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
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
|
REAL FUNCTION PCLANTR( NORM, UPLO, DIAG, M, N, A,
$ IA, JA, DESCA, WORK )
*
* -- 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 DIAG, NORM, UPLO
INTEGER IA, JA, M, N
* ..
* .. Array Arguments ..
INTEGER DESCA( * )
REAL WORK( * )
COMPLEX A( * )
* ..
*
* Purpose
* =======
*
* PCLANTR returns the value of the one norm, or the Frobenius norm,
* or the infinity norm, or the element of largest absolute value of a
* trapezoidal or triangular distributed matrix sub( A ) denoting
* A(IA:IA+M-1, JA:JA+N-1).
*
* PCLANTR returns the value
*
* ( max(abs(A(i,j))), NORM = 'M' or 'm' with ia <= i <= ia+m-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 PCLANTR as described
* above.
*
* UPLO (global input) CHARACTER
* Specifies whether the matrix sub( A ) is upper or lower
* trapezoidal.
* = 'U': Upper trapezoidal
* = 'L': Lower trapezoidal
* Note that sub( A ) is triangular instead of trapezoidal
* if M = N.
*
* DIAG (global input) CHARACTER
* Specifies whether or not the distributed matrix sub( A ) has
* unit diagonal.
* = 'N': Non-unit diagonal
* = 'U': Unit diagonal
*
* M (global input) INTEGER
* The number of rows to be operated on i.e the number of rows
* of the distributed submatrix sub( A ). When M = 0, PCLANTR is
* set to zero. 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( A ). When N = 0,
* PCLANTR is set to zero. N >= 0.
*
* A (local input) COMPLEX pointer into the local memory
* to an array of dimension (LLD_A, LOCc(JA+N-1) ) containing
* the local pieces of sub( A ).
*
* 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) REAL array dimension (LWORK)
* LWORK >= 0 if NORM = 'M' or 'm' (not referenced),
* Nq0 if NORM = '1', 'O' or 'o',
* Mp0 if NORM = 'I' or 'i',
* 0 if NORM = 'F', 'f', 'E' or 'e' (not referenced),
* where
*
* 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 ),
* Mp0 = NUMROC( M+IROFFA, MB_A, MYROW, IAROW, NPROW ),
* Nq0 = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ),
*
* 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 )
REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL UDIAG
INTEGER IACOL, IAROW, ICTXT, II, IIA, ICOFF, IOFFA,
$ IROFF, J, JB, JJ, JJA, JN, KK, LDA, LL, MP,
$ MYCOL, MYROW, NP, NPCOL, NPROW, NQ
REAL SCALE, SUM, VALUE
* ..
* .. Local Arrays ..
REAL RWORK( 2 )
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, CLASSQ, INFOG2L, PSTREECOMB,
$ SCOMBSSQ, SGEBR2D, SGEBS2D,
$ SGAMX2D, SGSUM2D
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ICEIL, ISAMAX, NUMROC
EXTERNAL LSAME, ICEIL, ISAMAX, NUMROC
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN, MOD, REAL, SQRT
* ..
* .. Executable Statements ..
*
* Get grid parameters
*
ICTXT = DESCA( CTXT_ )
CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
*
UDIAG = LSAME( DIAG, 'U' )
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_ ) )
MP = NUMROC( M+IROFF, DESCA( MB_ ), MYROW, IAROW, NPROW )
NQ = NUMROC( N+ICOFF, DESCA( NB_ ), MYCOL, IACOL, NPCOL )
IF( MYROW.EQ.IAROW )
$ MP = MP - IROFF
IF( MYCOL.EQ.IACOL )
$ NQ = NQ - ICOFF
LDA = DESCA( LLD_ )
IOFFA = ( JJA - 1 ) * LDA
*
IF( MIN( M, N ).EQ.0 ) THEN
*
VALUE = ZERO
*
ELSE IF( LSAME( NORM, 'M' ) ) THEN
*
* Find max(abs(A(i,j))).
