1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
|
SUBROUTINE PZLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, IV,
$ JV, DESCV, T, C, IC, JC, DESCC, WORK )
*
* -- ScaLAPACK routine (version 2.0.2) --
* Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver
* May 1 2012
*
* .. Scalar Arguments ..
CHARACTER SIDE, TRANS, DIRECT, STOREV
INTEGER IC, IV, JC, JV, K, M, N
* ..
* .. Array Arguments ..
INTEGER DESCC( * ), DESCV( * )
COMPLEX*16 C( * ), T( * ), V( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* PZLARFB applies a complex block reflector Q or its conjugate
* transpose Q**H to a complex M-by-N distributed matrix sub( C )
* denoting C(IC:IC+M-1,JC:JC+N-1), from the left or the right.
*
* Notes
* =====
*
* Each global data object is described by an associated description
* vector. This vector stores the information required to establish
* the mapping between an object element and its corresponding process
* and memory location.
*
* Let A be a generic term for any 2D block cyclicly distributed array.
* Such a global array has an associated description vector DESCA.
* In the following comments, the character _ should be read as
* "of the global array".
*
* NOTATION STORED IN EXPLANATION
* --------------- -------------- --------------------------------------
* DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
* DTYPE_A = 1.
* CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
* the BLACS process grid A is distribu-
* ted over. The context itself is glo-
* bal, but the handle (the integer
* value) may vary.
* M_A (global) DESCA( M_ ) The number of rows in the global
* array A.
* N_A (global) DESCA( N_ ) The number of columns in the global
* array A.
* MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
* the rows of the array.
* NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
* the columns of the array.
* RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
* row of the array A is distributed.
* CSRC_A (global) DESCA( CSRC_ ) The process column over which the
* first column of the array A is
* distributed.
* LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
* array. LLD_A >= MAX(1,LOCr(M_A)).
*
* Let K be the number of rows or columns of a distributed matrix,
* and assume that its process grid has dimension p x q.
* LOCr( K ) denotes the number of elements of K that a process
* would receive if K were distributed over the p processes of its
* process column.
* Similarly, LOCc( K ) denotes the number of elements of K that a
* process would receive if K were distributed over the q processes of
* its process row.
* The values of LOCr() and LOCc() may be determined via a call to the
* ScaLAPACK tool function, NUMROC:
* LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
* LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
* An upper bound for these quantities may be computed by:
* LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
* LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
*
* Arguments
* =========
*
* SIDE (global input) CHARACTER
* = 'L': apply Q or Q**H from the Left;
* = 'R': apply Q or Q**H from the Right.
*
* TRANS (global input) CHARACTER
* = 'N': No transpose, apply Q;
* = 'C': Conjugate transpose, apply Q**H.
*
* DIRECT (global input) CHARACTER
* Indicates how Q is formed from a product of elementary
* reflectors
* = 'F': Q = H(1) H(2) . . . H(k) (Forward)
* = 'B': Q = H(k) . . . H(2) H(1) (Backward)
*
* STOREV (global input) CHARACTER
* Indicates how the vectors which define the elementary
* reflectors are stored:
* = 'C': Columnwise
* = 'R': Rowwise
*
* M (global input) INTEGER
* The number of rows to be operated on i.e the number of rows
* of the distributed submatrix sub( C ). M >= 0.
*
* N (global input) INTEGER
* The number of columns to be operated on i.e the number of
* columns of the distributed submatrix sub( C ). N >= 0.
*
* K (global input) INTEGER
* The order of the matrix T (= the number of elementary
* reflectors whose product defines the block reflector).
*
* V (local input) COMPLEX*16 pointer into the local memory
* to an array of dimension ( LLD_V, LOCc(JV+K-1) ) if
* STOREV = 'C', ( LLD_V, LOCc(JV+M-1)) if STOREV = 'R' and
* SIDE = 'L', ( LLD_V, LOCc(JV+N-1) ) if STOREV = 'R' and
* SIDE = 'R'. It contains the local pieces of the distributed
* vectors V representing the Householder transformation.
* See further details.
* If STOREV = 'C' and SIDE = 'L', LLD_V >= MAX(1,LOCr(IV+M-1));
* if STOREV = 'C' and SIDE = 'R', LLD_V >= MAX(1,LOCr(IV+N-1));
* if STOREV = 'R', LLD_V >= LOCr(IV+K-1).
*
* IV (global input) INTEGER
* The row index in the global array V indicating the first
* row of sub( V ).
*
* JV (global input) INTEGER
* The column index in the global array V indicating the
* first column of sub( V ).
*
* DESCV (global and local input) INTEGER array of dimension DLEN_.
* The array descriptor for the distributed matrix V.
*
* T (local input) COMPLEX*16 array, dimension MB_V by MB_V
* if STOREV = 'R' and NB_V by NB_V if STOREV = 'C'. The trian-
* gular matrix T in the representation of the block reflector.
