xref: /petsc/src/dm/impls/plex/plexpartition.c (revision 12617df9807ded1e3dcd1e2297d7534b75cd260f)
1 #include <petsc/private/dmpleximpl.h>   /*I      "petscdmplex.h"   I*/
2 #include <petsc/private/hashseti.h>
3 
4 PetscClassId PETSCPARTITIONER_CLASSID = 0;
5 
6 PetscFunctionList PetscPartitionerList              = NULL;
7 PetscBool         PetscPartitionerRegisterAllCalled = PETSC_FALSE;
8 
9 PetscBool ChacoPartitionercite = PETSC_FALSE;
10 const char ChacoPartitionerCitation[] = "@inproceedings{Chaco95,\n"
11                                "  author    = {Bruce Hendrickson and Robert Leland},\n"
12                                "  title     = {A multilevel algorithm for partitioning graphs},\n"
13                                "  booktitle = {Supercomputing '95: Proceedings of the 1995 ACM/IEEE Conference on Supercomputing (CDROM)},"
14                                "  isbn      = {0-89791-816-9},\n"
15                                "  pages     = {28},\n"
16                                "  doi       = {http://doi.acm.org/10.1145/224170.224228},\n"
17                                "  publisher = {ACM Press},\n"
18                                "  address   = {New York},\n"
19                                "  year      = {1995}\n}\n";
20 
21 PetscBool ParMetisPartitionercite = PETSC_FALSE;
22 const char ParMetisPartitionerCitation[] = "@article{KarypisKumar98,\n"
23                                "  author  = {George Karypis and Vipin Kumar},\n"
24                                "  title   = {A Parallel Algorithm for Multilevel Graph Partitioning and Sparse Matrix Ordering},\n"
25                                "  journal = {Journal of Parallel and Distributed Computing},\n"
26                                "  volume  = {48},\n"
27                                "  pages   = {71--85},\n"
28                                "  year    = {1998}\n}\n";
29 
30 /*@C
31   DMPlexCreatePartitionerGraph - Create a CSR graph of point connections for the partitioner
32 
33   Input Parameters:
34 + dm      - The mesh DM dm
35 - height  - Height of the strata from which to construct the graph
36 
37   Output Parameter:
38 + numVertices     - Number of vertices in the graph
39 . offsets         - Point offsets in the graph
40 . adjacency       - Point connectivity in the graph
41 - globalNumbering - A map from the local cell numbering to the global numbering used in "adjacency".  Negative indicates that the cell is a duplicate from another process.
42 
43   The user can control the definition of adjacency for the mesh using DMSetAdjacency(). They should choose the combination appropriate for the function
44   representation on the mesh.
45 
46   Level: developer
47 
48 .seealso: PetscPartitionerGetType(), PetscPartitionerCreate(), DMSetAdjacency()
49 @*/
50 PetscErrorCode DMPlexCreatePartitionerGraph(DM dm, PetscInt height, PetscInt *numVertices, PetscInt **offsets, PetscInt **adjacency, IS *globalNumbering)
51 {
52   PetscInt       dim, depth, p, pStart, pEnd, a, adjSize, idx, size;
53   PetscInt      *adj = NULL, *vOffsets = NULL, *graph = NULL;
54   IS             cellNumbering;
55   const PetscInt *cellNum;
56   PetscBool      useCone, useClosure;
57   PetscSection   section;
58   PetscSegBuffer adjBuffer;
59   PetscSF        sfPoint;
60   PetscInt       *adjCells = NULL, *remoteCells = NULL;
61   const PetscInt *local;
62   PetscInt       nroots, nleaves, l;
63   PetscMPIInt    rank;
64   PetscErrorCode ierr;
65 
66   PetscFunctionBegin;
67   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRQ(ierr);
68   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
69   ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
70   if (dim != depth) {
71     /* We do not handle the uninterpolated case here */
72     ierr = DMPlexCreateNeighborCSR(dm, height, numVertices, offsets, adjacency);CHKERRQ(ierr);
73     /* DMPlexCreateNeighborCSR does not make a numbering */
74     if (globalNumbering) {ierr = DMPlexCreateCellNumbering_Internal(dm, PETSC_TRUE, globalNumbering);CHKERRQ(ierr);}
75     /* Different behavior for empty graphs */
76     if (!*numVertices) {
77       ierr = PetscMalloc1(1, offsets);CHKERRQ(ierr);
78       (*offsets)[0] = 0;
79     }
80     /* Broken in parallel */
81     if (rank && *numVertices) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Parallel partitioning of uninterpolated meshes not supported");
82     PetscFunctionReturn(0);
83   }
84   ierr = DMPlexGetHeightStratum(dm, height, &pStart, &pEnd);CHKERRQ(ierr);
85   ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);
86   ierr = PetscSFGetGraph(sfPoint, &nroots, NULL, NULL, NULL);CHKERRQ(ierr);
87   /* Build adjacency graph via a section/segbuffer */
88   ierr = PetscSectionCreate(PetscObjectComm((PetscObject) dm), &section);CHKERRQ(ierr);
89   ierr = PetscSectionSetChart(section, pStart, pEnd);CHKERRQ(ierr);
90   ierr = PetscSegBufferCreate(sizeof(PetscInt),1000,&adjBuffer);CHKERRQ(ierr);
91   /* Always use FVM adjacency to create partitioner graph */
92   ierr = DMGetBasicAdjacency(dm, &useCone, &useClosure);CHKERRQ(ierr);
93   ierr = DMSetBasicAdjacency(dm, PETSC_TRUE, PETSC_FALSE);CHKERRQ(ierr);
94   ierr = DMPlexCreateCellNumbering_Internal(dm, PETSC_TRUE, &cellNumbering);CHKERRQ(ierr);
95   if (globalNumbering) {
96     ierr = PetscObjectReference((PetscObject)cellNumbering);CHKERRQ(ierr);
97     *globalNumbering = cellNumbering;
98   }
99   ierr = ISGetIndices(cellNumbering, &cellNum);CHKERRQ(ierr);
100   /* For all boundary faces (including faces adjacent to a ghost cell), record the local cell in adjCells
101      Broadcast adjCells to remoteCells (to get cells from roots) and Reduce adjCells to remoteCells (to get cells from leaves)
102    */
103   ierr = PetscSFGetGraph(dm->sf, &nroots, &nleaves, &local, NULL);CHKERRQ(ierr);
104   if (nroots >= 0) {
105     PetscInt fStart, fEnd, f;
106 
107     ierr = PetscCalloc2(nroots, &adjCells, nroots, &remoteCells);CHKERRQ(ierr);
108     ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
109     for (l = 0; l < nroots; ++l) adjCells[l] = -3;
110     for (f = fStart; f < fEnd; ++f) {
111       const PetscInt *support;
112       PetscInt        supportSize;
113 
114       ierr = DMPlexGetSupport(dm, f, &support);CHKERRQ(ierr);
115       ierr = DMPlexGetSupportSize(dm, f, &supportSize);CHKERRQ(ierr);
116       if (supportSize == 1) adjCells[f] = cellNum[support[0]];
117       else if (supportSize == 2) {
118         ierr = PetscFindInt(support[0], nleaves, local, &p);CHKERRQ(ierr);
119         if (p >= 0) adjCells[f] = cellNum[support[1]];
120         ierr = PetscFindInt(support[1], nleaves, local, &p);CHKERRQ(ierr);
121         if (p >= 0) adjCells[f] = cellNum[support[0]];
122       }
123     }
124     for (l = 0; l < nroots; ++l) remoteCells[l] = -1;
125     ierr = PetscSFBcastBegin(dm->sf, MPIU_INT, adjCells, remoteCells);CHKERRQ(ierr);
126     ierr = PetscSFBcastEnd(dm->sf, MPIU_INT, adjCells, remoteCells);CHKERRQ(ierr);
127     ierr = PetscSFReduceBegin(dm->sf, MPIU_INT, adjCells, remoteCells, MPI_MAX);CHKERRQ(ierr);
128     ierr = PetscSFReduceEnd(dm->sf, MPIU_INT, adjCells, remoteCells, MPI_MAX);CHKERRQ(ierr);
129   }
130   /* Combine local and global adjacencies */
131   for (*numVertices = 0, p = pStart; p < pEnd; p++) {
132     const PetscInt *cone;
133     PetscInt        coneSize, c;
134 
135     /* Skip non-owned cells in parallel (ParMetis expects no overlap) */
136     if (nroots > 0) {if (cellNum[p] < 0) continue;}
137     /* Add remote cells */
138     if (remoteCells) {
139       ierr = DMPlexGetCone(dm, p, &cone);CHKERRQ(ierr);
140       ierr = DMPlexGetConeSize(dm, p, &coneSize);CHKERRQ(ierr);
141       for (c = 0; c < coneSize; ++c) {
142         if (remoteCells[cone[c]] != -1) {
143           PetscInt *PETSC_RESTRICT pBuf;
144 
145           ierr = PetscSectionAddDof(section, p, 1);CHKERRQ(ierr);
146           ierr = PetscSegBufferGetInts(adjBuffer, 1, &pBuf);CHKERRQ(ierr);
147           *pBuf = remoteCells[cone[c]];
148         }
149       }
150     }
151     /* Add local cells */
152     adjSize = PETSC_DETERMINE;
153     ierr = DMPlexGetAdjacency(dm, p, &adjSize, &adj);CHKERRQ(ierr);
154     for (a = 0; a < adjSize; ++a) {
155       const PetscInt point = adj[a];
156       if (point != p && pStart <= point && point < pEnd) {
157         PetscInt *PETSC_RESTRICT pBuf;
158         ierr = PetscSectionAddDof(section, p, 1);CHKERRQ(ierr);
159         ierr = PetscSegBufferGetInts(adjBuffer, 1, &pBuf);CHKERRQ(ierr);
160         *pBuf = cellNum[point];
161       }
162     }
163     (*numVertices)++;
164   }
165   ierr = PetscFree2(adjCells, remoteCells);CHKERRQ(ierr);
166   ierr = DMSetBasicAdjacency(dm, useCone, useClosure);CHKERRQ(ierr);
167   /* Derive CSR graph from section/segbuffer */
168   ierr = PetscSectionSetUp(section);CHKERRQ(ierr);
169   ierr = PetscSectionGetStorageSize(section, &size);CHKERRQ(ierr);
170   ierr = PetscMalloc1(*numVertices+1, &vOffsets);CHKERRQ(ierr);
171   for (idx = 0, p = pStart; p < pEnd; p++) {
172     if (nroots > 0) {if (cellNum[p] < 0) continue;}
173     ierr = PetscSectionGetOffset(section, p, &(vOffsets[idx++]));CHKERRQ(ierr);
174   }
175   vOffsets[*numVertices] = size;
176   if (offsets) *offsets = vOffsets;
177   ierr = PetscSegBufferExtractAlloc(adjBuffer, &graph);CHKERRQ(ierr);
178   ierr = ISRestoreIndices(cellNumbering, &cellNum);CHKERRQ(ierr);
179   ierr = ISDestroy(&cellNumbering);CHKERRQ(ierr);
180   if (adjacency) *adjacency = graph;
181   /* Clean up */
182   ierr = PetscSegBufferDestroy(&adjBuffer);CHKERRQ(ierr);
183   ierr = PetscSectionDestroy(&section);CHKERRQ(ierr);
184   ierr = PetscFree(adj);CHKERRQ(ierr);
185   PetscFunctionReturn(0);
186 }
187 
188 /*@C
189   DMPlexCreateNeighborCSR - Create a mesh graph (cell-cell adjacency) in parallel CSR format.
190 
191   Collective
192 
193   Input Arguments:
194 + dm - The DMPlex
195 - cellHeight - The height of mesh points to treat as cells (default should be 0)
196 
197   Output Arguments:
198 + numVertices - The number of local vertices in the graph, or cells in the mesh.
199 . offsets     - The offset to the adjacency list for each cell
200 - adjacency   - The adjacency list for all cells
201 
202   Note: This is suitable for input to a mesh partitioner like ParMetis.
203 
204   Level: advanced
205 
206 .seealso: DMPlexCreate()
207 @*/
208 PetscErrorCode DMPlexCreateNeighborCSR(DM dm, PetscInt cellHeight, PetscInt *numVertices, PetscInt **offsets, PetscInt **adjacency)
209 {
210   const PetscInt maxFaceCases = 30;
211   PetscInt       numFaceCases = 0;
212   PetscInt       numFaceVertices[30]; /* maxFaceCases, C89 sucks sucks sucks */
213   PetscInt      *off, *adj;
214   PetscInt      *neighborCells = NULL;
215   PetscInt       dim, cellDim, depth = 0, faceDepth, cStart, cEnd, c, numCells, cell;
216   PetscErrorCode ierr;
217 
218   PetscFunctionBegin;
219   /* For parallel partitioning, I think you have to communicate supports */
220   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
221   cellDim = dim - cellHeight;
222   ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
223   ierr = DMPlexGetHeightStratum(dm, cellHeight, &cStart, &cEnd);CHKERRQ(ierr);
224   if (cEnd - cStart == 0) {
225     if (numVertices) *numVertices = 0;
226     if (offsets)   *offsets   = NULL;
227     if (adjacency) *adjacency = NULL;
228     PetscFunctionReturn(0);
229   }
230   numCells  = cEnd - cStart;
231   faceDepth = depth - cellHeight;
232   if (dim == depth) {
233     PetscInt f, fStart, fEnd;
234 
235     ierr = PetscCalloc1(numCells+1, &off);CHKERRQ(ierr);
236     /* Count neighboring cells */
237     ierr = DMPlexGetHeightStratum(dm, cellHeight+1, &fStart, &fEnd);CHKERRQ(ierr);
238     for (f = fStart; f < fEnd; ++f) {
239       const PetscInt *support;
240       PetscInt        supportSize;
241       ierr = DMPlexGetSupportSize(dm, f, &supportSize);CHKERRQ(ierr);
242       ierr = DMPlexGetSupport(dm, f, &support);CHKERRQ(ierr);
243       if (supportSize == 2) {
244         PetscInt numChildren;
245 
246         ierr = DMPlexGetTreeChildren(dm,f,&numChildren,NULL);CHKERRQ(ierr);
247         if (!numChildren) {
248           ++off[support[0]-cStart+1];
249           ++off[support[1]-cStart+1];
250         }
251       }
252     }
253     /* Prefix sum */
254     for (c = 1; c <= numCells; ++c) off[c] += off[c-1];
255     if (adjacency) {
256       PetscInt *tmp;
257 
258       ierr = PetscMalloc1(off[numCells], &adj);CHKERRQ(ierr);
259       ierr = PetscMalloc1(numCells+1, &tmp);CHKERRQ(ierr);
260       ierr = PetscMemcpy(tmp, off, (numCells+1) * sizeof(PetscInt));CHKERRQ(ierr);
261       /* Get neighboring cells */
262       for (f = fStart; f < fEnd; ++f) {
263         const PetscInt *support;
264         PetscInt        supportSize;
265         ierr = DMPlexGetSupportSize(dm, f, &supportSize);CHKERRQ(ierr);
266         ierr = DMPlexGetSupport(dm, f, &support);CHKERRQ(ierr);
267         if (supportSize == 2) {
268           PetscInt numChildren;
269 
270           ierr = DMPlexGetTreeChildren(dm,f,&numChildren,NULL);CHKERRQ(ierr);
271           if (!numChildren) {
272             adj[tmp[support[0]-cStart]++] = support[1];
273             adj[tmp[support[1]-cStart]++] = support[0];
274           }
275         }
276       }
277 #if defined(PETSC_USE_DEBUG)
278       for (c = 0; c < cEnd-cStart; ++c) if (tmp[c] != off[c+1]) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Offset %d != %d for cell %d", tmp[c], off[c], c+cStart);
279 #endif
280       ierr = PetscFree(tmp);CHKERRQ(ierr);
281     }
282     if (numVertices) *numVertices = numCells;
283     if (offsets)   *offsets   = off;
284     if (adjacency) *adjacency = adj;
285     PetscFunctionReturn(0);
286   }
287   /* Setup face recognition */
288   if (faceDepth == 1) {
289     PetscInt cornersSeen[30] = {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}; /* Could use PetscBT */
290 
291     for (c = cStart; c < cEnd; ++c) {
292       PetscInt corners;
293 
294       ierr = DMPlexGetConeSize(dm, c, &corners);CHKERRQ(ierr);
295       if (!cornersSeen[corners]) {
296         PetscInt nFV;
297 
298         if (numFaceCases >= maxFaceCases) SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Exceeded maximum number of face recognition cases");
299         cornersSeen[corners] = 1;
300 
301         ierr = DMPlexGetNumFaceVertices(dm, cellDim, corners, &nFV);CHKERRQ(ierr);
302 
303         numFaceVertices[numFaceCases++] = nFV;
304       }
305     }
306   }
307   ierr = PetscCalloc1(numCells+1, &off);CHKERRQ(ierr);
308   /* Count neighboring cells */
309   for (cell = cStart; cell < cEnd; ++cell) {
310     PetscInt numNeighbors = PETSC_DETERMINE, n;
311 
312     ierr = DMPlexGetAdjacency_Internal(dm, cell, PETSC_TRUE, PETSC_FALSE, PETSC_FALSE, &numNeighbors, &neighborCells);CHKERRQ(ierr);
313     /* Get meet with each cell, and check with recognizer (could optimize to check each pair only once) */
314     for (n = 0; n < numNeighbors; ++n) {
315       PetscInt        cellPair[2];
316       PetscBool       found    = faceDepth > 1 ? PETSC_TRUE : PETSC_FALSE;
317       PetscInt        meetSize = 0;
318       const PetscInt *meet    = NULL;
319 
320       cellPair[0] = cell; cellPair[1] = neighborCells[n];
321       if (cellPair[0] == cellPair[1]) continue;
322       if (!found) {
323         ierr = DMPlexGetMeet(dm, 2, cellPair, &meetSize, &meet);CHKERRQ(ierr);
324         if (meetSize) {
325           PetscInt f;
326 
327           for (f = 0; f < numFaceCases; ++f) {
328             if (numFaceVertices[f] == meetSize) {
329               found = PETSC_TRUE;
330               break;
331             }
332           }
333         }
334         ierr = DMPlexRestoreMeet(dm, 2, cellPair, &meetSize, &meet);CHKERRQ(ierr);
335       }
336       if (found) ++off[cell-cStart+1];
337     }
338   }
339   /* Prefix sum */
340   for (cell = 1; cell <= numCells; ++cell) off[cell] += off[cell-1];
341 
342   if (adjacency) {
343     ierr = PetscMalloc1(off[numCells], &adj);CHKERRQ(ierr);
344     /* Get neighboring cells */
345     for (cell = cStart; cell < cEnd; ++cell) {
346       PetscInt numNeighbors = PETSC_DETERMINE, n;
347       PetscInt cellOffset   = 0;
348 
349       ierr = DMPlexGetAdjacency_Internal(dm, cell, PETSC_TRUE, PETSC_FALSE, PETSC_FALSE, &numNeighbors, &neighborCells);CHKERRQ(ierr);
350       /* Get meet with each cell, and check with recognizer (could optimize to check each pair only once) */
351       for (n = 0; n < numNeighbors; ++n) {
352         PetscInt        cellPair[2];
353         PetscBool       found    = faceDepth > 1 ? PETSC_TRUE : PETSC_FALSE;
354         PetscInt        meetSize = 0;
355         const PetscInt *meet    = NULL;
356 
357         cellPair[0] = cell; cellPair[1] = neighborCells[n];
358         if (cellPair[0] == cellPair[1]) continue;
359         if (!found) {
360           ierr = DMPlexGetMeet(dm, 2, cellPair, &meetSize, &meet);CHKERRQ(ierr);
361           if (meetSize) {
362             PetscInt f;
363 
364             for (f = 0; f < numFaceCases; ++f) {
365               if (numFaceVertices[f] == meetSize) {
366                 found = PETSC_TRUE;
367                 break;
368               }
369             }
370           }
371           ierr = DMPlexRestoreMeet(dm, 2, cellPair, &meetSize, &meet);CHKERRQ(ierr);
372         }
373         if (found) {
374           adj[off[cell-cStart]+cellOffset] = neighborCells[n];
375           ++cellOffset;
376         }
377       }
378     }
379   }
380   ierr = PetscFree(neighborCells);CHKERRQ(ierr);
381   if (numVertices) *numVertices = numCells;
382   if (offsets)   *offsets   = off;
383   if (adjacency) *adjacency = adj;
384   PetscFunctionReturn(0);
385 }
386 
387 /*@C
388   PetscPartitionerRegister - Adds a new PetscPartitioner implementation
389 
390   Not Collective
391 
392   Input Parameters:
393 + name        - The name of a new user-defined creation routine
394 - create_func - The creation routine itself
395 
396   Notes:
397   PetscPartitionerRegister() may be called multiple times to add several user-defined PetscPartitioners
398 
399   Sample usage:
400 .vb
401     PetscPartitionerRegister("my_part", MyPetscPartitionerCreate);
402 .ve
403 
404   Then, your PetscPartitioner type can be chosen with the procedural interface via
405 .vb
406     PetscPartitionerCreate(MPI_Comm, PetscPartitioner *);
407     PetscPartitionerSetType(PetscPartitioner, "my_part");
408 .ve
409    or at runtime via the option
410 .vb
411     -petscpartitioner_type my_part
412 .ve
413 
414   Level: advanced
415 
416 .keywords: PetscPartitioner, register
417 .seealso: PetscPartitionerRegisterAll(), PetscPartitionerRegisterDestroy()
418 
419 @*/
420 PetscErrorCode PetscPartitionerRegister(const char sname[], PetscErrorCode (*function)(PetscPartitioner))
421 {
422   PetscErrorCode ierr;
423 
424   PetscFunctionBegin;
425   ierr = PetscFunctionListAdd(&PetscPartitionerList, sname, function);CHKERRQ(ierr);
426   PetscFunctionReturn(0);
427 }
428 
429 /*@C
430   PetscPartitionerSetType - Builds a particular PetscPartitioner
431 
432   Collective on PetscPartitioner
433 
434   Input Parameters:
435 + part - The PetscPartitioner object
436 - name - The kind of partitioner
437 
438   Options Database Key:
439 . -petscpartitioner_type <type> - Sets the PetscPartitioner type; use -help for a list of available types
440 
441   Level: intermediate
442 
443 .keywords: PetscPartitioner, set, type
444 .seealso: PetscPartitionerGetType(), PetscPartitionerCreate()
445 @*/
446 PetscErrorCode PetscPartitionerSetType(PetscPartitioner part, PetscPartitionerType name)
447 {
448   PetscErrorCode (*r)(PetscPartitioner);
449   PetscBool      match;
450   PetscErrorCode ierr;
451 
452   PetscFunctionBegin;
453   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
454   ierr = PetscObjectTypeCompare((PetscObject) part, name, &match);CHKERRQ(ierr);
455   if (match) PetscFunctionReturn(0);
456 
457   ierr = PetscPartitionerRegisterAll();CHKERRQ(ierr);
458   ierr = PetscFunctionListFind(PetscPartitionerList, name, &r);CHKERRQ(ierr);
459   if (!r) SETERRQ1(PetscObjectComm((PetscObject) part), PETSC_ERR_ARG_UNKNOWN_TYPE, "Unknown PetscPartitioner type: %s", name);
460 
461   if (part->ops->destroy) {
462     ierr              = (*part->ops->destroy)(part);CHKERRQ(ierr);
463   }
464   ierr = PetscMemzero(part->ops, sizeof(struct _PetscPartitionerOps));CHKERRQ(ierr);
465   ierr = (*r)(part);CHKERRQ(ierr);
466   ierr = PetscObjectChangeTypeName((PetscObject) part, name);CHKERRQ(ierr);