*
IF( UDIAG ) THEN
VALUE = ONE
ELSE
VALUE = ZERO
END IF
*
IF( LSAME( UPLO, 'U' ) ) THEN
*
* Upper triangular matrix
*
II = IIA
JJ = JJA
JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 )
JB = JN-JA+1
*
IF( MYCOL.EQ.IACOL ) THEN
IF( MYROW.EQ.IAROW ) THEN
IF( UDIAG ) THEN
DO 20 LL = JJ, JJ + JB -1
DO 10 KK = IIA, MIN(II+LL-JJ+1,IIA+MP-1)
VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) )
10 CONTINUE
IOFFA = IOFFA + LDA
20 CONTINUE
ELSE
DO 40 LL = JJ, JJ + JB -1
DO 30 KK = IIA, MIN( II+LL-JJ, IIA+MP-1 )
VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) )
30 CONTINUE
IOFFA = IOFFA + LDA
40 CONTINUE
END IF
ELSE
DO 60 LL = JJ, JJ + JB -1
DO 50 KK = IIA, MIN( II-1, IIA+MP-1 )
VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) )
50 CONTINUE
IOFFA = IOFFA + LDA
60 CONTINUE
END IF
JJ = JJ + JB
END IF
*
IF( MYROW.EQ.IAROW )
$ II = II + JB
IAROW = MOD( IAROW+1, NPROW )
IACOL = MOD( IACOL+1, NPCOL )
*
* Loop over remaining block of columns
*
DO 130 J = JN+1, JA+N-1, DESCA( NB_ )
JB = MIN( JA+N-J, DESCA( NB_ ) )
*
IF( MYCOL.EQ.IACOL ) THEN
IF( MYROW.EQ.IAROW ) THEN
IF( UDIAG ) THEN
DO 80 LL = JJ, JJ + JB -1
DO 70 KK = IIA, MIN( II+LL-JJ+1, IIA+MP-1 )
VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) )
70 CONTINUE
IOFFA = IOFFA + LDA
80 CONTINUE
ELSE
DO 100 LL = JJ, JJ + JB -1
DO 90 KK = IIA, MIN( II+LL-JJ, IIA+MP-1 )
VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) )
90 CONTINUE
IOFFA = IOFFA + LDA
100 CONTINUE
END IF
ELSE
DO 120 LL = JJ, JJ + JB -1
DO 110 KK = IIA, MIN( II-1, IIA+MP-1 )
VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) )
110 CONTINUE
IOFFA = IOFFA + LDA
120 CONTINUE
END IF
JJ = JJ + JB
END IF
*
IF( MYROW.EQ.IAROW )
$ II = II + JB
IAROW = MOD( IAROW+1, NPROW )
IACOL = MOD( IACOL+1, NPCOL )
*
130 CONTINUE
*
ELSE
*
* Lower triangular matrix
*
II = IIA
JJ = JJA
JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 )
JB = JN-JA+1
*
IF( MYCOL.EQ.IACOL ) THEN
IF( MYROW.EQ.IAROW ) THEN
IF( UDIAG ) THEN
DO 150 LL = JJ, JJ + JB -1
DO 140 KK = II+LL-JJ+1, IIA+MP-1
VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) )
140 CONTINUE
IOFFA = IOFFA + LDA
150 CONTINUE
ELSE
DO 170 LL = JJ, JJ + JB -1
DO 160 KK = II+LL-JJ, IIA+MP-1
VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) )
