Blame view

laplace.c 19.5 KB
5a294ec2   James Caveen   initial commit fo...
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
# include <stdlib.h>
# include <stdio.h>
# include <math.h>

# include "mpi.h"

# define n 48            /* matrix is nxn, excluding boundary values     */
# define nodeedge 24     /* a task works on a nodeedge x nodeedge matrix */
# define nblock n/nodeedge   /* number of tasks per row of matrix            */
# define nproc nblock*nblock /* total number of tasks (processors)           */
//# define nproc nblock*nblock /* total number of tasks (processors)           */

int main ( int argc, char **argv );
void doblack ( double w, double M[][nodeedge+2] );
void dored ( double w, double M[][nodeedge+2] );
void exchange ( double M[][nodeedge+2], int comm[], int rank );
void iterate ( double w, double M[][nodeedge+2], double result[][n], int rank, int comm[] );
void setcomm ( int rank, int comm[] );
void setex ( double ex[], double M[][nodeedge+2], int which );
void initialize_matrix ( double M[][nodeedge+2] );
void unpack ( double M[][nodeedge+2], int where, double in[] );

/******************************************************************************/

int main ( int argc, char **argv )

/******************************************************************************/
/*
  Purpose:

    LAPLACE_MPI solves Laplace's equation on a rectangle, using MPI.

  Discussion:

    This program uses a finite difference scheme to solve
    Laplace's equation for a square matrix distributed over a square
    (logical) processor topology.  A complete description of the algorithm
    is found in Fox.

    This program works on the SPMD (single program, multiple data)
    paradigm.  It illustrates 2-d block decomposition, nodes exchanging
    edge values, and convergence checking.

    Each matrix element is updated based on the values of the four
    neighboring matrix elements.  This process is repeated until the data
    converges, that is, until the average change in any matrix element (compared
    to the value 20 iterations previous) is smaller than a specified value.

    To ensure reproducible results between runs, a red/black
    checkerboard algorithm is used.  Each process exchanges edge values
    with its four neighbors.  Then new values are calculated for the upper
    left and lower right corners (the "red" corners) of each node's
    matrix.  The processes exchange edge values again.  The upper right
    and lower left corners (the "black" corners) are then calculated.

    The program is currently configured for a 48x48 matrix
    distributed over four processors.  It can be edited to handle
    different matrix sizes or number of processors, as long as the matrix
    can be divided evenly between the processors.

  Modified:

    14 November 2011

  Author:

    Sequential C version by Robb Newman.
    MPI C version by Xianneng Shen.

  Reference:

    Geoffrey Fox, Mark Johnson, Gregory Lyzenga, Steve Otto, John Salmon, 
    David Walker,
    Solving Problems on Concurrent Processors,
    Volume 1: General Techniques and Regular Problems, 
    Prentice Hall, 1988,
    ISBN: 0-13-8230226,
    LC: QA76.5.F627.

  Local parameters:

    Local, int COMM[4], contains a 0 (no) or 1 (yes) if
    communication is needed for the UP(0), RIGHT(1), DOWN(2)
    and LEFT(3) neighbors.

    Local, FILE *fp, a pointer to the output file.

    Local, double M[nodeedge+2][nodeedge+2], the part of the results 
    kept by this process.

    Local, double RESULT[n][n], the results for the complete problem,
    kept by process 0.