467   PetscFunctionReturn(0);
468 }
469 
470 /*@C
471   PetscPartitionerGetType - Gets the PetscPartitioner type name (as a string) from the object.
472 
473   Not Collective
474 
475   Input Parameter:
476 . part - The PetscPartitioner
477 
478   Output Parameter:
479 . name - The PetscPartitioner type name
480 
481   Level: intermediate
482 
483 .keywords: PetscPartitioner, get, type, name
484 .seealso: PetscPartitionerSetType(), PetscPartitionerCreate()
485 @*/
486 PetscErrorCode PetscPartitionerGetType(PetscPartitioner part, PetscPartitionerType *name)
487 {
488   PetscErrorCode ierr;
489 
490   PetscFunctionBegin;
491   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
492   PetscValidPointer(name, 2);
493   ierr = PetscPartitionerRegisterAll();CHKERRQ(ierr);
494   *name = ((PetscObject) part)->type_name;
495   PetscFunctionReturn(0);
496 }
497 
498 /*@C
499   PetscPartitionerView - Views a PetscPartitioner
500 
501   Collective on PetscPartitioner
502 
503   Input Parameter:
504 + part - the PetscPartitioner object to view
505 - v    - the viewer
506 
507   Level: developer
508 
509 .seealso: PetscPartitionerDestroy()
510 @*/
511 PetscErrorCode PetscPartitionerView(PetscPartitioner part, PetscViewer v)
512 {
513   PetscMPIInt    size;
514   PetscBool      isascii;
515   PetscErrorCode ierr;
516 
517   PetscFunctionBegin;
518   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
519   if (!v) {ierr = PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject) part), &v);CHKERRQ(ierr);}
520   ierr = PetscObjectTypeCompare((PetscObject) v, PETSCVIEWERASCII, &isascii);CHKERRQ(ierr);
521   if (isascii) {
522     ierr = MPI_Comm_size(PetscObjectComm((PetscObject) part), &size);CHKERRQ(ierr);
523     ierr = PetscViewerASCIIPrintf(v, "Graph Partitioner: %d MPI Process%s\n", size, size > 1 ? "es" : "");CHKERRQ(ierr);
524     ierr = PetscViewerASCIIPrintf(v, "  type: %s\n", part->hdr.type_name);CHKERRQ(ierr);
525     ierr = PetscViewerASCIIPushTab(v);CHKERRQ(ierr);
526     ierr = PetscViewerASCIIPrintf(v, "edge cut: %D\n", part->edgeCut);CHKERRQ(ierr);
527     ierr = PetscViewerASCIIPrintf(v, "balance:  %.2g\n", part->balance);CHKERRQ(ierr);
528     ierr = PetscViewerASCIIPopTab(v);CHKERRQ(ierr);
529   }
530   if (part->ops->view) {ierr = (*part->ops->view)(part, v);CHKERRQ(ierr);}
531   PetscFunctionReturn(0);
532 }
533 
534 static PetscErrorCode PetscPartitionerGetDefaultType(const char *currentType, const char **defaultType)
535 {
536   PetscFunctionBegin;
537   if (!currentType) {
538 #if defined(PETSC_HAVE_CHACO)
539     *defaultType = PETSCPARTITIONERCHACO;
540 #elif defined(PETSC_HAVE_PARMETIS)
541     *defaultType = PETSCPARTITIONERPARMETIS;
542 #elif defined(PETSC_HAVE_PTSCOTCH)
543     *defaultType = PETSCPARTITIONERPTSCOTCH;
544 #else
545     *defaultType = PETSCPARTITIONERSIMPLE;
546 #endif
547   } else {
548     *defaultType = currentType;
549   }
550   PetscFunctionReturn(0);
551 }
552 
553 /*@
554   PetscPartitionerSetFromOptions - sets parameters in a PetscPartitioner from the options database
555 
556   Collective on PetscPartitioner
557 
558   Input Parameter:
559 . part - the PetscPartitioner object to set options for
560 
561   Level: developer
562 
563 .seealso: PetscPartitionerView()
564 @*/
565 PetscErrorCode PetscPartitionerSetFromOptions(PetscPartitioner part)
566 {
567   const char    *defaultType;
568   char           name[256];
569   PetscBool      flg;
570   PetscErrorCode ierr;
571 
572   PetscFunctionBegin;
573   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
574   ierr = PetscPartitionerRegisterAll();CHKERRQ(ierr);
575   ierr = PetscPartitionerGetDefaultType(((PetscObject) part)->type_name,&defaultType);CHKERRQ(ierr);
576   ierr = PetscObjectOptionsBegin((PetscObject) part);CHKERRQ(ierr);
577   ierr = PetscOptionsFList("-petscpartitioner_type", "Graph partitioner", "PetscPartitionerSetType", PetscPartitionerList, defaultType, name, sizeof(name), &flg);CHKERRQ(ierr);
578   if (flg) {
579     ierr = PetscPartitionerSetType(part, name);CHKERRQ(ierr);
580   } else if (!((PetscObject) part)->type_name) {
581     ierr = PetscPartitionerSetType(part, defaultType);CHKERRQ(ierr);
582   }
583   if (part->ops->setfromoptions) {
584     ierr = (*part->ops->setfromoptions)(PetscOptionsObject,part);CHKERRQ(ierr);
585   }
586   ierr = PetscOptionsGetViewer(((PetscObject) part)->comm, ((PetscObject) part)->options, ((PetscObject) part)->prefix, "-petscpartitioner_view_graph", &part->viewerGraph, &part->formatGraph, &part->viewGraph);CHKERRQ(ierr);
587   /* process any options handlers added with PetscObjectAddOptionsHandler() */
588   ierr = PetscObjectProcessOptionsHandlers(PetscOptionsObject,(PetscObject) part);CHKERRQ(ierr);
589   ierr = PetscOptionsEnd();CHKERRQ(ierr);
590   PetscFunctionReturn(0);
591 }
592 
593 /*@C
594   PetscPartitionerSetUp - Construct data structures for the PetscPartitioner
595 
596   Collective on PetscPartitioner
597 
598   Input Parameter:
599 . part - the PetscPartitioner object to setup
600 
601   Level: developer
602 
603 .seealso: PetscPartitionerView(), PetscPartitionerDestroy()
604 @*/
605 PetscErrorCode PetscPartitionerSetUp(PetscPartitioner part)
606 {
607   PetscErrorCode ierr;
608 
609   PetscFunctionBegin;
610   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
611   if (part->ops->setup) {ierr = (*part->ops->setup)(part);CHKERRQ(ierr);}
612   PetscFunctionReturn(0);
613 }
614 
615 /*@
616   PetscPartitionerDestroy - Destroys a PetscPartitioner object
617 
618   Collective on PetscPartitioner
619 
620   Input Parameter:
621 . part - the PetscPartitioner object to destroy
622 
623   Level: developer
624 
625 .seealso: PetscPartitionerView()
626 @*/
627 PetscErrorCode PetscPartitionerDestroy(PetscPartitioner *part)
628 {
629   PetscErrorCode ierr;
630 
631   PetscFunctionBegin;
632   if (!*part) PetscFunctionReturn(0);
633   PetscValidHeaderSpecific((*part), PETSCPARTITIONER_CLASSID, 1);
634 
635   if (--((PetscObject)(*part))->refct > 0) {*part = 0; PetscFunctionReturn(0);}
636   ((PetscObject) (*part))->refct = 0;
637 
638   ierr = PetscViewerDestroy(&(*part)->viewerGraph);CHKERRQ(ierr);
639   if ((*part)->ops->destroy) {ierr = (*(*part)->ops->destroy)(*part);CHKERRQ(ierr);}
640   ierr = PetscHeaderDestroy(part);CHKERRQ(ierr);
641   PetscFunctionReturn(0);
642 }
643 
644 /*@
645   PetscPartitionerCreate - Creates an empty PetscPartitioner object. The type can then be set with PetscPartitionerSetType().
646 
647   Collective on MPI_Comm
648 
649   Input Parameter:
650 . comm - The communicator for the PetscPartitioner object
651 
652   Output Parameter:
653 . part - The PetscPartitioner object
654 
655   Level: beginner
656 
657 .seealso: PetscPartitionerSetType(), PETSCPARTITIONERCHACO, PETSCPARTITIONERPARMETIS, PETSCPARTITIONERSHELL, PETSCPARTITIONERSIMPLE, PETSCPARTITIONERGATHER
658 @*/
659 PetscErrorCode PetscPartitionerCreate(MPI_Comm comm, PetscPartitioner *part)
660 {
661   PetscPartitioner p;
662   const char       *partitionerType = NULL;
663   PetscErrorCode   ierr;
664 
665   PetscFunctionBegin;
666   PetscValidPointer(part, 2);
667   *part = NULL;
668   ierr = DMInitializePackage();CHKERRQ(ierr);
669 
670   ierr = PetscHeaderCreate(p, PETSCPARTITIONER_CLASSID, "PetscPartitioner", "Graph Partitioner", "PetscPartitioner", comm, PetscPartitionerDestroy, PetscPartitionerView);CHKERRQ(ierr);
671   ierr = PetscPartitionerGetDefaultType(NULL,&partitionerType);CHKERRQ(ierr);
672   ierr = PetscPartitionerSetType(p,partitionerType);CHKERRQ(ierr);
673 
674   p->edgeCut = 0;
675   p->balance = 0.0;
676 
677   *part = p;
678   PetscFunctionReturn(0);
679 }
680 
681 /*@
682   PetscPartitionerPartition - Create a non-overlapping partition of the cells in the mesh
683 
684   Collective on DM
685 
686   Input Parameters:
687 + part    - The PetscPartitioner
688 - dm      - The mesh DM
689 
690   Output Parameters:
691 + partSection     - The PetscSection giving the division of points by partition
692 - partition       - The list of points by partition
693 
694   Options Database:
695 . -petscpartitioner_view_graph - View the graph we are partitioning
696 
697   Note: Instead of cells, points at a given height can be partitioned by calling PetscPartitionerSetPointHeight()
698 
699   Level: developer
700 
701 .seealso DMPlexDistribute(), PetscPartitionerSetPointHeight(), PetscPartitionerCreate()
702 @*/
703 PetscErrorCode PetscPartitionerPartition(PetscPartitioner part, DM dm, PetscSection partSection, IS *partition)
704 {
705   PetscMPIInt    size;
706   PetscErrorCode ierr;
707 
708   PetscFunctionBegin;
709   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
710   PetscValidHeaderSpecific(dm, DM_CLASSID, 2);
711   PetscValidHeaderSpecific(partSection, PETSC_SECTION_CLASSID, 4);
712   PetscValidPointer(partition, 5);
713   ierr = MPI_Comm_size(PetscObjectComm((PetscObject) part), &size);CHKERRQ(ierr);
714   if (size == 1) {
715     PetscInt *points;
716     PetscInt  cStart, cEnd, c;
717 
718     ierr = DMPlexGetHeightStratum(dm, part->height, &cStart, &cEnd);CHKERRQ(ierr);
719     ierr = PetscSectionSetChart(partSection, 0, size);CHKERRQ(ierr);
720     ierr = PetscSectionSetDof(partSection, 0, cEnd-cStart);CHKERRQ(ierr);
721     ierr = PetscSectionSetUp(partSection);CHKERRQ(ierr);
722     ierr = PetscMalloc1(cEnd-cStart, &points);CHKERRQ(ierr);
723     for (c = cStart; c < cEnd; ++c) points[c] = c;
724     ierr = ISCreateGeneral(PetscObjectComm((PetscObject) part), cEnd-cStart, points, PETSC_OWN_POINTER, partition);CHKERRQ(ierr);
725     PetscFunctionReturn(0);
726   }
727   if (part->height == 0) {
728     PetscInt numVertices;
729     PetscInt *start     = NULL;
730     PetscInt *adjacency = NULL;
731     IS       globalNumbering;
732 
733     ierr = DMPlexCreatePartitionerGraph(dm, 0, &numVertices, &start, &adjacency, &globalNumbering);CHKERRQ(ierr);
734     if (part->viewGraph) {
735       PetscViewer viewer = part->viewerGraph;
736       PetscBool   isascii;
737       PetscInt    v, i;
738       PetscMPIInt rank;
739 
740       ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) viewer), &rank);CHKERRQ(ierr);
741       ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &isascii);CHKERRQ(ierr);
742       if (isascii) {
743         ierr = PetscViewerASCIIPushSynchronized(viewer);CHKERRQ(ierr);
744         ierr = PetscViewerASCIISynchronizedPrintf(viewer, "[%d]Nv: %D\n", rank, numVertices);CHKERRQ(ierr);
745         for (v = 0; v < numVertices; ++v) {
746           const PetscInt s = start[v];
747           const PetscInt e = start[v+1];
748 
749           ierr = PetscViewerASCIISynchronizedPrintf(viewer, "[%d]  ", rank);CHKERRQ(ierr);
750           for (i = s; i < e; ++i) {ierr = PetscViewerASCIISynchronizedPrintf(viewer, "%D ", adjacency[i]);CHKERRQ(ierr);}
751           ierr = PetscViewerASCIISynchronizedPrintf(viewer, "[%D-%D)\n", s, e);CHKERRQ(ierr);
752         }
753         ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
754         ierr = PetscViewerASCIIPopSynchronized(viewer);CHKERRQ(ierr);
755       }
756     }
757     if (!part->ops->partition) SETERRQ(PetscObjectComm((PetscObject) part), PETSC_ERR_ARG_WRONGSTATE, "PetscPartitioner has no type");
758     ierr = (*part->ops->partition)(part, dm, size, numVertices, start, adjacency, partSection, partition);CHKERRQ(ierr);
759     ierr = PetscFree(start);CHKERRQ(ierr);
760     ierr = PetscFree(adjacency);CHKERRQ(ierr);
761     if (globalNumbering) { /* partition is wrt global unique numbering: change this to be wrt local numbering */
762       const PetscInt *globalNum;
763       const PetscInt *partIdx;
764       PetscInt *map, cStart, cEnd;
765       PetscInt *adjusted, i, localSize, offset;
766       IS    newPartition;
767 
768       ierr = ISGetLocalSize(*partition,&localSize);CHKERRQ(ierr);
769       ierr = PetscMalloc1(localSize,&adjusted);CHKERRQ(ierr);
770       ierr = ISGetIndices(globalNumbering,&globalNum);CHKERRQ(ierr);
771       ierr = ISGetIndices(*partition,&partIdx);CHKERRQ(ierr);
772       ierr = PetscMalloc1(localSize,&map);CHKERRQ(ierr);
773       ierr = DMPlexGetHeightStratum(dm, part->height, &cStart, &cEnd);CHKERRQ(ierr);
774       for (i = cStart, offset = 0; i < cEnd; i++) {
775         if (globalNum[i - cStart] >= 0) map[offset++] = i;
776       }
777       for (i = 0; i < localSize; i++) {
778         adjusted[i] = map[partIdx[i]];
779       }
780       ierr = PetscFree(map);CHKERRQ(ierr);
781       ierr = ISRestoreIndices(*partition,&partIdx);CHKERRQ(ierr);
782       ierr = ISRestoreIndices(globalNumbering,&globalNum);CHKERRQ(ierr);
783       ierr = ISCreateGeneral(PETSC_COMM_SELF,localSize,adjusted,PETSC_OWN_POINTER,&newPartition);CHKERRQ(ierr);
784       ierr = ISDestroy(&globalNumbering);CHKERRQ(ierr);
785       ierr = ISDestroy(partition);CHKERRQ(ierr);
786       *partition = newPartition;
787     }
788   } else SETERRQ1(PetscObjectComm((PetscObject) part), PETSC_ERR_ARG_OUTOFRANGE, "Invalid height %D for points to partition", part->height);
789   ierr = PetscPartitionerViewFromOptions(part, NULL, "-petscpartitioner_view");CHKERRQ(ierr);
790   PetscFunctionReturn(0);
791 }
792 
793 static PetscErrorCode PetscPartitionerDestroy_Shell(PetscPartitioner part)
794 {
795   PetscPartitioner_Shell *p = (PetscPartitioner_Shell *) part->data;
796   PetscErrorCode          ierr;
797 
798   PetscFunctionBegin;
799   ierr = PetscSectionDestroy(&p->section);CHKERRQ(ierr);
800   ierr = ISDestroy(&p->partition);CHKERRQ(ierr);
801   ierr = PetscFree(p);CHKERRQ(ierr);
802   PetscFunctionReturn(0);
803 }
804 
805 static PetscErrorCode PetscPartitionerView_Shell_Ascii(PetscPartitioner part, PetscViewer viewer)
806 {
807   PetscPartitioner_Shell *p = (PetscPartitioner_Shell *) part->data;
808   PetscErrorCode          ierr;
809 
810   PetscFunctionBegin;
811   if (p->random) {
812     ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
813     ierr = PetscViewerASCIIPrintf(viewer, "using random partition\n");CHKERRQ(ierr);
814     ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
815   }
816   PetscFunctionReturn(0);
817 }
818 
819 static PetscErrorCode PetscPartitionerView_Shell(PetscPartitioner part, PetscViewer viewer)
820 {
821   PetscBool      iascii;
822   PetscErrorCode ierr;
823 
824   PetscFunctionBegin;
825   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
826   PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
827   ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);CHKERRQ(ierr);
828   if (iascii) {ierr = PetscPartitionerView_Shell_Ascii(part, viewer);CHKERRQ(ierr);}
829   PetscFunctionReturn(0);
830 }
831 
832 static PetscErrorCode PetscPartitionerSetFromOptions_Shell(PetscOptionItems *PetscOptionsObject, PetscPartitioner part)
833 {
834   PetscPartitioner_Shell *p = (PetscPartitioner_Shell *) part->data;
835   PetscErrorCode          ierr;
836 
837   PetscFunctionBegin;
838   ierr = PetscOptionsHead(PetscOptionsObject, "PetscPartitioner Shell Options");CHKERRQ(ierr);
839   ierr = PetscOptionsBool("-petscpartitioner_shell_random", "Use a random partition", "PetscPartitionerView", PETSC_FALSE, &p->random, NULL);CHKERRQ(ierr);
840   ierr = PetscOptionsTail();CHKERRQ(ierr);
841   PetscFunctionReturn(0);
842 }
843 
844 static PetscErrorCode PetscPartitionerPartition_Shell(PetscPartitioner part, DM dm, PetscInt nparts, PetscInt numVertices, PetscInt start[], PetscInt adjacency[], PetscSection partSection, IS *partition)