*
* C (local input/local output) COMPLEX*16 pointer into the
* local memory to an array of dimension (LLD_C,LOCc(JC+N-1)).
* On entry, the M-by-N distributed matrix sub( C ). On exit,
* sub( C ) is overwritten by Q*sub( C ) or Q'*sub( C ) or
* sub( C )*Q or sub( C )*Q'.
*
* IC (global input) INTEGER
* The row index in the global array C indicating the first
* row of sub( C ).
*
* JC (global input) INTEGER
* The column index in the global array C indicating the
* first column of sub( C ).
*
* DESCC (global and local input) INTEGER array of dimension DLEN_.
* The array descriptor for the distributed matrix C.
*
* WORK (local workspace) COMPLEX*16 array, dimension (LWORK)
* If STOREV = 'C',
* if SIDE = 'L',
* LWORK >= ( NqC0 + MpC0 ) * K
* else if SIDE = 'R',
* LWORK >= ( NqC0 + MAX( NpV0 + NUMROC( NUMROC( N+ICOFFC,
* NB_V, 0, 0, NPCOL ), NB_V, 0, 0, LCMQ ),
* MpC0 ) ) * K
* end if
* else if STOREV = 'R',
* if SIDE = 'L',
* LWORK >= ( MpC0 + MAX( MqV0 + NUMROC( NUMROC( M+IROFFC,
* MB_V, 0, 0, NPROW ), MB_V, 0, 0, LCMP ),
* NqC0 ) ) * K
* else if SIDE = 'R',
* LWORK >= ( MpC0 + NqC0 ) * K
* end if
* end if
*
* where LCMQ = LCM / NPCOL with LCM = ICLM( NPROW, NPCOL ),
*
* IROFFV = MOD( IV-1, MB_V ), ICOFFV = MOD( JV-1, NB_V ),
* IVROW = INDXG2P( IV, MB_V, MYROW, RSRC_V, NPROW ),
* IVCOL = INDXG2P( JV, NB_V, MYCOL, CSRC_V, NPCOL ),
* MqV0 = NUMROC( M+ICOFFV, NB_V, MYCOL, IVCOL, NPCOL ),
* NpV0 = NUMROC( N+IROFFV, MB_V, MYROW, IVROW, NPROW ),
*
* IROFFC = MOD( IC-1, MB_C ), ICOFFC = MOD( JC-1, NB_C ),
* ICROW = INDXG2P( IC, MB_C, MYROW, RSRC_C, NPROW ),
* ICCOL = INDXG2P( JC, NB_C, MYCOL, CSRC_C, NPCOL ),
* MpC0 = NUMROC( M+IROFFC, MB_C, MYROW, ICROW, NPROW ),
* NpC0 = NUMROC( N+ICOFFC, MB_C, MYROW, ICROW, NPROW ),
* NqC0 = NUMROC( N+ICOFFC, NB_C, MYCOL, ICCOL, NPCOL ),
*
* ILCM, INDXG2P and NUMROC are ScaLAPACK tool functions;
* MYROW, MYCOL, NPROW and NPCOL can be determined by calling
* the subroutine BLACS_GRIDINFO.
*
* Alignment requirements
* ======================
*
* The distributed submatrices V(IV:*, JV:*) and C(IC:IC+M-1,JC:JC+N-1)
* must verify some alignment properties, namely the following
* expressions should be true:
*
* If STOREV = 'Columnwise'
* If SIDE = 'Left',
* ( MB_V.EQ.MB_C .AND. IROFFV.EQ.IROFFC .AND. IVROW.EQ.ICROW )
* If SIDE = 'Right',
* ( MB_V.EQ.NB_C .AND. IROFFV.EQ.ICOFFC )
* else if STOREV = 'Rowwise'
* If SIDE = 'Left',
* ( NB_V.EQ.MB_C .AND. ICOFFV.EQ.IROFFC )
* If SIDE = 'Right',
* ( NB_V.EQ.NB_C .AND. ICOFFV.EQ.ICOFFC .AND. IVCOL.EQ.ICCOL )
* end if
*
* =====================================================================
*
* .. Parameters ..
INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
$ LLD_, MB_, M_, NB_, N_, RSRC_
PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1,
$ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6,
$ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 )
COMPLEX*16 ONE, ZERO
PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
$ ZERO = ( 0.0D+0, 0.0D+0 ) )
* ..
* .. Local Scalars ..
