1 | *> \brief \b SLARFB |
---|
2 | * |
---|
3 | * =========== DOCUMENTATION =========== |
---|
4 | * |
---|
5 | * Online html documentation available at |
---|
6 | * http://www.netlib.org/lapack/explore-html/ |
---|
7 | * |
---|
8 | *> \htmlonly |
---|
9 | *> Download SLARFB + dependencies |
---|
10 | *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slarfb.f"> |
---|
11 | *> [TGZ]</a> |
---|
12 | *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slarfb.f"> |
---|
13 | *> [ZIP]</a> |
---|
14 | *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slarfb.f"> |
---|
15 | *> [TXT]</a> |
---|
16 | *> \endhtmlonly |
---|
17 | * |
---|
18 | * Definition: |
---|
19 | * =========== |
---|
20 | * |
---|
21 | * SUBROUTINE SLARFB( 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 | * REAL C( LDC, * ), T( LDT, * ), V( LDV, * ), |
---|
30 | * $ WORK( LDWORK, * ) |
---|
31 | * .. |
---|
32 | * |
---|
33 | * |
---|
34 | *> \par Purpose: |
---|
35 | * ============= |
---|
36 | *> |
---|
37 | *> \verbatim |
---|
38 | *> |
---|
39 | *> SLARFB 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 REAL 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 REAL 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 REAL 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 REAL 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 realOTHERauxiliary |
---|
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 SLARFB( 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 | REAL C( LDC, * ), T( LDT, * ), V( LDV, * ), |
---|
209 | $ WORK( LDWORK, * ) |
---|
210 | * .. |
---|
211 | * |
---|
212 | * ===================================================================== |
---|
213 | * |
---|
214 | * .. Parameters .. |
---|
215 | REAL ONE |
---|
216 | PARAMETER ( ONE = 1.0E+0 ) |
---|
217 | * .. |
---|
218 | * .. Local Scalars .. |
---|
219 | CHARACTER TRANST |
---|
220 | INTEGER I, J, LASTV, LASTC |
---|
221 | * .. |
---|
222 | * .. External Functions .. |
---|
223 | LOGICAL LSAME |
---|
224 | INTEGER ILASLR, ILASLC |
---|
225 | EXTERNAL LSAME, ILASLR, ILASLC |
---|
226 | * .. |
---|
227 | * .. External Subroutines .. |
---|
228 | EXTERNAL SCOPY, SGEMM, STRMM |
---|
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, ILASLR( M, K, V, LDV ) ) |
---|
257 | LASTC = ILASLC( 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 SCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 ) |
---|
265 | 10 CONTINUE |
---|
266 | * |
---|
267 | * W := W * V1 |
---|
268 | * |
---|
269 | CALL STRMM( '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 SGEMM( '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 STRMM( '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 SGEMM( '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 STRMM( '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, ILASLR( N, K, V, LDV ) ) |
---|
316 | LASTC = ILASLR( 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 SCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 ) |
---|
324 | 40 CONTINUE |
---|
325 | * |
---|
326 | * W := W * V1 |
---|
327 | * |
---|
328 | CALL STRMM( '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 SGEMM( '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 STRMM( '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 SGEMM( '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 STRMM( '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, ILASLR( M, K, V, LDV ) ) |
---|
383 | LASTC = ILASLC( 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 SCOPY( LASTC, C( LASTV-K+J, 1 ), LDC, |
---|
391 | $ WORK( 1, J ), 1 ) |
---|
392 | 70 CONTINUE |
---|
393 | * |
---|
394 | * W := W * V2 |
---|
395 | * |
---|
396 | CALL STRMM( '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 SGEMM( '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 STRMM( '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 SGEMM( '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 STRMM( '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, ILASLR( N, K, V, LDV ) ) |
---|
443 | LASTC = ILASLR( 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 SCOPY( LASTC, C( 1, N-K+J ), 1, WORK( 1, J ), 1 ) |
---|
451 | 100 CONTINUE |
---|
452 | * |
---|
453 | * W := W * V2 |
---|
454 | * |
---|
455 | CALL STRMM( '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 SGEMM( '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 STRMM( '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 SGEMM( '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 STRMM( '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, ILASLC( K, M, V, LDV ) ) |
---|
512 | LASTC = ILASLC( 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 SCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 ) |
---|
520 | 130 CONTINUE |
---|
521 | * |
---|
522 | * W := W * V1**T |
---|
523 | * |
---|
524 | CALL STRMM( '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 SGEMM( '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 STRMM( '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 SGEMM( '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 STRMM( '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, ILASLC( K, N, V, LDV ) ) |
---|
571 | LASTC = ILASLR( 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 SCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 ) |
---|
579 | 160 CONTINUE |
---|
580 | * |
---|
581 | * W := W * V1**T |
---|
582 | * |
---|
583 | CALL STRMM( '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 SGEMM( '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 STRMM( '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 SGEMM( '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 STRMM( '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, ILASLC( K, M, V, LDV ) ) |
---|
638 | LASTC = ILASLC( 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 SCOPY( LASTC, C( LASTV-K+J, 1 ), LDC, |
---|
646 | $ WORK( 1, J ), 1 ) |
---|
647 | 190 CONTINUE |
---|
648 | * |
---|
649 | * W := W * V2**T |
---|
650 | * |
---|
651 | CALL STRMM( '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 SGEMM( '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 STRMM( '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 SGEMM( '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 STRMM( '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, ILASLC( K, N, V, LDV ) ) |
---|
698 | LASTC = ILASLR( 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 SCOPY( LASTC, C( 1, LASTV-K+J ), 1, |
---|
706 | $ WORK( 1, J ), 1 ) |
---|
707 | 220 CONTINUE |
---|
708 | * |
---|
709 | * W := W * V2**T |
---|
710 | * |
---|
711 | CALL STRMM( '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 SGEMM( '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 STRMM( '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 SGEMM( '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 STRMM( '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 ) |
---|
750 | $ - WORK( I, J ) |
---|
751 | 230 CONTINUE |
---|
752 | 240 CONTINUE |
---|
753 | * |
---|
754 | END IF |
---|
755 | * |
---|
756 | END IF |
---|
757 | END IF |
---|
758 | * |
---|
759 | RETURN |
---|
760 | * |
---|
761 | * End of SLARFB |
---|
762 | * |
---|
763 | END |
---|