xref: /petsc/src/dm/impls/plex/plexpartition.c (revision ed44d2701abdca960b283fd73577758251cceaab)
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   ierr = SCOTCH_dgraphMapCompute(&grafdat, &mappdat, &stradat);CHKERRPTSCOTCH(ierr);
1756   SCOTCH_dgraphMapExit(&grafdat, &mappdat);
1757   SCOTCH_archExit(&archdat);
1758   SCOTCH_stratExit(&stradat);
1759   SCOTCH_dgraphExit(&grafdat);
1760   PetscFunctionReturn(0);
1761 }
1762 
1763 #endif /* PETSC_HAVE_PTSCOTCH */
1764 
1765 static PetscErrorCode PetscPartitionerDestroy_PTScotch(PetscPartitioner part)
1766 {
1767   PetscPartitioner_PTScotch *p = (PetscPartitioner_PTScotch *) part->data;
1768   PetscErrorCode             ierr;
1769 
1770   PetscFunctionBegin;
1771   ierr = PetscFree(p);CHKERRQ(ierr);
1772   PetscFunctionReturn(0);
1773 }
1774 
1775 static PetscErrorCode PetscPartitionerView_PTScotch_Ascii(PetscPartitioner part, PetscViewer viewer)
1776 {
1777   PetscPartitioner_PTScotch *p = (PetscPartitioner_PTScotch *) part->data;
1778   PetscErrorCode            ierr;
1779 
1780   PetscFunctionBegin;
1781   ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
1782   ierr = PetscViewerASCIIPrintf(viewer, "using partitioning strategy %s\n",PTScotchStrategyList[p->strategy]);CHKERRQ(ierr);
1783   ierr = PetscViewerASCIIPrintf(viewer, "using load imbalance ratio %g\n",(double)p->imbalance);CHKERRQ(ierr);
1784   ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
1785   PetscFunctionReturn(0);
1786 }
1787 
1788 static PetscErrorCode PetscPartitionerView_PTScotch(PetscPartitioner part, PetscViewer viewer)
1789 {
1790   PetscBool      iascii;
1791   PetscErrorCode ierr;
1792 
1793   PetscFunctionBegin;
1794   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
1795   PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
1796   ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);CHKERRQ(ierr);
1797   if (iascii) {ierr = PetscPartitionerView_PTScotch_Ascii(part, viewer);CHKERRQ(ierr);}
1798   PetscFunctionReturn(0);
1799 }
1800 
1801 static PetscErrorCode PetscPartitionerSetFromOptions_PTScotch(PetscOptionItems *PetscOptionsObject, PetscPartitioner part)
1802 {
1803   PetscPartitioner_PTScotch *p = (PetscPartitioner_PTScotch *) part->data;
1804   const char *const         *slist = PTScotchStrategyList;
1805   PetscInt                  nlist = (PetscInt)(sizeof(PTScotchStrategyList)/sizeof(PTScotchStrategyList[0]));
1806   PetscBool                 flag;
1807   PetscErrorCode            ierr;
1808 
1809   PetscFunctionBegin;
1810   ierr = PetscOptionsHead(PetscOptionsObject, "PetscPartitioner PTScotch Options");CHKERRQ(ierr);
1811   ierr = PetscOptionsEList("-petscpartitioner_ptscotch_strategy","Partitioning strategy","",slist,nlist,slist[p->strategy],&p->strategy,&flag);CHKERRQ(ierr);
1812   ierr = PetscOptionsReal("-petscpartitioner_ptscotch_imbalance","Load imbalance ratio","",p->imbalance,&p->imbalance,&flag);CHKERRQ(ierr);
1813   ierr = PetscOptionsTail();CHKERRQ(ierr);
1814   PetscFunctionReturn(0);
1815 }
1816 
1817 static PetscErrorCode PetscPartitionerPartition_PTScotch(PetscPartitioner part, DM dm, PetscInt nparts, PetscInt numVertices, PetscInt start[], PetscInt adjacency[], PetscSection partSection, IS *partition)
1818 {
1819 #if defined(PETSC_HAVE_PTSCOTCH)
1820   MPI_Comm       comm       = PetscObjectComm((PetscObject)part);
1821   PetscInt       nvtxs      = numVertices; /* The number of vertices in full graph */
1822   PetscInt      *vtxdist;                  /* Distribution of vertices across processes */
1823   PetscInt      *xadj       = start;       /* Start of edge list for each vertex */
1824   PetscInt      *adjncy     = adjacency;   /* Edge lists for all vertices */
1825   PetscInt      *vwgt       = NULL;        /* Vertex weights */
1826   PetscInt      *adjwgt     = NULL;        /* Edge weights */
1827   PetscInt       v, i, *assignment, *points;
1828   PetscMPIInt    size, rank, p;
1829   PetscErrorCode ierr;
1830 
1831   PetscFunctionBegin;
1832   ierr = MPI_Comm_size(comm, &size);CHKERRQ(ierr);
1833   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
1834   ierr = PetscMalloc2(nparts+1,&vtxdist,PetscMax(nvtxs,1),&assignment);CHKERRQ(ierr);
1835 
1836   /* Calculate vertex distribution */
