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
|
DOUBLE PRECISION FUNCTION PDLANSY( NORM, UPLO, N, A, IA, JA,
$ DESCA, WORK )
IMPLICIT NONE
*
* -- ScaLAPACK auxiliary routine (version 1.7) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* May 1, 1997
*
* .. Scalar Arguments ..
CHARACTER NORM, UPLO
INTEGER IA, JA, N
* ..
* .. Array Arguments ..
INTEGER DESCA( * )
DOUBLE PRECISION A( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* PDLANSY returns the value of the one norm, or the Frobenius norm,
* or the infinity norm, or the element of largest absolute value of a
* real symmetric distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1).
*
* PDLANSY returns the value
*
* ( max(abs(A(i,j))), NORM = 'M' or 'm' with IA <= i <= IA+N-1,
* ( and JA <= j <= JA+N-1,
* (
* ( norm1( sub( A ) ), NORM = '1', 'O' or 'o'
* (
* ( normI( sub( A ) ), NORM = 'I' or 'i'
* (
* ( normF( sub( A ) ), NORM = 'F', 'f', 'E' or 'e'
*
* where norm1 denotes the one norm of a matrix (maximum column sum),
* normI denotes the infinity norm of a matrix (maximum row sum) and
* normF denotes the Frobenius norm of a matrix (square root of sum of
* squares). Note that max(abs(A(i,j))) is not a matrix norm.
*
* 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
* =========
*
* NORM (global input) CHARACTER
* Specifies the value to be returned in PDLANSY as described
* above.
*
* UPLO (global input) CHARACTER
* Specifies whether the upper or lower triangular part of the
* symmetric matrix sub( A ) is to be referenced.
* = 'U': Upper triangular part of sub( A ) is referenced,
* = 'L': Lower triangular part of sub( A ) is referenced.
*
* N (global input) INTEGER
* The number of rows and columns to be operated on i.e the
* number of rows and columns of the distributed submatrix
* sub( A ). When N = 0, PDLANSY is set to zero. N >= 0.
*
* A (local input) DOUBLE PRECISION pointer into the local memory
* to an array of dimension (LLD_A, LOCc(JA+N-1)) containing the
* local pieces of the symmetric distributed matrix sub( A ).
* If UPLO = 'U', the leading N-by-N upper triangular part of
* sub( A ) contains the upper triangular matrix which norm is
* to be computed, and the strictly lower triangular part of
* this matrix is not referenced. If UPLO = 'L', the leading
* N-by-N lower triangular part of sub( A ) contains the lower
* triangular matrix which norm is to be computed, and the
* strictly upper triangular part of sub( A ) is not referenced.
*
* IA (global input) INTEGER
* The row index in the global array A indicating the first
* row of sub( A ).
*
* JA (global input) INTEGER
* The column index in the global array A indicating the
* first column of sub( A ).
*
* DESCA (global and local input) INTEGER array of dimension DLEN_.
* The array descriptor for the distributed matrix A.
*
* WORK (local workspace) DOUBLE PRECISION array dimension (LWORK)
* LWORK >= 0 if NORM = 'M' or 'm' (not referenced),
* 2*Nq0+Np0+LDW if NORM = '1', 'O', 'o', 'I' or 'i',
* where LDW is given by:
* IF( NPROW.NE.NPCOL ) THEN
* LDW = MB_A*CEIL(CEIL(Np0/MB_A)/(LCM/NPROW))
* ELSE
* LDW = 0
* END IF
* 0 if NORM = 'F', 'f', 'E' or 'e' (not referenced),
*
* where LCM is the least common multiple of NPROW and NPCOL
* LCM = ILCM( NPROW, NPCOL ) and CEIL denotes the ceiling
* operation (ICEIL).
*
* IROFFA = MOD( IA-1, MB_A ), ICOFFA = MOD( JA-1, NB_A ),
* IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ),
* IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ),
* Np0 = NUMROC( N+IROFFA, MB_A, MYROW, IAROW, NPROW ),
* Nq0 = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ),
*
* ICEIL, ILCM, INDXG2P and NUMROC are ScaLAPACK tool functions;
* MYROW, MYCOL, NPROW and NPCOL can be determined by calling
* the subroutine BLACS_GRIDINFO.