845 {
846   PetscPartitioner_Shell *p = (PetscPartitioner_Shell *) part->data;
847   PetscInt                np;
848   PetscErrorCode          ierr;
849 
850   PetscFunctionBegin;
851   if (p->random) {
852     PetscRandom r;
853     PetscInt   *sizes, *points, v, p;
854     PetscMPIInt rank;
855 
856     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRQ(ierr);
857     ierr = PetscRandomCreate(PETSC_COMM_SELF, &r);CHKERRQ(ierr);
858     ierr = PetscRandomSetInterval(r, 0.0, (PetscScalar) nparts);CHKERRQ(ierr);
859     ierr = PetscRandomSetFromOptions(r);CHKERRQ(ierr);
860     ierr = PetscCalloc2(nparts, &sizes, numVertices, &points);CHKERRQ(ierr);
861     for (v = 0; v < numVertices; ++v) {points[v] = v;}
862     for (p = 0; p < nparts; ++p) {sizes[p] = numVertices/nparts + (PetscInt) (p < numVertices % nparts);}
863     for (v = numVertices-1; v > 0; --v) {
864       PetscReal val;
865       PetscInt  w, tmp;
866 
867       ierr = PetscRandomSetInterval(r, 0.0, (PetscScalar) (v+1));CHKERRQ(ierr);
868       ierr = PetscRandomGetValueReal(r, &val);CHKERRQ(ierr);
869       w    = PetscFloorReal(val);
870       tmp       = points[v];
871       points[v] = points[w];
872       points[w] = tmp;
873     }
874     ierr = PetscRandomDestroy(&r);CHKERRQ(ierr);
875     ierr = PetscPartitionerShellSetPartition(part, nparts, sizes, points);CHKERRQ(ierr);
876     ierr = PetscFree2(sizes, points);CHKERRQ(ierr);
877   }
878   if (!p->section) SETERRQ(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Shell partitioner information not provided. Please call PetscPartitionerShellSetPartition()");
879   ierr = PetscSectionGetChart(p->section, NULL, &np);CHKERRQ(ierr);
880   if (nparts != np) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Number of requested partitions %d != configured partitions %d", nparts, np);
881   ierr = ISGetLocalSize(p->partition, &np);CHKERRQ(ierr);
882   if (numVertices != np) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Number of input vertices %d != configured vertices %d", numVertices, np);
883   ierr = PetscSectionCopy(p->section, partSection);CHKERRQ(ierr);
884   *partition = p->partition;
885   ierr = PetscObjectReference((PetscObject) p->partition);CHKERRQ(ierr);
886   PetscFunctionReturn(0);
887 }
888 
889 static PetscErrorCode PetscPartitionerInitialize_Shell(PetscPartitioner part)
890 {
891   PetscFunctionBegin;
892   part->ops->view           = PetscPartitionerView_Shell;
893   part->ops->setfromoptions = PetscPartitionerSetFromOptions_Shell;
894   part->ops->destroy        = PetscPartitionerDestroy_Shell;
895   part->ops->partition      = PetscPartitionerPartition_Shell;
896   PetscFunctionReturn(0);
897 }
898 
899 /*MC
900   PETSCPARTITIONERSHELL = "shell" - A PetscPartitioner object
901 
902   Level: intermediate
903 
904 .seealso: PetscPartitionerType, PetscPartitionerCreate(), PetscPartitionerSetType()
905 M*/
906 
907 PETSC_EXTERN PetscErrorCode PetscPartitionerCreate_Shell(PetscPartitioner part)
908 {
909   PetscPartitioner_Shell *p;
910   PetscErrorCode          ierr;
911 
912   PetscFunctionBegin;
913   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
914   ierr       = PetscNewLog(part, &p);CHKERRQ(ierr);
915   part->data = p;
916 
917   ierr = PetscPartitionerInitialize_Shell(part);CHKERRQ(ierr);
918   p->random = PETSC_FALSE;
919   PetscFunctionReturn(0);
920 }
921 
922 /*@C
923   PetscPartitionerShellSetPartition - Set an artifical partition for a mesh
924 
925   Collective on Part
926 
927   Input Parameters:
928 + part     - The PetscPartitioner
929 . size - The number of partitions
930 . sizes    - array of size size (or NULL) providing the number of points in each partition
931 - points   - array of size sum(sizes) (may be NULL iff sizes is NULL), a permutation of the points that groups those assigned to each partition in order (i.e., partition 0 first, partition 1 next, etc.)
932 
933   Level: developer
934 
935   Notes:
936 
937     It is safe to free the sizes and points arrays after use in this routine.
938 
939 .seealso DMPlexDistribute(), PetscPartitionerCreate()
940 @*/
941 PetscErrorCode PetscPartitionerShellSetPartition(PetscPartitioner part, PetscInt size, const PetscInt sizes[], const PetscInt points[])
942 {
943   PetscPartitioner_Shell *p = (PetscPartitioner_Shell *) part->data;
944   PetscInt                proc, numPoints;
945   PetscErrorCode          ierr;
946 
947   PetscFunctionBegin;
948   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
949   if (sizes)  {PetscValidPointer(sizes, 3);}
950   if (points) {PetscValidPointer(points, 4);}
951   ierr = PetscSectionDestroy(&p->section);CHKERRQ(ierr);
952   ierr = ISDestroy(&p->partition);CHKERRQ(ierr);
953   ierr = PetscSectionCreate(PetscObjectComm((PetscObject) part), &p->section);CHKERRQ(ierr);
954   ierr = PetscSectionSetChart(p->section, 0, size);CHKERRQ(ierr);
955   if (sizes) {
956     for (proc = 0; proc < size; ++proc) {
957       ierr = PetscSectionSetDof(p->section, proc, sizes[proc]);CHKERRQ(ierr);
958     }
959   }
960   ierr = PetscSectionSetUp(p->section);CHKERRQ(ierr);
961   ierr = PetscSectionGetStorageSize(p->section, &numPoints);CHKERRQ(ierr);
962   ierr = ISCreateGeneral(PetscObjectComm((PetscObject) part), numPoints, points, PETSC_COPY_VALUES, &p->partition);CHKERRQ(ierr);
963   PetscFunctionReturn(0);
964 }
965 
966 /*@
967   PetscPartitionerShellSetRandom - Set the flag to use a random partition
968 
969   Collective on Part
970 
971   Input Parameters:
972 + part   - The PetscPartitioner
973 - random - The flag to use a random partition
974 
975   Level: intermediate
976 
977 .seealso PetscPartitionerShellGetRandom(), PetscPartitionerCreate()
978 @*/
979 PetscErrorCode PetscPartitionerShellSetRandom(PetscPartitioner part, PetscBool random)
980 {
981   PetscPartitioner_Shell *p = (PetscPartitioner_Shell *) part->data;
982 
983   PetscFunctionBegin;
984   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
985   p->random = random;
986   PetscFunctionReturn(0);
987 }
988 
989 /*@
990   PetscPartitionerShellGetRandom - get the flag to use a random partition
991 
992   Collective on Part
993 
994   Input Parameter:
995 . part   - The PetscPartitioner
996 
997   Output Parameter
998 . random - The flag to use a random partition
999 
1000   Level: intermediate
1001 
1002 .seealso PetscPartitionerShellSetRandom(), PetscPartitionerCreate()
1003 @*/
1004 PetscErrorCode PetscPartitionerShellGetRandom(PetscPartitioner part, PetscBool *random)
1005 {
1006   PetscPartitioner_Shell *p = (PetscPartitioner_Shell *) part->data;
1007 
1008   PetscFunctionBegin;
1009   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
1010   PetscValidPointer(random, 2);
1011   *random = p->random;
1012   PetscFunctionReturn(0);
1013 }
1014 
1015 static PetscErrorCode PetscPartitionerDestroy_Simple(PetscPartitioner part)
1016 {
1017   PetscPartitioner_Simple *p = (PetscPartitioner_Simple *) part->data;
1018   PetscErrorCode          ierr;
1019 
1020   PetscFunctionBegin;
1021   ierr = PetscFree(p);CHKERRQ(ierr);
1022   PetscFunctionReturn(0);
1023 }
1024 
1025 static PetscErrorCode PetscPartitionerView_Simple_Ascii(PetscPartitioner part, PetscViewer viewer)
1026 {
1027   PetscFunctionBegin;
1028   PetscFunctionReturn(0);
1029 }
1030 
1031 static PetscErrorCode PetscPartitionerView_Simple(PetscPartitioner part, PetscViewer viewer)
1032 {
1033   PetscBool      iascii;
1034   PetscErrorCode ierr;
1035 
1036   PetscFunctionBegin;
1037   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
1038   PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
1039   ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);CHKERRQ(ierr);
1040   if (iascii) {ierr = PetscPartitionerView_Simple_Ascii(part, viewer);CHKERRQ(ierr);}
1041   PetscFunctionReturn(0);
1042 }
1043 
1044 static PetscErrorCode PetscPartitionerPartition_Simple(PetscPartitioner part, DM dm, PetscInt nparts, PetscInt numVertices, PetscInt start[], PetscInt adjacency[], PetscSection partSection, IS *partition)
1045 {
1046   MPI_Comm       comm;
1047   PetscInt       np;
1048   PetscMPIInt    size;
1049   PetscErrorCode ierr;
1050 
1051   PetscFunctionBegin;
1052   comm = PetscObjectComm((PetscObject)dm);
1053   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1054   ierr = PetscSectionSetChart(partSection, 0, nparts);CHKERRQ(ierr);
1055   ierr = ISCreateStride(PETSC_COMM_SELF, numVertices, 0, 1, partition);CHKERRQ(ierr);
1056   if (size == 1) {
1057     for (np = 0; np < nparts; ++np) {ierr = PetscSectionSetDof(partSection, np, numVertices/nparts + ((numVertices % nparts) > np));CHKERRQ(ierr);}
1058   }
1059   else {
1060     PetscMPIInt rank;
1061     PetscInt nvGlobal, *offsets, myFirst, myLast;
1062 
1063     ierr = PetscMalloc1(size+1,&offsets);CHKERRQ(ierr);
1064     offsets[0] = 0;
1065     ierr = MPI_Allgather(&numVertices,1,MPIU_INT,&offsets[1],1,MPIU_INT,comm);CHKERRQ(ierr);
1066     for (np = 2; np <= size; np++) {
1067       offsets[np] += offsets[np-1];
1068     }
1069     nvGlobal = offsets[size];
1070     ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1071     myFirst = offsets[rank];
1072     myLast  = offsets[rank + 1] - 1;
1073     ierr = PetscFree(offsets);CHKERRQ(ierr);
1074     if (numVertices) {
1075       PetscInt firstPart = 0, firstLargePart = 0;
1076       PetscInt lastPart = 0, lastLargePart = 0;
1077       PetscInt rem = nvGlobal % nparts;
1078       PetscInt pSmall = nvGlobal/nparts;
1079       PetscInt pBig = nvGlobal/nparts + 1;
1080 
1081 
1082       if (rem) {
1083         firstLargePart = myFirst / pBig;
1084         lastLargePart  = myLast  / pBig;
1085 
1086         if (firstLargePart < rem) {
1087           firstPart = firstLargePart;
1088         }
1089         else {
1090           firstPart = rem + (myFirst - (rem * pBig)) / pSmall;
1091         }
1092         if (lastLargePart < rem) {
1093           lastPart = lastLargePart;
1094         }
1095         else {
1096           lastPart = rem + (myLast - (rem * pBig)) / pSmall;
1097         }
1098       }
1099       else {
1100         firstPart = myFirst / (nvGlobal/nparts);
1101         lastPart  = myLast  / (nvGlobal/nparts);
1102       }
1103 
1104       for (np = firstPart; np <= lastPart; np++) {
1105         PetscInt PartStart =  np    * (nvGlobal/nparts) + PetscMin(nvGlobal % nparts,np);
1106         PetscInt PartEnd   = (np+1) * (nvGlobal/nparts) + PetscMin(nvGlobal % nparts,np+1);
1107 
1108         PartStart = PetscMax(PartStart,myFirst);
1109         PartEnd   = PetscMin(PartEnd,myLast+1);
1110         ierr = PetscSectionSetDof(partSection,np,PartEnd-PartStart);CHKERRQ(ierr);
1111       }
1112     }
1113   }
1114   ierr = PetscSectionSetUp(partSection);CHKERRQ(ierr);
1115   PetscFunctionReturn(0);
1116 }
1117 
1118 static PetscErrorCode PetscPartitionerInitialize_Simple(PetscPartitioner part)
1119 {
1120   PetscFunctionBegin;
1121   part->ops->view      = PetscPartitionerView_Simple;
1122   part->ops->destroy   = PetscPartitionerDestroy_Simple;
1123   part->ops->partition = PetscPartitionerPartition_Simple;
1124   PetscFunctionReturn(0);
1125 }
1126 
1127 /*MC
1128   PETSCPARTITIONERSIMPLE = "simple" - A PetscPartitioner object
1129 
1130   Level: intermediate
1131 
1132 .seealso: PetscPartitionerType, PetscPartitionerCreate(), PetscPartitionerSetType()
1133 M*/
1134 
1135 PETSC_EXTERN PetscErrorCode PetscPartitionerCreate_Simple(PetscPartitioner part)
1136 {
1137   PetscPartitioner_Simple *p;
1138   PetscErrorCode           ierr;
1139 
1140   PetscFunctionBegin;
1141   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
1142   ierr       = PetscNewLog(part, &p);CHKERRQ(ierr);
1143   part->data = p;
1144 
1145   ierr = PetscPartitionerInitialize_Simple(part);CHKERRQ(ierr);
1146   PetscFunctionReturn(0);
1147 }
1148 
1149 static PetscErrorCode PetscPartitionerDestroy_Gather(PetscPartitioner part)
1150 {
1151   PetscPartitioner_Gather *p = (PetscPartitioner_Gather *) part->data;
1152   PetscErrorCode          ierr;
1153 
1154   PetscFunctionBegin;
1155   ierr = PetscFree(p);CHKERRQ(ierr);
1156   PetscFunctionReturn(0);
1157 }
1158 
1159 static PetscErrorCode PetscPartitionerView_Gather_Ascii(PetscPartitioner part, PetscViewer viewer)
1160 {
1161   PetscFunctionBegin;
1162   PetscFunctionReturn(0);
1163 }
1164 
1165 static PetscErrorCode PetscPartitionerView_Gather(PetscPartitioner part, PetscViewer viewer)
1166 {
1167   PetscBool      iascii;
1168   PetscErrorCode ierr;
1169 
1170   PetscFunctionBegin;
1171   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
1172   PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
1173   ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);CHKERRQ(ierr);
1174   if (iascii) {ierr = PetscPartitionerView_Gather_Ascii(part, viewer);CHKERRQ(ierr);}
1175   PetscFunctionReturn(0);
1176 }
1177 
1178 static PetscErrorCode PetscPartitionerPartition_Gather(PetscPartitioner part, DM dm, PetscInt nparts, PetscInt numVertices, PetscInt start[], PetscInt adjacency[], PetscSection partSection, IS *partition)
1179 {
1180   PetscInt       np;
1181   PetscErrorCode ierr;
1182 
1183   PetscFunctionBegin;
1184   ierr = PetscSectionSetChart(partSection, 0, nparts);CHKERRQ(ierr);
1185   ierr = ISCreateStride(PETSC_COMM_SELF, numVertices, 0, 1, partition);CHKERRQ(ierr);
1186   ierr = PetscSectionSetDof(partSection,0,numVertices);CHKERRQ(ierr);
1187   for (np = 1; np < nparts; ++np) {ierr = PetscSectionSetDof(partSection, np, 0);CHKERRQ(ierr);}
1188   ierr = PetscSectionSetUp(partSection);CHKERRQ(ierr);
1189   PetscFunctionReturn(0);
1190 }
1191 
1192 static PetscErrorCode PetscPartitionerInitialize_Gather(PetscPartitioner part)
1193 {
1194   PetscFunctionBegin;
1195   part->ops->view      = PetscPartitionerView_Gather;
1196   part->ops->destroy   = PetscPartitionerDestroy_Gather;
1197   part->ops->partition = PetscPartitionerPartition_Gather;
1198   PetscFunctionReturn(0);
1199 }
1200 
1201 /*MC
1202   PETSCPARTITIONERGATHER = "gather" - A PetscPartitioner object
1203 
1204   Level: intermediate
1205 
1206 .seealso: PetscPartitionerType, PetscPartitionerCreate(), PetscPartitionerSetType()
1207 M*/
1208 
1209 PETSC_EXTERN PetscErrorCode PetscPartitionerCreate_Gather(PetscPartitioner part)
1210 {
1211   PetscPartitioner_Gather *p;
1212   PetscErrorCode           ierr;
1213 
1214   PetscFunctionBegin;
1215   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
1216   ierr       = PetscNewLog(part, &p);CHKERRQ(ierr);
1217   part->data = p;
1218 
1219   ierr = PetscPartitionerInitialize_Gather(part);CHKERRQ(ierr);
1220   PetscFunctionReturn(0);
1221 }
1222 
1223 
1224 static PetscErrorCode PetscPartitionerDestroy_Chaco(PetscPartitioner part)
1225 {
1226   PetscPartitioner_Chaco *p = (PetscPartitioner_Chaco *) part->data;
1227   PetscErrorCode          ierr;
1228 
1229   PetscFunctionBegin;
1230   ierr = PetscFree(p);CHKERRQ(ierr);
1231   PetscFunctionReturn(0);
1232 }
1233 
1234 static PetscErrorCode PetscPartitionerView_Chaco_Ascii(PetscPartitioner part, PetscViewer viewer)
1235 {
1236   PetscFunctionBegin;
1237   PetscFunctionReturn(0);
1238 }
1239 
1240 static PetscErrorCode PetscPartitionerView_Chaco(PetscPartitioner part, PetscViewer viewer)
1241 {
1242   PetscBool      iascii;
1243   PetscErrorCode ierr;