1837   vtxdist[0] = 0;
1838   ierr = MPI_Allgather(&nvtxs, 1, MPIU_INT, &vtxdist[1], 1, MPIU_INT, comm);CHKERRQ(ierr);
1839   for (p = 2; p <= size; ++p) {
1840     vtxdist[p] += vtxdist[p-1];
1841   }
1842 
1843   if (nparts == 1) {
1844     ierr = PetscMemzero(assignment, nvtxs * sizeof(PetscInt));CHKERRQ(ierr);
1845   } else {
1846     PetscSection section;
1847     /* Weight cells by dofs on cell by default */
1848     ierr = PetscMalloc1(PetscMax(nvtxs,1),&vwgt);CHKERRQ(ierr);
1849     ierr = DMGetSection(dm, &section);CHKERRQ(ierr);
1850     if (section) {
1851       PetscInt vStart, eEnd, dof;
1852       ierr = DMPlexGetHeightStratum(dm, 0, &vStart, &eEnd);CHKERRQ(ierr);
1853       for (v = vStart; v < eEnd; ++v) {
1854         ierr = PetscSectionGetDof(section, v, &dof);CHKERRQ(ierr);
1855         /* WARNING: Assumes that meshes with overlap have the overlapped cells at the end of the stratum. */
1856         /* To do this properly, we should use the cell numbering created in DMPlexCreatePartitionerGraph. */
1857         if (v-vStart < numVertices) vwgt[v-vStart] = PetscMax(dof, 1);
1858       }
1859     } else {
1860       for (v = 0; v < nvtxs; ++v) vwgt[v] = 1;
1861     }
1862     {
1863       PetscPartitioner_PTScotch *pts = (PetscPartitioner_PTScotch *) part->data;
1864       int                       strat = PTScotch_Strategy(pts->strategy);
1865       double                    imbal = (double)pts->imbalance;
1866 
1867       for (p = 0; !vtxdist[p+1] && p < size; ++p);
1868       if (vtxdist[p+1] == vtxdist[size]) {
1869         if (rank == p) {
1870           ierr = PTScotch_PartGraph_Seq(strat, imbal, nvtxs, xadj, adjncy, vwgt, adjwgt, nparts, assignment);CHKERRQ(ierr);
1871         }
1872       } else {
1873         ierr = PTScotch_PartGraph_MPI(strat, imbal, vtxdist, xadj, adjncy, vwgt, adjwgt, nparts, assignment, comm);CHKERRQ(ierr);
1874       }
1875     }
1876     ierr = PetscFree(vwgt);CHKERRQ(ierr);
1877   }
1878 
1879   /* Convert to PetscSection+IS */
1880   ierr = PetscSectionSetChart(partSection, 0, nparts);CHKERRQ(ierr);
1881   for (v = 0; v < nvtxs; ++v) {ierr = PetscSectionAddDof(partSection, assignment[v], 1);CHKERRQ(ierr);}
1882   ierr = PetscSectionSetUp(partSection);CHKERRQ(ierr);
1883   ierr = PetscMalloc1(nvtxs, &points);CHKERRQ(ierr);
1884   for (p = 0, i = 0; p < nparts; ++p) {
1885     for (v = 0; v < nvtxs; ++v) {
1886       if (assignment[v] == p) points[i++] = v;
1887     }
1888   }
1889   if (i != nvtxs) SETERRQ2(comm, PETSC_ERR_PLIB, "Number of points %D should be %D", i, nvtxs);
1890   ierr = ISCreateGeneral(comm, nvtxs, points, PETSC_OWN_POINTER, partition);CHKERRQ(ierr);
1891 
1892   ierr = PetscFree2(vtxdist,assignment);CHKERRQ(ierr);
1893   PetscFunctionReturn(0);
1894 #else
1895   SETERRQ(PetscObjectComm((PetscObject) part), PETSC_ERR_SUP, "Mesh partitioning needs external package support.\nPlease reconfigure with --download-ptscotch.");
1896 #endif
1897 }
1898 
1899 static PetscErrorCode PetscPartitionerInitialize_PTScotch(PetscPartitioner part)
1900 {
1901   PetscFunctionBegin;
1902   part->ops->view           = PetscPartitionerView_PTScotch;
1903   part->ops->destroy        = PetscPartitionerDestroy_PTScotch;
1904   part->ops->partition      = PetscPartitionerPartition_PTScotch;
1905   part->ops->setfromoptions = PetscPartitionerSetFromOptions_PTScotch;
1906   PetscFunctionReturn(0);
1907 }
1908 
1909 /*MC
1910   PETSCPARTITIONERPTSCOTCH = "ptscotch" - A PetscPartitioner object using the PT-Scotch library
1911 
1912   Level: intermediate
1913 
1914 .seealso: PetscPartitionerType, PetscPartitionerCreate(), PetscPartitionerSetType()
1915 M*/
1916 
1917 PETSC_EXTERN PetscErrorCode PetscPartitionerCreate_PTScotch(PetscPartitioner part)
1918 {
1919   PetscPartitioner_PTScotch *p;
1920   PetscErrorCode          ierr;
1921 
1922   PetscFunctionBegin;
1923   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
1924   ierr = PetscNewLog(part, &p);CHKERRQ(ierr);
1925   part->data = p;
1926 
1927   p->strategy  = 0;
1928   p->imbalance = 0.01;
1929 
1930   ierr = PetscPartitionerInitialize_PTScotch(part);CHKERRQ(ierr);
1931   ierr = PetscCitationsRegister(PTScotchPartitionerCitation, &PTScotchPartitionercite);CHKERRQ(ierr);