LOGICAL FORWARD
CHARACTER COLBTOP, ROWBTOP, TRANST, UPLO
INTEGER HEIGHT, IBASE, ICCOL, ICOFFC, ICOFFV, ICROW,
$ ICTXT, II, IIBEG, IIC, IIEND, IINXT, IIV,
$ ILASTCOL, ILASTROW, ILEFT, IOFF, IOFFC, IOFFV,
$ IPT, IPV, IPW, IPW1, IRIGHT, IROFFC, IROFFV,
$ ITOP, IVCOL, IVROW, JJ, JJBEG, JJC, JJEND,
$ JJNXT, JJV, KP, KQ, LDC, LDV, LV, LW, MBV, MPC,
$ MPC0, MQV, MQV0, MYCOL, MYDIST, MYROW, NBV,
$ NPV, NPV0, NPCOL, NPROW, NQC, NQC0, WIDE
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, INFOG1L, INFOG2L, PB_TOPGET,
$ PBZTRAN, ZGEBR2D, ZGEBS2D, ZGEMM,
$ ZGSUM2D, ZLAMOV, ZLASET, ZTRBR2D,
$ ZTRBS2D, ZTRMM
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN, MOD
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ICEIL, NUMROC
EXTERNAL ICEIL, LSAME, NUMROC
* ..
* .. Executable Statements ..
*
* Quick return if possible
*
IF( M.LE.0 .OR. N.LE.0 .OR. K.LE.0 )
$ RETURN
*
* Get grid parameters
*
ICTXT = DESCC( CTXT_ )
CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
*
IF( LSAME( TRANS, 'N' ) ) THEN
TRANST = 'C'
ELSE
TRANST = 'N'
END IF
FORWARD = LSAME( DIRECT, 'F' )
IF( FORWARD ) THEN
UPLO = 'U'
ELSE
UPLO = 'L'
END IF
*
CALL INFOG2L( IV, JV, DESCV, NPROW, NPCOL, MYROW, MYCOL, IIV, JJV,
$ IVROW, IVCOL )
CALL INFOG2L( IC, JC, DESCC, NPROW, NPCOL, MYROW, MYCOL, IIC, JJC,
$ ICROW, ICCOL )
LDC = DESCC( LLD_ )
LDV = DESCV( LLD_ )
IIC = MIN( IIC, LDC )
IIV = MIN( IIV, LDV )
IROFFC = MOD( IC-1, DESCC( MB_ ) )
ICOFFC = MOD( JC-1, DESCC( NB_ ) )
MBV = DESCV( MB_ )
NBV = DESCV( NB_ )
IROFFV = MOD( IV-1, MBV )
ICOFFV = MOD( JV-1, NBV )
MPC = NUMROC( M+IROFFC, DESCC( MB_ ), MYROW, ICROW, NPROW )
NQC = NUMROC( N+ICOFFC, DESCC( NB_ ), MYCOL, ICCOL, NPCOL )
IF( MYCOL.EQ.ICCOL )
$ NQC = NQC - ICOFFC
IF( MYROW.EQ.ICROW )
$ MPC = MPC - IROFFC
JJC = MIN( JJC, MAX( 1, JJC+NQC-1 ) )
JJV = MIN( JJV, MAX( 1, NUMROC( DESCV( N_ ), NBV, MYCOL,
$ DESCV( CSRC_ ), NPCOL ) ) )
IOFFC = IIC + ( JJC-1 ) * LDC
IOFFV = IIV + ( JJV-1 ) * LDV
*
IF( LSAME( STOREV, 'C' ) ) THEN
*
* V is stored columnwise
*
IF( LSAME( SIDE, 'L' ) ) THEN
*
* Form Q*sub( C ) or Q'*sub( C )
*
* Locally V( IOFFV ) is MPV x K, C( IOFFC ) is MPC x NQC
* WORK( IPV ) is MPC x K = V( IOFFV ), MPC = MPV
* WORK( IPW ) is NQC x K = C( IOFFC )' * V( IOFFV )
*
IPV = 1
IPW = IPV + MPC * K
LV = MAX( 1, MPC )
LW = MAX( 1, NQC )
*
* Broadcast V to the other process columns.
