-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathmmd.c
1025 lines (933 loc) · 28.9 KB
/
mmd.c
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
/*! \file
Copyright (c) 2003, The Regents of the University of California, through
Lawrence Berkeley National Laboratory (subject to receipt of any required
approvals from U.S. Dept. of Energy)
All rights reserved.
The source code is distributed under BSD license, see the file License.txt
at the top-level directory.
*/
/*! @file
* \brief Implements the minimum degree algorithm
*/
#include "superlu_defs.h"
/* *************************************************************** */
/* *************************************************************** */
/* **** GENMMD ..... MULTIPLE MINIMUM EXTERNAL DEGREE **** */
/* *************************************************************** */
/* *************************************************************** */
/* AUTHOR - JOSEPH W.H. LIU */
/* DEPT OF COMPUTER SCIENCE, YORK UNIVERSITY. */
/* PURPOSE - THIS ROUTINE IMPLEMENTS THE MINIMUM DEGREE */
/* ALGORITHM. IT MAKES USE OF THE IMPLICIT REPRESENTATION */
/* OF ELIMINATION GRAPHS BY QUOTIENT GRAPHS, AND THE */
/* NOTION OF INDISTINGUISHABLE NODES. IT ALSO IMPLEMENTS */
/* THE MODIFICATIONS BY MULTIPLE ELIMINATION AND MINIMUM */
/* EXTERNAL DEGREE. */
/* --------------------------------------------- */
/* CAUTION - THE ADJACENCY VECTOR ADJNCY WILL BE */
/* DESTROYED. */
/* --------------------------------------------- */
/* INPUT PARAMETERS - */
/* NEQNS - NUMBER OF EQUATIONS. */
/* (XADJ,ADJNCY) - THE ADJACENCY STRUCTURE. */
/* DELTA - TOLERANCE VALUE FOR MULTIPLE ELIMINATION. */
/* MAXINT - MAXIMUM MACHINE REPRESENTABLE (SHORT) INTEGER */
/* (ANY SMALLER ESTIMATE WILL DO) FOR MARKING */
/* NODES. */
/* OUTPUT PARAMETERS - */
/* PERM - THE MINIMUM DEGREE ORDERING. */
/* INVP - THE INVERSE OF PERM. */
/* NOFSUB - AN UPPER BOUND ON THE NUMBER OF NONZERO */
/* SUBSCRIPTS FOR THE COMPRESSED STORAGE SCHEME. */
/* WORKING PARAMETERS - */
/* DHEAD - VECTOR FOR HEAD OF DEGREE LISTS. */
/* INVP - USED TEMPORARILY FOR DEGREE FORWARD LINK. */
/* PERM - USED TEMPORARILY FOR DEGREE BACKWARD LINK. */
/* QSIZE - VECTOR FOR SIZE OF SUPERNODES. */
/* LLIST - VECTOR FOR TEMPORARY LINKED LISTS. */
/* MARKER - A TEMPORARY MARKER VECTOR. */
/* PROGRAM SUBROUTINES - */
/* MMDELM, MMDINT, MMDNUM, MMDUPD. */
/* *************************************************************** */
/* Subroutine */ int genmmd_dist_(int_t *neqns, int_t *xadj, int_t *adjncy,
int_t *invp, int_t *perm, int_t *delta, int_t *dhead,
int_t *qsize, int_t *llist, int_t *marker, int_t *maxint,
int_t *nofsub)
{
/* System generated locals */
int_t i__1;
/* Local variables */
static int_t mdeg, ehead, i, mdlmt, mdnode;
extern /* Subroutine */ int mmdelm_dist(int_t *, int_t *, int_t *,
int_t *, int_t *, int_t *, int_t *, int_t *,
int_t *, int_t *, int_t *), mmdupd_dist(int_t *, int_t *,