1932   PetscFunctionReturn(0);
1933 }
1934 
1935 
1936 /*@
1937   DMPlexGetPartitioner - Get the mesh partitioner
1938 
1939   Not collective
1940 
1941   Input Parameter:
1942 . dm - The DM
1943 
1944   Output Parameter:
1945 . part - The PetscPartitioner
1946 
1947   Level: developer
1948 
1949   Note: This gets a borrowed reference, so the user should not destroy this PetscPartitioner.
1950 
1951 .seealso DMPlexDistribute(), DMPlexSetPartitioner(), PetscPartitionerCreate()
1952 @*/
1953 PetscErrorCode DMPlexGetPartitioner(DM dm, PetscPartitioner *part)
1954 {
1955   DM_Plex       *mesh = (DM_Plex *) dm->data;
1956 
1957   PetscFunctionBegin;
1958   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1959   PetscValidPointer(part, 2);
1960   *part = mesh->partitioner;
1961   PetscFunctionReturn(0);
1962 }
1963 
1964 /*@
1965   DMPlexSetPartitioner - Set the mesh partitioner
1966 
1967   logically collective on dm and part
1968 
1969   Input Parameters:
1970 + dm - The DM
1971 - part - The partitioner
1972 
1973   Level: developer
1974 
1975   Note: Any existing PetscPartitioner will be destroyed.
1976 
1977 .seealso DMPlexDistribute(), DMPlexGetPartitioner(), PetscPartitionerCreate()
1978 @*/
1979 PetscErrorCode DMPlexSetPartitioner(DM dm, PetscPartitioner part)
1980 {
1981   DM_Plex       *mesh = (DM_Plex *) dm->data;
1982   PetscErrorCode ierr;
1983 
1984   PetscFunctionBegin;
1985   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1986   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 2);
1987   ierr = PetscObjectReference((PetscObject)part);CHKERRQ(ierr);
1988   ierr = PetscPartitionerDestroy(&mesh->partitioner);CHKERRQ(ierr);
1989   mesh->partitioner = part;
1990   PetscFunctionReturn(0);
1991 }
1992 
1993 static PetscErrorCode DMPlexAddClosure_Tree(DM dm, PetscHSetI ht, PetscInt point, PetscBool up, PetscBool down)
1994 {
1995   PetscErrorCode ierr;
1996 
1997   PetscFunctionBegin;
1998   if (up) {
1999     PetscInt parent;
2000 
2001     ierr = DMPlexGetTreeParent(dm,point,&parent,NULL);CHKERRQ(ierr);
2002     if (parent != point) {
2003       PetscInt closureSize, *closure = NULL, i;
2004 
2005       ierr = DMPlexGetTransitiveClosure(dm,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
2006       for (i = 0; i < closureSize; i++) {
2007         PetscInt cpoint = closure[2*i];
2008 
2009         ierr = PetscHSetIAdd(ht, cpoint);CHKERRQ(ierr);
2010         ierr = DMPlexAddClosure_Tree(dm,ht,cpoint,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
2011       }
2012       ierr = DMPlexRestoreTransitiveClosure(dm,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
2013     }
2014   }
2015   if (down) {
2016     PetscInt numChildren;
2017     const PetscInt *children;
2018 
2019     ierr = DMPlexGetTreeChildren(dm,point,&numChildren,&children);CHKERRQ(ierr);
2020     if (numChildren) {
2021       PetscInt i;
2022 
2023       for (i = 0; i < numChildren; i++) {
2024         PetscInt cpoint = children[i];
2025 
2026         ierr = PetscHSetIAdd(ht, cpoint);CHKERRQ(ierr);
2027         ierr = DMPlexAddClosure_Tree(dm,ht,cpoint,PETSC_FALSE,PETSC_TRUE);CHKERRQ(ierr);
2028       }
2029     }
2030   }
2031   PetscFunctionReturn(0);
2032 }
2033 
2034 /*@
2035   DMPlexPartitionLabelClosure - Add the closure of all points to the partition label
2036 
2037   Input Parameters:
2038 + dm     - The DM
2039 - label  - DMLabel assinging ranks to remote roots
2040 
2041   Level: developer
2042 
2043 .seealso: DMPlexPartitionLabelCreateSF, DMPlexDistribute(), DMPlexCreateOverlap
2044 @*/
2045 PetscErrorCode DMPlexPartitionLabelClosure(DM dm, DMLabel label)
2046 {
2047   IS              rankIS,   pointIS;
2048   const PetscInt *ranks,   *points;
2049   PetscInt        numRanks, numPoints, r, p, c, closureSize;
2050   PetscInt       *closure = NULL;
2051   DM_Plex        *mesh    = (DM_Plex *)dm->data;
2052   PetscBool       hasTree = (mesh->parentSection || mesh->childSection) ? PETSC_TRUE : PETSC_FALSE;
2053   PetscErrorCode  ierr;
2054 
2055   PetscFunctionBegin;
2056   ierr = DMLabelGetValueIS(label, &rankIS);CHKERRQ(ierr);