1244 
1245   PetscFunctionBegin;
1246   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
1247   PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
1248   ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);CHKERRQ(ierr);
1249   if (iascii) {ierr = PetscPartitionerView_Chaco_Ascii(part, viewer);CHKERRQ(ierr);}
1250   PetscFunctionReturn(0);
1251 }
1252 
1253 #if defined(PETSC_HAVE_CHACO)
1254 #if defined(PETSC_HAVE_UNISTD_H)
1255 #include <unistd.h>
1256 #endif
1257 #if defined(PETSC_HAVE_CHACO_INT_ASSIGNMENT)
1258 #include <chaco.h>
1259 #else
1260 /* Older versions of Chaco do not have an include file */
1261 PETSC_EXTERN int interface(int nvtxs, int *start, int *adjacency, int *vwgts,
1262                        float *ewgts, float *x, float *y, float *z, char *outassignname,
1263                        char *outfilename, short *assignment, int architecture, int ndims_tot,
1264                        int mesh_dims[3], double *goal, int global_method, int local_method,
1265                        int rqi_flag, int vmax, int ndims, double eigtol, long seed);
1266 #endif
1267 extern int FREE_GRAPH;
1268 #endif
1269 
1270 static PetscErrorCode PetscPartitionerPartition_Chaco(PetscPartitioner part, DM dm, PetscInt nparts, PetscInt numVertices, PetscInt start[], PetscInt adjacency[], PetscSection partSection, IS *partition)
1271 {
1272 #if defined(PETSC_HAVE_CHACO)
1273   enum {DEFAULT_METHOD = 1, INERTIAL_METHOD = 3};
1274   MPI_Comm       comm;
1275   int            nvtxs          = numVertices; /* number of vertices in full graph */
1276   int           *vwgts          = NULL;   /* weights for all vertices */
1277   float         *ewgts          = NULL;   /* weights for all edges */
1278   float         *x              = NULL, *y = NULL, *z = NULL; /* coordinates for inertial method */
1279   char          *outassignname  = NULL;   /*  name of assignment output file */
1280   char          *outfilename    = NULL;   /* output file name */
1281   int            architecture   = 1;      /* 0 => hypercube, d => d-dimensional mesh */
1282   int            ndims_tot      = 0;      /* total number of cube dimensions to divide */
1283   int            mesh_dims[3];            /* dimensions of mesh of processors */
1284   double        *goal          = NULL;    /* desired set sizes for each set */
1285   int            global_method = 1;       /* global partitioning algorithm */
1286   int            local_method  = 1;       /* local partitioning algorithm */
1287   int            rqi_flag      = 0;       /* should I use RQI/Symmlq eigensolver? */
1288   int            vmax          = 200;     /* how many vertices to coarsen down to? */
1289   int            ndims         = 1;       /* number of eigenvectors (2^d sets) */
1290   double         eigtol        = 0.001;   /* tolerance on eigenvectors */
1291   long           seed          = 123636512; /* for random graph mutations */
1292 #if defined(PETSC_HAVE_CHACO_INT_ASSIGNMENT)
1293   int           *assignment;              /* Output partition */
1294 #else
1295   short int     *assignment;              /* Output partition */
1296 #endif
1297   int            fd_stdout, fd_pipe[2];
1298   PetscInt      *points;
1299   int            i, v, p;
1300   PetscErrorCode ierr;
1301 
1302   PetscFunctionBegin;
1303   ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
1304 #if defined (PETSC_USE_DEBUG)
1305   {
1306     int ival,isum;
1307     PetscBool distributed;
1308 
1309     ival = (numVertices > 0);
1310     ierr = MPI_Allreduce(&ival, &isum, 1, MPI_INT, MPI_SUM, comm);CHKERRQ(ierr);
1311     distributed = (isum > 1) ? PETSC_TRUE : PETSC_FALSE;
1312     if (distributed) SETERRQ(comm, PETSC_ERR_SUP, "Chaco cannot partition a distributed graph");
1313   }
1314 #endif
1315   if (!numVertices) {
1316     ierr = PetscSectionSetChart(partSection, 0, nparts);CHKERRQ(ierr);
1317     ierr = PetscSectionSetUp(partSection);CHKERRQ(ierr);
1318     ierr = ISCreateGeneral(comm, 0, NULL, PETSC_OWN_POINTER, partition);CHKERRQ(ierr);
1319     PetscFunctionReturn(0);
1320   }
1321   FREE_GRAPH = 0;                         /* Do not let Chaco free my memory */
1322   for (i = 0; i < start[numVertices]; ++i) ++adjacency[i];
1323 
1324   if (global_method == INERTIAL_METHOD) {
1325     /* manager.createCellCoordinates(nvtxs, &x, &y, &z); */
1326     SETERRQ(comm, PETSC_ERR_SUP, "Inertial partitioning not yet supported");
1327   }
1328   mesh_dims[0] = nparts;
1329   mesh_dims[1] = 1;
1330   mesh_dims[2] = 1;
1331   ierr = PetscMalloc1(nvtxs, &assignment);CHKERRQ(ierr);
1332   /* Chaco outputs to stdout. We redirect this to a buffer. */
1333   /* TODO: check error codes for UNIX calls */
1334 #if defined(PETSC_HAVE_UNISTD_H)
1335   {
1336     int piperet;
1337     piperet = pipe(fd_pipe);
1338     if (piperet) SETERRQ(comm,PETSC_ERR_SYS,"Could not create pipe");
1339     fd_stdout = dup(1);
1340     close(1);
1341     dup2(fd_pipe[1], 1);
1342   }
1343 #endif
1344   ierr = interface(nvtxs, (int*) start, (int*) adjacency, vwgts, ewgts, x, y, z, outassignname, outfilename,
1345                    assignment, architecture, ndims_tot, mesh_dims, goal, global_method, local_method, rqi_flag,
1346                    vmax, ndims, eigtol, seed);
1347 #if defined(PETSC_HAVE_UNISTD_H)
1348   {
1349     char msgLog[10000];
1350     int  count;
1351 
1352     fflush(stdout);
1353     count = read(fd_pipe[0], msgLog, (10000-1)*sizeof(char));
1354     if (count < 0) count = 0;
1355     msgLog[count] = 0;
1356     close(1);
1357     dup2(fd_stdout, 1);
1358     close(fd_stdout);
1359     close(fd_pipe[0]);
1360     close(fd_pipe[1]);
1361     if (ierr) SETERRQ1(comm, PETSC_ERR_LIB, "Error in Chaco library: %s", msgLog);
1362   }
1363 #else
1364   if (ierr) SETERRQ1(comm, PETSC_ERR_LIB, "Error in Chaco library: %s", "error in stdout");
1365 #endif
1366   /* Convert to PetscSection+IS */
1367   ierr = PetscSectionSetChart(partSection, 0, nparts);CHKERRQ(ierr);
1368   for (v = 0; v < nvtxs; ++v) {
1369     ierr = PetscSectionAddDof(partSection, assignment[v], 1);CHKERRQ(ierr);
1370   }
1371   ierr = PetscSectionSetUp(partSection);CHKERRQ(ierr);
1372   ierr = PetscMalloc1(nvtxs, &points);CHKERRQ(ierr);
1373   for (p = 0, i = 0; p < nparts; ++p) {
1374     for (v = 0; v < nvtxs; ++v) {
1375       if (assignment[v] == p) points[i++] = v;
1376     }
1377   }
1378   if (i != nvtxs) SETERRQ2(comm, PETSC_ERR_PLIB, "Number of points %D should be %D", i, nvtxs);
1379   ierr = ISCreateGeneral(comm, nvtxs, points, PETSC_OWN_POINTER, partition);CHKERRQ(ierr);
1380   if (global_method == INERTIAL_METHOD) {
1381     /* manager.destroyCellCoordinates(nvtxs, &x, &y, &z); */
1382   }
1383   ierr = PetscFree(assignment);CHKERRQ(ierr);
1384   for (i = 0; i < start[numVertices]; ++i) --adjacency[i];
1385   PetscFunctionReturn(0);
1386 #else
1387   SETERRQ(PetscObjectComm((PetscObject) part), PETSC_ERR_SUP, "Mesh partitioning needs external package support.\nPlease reconfigure with --download-chaco.");
1388 #endif
1389 }
1390 
1391 static PetscErrorCode PetscPartitionerInitialize_Chaco(PetscPartitioner part)
1392 {
1393   PetscFunctionBegin;
1394   part->ops->view      = PetscPartitionerView_Chaco;
1395   part->ops->destroy   = PetscPartitionerDestroy_Chaco;
1396   part->ops->partition = PetscPartitionerPartition_Chaco;
1397   PetscFunctionReturn(0);
1398 }
1399 
1400 /*MC
1401   PETSCPARTITIONERCHACO = "chaco" - A PetscPartitioner object using the Chaco library
1402 
1403   Level: intermediate
1404 
1405 .seealso: PetscPartitionerType, PetscPartitionerCreate(), PetscPartitionerSetType()
1406 M*/
1407 
1408 PETSC_EXTERN PetscErrorCode PetscPartitionerCreate_Chaco(PetscPartitioner part)
1409 {
1410   PetscPartitioner_Chaco *p;
1411   PetscErrorCode          ierr;
1412 
1413   PetscFunctionBegin;
1414   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
1415   ierr       = PetscNewLog(part, &p);CHKERRQ(ierr);
1416   part->data = p;
1417 
1418   ierr = PetscPartitionerInitialize_Chaco(part);CHKERRQ(ierr);
1419   ierr = PetscCitationsRegister(ChacoPartitionerCitation, &ChacoPartitionercite);CHKERRQ(ierr);
1420   PetscFunctionReturn(0);
1421 }
1422 
1423 static const char *ptypes[] = {"kway", "rb"};
1424 
1425 static PetscErrorCode PetscPartitionerDestroy_ParMetis(PetscPartitioner part)
1426 {
1427   PetscPartitioner_ParMetis *p = (PetscPartitioner_ParMetis *) part->data;
1428   PetscErrorCode             ierr;
1429 
1430   PetscFunctionBegin;
1431   ierr = PetscFree(p);CHKERRQ(ierr);
1432   PetscFunctionReturn(0);
1433 }
1434 
1435 static PetscErrorCode PetscPartitionerView_ParMetis_Ascii(PetscPartitioner part, PetscViewer viewer)
1436 {
1437   PetscPartitioner_ParMetis *p = (PetscPartitioner_ParMetis *) part->data;
1438   PetscErrorCode             ierr;
1439 
1440   PetscFunctionBegin;
1441   ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
1442   ierr = PetscViewerASCIIPrintf(viewer, "ParMetis type: %s\n", ptypes[p->ptype]);CHKERRQ(ierr);
1443   ierr = PetscViewerASCIIPrintf(viewer, "load imbalance ratio %g\n", (double) p->imbalanceRatio);CHKERRQ(ierr);
1444   ierr = PetscViewerASCIIPrintf(viewer, "debug flag %D\n", p->debugFlag);CHKERRQ(ierr);
1445   ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
1446   PetscFunctionReturn(0);
1447 }
1448 
1449 static PetscErrorCode PetscPartitionerView_ParMetis(PetscPartitioner part, PetscViewer viewer)
1450 {
1451   PetscBool      iascii;
1452   PetscErrorCode ierr;
1453 
1454   PetscFunctionBegin;
1455   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
1456   PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
1457   ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);CHKERRQ(ierr);
1458   if (iascii) {ierr = PetscPartitionerView_ParMetis_Ascii(part, viewer);CHKERRQ(ierr);}
1459   PetscFunctionReturn(0);
1460 }
1461 
1462 static PetscErrorCode PetscPartitionerSetFromOptions_ParMetis(PetscOptionItems *PetscOptionsObject, PetscPartitioner part)
1463 {
1464   PetscPartitioner_ParMetis *p = (PetscPartitioner_ParMetis *) part->data;
1465   PetscErrorCode            ierr;
1466 
1467   PetscFunctionBegin;
1468   ierr = PetscOptionsHead(PetscOptionsObject, "PetscPartitioner ParMetis Options");CHKERRQ(ierr);
1469   ierr = PetscOptionsEList("-petscpartitioner_parmetis_type", "Partitioning method", "", ptypes, 2, ptypes[p->ptype], &p->ptype, NULL);CHKERRQ(ierr);
1470   ierr = PetscOptionsReal("-petscpartitioner_parmetis_imbalance_ratio", "Load imbalance ratio limit", "", p->imbalanceRatio, &p->imbalanceRatio, NULL);CHKERRQ(ierr);
1471   ierr = PetscOptionsInt("-petscpartitioner_parmetis_debug", "Debugging flag", "", p->debugFlag, &p->debugFlag, NULL);CHKERRQ(ierr);
1472   ierr = PetscOptionsTail();CHKERRQ(ierr);
1473   PetscFunctionReturn(0);
1474 }
1475 
1476 #if defined(PETSC_HAVE_PARMETIS)
1477 #include <parmetis.h>
1478 #endif
1479 
1480 static PetscErrorCode PetscPartitionerPartition_ParMetis(PetscPartitioner part, DM dm, PetscInt nparts, PetscInt numVertices, PetscInt start[], PetscInt adjacency[], PetscSection partSection, IS *partition)
1481 {
1482 #if defined(PETSC_HAVE_PARMETIS)
1483   PetscPartitioner_ParMetis *pm = (PetscPartitioner_ParMetis *) part->data;
1484   MPI_Comm       comm;
1485   PetscSection   section;
1486   PetscInt       nvtxs       = numVertices; /* The number of vertices in full graph */
1487   PetscInt      *vtxdist;                   /* Distribution of vertices across processes */
1488   PetscInt      *xadj        = start;       /* Start of edge list for each vertex */
1489   PetscInt      *adjncy      = adjacency;   /* Edge lists for all vertices */
1490   PetscInt      *vwgt        = NULL;        /* Vertex weights */
1491   PetscInt      *adjwgt      = NULL;        /* Edge weights */
1492   PetscInt       wgtflag     = 0;           /* Indicates which weights are present */
1493   PetscInt       numflag     = 0;           /* Indicates initial offset (0 or 1) */
1494   PetscInt       ncon        = 1;           /* The number of weights per vertex */
1495   PetscInt       metis_ptype = pm->ptype;   /* kway or recursive bisection */
1496   real_t        *tpwgts;                    /* The fraction of vertex weights assigned to each partition */
1497   real_t        *ubvec;                     /* The balance intolerance for vertex weights */
1498   PetscInt       options[64];               /* Options */
1499   /* Outputs */
1500   PetscInt       v, i, *assignment, *points;
1501   PetscMPIInt    size, rank, p;
1502   PetscErrorCode ierr;
1503 
1504   PetscFunctionBegin;
1505   ierr = PetscObjectGetComm((PetscObject) part, &comm);CHKERRQ(ierr);
1506   ierr = MPI_Comm_size(comm, &size);CHKERRQ(ierr);
1507   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
1508   /* Calculate vertex distribution */
1509   ierr = PetscMalloc5(size+1,&vtxdist,nparts*ncon,&tpwgts,ncon,&ubvec,nvtxs,&assignment,nvtxs,&vwgt);CHKERRQ(ierr);
1510   vtxdist[0] = 0;
1511   ierr = MPI_Allgather(&nvtxs, 1, MPIU_INT, &vtxdist[1], 1, MPIU_INT, comm);CHKERRQ(ierr);
1512   for (p = 2; p <= size; ++p) {
1513     vtxdist[p] += vtxdist[p-1];
1514   }
1515   /* Calculate partition weights */
1516   for (p = 0; p < nparts; ++p) {
1517     tpwgts[p] = 1.0/nparts;
1518   }
1519   ubvec[0] = pm->imbalanceRatio;
1520   /* Weight cells by dofs on cell by default */
1521   ierr = DMGetSection(dm, &section);CHKERRQ(ierr);
1522   if (section) {
1523     PetscInt cStart, cEnd, dof;
1524 
1525     ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1526     for (v = cStart; v < cEnd; ++v) {
1527       ierr = PetscSectionGetDof(section, v, &dof);CHKERRQ(ierr);
1528       /* WARNING: Assumes that meshes with overlap have the overlapped cells at the end of the stratum. */
1529       /* To do this properly, we should use the cell numbering created in DMPlexCreatePartitionerGraph. */
1530       if (v-cStart < numVertices) vwgt[v-cStart] = PetscMax(dof, 1);
1531     }
1532   } else {
1533     for (v = 0; v < nvtxs; ++v) vwgt[v] = 1;
1534   }
1535   wgtflag |= 2; /* have weights on graph vertices */
1536 
1537   if (nparts == 1) {
1538     ierr = PetscMemzero(assignment, nvtxs * sizeof(PetscInt));CHKERRQ(ierr);
1539   } else {
1540     for (p = 0; !vtxdist[p+1] && p < size; ++p);
1541     if (vtxdist[p+1] == vtxdist[size]) {
1542       if (rank == p) {
1543         ierr = METIS_SetDefaultOptions(options); /* initialize all defaults */
1544         if (ierr != METIS_OK) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in METIS_SetDefaultOptions()");
1545         if (metis_ptype == 1) {
1546           PetscStackPush("METIS_PartGraphRecursive");
1547           ierr = METIS_PartGraphRecursive(&nvtxs, &ncon, xadj, adjncy, vwgt, NULL, adjwgt, &nparts, tpwgts, ubvec, options, &part->edgeCut, assignment);
1548           PetscStackPop;
1549           if (ierr != METIS_OK) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in METIS_PartGraphRecursive()");
1550         } else {
1551           /*
1552            It would be nice to activate the two options below, but they would need some actual testing.
1553            - Turning on these options may exercise path of the METIS code that have bugs and may break production runs.
1554            - If CONTIG is set to 1, METIS will exit with error if the graph is disconnected, despite the manual saying the option is ignored in such case.