*
* =====================================================================
*
* .. 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 )
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, IAROW, IACOL, IB, ICOFF, ICTXT, ICURCOL,
$ ICURROW, II, IIA, IN, IROFF, ICSR, ICSR0,
$ IOFFA, IRSC, IRSC0, IRSR, IRSR0, JJ, JJA, K,
$ LDA, LL, MYCOL, MYROW, NP, NPCOL, NPROW, NQ
DOUBLE PRECISION SUM, VALUE
* ..
* .. Local Arrays ..
DOUBLE PRECISION SSQ( 2 ), COLSSQ( 2 )
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, DAXPY, DCOMBSSQ,
$ DGAMX2D, DGSUM2D, DGEBR2D,
$ DGEBS2D, DLASSQ, PDCOL2ROW,
$ PDTREECOMB
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ICEIL, IDAMAX, NUMROC
EXTERNAL ICEIL, IDAMAX, LSAME, NUMROC
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN, MOD, SQRT
* ..
* .. Executable Statements ..
*
* Get grid parameters and local indexes.
*
ICTXT = DESCA( CTXT_ )
CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL,
$ IIA, JJA, IAROW, IACOL )
*
IROFF = MOD( IA-1, DESCA( MB_ ) )
ICOFF = MOD( JA-1, DESCA( NB_ ) )
NP = NUMROC( N+IROFF, DESCA( MB_ ), MYROW, IAROW, NPROW )
NQ = NUMROC( N+ICOFF, DESCA( NB_ ), MYCOL, IACOL, NPCOL )
ICSR = 1
IRSR = ICSR + NQ
IRSC = IRSR + NQ
IF( MYROW.EQ.IAROW ) THEN
IRSC0 = IRSC + IROFF
NP = NP - IROFF
ELSE
IRSC0 = IRSC
END IF
IF( MYCOL.EQ.IACOL ) THEN
ICSR0 = ICSR + ICOFF
IRSR0 = IRSR + ICOFF
NQ = NQ - ICOFF
ELSE
ICSR0 = ICSR
IRSR0 = IRSR
END IF
IN = MIN( ICEIL( IA, DESCA( MB_ ) ) * DESCA( MB_ ), IA+N-1 )
LDA = DESCA( LLD_ )
*
* If the matrix is symmetric, we address only a triangular portion
* of the matrix. A sum of row (column) i of the complete matrix
* can be obtained by adding along row i and column i of the the
* triangular matrix, stopping/starting at the diagonal, which is
* the point of reflection. The pictures below demonstrate this.
* In the following code, the row sums created by --- rows below are
* refered to as ROWSUMS, and the column sums shown by | are refered
* to as COLSUMS. Infinity-norm = 1-norm = ROWSUMS+COLSUMS.
*
* UPLO = 'U' UPLO = 'L'
* ____i______ ___________
* |\ | | |\ |
* | \ | | | \ |
* | \ | | | \ |
* | \|------| i i|---\ |
* | \ | | |\ |
* | \ | | | \ |
* | \ | | | \ |
* | \ | | | \ |
* | \ | | | \ |
* | \ | | | \ |
* |__________\| |___|______\|
* i
*
* II, JJ : local indices into array A
* ICURROW : process row containing diagonal block
* ICURCOL : process column containing diagonal block
* IRSC0 : pointer to part of work used to store the ROWSUMS while
* they are stored along a process column
* IRSR0 : pointer to part of work used to store the ROWSUMS after
* they have been transposed to be along a process row
*
II = IIA
JJ = JJA
*
IF( N.EQ.0 ) THEN
*
VALUE = ZERO
*
************************************************************************
* max norm
*
ELSE IF( LSAME( NORM, 'M' ) ) THEN
*
* Find max(abs(A(i,j))).