2057   ierr = ISGetLocalSize(rankIS, &numRanks);CHKERRQ(ierr);
2058   ierr = ISGetIndices(rankIS, &ranks);CHKERRQ(ierr);
2059 
2060   for (r = 0; r < numRanks; ++r) {
2061     const PetscInt rank = ranks[r];
2062     PetscHSetI     ht;
2063     PetscInt       nelems, *elems, off = 0;
2064 
2065     ierr = DMLabelGetStratumIS(label, rank, &pointIS);CHKERRQ(ierr);
2066     ierr = ISGetLocalSize(pointIS, &numPoints);CHKERRQ(ierr);
2067     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
2068     ierr = PetscHSetICreate(&ht);CHKERRQ(ierr);
2069     ierr = PetscHSetIResize(ht, numPoints*16);CHKERRQ(ierr);
2070     for (p = 0; p < numPoints; ++p) {
2071       ierr = DMPlexGetTransitiveClosure(dm, points[p], PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
2072       for (c = 0; c < closureSize*2; c += 2) {
2073         ierr = PetscHSetIAdd(ht, closure[c]);CHKERRQ(ierr);
2074         if (hasTree) {ierr = DMPlexAddClosure_Tree(dm, ht, closure[c], PETSC_TRUE, PETSC_TRUE);CHKERRQ(ierr);}
2075       }
2076     }
2077     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
2078     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2079     ierr = PetscHSetIGetSize(ht, &nelems);CHKERRQ(ierr);
2080     ierr = PetscMalloc1(nelems, &elems);CHKERRQ(ierr);
2081     ierr = PetscHSetIGetElems(ht, &off, elems);CHKERRQ(ierr);
2082     ierr = PetscHSetIDestroy(&ht);CHKERRQ(ierr);
2083     ierr = PetscSortInt(nelems, elems);CHKERRQ(ierr);
2084     ierr = ISCreateGeneral(PETSC_COMM_SELF, nelems, elems, PETSC_OWN_POINTER, &pointIS);CHKERRQ(ierr);
2085     ierr = DMLabelSetStratumIS(label, rank, pointIS);CHKERRQ(ierr);
2086     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2087   }
2088 
2089   if (closure) {ierr = DMPlexRestoreTransitiveClosure(dm, 0, PETSC_TRUE, NULL, &closure);CHKERRQ(ierr);}
2090   ierr = ISRestoreIndices(rankIS, &ranks);CHKERRQ(ierr);
2091   ierr = ISDestroy(&rankIS);CHKERRQ(ierr);
2092   PetscFunctionReturn(0);
2093 }
2094 
2095 /*@
2096   DMPlexPartitionLabelAdjacency - Add one level of adjacent points to the partition label
2097 
2098   Input Parameters:
2099 + dm     - The DM
2100 - label  - DMLabel assinging ranks to remote roots
2101 
2102   Level: developer
2103 
2104 .seealso: DMPlexPartitionLabelCreateSF, DMPlexDistribute(), DMPlexCreateOverlap
2105 @*/
2106 PetscErrorCode DMPlexPartitionLabelAdjacency(DM dm, DMLabel label)
2107 {
2108   IS              rankIS,   pointIS;
2109   const PetscInt *ranks,   *points;
2110   PetscInt        numRanks, numPoints, r, p, a, adjSize;
2111   PetscInt       *adj = NULL;
2112   PetscErrorCode  ierr;
2113 
2114   PetscFunctionBegin;
2115   ierr = DMLabelGetValueIS(label, &rankIS);CHKERRQ(ierr);
2116   ierr = ISGetLocalSize(rankIS, &numRanks);CHKERRQ(ierr);
2117   ierr = ISGetIndices(rankIS, &ranks);CHKERRQ(ierr);
2118   for (r = 0; r < numRanks; ++r) {
2119     const PetscInt rank = ranks[r];
2120 
2121     ierr = DMLabelGetStratumIS(label, rank, &pointIS);CHKERRQ(ierr);
2122     ierr = ISGetLocalSize(pointIS, &numPoints);CHKERRQ(ierr);
2123     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
2124     for (p = 0; p < numPoints; ++p) {
2125       adjSize = PETSC_DETERMINE;
2126       ierr = DMPlexGetAdjacency(dm, points[p], &adjSize, &adj);CHKERRQ(ierr);
2127       for (a = 0; a < adjSize; ++a) {ierr = DMLabelSetValue(label, adj[a], rank);CHKERRQ(ierr);}
2128     }
2129     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
2130     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2131   }
2132   ierr = ISRestoreIndices(rankIS, &ranks);CHKERRQ(ierr);
2133   ierr = ISDestroy(&rankIS);CHKERRQ(ierr);
2134   ierr = PetscFree(adj);CHKERRQ(ierr);
2135   PetscFunctionReturn(0);
2136 }
2137 
2138 /*@
2139   DMPlexPartitionLabelPropagate - Propagate points in a partition label over the point SF
2140 
2141   Input Parameters:
2142 + dm     - The DM
2143 - label  - DMLabel assinging ranks to remote roots
2144 
2145   Level: developer
2146 
2147   Note: This is required when generating multi-level overlaps to capture
2148   overlap points from non-neighbouring partitions.