*
CALL PB_TOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP )
IF( MYCOL.EQ.IVCOL ) THEN
CALL ZGEBS2D( ICTXT, 'Rowwise', ROWBTOP, MPC, K,
$ V( IOFFV ), LDV )
IF( MYROW.EQ.IVROW )
$ CALL ZTRBS2D( ICTXT, 'Rowwise', ROWBTOP, UPLO,
$ 'Non unit', K, K, T, NBV )
CALL ZLAMOV( 'All', MPC, K, V( IOFFV ), LDV, WORK( IPV ),
$ LV )
ELSE
CALL ZGEBR2D( ICTXT, 'Rowwise', ROWBTOP, MPC, K,
$ WORK( IPV ), LV, MYROW, IVCOL )
IF( MYROW.EQ.IVROW )
$ CALL ZTRBR2D( ICTXT, 'Rowwise', ROWBTOP, UPLO,
$ 'Non unit', K, K, T, NBV, MYROW, IVCOL )
END IF
*
IF( FORWARD ) THEN
*
* WORK(IPV) = ( V1 ) where V1 is unit lower triangular,
* ( V2 ) zeroes upper triangular part of V1
*
MYDIST = MOD( MYROW-IVROW+NPROW, NPROW )
ITOP = MAX( 0, MYDIST*MBV - IROFFV )
IIBEG = IIV
IIEND = IIBEG + MPC - 1
IINXT = MIN( ICEIL( IIBEG, MBV )*MBV, IIEND )
*
10 CONTINUE
IF( K-ITOP .GT.0 ) THEN
CALL ZLASET( 'Upper', IINXT-IIBEG+1, K-ITOP, ZERO,
$ ONE, WORK( IPV+IIBEG-IIV+ITOP*LV ), LV )
MYDIST = MYDIST + NPROW
ITOP = MYDIST * MBV - IROFFV
IIBEG = IINXT + 1
IINXT = MIN( IINXT+MBV, IIEND )
GO TO 10
END IF
*
ELSE
*
* WORK(IPV) = ( V1 ) where V2 is unit upper triangular,
* ( V2 ) zeroes lower triangular part of V2
*
JJ = JJV
IOFF = MOD( IV+M-K-1, MBV )
CALL INFOG1L( IV+M-K, MBV, NPROW, MYROW, DESCV( RSRC_ ),
$ II, ILASTROW )
KP = NUMROC( K+IOFF, MBV, MYROW, ILASTROW, NPROW )
IF( MYROW.EQ.ILASTROW )
$ KP = KP - IOFF
MYDIST = MOD( MYROW-ILASTROW+NPROW, NPROW )
ITOP = MYDIST * MBV - IOFF
IBASE = MIN( ITOP+MBV, K )
ITOP = MIN( MAX( 0, ITOP ), K )
*
20 CONTINUE
IF( JJ.LE.( JJV+K-1 ) ) THEN
HEIGHT = IBASE - ITOP
CALL ZLASET( 'All', KP, ITOP-JJ+JJV, ZERO, ZERO,
$ WORK( IPV+II-IIV+(JJ-JJV)*LV ), LV )
CALL ZLASET( 'Lower', KP, HEIGHT, ZERO, ONE,
$ WORK( IPV+II-IIV+ITOP*LV ), LV )
KP = MAX( 0, KP - HEIGHT )
II = II + HEIGHT
JJ = JJV + IBASE
MYDIST = MYDIST + NPROW
ITOP = MYDIST * MBV - IOFF
IBASE = MIN( ITOP + MBV, K )
ITOP = MIN( ITOP, K )
GO TO 20
END IF
*
END IF
*
* WORK( IPW ) = C( IOFFC )' * V (NQC x MPC x K) -> NQC x K
*
IF( MPC.GT.0 ) THEN
CALL ZGEMM( 'Conjugate transpose', 'No transpose', NQC,
$ K, MPC, ONE, C( IOFFC ), LDC, WORK( IPV ), LV,
$ ZERO, WORK( IPW ), LW )
ELSE
CALL ZLASET( 'All', NQC, K, ZERO, ZERO, WORK( IPW ), LW )
END IF
*
CALL ZGSUM2D( ICTXT, 'Columnwise', ' ', NQC, K, WORK( IPW ),
$ LW, IVROW, MYCOL )
*
IF( MYROW.EQ.IVROW ) THEN
*
* WORK( IPW ) = WORK( IPW ) * T' or WORK( IPW ) * T
*
CALL ZTRMM( 'Right', UPLO, TRANST, 'Non unit', NQC, K,
$ ONE, T, NBV, WORK( IPW ), LW )
CALL ZGEBS2D( ICTXT, 'Columnwise', ' ', NQC, K,
$ WORK( IPW ), LW )
ELSE
CALL ZGEBR2D( ICTXT, 'Columnwise', ' ', NQC, K,
$ WORK( IPW ), LW, IVROW, MYCOL )
END IF
*
* C C - V * W'
* C( IOFFC ) = C( IOFFC ) - WORK( IPV ) * WORK( IPW )'
* MPC x NQC MPC x K K x NQC
*
CALL ZGEMM( 'No transpose', 'Conjugate transpose', MPC, NQC,
$ K, -ONE, WORK( IPV ), LV, WORK( IPW ), LW, ONE,
$ C( IOFFC ), LDC )
*
ELSE
*
* Form sub( C )*Q or sub( C )*Q'
*
* ICOFFC = IROFFV is required by the current transposition
* routine PBZTRAN
*
