Annotation of rpl/lapack/lapack/dlarfb.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b DLARFB
! 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: *
! 162: *> \date November 2011
! 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: *
1.9 ! 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: 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
220: INTEGER I, J, LASTV, LASTC
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: *
382: LASTV = MAX( K, ILADLR( M, K, V, LDV ) )
383: LASTC = ILADLC( LASTV, N, C, LDC )
384: *
1.8 bertrand 385: * W := C**T * V = (C1**T * V1 + C2**T * V2) (stored in WORK)
1.1 bertrand 386: *
1.8 bertrand 387: * W := C2**T
1.1 bertrand 388: *
389: DO 70 J = 1, K
390: CALL DCOPY( LASTC, C( LASTV-K+J, 1 ), LDC,
391: $ WORK( 1, J ), 1 )
392: 70 CONTINUE
393: *
394: * W := W * V2
395: *
396: CALL DTRMM( '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: *
1.8 bertrand 401: * W := W + C1**T*V1
1.1 bertrand 402: *
403: CALL DGEMM( 'Transpose', 'No transpose',
404: $ LASTC, K, LASTV-K, ONE, C, LDC, V, LDV,
405: $ ONE, WORK, LDWORK )
406: END IF
407: *
1.8 bertrand 408: * W := W * T**T or W * T
1.1 bertrand 409: *
410: CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit',
411: $ LASTC, K, ONE, T, LDT, WORK, LDWORK )
412: *
1.8 bertrand 413: * C := C - V * W**T
1.1 bertrand 414: *
415: IF( LASTV.GT.K ) THEN
416: *
1.8 bertrand 417: * C1 := C1 - V1 * W**T
1.1 bertrand 418: *
419: CALL DGEMM( 'No transpose', 'Transpose',
420: $ LASTV-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK,
421: $ ONE, C, LDC )
422: END IF
423: *
1.8 bertrand 424: * W := W * V2**T
1.1 bertrand 425: *
426: CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit',
427: $ LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,
428: $ WORK, LDWORK )
429: *
1.8 bertrand 430: * C2 := C2 - W**T
1.1 bertrand 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: *
1.8 bertrand 440: * Form C * H or C * H**T where C = ( C1 C2 )
1.1 bertrand 441: *
442: LASTV = MAX( K, ILADLR( N, K, V, LDV ) )
443: LASTC = ILADLR( 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 DCOPY( LASTC, C( 1, N-K+J ), 1, WORK( 1, J ), 1 )
451: 100 CONTINUE
452: *
453: * W := W * V2
454: *
455: CALL DTRMM( '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 DGEMM( 'No transpose', 'No transpose',
463: $ LASTC, K, LASTV-K, ONE, C, LDC, V, LDV,
464: $ ONE, WORK, LDWORK )
465: END IF
466: *
1.8 bertrand 467: * W := W * T or W * T**T
1.1 bertrand 468: *
469: CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit',
470: $ LASTC, K, ONE, T, LDT, WORK, LDWORK )
471: *
1.8 bertrand 472: * C := C - W * V**T
1.1 bertrand 473: *
474: IF( LASTV.GT.K ) THEN
475: *
1.8 bertrand 476: * C1 := C1 - W * V1**T
1.1 bertrand 477: *
478: CALL DGEMM( 'No transpose', 'Transpose',
479: $ LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV,
480: $ ONE, C, LDC )
481: END IF
482: *
1.8 bertrand 483: * W := W * V2**T
1.1 bertrand 484: *
485: CALL DTRMM( '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: *
1.8 bertrand 508: * Form H * C or H**T * C where C = ( C1 )
509: * ( C2 )
1.1 bertrand 510: *
511: LASTV = MAX( K, ILADLC( K, M, V, LDV ) )
512: LASTC = ILADLC( LASTV, N, C, LDC )
513: *
1.8 bertrand 514: * W := C**T * V**T = (C1**T * V1**T + C2**T * V2**T) (stored in WORK)
1.1 bertrand 515: *
1.8 bertrand 516: * W := C1**T
1.1 bertrand 517: *
518: DO 130 J = 1, K
519: CALL DCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 )
520: 130 CONTINUE
521: *
1.8 bertrand 522: * W := W * V1**T
1.1 bertrand 523: *
524: CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit',
525: $ LASTC, K, ONE, V, LDV, WORK, LDWORK )
526: IF( LASTV.GT.K ) THEN
527: *
1.8 bertrand 528: * W := W + C2**T*V2**T
1.1 bertrand 529: *
530: CALL DGEMM( '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: *
1.8 bertrand 536: * W := W * T**T or W * T
1.1 bertrand 537: *
538: CALL DTRMM( 'Right', 'Upper', TRANST, 'Non-unit',
539: $ LASTC, K, ONE, T, LDT, WORK, LDWORK )
540: *
1.8 bertrand 541: * C := C - V**T * W**T
1.1 bertrand 542: *
543: IF( LASTV.GT.K ) THEN
544: *
1.8 bertrand 545: * C2 := C2 - V2**T * W**T
1.1 bertrand 546: *