2149 
2150 .seealso: DMPlexPartitionLabelCreateSF, DMPlexDistribute(), DMPlexCreateOverlap
2151 @*/
2152 PetscErrorCode DMPlexPartitionLabelPropagate(DM dm, DMLabel label)
2153 {
2154   MPI_Comm        comm;
2155   PetscMPIInt     rank;
2156   PetscSF         sfPoint;
2157   DMLabel         lblRoots, lblLeaves;
2158   IS              rankIS, pointIS;
2159   const PetscInt *ranks;
2160   PetscInt        numRanks, r;
2161   PetscErrorCode  ierr;
2162 
2163   PetscFunctionBegin;
2164   ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr);
2165   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
2166   ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);
2167   /* Pull point contributions from remote leaves into local roots */
2168   ierr = DMLabelGather(label, sfPoint, &lblLeaves);CHKERRQ(ierr);
2169   ierr = DMLabelGetValueIS(lblLeaves, &rankIS);CHKERRQ(ierr);
2170   ierr = ISGetLocalSize(rankIS, &numRanks);CHKERRQ(ierr);
2171   ierr = ISGetIndices(rankIS, &ranks);CHKERRQ(ierr);
2172   for (r = 0; r < numRanks; ++r) {
2173     const PetscInt remoteRank = ranks[r];
2174     if (remoteRank == rank) continue;
2175     ierr = DMLabelGetStratumIS(lblLeaves, remoteRank, &pointIS);CHKERRQ(ierr);
2176     ierr = DMLabelInsertIS(label, pointIS, remoteRank);CHKERRQ(ierr);
2177     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2178   }
2179   ierr = ISRestoreIndices(rankIS, &ranks);CHKERRQ(ierr);
2180   ierr = ISDestroy(&rankIS);CHKERRQ(ierr);
2181   ierr = DMLabelDestroy(&lblLeaves);CHKERRQ(ierr);
2182   /* Push point contributions from roots into remote leaves */
2183   ierr = DMLabelDistribute(label, sfPoint, &lblRoots);CHKERRQ(ierr);
2184   ierr = DMLabelGetValueIS(lblRoots, &rankIS);CHKERRQ(ierr);
2185   ierr = ISGetLocalSize(rankIS, &numRanks);CHKERRQ(ierr);
2186   ierr = ISGetIndices(rankIS, &ranks);CHKERRQ(ierr);
2187   for (r = 0; r < numRanks; ++r) {
2188     const PetscInt remoteRank = ranks[r];
2189     if (remoteRank == rank) continue;
2190     ierr = DMLabelGetStratumIS(lblRoots, remoteRank, &pointIS);CHKERRQ(ierr);
2191     ierr = DMLabelInsertIS(label, pointIS, remoteRank);CHKERRQ(ierr);
2192     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2193   }
2194   ierr = ISRestoreIndices(rankIS, &ranks);CHKERRQ(ierr);
2195   ierr = ISDestroy(&rankIS);CHKERRQ(ierr);
2196   ierr = DMLabelDestroy(&lblRoots);CHKERRQ(ierr);
2197   PetscFunctionReturn(0);
2198 }
2199 
2200 /*@
2201   DMPlexPartitionLabelInvert - Create a partition label of remote roots from a local root label
2202 
2203   Input Parameters:
2204 + dm        - The DM
2205 . rootLabel - DMLabel assinging ranks to local roots
2206 . processSF - A star forest mapping into the local index on each remote rank
2207 
2208   Output Parameter:
2209 - leafLabel - DMLabel assinging ranks to remote roots
2210 
2211   Note: The rootLabel defines a send pattern by mapping local points to remote target ranks. The
2212   resulting leafLabel is a receiver mapping of remote roots to their parent rank.
2213 
2214   Level: developer
2215 
2216 .seealso: DMPlexPartitionLabelCreateSF, DMPlexDistribute(), DMPlexCreateOverlap
2217 @*/
2218 PetscErrorCode DMPlexPartitionLabelInvert(DM dm, DMLabel rootLabel, PetscSF processSF, DMLabel leafLabel)
2219 {
2220   MPI_Comm           comm;
2221   PetscMPIInt        rank, size;
2222   PetscInt           p, n, numNeighbors, ssize, l, nleaves;
2223   PetscSF            sfPoint;
2224   PetscSFNode       *rootPoints, *leafPoints;
2225   PetscSection       rootSection, leafSection;
2226   const PetscSFNode *remote;
2227   const PetscInt    *local, *neighbors;
2228   IS                 valueIS;
2229   PetscErrorCode     ierr;
2230 
2231   PetscFunctionBegin;
2232   ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr);
2233   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
2234   ierr = MPI_Comm_size(comm, &size);CHKERRQ(ierr);
2235   ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);
2236 
2237   /* Convert to (point, rank) and use actual owners */
2238   ierr = PetscSectionCreate(comm, &rootSection);CHKERRQ(ierr);
2239   ierr = PetscSectionSetChart(rootSection, 0, size);CHKERRQ(ierr);
2240   ierr = DMLabelGetValueIS(rootLabel, &valueIS);CHKERRQ(ierr);
2241   ierr = ISGetLocalSize(valueIS, &numNeighbors);CHKERRQ(ierr);
2242   ierr = ISGetIndices(valueIS, &neighbors);CHKERRQ(ierr);
2243   for (n = 0; n < numNeighbors; ++n) {
2244     PetscInt numPoints;
2245 
2246     ierr = DMLabelGetStratumSize(rootLabel, neighbors[n], &numPoints);CHKERRQ(ierr);
2247     ierr = PetscSectionAddDof(rootSection, neighbors[n], numPoints);CHKERRQ(ierr);
2248   }
2249   ierr = PetscSectionSetUp(rootSection);CHKERRQ(ierr);
2250   ierr = PetscSectionGetStorageSize(rootSection, &ssize);CHKERRQ(ierr);
2251   ierr = PetscMalloc1(ssize, &rootPoints);CHKERRQ(ierr);
2252   ierr = PetscSFGetGraph(sfPoint, NULL, &nleaves, &local, &remote);CHKERRQ(ierr);