    Local, double W, the SOR factor, which must be strictly between 0 and 2.
*/ 
{
  int comm[4];
  FILE *fp;
  int i;
  int j;
  double M[nodeedge+2][nodeedge+2];
  int ntasks;
  int rank;
  double result[n][n];
  double w;
  double wtime;

  MPI_Init ( &argc, &argv );

  MPI_Comm_rank ( MPI_COMM_WORLD, &rank );

  MPI_Comm_size ( MPI_COMM_WORLD, &ntasks );

  wtime = MPI_Wtime ( );

  if ( rank == 0 ) 
  {
    printf ( "\n" );
    printf ( "LAPLACE_MPI:\n" );
    printf ( "  C/MPI version\n" );
    printf ( "  Solve the Laplace equation using MPI.\n" );
  }

  if ( ntasks != nproc )
  {
    if ( rank == 0 ) 
    {
      printf ( "\n" );
      printf ( "Fatal error!\n" );
      printf ( "  MP_PROCS should be set to %i!\n", nproc );
    }
    MPI_Finalize ( );
    exit ( 1 );
  }

  if ( rank == 0 ) 
  {
    printf ( "\n" );
    printf ( "  MPI has been set up.\n" );
  }
/* 
  Initialize the matrix M.
*/
  if ( rank == 0 ) 
  {
    printf ( "  Initialize the matrix M.\n" );
  }
  initialize_matrix ( M );
/* 
  Figure out who I communicate with.
*/
  if ( rank == 0 ) 
  {
    printf ( "  Set the list of neighbors.\n" );
  }
  setcomm ( rank, comm );
/* 
  Update M, using SOR value W, until convergence.
*/
  if ( rank == 0 ) 
  {
    printf ( "  Begin the iteration.\n" );
  }
  w = 1.2;
  iterate ( w, M, result, rank, comm );
/* 
  Report timing 
*/ 
  wtime = MPI_Wtime ( ) - wtime;

  printf ( "  Task %i took %6.3f seconds\n", rank, wtime );
/*
  Write the solution to a file.
*/
  if ( rank == 0 )
  {
    fp = fopen ( "laplace_solution.txt", "w" );

    for ( i = 0; i < n; i++ ) 
    {
      for ( j = 0; j < n; j++ )
      {
        fprintf ( fp, "%f\n ", result[i][j] );
      }  
        fprintf ( fp, "\n");
    }
    fclose ( fp );
    printf ( "  Solution written to \"laplace_solution.txt\".\n" );
  }
/*
  Terminate MPI.
*/
  MPI_Finalize ( );
/*
  Terminate.
*/
  if ( rank == 0 )
  {
    printf ( "\n" );
    printf ( "LAPLACE_MPI:\n" );
    printf ( "  Normal end of execution.\n" );
  }
  return 0;
}
/******************************************************************************/

void doblack ( double w, double M[][nodeedge+2] )

/******************************************************************************/
/*
  Purpose:

    DOBLACK iterates on the upper right and lower left corners of my matrix.

  Modified:

    16 February 2013

  Author:

    Sequential C version by Robb Newman.
    MPI C version by Xianneng Shen.

  Parameters:

    Input, double W, the SOR factor, which must be strictly between 0 and 2.

    Input/output, double M[nodeedge+2][nodeedge+2], the part of the results 
    kept by this process.
*/
{
  int i;
  int j;
/*
  Upper right corner.
*/
  for ( i = 1; i <= nodeedge / 2; i++ )
  {
    for ( j = nodeedge / 2 + 1; j <= nodeedge; j++ )
    {
      M[i][j] = w / 4.0 * ( M[i-1][j] + M[i][j-1] + M[i+1][j] + M[i][j+1] )
        + ( 1.0 - w ) * M[i][j];
    }
  }
/*
  Lower left corner.
*/
  for ( i = nodeedge / 2 + 1; i <= nodeedge; i++ )
  {
    for ( j = 1; j <= nodeedge / 2; j++ )
    {
      M[i][j] = w / 4.0 * ( M[i-1][j] + M[i][j-1] + M[i+1][j] + M[i][j+1] )
        + ( 1.0 - w ) * M[i][j];
    }
  }
  return;
}
/******************************************************************************/

void dored ( double w, double M[][nodeedge+2] )

/******************************************************************************/   
/*
  Purpose:

    DORED iterates on the upper left and lower right corners of my matrix.