NPV0 = NUMROC( N+IROFFV, MBV, MYROW, IVROW, NPROW )
IF( MYROW.EQ.IVROW ) THEN
NPV = NPV0 - IROFFV
ELSE
NPV = NPV0
END IF
IF( MYCOL.EQ.ICCOL ) THEN
NQC0 = NQC + ICOFFC
ELSE
NQC0 = NQC
END IF
*
* Locally V( IOFFV ) is NPV x K C( IOFFC ) is MPC x NQC
* WORK( IPV ) is K x NQC0 = [ . V( IOFFV ) ]'
* WORK( IPW ) is NPV0 x K = [ . V( IOFFV )' ]'
* WORK( IPT ) is the workspace for PBZTRAN
*
IPV = 1
IPW = IPV + K * NQC0
IPT = IPW + NPV0 * K
LV = MAX( 1, K )
LW = MAX( 1, NPV0 )
*
IF( MYCOL.EQ.IVCOL ) THEN
IF( MYROW.EQ.IVROW ) THEN
CALL ZLASET( 'All', IROFFV, K, ZERO, ZERO,
$ WORK( IPW ), LW )
IPW1 = IPW + IROFFV
CALL ZLAMOV( 'All', NPV, K, V( IOFFV ), LDV,
$ WORK( IPW1 ), LW )
ELSE
IPW1 = IPW
CALL ZLAMOV( 'All', NPV, K, V( IOFFV ), LDV,
$ WORK( IPW1 ), LW )
END IF
*
IF( FORWARD ) THEN
*
* WORK(IPW) = ( . V1' V2' )' where V1 is unit lower
* triangular, zeroes upper triangular part of V1
*
MYDIST = MOD( MYROW-IVROW+NPROW, NPROW )
ITOP = MAX( 0, MYDIST*MBV - IROFFV )
IIBEG = IIV
IIEND = IIBEG + NPV - 1
IINXT = MIN( ICEIL( IIBEG, MBV )*MBV, IIEND )
*
30 CONTINUE
IF( ( K-ITOP ).GT.0 ) THEN
CALL ZLASET( 'Upper', IINXT-IIBEG+1, K-ITOP, ZERO,
$ ONE, WORK( IPW1+IIBEG-IIV+ITOP*LW ),
$ LW )
MYDIST = MYDIST + NPROW
ITOP = MYDIST * MBV - IROFFV
IIBEG = IINXT + 1
IINXT = MIN( IINXT+MBV, IIEND )
GO TO 30
END IF
*
ELSE
*
* WORK( IPW ) = ( . V1' V2' )' where V2 is unit upper
* triangular, zeroes lower triangular part of V2.
*
JJ = JJV
CALL INFOG1L( IV+N-K, MBV, NPROW, MYROW,
$ DESCV( RSRC_ ), II, ILASTROW )
IOFF = MOD( IV+N-K-1, MBV )
KP = NUMROC( K+IOFF, MBV, MYROW, ILASTROW, NPROW )
IF( MYROW.EQ.ILASTROW )
$ KP = KP - IOFF
MYDIST = MOD( MYROW-ILASTROW+NPROW, NPROW )
ITOP = MYDIST * MBV - IOFF
IBASE = MIN( ITOP+MBV, K )
ITOP = MIN( MAX( 0, ITOP ), K )
*
40 CONTINUE
IF( JJ.LE.( JJV+K-1 ) ) THEN
HEIGHT = IBASE - ITOP
CALL ZLASET( 'All', KP, ITOP-JJ+JJV, ZERO, ZERO,
$ WORK( IPW1+II-IIV+(JJ-JJV)*LW ), LW )
CALL ZLASET( 'Lower', KP, HEIGHT, ZERO, ONE,
$ WORK( IPW1+II-IIV+ITOP*LW ), LW )
KP = MAX( 0, KP - HEIGHT )
II = II + HEIGHT
JJ = JJV + IBASE
MYDIST = MYDIST + NPROW
ITOP = MYDIST * MBV - IOFF
IBASE = MIN( ITOP + MBV, K )
ITOP = MIN( ITOP, K )
GO TO 40
END IF
END IF
END IF
*
CALL PBZTRAN( ICTXT, 'Columnwise', 'Conjugate transpose',
$ N+IROFFV, K, MBV, WORK( IPW ), LW, ZERO,
$ WORK( IPV ), LV, IVROW, IVCOL, -1, ICCOL,
$ WORK( IPT ) )
*
* WORK( IPV ) = ( . V' ) -> WORK( IPV ) = V' is K x NQC
*
IF( MYCOL.EQ.ICCOL )
$ IPV = IPV + ICOFFC * LV
*
* WORK( IPW ) becomes MPC x K = C( IOFFC ) * V
* WORK( IPW ) = C( IOFFC ) * V (MPC x NQC x K) -> MPC x K
*
LW = MAX( 1, MPC )
*
IF( NQC.GT.0 ) THEN
CALL ZGEMM( 'No transpose', 'Conjugate transpose', MPC,
$ K, NQC, ONE, C( IOFFC ), LDC, WORK( IPV ),
$ LV, ZERO, WORK( IPW ), LW )
ELSE
CALL ZLASET( 'All', MPC, K, ZERO, ZERO, WORK( IPW ), LW )
END IF
*
CALL ZGSUM2D( ICTXT, 'Rowwise', ' ', MPC, K, WORK( IPW ),
$ LW, MYROW, IVCOL )
*
* WORK( IPW ) = WORK( IPW ) * T' or WORK( IPW ) * T
*
IF( MYCOL.EQ.IVCOL ) THEN
IF( MYROW.EQ.IVROW ) THEN
*
* Broadcast the block reflector to the other rows.