2253   for (n = 0; n < numNeighbors; ++n) {
2254     IS              pointIS;
2255     const PetscInt *points;
2256     PetscInt        off, numPoints, p;
2257 
2258     ierr = PetscSectionGetOffset(rootSection, neighbors[n], &off);CHKERRQ(ierr);
2259     ierr = DMLabelGetStratumIS(rootLabel, neighbors[n], &pointIS);CHKERRQ(ierr);
2260     ierr = ISGetLocalSize(pointIS, &numPoints);CHKERRQ(ierr);
2261     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
2262     for (p = 0; p < numPoints; ++p) {
2263       if (local) {ierr = PetscFindInt(points[p], nleaves, local, &l);CHKERRQ(ierr);}
2264       else       {l = -1;}
2265       if (l >= 0) {rootPoints[off+p] = remote[l];}
2266       else        {rootPoints[off+p].index = points[p]; rootPoints[off+p].rank = rank;}
2267     }
2268     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
2269     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2270   }
2271   ierr = ISRestoreIndices(valueIS, &neighbors);CHKERRQ(ierr);
2272   ierr = ISDestroy(&valueIS);CHKERRQ(ierr);
2273   /* Communicate overlap */
2274   ierr = PetscSectionCreate(comm, &leafSection);CHKERRQ(ierr);
2275   ierr = DMPlexDistributeData(dm, processSF, rootSection, MPIU_2INT, rootPoints, leafSection, (void**) &leafPoints);CHKERRQ(ierr);
2276   /* Filter remote contributions (ovLeafPoints) into the overlapSF */
2277   ierr = PetscSectionGetStorageSize(leafSection, &ssize);CHKERRQ(ierr);
2278   for (p = 0; p < ssize; p++) {
2279     ierr = DMLabelSetValue(leafLabel, leafPoints[p].index, leafPoints[p].rank);CHKERRQ(ierr);
2280   }
2281   ierr = PetscFree(rootPoints);CHKERRQ(ierr);
2282   ierr = PetscSectionDestroy(&rootSection);CHKERRQ(ierr);
2283   ierr = PetscFree(leafPoints);CHKERRQ(ierr);
2284   ierr = PetscSectionDestroy(&leafSection);CHKERRQ(ierr);
2285   PetscFunctionReturn(0);
2286 }
2287 
2288 /*@
2289   DMPlexPartitionLabelCreateSF - Create a star forest from a label that assigns ranks to points
2290 
2291   Input Parameters:
2292 + dm    - The DM
2293 . label - DMLabel assinging ranks to remote roots
2294 
2295   Output Parameter:
2296 - sf    - The star forest communication context encapsulating the defined mapping
2297 
2298   Note: The incoming label is a receiver mapping of remote points to their parent rank.
2299 
2300   Level: developer
2301 
2302 .seealso: DMPlexDistribute(), DMPlexCreateOverlap
2303 @*/
2304 PetscErrorCode DMPlexPartitionLabelCreateSF(DM dm, DMLabel label, PetscSF *sf)
2305 {
2306   PetscMPIInt     rank, size;
2307   PetscInt        n, numRemote, p, numPoints, pStart, pEnd, idx = 0;
2308   PetscSFNode    *remotePoints;
2309   IS              remoteRootIS;
2310   const PetscInt *remoteRoots;
2311   PetscErrorCode ierr;
2312 
2313   PetscFunctionBegin;
2314   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRQ(ierr);
2315   ierr = MPI_Comm_size(PetscObjectComm((PetscObject) dm), &size);CHKERRQ(ierr);
2316 
2317   for (numRemote = 0, n = 0; n < size; ++n) {
2318     ierr = DMLabelGetStratumSize(label, n, &numPoints);CHKERRQ(ierr);
2319     numRemote += numPoints;
2320   }
2321   ierr = PetscMalloc1(numRemote, &remotePoints);CHKERRQ(ierr);
2322   /* Put owned points first */
2323   ierr = DMLabelGetStratumSize(label, rank, &numPoints);CHKERRQ(ierr);
2324   if (numPoints > 0) {
2325     ierr = DMLabelGetStratumIS(label, rank, &remoteRootIS);CHKERRQ(ierr);
2326     ierr = ISGetIndices(remoteRootIS, &remoteRoots);CHKERRQ(ierr);
2327     for (p = 0; p < numPoints; p++) {
2328       remotePoints[idx].index = remoteRoots[p];
2329       remotePoints[idx].rank = rank;
2330       idx++;
2331     }
2332     ierr = ISRestoreIndices(remoteRootIS, &remoteRoots);CHKERRQ(ierr);
2333     ierr = ISDestroy(&remoteRootIS);CHKERRQ(ierr);
2334   }
2335   /* Now add remote points */
2336   for (n = 0; n < size; ++n) {
2337     ierr = DMLabelGetStratumSize(label, n, &numPoints);CHKERRQ(ierr);
2338     if (numPoints <= 0 || n == rank) continue;
2339     ierr = DMLabelGetStratumIS(label, n, &remoteRootIS);CHKERRQ(ierr);
2340     ierr = ISGetIndices(remoteRootIS, &remoteRoots);CHKERRQ(ierr);
2341     for (p = 0; p < numPoints; p++) {
2342       remotePoints[idx].index = remoteRoots[p];
2343       remotePoints[idx].rank = n;
2344       idx++;
2345     }
2346     ierr = ISRestoreIndices(remoteRootIS, &remoteRoots);CHKERRQ(ierr);
2347     ierr = ISDestroy(&remoteRootIS);CHKERRQ(ierr);
2348   }
2349   ierr = PetscSFCreate(PetscObjectComm((PetscObject) dm), sf);CHKERRQ(ierr);
2350   ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
2351   ierr = PetscSFSetGraph(*sf, pEnd-pStart, numRemote, NULL, PETSC_OWN_POINTER, remotePoints, PETSC_OWN_POINTER);CHKERRQ(ierr);
2352   PetscFunctionReturn(0);
2353 }
2354 
2355 /*@
2356   DMPlexRebalanceSharedPoints - Redistribute points in the plex that are shared in order to achieve better balancing.