1555           */
1556           /* options[METIS_OPTION_CONTIG]  = 1; */ /* try to produce partitions that are contiguous */
1557           /* options[METIS_OPTION_MINCONN] = 1; */ /* minimize the maximum degree of the subdomain graph */
1558           PetscStackPush("METIS_PartGraphKway");
1559           ierr = METIS_PartGraphKway(&nvtxs, &ncon, xadj, adjncy, vwgt, NULL, adjwgt, &nparts, tpwgts, ubvec, options, &part->edgeCut, assignment);
1560           PetscStackPop;
1561           if (ierr != METIS_OK) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in METIS_PartGraphKway()");
1562         }
1563       }
1564     } else {
1565       options[0] = 1;
1566       options[1] = pm->debugFlag;
1567       PetscStackPush("ParMETIS_V3_PartKway");
1568       ierr = ParMETIS_V3_PartKway(vtxdist, xadj, adjncy, vwgt, adjwgt, &wgtflag, &numflag, &ncon, &nparts, tpwgts, ubvec, options, &part->edgeCut, assignment, &comm);
1569       PetscStackPop;
1570       if (ierr != METIS_OK) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_LIB, "Error %d in ParMETIS_V3_PartKway()", ierr);
1571     }
1572   }
1573   /* Convert to PetscSection+IS */
1574   ierr = PetscSectionSetChart(partSection, 0, nparts);CHKERRQ(ierr);
1575   for (v = 0; v < nvtxs; ++v) {ierr = PetscSectionAddDof(partSection, assignment[v], 1);CHKERRQ(ierr);}
1576   ierr = PetscSectionSetUp(partSection);CHKERRQ(ierr);
1577   ierr = PetscMalloc1(nvtxs, &points);CHKERRQ(ierr);
1578   for (p = 0, i = 0; p < nparts; ++p) {
1579     for (v = 0; v < nvtxs; ++v) {
1580       if (assignment[v] == p) points[i++] = v;
1581     }
1582   }
1583   if (i != nvtxs) SETERRQ2(comm, PETSC_ERR_PLIB, "Number of points %D should be %D", i, nvtxs);
1584   ierr = ISCreateGeneral(comm, nvtxs, points, PETSC_OWN_POINTER, partition);CHKERRQ(ierr);
1585   ierr = PetscFree5(vtxdist,tpwgts,ubvec,assignment,vwgt);CHKERRQ(ierr);
1586   PetscFunctionReturn(0);
1587 #else
1588   SETERRQ(PetscObjectComm((PetscObject) part), PETSC_ERR_SUP, "Mesh partitioning needs external package support.\nPlease reconfigure with --download-parmetis.");
1589 #endif
1590 }
1591 
1592 static PetscErrorCode PetscPartitionerInitialize_ParMetis(PetscPartitioner part)
1593 {
1594   PetscFunctionBegin;
1595   part->ops->view           = PetscPartitionerView_ParMetis;
1596   part->ops->setfromoptions = PetscPartitionerSetFromOptions_ParMetis;
1597   part->ops->destroy        = PetscPartitionerDestroy_ParMetis;
1598   part->ops->partition      = PetscPartitionerPartition_ParMetis;
1599   PetscFunctionReturn(0);
1600 }
1601 
1602 /*MC
1603   PETSCPARTITIONERPARMETIS = "parmetis" - A PetscPartitioner object using the ParMetis library
1604 
1605   Level: intermediate
1606 
1607 .seealso: PetscPartitionerType, PetscPartitionerCreate(), PetscPartitionerSetType()
1608 M*/
1609 
1610 PETSC_EXTERN PetscErrorCode PetscPartitionerCreate_ParMetis(PetscPartitioner part)
1611 {
1612   PetscPartitioner_ParMetis *p;
1613   PetscErrorCode          ierr;
1614 
1615   PetscFunctionBegin;
1616   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
1617   ierr       = PetscNewLog(part, &p);CHKERRQ(ierr);
1618   part->data = p;
1619 
1620   p->ptype          = 0;
1621   p->imbalanceRatio = 1.05;
1622   p->debugFlag      = 0;
1623 
1624   ierr = PetscPartitionerInitialize_ParMetis(part);CHKERRQ(ierr);
1625   ierr = PetscCitationsRegister(ParMetisPartitionerCitation, &ParMetisPartitionercite);CHKERRQ(ierr);
1626   PetscFunctionReturn(0);
1627 }
1628 
1629 
1630 PetscBool PTScotchPartitionercite = PETSC_FALSE;
1631 const char PTScotchPartitionerCitation[] =
1632   "@article{PTSCOTCH,\n"
1633   "  author  = {C. Chevalier and F. Pellegrini},\n"
1634   "  title   = {{PT-SCOTCH}: a tool for efficient parallel graph ordering},\n"
1635   "  journal = {Parallel Computing},\n"
1636   "  volume  = {34},\n"
1637   "  number  = {6},\n"
1638   "  pages   = {318--331},\n"
1639   "  year    = {2008},\n"
1640   "  doi     = {https://doi.org/10.1016/j.parco.2007.12.001}\n"
1641   "}\n";
1642 
1643 typedef struct {
1644   PetscInt  strategy;
1645   PetscReal imbalance;
1646 } PetscPartitioner_PTScotch;
1647 
1648 static const char *const
1649 PTScotchStrategyList[] = {
1650   "DEFAULT",
1651   "QUALITY",
1652   "SPEED",
1653   "BALANCE",
1654   "SAFETY",
1655   "SCALABILITY",
1656   "RECURSIVE",
1657   "REMAP"
1658 };
1659 
1660 #if defined(PETSC_HAVE_PTSCOTCH)
1661 
1662 EXTERN_C_BEGIN
1663 #include <ptscotch.h>
1664 EXTERN_C_END
1665 
1666 #define CHKERRPTSCOTCH(ierr) do { if (ierr) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error calling PT-Scotch library"); } while(0)
1667 
1668 static int PTScotch_Strategy(PetscInt strategy)
1669 {
1670   switch (strategy) {
1671   case  0: return SCOTCH_STRATDEFAULT;
1672   case  1: return SCOTCH_STRATQUALITY;
1673   case  2: return SCOTCH_STRATSPEED;
1674   case  3: return SCOTCH_STRATBALANCE;
1675   case  4: return SCOTCH_STRATSAFETY;
1676   case  5: return SCOTCH_STRATSCALABILITY;
1677   case  6: return SCOTCH_STRATRECURSIVE;
1678   case  7: return SCOTCH_STRATREMAP;
1679   default: return SCOTCH_STRATDEFAULT;
1680   }
1681 }
1682 
1683 
1684 static PetscErrorCode PTScotch_PartGraph_Seq(SCOTCH_Num strategy, double imbalance, SCOTCH_Num n, SCOTCH_Num xadj[], SCOTCH_Num adjncy[],
1685                                              SCOTCH_Num vtxwgt[], SCOTCH_Num adjwgt[], SCOTCH_Num nparts, SCOTCH_Num part[])
1686 {
1687   SCOTCH_Graph   grafdat;
1688   SCOTCH_Strat   stradat;
1689   SCOTCH_Num     vertnbr = n;
1690   SCOTCH_Num     edgenbr = xadj[n];
1691   SCOTCH_Num*    velotab = vtxwgt;
1692   SCOTCH_Num*    edlotab = adjwgt;
1693   SCOTCH_Num     flagval = strategy;
1694   double         kbalval = imbalance;
1695   PetscErrorCode ierr;
1696 
1697   PetscFunctionBegin;
1698   {
1699     PetscBool flg = PETSC_TRUE;
1700     ierr = PetscOptionsGetBool(NULL, NULL, "-petscpartititoner_ptscotch_vertex_weight", &flg, NULL);CHKERRQ(ierr);
1701     if (!flg) velotab = NULL;
1702   }
1703   ierr = SCOTCH_graphInit(&grafdat);CHKERRPTSCOTCH(ierr);
1704   ierr = SCOTCH_graphBuild(&grafdat, 0, vertnbr, xadj, xadj + 1, velotab, NULL, edgenbr, adjncy, edlotab);CHKERRPTSCOTCH(ierr);
1705   ierr = SCOTCH_stratInit(&stradat);CHKERRPTSCOTCH(ierr);
1706   ierr = SCOTCH_stratGraphMapBuild(&stradat, flagval, nparts, kbalval);CHKERRPTSCOTCH(ierr);
1707 #if defined(PETSC_USE_DEBUG)
1708   ierr = SCOTCH_graphCheck(&grafdat);CHKERRPTSCOTCH(ierr);
1709 #endif
1710   ierr = SCOTCH_graphPart(&grafdat, nparts, &stradat, part);CHKERRPTSCOTCH(ierr);
1711   SCOTCH_stratExit(&stradat);
1712   SCOTCH_graphExit(&grafdat);
1713   PetscFunctionReturn(0);
1714 }
1715 
1716 static PetscErrorCode PTScotch_PartGraph_MPI(SCOTCH_Num strategy, double imbalance, SCOTCH_Num vtxdist[], SCOTCH_Num xadj[], SCOTCH_Num adjncy[],
1717                                              SCOTCH_Num vtxwgt[], SCOTCH_Num adjwgt[], SCOTCH_Num nparts, SCOTCH_Num part[], MPI_Comm comm)
1718 {
1719   PetscMPIInt     procglbnbr;
1720   PetscMPIInt     proclocnum;
1721   SCOTCH_Arch     archdat;
1722   SCOTCH_Dgraph   grafdat;
1723   SCOTCH_Dmapping mappdat;
1724   SCOTCH_Strat    stradat;
1725   SCOTCH_Num      vertlocnbr;
1726   SCOTCH_Num      edgelocnbr;
1727   SCOTCH_Num*     veloloctab = vtxwgt;
1728   SCOTCH_Num*     edloloctab = adjwgt;
1729   SCOTCH_Num      flagval = strategy;
1730   double          kbalval = imbalance;
1731   PetscErrorCode  ierr;
1732 
1733   PetscFunctionBegin;
1734   {
1735     PetscBool flg = PETSC_TRUE;
1736     ierr = PetscOptionsGetBool(NULL, NULL, "-petscpartititoner_ptscotch_vertex_weight", &flg, NULL);CHKERRQ(ierr);
1737     if (!flg) veloloctab = NULL;
1738   }
1739   ierr = MPI_Comm_size(comm, &procglbnbr);CHKERRQ(ierr);
1740   ierr = MPI_Comm_rank(comm, &proclocnum);CHKERRQ(ierr);
1741   vertlocnbr = vtxdist[proclocnum + 1] - vtxdist[proclocnum];
1742   edgelocnbr = xadj[vertlocnbr];
1743 
1744   ierr = SCOTCH_dgraphInit(&grafdat, comm);CHKERRPTSCOTCH(ierr);
1745   ierr = SCOTCH_dgraphBuild(&grafdat, 0, vertlocnbr, vertlocnbr, xadj, xadj + 1, veloloctab, NULL, edgelocnbr, edgelocnbr, adjncy, NULL, edloloctab);CHKERRPTSCOTCH(ierr);
1746 /*#if defined(PETSC_USE_DEBUG)*/
1747   ierr = SCOTCH_dgraphCheck(&grafdat);CHKERRPTSCOTCH(ierr);
1748 /*#endif*/
1749   ierr = SCOTCH_stratInit(&stradat);CHKERRPTSCOTCH(ierr);
1750   ierr = SCOTCH_stratDgraphMapBuild(&stradat, flagval, procglbnbr, nparts, kbalval);CHKERRQ(ierr);
1751   ierr = SCOTCH_archInit(&archdat);CHKERRPTSCOTCH(ierr);
1752   ierr = SCOTCH_archCmplt(&archdat, nparts);CHKERRPTSCOTCH(ierr);
1753   ierr = SCOTCH_dgraphMapInit(&grafdat, &mappdat, &archdat, part);CHKERRPTSCOTCH(ierr);
1754 
1755   /*PetscSynchronizedPrintf(comm,"[%d] part: ", proclocnum);*/
1756   /*for(int i=0;i<vertlocnbr;i++) {*/
1757   /*  PetscSynchronizedPrintf(comm, "%i ", part[i]);*/
1758   /*}*/
1759   /*PetscSynchronizedPrintf(comm, "\n");*/
1760   /*PetscSynchronizedFlush(comm, PETSC_STDOUT);*/
1761   /*PetscSynchronizedPrintf(comm,"[%d] veloloctab: ", proclocnum);*/
1762   /*for(int i=0;i<vertlocnbr;i++) {*/
1763   /*  PetscSynchronizedPrintf(comm, "%i ", veloloctab[i]);*/
1764   /*}*/
1765   /*PetscSynchronizedPrintf(comm, "\n");*/
1766   /*PetscSynchronizedFlush(comm, PETSC_STDOUT);*/
1767   ierr = SCOTCH_dgraphMapCompute(&grafdat, &mappdat, &stradat);CHKERRPTSCOTCH(ierr);
1768   SCOTCH_dgraphMapExit(&grafdat, &mappdat);
1769   SCOTCH_archExit(&archdat);
1770   SCOTCH_stratExit(&stradat);
1771   SCOTCH_dgraphExit(&grafdat);
1772   PetscFunctionReturn(0);
1773 }
1774 
1775 #endif /* PETSC_HAVE_PTSCOTCH */
1776 
1777 static PetscErrorCode PetscPartitionerDestroy_PTScotch(PetscPartitioner part)
1778 {
1779   PetscPartitioner_PTScotch *p = (PetscPartitioner_PTScotch *) part->data;
1780   PetscErrorCode             ierr;
1781 
1782   PetscFunctionBegin;
1783   ierr = PetscFree(p);CHKERRQ(ierr);
1784   PetscFunctionReturn(0);
1785 }
1786 
1787 static PetscErrorCode PetscPartitionerView_PTScotch_Ascii(PetscPartitioner part, PetscViewer viewer)
1788 {
1789   PetscPartitioner_PTScotch *p = (PetscPartitioner_PTScotch *) part->data;
1790   PetscErrorCode            ierr;
1791 
1792   PetscFunctionBegin;
1793   ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
1794   ierr = PetscViewerASCIIPrintf(viewer, "using partitioning strategy %s\n",PTScotchStrategyList[p->strategy]);CHKERRQ(ierr);
1795   ierr = PetscViewerASCIIPrintf(viewer, "using load imbalance ratio %g\n",(double)p->imbalance);CHKERRQ(ierr);
1796   ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
1797   PetscFunctionReturn(0);
1798 }
1799 
1800 static PetscErrorCode PetscPartitionerView_PTScotch(PetscPartitioner part, PetscViewer viewer)
1801 {
1802   PetscBool      iascii;
1803   PetscErrorCode ierr;
1804 
1805   PetscFunctionBegin;
1806   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
1807   PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
1808   ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);CHKERRQ(ierr);
1809   if (iascii) {ierr = PetscPartitionerView_PTScotch_Ascii(part, viewer);CHKERRQ(ierr);}
1810   PetscFunctionReturn(0);
1811 }
1812 
1813 static PetscErrorCode PetscPartitionerSetFromOptions_PTScotch(PetscOptionItems *PetscOptionsObject, PetscPartitioner part)
1814 {
1815   PetscPartitioner_PTScotch *p = (PetscPartitioner_PTScotch *) part->data;
1816   const char *const         *slist = PTScotchStrategyList;
1817   PetscInt                  nlist = (PetscInt)(sizeof(PTScotchStrategyList)/sizeof(PTScotchStrategyList[0]));
1818   PetscBool                 flag;
1819   PetscErrorCode            ierr;
1820 
1821   PetscFunctionBegin;
1822   ierr = PetscOptionsHead(PetscOptionsObject, "PetscPartitioner PTScotch Options");CHKERRQ(ierr);
1823   ierr = PetscOptionsEList("-petscpartitioner_ptscotch_strategy","Partitioning strategy","",slist,nlist,slist[p->strategy],&p->strategy,&flag);CHKERRQ(ierr);
1824   ierr = PetscOptionsReal("-petscpartitioner_ptscotch_imbalance","Load imbalance ratio","",p->imbalance,&p->imbalance,&flag);CHKERRQ(ierr);
1825   ierr = PetscOptionsTail();CHKERRQ(ierr);
1826   PetscFunctionReturn(0);
1827 }
1828 
1829 static PetscErrorCode PetscPartitionerPartition_PTScotch(PetscPartitioner part, DM dm, PetscInt nparts, PetscInt numVertices, PetscInt start[], PetscInt adjacency[], PetscSection partSection, IS *partition)
1830 {
1831 #if defined(PETSC_HAVE_PTSCOTCH)
1832   MPI_Comm       comm       = PetscObjectComm((PetscObject)part);
1833   PetscInt       nvtxs      = numVertices; /* The number of vertices in full graph */
1834   PetscInt      *vtxdist;                  /* Distribution of vertices across processes */
1835   PetscInt      *xadj       = start;       /* Start of edge list for each vertex */
1836   PetscInt      *adjncy     = adjacency;   /* Edge lists for all vertices */
1837   PetscInt      *vwgt       = NULL;        /* Vertex weights */
1838   PetscInt      *adjwgt     = NULL;        /* Edge weights */
1839   PetscInt       v, i, *assignment, *points;
1840   PetscMPIInt    size, rank, p;
1841   PetscErrorCode ierr;
1842 
1843   PetscFunctionBegin;
1844   ierr = MPI_Comm_size(comm, &size);CHKERRQ(ierr);
1845   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
1846   ierr = PetscMalloc2(nparts+1,&vtxdist,PetscMax(nvtxs,1),&assignment);CHKERRQ(ierr);
1847 
1848   /* Calculate vertex distribution */
1849   vtxdist[0] = 0;
1850   ierr = MPI_Allgather(&nvtxs, 1, MPIU_INT, &vtxdist[1], 1, MPIU_INT, comm);CHKERRQ(ierr);
1851   for (p = 2; p <= size; ++p) {
1852     vtxdist[p] += vtxdist[p-1];
1853   }
1854 
1855   if (nparts == 1) {
1856     ierr = PetscMemzero(assignment, nvtxs * sizeof(PetscInt));CHKERRQ(ierr);
1857   } else {
1858     PetscSection section;
1859     /* Weight cells by dofs on cell by default */
1860     ierr = PetscMalloc1(PetscMax(nvtxs,1),&vwgt);CHKERRQ(ierr);
1861     ierr = DMGetSection(dm, &section);CHKERRQ(ierr);
1862     if (section) {
1863       PetscInt vStart, eEnd, dof;
1864       ierr = DMPlexGetHeightStratum(dm, 0, &vStart, &eEnd);CHKERRQ(ierr);
1865       for (v = vStart; v < eEnd; ++v) {
1866         ierr = PetscSectionGetDof(section, v, &dof);CHKERRQ(ierr);
1867         /* WARNING: Assumes that meshes with overlap have the overlapped cells at the end of the stratum. */
1868         /* To do this properly, we should use the cell numbering created in DMPlexCreatePartitionerGraph. */
1869         if (v-vStart < numVertices) vwgt[v-vStart] = PetscMax(dof, 1);
1870       }
1871     } else {
1872       for (v = 0; v < nvtxs; ++v) vwgt[v] = 1;
1873     }
1874     {
1875       PetscPartitioner_PTScotch *pts = (PetscPartitioner_PTScotch *) part->data;
1876       int                       strat = PTScotch_Strategy(pts->strategy);
1877       double                    imbal = (double)pts->imbalance;
1878 
1879       for (p = 0; !vtxdist[p+1] && p < size; ++p);
1880       if (vtxdist[p+1] == vtxdist[size]) {
1881         if (rank == p) {
1882           ierr = PTScotch_PartGraph_Seq(strat, imbal, nvtxs, xadj, adjncy, vwgt, adjwgt, nparts, assignment);CHKERRQ(ierr);
1883         }
1884       } else {
1885         ierr = PTScotch_PartGraph_MPI(strat, imbal, vtxdist, xadj, adjncy, vwgt, adjwgt, nparts, assignment, comm);CHKERRQ(ierr);
1886       }
1887     }
1888     ierr = PetscFree(vwgt);CHKERRQ(ierr);
1889   }
1890 
1891   /* Convert to PetscSection+IS */
1892   ierr = PetscSectionSetChart(partSection, 0, nparts);CHKERRQ(ierr);
1893   for (v = 0; v < nvtxs; ++v) {ierr = PetscSectionAddDof(partSection, assignment[v], 1);CHKERRQ(ierr);}
1894   ierr = PetscSectionSetUp(partSection);CHKERRQ(ierr);
1895   ierr = PetscMalloc1(nvtxs, &points);CHKERRQ(ierr);
1896   for (p = 0, i = 0; p < nparts; ++p) {
1897     for (v = 0; v < nvtxs; ++v) {
1898       if (assignment[v] == p) points[i++] = v;
1899     }
1900   }
1901   if (i != nvtxs) SETERRQ2(comm, PETSC_ERR_PLIB, "Number of points %D should be %D", i, nvtxs);
1902   ierr = ISCreateGeneral(comm, nvtxs, points, PETSC_OWN_POINTER, partition);CHKERRQ(ierr);
1903 
1904   ierr = PetscFree2(vtxdist,assignment);CHKERRQ(ierr);
1905   PetscFunctionReturn(0);
1906 #else
1907   SETERRQ(PetscObjectComm((PetscObject) part), PETSC_ERR_SUP, "Mesh partitioning needs external package support.\nPlease reconfigure with --download-ptscotch.");
1908 #endif
1909 }
1910 
1911 static PetscErrorCode PetscPartitionerInitialize_PTScotch(PetscPartitioner part)
1912 {
1913   PetscFunctionBegin;
1914   part->ops->view           = PetscPartitionerView_PTScotch;
1915   part->ops->destroy        = PetscPartitionerDestroy_PTScotch;
1916   part->ops->partition      = PetscPartitionerPartition_PTScotch;
1917   part->ops->setfromoptions = PetscPartitionerSetFromOptions_PTScotch;
1918   PetscFunctionReturn(0);
1919 }
1920 
1921 /*MC
1922   PETSCPARTITIONERPTSCOTCH = "ptscotch" - A PetscPartitioner object using the PT-Scotch library
1923 
1924   Level: intermediate
1925 
1926 .seealso: PetscPartitionerType, PetscPartitionerCreate(), PetscPartitionerSetType()
1927 M*/
1928 
1929 PETSC_EXTERN PetscErrorCode PetscPartitionerCreate_PTScotch(PetscPartitioner part)
1930 {
1931   PetscPartitioner_PTScotch *p;
1932   PetscErrorCode          ierr;
1933 
1934   PetscFunctionBegin;
1935   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
1936   ierr = PetscNewLog(part, &p);CHKERRQ(ierr);
1937   part->data = p;
1938 
1939   p->strategy  = 0;
1940   p->imbalance = 0.01;
1941 
1942   ierr = PetscPartitionerInitialize_PTScotch(part);CHKERRQ(ierr);
1943   ierr = PetscCitationsRegister(PTScotchPartitionerCitation, &PTScotchPartitionercite);CHKERRQ(ierr);