*
VALUE = ZERO
*
IF( LSAME( UPLO, 'U' ) ) THEN
*
* Handle first block separately
*
IB = IN-IA+1
*
* Find COLMAXS
*
IF( MYCOL.EQ.IACOL ) THEN
DO 20 K = (JJ-1)*LDA, (JJ+IB-2)*LDA, LDA
IF( II.GT.IIA ) THEN
DO 10 LL = IIA, II-1
VALUE = MAX( VALUE, ABS( A( LL+K ) ) )
10 CONTINUE
END IF
IF( MYROW.EQ.IAROW )
$ II = II + 1
20 CONTINUE
*
* Reset local indices so we can find ROWMAXS
*
IF( MYROW.EQ.IAROW )
$ II = II - IB
*
END IF
*
* Find ROWMAXS
*
IF( MYROW.EQ.IAROW ) THEN
DO 40 K = II, II+IB-1
IF( JJ.LE.JJA+NQ-1 ) THEN
DO 30 LL = (JJ-1)*LDA, (JJA+NQ-2)*LDA, LDA
VALUE = MAX( VALUE, ABS( A( K+LL ) ) )
30 CONTINUE
END IF
IF( MYCOL.EQ.IACOL )
$ JJ = JJ + 1
40 CONTINUE
II = II + IB
ELSE IF( MYCOL.EQ.IACOL ) THEN
JJ = JJ + IB
END IF
*
ICURROW = MOD( IAROW+1, NPROW )
ICURCOL = MOD( IACOL+1, NPCOL )
*
* Loop over the remaining rows/columns of the matrix.
*
DO 90 I = IN+1, IA+N-1, DESCA( MB_ )
IB = MIN( DESCA( MB_ ), IA+N-I )
*
* Find COLMAXS
*
IF( MYCOL.EQ.ICURCOL ) THEN
DO 60 K = (JJ-1)*LDA, (JJ+IB-2)*LDA, LDA
IF( II.GT.IIA ) THEN
DO 50 LL = IIA, II-1
VALUE = MAX( VALUE, ABS( A( LL+K ) ) )
50 CONTINUE
END IF
IF( MYROW.EQ.ICURROW )
$ II = II + 1
60 CONTINUE
*
* Reset local indices so we can find ROWMAXS
*
IF( MYROW.EQ.ICURROW )
$ II = II - IB
END IF
*
* Find ROWMAXS
*
IF( MYROW.EQ.ICURROW ) THEN
DO 80 K = II, II+IB-1
IF( JJ.LE.JJA+NQ-1 ) THEN
DO 70 LL = (JJ-1)*LDA, (JJA+NQ-2)*LDA, LDA
VALUE = MAX( VALUE, ABS( A( K+LL ) ) )
70 CONTINUE
END IF
IF( MYCOL.EQ.ICURCOL )
$ JJ = JJ + 1
80 CONTINUE
II = II + IB
ELSE IF( MYCOL.EQ.ICURCOL ) THEN
JJ = JJ + IB
END IF
ICURROW = MOD( ICURROW+1, NPROW )
ICURCOL = MOD( ICURCOL+1, NPCOL )
90 CONTINUE
*
ELSE
*
* Handle first block separately
*
IB = IN-IA+1
*
* Find COLMAXS
*
IF( MYCOL.EQ.IACOL ) THEN
DO 110 K = (JJ-1)*LDA, (JJ+IB-2)*LDA, LDA
IF( II.LE.IIA+NP-1 ) THEN
DO 100 LL = II, IIA+NP-1
VALUE = MAX( VALUE, ABS( A( LL+K ) ) )
100 CONTINUE
END IF
IF( MYROW.EQ.IAROW )
$ II = II + 1
110 CONTINUE
*
* Reset local indices so we can find ROWMAXS
*
IF( MYROW.EQ.IAROW )
$ II = II - IB
END IF
*
* Find ROWMAXS
*
IF( MYROW.EQ.IAROW ) THEN
DO 130 K = 0, IB-1
IF( JJ.GT.JJA ) THEN
DO 120 LL = (JJA-1)*LDA, (JJ-2)*LDA, LDA
VALUE = MAX( VALUE, ABS( A( II+LL ) ) )
120 CONTINUE
END IF
II = II + 1
IF( MYCOL.EQ.IACOL )
$ JJ = JJ + 1
130 CONTINUE
ELSE IF( MYCOL.EQ.IACOL ) THEN
JJ = JJ + IB
END IF
*
ICURROW = MOD( IAROW+1, NPROW )
ICURCOL = MOD( IACOL+1, NPCOL )
*
* Loop over rows/columns of global matrix.