160 CONTINUE
IOFFA = IOFFA + LDA
170 CONTINUE
END IF
ELSE
DO 190 LL = JJ, JJ + JB -1
DO 180 KK = II, IIA+MP-1
VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) )
180 CONTINUE
IOFFA = IOFFA + LDA
190 CONTINUE
END IF
JJ = JJ + JB
END IF
*
IF( MYROW.EQ.IAROW )
$ II = II + JB
IAROW = MOD( IAROW+1, NPROW )
IACOL = MOD( IACOL+1, NPCOL )
*
* Loop over remaining block of columns
*
DO 260 J = JN+1, JA+N-1, DESCA( NB_ )
JB = MIN( JA+N-J, DESCA( NB_ ) )
*
IF( MYCOL.EQ.IACOL ) THEN
IF( MYROW.EQ.IAROW ) THEN
IF( UDIAG ) THEN
DO 210 LL = JJ, JJ + JB -1
DO 200 KK = II+LL-JJ+1, IIA+MP-1
VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) )
200 CONTINUE
IOFFA = IOFFA + LDA
210 CONTINUE
ELSE
DO 230 LL = JJ, JJ + JB -1
DO 220 KK = II+LL-JJ, IIA+MP-1
VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) )
220 CONTINUE
IOFFA = IOFFA + LDA
230 CONTINUE
END IF
ELSE
DO 250 LL = JJ, JJ + JB -1
DO 240 KK = II, IIA+MP-1
VALUE = MAX( VALUE, ABS( A( IOFFA+KK ) ) )
240 CONTINUE
IOFFA = IOFFA + LDA
250 CONTINUE
END IF
JJ = JJ + JB
END IF
*
IF( MYROW.EQ.IAROW )
$ II = II + JB
IAROW = MOD( IAROW+1, NPROW )
IACOL = MOD( IACOL+1, NPCOL )
*
260 CONTINUE
*
END IF
*
* Gather the intermediate results to process (0,0).
*
CALL SGAMX2D( ICTXT, 'All', ' ', 1, 1, VALUE, 1, KK, LL, -1,
$ 0, 0 )
*
ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' ) THEN
*
VALUE = ZERO
*
IF( LSAME( UPLO, 'U' ) ) THEN
*
* Upper triangular matrix
*
II = IIA
JJ = JJA
JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 )
JB = JN-JA+1
*
IF( MYCOL.EQ.IACOL ) THEN
IF( MYROW.EQ.IAROW ) THEN
IF( UDIAG ) THEN
DO 280 LL = JJ, JJ + JB -1
SUM = ONE
DO 270 KK = IIA, MIN( II+LL-JJ, IIA+MP-1 )
SUM = SUM + ABS( A( IOFFA+KK ) )
270 CONTINUE
IOFFA = IOFFA + LDA
WORK( LL-JJA+1 ) = SUM
280 CONTINUE
ELSE
DO 300 LL = JJ, JJ + JB -1
SUM = ZERO
DO 290 KK = IIA, MIN( II+LL-JJ+1, IIA+MP-1 )
SUM = SUM + ABS( A( IOFFA+KK ) )
290 CONTINUE
IOFFA = IOFFA + LDA
WORK( LL-JJA+1 ) = SUM
300 CONTINUE
END IF
ELSE
DO 320 LL = JJ, JJ + JB -1
SUM = ZERO
DO 310 KK = IIA, MIN( II-1, IIA+MP-1 )
SUM = SUM + ABS( A( IOFFA+KK ) )
310 CONTINUE
IOFFA = IOFFA + LDA
WORK( LL-JJA+1 ) = SUM
320 CONTINUE
END IF
JJ = JJ + JB
END IF
*
IF( MYROW.EQ.IAROW )
$ II = II + JB