2357 
2358   Input parameters:
2359   + dm - The DMPlex object.
2360   + entityDepth: depth of the entity to balance (0 -> balance vertices).
2361   + useInitialGuess: whether to use the current distribution as initial guess (only used by ParMETIS).
2362   + parallel: Whether to use ParMETIS and do the partition in parallel or whether to gather the graph onto a single process and use METIS.
2363 
2364   Level: user
2365 
2366 @*/
2367 
2368 PetscErrorCode DMPlexRebalanceSharedPoints(DM dm, PetscInt entityDepth, PetscBool useInitialGuess, PetscBool parallel)
2369 {
2370 #if defined(PETSC_HAVE_PARMETIS)
2371   PetscSF     sf;
2372   PetscInt    ierr, i, j;
2373   PetscInt    eBegin, eEnd, nroots, nleafs, pStart, pEnd, sumDegrees;
2374   const       PetscInt *degree, *ilocal;
2375   const       PetscSFNode *iremote; /* Do I need to free these? */
2376   PetscBool   *toBalance, *isLeaf, *isExclusivelyOwned, *isNonExclusivelyOwned;
2377   PetscInt    numExclusivelyOwned, numNonExclusivelyOwned;
2378   PetscMPIInt rank, size;
2379   PetscInt    *numLocalVerticesAllProcesses, *cumSumVertices, *cumSumDegrees, *globalNumbersOfLocalOwnedVertices, *locationsOfLeafs, *rankOnLeafs, *remoteLocalPointOfLeafs, *points, *leafGlobalNumbers;
2380   PetscInt    offset, counter;
2381   PetscInt    lenadjncy, numNonExclusivelyOwnedConnectTo, numLeafs;
2382   PetscInt    *xadj, *adjncy, *vtxwgt;
2383   PetscInt    lenxadj;
2384 
2385   PetscInt    *adjwgt = NULL;
2386   PetscInt    *part, *options;
2387   PetscInt    nparts, wgtflag, numflag, ncon, edgecut;
2388   real_t      *ubvec;
2389   PetscInt    *firstVertices, *renumbering;
2390   PetscInt    failed, failedGlobal;
2391   MPI_Comm    comm;
2392   PetscInt    leafCounter;
2393   PetscInt    *leafsNew;
2394   PetscSFNode *leafLocationsNew;
2395   Mat         A, Apre;
2396   PetscScalar one = 1;
2397   PetscBool   flg = PETSC_FALSE;
2398   const char *prefix = NULL;
2399   PetscViewer       viewer;
2400   PetscViewerFormat format;
2401 
2402   PetscFunctionBegin;
2403 
2404   ierr = PetscObjectGetOptionsPrefix((PetscObject)dm, &prefix);CHKERRQ(ierr);
2405   ierr = PetscOptionsGetBool(NULL, prefix, "-dm_rebalance_partition_view", &flg, NULL);
2406 
2407   ierr = PetscLogEventBegin(DMPLEX_RebalanceSharedPoints, dm, 0, 0, 0);CHKERRQ(ierr);
2408 
2409   ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr);
2410 
2411   if (flg) {
2412     ierr = PetscOptionsGetViewer(comm,((PetscObject)dm)->options, prefix,"-dm_rebalance_partition_view",&viewer,&format,NULL);
2413     ierr = PetscViewerPushFormat(viewer,format);
2414   }
2415 
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. */
2422   ierr = DMPlexGetDepthStratum(dm, entityDepth, &eBegin, &eEnd);CHKERRQ(ierr);
2423   ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
2424   ierr = PetscMalloc1(pEnd-pStart, &toBalance);CHKERRQ(ierr);
2425 
2426   for (i=0; i<pEnd-pStart; i++) {
2427     toBalance[i] = (i-pStart>=eBegin && i-pStart<eEnd);
2428   }
2429 
2430 
2431   /* There are three types of points:
2432    * exclusivelyOwned: points that are owned by this process and only seen by this process
2433    * nonExclusivelyOwned: points that are owned by this process but seen by at least another process
2434    * leaf: a point that is seen by this process but owned by a different process
2435    */
2436   ierr = DMGetPointSF(dm, &sf);CHKERRQ(ierr);
2437   ierr = PetscSFGetGraph(sf, &nroots, &nleafs, &ilocal, &iremote); CHKERRQ(ierr);
2438   ierr = PetscMalloc1(pEnd-pStart, &isLeaf);CHKERRQ(ierr);