*
DO 180 I = IN+1, IA+N-1, DESCA( MB_ )
IB = MIN( DESCA( MB_ ), IA+N-I )
*
* Find COLMAXS
*
IF( MYCOL.EQ.ICURCOL ) THEN
DO 150 K = (JJ-1)*LDA, (JJ+IB-2)*LDA, LDA
IF( II.LE.IIA+NP-1 ) THEN
DO 140 LL = II, IIA+NP-1
VALUE = MAX( VALUE, ABS( A( LL+K ) ) )
140 CONTINUE
END IF
IF( MYROW.EQ.ICURROW )
$ II = II + 1
150 CONTINUE
*
* Reset local indices so we can find ROWMAXS
*
IF( MYROW.EQ.ICURROW )
$ II = II - IB
END IF
*
* Find ROWMAXS
*
IF( MYROW.EQ.ICURROW ) THEN
DO 170 K = 0, IB-1
IF( JJ.GT.JJA ) THEN
DO 160 LL = (JJA-1)*LDA, (JJ-2)*LDA, LDA
VALUE = MAX( VALUE, ABS( A( II+LL ) ) )
160 CONTINUE
END IF
II = II + 1
IF( MYCOL.EQ.ICURCOL )
$ JJ = JJ + 1
170 CONTINUE
ELSE IF( MYCOL.EQ.ICURCOL ) THEN
JJ = JJ + IB
END IF
ICURROW = MOD( ICURROW+1, NPROW )
ICURCOL = MOD( ICURCOL+1, NPCOL )
*
180 CONTINUE
*
END IF
*
* Gather the result on process (IAROW,IACOL).
*
CALL DGAMX2D( ICTXT, 'All', ' ', 1, 1, VALUE, 1, I, K, -1,
$ IAROW, IACOL )
*
************************************************************************
* one or inf norm
*
ELSE IF( LSAME( NORM, 'I' ) .OR. LSAME( NORM, 'O' ) .OR.
$ NORM.EQ.'1' ) THEN
*
* Find normI( sub( A ) ) ( = norm1( sub( A ) ), since sub( A ) is
* symmetric).
*
IF( LSAME( UPLO, 'U' ) ) THEN
*
* Handle first block separately
*
IB = IN-IA+1
*
* Find COLSUMS
*
IF( MYCOL.EQ.IACOL ) THEN
IOFFA = ( JJ - 1 ) * LDA
DO 200 K = 0, IB-1
SUM = ZERO
IF( II.GT.IIA ) THEN
DO 190 LL = IIA, II-1
SUM = SUM + ABS( A( LL+IOFFA ) )
190 CONTINUE
END IF
IOFFA = IOFFA + LDA
WORK( JJ+K-JJA+ICSR0 ) = SUM
IF( MYROW.EQ.IAROW )
$ II = II + 1
200 CONTINUE
*
* Reset local indices so we can find ROWSUMS
*
IF( MYROW.EQ.IAROW )
$ II = II - IB
*
END IF
*
* Find ROWSUMS
*
IF( MYROW.EQ.IAROW ) THEN
DO 220 K = II, II+IB-1
SUM = ZERO
IF( JJA+NQ.GT.JJ ) THEN
DO 210 LL = (JJ-1)*LDA, (JJA+NQ-2)*LDA, LDA
SUM = SUM + ABS( A( K+LL ) )
210 CONTINUE
END IF
WORK( K-IIA+IRSC0 ) = SUM
IF( MYCOL.EQ.IACOL )
$ JJ = JJ + 1
220 CONTINUE
II = II + IB
ELSE IF( MYCOL.EQ.IACOL ) THEN
JJ = JJ + IB
END IF
*
ICURROW = MOD( IAROW+1, NPROW )
ICURCOL = MOD( IACOL+1, NPCOL )
*
* Loop over remaining rows/columns of global matrix.