IAROW = MOD( IAROW+1, NPROW )
IACOL = MOD( IACOL+1, NPCOL )
*
* Loop over remaining block of columns
*
DO 390 J = JN+1, JA+N-1, DESCA( NB_ )
JB = MIN( JA+N-J, DESCA( NB_ ) )
*
IF( MYCOL.EQ.IACOL ) THEN
IF( MYROW.EQ.IAROW ) THEN
IF( UDIAG ) THEN
DO 340 LL = JJ, JJ + JB -1
SUM = ONE
DO 330 KK = IIA, MIN( II+LL-JJ+1, IIA+MP-1 )
SUM = SUM + ABS( A( IOFFA+KK ) )
330 CONTINUE
IOFFA = IOFFA + LDA
WORK( LL-JJA+1 ) = SUM
340 CONTINUE
ELSE
DO 360 LL = JJ, JJ + JB -1
SUM = ZERO
DO 350 KK = IIA, MIN( II+LL-JJ, IIA+MP-1 )
SUM = SUM + ABS( A( IOFFA+KK ) )
350 CONTINUE
IOFFA = IOFFA + LDA
WORK( LL-JJA+1 ) = SUM
360 CONTINUE
END IF
ELSE
DO 380 LL = JJ, JJ + JB -1
SUM = ZERO
DO 370 KK = IIA, MIN( II-1, IIA+MP-1 )
SUM = SUM + ABS( A( IOFFA+KK ) )
370 CONTINUE
IOFFA = IOFFA + LDA
WORK( LL-JJA+1 ) = SUM
380 CONTINUE
END IF
JJ = JJ + JB
END IF
*
IF( MYROW.EQ.IAROW )
$ II = II + JB
IAROW = MOD( IAROW+1, NPROW )
IACOL = MOD( IACOL+1, NPCOL )
*
390 CONTINUE
*
ELSE
*
* Lower triangular matrix
*
II = IIA
JJ = JJA
JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 )
JB = JN-JA+1
*
IF( MYCOL.EQ.IACOL ) THEN
IF( MYROW.EQ.IAROW ) THEN
IF( UDIAG ) THEN
DO 410 LL = JJ, JJ + JB -1
SUM = ONE
DO 400 KK = II+LL-JJ+1, IIA+MP-1
SUM = SUM + ABS( A( IOFFA+KK ) )
400 CONTINUE
IOFFA = IOFFA + LDA
WORK( LL-JJA+1 ) = SUM
410 CONTINUE
ELSE
DO 430 LL = JJ, JJ + JB -1
SUM = ZERO
DO 420 KK = II+LL-JJ, IIA+MP-1
SUM = SUM + ABS( A( IOFFA+KK ) )
420 CONTINUE
IOFFA = IOFFA + LDA
WORK( LL-JJA+1 ) = SUM
430 CONTINUE
END IF
ELSE
DO 450 LL = JJ, JJ + JB -1
SUM = ZERO
DO 440 KK = II, IIA+MP-1
SUM = SUM + ABS( A( IOFFA+KK ) )
440 CONTINUE
IOFFA = IOFFA + LDA
WORK( LL-JJA+1 ) = SUM
450 CONTINUE
END IF
JJ = JJ + JB
END IF
*
IF( MYROW.EQ.IAROW )
$ II = II + JB
IAROW = MOD( IAROW+1, NPROW )
IACOL = MOD( IACOL+1, NPCOL )
*
* Loop over remaining block of columns
*
DO 520 J = JN+1, JA+N-1, DESCA( NB_ )
JB = MIN( JA+N-J, DESCA( NB_ ) )
*
IF( MYCOL.EQ.IACOL ) THEN
IF( MYROW.EQ.IAROW ) THEN
IF( UDIAG ) THEN
DO 470 LL = JJ, JJ + JB -1
SUM = ONE
DO 460 KK = II+LL-JJ+1, IIA+MP-1
SUM = SUM + ABS( A( IOFFA+KK ) )
460 CONTINUE
IOFFA = IOFFA + LDA
WORK( LL-JJA+1 ) = SUM
470 CONTINUE
ELSE
DO 490 LL = JJ, JJ + JB -1
SUM = ZERO
DO 480 KK = II+LL-JJ, IIA+MP-1
SUM = SUM + ABS( A( IOFFA+KK ) )
480 CONTINUE
IOFFA = IOFFA + LDA
WORK( LL-JJA+1 ) = SUM
490 CONTINUE
END IF
ELSE
DO 510 LL = JJ, JJ + JB -1
SUM = ZERO
DO 500 KK = II, IIA+MP-1
SUM = SUM + ABS( A( IOFFA+KK ) )
500 CONTINUE
IOFFA = IOFFA + LDA
WORK( LL-JJA+1 ) = SUM
510 CONTINUE
END IF
JJ = JJ + JB
END IF
*
IF( MYROW.EQ.IAROW )
$ II = II + JB
IAROW = MOD( IAROW+1, NPROW )
IACOL = MOD( IACOL+1, NPCOL )
*
520 CONTINUE
*
END IF
*
* Find sum of global matrix columns and store on row 0 of
* process grid
*
CALL SGSUM2D( ICTXT, 'Columnwise', ' ', 1, NQ, WORK, 1,
$ 0, MYCOL )
*
* Find maximum sum of columns for 1-norm
*
IF( MYROW.EQ.0 ) THEN
IF( NQ.GT.0 ) THEN
VALUE = WORK( ISAMAX( NQ, WORK, 1 ) )
ELSE
VALUE = ZERO
END IF
CALL SGAMX2D( ICTXT, 'Rowwise', ' ', 1, 1, VALUE, 1, KK, LL,
$ -1, 0, 0 )
END IF
*
ELSE IF( LSAME( NORM, 'I' ) ) THEN
*
IF( LSAME( UPLO, 'U' ) ) THEN
IF( UDIAG ) THEN
DO 530 KK = IIA, IIA+MP-1
WORK( KK ) = ONE
530 CONTINUE
ELSE
DO 540 KK = IIA, IIA+MP-1
WORK( KK ) = ZERO
540 CONTINUE
END IF
ELSE
IF( UDIAG ) THEN
NP = NUMROC( N+IROFF, DESCA( MB_ ), MYROW, IAROW, NPROW )
IF( MYROW.EQ.IAROW )
$ NP = NP - IROFF
DO 550 KK = IIA, IIA+NP-1
WORK( KK ) = ONE
550 CONTINUE
DO 560 KK = IIA+NP, IIA+MP-1
WORK( KK ) = ZERO
560 CONTINUE
ELSE
DO 570 KK = IIA, IIA+MP-1
WORK( KK ) = ZERO
570 CONTINUE
END IF
END IF
*
IF( LSAME( UPLO, 'U' ) ) THEN
*
* Upper triangular matrix
*
II = IIA
JJ = JJA
JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 )
JB = JN-JA+1
*
IF( MYCOL.EQ.IACOL ) THEN
IF( MYROW.EQ.IAROW ) THEN
IF( UDIAG ) THEN
DO 590 LL = JJ, JJ + JB -1
DO 580 KK = IIA, MIN( II+LL-JJ, IIA+MP-1 )
WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) +
$ ABS( A( IOFFA+KK ) )
580 CONTINUE
IOFFA = IOFFA + LDA
590 CONTINUE
ELSE
DO 610 LL = JJ, JJ + JB -1
DO 600 KK = IIA, MIN(II+LL-JJ+1,IIA+MP-1)
WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) +
$ ABS( A( IOFFA+KK ) )
600 CONTINUE
IOFFA = IOFFA + LDA
610 CONTINUE
END IF
ELSE
DO 630 LL = JJ, JJ + JB -1
DO 620 KK = IIA, MIN( II-1, IIA+MP-1 )
WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) +
$ ABS( A( IOFFA+KK ) )
620 CONTINUE
IOFFA = IOFFA + LDA
630 CONTINUE
END IF
JJ = JJ + JB
END IF
*
IF( MYROW.EQ.IAROW )
$ II = II + JB
IAROW = MOD( IAROW+1, NPROW )
IACOL = MOD( IACOL+1, NPCOL )
*
* Loop over remaining block of columns
*
DO 700 J = JN+1, JA+N-1, DESCA( NB_ )
JB = MIN( JA+N-J, DESCA( NB_ ) )
*
IF( MYCOL.EQ.IACOL ) THEN
IF( MYROW.EQ.IAROW ) THEN
IF( UDIAG ) THEN
DO 650 LL = JJ, JJ + JB -1
DO 640 KK = IIA, MIN( II+LL-JJ+1, IIA+MP-1 )
WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) +
$ ABS( A( IOFFA+KK ) )
640 CONTINUE
IOFFA = IOFFA + LDA
650 CONTINUE
ELSE
DO 670 LL = JJ, JJ + JB -1
DO 660 KK = IIA, MIN( II+LL-JJ, IIA+MP-1 )
WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) +
$ ABS( A( IOFFA+KK ) )
660 CONTINUE
IOFFA = IOFFA + LDA
670 CONTINUE
END IF
ELSE
DO 690 LL = JJ, JJ + JB -1
DO 680 KK = IIA, MIN( II-1, IIA+MP-1 )
WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) +
$ ABS( A( IOFFA+KK ) )
680 CONTINUE
IOFFA = IOFFA + LDA
690 CONTINUE
END IF
JJ = JJ + JB
END IF
*
IF( MYROW.EQ.IAROW )
$ II = II + JB
IAROW = MOD( IAROW+1, NPROW )
IACOL = MOD( IACOL+1, NPCOL )
*
700 CONTINUE
*
ELSE
*
* Lower triangular matrix
*
II = IIA
JJ = JJA
JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 )
JB = JN-JA+1
*
IF( MYCOL.EQ.IACOL ) THEN
IF( MYROW.EQ.IAROW ) THEN
IF( UDIAG ) THEN
DO 720 LL = JJ, JJ + JB -1
DO 710 KK = II+LL-JJ+1, IIA+MP-1
WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) +
$ ABS( A( IOFFA+KK ) )
710 CONTINUE
IOFFA = IOFFA + LDA
720 CONTINUE
ELSE
DO 740 LL = JJ, JJ + JB -1
DO 730 KK = II+LL-JJ, IIA+MP-1
WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) +
$ ABS( A( IOFFA+KK ) )
730 CONTINUE
IOFFA = IOFFA + LDA
740 CONTINUE
END IF
ELSE
DO 760 LL = JJ, JJ + JB -1
DO 750 KK = II, IIA+MP-1
WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) +
$ ABS( A( IOFFA+KK ) )
750 CONTINUE
IOFFA = IOFFA + LDA
760 CONTINUE
END IF
JJ = JJ + JB
END IF
*
IF( MYROW.EQ.IAROW )
$ II = II + JB
IAROW = MOD( IAROW+1, NPROW )
IACOL = MOD( IACOL+1, NPCOL )
*
* Loop over remaining block of columns
*
DO 830 J = JN+1, JA+N-1, DESCA( NB_ )
JB = MIN( JA+N-J, DESCA( NB_ ) )
*
IF( MYCOL.EQ.IACOL ) THEN
IF( MYROW.EQ.IAROW ) THEN
IF( UDIAG ) THEN
DO 780 LL = JJ, JJ + JB -1
DO 770 KK = II+LL-JJ+1, IIA+MP-1
WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) +
$ ABS( A( IOFFA+KK ) )
770 CONTINUE
IOFFA = IOFFA + LDA
780 CONTINUE
ELSE
DO 800 LL = JJ, JJ + JB -1
DO 790 KK = II+LL-JJ, IIA+MP-1
WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) +
$ ABS( A( IOFFA+KK ) )
790 CONTINUE
IOFFA = IOFFA + LDA
800 CONTINUE
END IF
ELSE
DO 820 LL = JJ, JJ + JB -1
DO 810 KK = II, IIA+MP-1
WORK( KK-IIA+1 ) = WORK( KK-IIA+1 ) +
$ ABS( A( IOFFA+KK ) )
810 CONTINUE
IOFFA = IOFFA + LDA
820 CONTINUE
END IF
JJ = JJ + JB
END IF
*
IF( MYROW.EQ.IAROW )
$ II = II + JB
IAROW = MOD( IAROW+1, NPROW )
IACOL = MOD( IACOL+1, NPCOL )
*
830 CONTINUE
*
END IF
*
* Find sum of global matrix rows and store on column 0 of
* process grid
*
CALL SGSUM2D( ICTXT, 'Rowwise', ' ', MP, 1, WORK, MAX( 1, MP ),
$ MYROW, 0 )
*
* Find maximum sum of rows for Infinity-norm
*
IF( MYCOL.EQ.0 ) THEN
IF( MP.GT.0 ) THEN
VALUE = WORK( ISAMAX( MP, WORK, 1 ) )
ELSE
VALUE = ZERO
END IF
CALL SGAMX2D( ICTXT, 'Columnwise', ' ', 1, 1, VALUE, 1, KK,
$ LL, -1, 0, 0 )
END IF
*
ELSE IF( LSAME( NORM, 'F' ) .OR. LSAME( NORM, 'E' ) ) THEN
*
IF( UDIAG ) THEN
SCALE = ONE
SUM = REAL( MIN( M, N ) ) / REAL( NPROW*NPCOL )
ELSE
SCALE = ZERO
SUM = ONE
END IF
*
IF( LSAME( UPLO, 'U' ) ) THEN
*
* Upper triangular matrix
*
II = IIA
JJ = JJA
JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 )
JB = JN-JA+1
*
IF( MYCOL.EQ.IACOL ) THEN
IF( MYROW.EQ.IAROW ) THEN
IF( UDIAG ) THEN
DO 840 LL = JJ, JJ + JB -1
CALL CLASSQ( MIN( II+LL-JJ, IIA+MP-1 )-IIA+1,
$ A( IIA+IOFFA ), 1, SCALE, SUM )
IOFFA = IOFFA + LDA
840 CONTINUE
ELSE
DO 850 LL = JJ, JJ + JB -1
CALL CLASSQ( MIN( II+LL-JJ+1, IIA+MP-1 )-IIA+1,
$ A( IIA+IOFFA ), 1, SCALE, SUM )
IOFFA = IOFFA + LDA
850 CONTINUE
END IF
ELSE
DO 860 LL = JJ, JJ + JB -1
CALL CLASSQ( MIN( II-1, IIA+MP-1 )-IIA+1,
$ A( IIA+IOFFA ), 1, SCALE, SUM )
IOFFA = IOFFA + LDA
860 CONTINUE
END IF
JJ = JJ + JB
END IF
*
IF( MYROW.EQ.IAROW )
$ II = II + JB
IAROW = MOD( IAROW+1, NPROW )
IACOL = MOD( IACOL+1, NPCOL )
*
* Loop over remaining block of columns
*
DO 900 J = JN+1, JA+N-1, DESCA( NB_ )
JB = MIN( JA+N-J, DESCA( NB_ ) )
*
IF( MYCOL.EQ.IACOL ) THEN
IF( MYROW.EQ.IAROW ) THEN
IF( UDIAG ) THEN
DO 870 LL = JJ, JJ + JB -1
CALL CLASSQ( MIN( II+LL-JJ+1, IIA+MP-1 )-
$ IIA+1, A( IIA+IOFFA ), 1, SCALE,
$ SUM )
IOFFA = IOFFA + LDA
870 CONTINUE
ELSE
DO 880 LL = JJ, JJ + JB -1
CALL CLASSQ( MIN( II+LL-JJ, IIA+MP-1 )-
$ IIA+1, A( IIA+IOFFA ), 1, SCALE,