1944   PetscFunctionReturn(0);
1945 }
1946 
1947 
1948 /*@
1949   DMPlexGetPartitioner - Get the mesh partitioner
1950 
1951   Not collective
1952 
1953   Input Parameter:
1954 . dm - The DM
1955 
1956   Output Parameter:
1957 . part - The PetscPartitioner
1958 
1959   Level: developer
1960 
1961   Note: This gets a borrowed reference, so the user should not destroy this PetscPartitioner.
1962 
1963 .seealso DMPlexDistribute(), DMPlexSetPartitioner(), PetscPartitionerCreate()
1964 @*/
1965 PetscErrorCode DMPlexGetPartitioner(DM dm, PetscPartitioner *part)
1966 {
1967   DM_Plex       *mesh = (DM_Plex *) dm->data;
1968 
1969   PetscFunctionBegin;
1970   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1971   PetscValidPointer(part, 2);
1972   *part = mesh->partitioner;
1973   PetscFunctionReturn(0);
1974 }
1975 
1976 /*@
1977   DMPlexSetPartitioner - Set the mesh partitioner
1978 
1979   logically collective on dm and part
1980 
1981   Input Parameters:
1982 + dm - The DM
1983 - part - The partitioner
1984 
1985   Level: developer
1986 
1987   Note: Any existing PetscPartitioner will be destroyed.
1988 
1989 .seealso DMPlexDistribute(), DMPlexGetPartitioner(), PetscPartitionerCreate()
1990 @*/
1991 PetscErrorCode DMPlexSetPartitioner(DM dm, PetscPartitioner part)
1992 {
1993   DM_Plex       *mesh = (DM_Plex *) dm->data;
1994   PetscErrorCode ierr;
1995 
1996   PetscFunctionBegin;
1997   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1998   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 2);
1999   ierr = PetscObjectReference((PetscObject)part);CHKERRQ(ierr);
2000   ierr = PetscPartitionerDestroy(&mesh->partitioner);CHKERRQ(ierr);
2001   mesh->partitioner = part;
2002   PetscFunctionReturn(0);
2003 }
2004 
2005 static PetscErrorCode DMPlexAddClosure_Tree(DM dm, PetscHSetI ht, PetscInt point, PetscBool up, PetscBool down)
2006 {
2007   PetscErrorCode ierr;
2008 
2009   PetscFunctionBegin;
2010   if (up) {
2011     PetscInt parent;
2012 
2013     ierr = DMPlexGetTreeParent(dm,point,&parent,NULL);CHKERRQ(ierr);
2014     if (parent != point) {
2015       PetscInt closureSize, *closure = NULL, i;
2016 
2017       ierr = DMPlexGetTransitiveClosure(dm,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
2018       for (i = 0; i < closureSize; i++) {
2019         PetscInt cpoint = closure[2*i];
2020 
2021         ierr = PetscHSetIAdd(ht, cpoint);CHKERRQ(ierr);
2022         ierr = DMPlexAddClosure_Tree(dm,ht,cpoint,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
2023       }
2024       ierr = DMPlexRestoreTransitiveClosure(dm,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
2025     }
2026   }
2027   if (down) {
2028     PetscInt numChildren;
2029     const PetscInt *children;
2030 
2031     ierr = DMPlexGetTreeChildren(dm,point,&numChildren,&children);CHKERRQ(ierr);
2032     if (numChildren) {
2033       PetscInt i;
2034 
2035       for (i = 0; i < numChildren; i++) {
2036         PetscInt cpoint = children[i];
2037 
2038         ierr = PetscHSetIAdd(ht, cpoint);CHKERRQ(ierr);
2039         ierr = DMPlexAddClosure_Tree(dm,ht,cpoint,PETSC_FALSE,PETSC_TRUE);CHKERRQ(ierr);
2040       }
2041     }
2042   }
2043   PetscFunctionReturn(0);
2044 }
2045 
2046 /*@
2047   DMPlexPartitionLabelClosure - Add the closure of all points to the partition label
2048 
2049   Input Parameters:
2050 + dm     - The DM
2051 - label  - DMLabel assinging ranks to remote roots
2052 
2053   Level: developer
2054 
2055 .seealso: DMPlexPartitionLabelCreateSF, DMPlexDistribute(), DMPlexCreateOverlap
2056 @*/
2057 PetscErrorCode DMPlexPartitionLabelClosure(DM dm, DMLabel label)
2058 {
2059   IS              rankIS,   pointIS;
2060   const PetscInt *ranks,   *points;
2061   PetscInt        numRanks, numPoints, r, p, c, closureSize;
2062   PetscInt       *closure = NULL;
2063   DM_Plex        *mesh    = (DM_Plex *)dm->data;
2064   PetscBool       hasTree = (mesh->parentSection || mesh->childSection) ? PETSC_TRUE : PETSC_FALSE;
2065   PetscErrorCode  ierr;
2066 
2067   PetscFunctionBegin;
2068   ierr = DMLabelGetValueIS(label, &rankIS);CHKERRQ(ierr);
2069   ierr = ISGetLocalSize(rankIS, &numRanks);CHKERRQ(ierr);
2070   ierr = ISGetIndices(rankIS, &ranks);CHKERRQ(ierr);
2071 
2072   for (r = 0; r < numRanks; ++r) {
2073     const PetscInt rank = ranks[r];
2074     PetscHSetI     ht;
2075     PetscInt       nelems, *elems, off = 0;
2076 
2077     ierr = DMLabelGetStratumIS(label, rank, &pointIS);CHKERRQ(ierr);
2078     ierr = ISGetLocalSize(pointIS, &numPoints);CHKERRQ(ierr);
2079     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
2080     ierr = PetscHSetICreate(&ht);CHKERRQ(ierr);
2081     ierr = PetscHSetIResize(ht, numPoints*16);CHKERRQ(ierr);
2082     for (p = 0; p < numPoints; ++p) {
2083       ierr = DMPlexGetTransitiveClosure(dm, points[p], PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
2084       for (c = 0; c < closureSize*2; c += 2) {
2085         ierr = PetscHSetIAdd(ht, closure[c]);CHKERRQ(ierr);
2086         if (hasTree) {ierr = DMPlexAddClosure_Tree(dm, ht, closure[c], PETSC_TRUE, PETSC_TRUE);CHKERRQ(ierr);}
2087       }
2088     }
2089     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
2090     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2091     ierr = PetscHSetIGetSize(ht, &nelems);CHKERRQ(ierr);
2092     ierr = PetscMalloc1(nelems, &elems);CHKERRQ(ierr);
2093     ierr = PetscHSetIGetElems(ht, &off, elems);CHKERRQ(ierr);
2094     ierr = PetscHSetIDestroy(&ht);CHKERRQ(ierr);
2095     ierr = PetscSortInt(nelems, elems);CHKERRQ(ierr);
2096     ierr = ISCreateGeneral(PETSC_COMM_SELF, nelems, elems, PETSC_OWN_POINTER, &pointIS);CHKERRQ(ierr);
2097     ierr = DMLabelSetStratumIS(label, rank, pointIS);CHKERRQ(ierr);
2098     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2099   }
2100 
2101   if (closure) {ierr = DMPlexRestoreTransitiveClosure(dm, 0, PETSC_TRUE, NULL, &closure);CHKERRQ(ierr);}
2102   ierr = ISRestoreIndices(rankIS, &ranks);CHKERRQ(ierr);
2103   ierr = ISDestroy(&rankIS);CHKERRQ(ierr);
2104   PetscFunctionReturn(0);
2105 }
2106 
2107 /*@
2108   DMPlexPartitionLabelAdjacency - Add one level of adjacent points to the partition label
2109 
2110   Input Parameters:
2111 + dm     - The DM
2112 - label  - DMLabel assinging ranks to remote roots
2113 
2114   Level: developer
2115 
2116 .seealso: DMPlexPartitionLabelCreateSF, DMPlexDistribute(), DMPlexCreateOverlap
2117 @*/
2118 PetscErrorCode DMPlexPartitionLabelAdjacency(DM dm, DMLabel label)
2119 {
2120   IS              rankIS,   pointIS;
2121   const PetscInt *ranks,   *points;
2122   PetscInt        numRanks, numPoints, r, p, a, adjSize;
2123   PetscInt       *adj = NULL;
2124   PetscErrorCode  ierr;
2125 
2126   PetscFunctionBegin;
2127   ierr = DMLabelGetValueIS(label, &rankIS);CHKERRQ(ierr);
2128   ierr = ISGetLocalSize(rankIS, &numRanks);CHKERRQ(ierr);
2129   ierr = ISGetIndices(rankIS, &ranks);CHKERRQ(ierr);
2130   for (r = 0; r < numRanks; ++r) {
2131     const PetscInt rank = ranks[r];
2132 
2133     ierr = DMLabelGetStratumIS(label, rank, &pointIS);CHKERRQ(ierr);
2134     ierr = ISGetLocalSize(pointIS, &numPoints);CHKERRQ(ierr);
2135     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
2136     for (p = 0; p < numPoints; ++p) {
2137       adjSize = PETSC_DETERMINE;
2138       ierr = DMPlexGetAdjacency(dm, points[p], &adjSize, &adj);CHKERRQ(ierr);
2139       for (a = 0; a < adjSize; ++a) {ierr = DMLabelSetValue(label, adj[a], rank);CHKERRQ(ierr);}
2140     }
2141     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
2142     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2143   }
2144   ierr = ISRestoreIndices(rankIS, &ranks);CHKERRQ(ierr);
2145   ierr = ISDestroy(&rankIS);CHKERRQ(ierr);
2146   ierr = PetscFree(adj);CHKERRQ(ierr);
2147   PetscFunctionReturn(0);
2148 }
2149 
2150 /*@
2151   DMPlexPartitionLabelPropagate - Propagate points in a partition label over the point SF
2152 
2153   Input Parameters:
2154 + dm     - The DM
2155 - label  - DMLabel assinging ranks to remote roots
2156 
2157   Level: developer
2158 
2159   Note: This is required when generating multi-level overlaps to capture
2160   overlap points from non-neighbouring partitions.
2161 
2162 .seealso: DMPlexPartitionLabelCreateSF, DMPlexDistribute(), DMPlexCreateOverlap
2163 @*/
2164 PetscErrorCode DMPlexPartitionLabelPropagate(DM dm, DMLabel label)
2165 {
2166   MPI_Comm        comm;
2167   PetscMPIInt     rank;
2168   PetscSF         sfPoint;
2169   DMLabel         lblRoots, lblLeaves;
2170   IS              rankIS, pointIS;
2171   const PetscInt *ranks;
2172   PetscInt        numRanks, r;
2173   PetscErrorCode  ierr;
2174 
2175   PetscFunctionBegin;
2176   ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr);
2177   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
2178   ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);
2179   /* Pull point contributions from remote leaves into local roots */
2180   ierr = DMLabelGather(label, sfPoint, &lblLeaves);CHKERRQ(ierr);
2181   ierr = DMLabelGetValueIS(lblLeaves, &rankIS);CHKERRQ(ierr);
2182   ierr = ISGetLocalSize(rankIS, &numRanks);CHKERRQ(ierr);
2183   ierr = ISGetIndices(rankIS, &ranks);CHKERRQ(ierr);
2184   for (r = 0; r < numRanks; ++r) {
2185     const PetscInt remoteRank = ranks[r];
2186     if (remoteRank == rank) continue;
2187     ierr = DMLabelGetStratumIS(lblLeaves, remoteRank, &pointIS);CHKERRQ(ierr);
2188     ierr = DMLabelInsertIS(label, pointIS, remoteRank);CHKERRQ(ierr);
2189     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2190   }
2191   ierr = ISRestoreIndices(rankIS, &ranks);CHKERRQ(ierr);
2192   ierr = ISDestroy(&rankIS);CHKERRQ(ierr);
2193   ierr = DMLabelDestroy(&lblLeaves);CHKERRQ(ierr);
2194   /* Push point contributions from roots into remote leaves */
2195   ierr = DMLabelDistribute(label, sfPoint, &lblRoots);CHKERRQ(ierr);
2196   ierr = DMLabelGetValueIS(lblRoots, &rankIS);CHKERRQ(ierr);
2197   ierr = ISGetLocalSize(rankIS, &numRanks);CHKERRQ(ierr);
2198   ierr = ISGetIndices(rankIS, &ranks);CHKERRQ(ierr);
2199   for (r = 0; r < numRanks; ++r) {
2200     const PetscInt remoteRank = ranks[r];
2201     if (remoteRank == rank) continue;
2202     ierr = DMLabelGetStratumIS(lblRoots, remoteRank, &pointIS);CHKERRQ(ierr);
2203     ierr = DMLabelInsertIS(label, pointIS, remoteRank);CHKERRQ(ierr);
2204     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2205   }
2206   ierr = ISRestoreIndices(rankIS, &ranks);CHKERRQ(ierr);
2207   ierr = ISDestroy(&rankIS);CHKERRQ(ierr);
2208   ierr = DMLabelDestroy(&lblRoots);CHKERRQ(ierr);
2209   PetscFunctionReturn(0);
2210 }
2211 
2212 /*@
2213   DMPlexPartitionLabelInvert - Create a partition label of remote roots from a local root label
2214 
2215   Input Parameters:
2216 + dm        - The DM
2217 . rootLabel - DMLabel assinging ranks to local roots
2218 . processSF - A star forest mapping into the local index on each remote rank
2219 
2220   Output Parameter:
2221 - leafLabel - DMLabel assinging ranks to remote roots
2222 
2223   Note: The rootLabel defines a send pattern by mapping local points to remote target ranks. The
2224   resulting leafLabel is a receiver mapping of remote roots to their parent rank.
2225 
2226   Level: developer
2227 
2228 .seealso: DMPlexPartitionLabelCreateSF, DMPlexDistribute(), DMPlexCreateOverlap
2229 @*/
2230 PetscErrorCode DMPlexPartitionLabelInvert(DM dm, DMLabel rootLabel, PetscSF processSF, DMLabel leafLabel)
2231 {
2232   MPI_Comm           comm;
2233   PetscMPIInt        rank, size;
2234   PetscInt           p, n, numNeighbors, ssize, l, nleaves;
2235   PetscSF            sfPoint;
2236   PetscSFNode       *rootPoints, *leafPoints;
2237   PetscSection       rootSection, leafSection;
2238   const PetscSFNode *remote;
2239   const PetscInt    *local, *neighbors;
2240   IS                 valueIS;
2241   PetscErrorCode     ierr;
2242 
2243   PetscFunctionBegin;
2244   ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr);
2245   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
2246   ierr = MPI_Comm_size(comm, &size);CHKERRQ(ierr);
2247   ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);
2248 
2249   /* Convert to (point, rank) and use actual owners */
2250   ierr = PetscSectionCreate(comm, &rootSection);CHKERRQ(ierr);
2251   ierr = PetscSectionSetChart(rootSection, 0, size);CHKERRQ(ierr);
2252   ierr = DMLabelGetValueIS(rootLabel, &valueIS);CHKERRQ(ierr);
2253   ierr = ISGetLocalSize(valueIS, &numNeighbors);CHKERRQ(ierr);
2254   ierr = ISGetIndices(valueIS, &neighbors);CHKERRQ(ierr);
2255   for (n = 0; n < numNeighbors; ++n) {
2256     PetscInt numPoints;
2257 
2258     ierr = DMLabelGetStratumSize(rootLabel, neighbors[n], &numPoints);CHKERRQ(ierr);
2259     ierr = PetscSectionAddDof(rootSection, neighbors[n], numPoints);CHKERRQ(ierr);
2260   }
2261   ierr = PetscSectionSetUp(rootSection);CHKERRQ(ierr);
2262   ierr = PetscSectionGetStorageSize(rootSection, &ssize);CHKERRQ(ierr);
2263   ierr = PetscMalloc1(ssize, &rootPoints);CHKERRQ(ierr);
2264   ierr = PetscSFGetGraph(sfPoint, NULL, &nleaves, &local, &remote);CHKERRQ(ierr);
2265   for (n = 0; n < numNeighbors; ++n) {
2266     IS              pointIS;
2267     const PetscInt *points;
2268     PetscInt        off, numPoints, p;
2269 
2270     ierr = PetscSectionGetOffset(rootSection, neighbors[n], &off);CHKERRQ(ierr);
2271     ierr = DMLabelGetStratumIS(rootLabel, neighbors[n], &pointIS);CHKERRQ(ierr);
2272     ierr = ISGetLocalSize(pointIS, &numPoints);CHKERRQ(ierr);
2273     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
2274     for (p = 0; p < numPoints; ++p) {
2275       if (local) {ierr = PetscFindInt(points[p], nleaves, local, &l);CHKERRQ(ierr);}
2276       else       {l = -1;}
2277       if (l >= 0) {rootPoints[off+p] = remote[l];}
2278       else        {rootPoints[off+p].index = points[p]; rootPoints[off+p].rank = rank;}
2279     }
2280     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
2281     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2282   }
2283   ierr = ISRestoreIndices(valueIS, &neighbors);CHKERRQ(ierr);
2284   ierr = ISDestroy(&valueIS);CHKERRQ(ierr);
2285   /* Communicate overlap */
2286   ierr = PetscSectionCreate(comm, &leafSection);CHKERRQ(ierr);
2287   ierr = DMPlexDistributeData(dm, processSF, rootSection, MPIU_2INT, rootPoints, leafSection, (void**) &leafPoints);CHKERRQ(ierr);
2288   /* Filter remote contributions (ovLeafPoints) into the overlapSF */
2289   ierr = PetscSectionGetStorageSize(leafSection, &ssize);CHKERRQ(ierr);
2290   for (p = 0; p < ssize; p++) {
2291     ierr = DMLabelSetValue(leafLabel, leafPoints[p].index, leafPoints[p].rank);CHKERRQ(ierr);
2292   }
2293   ierr = PetscFree(rootPoints);CHKERRQ(ierr);
2294   ierr = PetscSectionDestroy(&rootSection);CHKERRQ(ierr);
2295   ierr = PetscFree(leafPoints);CHKERRQ(ierr);
2296   ierr = PetscSectionDestroy(&leafSection);CHKERRQ(ierr);
2297   PetscFunctionReturn(0);
2298 }
2299 
2300 /*@
2301   DMPlexPartitionLabelCreateSF - Create a star forest from a label that assigns ranks to points
2302 
2303   Input Parameters:
2304 + dm    - The DM
2305 . label - DMLabel assinging ranks to remote roots
2306 
2307   Output Parameter:
2308 - sf    - The star forest communication context encapsulating the defined mapping