*
CALL ZTRBS2D( ICTXT, 'Columnwise', ' ', UPLO,
$ 'Non unit', K, K, T, NBV )
ELSE
CALL ZTRBR2D( ICTXT, 'Columnwise', ' ', UPLO,
$ 'Non unit', K, K, T, NBV, IVROW, MYCOL )
END IF
CALL ZTRMM( 'Right', UPLO, TRANS, 'Non unit', MPC, K,
$ ONE, T, NBV, WORK( IPW ), LW )
*
CALL ZGEBS2D( ICTXT, 'Rowwise', ' ', MPC, K, WORK( IPW ),
$ LW )
ELSE
CALL ZGEBR2D( ICTXT, 'Rowwise', ' ', MPC, K, WORK( IPW ),
$ LW, MYROW, IVCOL )
END IF
*
* C C - W * V'
* C( IOFFC ) = C( IOFFC ) - WORK( IPW ) * WORK( IPV )
* MPC x NQC MPC x K K x NQC
*
CALL ZGEMM( 'No transpose', 'No transpose', MPC, NQC, K,
$ -ONE, WORK( IPW ), LW, WORK( IPV ), LV, ONE,
$ C( IOFFC ), LDC )
END IF
*
ELSE
*
* V is stored rowwise
*
IF( LSAME( SIDE, 'L' ) ) THEN
*
* Form Q*sub( C ) or Q'*sub( C )
*
* IROFFC = ICOFFV is required by the current transposition
* routine PBZTRAN
*
MQV0 = NUMROC( M+ICOFFV, NBV, MYCOL, IVCOL, NPCOL )
IF( MYCOL.EQ.IVCOL ) THEN
MQV = MQV0 - ICOFFV
ELSE
MQV = MQV0
END IF
IF( MYROW.EQ.ICROW ) THEN
MPC0 = MPC + IROFFC
ELSE
MPC0 = MPC
END IF
*
* Locally V( IOFFV ) is K x MQV, C( IOFFC ) is MPC x NQC
* WORK( IPV ) is MPC0 x K = [ . V( IOFFV ) ]'
* WORK( IPW ) is K x MQV0 = [ . V( IOFFV ) ]
* WORK( IPT ) is the workspace for PBZTRAN
*
IPV = 1
IPW = IPV + MPC0 * K
IPT = IPW + K * MQV0
LV = MAX( 1, MPC0 )
LW = MAX( 1, K )
*
IF( MYROW.EQ.IVROW ) THEN
IF( MYCOL.EQ.IVCOL ) THEN
CALL ZLASET( 'All', K, ICOFFV, ZERO, ZERO,
$ WORK( IPW ), LW )
IPW1 = IPW + ICOFFV * LW
CALL ZLAMOV( 'All', K, MQV, V( IOFFV ), LDV,
$ WORK( IPW1 ), LW )
ELSE
IPW1 = IPW
CALL ZLAMOV( 'All', K, MQV, V( IOFFV ), LDV,
$ WORK( IPW1 ), LW )
END IF
*
IF( FORWARD ) THEN
*
* WORK( IPW ) = ( . V1 V2 ) where V1 is unit upper
* triangular, zeroes lower triangular part of V1
*
MYDIST = MOD( MYCOL-IVCOL+NPCOL, NPCOL )
ILEFT = MAX( 0, MYDIST * NBV - ICOFFV )
JJBEG = JJV
JJEND = JJV + MQV - 1
JJNXT = MIN( ICEIL( JJBEG, NBV ) * NBV, JJEND )
*
50 CONTINUE
IF( ( K-ILEFT ).GT.0 ) THEN
CALL ZLASET( 'Lower', K-ILEFT, JJNXT-JJBEG+1, ZERO,
$ ONE,
$ WORK( IPW1+ILEFT+(JJBEG-JJV)*LW ),
$ LW )
MYDIST = MYDIST + NPCOL
ILEFT = MYDIST * NBV - ICOFFV
JJBEG = JJNXT + 1
JJNXT = MIN( JJNXT+NBV, JJEND )
GO TO 50
END IF
*
ELSE
*
* WORK( IPW ) = ( . V1 V2 ) where V2 is unit lower
* triangular, zeroes upper triangular part of V2.