547: CALL DGEMM( '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 DTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
556: $ LASTC, K, ONE, V, LDV, WORK, LDWORK )
557: *
1.8 bertrand 558: * C1 := C1 - W**T
1.1 bertrand 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: *
1.8 bertrand 568: * Form C * H or C * H**T where C = ( C1 C2 )
1.1 bertrand 569: *
570: LASTV = MAX( K, ILADLC( K, N, V, LDV ) )
571: LASTC = ILADLR( M, LASTV, C, LDC )
572: *
1.8 bertrand 573: * W := C * V**T = (C1*V1**T + C2*V2**T) (stored in WORK)
1.1 bertrand 574: *
575: * W := C1
576: *
577: DO 160 J = 1, K
578: CALL DCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 )
579: 160 CONTINUE
580: *
1.8 bertrand 581: * W := W * V1**T
1.1 bertrand 582: *
583: CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit',
584: $ LASTC, K, ONE, V, LDV, WORK, LDWORK )
585: IF( LASTV.GT.K ) THEN
586: *
1.8 bertrand 587: * W := W + C2 * V2**T
1.1 bertrand 588: *
589: CALL DGEMM( '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: *
1.8 bertrand 595: * W := W * T or W * T**T
1.1 bertrand 596: *
597: CALL DTRMM( '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 DGEMM( '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 DTRMM( '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: *
1.8 bertrand 634: * Form H * C or H**T * C where C = ( C1 )
635: * ( C2 )
1.1 bertrand 636: *
637: LASTV = MAX( K, ILADLC( K, M, V, LDV ) )
638: LASTC = ILADLC( LASTV, N, C, LDC )
639: *
1.8 bertrand 640: * W := C**T * V**T = (C1**T * V1**T + C2**T * V2**T) (stored in WORK)
1.1 bertrand 641: *
1.8 bertrand 642: * W := C2**T
1.1 bertrand 643: *
644: DO 190 J = 1, K
645: CALL DCOPY( LASTC, C( LASTV-K+J, 1 ), LDC,
646: $ WORK( 1, J ), 1 )
647: 190 CONTINUE
648: *
1.8 bertrand 649: * W := W * V2**T
1.1 bertrand 650: *
651: CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit',
652: $ LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
653: $ WORK, LDWORK )
654: IF( LASTV.GT.K ) THEN
655: *
1.8 bertrand 656: * W := W + C1**T * V1**T
1.1 bertrand 657: *
658: CALL DGEMM( 'Transpose', 'Transpose',
659: $ LASTC, K, LASTV-K, ONE, C, LDC, V, LDV,
660: $ ONE, WORK, LDWORK )
661: END IF
662: *
1.8 bertrand 663: * W := W * T**T or W * T
1.1 bertrand 664: *
665: CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit',
666: $ LASTC, K, ONE, T, LDT, WORK, LDWORK )
667: *
1.8 bertrand 668: * C := C - V**T * W**T
1.1 bertrand 669: *
670: IF( LASTV.GT.K ) THEN
671: *
1.8 bertrand 672: * C1 := C1 - V1**T * W**T
1.1 bertrand 673: *
674: CALL DGEMM( '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 DTRMM( 'Right', 'Lower', 'No transpose', 'Unit',
682: $ LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
683: $ WORK, LDWORK )
684: *
1.8 bertrand 685: * C2 := C2 - W**T
1.1 bertrand 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: *
1.8 bertrand 695: * Form C * H or C * H**T where C = ( C1 C2 )
1.1 bertrand 696: *
697: LASTV = MAX( K, ILADLC( K, N, V, LDV ) )
698: LASTC = ILADLR( M, LASTV, C, LDC )
699: *
1.8 bertrand 700: * W := C * V**T = (C1*V1**T + C2*V2**T) (stored in WORK)
1.1 bertrand 701: *
702: * W := C2
703: *
704: DO 220 J = 1, K
705: CALL DCOPY( LASTC, C( 1, LASTV-K+J ), 1,
706: $ WORK( 1, J ), 1 )
707: 220 CONTINUE
708: *
1.8 bertrand 709: * W := W * V2**T
1.1 bertrand 710: *
711: CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit',
712: $ LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
713: $ WORK, LDWORK )
714: IF( LASTV.GT.K ) THEN
715: *
1.8 bertrand 716: * W := W + C1 * V1**T
1.1 bertrand 717: *
718: CALL DGEMM( 'No transpose', 'Transpose',
719: $ LASTC, K, LASTV-K, ONE, C, LDC, V, LDV,
720: $ ONE, WORK, LDWORK )
721: END IF
722: *
1.8 bertrand 723: * W := W * T or W * T**T
1.1 bertrand 724: *
725: CALL DTRMM( '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 DGEMM( '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 DTRMM( '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 ) - WORK(I, J)
750: 230 CONTINUE
751: 240 CONTINUE
752: *
753: END IF
754: *
755: END IF
756: END IF
757: *
758: RETURN
759: *
760: * End of DLARFB
761: *
762: END
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