int_t *, int_t *, int_t *, int_t *, int_t *, int_t
*, int_t *, int_t *, int_t *, int_t *, int_t *,
int_t *), mmdint_dist(int_t *, int_t *, int_t *, int_t *,
int_t *, int_t *, int_t *, int_t *, int_t *),
mmdnum_dist(int_t *, int_t *, int_t *, int_t *);
static int_t nextmd, tag, num;
/* *************************************************************** */
/* *************************************************************** */
/* Parameter adjustments */
--marker;
--llist;
--qsize;
--dhead;
--perm;
--invp;
--adjncy;
--xadj;
/* Function Body */
if (*neqns <= 0) {
return 0;
}
/* ------------------------------------------------ */
/* INITIALIZATION FOR THE MINIMUM DEGREE ALGORITHM. */
/* ------------------------------------------------ */
*nofsub = 0;
mmdint_dist(neqns, &xadj[1], &adjncy[1], &dhead[1], &invp[1], &perm[1],
&qsize[1], &llist[1], &marker[1]);
/* ---------------------------------------------- */
/* NUM COUNTS THE NUMBER OF ORDERED NODES PLUS 1. */
/* ---------------------------------------------- */
num = 1;
/* ----------------------------- */
/* ELIMINATE ALL ISOLATED NODES. */
/* ----------------------------- */
nextmd = dhead[1];
L100:
if (nextmd <= 0) {
goto L200;
}
mdnode = nextmd;
nextmd = invp[mdnode];
marker[mdnode] = *maxint;
invp[mdnode] = -num;
++num;
goto L100;
L200:
/* ---------------------------------------- */
/* SEARCH FOR NODE OF THE MINIMUM DEGREE. */
/* MDEG IS THE CURRENT MINIMUM DEGREE; */
/* TAG IS USED TO FACILITATE MARKING NODES. */
/* ---------------------------------------- */
if (num > *neqns) {
goto L1000;
}
tag = 1;
dhead[1] = 0;
mdeg = 2;
L300:
if (dhead[mdeg] > 0) {
goto L400;
}
++mdeg;
goto L300;
L400:
/* ------------------------------------------------- */
/* USE VALUE OF DELTA TO SET UP MDLMT, WHICH GOVERNS */
/* WHEN A DEGREE UPDATE IS TO BE PERFORMED. */
/* ------------------------------------------------- */
mdlmt = mdeg + *delta;
ehead = 0;
L500:
mdnode = dhead[mdeg];
if (mdnode > 0) {
goto L600;
}
++mdeg;
if (mdeg > mdlmt) {
goto L900;
}
goto L500;
L600:
/* ---------------------------------------- */
/* REMOVE MDNODE FROM THE DEGREE STRUCTURE. */
/* ---------------------------------------- */
nextmd = invp[mdnode];
dhead[mdeg] = nextmd;
if (nextmd > 0) {
perm[nextmd] = -mdeg;
}
invp[mdnode] = -num;
*nofsub = *nofsub + mdeg + qsize[mdnode] - 2;
if (num + qsize[mdnode] > *neqns) {
goto L1000;
}
/* ---------------------------------------------- */
/* ELIMINATE MDNODE AND PERFORM QUOTIENT GRAPH */
/* TRANSFORMATION. RESET TAG VALUE IF NECESSARY. */
/* ---------------------------------------------- */
++tag;
if (tag < *maxint) {
goto L800;
}
tag = 1;
i__1 = *neqns;
for (i = 1; i <= i__1; ++i) {
if (marker[i] < *maxint) {
marker[i] = 0;
}
/* L700: */
}
L800:
mmdelm_dist(&mdnode, &xadj[1], &adjncy[1], &dhead[1], &invp[1], &perm[1],
&qsize[1], &llist[1], &marker[1], maxint, &tag);
num += qsize[mdnode];
llist[mdnode] = ehead;