  Modified:

    16 February 2013

  Author:

    Sequential C version by Robb Newman.
    MPI C version by Xianneng Shen.

  Parameters:

    Input, double W, the SOR factor, which must be strictly between 0 and 2.

    Input/output, double M[nodeedge+2][nodeedge+2], the part of the results 
    kept by this process.
*/  
{
  int i;
  int j;
/*
  Upper left corner.
*/
  for ( i = 1; i <= nodeedge / 2; i++ )
  {
    for ( j = 1; j <= nodeedge / 2; j++ ) 
    {
      M[i][j] = w / 4.0 * ( M[i-1][j] + M[i][j-1] + M[i+1][j] + M[i][j+1] )
        + ( 1.0 - w ) * M[i][j];
    }
  }
/*
  Lower right corner.
*/
  for ( i = nodeedge / 2 + 1; i <= nodeedge; i++ )
  {
    for ( j = nodeedge / 2 + 1; j <= nodeedge; j++ )
    {
      M[i][j] = w / 4.0 * ( M[i-1][j] + M[i][j-1] + M[i+1][j] + M[i][j+1] )
        + ( 1.0 - w ) * M[i][j];
    }
  }
  return;
}
/******************************************************************************/

void exchange ( double M[][nodeedge+2], int comm[], int rank )

/******************************************************************************/
/*
  Purpose:

   EXCHANGE trades edge values with up to four neighbors.

  Discussion:

    Up to 4 MPI sends are carried out, and up to 4 MPI receives.

  Modified:

    14 November 2011

  Author:

    Sequential C version by Robb Newman.
    MPI C version by Xianneng Shen.

  Parameters:

    Input/output, double M[nodeedge+2][nodeedge+2], the part of the results 
    kept by this process.

    Input, int COMM[4], contains a 0 (no) or 1 (yes) if
    communication is needed for the UP(0), RIGHT(1), DOWN(2)
    and LEFT(3) neighbors.

    Input, int RANK, the rank of this process.
*/
{
  double ex0[nodeedge];
  double ex1[nodeedge];
  double ex2[nodeedge];
  double ex3[nodeedge];
  int i;
  double in0[nodeedge];
  double in1[nodeedge];
  double in2[nodeedge];
  double in3[nodeedge];
  int partner;
  MPI_Request requests[8];
  MPI_Status status[8];
  int tag;
/* 
  Initialize requests.
*/
  for ( i = 0; i < 8; i++ ) 
  {
    requests[i] = MPI_REQUEST_NULL; 
  }
/* 
  Receive from UP neighbor (0).
*/
  if ( comm[0] == 1 )
  {
    partner = rank - nblock;
    tag = 0;
    MPI_Irecv ( &in0, nodeedge, MPI_DOUBLE, partner, tag, MPI_COMM_WORLD, 
      &requests[0] );
  }
/*
  Receive from RIGHT neighbor (1).
*/
  if ( comm[1] == 1 )
  {
    partner = rank + 1;
    tag = 1;
    MPI_Irecv ( &in1, nodeedge, MPI_DOUBLE, partner, tag, MPI_COMM_WORLD,
      &requests[1] );
  }
/*
  Receive from DOWN neighbor (2).
*/
  if ( comm[2] == 1 )
  {
    partner = rank + nblock;
    tag = 2;
    MPI_Irecv ( &in2, nodeedge, MPI_DOUBLE, partner, tag, MPI_COMM_WORLD,
      &requests[2] );
  }
/*
  Receive from LEFT neighbor (3).
*/
  if ( comm[3] == 1 )
  {
    partner = rank - 1;
    tag = 3;
    MPI_Irecv ( &in3, nodeedge, MPI_DOUBLE, partner, tag, MPI_COMM_WORLD,
      &requests[3] );
  }
/*
  Send up from DOWN (2) neighbor.
*/
  if ( comm[0] == 1 )
  {
    partner = rank - nblock;
    tag = 2;
    setex ( ex0, M, 0 );
    MPI_Isend ( &ex0, nodeedge, MPI_DOUBLE, partner, tag, MPI_COMM_WORLD,
      &requests[4] );
  }
/*
  Send right form LEFT (3) neighbor.
*/
  if (comm[1] == 1 )
  {
    partner = rank + 1;
    tag = 3;
    setex ( ex1, M, 1 );
    MPI_Isend ( &ex1, nodeedge, MPI_DOUBLE, partner, tag, MPI_COMM_WORLD,
      &requests[5] );
  }
/*
  Send down from UP (0) neighbor.
*/
  if ( comm[2] == 1 )
  {
    partner = rank + nblock;
    tag = 0;
    setex ( ex2, M, 2 );
    MPI_Isend ( &ex2, nodeedge, MPI_DOUBLE, partner, tag, MPI_COMM_WORLD,
      &requests[6] );
  }
/*
  Send left from RIGHT (1) neighbor.
*/
  if ( comm[3] == 1 )
  {
    partner = rank - 1;
    tag = 1;
    setex ( ex3, M, 3 );
    MPI_Isend ( &ex3, nodeedge, MPI_DOUBLE, partner, tag, MPI_COMM_WORLD,
      &requests[7] );
  }
/* 
  Wait for all communication to complete.
*/ 
  MPI_Waitall ( 8, requests, status );
/*
  Copy boundary values, sent by neighbors, into M.
*/
  if ( comm[0] == 1 ) 
  {
    unpack ( M, 0, in0 );
  }
  if ( comm[1] == 1 ) 
  {
    unpack ( M, 1, in1 );
  }
  if ( comm[2] == 1 ) 
  {
    unpack ( M, 2, in2 );
  }
  if ( comm[3] == 1 ) 
  {
    unpack ( M, 3, in3 );
  }