*
II = IIV
CALL INFOG1L( JV+M-K, NBV, NPCOL, MYCOL,
$ DESCV( CSRC_ ), JJ, ILASTCOL )
IOFF = MOD( JV+M-K-1, NBV )
KQ = NUMROC( K+IOFF, NBV, MYCOL, ILASTCOL, NPCOL )
IF( MYCOL.EQ.ILASTCOL )
$ KQ = KQ - IOFF
MYDIST = MOD( MYCOL-ILASTCOL+NPCOL, NPCOL )
ILEFT = MYDIST * NBV - IOFF
IRIGHT = MIN( ILEFT+NBV, K )
ILEFT = MIN( MAX( 0, ILEFT ), K )
*
60 CONTINUE
IF( II.LE.( IIV+K-1 ) ) THEN
WIDE = IRIGHT - ILEFT
CALL ZLASET( 'All', ILEFT-II+IIV, KQ, ZERO, ZERO,
$ WORK( IPW1+II-IIV+(JJ-JJV)*LW ), LW )
CALL ZLASET( 'Upper', WIDE, KQ, ZERO, ONE,
$ WORK( IPW1+ILEFT+(JJ-JJV)*LW ), LW )
KQ = MAX( 0, KQ - WIDE )
II = IIV + IRIGHT
JJ = JJ + WIDE
MYDIST = MYDIST + NPCOL
ILEFT = MYDIST * NBV - IOFF
IRIGHT = MIN( ILEFT + NBV, K )
ILEFT = MIN( ILEFT, K )
GO TO 60
END IF
END IF
END IF
*
* WORK( IPV ) = WORK( IPW )' (replicated) is MPC0 x K
*
CALL PBZTRAN( ICTXT, 'Rowwise', 'Conjugate transpose', K,
$ M+ICOFFV, NBV, WORK( IPW ), LW, ZERO,
$ WORK( IPV ), LV, IVROW, IVCOL, ICROW, -1,
$ WORK( IPT ) )
*
* WORK( IPV ) = ( . V )' -> WORK( IPV ) = V' is MPC x K
*
IF( MYROW.EQ.ICROW )
$ IPV = IPV + IROFFC
*
* WORK( IPW ) becomes NQC x K = C( IOFFC )' * V'
* WORK( IPW ) = C( IOFFC )' * V' (NQC x MPC x K) -> NQC x K
*
LW = MAX( 1, NQC )
*
IF( MPC.GT.0 ) THEN
CALL ZGEMM( 'Conjugate transpose', 'No transpose', NQC,
$ K, MPC, ONE, C( IOFFC ), LDC, WORK( IPV ),
$ LV, ZERO, WORK( IPW ), LW )
ELSE
CALL ZLASET( 'All', NQC, K, ZERO, ZERO, WORK( IPW ), LW )
END IF
*
CALL ZGSUM2D( ICTXT, 'Columnwise', ' ', NQC, K, WORK( IPW ),
$ LW, IVROW, MYCOL )
*
* WORK( IPW ) = WORK( IPW ) * T' or WORK( IPW ) * T
*
IF( MYROW.EQ.IVROW ) THEN
IF( MYCOL.EQ.IVCOL ) THEN
*
* Broadcast the block reflector to the other columns.
*
CALL ZTRBS2D( ICTXT, 'Rowwise', ' ', UPLO, 'Non unit',
$ K, K, T, MBV )
ELSE
CALL ZTRBR2D( ICTXT, 'Rowwise', ' ', UPLO, 'Non unit',
$ K, K, T, MBV, MYROW, IVCOL )
END IF
CALL ZTRMM( 'Right', UPLO, TRANST, 'Non unit', NQC, K,
$ ONE, T, MBV, WORK( IPW ), LW )
*
CALL ZGEBS2D( ICTXT, 'Columnwise', ' ', NQC, K,
$ WORK( IPW ), LW )
ELSE
CALL ZGEBR2D( ICTXT, 'Columnwise', ' ', NQC, K,
$ WORK( IPW ), LW, IVROW, MYCOL )
END IF
*
* C C - V' * W'
* C( IOFFC ) = C( IOFFC ) - WORK( IPV ) * WORK( IPW )'
* MPC x NQC MPC x K K x NQC
*
CALL ZGEMM( 'No transpose', 'Conjugate transpose', MPC, NQC,
$ K, -ONE, WORK( IPV ), LV, WORK( IPW ), LW, ONE,
$ C( IOFFC ), LDC )
*
ELSE
*
* Form Q*sub( C ) or Q'*sub( C )
*
* Locally V( IOFFV ) is K x NQV, C( IOFFC ) is MPC x NQC
* WORK( IPV ) is K x NQV = V( IOFFV ), NQV = NQC
* WORK( IPW ) is MPC x K = C( IOFFC ) * V( IOFFV )'
*
IPV = 1
IPW = IPV + K * NQC
LV = MAX( 1, K )
LW = MAX( 1, MPC )
*
* Broadcast V to the other process rows.