*
DO 270 I = IN+1, IA+N-1, DESCA( MB_ )
IB = MIN( DESCA( MB_ ), IA+N-I )
*
* Find COLSUMS
*
IF( MYCOL.EQ.ICURCOL ) THEN
IOFFA = ( JJ - 1 ) * LDA
DO 240 K = 0, IB-1
SUM = ZERO
IF( II.GT.IIA ) THEN
DO 230 LL = IIA, II-1
SUM = SUM + ABS( A( IOFFA+LL ) )
230 CONTINUE
END IF
IOFFA = IOFFA + LDA
WORK( JJ+K-JJA+ICSR0 ) = SUM
IF( MYROW.EQ.ICURROW )
$ II = II + 1
240 CONTINUE
*
* Reset local indices so we can find ROWSUMS
*
IF( MYROW.EQ.ICURROW )
$ II = II - IB
*
END IF
*
* Find ROWSUMS
*
IF( MYROW.EQ.ICURROW ) THEN
DO 260 K = II, II+IB-1
SUM = ZERO
IF( JJA+NQ.GT.JJ ) THEN
DO 250 LL = (JJ-1)*LDA, (JJA+NQ-2)*LDA, LDA
SUM = SUM + ABS( A( K+LL ) )
250 CONTINUE
END IF
WORK( K-IIA+IRSC0 ) = SUM
IF( MYCOL.EQ.ICURCOL )
$ JJ = JJ + 1
260 CONTINUE
II = II + IB
ELSE IF( MYCOL.EQ.ICURCOL ) THEN
JJ = JJ + IB
END IF
*
ICURROW = MOD( ICURROW+1, NPROW )
ICURCOL = MOD( ICURCOL+1, NPCOL )
*
270 CONTINUE
*
ELSE
*
* Handle first block separately
*
IB = IN-IA+1
*
* Find COLSUMS
*
IF( MYCOL.EQ.IACOL ) THEN
IOFFA = (JJ-1)*LDA
DO 290 K = 0, IB-1
SUM = ZERO
IF( IIA+NP.GT.II ) THEN
DO 280 LL = II, IIA+NP-1
SUM = SUM + ABS( A( IOFFA+LL ) )
280 CONTINUE
END IF
IOFFA = IOFFA + LDA
WORK( JJ+K-JJA+ICSR0 ) = SUM
IF( MYROW.EQ.IAROW )
$ II = II + 1
290 CONTINUE
*
* Reset local indices so we can find ROWSUMS
*
IF( MYROW.EQ.IAROW )
$ II = II - IB
*
END IF
*
* Find ROWSUMS
*
IF( MYROW.EQ.IAROW ) THEN
DO 310 K = II, II+IB-1
SUM = ZERO
IF( JJ.GT.JJA ) THEN
DO 300 LL = (JJA-1)*LDA, (JJ-2)*LDA, LDA
SUM = SUM + ABS( A( K+LL ) )
300 CONTINUE
END IF
WORK( K-IIA+IRSC0 ) = SUM
IF( MYCOL.EQ.IACOL )
$ JJ = JJ + 1
310 CONTINUE
II = II + IB
ELSE IF( MYCOL.EQ.IACOL ) THEN
JJ = JJ + IB
END IF
*
ICURROW = MOD( IAROW+1, NPROW )
ICURCOL = MOD( IACOL+1, NPCOL )
*
* Loop over rows/columns of global matrix.