ehead = mdnode;
if (*delta >= 0) {
goto L500;
}
L900:
/* ------------------------------------------- */
/* UPDATE DEGREES OF THE NODES INVOLVED IN THE */
/* MINIMUM DEGREE NODES ELIMINATION. */
/* ------------------------------------------- */
if (num > *neqns) {
goto L1000;
}
mmdupd_dist(&ehead, neqns, &xadj[1], &adjncy[1], delta, &mdeg, &dhead[1],
&invp[1], &perm[1], &qsize[1], &llist[1], &marker[1], maxint,
&tag);
goto L300;
L1000:
mmdnum_dist(neqns, &perm[1], &invp[1], &qsize[1]);
return 0;
} /* genmmd_dist_ */
/* *************************************************************** */
/* *************************************************************** */
/* *** MMDINT ..... MULT MINIMUM DEGREE INITIALIZATION *** */
/* *************************************************************** */
/* *************************************************************** */
/* AUTHOR - JOSEPH W.H. LIU */
/* DEPT OF COMPUTER SCIENCE, YORK UNIVERSITY. */
/* PURPOSE - THIS ROUTINE PERFORMS INITIALIZATION FOR THE */
/* MULTIPLE ELIMINATION VERSION OF THE MINIMUM DEGREE */
/* ALGORITHM. */
/* INPUT PARAMETERS - */
/* NEQNS - NUMBER OF EQUATIONS. */
/* (XADJ,ADJNCY) - ADJACENCY STRUCTURE. */
/* OUTPUT PARAMETERS - */
/* (DHEAD,DFORW,DBAKW) - DEGREE DOUBLY LINKED STRUCTURE. */
/* QSIZE - SIZE OF SUPERNODE (INITIALIZED TO ONE). */
/* LLIST - LINKED LIST. */
/* MARKER - MARKER VECTOR. */
/* *************************************************************** */
/* Subroutine */ int mmdint_dist(int_t *neqns, int_t *xadj, int_t *adjncy,
int_t *dhead, int_t *dforw, int_t *dbakw, int_t *qsize,
int_t *llist, int_t *marker)
{
/* System generated locals */
int_t i__1;
/* Local variables */
static int_t ndeg, node, fnode;
/* *************************************************************** */
/* *************************************************************** */
/* Parameter adjustments */
--marker;
--llist;
--qsize;
--dbakw;
--dforw;
--dhead;
--adjncy;
--xadj;
/* Function Body */
i__1 = *neqns;
for (node = 1; node <= i__1; ++node) {
dhead[node] = 0;
qsize[node] = 1;
marker[node] = 0;
llist[node] = 0;
/* L100: */
}
/* ------------------------------------------ */
/* INITIALIZE THE DEGREE DOUBLY LINKED LISTS. */
/* ------------------------------------------ */
i__1 = *neqns;
for (node = 1; node <= i__1; ++node) {
ndeg = xadj[node + 1] - xadj[node] + 1;
fnode = dhead[ndeg];
dforw[node] = fnode;
dhead[ndeg] = node;
if (fnode > 0) {
dbakw[fnode] = node;
}
dbakw[node] = -ndeg;
/* L200: */
}
return 0;
} /* mmdint_dist */
/* *************************************************************** */
/* *************************************************************** */
/* ** MMDELM ..... MULTIPLE MINIMUM DEGREE ELIMINATION *** */
/* *************************************************************** */
/* *************************************************************** */
/* AUTHOR - JOSEPH W.H. LIU */
/* DEPT OF COMPUTER SCIENCE, YORK UNIVERSITY. */
