( I, N-K+J ) = C( I, N-K+J ) - WORK(I, J)
1.1 bertrand 492: 110 CONTINUE
493: 120 CONTINUE
494: END IF
495: END IF
496: *
497: ELSE IF( LSAME( STOREV, 'R' ) ) THEN
498: *
499: IF( LSAME( DIRECT, 'F' ) ) THEN
500: *
501: * Let V = ( V1 V2 ) (V1: first K columns)
502: * where V1 is unit upper triangular.
503: *
504: IF( LSAME( SIDE, 'L' ) ) THEN
505: *
1.8 bertrand 506: * Form H * C or H**T * C where C = ( C1 )
507: * ( C2 )
1.1 bertrand 508: *
509: LASTV = MAX( K, ILADLC( K, M, V, LDV ) )
510: LASTC = ILADLC( LASTV, N, C, LDC )
511: *
1.8 bertrand 512: * W := C**T * V**T = (C1**T * V1**T + C2**T * V2**T) (stored in WORK)
1.1 bertrand 513: *
1.8 bertrand 514: * W := C1**T
1.1 bertrand 515: *
516: DO 130 J = 1, K
517: CALL DCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 )
518: 130 CONTINUE
519: *
1.8 bertrand 520: * W := W * V1**T
1.1 bertrand 521: *
522: CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit',
523: $ LASTC, K, ONE, V, LDV, WORK, LDWORK )
524: IF( LASTV.GT.K ) THEN
525: *
1.8 bertrand 526: * W := W + C2**T*V2**T
1.1 bertrand 527: *
528: CALL DGEMM( 'Transpose', 'Transpose',
529: $ LASTC, K, LASTV-K,
530: $ ONE, C( K+1, 1 ), LDC, V( 1, K+1 ), LDV,
531: $ ONE, WORK, LDWORK )
532: END IF
533: *
1.8 bertrand 534: * W := W * T**T or W * T
1.1 bertrand 535: *
536: CALL DTRMM( 'Right', 'Upper', TRANST, 'Non-unit',
537: $ LASTC, K, ONE, T, LDT, WORK, LDWORK )
538: *
1.8 bertrand 539: * C := C - V**T * W**T
1.1 bertrand 540: *
541: IF( LASTV.GT.K ) THEN
542: *
1.8 bertrand 543: * C2 := C2 - V2**T * W**T
1.1 bertrand 544: *
545: CALL DGEMM( 'Transpose', 'Transpose',
546: $ LASTV-K, LASTC, K,
547: $ -ONE, V( 1, K+1 ), LDV, WORK, LDWORK,
548: $ ONE, C( K+1, 1 ), LDC )
549: END IF
550: *
551: * W := W * V1
552: *
553: CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
554: $ LASTC, K, ONE, V, LDV, WORK, LDWORK )
555: *
1.8 bertrand 556: * C1 := C1 - W**T
1.1 bertrand 557: *
558: DO 150 J = 1, K
559: DO 140 I = 1, LASTC
560: C( J, I ) = C( J, I ) - WORK( I, J )
561: 140 CONTINUE
562: 150 CONTINUE
563: *
564: ELSE IF( LSAME( SIDE, 'R' ) ) THEN
565: *
1.8 bertrand 566: * Form C * H or C * H**T where C = ( C1 C2 )
1.1 bertrand 567: *
568: LASTV = MAX( K, ILADLC( K, N, V, LDV ) )
569: LASTC = ILADLR( M, LASTV, C, LDC )
570: *
1.8 bertrand 571: * W := C * V**T = (C1*V1**T + C2*V2**T) (stored in WORK)
1.1 bertrand 572: *
573: * W := C1
574: *
575: DO 160 J = 1, K
576: CALL DCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 )
577: 160 CONTINUE
578: *
1.8 bertrand 579: * W := W * V1**T
1.1 bertrand 580: *
581: CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit',
582: $ LASTC, K, ONE, V, LDV, WORK, LDWORK )
583: IF( LASTV.GT.K ) THEN
584: *
1.8 bertrand 585: * W := W + C2 * V2**T
1.1 bertrand 586: *
587: CALL DGEMM( 'No transpose', 'Transpose',
588: $ LASTC, K, LASTV-K,
589: $ ONE, C( 1, K+1 ), LDC, V( 1, K+1 ), LDV,
590: $ ONE, WORK, LDWORK )
591: END IF
592: *
1.8 bertrand 593: * W := W * T or W * T**T
1.1 bertrand 594: *
595: CALL DTRMM( 'Right', 'Upper', TRANS, 'Non-unit',
596: $ LASTC, K, ONE, T, LDT, WORK, LDWORK )
597: *
598: * C := C - W * V
599: *
600: IF( LASTV.GT.K ) THEN
601: *
602: * C2 := C2 - W * V2
603: *
604: CALL DGEMM( 'No transpose', 'No transpose',
605: $ LASTC, LASTV-K, K,
606: $ -ONE, WORK, LDWORK, V( 1, K+1 ), LDV,
607: $ ONE, C( 1, K+1 ), LDC )
608: END IF
609: *
610: * W := W * V1
611: *
612: CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
613: $ LASTC, K, ONE, V, LDV, WORK, LDWORK )
614: *
615: * C1 := C1 - W
616: *
617: DO 180 J = 1, K
618: DO 170 I = 1, LASTC
619: C( I, J ) = C( I, J ) - WORK( I, J )
620: 170 CONTINUE
621: 180 CONTINUE
622: *
623: END IF
624: *
625: ELSE
626: *
627: * Let V = ( V1 V2 ) (V2: last K columns)
628: * where V2 is unit lower triangular.