*
DO 360 I = IN+1, IA+N-1, DESCA( MB_ )
IB = MIN( DESCA( MB_ ), IA+N-I )
*
* Find COLSUMS
*
IF( MYCOL.EQ.ICURCOL ) THEN
IOFFA = ( JJ - 1 ) * LDA
DO 330 K = 0, IB-1
SUM = ZERO
IF( IIA+NP.GT.II ) THEN
DO 320 LL = II, IIA+NP-1
SUM = SUM + ABS( A( LL+IOFFA ) )
320 CONTINUE
END IF
IOFFA = IOFFA + LDA
WORK( JJ+K-JJA+ICSR0 ) = SUM
IF( MYROW.EQ.ICURROW )
$ II = II + 1
330 CONTINUE
*
* Reset local indices so we can find ROWSUMS
*
IF( MYROW.EQ.ICURROW )
$ II = II - IB
*
END IF
*
* Find ROWSUMS
*
IF( MYROW.EQ.ICURROW ) THEN
DO 350 K = II, II+IB-1
SUM = ZERO
IF( JJ.GT.JJA ) THEN
DO 340 LL = (JJA-1)*LDA, (JJ-2)*LDA, LDA
SUM = SUM + ABS( A( K+LL ) )
340 CONTINUE
END IF
WORK(K-IIA+IRSC0) = SUM
IF( MYCOL.EQ.ICURCOL )
$ JJ = JJ + 1
350 CONTINUE
II = II + IB
ELSE IF( MYCOL.EQ.ICURCOL ) THEN
JJ = JJ + IB
END IF
*
ICURROW = MOD( ICURROW+1, NPROW )
ICURCOL = MOD( ICURCOL+1, NPCOL )
*
360 CONTINUE
END IF
*
* After calls to DGSUM2D, process row 0 will have global
* COLSUMS and process column 0 will have global ROWSUMS.
* Transpose ROWSUMS and add to COLSUMS to get global row/column
* sum, the max of which is the infinity or 1 norm.
*
IF( MYCOL.EQ.IACOL )
$ NQ = NQ + ICOFF
CALL DGSUM2D( ICTXT, 'Columnwise', ' ', 1, NQ, WORK( ICSR ), 1,
$ IAROW, MYCOL )
IF( MYROW.EQ.IAROW )
$ NP = NP + IROFF
CALL DGSUM2D( ICTXT, 'Rowwise', ' ', NP, 1, WORK( IRSC ),
$ MAX( 1, NP ), MYROW, IACOL )
*
CALL PDCOL2ROW( ICTXT, N, 1, DESCA( MB_ ), WORK( IRSC ),
$ MAX( 1, NP ), WORK( IRSR ), MAX( 1, NQ ),
$ IAROW, IACOL, IAROW, IACOL, WORK( IRSC+NP ) )
*
IF( MYROW.EQ.IAROW ) THEN
IF( MYCOL.EQ.IACOL )
$ NQ = NQ - ICOFF
CALL DAXPY( NQ, ONE, WORK( IRSR0 ), 1, WORK( ICSR0 ), 1 )
IF( NQ.LT.1 ) THEN
VALUE = ZERO
ELSE
VALUE = WORK( IDAMAX( NQ, WORK( ICSR0 ), 1 ) )
END IF
CALL DGAMX2D( ICTXT, 'Rowwise', ' ', 1, 1, VALUE, 1, I, K,
$ -1, IAROW, IACOL )
END IF
*
************************************************************************
* Frobenius norm
* SSQ(1) is scale
* SSQ(2) is sum-of-squares
*
ELSE IF( LSAME( NORM, 'F' ) .OR. LSAME( NORM, 'E' ) ) THEN
*
* Find normF( sub( A ) ).
*
SSQ(1) = ZERO
SSQ(2) = ONE
*
* Add off-diagonal entries, first
*
IF( LSAME( UPLO, 'U' ) ) THEN
*
* Handle first block separately
*
IB = IN-IA+1
*
IF( MYCOL.EQ.IACOL ) THEN
DO 370 K = (JJ-1)*LDA, (JJ+IB-2)*LDA, LDA
COLSSQ(1) = ZERO
COLSSQ(2) = ONE
CALL DLASSQ( II-IIA, A( IIA+K ), 1,
$ COLSSQ(1), COLSSQ(2) )
IF( MYROW.EQ.IAROW )
$ II = II + 1
CALL DLASSQ( II-IIA, A( IIA+K ), 1,
$ COLSSQ(1), COLSSQ(2) )
CALL DCOMBSSQ( SSQ, COLSSQ )
370 CONTINUE
*
JJ = JJ + IB
ELSE IF( MYROW.EQ.IAROW ) THEN
II = II + IB
END IF
*
ICURROW = MOD( IAROW+1, NPROW )
ICURCOL = MOD( IACOL+1, NPCOL )
*
* Loop over rows/columns of global matrix.