/* PURPOSE - THIS ROUTINE ELIMINATES THE NODE MDNODE OF */
/* MINIMUM DEGREE FROM THE ADJACENCY STRUCTURE, WHICH */
/* IS STORED IN THE QUOTIENT GRAPH FORMAT. IT ALSO */
/* TRANSFORMS THE QUOTIENT GRAPH REPRESENTATION OF THE */
/* ELIMINATION GRAPH. */
/* INPUT PARAMETERS - */
/* MDNODE - NODE OF MINIMUM DEGREE. */
/* MAXINT - ESTIMATE OF MAXIMUM REPRESENTABLE (SHORT) */
/* INT. */
/* TAG - TAG VALUE. */
/* UPDATED PARAMETERS - */
/* (XADJ,ADJNCY) - UPDATED ADJACENCY STRUCTURE. */
/* (DHEAD,DFORW,DBAKW) - DEGREE DOUBLY LINKED STRUCTURE. */
/* QSIZE - SIZE OF SUPERNODE. */
/* MARKER - MARKER VECTOR. */
/* LLIST - TEMPORARY LINKED LIST OF ELIMINATED NABORS. */
/* *************************************************************** */
/* Subroutine */ int mmdelm_dist(int_t *mdnode, int_t *xadj, int_t *adjncy,
int_t *dhead, int_t *dforw, int_t *dbakw, int_t *qsize,
int_t *llist, int_t *marker, int_t *maxint, int_t *tag)
{
/* System generated locals */
int_t i__1, i__2;
/* Local variables */
static int_t node, link, rloc, rlmt, i, j, nabor, rnode, elmnt, xqnbr,
istop, jstop, istrt, jstrt, nxnode, pvnode, nqnbrs, npv;
/* *************************************************************** */
/* *************************************************************** */
/* ----------------------------------------------- */
/* FIND REACHABLE SET AND PLACE IN DATA STRUCTURE. */
/* ----------------------------------------------- */
/* Parameter adjustments */
--marker;
--llist;
--qsize;
--dbakw;
--dforw;
--dhead;
--adjncy;
--xadj;
/* Function Body */
marker[*mdnode] = *tag;
istrt = xadj[*mdnode];
istop = xadj[*mdnode + 1] - 1;
/* ------------------------------------------------------- */
/* ELMNT POINTS TO THE BEGINNING OF THE LIST OF ELIMINATED */
/* NABORS OF MDNODE, AND RLOC GIVES THE STORAGE LOCATION */
/* FOR THE NEXT REACHABLE NODE. */
/* ------------------------------------------------------- */
elmnt = 0;
rloc = istrt;
rlmt = istop;
i__1 = istop;
for (i = istrt; i <= i__1; ++i) {
nabor = adjncy[i];
if (nabor == 0) {
goto L300;
}
if (marker[nabor] >= *tag) {
goto L200;
}
marker[nabor] = *tag;
if (dforw[nabor] < 0) {
goto L100;
}
adjncy[rloc] = nabor;
++rloc;
goto L200;
L100:
llist[nabor] = elmnt;
elmnt = nabor;
L200:
;
}
L300:
/* ----------------------------------------------------- */
/* MERGE WITH REACHABLE NODES FROM GENERALIZED ELEMENTS. */
/* ----------------------------------------------------- */
if (elmnt <= 0) {
goto L1000;
}
adjncy[rlmt] = -elmnt;
link = elmnt;
L400:
jstrt = xadj[link];
jstop = xadj[link + 1] - 1;
i__1 = jstop;
for (j = jstrt; j <= i__1; ++j) {
node = adjncy[j];
link = -node;
if (node < 0) {
goto L400;
} else if (node == 0) {
goto L900;
} else {
goto L500;
}
L500:
if (marker[node] >= *tag || dforw[node] < 0) {
goto L800;
}
marker[node] = *tag;
/* --------------------------------- */
/* USE STORAGE FROM ELIMINATED NODES */
/* IF NECESSARY. */