*
CALL PB_TOPGET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP )
IF( MYROW.EQ.IVROW ) THEN
CALL ZGEBS2D( ICTXT, 'Columnwise', COLBTOP, K, NQC,
$ V( IOFFV ), LDV )
IF( MYCOL.EQ.IVCOL )
$ CALL ZTRBS2D( ICTXT, 'Columnwise', COLBTOP, UPLO,
$ 'Non unit', K, K, T, MBV )
CALL ZLAMOV( 'All', K, NQC, V( IOFFV ), LDV, WORK( IPV ),
$ LV )
ELSE
CALL ZGEBR2D( ICTXT, 'Columnwise', COLBTOP, K, NQC,
$ WORK( IPV ), LV, IVROW, MYCOL )
IF( MYCOL.EQ.IVCOL )
$ CALL ZTRBR2D( ICTXT, 'Columnwise', COLBTOP, UPLO,
$ 'Non unit', K, K, T, MBV, IVROW, MYCOL )
END IF
*
IF( FORWARD ) THEN
*
* WORK(IPW) = ( V1 V2 ) where V1 is unit upper
* triangular, zeroes lower triangular part of V1
*
MYDIST = MOD( MYCOL-IVCOL+NPCOL, NPCOL )
ILEFT = MAX( 0, MYDIST * NBV - ICOFFV )
JJBEG = JJV
JJEND = JJV + NQC - 1
JJNXT = MIN( ICEIL( JJBEG, NBV ) * NBV, JJEND )
*
70 CONTINUE
IF( ( K-ILEFT ).GT.0 ) THEN
CALL ZLASET( 'Lower', K-ILEFT, JJNXT-JJBEG+1, ZERO,
$ ONE, WORK( IPV+ILEFT+(JJBEG-JJV)*LV ),
$ LV )
MYDIST = MYDIST + NPCOL
ILEFT = MYDIST * NBV - ICOFFV
JJBEG = JJNXT + 1
JJNXT = MIN( JJNXT+NBV, JJEND )
GO TO 70
END IF
*
ELSE
*
* WORK( IPW ) = ( . V1 V2 ) where V2 is unit lower
* triangular, zeroes upper triangular part of V2.
*
II = IIV
CALL INFOG1L( JV+N-K, NBV, NPCOL, MYCOL, DESCV( CSRC_ ),
$ JJ, ILASTCOL )
IOFF = MOD( JV+N-K-1, NBV )
KQ = NUMROC( K+IOFF, NBV, MYCOL, ILASTCOL, NPCOL )
IF( MYCOL.EQ.ILASTCOL )
$ KQ = KQ - IOFF
MYDIST = MOD( MYCOL-ILASTCOL+NPCOL, NPCOL )
ILEFT = MYDIST * NBV - IOFF
IRIGHT = MIN( ILEFT+NBV, K )
ILEFT = MIN( MAX( 0, ILEFT ), K )
*
80 CONTINUE
IF( II.LE.( IIV+K-1 ) ) THEN
WIDE = IRIGHT - ILEFT
CALL ZLASET( 'All', ILEFT-II+IIV, KQ, ZERO, ZERO,
$ WORK( IPV+II-IIV+(JJ-JJV)*LV ), LV )
CALL ZLASET( 'Upper', WIDE, KQ, ZERO, ONE,
$ WORK( IPV+ILEFT+(JJ-JJV)*LV ), LV )
KQ = MAX( 0, KQ - WIDE )
II = IIV + IRIGHT
JJ = JJ + WIDE
MYDIST = MYDIST + NPCOL
ILEFT = MYDIST * NBV - IOFF
IRIGHT = MIN( ILEFT + NBV, K )
ILEFT = MIN( ILEFT, K )
GO TO 80
END IF
*
END IF
*
* WORK( IPV ) is K x NQC = V = V( IOFFV )
* WORK( IPW ) = C( IOFFC ) * V' (MPC x NQC x K) -> MPC x K
*
IF( NQC.GT.0 ) THEN
CALL ZGEMM( 'No transpose', 'Conjugate transpose', MPC,
$ K, NQC, ONE, C( IOFFC ), LDC, WORK( IPV ),
$ LV, ZERO, WORK( IPW ), LW )
ELSE
CALL ZLASET( 'All', MPC, K, ZERO, ZERO, WORK( IPW ), LW )
END IF
*
CALL ZGSUM2D( ICTXT, 'Rowwise', ' ', MPC, K, WORK( IPW ),
$ LW, MYROW, IVCOL )
*
* WORK( IPW ) = WORK( IPW ) * T' or WORK( IPW ) * T
*
IF( MYCOL.EQ.IVCOL ) THEN
CALL ZTRMM( 'Right', UPLO, TRANS, 'Non unit', MPC, K,
$ ONE, T, MBV, WORK( IPW ), LW )
CALL ZGEBS2D( ICTXT, 'Rowwise', ' ', MPC, K, WORK( IPW ),
$ LW )
ELSE
CALL ZGEBR2D( ICTXT, 'Rowwise', ' ', MPC, K, WORK( IPW ),
$ LW, MYROW, IVCOL )
END IF
*
* C C - W * V
* C( IOFFC ) = C( IOFFC ) - WORK( IPW ) * WORK( IPV )
* MPC x NQC MPC x K K x NQC
*
CALL ZGEMM( 'No transpose', 'No transpose', MPC, NQC, K,
$ -ONE, WORK( IPW ), LW, WORK( IPV ), LV, ONE,
$ C( IOFFC ), LDC )
*
END IF
*
END IF
*
RETURN
*
* End of PZLARFB
*
END
|