  return;
}
/******************************************************************************/

void initialize_matrix ( double M[][nodeedge+2] )

/******************************************************************************/
/*
  Purpose:

    INITIALIZE_MATRIX initializes the partial results array M.

  Modified:

    10 January 2012

  Author:

    Sequential C version by Robb Newman.
    MPI C version by Xianneng Shen.

  Parameters:

    Output, double M[nodeedge+2][nodeedge+2], the initialized partial 
    results array.
*/
{
  double avg;
  double bv[4];
  int i;
  int j;

  bv[0] = 100.0;
  bv[1] = 0.0;
  bv[2] = 0.0;
  bv[3] = 0.0;
/* 
  Put the boundary values into M.
*/ 
  for ( i = 1; i <= nodeedge; i++ )
  { 
    M[0][i] =          bv[0];
    M[i][nodeedge+1] = bv[1];
    M[nodeedge+1][i] = bv[2];
    M[i][0] =          bv[3];
  }
/* 
  Set all interior values to be the average of the boundary values.
*/ 
  avg = ( bv[0] + bv[1] + bv[2] + bv[3] ) / 4.0;

  for ( i = 1; i <= nodeedge; i++ )
  {
    for ( j = 1; j <= nodeedge; j++ )
    {
      M[i][j] = avg;
    }
  }

  return;
}
/******************************************************************************/

void iterate ( double w, double M[][nodeedge+2], double result[][n], int rank, 
  int comm[] )

/******************************************************************************/
/*
  Purpose:

    ITERATE controls the iteration, including convergence checking.

  Modified:

    16 February 2013

  Author:

    Sequential C version by Robb Newman.
    MPI C version by Xianneng Shen.

  Parameters:

    Input, double W, the SOR factor, which must be strictly between 0 and 2.

    Input/output, double M[nodeedge+2][nodeedge+2], the part of the results 
    kept by this process.

    Output, double RESULT[n][n], the results for the complete problem,
    kept by process 0.

    Input, int RANK, the rank of the process.