/* --------------------------------- */
L600:
if (rloc < rlmt) {
goto L700;
}
link = -adjncy[rlmt];
rloc = xadj[link];
rlmt = xadj[link + 1] - 1;
goto L600;
L700:
adjncy[rloc] = node;
++rloc;
L800:
;
}
L900:
elmnt = llist[elmnt];
goto L300;
L1000:
if (rloc <= rlmt) {
adjncy[rloc] = 0;
}
/* -------------------------------------------------------- */
/* FOR EACH NODE IN THE REACHABLE SET, DO THE FOLLOWING ... */
/* -------------------------------------------------------- */
link = *mdnode;
L1100:
istrt = xadj[link];
istop = xadj[link + 1] - 1;
i__1 = istop;
for (i = istrt; i <= i__1; ++i) {
rnode = adjncy[i];
link = -rnode;
if (rnode < 0) {
goto L1100;
} else if (rnode == 0) {
goto L1800;
} else {
goto L1200;
}
L1200:
/* -------------------------------------------- */
/* IF RNODE IS IN THE DEGREE LIST STRUCTURE ... */
/* -------------------------------------------- */
pvnode = dbakw[rnode];
if (pvnode == 0 || pvnode == -(*maxint)) {
goto L1300;
}
/* ------------------------------------- */
/* THEN REMOVE RNODE FROM THE STRUCTURE. */
/* ------------------------------------- */
nxnode = dforw[rnode];
if (nxnode > 0) {
dbakw[nxnode] = pvnode;
}
if (pvnode > 0) {
dforw[pvnode] = nxnode;
}
npv = -pvnode;
if (pvnode < 0) {
dhead[npv] = nxnode;
}
L1300:
/* ---------------------------------------- */
/* PURGE INACTIVE QUOTIENT NABORS OF RNODE. */
/* ---------------------------------------- */
jstrt = xadj[rnode];
jstop = xadj[rnode + 1] - 1;
xqnbr = jstrt;
i__2 = jstop;
for (j = jstrt; j <= i__2; ++j) {
nabor = adjncy[j];
if (nabor == 0) {
goto L1500;
}
if (marker[nabor] >= *tag) {
goto L1400;
}
adjncy[xqnbr] = nabor;
++xqnbr;
L1400:
;
}
L1500:
/* ---------------------------------------- */
/* IF NO ACTIVE NABOR AFTER THE PURGING ... */
/* ---------------------------------------- */
nqnbrs = xqnbr - jstrt;
if (nqnbrs > 0) {
goto L1600;
}
/* ----------------------------- */
/* THEN MERGE RNODE WITH MDNODE. */
/* ----------------------------- */
qsize[*mdnode] += qsize[rnode];
qsize[rnode] = 0;
marker[rnode] = *maxint;
dforw[rnode] = -(*mdnode);
dbakw[rnode] = -(*maxint);
goto L1700;
L1600:
/* -------------------------------------- */
/* ELSE FLAG RNODE FOR DEGREE UPDATE, AND */
/* ADD MDNODE AS A NABOR OF RNODE. */
/* -------------------------------------- */
dforw[rnode] = nqnbrs + 1;
dbakw[rnode] = 0;
adjncy[xqnbr] = *mdnode;
++xqnbr;
if (xqnbr <= jstop) {
adjncy[xqnbr] = 0;
}
L1700:
;
}
L1800:
return 0;
} /* mmdelm_dist */
/* *************************************************************** */
/* *************************************************************** */
/* ***** MMDUPD ..... MULTIPLE MINIMUM DEGREE UPDATE ***** */
/* *************************************************************** */
/* *************************************************************** */
/* AUTHOR - JOSEPH W.H. LIU */
/* DEPT OF COMPUTER SCIENCE, YORK UNIVERSITY. */
/* PURPOSE - THIS ROUTINE UPDATES THE DEGREES OF NODES */