2309 
2310   Note: The incoming label is a receiver mapping of remote points to their parent rank.
2311 
2312   Level: developer
2313 
2314 .seealso: DMPlexDistribute(), DMPlexCreateOverlap
2315 @*/
2316 PetscErrorCode DMPlexPartitionLabelCreateSF(DM dm, DMLabel label, PetscSF *sf)
2317 {
2318   PetscMPIInt     rank, size;
2319   PetscInt        n, numRemote, p, numPoints, pStart, pEnd, idx = 0;
2320   PetscSFNode    *remotePoints;
2321   IS              remoteRootIS;
2322   const PetscInt *remoteRoots;
2323   PetscErrorCode ierr;
2324 
2325   PetscFunctionBegin;
2326   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRQ(ierr);
2327   ierr = MPI_Comm_size(PetscObjectComm((PetscObject) dm), &size);CHKERRQ(ierr);
2328 
2329   for (numRemote = 0, n = 0; n < size; ++n) {
2330     ierr = DMLabelGetStratumSize(label, n, &numPoints);CHKERRQ(ierr);
2331     numRemote += numPoints;
2332   }
2333   ierr = PetscMalloc1(numRemote, &remotePoints);CHKERRQ(ierr);
2334   /* Put owned points first */
2335   ierr = DMLabelGetStratumSize(label, rank, &numPoints);CHKERRQ(ierr);
2336   if (numPoints > 0) {
2337     ierr = DMLabelGetStratumIS(label, rank, &remoteRootIS);CHKERRQ(ierr);
2338     ierr = ISGetIndices(remoteRootIS, &remoteRoots);CHKERRQ(ierr);
2339     for (p = 0; p < numPoints; p++) {
2340       remotePoints[idx].index = remoteRoots[p];
2341       remotePoints[idx].rank = rank;
2342       idx++;
2343     }
2344     ierr = ISRestoreIndices(remoteRootIS, &remoteRoots);CHKERRQ(ierr);
2345     ierr = ISDestroy(&remoteRootIS);CHKERRQ(ierr);
2346   }
2347   /* Now add remote points */
2348   for (n = 0; n < size; ++n) {
2349     ierr = DMLabelGetStratumSize(label, n, &numPoints);CHKERRQ(ierr);
2350     if (numPoints <= 0 || n == rank) continue;
2351     ierr = DMLabelGetStratumIS(label, n, &remoteRootIS);CHKERRQ(ierr);
2352     ierr = ISGetIndices(remoteRootIS, &remoteRoots);CHKERRQ(ierr);
2353     for (p = 0; p < numPoints; p++) {
2354       remotePoints[idx].index = remoteRoots[p];
2355       remotePoints[idx].rank = n;
2356       idx++;
2357     }
2358     ierr = ISRestoreIndices(remoteRootIS, &remoteRoots);CHKERRQ(ierr);
2359     ierr = ISDestroy(&remoteRootIS);CHKERRQ(ierr);
2360   }
2361   ierr = PetscSFCreate(PetscObjectComm((PetscObject) dm), sf);CHKERRQ(ierr);
2362   ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
2363   ierr = PetscSFSetGraph(*sf, pEnd-pStart, numRemote, NULL, PETSC_OWN_POINTER, remotePoints, PETSC_OWN_POINTER);CHKERRQ(ierr);
2364   PetscFunctionReturn(0);
2365 }
2366 
2367 /*@
2368   DMPlexRebalanceSharedPoints - Redistribute points in the plex that are shared in order to achieve better balancing.
2369 
2370   Input parameters:
2371   + dm - The DMPlex object
2372 
2373   Level: user
2374 
2375 @*/
2376 
2377 PetscErrorCode DMPlexRebalanceSharedPoints(DM dm, PetscInt entityDepth, PetscBool useInitialGuess, PetscBool parallel)
2378 {
2379 #if defined(PETSC_HAVE_PARMETIS)
2380   PetscSF     sf;
2381   PetscInt    ierr, i, j;
2382   PetscInt    eBegin, eEnd, nroots, nleafs, pStart, pEnd, sumDegrees;
2383   const       PetscInt *degree, *ilocal;
2384   const       PetscSFNode *iremote; /* Do I need to free these? */
2385   PetscBool   *toBalance, *isLeaf, *isExclusivelyOwned, *isNonExclusivelyOwned;
2386   PetscInt    numExclusivelyOwned, numNonExclusivelyOwned;
2387   PetscMPIInt rank, size;
2388   PetscInt    *numLocalVerticesAllProcesses, *cumSumVertices, *cumSumDegrees, *globalNumbersOfLocalOwnedVertices, *locationsOfLeafs, *rankOnLeafs, *remoteLocalPointOfLeafs, *points, *leafGlobalNumbers;
2389   PetscInt    offset, counter;
2390   PetscInt    lenadjncy, numNonExclusivelyOwnedConnectTo, numLeafs;
2391   PetscInt    *xadj, *adjncy, *vtxwgt;
2392   PetscInt    lenxadj;
2393 
2394   PetscInt    *adjwgt = NULL;
2395   PetscInt    *part, *options;
2396   PetscInt    nparts, wgtflag, numflag, ncon, edgecut;
2397   real_t      *ubvec;
2398   PetscInt    *firstVertices, *renumbering;
2399   PetscInt    failed, failedGlobal;
2400   MPI_Comm    comm;
2401   PetscInt    leafCounter;
2402   PetscInt    *leafsNew;
2403   PetscSFNode *leafLocationsNew;
2404   Mat         A;
2405   PetscBool   flg = PETSC_FALSE;
2406   const char *prefix = NULL;
2407 
2408   PetscFunctionBegin;
2409 
2410   ierr = PetscObjectGetOptionsPrefix((PetscObject)dm, &prefix);CHKERRQ(ierr);
2411   ierr = PetscOptionsGetBool(NULL, prefix, "-dm_rebalance_partition_view", &flg, NULL);
2412 
2413   ierr = PetscLogEventBegin(DMPLEX_RebalanceSharedPoints, dm, 0, 0, 0);CHKERRQ(ierr);
2414 
2415   ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr);
2416 
2417   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
2418   ierr = MPI_Comm_size(comm, &size);CHKERRQ(ierr);
2419   if (size==1) PetscFunctionReturn(0);
2420 
2421   /* Figure out all points in the plex that we are interested in balancing.  In
2422    * this case we are just interested in vertices. Should generalize that at
2423    * some point.  */
2424   ierr = DMPlexGetDepthStratum(dm, entityDepth, &eBegin, &eEnd);CHKERRQ(ierr);
2425   ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
2426   ierr = PetscMalloc1(pEnd-pStart, &toBalance);CHKERRQ(ierr);
2427 
2428   for (i=0; i<pEnd-pStart; i++) {
2429     toBalance[i] = (i-pStart>=eBegin && i-pStart<eEnd);
2430   }
2431 
2432 
2433   /* There are three types of points:
2434    * exclusivelyOwned: points that are owned by this process and only seen by this process
2435    * nonExclusivelyOwned: points that are owned by this process but seen by at least another process
2436    * leaf: a point that is seen by this process but owned by a different process
2437    */
2438   ierr = DMGetPointSF(dm, &sf);CHKERRQ(ierr);
2439   ierr = PetscSFGetGraph(sf, &nroots, &nleafs, &ilocal, &iremote); CHKERRQ(ierr);
2440   ierr = PetscMalloc1(pEnd-pStart, &isLeaf);CHKERRQ(ierr);
2441   ierr = PetscMalloc1(pEnd-pStart, &isNonExclusivelyOwned);CHKERRQ(ierr);
2442   ierr = PetscMalloc1(pEnd-pStart, &isExclusivelyOwned);CHKERRQ(ierr);
2443   for (i=0; i<pEnd-pStart; i++) {
2444     isNonExclusivelyOwned[i] = PETSC_FALSE;
2445     isExclusivelyOwned[i] = PETSC_FALSE;
2446     isLeaf[i] = PETSC_FALSE;
2447   }
2448 
2449 
2450   /* start by marking all the leafs */
2451   for (i=0; i<nleafs; i++) {
2452     isLeaf[ilocal[i]-pStart] = PETSC_TRUE;
2453   }
2454 
2455   /* for an owned point, we can figure out whether another processor sees it or
2456    * not by calculating its degree */
2457   ierr = PetscSFComputeDegreeBegin(sf, &degree);CHKERRQ(ierr);
2458   ierr = PetscSFComputeDegreeEnd(sf, &degree);CHKERRQ(ierr);
2459 
2460   numExclusivelyOwned=0;
2461   numNonExclusivelyOwned=0;
2462   for (i=0; i<pEnd-pStart; i++) {
2463     if (toBalance[i]) {
2464       if (degree[i] > 0) {
2465         isNonExclusivelyOwned[i] = PETSC_TRUE;
2466         numNonExclusivelyOwned += 1;
2467       } else {
2468         if (!isLeaf[i]) {
2469           isExclusivelyOwned[i] = PETSC_TRUE;
2470           numExclusivelyOwned += 1;
2471         }
2472       }
2473     }
2474   }
2475 
2476 
2477   /* We are going to build a graph with one vertex per core representing the
2478    * exclusively owned points and then one vertex per nonExclusively owned
2479    * point. */
2480   ierr = PetscMalloc1(size, &numLocalVerticesAllProcesses);CHKERRQ(ierr);
2481   numLocalVerticesAllProcesses[rank] = 1 + numNonExclusivelyOwned;
2482   /* For numbering purposes we need to figure out how many vertices are on each core. */
2483   ierr = MPI_Allgather(MPI_IN_PLACE,0,MPI_DATATYPE_NULL,numLocalVerticesAllProcesses,1,MPIU_INT,comm);CHKERRQ(ierr);
2484 
2485   ierr = PetscMalloc1(size+1, &cumSumVertices);CHKERRQ(ierr);
2486   cumSumVertices[0] = 0;
2487   for (i=1; i<=size; i++) {
2488     cumSumVertices[i] = cumSumVertices[i-1] + numLocalVerticesAllProcesses[i-1];
2489   }
2490   ierr = PetscFree(numLocalVerticesAllProcesses);CHKERRQ(ierr);
2491   ierr = PetscMalloc1(pEnd-pStart+1, &cumSumDegrees);CHKERRQ(ierr);
2492   cumSumDegrees[0] = 0;
2493   for (i=1; i<=pEnd-pStart; i++) {
2494     cumSumDegrees[i] = cumSumDegrees[i-1] + degree[i-1];
2495   }
2496   ierr = PetscMalloc1(pEnd-pStart, &globalNumbersOfLocalOwnedVertices);CHKERRQ(ierr);
2497 
2498   offset = cumSumVertices[rank];
2499   counter = 0;
2500   for (i=0; i<pEnd-pStart; i++) {
2501     if (toBalance[i]) {
2502       if (degree[i] > 0) {
2503         globalNumbersOfLocalOwnedVertices[i] = counter + 1 + offset;
2504         counter++;
2505       }
2506     }
2507   }
2508 
2509   /* get the location of my leafs (we have sumDegrees many leafs pointing at our roots) */
2510   sumDegrees = 0;
2511   for (i=0; i<pEnd-pStart; i++) {
2512     sumDegrees += degree[i];
2513   }
2514 
2515   ierr = PetscMalloc1(sumDegrees, &locationsOfLeafs);CHKERRQ(ierr);
2516   ierr = PetscMalloc1(pEnd-pStart, &rankOnLeafs);CHKERRQ(ierr);
2517   for (i=0; i<pEnd-pStart; i++) {
2518     rankOnLeafs[i] = rank;
2519   }
2520   ierr = PetscSFGatherBegin(sf, MPIU_INT, rankOnLeafs, locationsOfLeafs);CHKERRQ(ierr);
2521   ierr = PetscSFGatherEnd(sf, MPIU_INT, rankOnLeafs, locationsOfLeafs);CHKERRQ(ierr);
2522   ierr = PetscFree(rankOnLeafs);CHKERRQ(ierr);
2523 
2524   /* get the remote local points of my leaves */
2525   ierr = PetscMalloc1(sumDegrees, &remoteLocalPointOfLeafs);CHKERRQ(ierr);
2526   ierr = PetscMalloc1(pEnd-pStart, &points);CHKERRQ(ierr);
2527   for (i=0; i<pEnd-pStart; i++) {
2528     points[i] = pStart+i;
2529   }
2530   ierr = PetscSFGatherBegin(sf, MPIU_INT, points, remoteLocalPointOfLeafs);CHKERRQ(ierr);
2531   ierr = PetscSFGatherEnd(sf, MPIU_INT, points, remoteLocalPointOfLeafs);CHKERRQ(ierr);
2532   ierr = PetscFree(points);CHKERRQ(ierr);
2533 
2534   /* send the global numbers of vertices I own to the leafs so that they know to connect to it */
2535   ierr = PetscMalloc1(pEnd-pStart, &leafGlobalNumbers);CHKERRQ(ierr);
2536   ierr = PetscSFBcastBegin(sf, MPIU_INT, globalNumbersOfLocalOwnedVertices, leafGlobalNumbers);CHKERRQ(ierr);
2537   ierr = PetscSFBcastEnd(sf, MPIU_INT, globalNumbersOfLocalOwnedVertices, leafGlobalNumbers);CHKERRQ(ierr);
2538 
2539   /* Now start building the data structur for ParMETIS */
2540   /* vtxdist = cum_sum_vertices */
2541 
2542   numNonExclusivelyOwnedConnectTo = 0;
2543   numLeafs = 0;
2544   for (i=0; i<pEnd-pStart; i++) {
2545     if (toBalance[i]) {
2546       if (isNonExclusivelyOwned[i]) {
2547         numNonExclusivelyOwnedConnectTo += 1 + degree[i];
2548       }
2549       if (isLeaf[i]) {
2550         numLeafs++;
2551       }
2552     }
2553   }
2554 
2555 
2556 
2557   ierr = MatCreate(comm, &A);CHKERRQ(ierr);
2558   ierr = MatSetType(A, MATMPIAIJ);CHKERRQ(ierr);
2559   ierr = MatSetSizes(A, 1+numNonExclusivelyOwned, 1+numNonExclusivelyOwned, PETSC_DETERMINE, PETSC_DETERMINE);CHKERRQ(ierr);
2560   ierr = MatSetUp(A);CHKERRQ(ierr);
2561 
2562   for (i=0; i<pEnd-pStart; i++) {
2563     if (toBalance[i]) {
2564       if (isNonExclusivelyOwned[i]) {
2565         PetscInt adjSize = PETSC_DETERMINE;
2566         PetscInt *adj = NULL;
2567         ierr = MatSetValue(A, cumSumVertices[rank], globalNumbersOfLocalOwnedVertices[i], 1, INSERT_VALUES);CHKERRQ(ierr);
2568         ierr = MatSetValue(A, globalNumbersOfLocalOwnedVertices[i], cumSumVertices[rank], 1, INSERT_VALUES);CHKERRQ(ierr);
2569         ierr = DMPlexGetAdjacency(dm, i+pStart, &adjSize, &adj);CHKERRQ(ierr);
2570         adjSize = 0;
2571         for (j=0; j<adjSize; j++) {
2572           if (toBalance[adj[j]] && i+pStart != adj[j]) {
2573             if (isNonExclusivelyOwned[adj[j]]) {
2574               ierr = MatSetValue(A, globalNumbersOfLocalOwnedVertices[i], globalNumbersOfLocalOwnedVertices[adj[j]], 1, INSERT_VALUES);CHKERRQ(ierr);
2575               ierr = MatSetValue(A, globalNumbersOfLocalOwnedVertices[adj[j]], globalNumbersOfLocalOwnedVertices[i], 1, INSERT_VALUES);CHKERRQ(ierr);
2576             }
2577             else if (isLeaf[adj[j]]) {
2578               ierr = MatSetValue(A, globalNumbersOfLocalOwnedVertices[i], leafGlobalNumbers[adj[j]], 1, INSERT_VALUES);CHKERRQ(ierr);
2579               ierr = MatSetValue(A, leafGlobalNumbers[adj[j]], globalNumbersOfLocalOwnedVertices[i], 1, INSERT_VALUES);CHKERRQ(ierr);
2580             }
2581           }
2582         }
2583         ierr = PetscFree(adj);CHKERRQ(ierr);
2584       } else if (isLeaf[i]) {
2585         PetscInt adjSize = PETSC_DETERMINE;
2586         PetscInt *adj = NULL;
2587         ierr = MatSetValue(A, cumSumVertices[rank], leafGlobalNumbers[i], 1, INSERT_VALUES);CHKERRQ(ierr);
2588         ierr = MatSetValue(A, leafGlobalNumbers[i], cumSumVertices[rank], 1, INSERT_VALUES);CHKERRQ(ierr);
2589         ierr = DMPlexGetAdjacency(dm, i+pStart, &adjSize, &adj);CHKERRQ(ierr);
2590         adjSize = 0;
2591         for (j=0; j<adjSize; j++) {
2592           if (toBalance[adj[j]] && i+pStart != adj[j]) {
2593             if (isNonExclusivelyOwned[adj[j]]) {
2594               ierr = MatSetValue(A, leafGlobalNumbers[i], globalNumbersOfLocalOwnedVertices[adj[j]], 1, INSERT_VALUES);CHKERRQ(ierr);
2595               ierr = MatSetValue(A, globalNumbersOfLocalOwnedVertices[adj[j]], leafGlobalNumbers[i], 1, INSERT_VALUES);CHKERRQ(ierr);
2596             } else if (isLeaf[adj[j]]) {
2597               ierr = MatSetValue(A, leafGlobalNumbers[i], leafGlobalNumbers[adj[j]], 1, INSERT_VALUES);CHKERRQ(ierr);
2598               ierr = MatSetValue(A, leafGlobalNumbers[adj[j]], leafGlobalNumbers[i], 1, INSERT_VALUES);CHKERRQ(ierr);
2599             }
2600           }
2601         }
2602         ierr = PetscFree(adj);CHKERRQ(ierr);
2603       }
2604     }
2605   }
2606   ierr = PetscFree(leafGlobalNumbers);CHKERRQ(ierr);
2607   ierr = PetscFree(globalNumbersOfLocalOwnedVertices);CHKERRQ(ierr);
2608 
2609   ierr = MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2610   ierr = MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2611   /*MatView(A, 	PETSC_VIEWER_STDOUT_WORLD);*/
2612   nparts = size;
2613   wgtflag = 2;
2614 
2615   numflag = 0;
2616   ncon = 2;
2617   real_t *tpwgts;
2618   ierr = PetscMalloc1(ncon * nparts, &tpwgts);CHKERRQ(ierr);
2619 
2620   for (i=0; i<ncon*nparts; i++) {
2621     tpwgts[i] = 1./(nparts);
2622   }
2623 
2624 
2625   ierr = PetscMalloc1(ncon, &ubvec);CHKERRQ(ierr);
2626   ubvec[0] = 1.01;
2627   if (ncon>1) ubvec[1] = 1.01;
2628   ierr = PetscMalloc1(1, &options);CHKERRQ(ierr);
2629   options[0] = 0;
2630     lenadjncy = 0;
2631     for (i=0; i<1+numNonExclusivelyOwned; i++) {
2632       PetscInt temp=0;
2633       ierr = MatGetRow(A, cumSumVertices[rank] + i, &temp, NULL, NULL);CHKERRQ(ierr);
2634       lenadjncy += temp;