629: *
630: IF( LSAME( SIDE, 'L' ) ) THEN
631: *
1.8 bertrand 632: * Form H * C or H**T * C where C = ( C1 )
633: * ( C2 )
1.1 bertrand 634: *
1.12 ! bertrand 635: LASTC = ILADLC( M, N, C, LDC )
1.1 bertrand 636: *
1.8 bertrand 637: * W := C**T * V**T = (C1**T * V1**T + C2**T * V2**T) (stored in WORK)
1.1 bertrand 638: *
1.8 bertrand 639: * W := C2**T
1.1 bertrand 640: *
641: DO 190 J = 1, K
1.12 ! bertrand 642: CALL DCOPY( LASTC, C( M-K+J, 1 ), LDC,
1.1 bertrand 643: $ WORK( 1, J ), 1 )
644: 190 CONTINUE
645: *
1.8 bertrand 646: * W := W * V2**T
1.1 bertrand 647: *
648: CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit',
1.12 ! bertrand 649: $ LASTC, K, ONE, V( 1, M-K+1 ), LDV,
1.1 bertrand 650: $ WORK, LDWORK )
1.12 ! bertrand 651: IF( M.GT.K ) THEN
1.1 bertrand 652: *
1.8 bertrand 653: * W := W + C1**T * V1**T
1.1 bertrand 654: *
655: CALL DGEMM( 'Transpose', 'Transpose',
1.12 ! bertrand 656: $ LASTC, K, M-K, ONE, C, LDC, V, LDV,
1.1 bertrand 657: $ ONE, WORK, LDWORK )
658: END IF
659: *
1.8 bertrand 660: * W := W * T**T or W * T
1.1 bertrand 661: *
662: CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit',
663: $ LASTC, K, ONE, T, LDT, WORK, LDWORK )
664: *
1.8 bertrand 665: * C := C - V**T * W**T
1.1 bertrand 666: *
1.12 ! bertrand 667: IF( M.GT.K ) THEN
1.1 bertrand 668: *
1.8 bertrand 669: * C1 := C1 - V1**T * W**T
1.1 bertrand 670: *
671: CALL DGEMM( 'Transpose', 'Transpose',
1.12 ! bertrand 672: $ M-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK,
1.1 bertrand 673: $ ONE, C, LDC )
674: END IF
675: *
676: * W := W * V2
677: *
678: CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit',
1.12 ! bertrand 679: $ LASTC, K, ONE, V( 1, M-K+1 ), LDV,
1.1 bertrand 680: $ WORK, LDWORK )
681: *
1.8 bertrand 682: * C2 := C2 - W**T
1.1 bertrand 683: *
684: DO 210 J = 1, K
685: DO 200 I = 1, LASTC
1.12 ! bertrand 686: C( M-K+J, I ) = C( M-K+J, I ) - WORK(I, J)
1.1 bertrand 687: 200 CONTINUE
688: 210 CONTINUE
689: *
690: ELSE IF( LSAME( SIDE, 'R' ) ) THEN
691: *
1.8 bertrand 692: * Form C * H or C * H**T where C = ( C1 C2 )
1.1 bertrand 693: *
1.12 ! bertrand 694: LASTC = ILADLR( M, N, C, LDC )
1.1 bertrand 695: *
1.8 bertrand 696: * W := C * V**T = (C1*V1**T + C2*V2**T) (stored in WORK)
1.1 bertrand 697: *
698: * W := C2
699: *
700: DO 220 J = 1, K
1.12 ! bertrand 701: CALL DCOPY( LASTC, C( 1, N-K+J ), 1,
1.1 bertrand 702: $ WORK( 1, J ), 1 )
703: 220 CONTINUE
704: *
1.8 bertrand 705: * W := W * V2**T
1.1 bertrand 706: *
707: CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit',
1.12 ! bertrand 708: $ LASTC, K, ONE, V( 1, N-K+1 ), LDV,
1.1 bertrand 709: $ WORK, LDWORK )
1.12 ! bertrand 710: IF( N.GT.K ) THEN
1.1 bertrand 711: *
1.8 bertrand 712: * W := W + C1 * V1**T
1.1 bertrand 713: *
714: CALL DGEMM( 'No transpose', 'Transpose',
1.12 ! bertrand 715: $ LASTC, K, N-K, ONE, C, LDC, V, LDV,
1.1 bertrand 716: $ ONE, WORK, LDWORK )
717: END IF
718: *
1.8 bertrand 719: * W := W * T or W * T**T
1.1 bertrand 720: *
721: CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit',
722: $ LASTC, K, ONE, T, LDT, WORK, LDWORK )
723: *
724: * C := C - W * V
725: *
1.12 ! bertrand 726: IF( N.GT.K ) THEN
1.1 bertrand 727: *
728: * C1 := C1 - W * V1
729: *
730: CALL DGEMM( 'No transpose', 'No transpose',
1.12 ! bertrand 731: $ LASTC, N-K, K, -ONE, WORK, LDWORK, V, LDV,
1.1 bertrand 732: $ ONE, C, LDC )
733: END IF
734: *
735: * W := W * V2
736: *
737: CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit',
1.12 ! bertrand 738: $ LASTC, K, ONE, V( 1, N-K+1 ), LDV,
1.1 bertrand 739: $ WORK, LDWORK )
740: *
741: * C1 := C1 - W
742: *
743: DO 240 J = 1, K
744: DO 230 I = 1, LASTC
1.12 ! bertrand 745: C( I, N-K+J ) = C( I, N-K+J ) - WORK(I, J)
1.1 bertrand 746: 230 CONTINUE
747: 240 CONTINUE
748: *
749: END IF
750: *
751: END IF
752: END IF
753: *
754: RETURN
755: *
756: * End of DLARFB
757: *
758: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to dlarfb.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack