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
|
c----------------------------------------------------------------------c
c S P A R S K I T c
c----------------------------------------------------------------------c
c REORDERING ROUTINES -- STRONGLY CONNECTED COMPONENTS c
c----------------------------------------------------------------------c
c Contributed by:
C Laura C. Dutto - email: dutto@cerca.umontreal.ca
c July 1992 - Update: March 1994
C-----------------------------------------------------------------------
c CONTENTS:
c --------
c blccnx : Driver routine to reduce the structure of a matrix
c to its strongly connected components.
c cconex : Main routine to compute the strongly connected components
c of a (block diagonal) matrix.
c anccnx : We put in ICCNEX the vertices marked in the component MCCNEX.
c newcnx : We put in ICCNEX the vertices marked in the component
c MCCNEX. We modify also the vector KPW.
c blccn1 : Parallel computation of the connected components of a
c matrix. The parallel loop is performed only if the matrix
c has a block diagonal structure.
c ccnicopy:We copy an integer vector into anothoer.
c compos : We calculate the composition between two permutation
c vectors.
c invlpw : We calculate the inverse of a permutation vector.
c numini : We initialize a vector to the identity.
c tbzero : We initialize to ZERO an integer vector.
c iplusa : Given two integers IALPHA and IBETA, for an integer vector
c IA we calculate IA(i) = ialpha + ibeta * ia(i)
C
c----------------------------------------------------------------------c
subroutine BLCCNX(n, nbloc, nblcmx, nsbloc, job, lpw, amat, ja,
* ia, iout, ier, izs, nw)
C-----------------------------------------------------------------------
c
c This routine determines if the matrix given by the structure
c IA et JA is irreductible. If not, it orders the unknowns such
c that all the consecutive unknowns in KPW between NSBLOC(i-1)+1
c and NSBLOC(i) belong to the ith component of the matrix.
c The numerical values of the matrix are in AMAT. They are modified
c only if JOB = 1 and if we have more than one connected component.
c
c On entry:
c --------
c n = row and column dimension of the matrix
c nblcmx = maximum number of connected components allowed. The size
c of NSBLOC is nblcmx + 1 (in fact, it starts at 0).
c job = integer indicating the work to be done:
c job = 1 if the permutation LPW is modified, we
c permute not only the structure of the matrix
c but also its numerical values.
c job.ne.1 if the permutation LPW is modified, we permute
c the structure of the matrix ignoring real values.
c iout = impression parameter. If 0 < iout < 100, we print
c comments and error messages on unit IOUT.
c nw = length of the work vector IZS.
c
c Input / output:
c --------------
c nbloc = number of connected components of the matrix. If the
c matrix is not irreductible, nbloc > 1. We allow
c nbloc > 1 on entry; in this case we calculate the
c number of connected components in each previous one.
c nsbloc = integer array of length NBLOC + 1 containing the pointers
c to the first node of each component on the old (input)
c and on the new (output) ordering.
c lpw = integer array of length N corresponding to the
c permutation of the unknowns. We allow LPW to be a vector
c different from the identity on input.
c amat = real*8 values of the matrix given by the structure IA, JA.
c ja = integer array of length NNZERO (= IA(N+1)-IA(1)) corresponding
c to the column indices of nonzero elements of the matrix, stored
c rowwise. It is modified only if the matrix has more
c than one connected component.
c ia = integer array of length N+1 corresponding to the
c pointer to the beginning of each row in JA (compressed
c sparse row storage). It is modified only if
c the matrix has more than one connected component.
c
c On return:
c ----------
c ier = integer. Error message. Normal return ier = 0.
c
c Work space:
c ----------
c izs = integer vector of length NW
c
C-----------------------------------------------------------------------
C Laura C. Dutto - email: dutto@cerca.umontreal.ca
c July 1992 - Update: March 1994
C-----------------------------------------------------------------------
integer izs(nw), lpw(n), nsbloc(0:nblcmx), ia(n+1), ja(*)
real*8 amat(*), iziama(1)
logical impr
character*6 chsubr
C-----------------------------------------------------------------------
ier = 0
impr = iout.gt.0.and.iout.le.99
ntb = ia(n+1) - 1
mxccex = max(nblcmx,20)
c.....The matrix AMAT is a real*8 vector
ireal = 2
c
c.....MXPTBL: maximal number of vertices by block
mxptbl = 0
do ibloc = 1, nbloc
mxptbl = max( mxptbl, nsbloc(ibloc) - nsbloc(ibloc-1))
enddo
c
long1 = nbloc * mxptbl
long2 = nbloc * (mxccex+1)
c.....Dynamic allocation of memory
iend = 1
iiend = iend
ilpw = iiend
ikpw = ilpw + n
ilccnx = ikpw + long1
imark = ilccnx + long2
iend = imark + n
if(iend .gt. nw) go to 220
c
nbloc0 = nbloc
chsubr = 'BLCCN1'
c.....We determine if the matrix has more than NBLOC0 connected components.
call BLCCN1(n, nbloc, nblcmx, nsbloc, izs(ilpw), izs(ikpw), ia,
* ja, izs(imark), mxccex, izs(ilccnx), mxptbl, iout,
* ier)
if(ier.ne.0) go to 210
c
if(nbloc .gt. nbloc0) then
c..........The matrix has more than NBLOC0 conneted components. So, we
c..........modify the vectors IA and JA to take account of the new permutation.
nfree = iend - ikpw
call tbzero(izs(ikpw), nfree)
iiat = ikpw
ijat = iiat + n + 1
iamat = ijat + ntb
iend = iamat
if(job .eq. 1) iend = iamat + ireal * ntb
if(iend .gt. nw) go to 220
c
c..........We copy IA and JA on IAT and JAT respectively
call ccnicopy(n+1, ia, izs(iiat))
call ccnicopy(ntb, ja, izs(ijat))
if(job .eq. 1) call dcopy(ntb, amat, 1, izs(iamat), 1)
call dperm(n, izs(iamat), izs(ijat), izs(iiat), amat,
* ja, ia, izs(ilpw), izs(ilpw), job)
ipos = 1
c..........We sort columns inside JA.
iziama(1) = izs(iamat)
call csrcsc(n, job, ipos, amat, ja, ia, iziama,
* izs(ijat), izs(iiat))
call csrcsc(n, job, ipos, iziama, izs(ijat), izs(iiat),
* amat, ja, ia)
izs(iamat) = iziama(1)
endif
c.....We modify the ordering of unknowns in LPW
call compos(n, lpw, izs(ilpw))
c
120 nfree = iend - iiend
call tbzero(izs(iiend), nfree)
iend = iiend
return
c
210 IF(IMPR) WRITE(IOUT,310) chsubr,ier
go to 120
220 IF(IMPR) WRITE(IOUT,320) nw, iend
if(ier.eq.0) ier = -1
go to 120
c
310 FORMAT(' ***BLCCNX*** ERROR IN ',a6,'. IER = ',i8)
320 FORMAT(' ***BLCCNX*** THERE IS NOT ENOUGH MEMORY IN THE WORK',
1 ' VECTOR.'/13X,' ALLOWED MEMORY = ',I10,' - NEEDED',
2 ' MEMORY = ',I10)
end
c **********************************************************************
subroutine CCONEX(n, icol0, mxccnx, lccnex, kpw, ia, ja, mark,
* iout, ier)
C-----------------------------------------------------------------------
c
c This routine determines if the matrix given by the structure
c IA and JA is irreductible. If not, it orders the unknowns such
c that all the consecutive unknowns in KPW between LCCNEX(i-1)+1
c and LCCNEX(i) belong to the ith component of the matrix.
c The structure of the matrix could be nonsymmetric.
c The diagonal vertices (if any) will belong to the last connected
c component (convention).
c
c On entry:
c --------
c n = row and column dimension of the matrix
c icol0 = the columns of the matrix are between ICOL0+1 and ICOL0+N
c iout = impression parameter. If 0 < IOUT < 100, we print
c comments and error messages on unit IOUT.
c ia = integer array of length N+1 corresponding to the
c pointer to the beginning of each row in JA (compressed
c sparse row storage).
c ja = integer array of length NNZERO (= IA(N+1)-IA(1))
c corresponding to the column indices of nonzero elements
c of the matrix, stored rowwise.
c
c Input/Output:
c ------------
c mxccnx = maximum number of connected components allowed on input,
c and number of connected components of the matrix, on output.
c
c On return:
c ----------
c lccnex = integer array of length MXCCNX + 1 containing the pointers
c to the first node of each component, in the vector KPW.
c kpw = integer array of length N corresponding to the
c inverse of permutation vector.
c ier = integer. Error message. Normal return ier = 0.
c
c Work space:
c ----------
c mark = integer vector of length N
c
C-----------------------------------------------------------------------
C Laura C. Dutto - email: dutto@cerca.umontreal.ca
c July 1992 - Update: March 1994
C-----------------------------------------------------------------------
dimension ia(n+1), lccnex(0:mxccnx), kpw(n), ja(*), mark(n)
logical impr
C-----------------------------------------------------------------------
ier = 0
ipos = ia(1) - 1
impr = iout.gt.0.and.iout.le.99
c
nccnex = 0
c.....We initialize MARK to zero. At the end of the algorithm, it would
c.....indicate the number of connected component associated with the vertex.
c.....The number (-1) indicates that the row associated with this vertex
c.....is a diagonal row. This value could be modified because we accept
c.....a non symmetric matrix. All the diagonal vertices will be put in
c.....the same connected component.
call tbzero(mark, n)
c
5 do i = 1,n
if(mark(i) .eq. 0) then
ideb = i
go to 15
endif
enddo
go to 35
c
15 if( ia(ideb+1) - ia(ideb) .eq. 1) then
c..........The row is a diagonal row.
mark(ideb) = -1
go to 5
endif
iccnex = nccnex + 1
if(iccnex .gt. mxccnx) go to 220
index = 0
newind = 0
jref = 0
mark(ideb) = iccnex
index = index + 1
kpw(index) = ideb
c
20 jref = jref + 1
ideb = kpw(jref)
do 30 ir = ia(ideb)-ipos, ia(ideb+1)-ipos-1
j = ja(ir) - icol0
mccnex = mark(j)
if(mccnex .le. 0) then
index = index + 1
kpw(index) = j
mark(j) = iccnex
else if( mccnex .eq. iccnex) then
go to 30
else if( mccnex .gt. iccnex) then
c.............We realize that the connected component MCCNX is,
c.............in fact, included in this one. We modify MARK and KPW.
call NEWCNX(n, mccnex, iccnex, index, kpw, mark)
if(mccnex .eq. nccnex) nccnex = nccnex - 1
else
c.............We realize that the previously marked vertices belong,
c.............in fact, to the connected component ICCNX. We modify MARK.
call ANCCNX(n, iccnex, mccnex, mark, nwindx)
iccnex = mccnex
newind = newind + nwindx
endif
30 continue
if(jref .lt. index) go to 20
c
c.....We have finished with this connected component.
index = index + newind
if(iccnex .eq. nccnex+1) nccnex = nccnex + 1
go to 5
c.......................................................................
c
c We have partitioned the graph in its connected components!
c
c.......................................................................
35 continue
c
c.....All the vertices have been already marked. Before modifying KPW
c.....(if necessary), we put the diagonal vertex (if any) in the last
c.....connected component.
call tbzero(lccnex(1), nccnex)
c
idiag = 0
do i = 1, n
iccnex = mark(i)
if(iccnex .eq. -1) then
idiag = idiag + 1
if(idiag .eq. 1) then
nccnex = nccnex + 1
if(nccnex .gt. mxccnx) go to 220
if(impr) write(iout,340)
endif
mark(i) = nccnex
else
lccnex(iccnex) = lccnex(iccnex) + 1
endif
enddo
if(idiag .ge. 1) lccnex(nccnex) = idiag
c
if(nccnex .eq. 1) then
lccnex(nccnex) = n
go to 40
endif
c
iccnex = 1
8 if(iccnex .gt. nccnex) go to 12
if(lccnex(iccnex) .le. 0) then
do i = 1, n
if(mark(i) .ge. iccnex) mark(i) = mark(i) - 1
enddo
nccnex = nccnex - 1
do mccnex = iccnex, nccnex
lccnex(mccnex) = lccnex(mccnex + 1)
enddo
else
iccnex = iccnex + 1
endif
go to 8
c
12 index = 0
do iccnex = 1, nccnex
noeicc = lccnex(iccnex)
lccnex(iccnex) = index
index = index + noeicc
enddo
if(index .ne. n) go to 210
c
c.....We define correctly KPW
do i = 1,n
iccnex = mark(i)
index = lccnex(iccnex) + 1
kpw(index) = i
lccnex(iccnex) = index
enddo
c
40 mxccnx = nccnex
lccnex(0) = nccnex
if(nccnex .eq. 1) call numini(n, kpw)
return
c
210 if(impr) write(iout,310) index,n
go to 235
220 if(impr) write(iout,320) nccnex, mxccnx
go to 235
235 ier = -1
return
c
310 format(' ***CCONEX*** ERROR TRYING TO DETERMINE THE NUMBER',
* ' OF CONNECTED COMPONENTS.'/13X,' NUMBER OF MARKED',
* ' VERTICES =',i7,3x,'TOTAL NUMBER OF VERTICES =',I7)
320 format(' ***CCONEX*** THE ALLOWED NUMBER OF CONNECTED COMPONENTS',
* ' IS NOT ENOUGH.'/13X,' NECESSARY NUMBER = ',I4,
* 5x,' ALLOWED NUMBER = ',I4)
323 format(' ***CCONEX*** ERROR IN ',A6,'. IER = ',I8)
340 format(/' ***CCONEX*** THE LAST CONNECTED COMPONENT WILL',
* ' HAVE THE DIAGONAL VERTICES.')
end
c **********************************************************************
subroutine ANCCNX(n, mccnex, iccnex, mark, ncount)
C-----------------------------------------------------------------------
c
c We put in ICCNEX the vertices marked in the component MCCNEX.
C
C-----------------------------------------------------------------------
c include "NSIMPLIC"
dimension mark(n)
C-----------------------------------------------------------------------
C Laura C. Dutto - email: dutto@cerca.umontreal.ca - December 1993
C-----------------------------------------------------------------------
ncount = 0
do i = 1, n
if( mark(i) .eq. mccnex) then
mark(i) = iccnex
ncount = ncount + 1
endif
enddo
c
return
end
c **********************************************************************
subroutine NEWCNX(n, mccnex, iccnex, index, kpw, mark)
C-----------------------------------------------------------------------
c
c We put in ICCNEX the vertices marked in the component MCCNEX. We
c modify also the vector KPW.
C
C-----------------------------------------------------------------------
c include "NSIMPLIC"
dimension kpw(*), mark(n)
C-----------------------------------------------------------------------
C Laura C. Dutto - email: dutto@cerca.umontreal.ca - December 1993
C-----------------------------------------------------------------------
do i = 1, n
if( mark(i) .eq. mccnex) then
mark(i) = iccnex
index = index + 1
kpw(index) = i
endif
enddo
c
return
end
c **********************************************************************
subroutine BLCCN1(n, nbloc, nblcmx, nsbloc, lpw, kpw, ia, ja,
* mark, mxccex, lccnex, mxptbl, iout, ier)
C-----------------------------------------------------------------------
c
c This routine determines if the matrix given by the structure
c IA et JA is irreductible. If not, it orders the unknowns such
c that all the consecutive unknowns in KPW between NSBLOC(i-1)+1
c and NSBLOC(i) belong to the ith component of the matrix.
c
c On entry:
c --------
c n = row and column dimension of the matrix
c nblcmx = The size of NSBLOC is nblcmx + 1 (in fact, it starts at 0).
c ia = integer array of length N+1 corresponding to the
c pointer to the beginning of each row in JA (compressed
c sparse row storage).
c ja = integer array of length NNZERO (= IA(N+1)-IA(1)) corresponding
c to the column indices of nonzero elements of the matrix,
c stored rowwise.
c mxccex = maximum number of connected components allowed by block.
c mxptbl = maximum number of points (or unknowns) in each connected
c component (mxptbl .le. n).
c iout = impression parameter. If 0 < iout < 100, we print
c comments and error messages on unit IOUT.
c
c Input/Output:
c ------------
c nbloc = number of connected components of the matrix. If the
c matrix is not irreductible, nbloc > 1. We allow
c nbloc > 1 on entry; in this case we calculate the
c number of connected components in each previous one.
c nsbloc = integer array of length NBLOC + 1 containing the pointers
c to the first node of each component on the new ordering.
c Normally, on entry you put: NBLOC = 1, NSBLOC(0) = 0,
c NSBLOC(NBLOC) = N.
c
c On return:
c ----------
c lpw = integer array of length N corresponding to the
c permutation vector (the row i goes to lpw(i)).
c ier = integer. Error message. Normal return ier = 0.
c
c Work space:
c ----------
c kpw = integer vector of length MXPTBL*NBLOC necessary for parallel
c computation.
c mark = integer vector of length N
c lccnex = integer vector of length (MXCCEX+1)*NBLOC necessary for parallel
c computation.
c
C-----------------------------------------------------------------------
C Laura C. Dutto - e-mail: dutto@cerca.umontreal.ca
c Juillet 1992. Update: March 1994
C-----------------------------------------------------------------------
dimension lpw(n), kpw(mxptbl*nbloc), ia(n+1), ja(*),
* lccnex((mxccex+1)*nbloc), nsbloc(0:nbloc), mark(n)
logical impr
character chsubr*6
C-----------------------------------------------------------------------
ier = 0
impr = iout.gt.0.and.iout.le.99
isor = 0
c
chsubr = 'CCONEX'
newblc = 0
C$DOACROSS if(nbloc.gt.1), LOCAL(ibloc, ik0, ik1, ins0, ntb0,
C$& nccnex, ilccnx, info, kpibl), REDUCTION(ier, newblc)
do 100 ibloc = 1,nbloc
ik0 = nsbloc(ibloc - 1)
ik1 = nsbloc(ibloc)
ntb0 = ia(ik0+1)
if(ia(ik1+1) - ntb0 .le. 1) go to 100
ntb0 = ntb0 - 1
ins0 = ik1 - ik0
c........We need more memory place for KPW1 because of parallel computation
kpibl = (ibloc-1) * mxptbl
call numini( ins0, kpw(kpibl+1))
nccnex = mxccex
ilccnx = (mxccex+1) * (ibloc-1) + 1
c.......................................................................
c
c Call to the main routine: CCONEX
c
c.......................................................................
call cconex(ins0, ik0, nccnex, lccnex(ilccnx), kpw(kpibl+1),
* ia(ik0+1), ja(ntb0+1), mark(ik0+1), isor, info)
ier = ier + info
if(info .ne. 0 .or. nccnex .lt. 1) go to 100
c
c........We add the new connected components on NEWBLC
newblc = newblc + nccnex
c........We define LPW different from the identity only if there are more
c........than one connected component in this block
if(nccnex .eq. 1) then
call numini(ins0, lpw(ik0+1))
else
call invlpw(ins0, kpw(kpibl+1), lpw(ik0+1))
endif
call iplusa(ins0, ik0, 1, lpw(ik0+1))
100 continue
c
if(ier .ne. 0) go to 218
if(newblc .eq. nbloc) go to 120
if(newblc .gt. nblcmx) go to 230
c
c.....We modify the number of blocks to indicate the number of connected
c.....components in the matrix.
newblc = 0
nsfin = 0
CDIR$ NEXT SCALAR
do ibloc = 1, nbloc
ilccnx = (mxccex+1) * (ibloc-1) + 1
nccnex = lccnex(ilccnx)
if(nccnex .gt. 1 .and. impr) write(iout,420) ibloc,nccnex
lcc0 = 0
CDIR$ NEXT SCALAR
do icc = 1,nccnex
newblc = newblc + 1
nsb = lccnex(ilccnx+icc)
c...........Be careful! In LCCNEX we have the cumulated number of vertices
nsbloc(newblc) = nsfin + nsb
if(nccnex .gt. 1 .and. impr) write(iout,425) icc,nsb-lcc0
lcc0 = nsb
enddo
nsfin = nsfin + nsb
enddo
nbloc = newblc
c
120 return
c
218 if(impr) write(iout,318) chsubr,ier
go to 120
230 if(impr) write(iout,330) newblc,nblcmx
if(ier.eq.0) ier = -1
go to 120
c
318 format(' ***BLCCN1*** ERROR IN ',a6,'. IER = ',i8)
330 format(' ***BLCCN1*** THE MEMORY SPACE ALLOWED FOR NSBLOC IS',
* ' NOT ENOUGH.'/13X,' NUMBER (NECESSARY) OF CONNECTED',
* ' COMPONENTS = ',I5/13X,' MAXIMAL NUMBER OF BLOCKS',14x,
* '= ',i5)
420 FORMAT(' *** The block ',i3,' has ',i3,' strongly connected',
* ' components. The number of vertices by component is:')
425 format(5x,'Component No.',i3,' - Number of vertices = ',i6)
end
C***********************************************************************
SUBROUTINE CCNICOPY(N,IX,IY)
C.......................................................................
C We copy the vector IX on the vector IY
C.......................................................................
DIMENSION IX(n),IY(n)
C.......................................................................
IF(N.LE.0) RETURN
C$DOACROSS if(n .gt. 250), local(i)
DO 10 I = 1,N
IY(I) = IX(I)
10 CONTINUE
C
RETURN
END
c***********************************************************************
SUBROUTINE COMPOS(n, lpw0, lpw1)
C-----------------------------------------------------------------------
c
c We take account of the original order of unknowns. We put the
c final result on LPW0.
c
C-----------------------------------------------------------------------
DIMENSION lpw0(n), lpw1(n)
C-----------------------------------------------------------------------
c Laura C. Dutto - Mars 1994
C-----------------------------------------------------------------------
C$DOACROSS if(n .gt. 250), local(i0)
do i0 = 1, n
lpw0(i0) = lpw1(lpw0(i0))
enddo
c
return
end
C **********************************************************************
SUBROUTINE INVLPW(n, lpw, kpw)
c.......................................................................
c
c KPW is the inverse of LPW
c
c.......................................................................
dimension lpw(n), kpw(n)
c.......................................................................
c Laura C. Dutto - Novembre 1993
c.......................................................................
C$DOACROSS if(n .gt. 200), local(i0, i1)
do i0 = 1, n
i1 = lpw(i0)
kpw(i1) = i0
enddo
c
return
end
C **********************************************************************
subroutine NUMINI(n, lpw)
c.......................................................................
dimension lpw(n)
c.......................................................................
c
c The vector LPW is initialized as the identity.
c
c.......................................................................
c Laura C. Dutto - Novembre 1993
c.......................................................................
C$DOACROSS if(n .gt. 250), local(i)
do i=1,n
lpw(i) = i
enddo
c
return
end
C***********************************************************************
SUBROUTINE TBZERO(M,NMOT)
C.......................................................................
C We initialize to ZERO an integer vector of length NMOT.
C.......................................................................
DIMENSION M(NMOT)
C.......................................................................
IF(NMOT.le.0) return
C$DOACROSS if(nmot.gt.500), LOCAL(i)
DO 1 I=1,NMOT
M(I)=0
1 CONTINUE
RETURN
END
C **********************************************************************
SUBROUTINE IPLUSA (n, nalpha, nbeta, ia)
c.......................................................................
C
c We add NALPHA to each element of NBETA * IA:
c
c ia(i) = nalpha + nbeta * ia(i)
c
c.......................................................................
integer ia(n)
c.......................................................................
c Laura C. Dutto - February 1994
c.......................................................................
if(n .le. 0) return
c
nmax = 500
if(nalpha .eq. 0) then
if(nbeta .eq. 1) return
if(nbeta .eq. -1) then
C$DOACROSS if(n .gt. nmax), local (i)
do i = 1, n
ia(i) = - ia(i)
enddo
else
C$DOACROSS if(n .gt. nmax/2), local (i)
do i = 1, n
ia(i) = nbeta * ia(i)
enddo
endif
return
endif
if(nbeta .eq. 0) then
C$DOACROSS if(n .gt. nmax), local (i)
do i = 1, n
ia(i) = nalpha
enddo
return
endif
if(nbeta .eq. -1) then
C$DOACROSS if(n .gt. nmax/2), local (i)
do i = 1, n
ia(i) = nalpha - ia(i)
enddo
else if(nbeta .eq. 1) then
C$DOACROSS if(n .gt. nmax/2), local (i)
do i = 1, n
ia(i) = nalpha + ia(i)
enddo
else
C$DOACROSS if(n .gt. nmax/3), local (i)
do i = 1, n
ia(i) = nalpha + nbeta * ia(i)
enddo
endif
c
return
end
|