*
DO 390 I = IN+1, IA+N-1, DESCA( MB_ )
IB = MIN( DESCA( MB_ ), IA+N-I )
*
IF( MYCOL.EQ.ICURCOL ) THEN
DO 380 K = (JJ-1)*LDA, (JJ+IB-2)*LDA, LDA
COLSSQ(1) = ZERO
COLSSQ(2) = ONE
CALL DLASSQ( II-IIA, A( IIA+K ), 1,
$ COLSSQ(1), COLSSQ(2) )
IF( MYROW.EQ.ICURROW )
$ II = II + 1
CALL DLASSQ( II-IIA, A (IIA+K ), 1,
$ COLSSQ(1), COLSSQ(2) )
CALL DCOMBSSQ( SSQ, COLSSQ )
380 CONTINUE
*
JJ = JJ + IB
ELSE IF( MYROW.EQ.ICURROW ) THEN
II = II + IB
END IF
*
ICURROW = MOD( ICURROW+1, NPROW )
ICURCOL = MOD( ICURCOL+1, NPCOL )
*
390 CONTINUE
*
ELSE
*
* Handle first block separately
*
IB = IN-IA+1
*
IF( MYCOL.EQ.IACOL ) THEN
DO 400 K = (JJ-1)*LDA, (JJ+IB-2)*LDA, LDA
COLSSQ(1) = ZERO
COLSSQ(2) = ONE
CALL DLASSQ( IIA+NP-II, A( II+K ), 1,
$ COLSSQ(1), COLSSQ(2) )
IF( MYROW.EQ.IAROW )
$ II = II + 1
CALL DLASSQ( IIA+NP-II, A( II+K ), 1,
$ COLSSQ(1), COLSSQ(2) )
CALL DCOMBSSQ( SSQ, COLSSQ )
400 CONTINUE
*
JJ = JJ + IB
ELSE IF( MYROW.EQ.IAROW ) THEN
II = II + IB
END IF
*
ICURROW = MOD( IAROW+1, NPROW )
ICURCOL = MOD( IACOL+1, NPCOL )
*
* Loop over rows/columns of global matrix.
*
DO 420 I = IN+1, IA+N-1, DESCA( MB_ )
IB = MIN( DESCA( MB_ ), IA+N-I )
*
IF( MYCOL.EQ.ICURCOL ) THEN
DO 410 K = (JJ-1)*LDA, (JJ+IB-2)*LDA, LDA
COLSSQ(1) = ZERO
COLSSQ(2) = ONE
CALL DLASSQ( IIA+NP-II, A( II+K ), 1,
$ COLSSQ(1), COLSSQ(2) )
IF( MYROW.EQ.ICURROW )
$ II = II + 1
CALL DLASSQ( IIA+NP-II, A( II+K ), 1,
$ COLSSQ(1), COLSSQ(2) )
CALL DCOMBSSQ( SSQ, COLSSQ )
410 CONTINUE
*
JJ = JJ + IB
ELSE IF( MYROW.EQ.ICURROW ) THEN
II = II + IB
END IF
*
ICURROW = MOD( ICURROW+1, NPROW )
ICURCOL = MOD( ICURCOL+1, NPCOL )
*
420 CONTINUE
*
END IF
*
* Perform the global scaled sum
*
CALL PDTREECOMB( ICTXT, 'All', 2, SSQ, IAROW, IACOL,
$ DCOMBSSQ )
VALUE = SSQ( 1 ) * SQRT( SSQ( 2 ) )
*
END IF
*
* Broadcast the result to the other processes
*
IF( MYROW.EQ.IAROW .AND. MYCOL.EQ.IACOL ) THEN
CALL DGEBS2D( ICTXT, 'All', ' ', 1, 1, VALUE, 1 )
ELSE
CALL DGEBR2D( ICTXT, 'All', ' ', 1, 1, VALUE, 1, IAROW,
$ IACOL )
END IF
*
PDLANSY = VALUE
*
RETURN
*
* End of PDLANSY
*
END
|