    Input, int COMM[4], contains a 0 (no) or 1 (yes) if
    communication is needed for the UP(0), RIGHT(1), DOWN(2)
    and LEFT(3) neighbors.

  Local parameters:

    Local, int COUNT, the length, in elements, of messages.

    Local, double DIFF, the average absolute difference in elements
    of M since the last comparison.

    Local, int IT, the iteration counter.

    Local, double MM[n*n], a vector, used to gather the data from
    all processes.  This data is then rearranged into a 2D array.
*/
{
  int count;
  double diff;
  int done;
  double ediff;
  int i;
  double in;
  int index;
  int it;
  int j;
  int k;
  int l;
  double MM[n*n];
  double mold[nodeedge+2][nodeedge+2];
  double send[nodeedge][nodeedge];

  it = 0;
  done = 0;
  for ( i = 1; i <= nodeedge; i++ )
  {
    for ( j = 1; j <= nodeedge; j++ )
    {
      mold[i][j] = M[i][j];
    }
  }

  while ( done == 0 )
  {
    it++;
/*
  Exchange values with neighbors, update red squares, exchange values
  with neighbors, update black squares.
*/
    exchange ( M, comm, rank );
    dored ( w, M );
    exchange ( M, comm, rank );
    doblack ( w, M );
/*
  Check for convergence every 20 iterations.
  Find the average absolute change in elements of M.
  Maximum iterations is 5000.
*/
    if ( 5000 < it )
    {
      done = 1;
    }

    if ( ( it % 20 == 0 ) && ( done != 1 ) )
    { 
      diff = 0.0;
      for ( i = 1; i <= nodeedge; i++ )
      {
        for ( j = 1; j <= nodeedge; j++ )
        {
          ediff = M[i][j] - mold[i][j];
          if ( ediff < 0.0 ) 
          {
            ediff = - ediff;
          }
          diff = diff + ediff;
          mold[i][j] = M[i][j];
        }
      }
      diff = diff / ( ( double ) ( nodeedge * nodeedge ) );
/*
  IN = sum of DIFF over all processes.
*/
      MPI_Allreduce ( &diff, &in, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD );

      if ( in < ( double ) nproc * 0.001 ) 
      {
        done = 1;
      }
    }
  }
/* 
  Send results to task 0.
*/ 
  for ( i = 0; i < nodeedge; i++ )
  {
    for ( j = 0; j < nodeedge; j++ )
    {
      send[i][j] = M[i+1][j+1];
    }
  }

  count = nodeedge * nodeedge;

  MPI_Gather ( &send, count, MPI_DOUBLE, &MM, count, MPI_DOUBLE, 0, 
    MPI_COMM_WORLD );

  printf ( "  ITERATE gathered updated results to process 0.\n" );
/* 
  Storage on task 0 has to be consistent with a NBLOCK x NBLOCK decomposition.

  I believe the array form of RESULT is only needed at the end of the
  program (and not even then, really).  So we could probably skip this
  work of rearranging the data here.  JVB, 11 January 2012.
*/
  if ( rank == 0 ) 
  {
    printf ( "did %i iterations\n", it );

    index = 0;
    for ( k = 0; k < nblock; k++ )
    {
      for ( l = 0; l < nblock; l++ )
      {
        for ( i = k * nodeedge; i < ( k + 1 ) * nodeedge; i++ )
        {
          for ( j = l * nodeedge; j < ( l + 1 ) * nodeedge; j++ )
          {
            result[i][j] = MM[index];
            index++;
          }
        }
      }
    }
  }
  return;
}
/******************************************************************************/

void setcomm ( int rank, int comm[] )

/******************************************************************************/
/*
  Purpose:

    SETCOMM determines the active communication directions.

  Discussion:

    In this picture, we're assuming the RESULTS array is split among 
    four processes, numbered 0 through 3 and arranged as suggested by the 
    following:

        0  |  1
     ------+-------
        2  |  3

    Then process 0 must communicate with processes 1 and 2 only,
    so its COMM array would be { 0, 1, 1, 0 }.