/* AFTER A MULTIPLE ELIMINATION STEP. */
/* INPUT PARAMETERS - */
/* EHEAD - THE BEGINNING OF THE LIST OF ELIMINATED */
/* NODES (I.E., NEWLY FORMED ELEMENTS). */
/* NEQNS - NUMBER OF EQUATIONS. */
/* (XADJ,ADJNCY) - ADJACENCY STRUCTURE. */
/* DELTA - TOLERANCE VALUE FOR MULTIPLE ELIMINATION. */
/* MAXINT - MAXIMUM MACHINE REPRESENTABLE (SHORT) */
/* INTEGER. */
/* UPDATED PARAMETERS - */
/* MDEG - NEW MINIMUM DEGREE AFTER DEGREE UPDATE. */
/* (DHEAD,DFORW,DBAKW) - DEGREE DOUBLY LINKED STRUCTURE. */
/* QSIZE - SIZE OF SUPERNODE. */
/* LLIST - WORKING LINKED LIST. */
/* MARKER - MARKER VECTOR FOR DEGREE UPDATE. */
/* TAG - TAG VALUE. */
/* *************************************************************** */
/* Subroutine */ int mmdupd_dist(int_t *ehead, int_t *neqns, int_t *xadj,
int_t *adjncy, int_t *delta, int_t *mdeg, int_t *dhead,
int_t *dforw, int_t *dbakw, int_t *qsize, int_t *llist,
int_t *marker, int_t *maxint, int_t *tag)
{
/* System generated locals */
int_t i__1, i__2;
/* Local variables */
static int_t node, mtag, link, mdeg0, i, j, enode, fnode, nabor, elmnt,
istop, jstop, q2head, istrt, jstrt, qxhead, iq2, deg, deg0;
/* *************************************************************** */
/* *************************************************************** */
/* Parameter adjustments */
--marker;
--llist;
--qsize;
--dbakw;
--dforw;
--dhead;
--adjncy;
--xadj;
/* Function Body */
mdeg0 = *mdeg + *delta;
elmnt = *ehead;
L100:
/* ------------------------------------------------------- */
/* FOR EACH OF THE NEWLY FORMED ELEMENT, DO THE FOLLOWING. */
/* (RESET TAG VALUE IF NECESSARY.) */
/* ------------------------------------------------------- */
if (elmnt <= 0) {
return 0;
}
mtag = *tag + mdeg0;
if (mtag < *maxint) {
goto L300;
}
*tag = 1;
i__1 = *neqns;
for (i = 1; i <= i__1; ++i) {
if (marker[i] < *maxint) {
marker[i] = 0;
}
/* L200: */
}
mtag = *tag + mdeg0;
L300:
/* --------------------------------------------- */
/* CREATE TWO LINKED LISTS FROM NODES ASSOCIATED */
/* WITH ELMNT: ONE WITH TWO NABORS (Q2HEAD) IN */
/* ADJACENCY STRUCTURE, AND THE OTHER WITH MORE */
/* THAN TWO NABORS (QXHEAD). ALSO COMPUTE DEG0, */
/* NUMBER OF NODES IN THIS ELEMENT. */
/* --------------------------------------------- */
q2head = 0;
qxhead = 0;
deg0 = 0;
link = elmnt;
L400:
istrt = xadj[link];
istop = xadj[link + 1] - 1;
i__1 = istop;
for (i = istrt; i <= i__1; ++i) {
enode = adjncy[i];
link = -enode;
if (enode < 0) {
goto L400;
} else if (enode == 0) {
goto L800;
} else {
goto L500;
}
L500:
if (qsize[enode] == 0) {
goto L700;
}
deg0 += qsize[enode];
marker[enode] = mtag;
/* ---------------------------------- */
/* IF ENODE REQUIRES A DEGREE UPDATE, */
/* THEN DO THE FOLLOWING. */
/* ---------------------------------- */
if (dbakw[enode] != 0) {
goto L700;
}
/* ---------------------------------------
*/
/* PLACE EITHER IN QXHEAD OR Q2HEAD LISTS.