2635       ierr = MatRestoreRow(A, cumSumVertices[rank] + i, &temp, NULL, NULL);CHKERRQ(ierr);
2636     }
2637     ierr = PetscMalloc1(lenadjncy, &adjncy);CHKERRQ(ierr);
2638     lenxadj = 2 + numNonExclusivelyOwned;
2639     ierr = PetscMalloc1(lenxadj, &xadj);CHKERRQ(ierr);
2640     xadj[0] = 0;
2641     counter = 0;
2642     for (i=0; i<1+numNonExclusivelyOwned; i++) {
2643       PetscInt        temp=0;
2644       const PetscInt *cols;
2645       ierr = MatGetRow(A, cumSumVertices[rank] + i, &temp, &cols, NULL);CHKERRQ(ierr);
2646       for (j=0; j<temp; j++) {
2647         adjncy[counter+j] = cols[j];
2648       }
2649       counter += temp;
2650       xadj[i+1] = counter;
2651       ierr = MatRestoreRow(A, cumSumVertices[rank] + i, &temp, &cols, NULL);CHKERRQ(ierr);
2652     }
2653 
2654 
2655   ierr = PetscMalloc1(cumSumVertices[rank+1]-cumSumVertices[rank], &part);CHKERRQ(ierr);
2656   ierr = PetscMalloc1(ncon*(1 + numNonExclusivelyOwned), &vtxwgt);CHKERRQ(ierr);
2657   vtxwgt[0] = numExclusivelyOwned;
2658   if (ncon>1) vtxwgt[1] = 1;
2659   for (i=0; i<numNonExclusivelyOwned; i++) {
2660     vtxwgt[ncon*(i+1)] = 1;
2661     if (ncon>1) vtxwgt[ncon*(i+1)+1] = 0;
2662   }
2663 
2664   if (flg) {
2665     ierr = PetscPrintf(comm, "Attempt rebalancing of shared points of depth %D on interface of mesh distribution.\n", entityDepth);CHKERRQ(ierr);
2666     ierr = PetscPrintf(comm, "Size of generated auxiliary graph: %D\n", cumSumVertices[size]);CHKERRQ(ierr);
2667   }
2668   if (parallel) {
2669     if (flg) { ierr = PetscPrintf(comm, "Using ParMETIS to partition graph.\n");CHKERRQ(ierr); }
2670     if (useInitialGuess) {
2671       if (flg) { ierr = PetscPrintf(comm, "Using current distribution of points as initial guess.\n");CHKERRQ(ierr); }
2672       PetscStackPush("ParMETIS_V3_RefineKway");
2673       ierr = ParMETIS_V3_RefineKway(cumSumVertices, xadj, adjncy, vtxwgt, adjwgt, &wgtflag, &numflag, &ncon, &nparts, tpwgts, ubvec, options, &edgecut, part, &comm);
2674       PetscStackPop;
2675     } else {
2676       PetscStackPush("ParMETIS_V3_PartKway");
2677       ierr = ParMETIS_V3_PartKway(cumSumVertices, xadj, adjncy, vtxwgt, adjwgt, &wgtflag, &numflag, &ncon, &nparts, tpwgts, ubvec, options, &edgecut, part, &comm);
2678       PetscStackPop;
2679     }
2680   } else {
2681     if (flg) { ierr = PetscPrintf(comm, "Using METIS to partition graph.\n");CHKERRQ(ierr); }
2682     Mat As;
2683     PetscInt numRows;
2684     PetscInt *partGlobal;
2685     ierr = MatCreateRedundantMatrix(A, size, MPI_COMM_NULL, MAT_INITIAL_MATRIX, &As);CHKERRQ(ierr);
2686 
2687     PetscInt *numExclusivelyOwnedAll;
2688     ierr = PetscMalloc1(size, &numExclusivelyOwnedAll);CHKERRQ(ierr);
2689     numExclusivelyOwnedAll[rank] = numExclusivelyOwned;
2690     ierr = MPI_Allgather(MPI_IN_PLACE,0,MPI_DATATYPE_NULL,numExclusivelyOwnedAll,1,MPIU_INT,comm);CHKERRQ(ierr);
2691 
2692     ierr = MatGetSize(As, &numRows, NULL);CHKERRQ(ierr);
2693     ierr = PetscMalloc1(numRows, &partGlobal);CHKERRQ(ierr);
2694     if (rank == 0) {
2695       PetscInt *adjncy_g, *xadj_g, *vtxwgt_g;
2696       lenadjncy = 0;
2697 
2698       for (i=0; i<numRows; i++) {
2699         PetscInt temp=0;
2700         ierr = MatGetRow(As, i, &temp, NULL, NULL);CHKERRQ(ierr);
2701         lenadjncy += temp;
2702         ierr = MatRestoreRow(As, i, &temp, NULL, NULL);CHKERRQ(ierr);
2703       }
2704       ierr = PetscMalloc1(lenadjncy, &adjncy_g);CHKERRQ(ierr);
2705       lenxadj = 1 + numRows;
2706       ierr = PetscMalloc1(lenxadj, &xadj_g);CHKERRQ(ierr);
2707       xadj_g[0] = 0;
2708       counter = 0;
2709       for (i=0; i<numRows; i++) {
2710         PetscInt        temp=0;
2711         const PetscInt *cols;
2712         ierr = MatGetRow(As, i, &temp, &cols, NULL);CHKERRQ(ierr);
2713         for (j=0; j<temp; j++) {
2714           adjncy_g[counter+j] = cols[j];
2715         }
2716         counter += temp;
2717         xadj_g[i+1] = counter;
2718         ierr = MatRestoreRow(As, i, &temp, &cols, NULL);CHKERRQ(ierr);
2719       }
2720       /*METIS_PartGraphKway(&numRows, &ncon, xadj_g, adjncy_g, vwgt, NULL, adjwgt, &nparts, tpwgts, ubvec, options, &edgecut, part);*/
2721       ierr = PetscMalloc1(2*numRows, &vtxwgt_g);CHKERRQ(ierr);
2722       for (i=0; i<size; i++){
2723         vtxwgt_g[ncon*cumSumVertices[i]] = numExclusivelyOwnedAll[i];
2724         if (ncon>1) vtxwgt_g[ncon*cumSumVertices[i]+1] = 1;
2725         for (j=cumSumVertices[i]+1; j<cumSumVertices[i+1]; j++) {
2726           vtxwgt_g[ncon*j] = 1;
2727           if (ncon>1) vtxwgt_g[2*j+1] = 0;
2728         }
2729       }
2730       ierr = PetscMalloc1(64, &options);CHKERRQ(ierr);
2731       ierr = METIS_SetDefaultOptions(options); /* initialize all defaults */
2732       options[METIS_OPTION_CONTIG]  = 1;
2733       PetscStackPush("METIS_PartGraphKway");
2734       METIS_PartGraphKway(&numRows, &ncon, xadj_g, adjncy_g, vtxwgt_g, NULL, NULL, &nparts, tpwgts, ubvec, options, &edgecut, partGlobal);
2735       PetscStackPop;
2736       PetscInt *distribution;
2737       ierr = PetscCalloc1(size, &distribution);CHKERRQ(ierr);
2738       for (i=0; i<numRows; i++) {
2739           distribution[partGlobal[i]] += vtxwgt_g[ncon*i];
2740       }
2741       if (flg) {
2742         ierr = PetscIntView(size, distribution, PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
2743       }
2744       ierr = PetscFree(distribution);CHKERRQ(ierr);
2745       ierr = PetscFree(xadj_g);CHKERRQ(ierr);
2746       ierr = PetscFree(adjncy_g);CHKERRQ(ierr);
2747       ierr = PetscFree(vtxwgt_g);CHKERRQ(ierr);
2748     }
2749     ierr = PetscFree(numExclusivelyOwnedAll);CHKERRQ(ierr);
2750 
2751     ierr = MPI_Bcast(partGlobal,numRows,MPIU_INT,0, comm);CHKERRQ(ierr);
2752     for (i=cumSumVertices[rank]; i<cumSumVertices[rank+1]; i++) {
2753       part[i-cumSumVertices[rank]] = partGlobal[i];
2754     }
2755     ierr = PetscFree(partGlobal);CHKERRQ(ierr);
2756     ierr = MatDestroy(&As);CHKERRQ(ierr);
2757   }
2758 
2759   ierr = MatDestroy(&A);CHKERRQ(ierr);
2760   ierr = PetscFree(ubvec);CHKERRQ(ierr);
2761   ierr = PetscFree(tpwgts);CHKERRQ(ierr);
2762   ierr = PetscFree(options);CHKERRQ(ierr);
2763 
2764 
2765   /* Now rename the result so that the vertex resembling the exclusively owned points stays on the same rank */
2766 
2767   ierr = PetscMalloc1(size, &firstVertices);CHKERRQ(ierr);
2768   ierr = PetscMalloc1(size, &renumbering);CHKERRQ(ierr);
2769   firstVertices[rank] = part[0];
2770   ierr = MPI_Allgather(MPI_IN_PLACE,0,MPI_DATATYPE_NULL,firstVertices,1,MPIU_INT,comm);CHKERRQ(ierr);
2771   for (i=0; i<size; i++) {
2772     renumbering[firstVertices[i]] = i;
2773   }
2774   for (i=0; i<cumSumVertices[rank+1]-cumSumVertices[rank]; i++) {
2775     part[i] = renumbering[part[i]];
2776   }
2777   /* Check if the renumbering worked (this can fail when ParMETIS gives fewer partitions than there are processes) */
2778   failed = (PetscInt)(part[0] != rank);
2779   ierr = MPI_Allreduce(&failed, &failedGlobal, 1, MPIU_INT, MPI_SUM, comm);CHKERRQ(ierr);
2780 
2781   if (failedGlobal > 0) {
2782     PetscFunctionReturn(1);
2783   }
2784 
2785 
2786   /*Let's check how well we did distributing points*/
2787   if (flg) {
2788     PetscInt *distribution, *distribution_before, min, max, min_before, max_before;
2789     ierr = PetscCalloc1(size, &distribution);CHKERRQ(ierr);
2790     ierr = PetscCalloc1(size, &distribution_before);CHKERRQ(ierr);
2791     for (i=0; i<cumSumVertices[rank+1]-cumSumVertices[rank]; i++) {
2792       distribution[part[i]] += vtxwgt[ncon*i];
2793       distribution_before[rank] += vtxwgt[ncon*i];
2794     }
2795     ierr = MPI_Allreduce(MPI_IN_PLACE, distribution, size, MPIU_INT, MPI_SUM, comm);CHKERRQ(ierr);
2796     ierr = MPI_Allreduce(MPI_IN_PLACE, distribution_before, size, MPIU_INT, MPI_SUM, comm);CHKERRQ(ierr);
2797     min = distribution[0];
2798     max = distribution[0];
2799     min_before = distribution_before[0];
2800     max_before = distribution_before[0];
2801     for (i=1; i<size; i++) {
2802       if (distribution[i]<min) min=distribution[i];
2803       if (distribution[i]>max) max=distribution[i];
2804       if (distribution_before[i]<min_before) min_before=distribution_before[i];
2805       if (distribution_before[i]>max_before) max_before=distribution_before[i];
2806     }
2807     PetscPrintf(comm, "Comparing number of owned entities of depth %D on each process before rebalancing, after rebalancing, and after consistency checks.\n", entityDepth);
2808     ierr = PetscPrintf(comm, "Initial.     Min: %D, Max: %D, Ratio: %f\n", min_before, max_before, (max_before*1.)/min_before);CHKERRQ(ierr);
2809     ierr = PetscPrintf(comm, "Rebalanced.  Min: %D, Max: %D, Ratio: %f\n", min, max, (max*1.)/min);CHKERRQ(ierr);
2810     ierr = PetscFree(distribution);CHKERRQ(ierr);
2811     ierr = PetscFree(distribution_before);CHKERRQ(ierr);
2812   }
2813 
2814   /* Now check that every vertex is owned by a process that it is actually connected to. */
2815   for (i=1; i<=numNonExclusivelyOwned; i++) {
2816     PetscInt loc = 0;
2817     ierr = PetscFindInt(cumSumVertices[part[i]], xadj[i+1]-xadj[i], &adjncy[xadj[i]], &loc);CHKERRQ(ierr);
2818     /* If not, then just set the owner to the original owner (hopefully a rare event, it means that a vertex has been isolated) */
2819     if (loc<0) {
2820       part[i] = rank;
2821     }
2822   }
2823 
2824   /* Let's see how significant the influences of the previous fixing up step was.*/
2825   if (flg) {
2826     PetscInt *distribution, min, max;
2827     ierr = PetscCalloc1(size, &distribution);CHKERRQ(ierr);
2828     for (i=0; i<cumSumVertices[rank+1]-cumSumVertices[rank]; i++) {
2829       distribution[part[i]] += vtxwgt[ncon*i];
2830     }
2831     ierr = MPI_Allreduce(MPI_IN_PLACE, distribution, size, MPIU_INT, MPI_SUM, comm);CHKERRQ(ierr);
2832     min = distribution[0];
2833     max = distribution[0];
2834     for (i=1; i<size; i++) {
2835       if (distribution[i]<min) min=distribution[i];
2836       if (distribution[i]>max) max=distribution[i];
2837     }
2838     ierr = PetscPrintf(comm, "After.      Min: %D, Max: %D, Ratio: %f\n", min, max, (max*1.)/min);CHKERRQ(ierr);
2839     ierr = PetscFree(distribution);CHKERRQ(ierr);
2840   }
2841 
2842   ierr = PetscFree(cumSumVertices);CHKERRQ(ierr);
2843   ierr = PetscFree(firstVertices);CHKERRQ(ierr);
2844   ierr = PetscFree(renumbering);CHKERRQ(ierr);
2845   ierr = PetscFree(xadj);CHKERRQ(ierr);
2846   ierr = PetscFree(adjncy);CHKERRQ(ierr);
2847   ierr = PetscFree(vtxwgt);CHKERRQ(ierr);
2848 
2849 
2850   /* Figure out the new owners of the vertices that are up for grabs and their numbers on the new owners */
2851   PetscInt *newOwners, *newNumbers;
2852   ierr = PetscMalloc1(pEnd-pStart, &newOwners);CHKERRQ(ierr);
2853   ierr = PetscMalloc1(pEnd-pStart, &newNumbers);CHKERRQ(ierr);
2854   for (i=0; i<pEnd-pStart; i++) {
2855     newOwners[i] = -1;
2856     newNumbers[i] = -1;
2857   }
2858   {
2859     PetscInt oldNumber, newNumber, oldOwner, newOwner;
2860     counter = 1;
2861     for (i=0; i<pEnd-pStart; i++) {
2862       if (toBalance[i]) {
2863         if (isNonExclusivelyOwned[i]) {
2864           oldNumber = i;
2865           newNumber = -1;
2866           oldOwner = rank;
2867           newOwner = part[counter];
2868           if (oldOwner == newOwner) {
2869             newNumber = oldNumber;
2870           } else {
2871             for (j=0; j<degree[i]; j++) {
2872               if (locationsOfLeafs[cumSumDegrees[oldNumber]+j] == newOwner) {
2873                 newNumber = remoteLocalPointOfLeafs[cumSumDegrees[oldNumber]+j];
2874                 break;
2875               }
2876             }
2877           }
2878           if (newNumber == -1) {
2879             SETERRQ(PetscObjectComm((PetscObject) part), PETSC_ERR_SUP, "Couldn't find the new owner of vertex.");
2880           }
2881           newOwners[oldNumber] = newOwner;
2882           newNumbers[oldNumber] = newNumber;
2883           counter++;
2884         }
2885       }
2886     }
2887   }
2888   ierr = PetscFree(cumSumDegrees);CHKERRQ(ierr);
2889   ierr = PetscFree(locationsOfLeafs);CHKERRQ(ierr);
2890   ierr = PetscFree(remoteLocalPointOfLeafs);CHKERRQ(ierr);
2891 
2892   PetscSFBcastBegin(sf, MPIU_INT, newOwners, newOwners);
2893   PetscSFBcastEnd(sf, MPIU_INT, newOwners, newOwners);
2894   PetscSFBcastBegin(sf, MPIU_INT, newNumbers, newNumbers);
2895   PetscSFBcastEnd(sf, MPIU_INT, newNumbers, newNumbers);
2896 
2897   /* Now count how many leafs we have on each processor. */
2898   leafCounter=0;
2899   for (i=0; i<pEnd-pStart; i++) {
2900     if (toBalance[i]){
2901       if (newOwners[i] >= 0 && newOwners[i] != rank) {
2902         leafCounter++;
2903       }
2904     } else {
2905       if (isLeaf[i]) {
2906         leafCounter++;
2907       }
2908     }
2909   }
2910 
2911   /* Now set up the new sf by creating the leaf arrays */
2912   ierr = PetscMalloc1(leafCounter, &leafsNew);CHKERRQ(ierr);
2913   ierr = PetscMalloc1(leafCounter, &leafLocationsNew);CHKERRQ(ierr);
2914 
2915   counter = 0;
2916   leafCounter = 0;
2917   for (i=0; i<pEnd-pStart; i++) {
2918     if (toBalance[i]){
2919       if (isLeaf[i]) {
2920         counter++;
2921       }
2922       if (newOwners[i] >= 0 && newOwners[i] != rank) {
2923         leafsNew[leafCounter] = i;
2924         leafLocationsNew[leafCounter].rank = newOwners[i];
2925         leafLocationsNew[leafCounter].index = newNumbers[i];
2926         leafCounter++;
2927       }
2928     } else {
2929       if (isLeaf[i]) {
2930         leafsNew[leafCounter] = i;
2931         leafLocationsNew[leafCounter].rank = iremote[counter].rank;
2932         leafLocationsNew[leafCounter].index = iremote[counter].index;
2933         leafCounter++;
2934         counter++;
2935       }
2936     }
2937   }
2938 
2939   ierr = PetscSFSetGraph(sf, nroots, leafCounter, leafsNew, PETSC_OWN_POINTER, leafLocationsNew, PETSC_OWN_POINTER);CHKERRQ(ierr);
2940 
2941 
2942   ierr = PetscFree(toBalance);CHKERRQ(ierr);
2943   ierr = PetscFree(isLeaf);CHKERRQ(ierr);
2944   ierr = PetscFree(isNonExclusivelyOwned);CHKERRQ(ierr);
2945   ierr = PetscFree(isExclusivelyOwned);CHKERRQ(ierr);
2946   ierr = PetscFree(newOwners);CHKERRQ(ierr);
2947   ierr = PetscFree(newNumbers);CHKERRQ(ierr);
2948   ierr = PetscLogEventEnd(DMPLEX_RebalanceSharedPoints, dm, 0, 0, 0);CHKERRQ(ierr);
2949 #else
2950   SETERRQ(PetscObjectComm((PetscObject) part), PETSC_ERR_SUP, "Mesh partitioning needs external package support.\nPlease reconfigure with --download-parmetis.");
2951 #endif
2952   PetscFunctionReturn(0);
2953 }
2954