  Modified:

    14 November 2011

  Author:

    Sequential C version by Robb Newman.
    MPI C version by Xianneng Shen.

  Parameters:

    Input, int RANK, the rank of the process.

    Output, int COMM[4], contains a 0 (no) or 1 (yes) if
    communication is needed for the UP(0), RIGHT(1), DOWN(2)
    and LEFT(3) neighbors.
*/
{
  int i;
/*
  Start out by assuming all four neighbors exist.
*/
  for ( i = 0; i < 4; i++ ) 
  {
    comm[i] = 1;
  }
/*
  Up neighbor?
*/
  if ( rank < nblock )
  {
    comm[0] = 0;    
  }
/*
  Right neighbor?
*/
  if ( ( rank + 1 ) % nblock == 0 )
  {
    comm[1] = 0;
  }
/*
  Down neighbor?
*/
  if ( rank > (nblock*(nblock-1)-1) )
  {
    comm[2] = 0;
  }
/*
  Left neighbor?
*/
  if ( ( rank % nblock ) == 0 )
  {
    comm[3] = 0;
  }

  return;
}
/******************************************************************************/

void setex ( double ex[], double M[][nodeedge+2], int which )

/******************************************************************************/
/*
  Purpose:

    SETEX pulls off the edge values of M to send to another task.

  Modified:

    14 November 2011

  Author:

    Sequential C version by Robb Newman.
    MPI C version by Xianneng Shen.

  Parameters:

    Output, double EX[NODEEDGE], the values to be exchanged.

    Input, double M[nodeedge+2][nodeedge+2], the part of the results 
    kept by this process. 

    Input, int WHICH, 0, 1, 2, or 3, indicates the edge from which
    the data is to be copied.
*/                  
{
  int i;

  switch ( which ) 
  {
    case 0:
    {
      for ( i = 1; i <= nodeedge; i++) 
      {
        ex[i-1] = M[1][i];
      }
      break;
    }
    case 1:
    {
      for ( i = 1; i <= nodeedge; i++)
      {
        ex[i-1] = M[i][nodeedge];
      }
      break;
    }
    case 2:
    {
      for ( i = 1; i <= nodeedge; i++)
      {
        ex[i-1] = M[nodeedge][i];
      }
      break;
    }
    case 3:
    {
      for ( i = 1; i <= nodeedge; i++)
      {
        ex[i-1] = M[i][1];
      }
      break;
    }
  }
  return;
}
/******************************************************************************/

void unpack ( double M[][nodeedge+2], int where, double in[] )

/******************************************************************************/
/*
  Purpose:

    UNPACK puts the vector of new edge values into the edges of M.

  Modified:

    14 November 2011

  Author:

    Sequential C version by Robb Newman.
    MPI C version by Xianneng Shen.

  Parameters:

    Output, double M[nodeedge+2][nodeedge+2], the part of the results 
    kept by this process.

    Input, int WHERE, 0, 1, 2, or 3, indicates the edge to which the 
    data is to be applied.

    Input, int IN[nodeedge], the boundary data.
*/
{
  int i;

  if ( where == 0 )
  {
    for ( i = 0; i < nodeedge; i++ )
    {
      M[0][i+1] = in[i]; 
    }
  }
  else if ( where == 1 )
  {
    for ( i = 0; i < nodeedge; i++ )
    {
      M[i+1][nodeedge+1] = in[i];
    }
  }
  else if ( where == 2 )
  {
    for ( i = 0; i < nodeedge; i++ )
    {
      M[nodeedge+1][i+1] = in[i];
    }
  }
  else if ( where == 3 )
  {
    for ( i = 0; i < nodeedge; i++ )
    {
      M[i+1][0] = in[i];
    }
  }

  return;
}