$ SUM )
IOFFA = IOFFA + LDA
880 CONTINUE
END IF
ELSE
DO 890 LL = JJ, JJ + JB -1
CALL CLASSQ( MIN( II-1, IIA+MP-1 )-IIA+1,
$ A( IIA+IOFFA ), 1, SCALE, SUM )
IOFFA = IOFFA + LDA
890 CONTINUE
END IF
JJ = JJ + JB
END IF
*
IF( MYROW.EQ.IAROW )
$ II = II + JB
IAROW = MOD( IAROW+1, NPROW )
IACOL = MOD( IACOL+1, NPCOL )
*
900 CONTINUE
*
ELSE
*
* Lower triangular matrix
*
II = IIA
JJ = JJA
JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 )
JB = JN-JA+1
*
IF( MYCOL.EQ.IACOL ) THEN
IF( MYROW.EQ.IAROW ) THEN
IF( UDIAG ) THEN
DO 910 LL = JJ, JJ + JB -1
CALL CLASSQ( IIA+MP-(II+LL-JJ+1),
$ A( II+LL-JJ+IOFFA ), 1, SCALE,
$ SUM )
IOFFA = IOFFA + LDA
910 CONTINUE
ELSE
DO 920 LL = JJ, JJ + JB -1
CALL CLASSQ( IIA+MP-(II+LL-JJ),
$ A( II+LL-JJ+IOFFA ), 1, SCALE,
$ SUM )
IOFFA = IOFFA + LDA
920 CONTINUE
END IF
ELSE
DO 930 LL = JJ, JJ + JB -1
CALL CLASSQ( IIA+MP-II, A( II+IOFFA ), 1, SCALE,
$ SUM )
IOFFA = IOFFA + LDA
930 CONTINUE
END IF
JJ = JJ + JB
END IF
*
IF( MYROW.EQ.IAROW )
$ II = II + JB
IAROW = MOD( IAROW+1, NPROW )
IACOL = MOD( IACOL+1, NPCOL )
*
* Loop over remaining block of columns
*
DO 970 J = JN+1, JA+N-1, DESCA( NB_ )
JB = MIN( JA+N-J, DESCA( NB_ ) )
*
IF( MYCOL.EQ.IACOL ) THEN
IF( MYROW.EQ.IAROW ) THEN
IF( UDIAG ) THEN
DO 940 LL = JJ, JJ + JB -1
CALL CLASSQ( IIA+MP-(II+LL-JJ+1),
$ A( II+LL-JJ+IOFFA ), 1, SCALE,
$ SUM )
IOFFA = IOFFA + LDA
940 CONTINUE
ELSE
DO 950 LL = JJ, JJ + JB -1
CALL CLASSQ( IIA+MP-(II+LL-JJ),
$ A( II+LL-JJ+IOFFA ), 1, SCALE,
$ SUM )
IOFFA = IOFFA + LDA
950 CONTINUE
END IF
ELSE
DO 960 LL = JJ, JJ + JB -1
CALL CLASSQ( IIA+MP-II, A( II+IOFFA ), 1, SCALE,
$ SUM )
IOFFA = IOFFA + LDA
960 CONTINUE
END IF
JJ = JJ + JB
END IF
*
IF( MYROW.EQ.IAROW )
$ II = II + JB
IAROW = MOD( IAROW+1, NPROW )
IACOL = MOD( IACOL+1, NPCOL )
*
970 CONTINUE
*
END IF
*
* Perform the global scaled sum
*
RWORK( 1 ) = SCALE
RWORK( 2 ) = SUM
CALL PSTREECOMB( ICTXT, 'All', 2, RWORK, 0, 0, SCOMBSSQ )
VALUE = RWORK( 1 ) * SQRT( RWORK( 2 ) )
*
END IF
*
* Broadcast the result to every process in the grid.
*
IF( MYROW.EQ.0 .AND. MYCOL.EQ.0 ) THEN
CALL SGEBS2D( ICTXT, 'All', ' ', 1, 1, VALUE, 1 )
ELSE
CALL SGEBR2D( ICTXT, 'All', ' ', 1, 1, VALUE, 1, 0, 0 )
END IF
*
PCLANTR = VALUE
*
RETURN
*
* End of PCLANTR
*
END
|