*/
/* ---------------------------------------
*/
if (dforw[enode] == 2) {
goto L600;
}
llist[enode] = qxhead;
qxhead = enode;
goto L700;
L600:
llist[enode] = q2head;
q2head = enode;
L700:
;
}
L800:
/* -------------------------------------------- */
/* FOR EACH ENODE IN Q2 LIST, DO THE FOLLOWING. */
/* -------------------------------------------- */
enode = q2head;
iq2 = 1;
L900:
if (enode <= 0) {
goto L1500;
}
if (dbakw[enode] != 0) {
goto L2200;
}
++(*tag);
deg = deg0;
/* ------------------------------------------ */
/* IDENTIFY THE OTHER ADJACENT ELEMENT NABOR. */
/* ------------------------------------------ */
istrt = xadj[enode];
nabor = adjncy[istrt];
if (nabor == elmnt) {
nabor = adjncy[istrt + 1];
}
/* ------------------------------------------------ */
/* IF NABOR IS UNELIMINATED, INCREASE DEGREE COUNT. */
/* ------------------------------------------------ */
link = nabor;
if (dforw[nabor] < 0) {
goto L1000;
}
deg += qsize[nabor];
goto L2100;
L1000:
/* -------------------------------------------- */
/* OTHERWISE, FOR EACH NODE IN THE 2ND ELEMENT, */
/* DO THE FOLLOWING. */
/* -------------------------------------------- */
istrt = xadj[link];
istop = xadj[link + 1] - 1;
i__1 = istop;
for (i = istrt; i <= i__1; ++i) {
node = adjncy[i];
link = -node;
if (node == enode) {
goto L1400;
}
if (node < 0) {
goto L1000;
} else if (node == 0) {
goto L2100;
} else {
goto L1100;
}
L1100:
if (qsize[node] == 0) {
goto L1400;
}
if (marker[node] >= *tag) {
goto L1200;
}
/* -----------------------------------
-- */
/* CASE WHEN NODE IS NOT YET CONSIDERED
. */
/* -----------------------------------
-- */
marker[node] = *tag;
deg += qsize[node];
goto L1400;
L1200:
/* ----------------------------------------
*/
/* CASE WHEN NODE IS INDISTINGUISHABLE FROM
*/
/* ENODE. MERGE THEM INTO A NEW SUPERNODE.
*/
/* ----------------------------------------
*/
if (dbakw[node] != 0) {
goto L1400;
}
if (dforw[node] != 2) {
goto L1300;
}
qsize[enode] += qsize[node];
qsize[node] = 0;
marker[node] = *maxint;
dforw[node] = -enode;
dbakw[node] = -(*maxint);
goto L1400;
L1300:
/* --------------------------------------
*/
/* CASE WHEN NODE IS OUTMATCHED BY ENODE.
*/
/* --------------------------------------
*/
if (dbakw[node] == 0) {
dbakw[node] = -(*maxint);
}
L1400:
;
}
goto L2100;
L1500:
/* ------------------------------------------------ */
/* FOR EACH ENODE IN THE QX LIST, DO THE FOLLOWING. */
/* ------------------------------------------------ */
enode = qxhead;
iq2 = 0;
L1600:
if (enode <= 0) {
goto L2300;
}
if (dbakw[enode] != 0) {
goto L2200;
}
++(*tag);
deg = deg0;
/* --------------------------------- */
/* FOR EACH UNMARKED NABOR OF ENODE, */
/* DO THE FOLLOWING. */
/* --------------------------------- */
istrt = xadj[enode];
istop = xadj[enode + 1] - 1;
i__1 = istop;
for (i = istrt; i <= i__1; ++i) {
nabor = adjncy[i];
if (nabor == 0) {
goto L2100;
}
if (marker[nabor] >= *tag) {
goto L2000;
}
marker[nabor] = *tag;
link = nabor;
/* ------------------------------ */
/* IF UNELIMINATED, INCLUDE IT IN */
/* DEG COUNT. */
/* ------------------------------ */
if (dforw[nabor] < 0) {
goto L1700;
}
deg += qsize[nabor];
goto L2000;
L1700:
/* -------------------------------
*/
/* IF ELIMINATED, INCLUDE UNMARKED
*/
/* NODES IN THIS ELEMENT INTO THE
*/
/* DEGREE COUNT. */
/* -------------------------------
*/
jstrt = xadj[link];
jstop = xadj[link + 1] - 1;
i__2 = jstop;
for (j = jstrt; j <= i__2; ++j) {
node = adjncy[j];
link = -node;
if (node < 0) {
goto L1700;
} else if (node == 0) {
goto L2000;
} else {
goto L1800;
}
L1800:
if (marker[node] >= *tag) {
goto L1900;
}
marker[node] = *tag;
deg += qsize[node];
L1900:
;
}
L2000:
;
}
L2100:
/* ------------------------------------------- */
/* UPDATE EXTERNAL DEGREE OF ENODE IN DEGREE */
/* STRUCTURE, AND MDEG (MIN DEG) IF NECESSARY. */
/* ------------------------------------------- */
deg = deg - qsize[enode] + 1;
fnode = dhead[deg];
dforw[enode] = fnode;
dbakw[enode] = -deg;
if (fnode > 0) {
dbakw[fnode] = enode;
}
dhead[deg] = enode;
if (deg < *mdeg) {
*mdeg = deg;
}
L2200:
/* ---------------------------------- */
/* GET NEXT ENODE IN CURRENT ELEMENT. */
/* ---------------------------------- */
enode = llist[enode];
if (iq2 == 1) {
goto L900;
}
goto L1600;
L2300:
/* ----------------------------- */
/* GET NEXT ELEMENT IN THE LIST. */
/* ----------------------------- */
*tag = mtag;
elmnt = llist[elmnt];
goto L100;
} /* mmdupd_dist */
/* *************************************************************** */
/* *************************************************************** */
/* ***** MMDNUM ..... MULTI MINIMUM DEGREE NUMBERING ***** */
/* *************************************************************** */
/* *************************************************************** */
/* AUTHOR - JOSEPH W.H. LIU */
/* DEPT OF COMPUTER SCIENCE, YORK UNIVERSITY. */
/* PURPOSE - THIS ROUTINE PERFORMS THE FINAL STEP IN */
/* PRODUCING THE PERMUTATION AND INVERSE PERMUTATION */
/* VECTORS IN THE MULTIPLE ELIMINATION VERSION OF THE */
/* MINIMUM DEGREE ORDERING ALGORITHM. */
/* INPUT PARAMETERS - */
/* NEQNS - NUMBER OF EQUATIONS. */
/* QSIZE - SIZE OF SUPERNODES AT ELIMINATION. */
/* UPDATED PARAMETERS - */
/* INVP - INVERSE PERMUTATION VECTOR. ON INPUT, */
/* IF QSIZE(NODE)=0, THEN NODE HAS BEEN MERGED */
/* INTO THE NODE -INVP(NODE); OTHERWISE, */
/* -INVP(NODE) IS ITS INVERSE LABELLING. */
/* OUTPUT PARAMETERS - */
/* PERM - THE PERMUTATION VECTOR. */
/* *************************************************************** */
/* Subroutine */ int mmdnum_dist(int_t *neqns, int_t *perm, int_t *invp,
int_t *qsize)
{
/* System generated locals */
int_t i__1;
/* Local variables */
static int_t node, root, nextf, father, nqsize, num;
/* *************************************************************** */
/* *************************************************************** */
/* Parameter adjustments */
--qsize;
--invp;
--perm;
/* Function Body */
i__1 = *neqns;
for (node = 1; node <= i__1; ++node) {
nqsize = qsize[node];
if (nqsize <= 0) {
perm[node] = invp[node];
}
if (nqsize > 0) {
perm[node] = -invp[node];
}
/* L100: */
}
/* ------------------------------------------------------ */
/* FOR EACH NODE WHICH HAS BEEN MERGED, DO THE FOLLOWING. */
/* ------------------------------------------------------ */
i__1 = *neqns;
for (node = 1; node <= i__1; ++node) {
if (perm[node] > 0) {
goto L500;
}
/* ----------------------------------------- */
/* TRACE THE MERGED TREE UNTIL ONE WHICH HAS */
/* NOT BEEN MERGED, CALL IT ROOT. */
/* ----------------------------------------- */
father = node;
L200:
if (perm[father] > 0) {
goto L300;
}
father = -perm[father];
goto L200;
L300:
/* ----------------------- */
/* NUMBER NODE AFTER ROOT. */
/* ----------------------- */
root = father;
num = perm[root] + 1;
invp[node] = -num;
perm[root] = num;
/* ------------------------ */
/* SHORTEN THE MERGED TREE. */
/* ------------------------ */
father = node;