2439   ierr = PetscMalloc1(pEnd-pStart, &isNonExclusivelyOwned);CHKERRQ(ierr);
2440   ierr = PetscMalloc1(pEnd-pStart, &isExclusivelyOwned);CHKERRQ(ierr);
2441   for (i=0; i<pEnd-pStart; i++) {
2442     isNonExclusivelyOwned[i] = PETSC_FALSE;
2443     isExclusivelyOwned[i] = PETSC_FALSE;
2444     isLeaf[i] = PETSC_FALSE;
2445   }
2446 
2447 
2448   /* start by marking all the leafs */
2449   for (i=0; i<nleafs; i++) {
2450     isLeaf[ilocal[i]-pStart] = PETSC_TRUE;
2451   }
2452 
2453   /* for an owned point, we can figure out whether another processor sees it or
2454    * not by calculating its degree */
2455   ierr = PetscSFComputeDegreeBegin(sf, &degree);CHKERRQ(ierr);
2456   ierr = PetscSFComputeDegreeEnd(sf, &degree);CHKERRQ(ierr);
2457 
2458   numExclusivelyOwned=0;
2459   numNonExclusivelyOwned=0;
2460   for (i=0; i<pEnd-pStart; i++) {
2461     if (toBalance[i]) {
2462       if (degree[i] > 0) {
2463         isNonExclusivelyOwned[i] = PETSC_TRUE;
2464         numNonExclusivelyOwned += 1;
2465       } else {
2466         if (!isLeaf[i]) {
2467           isExclusivelyOwned[i] = PETSC_TRUE;
2468           numExclusivelyOwned += 1;
2469         }
2470       }
2471     }
2472   }
2473 
2474 
2475   /* We are going to build a graph with one vertex per core representing the
2476    * exclusively owned points and then one vertex per nonExclusively owned
2477    * point. */
2478   ierr = PetscMalloc1(size, &numLocalVerticesAllProcesses);CHKERRQ(ierr);
2479   numLocalVerticesAllProcesses[rank] = 1 + numNonExclusivelyOwned;
2480   /* For numbering purposes we need to figure out how many vertices are on each core. */
2481   ierr = MPI_Allgather(MPI_IN_PLACE,0,MPI_DATATYPE_NULL,numLocalVerticesAllProcesses,1,MPIU_INT,comm);CHKERRQ(ierr);
2482 
2483   ierr = PetscMalloc1(size+1, &cumSumVertices);CHKERRQ(ierr);
2484   cumSumVertices[0] = 0;
2485   for (i=1; i<=size; i++) {
2486     cumSumVertices[i] = cumSumVertices[i-1] + numLocalVerticesAllProcesses[i-1];
2487   }
2488   ierr = PetscFree(numLocalVerticesAllProcesses);CHKERRQ(ierr);
2489   ierr = PetscMalloc1(pEnd-pStart+1, &cumSumDegrees);CHKERRQ(ierr);
2490   cumSumDegrees[0] = 0;
2491   for (i=1; i<=pEnd-pStart; i++) {
2492     cumSumDegrees[i] = cumSumDegrees[i-1] + degree[i-1];
2493   }
2494   ierr = PetscMalloc1(pEnd-pStart, &globalNumbersOfLocalOwnedVertices);CHKERRQ(ierr);
2495 
2496   offset = cumSumVertices[rank];
2497   counter = 0;
2498   for (i=0; i<pEnd-pStart; i++) {
2499     if (toBalance[i]) {
2500       if (degree[i] > 0) {
2501         globalNumbersOfLocalOwnedVertices[i] = counter + 1 + offset;
2502         counter++;
2503       }
2504     }
2505   }
2506 
2507   /* get the location of my leafs (we have sumDegrees many leafs pointing at our roots) */
2508   sumDegrees = 0;
2509   for (i=0; i<pEnd-pStart; i++) {
2510     sumDegrees += degree[i];
2511   }
2512 
2513   ierr = PetscMalloc1(sumDegrees, &locationsOfLeafs);CHKERRQ(ierr);
2514   ierr = PetscMalloc1(pEnd-pStart, &rankOnLeafs);CHKERRQ(ierr);
2515   for (i=0; i<pEnd-pStart; i++) {
2516     rankOnLeafs[i] = rank;
2517   }
2518   ierr = PetscSFGatherBegin(sf, MPIU_INT, rankOnLeafs, locationsOfLeafs);CHKERRQ(ierr);
2519   ierr = PetscSFGatherEnd(sf, MPIU_INT, rankOnLeafs, locationsOfLeafs);CHKERRQ(ierr);
2520   ierr = PetscFree(rankOnLeafs);CHKERRQ(ierr);
2521 
2522   /* get the remote local points of my leaves */
2523   ierr = PetscMalloc1(sumDegrees, &remoteLocalPointOfLeafs);CHKERRQ(ierr);
2524   ierr = PetscMalloc1(pEnd-pStart, &points);CHKERRQ(ierr);
2525   for (i=0; i<pEnd-pStart; i++) {
2526     points[i] = pStart+i;
2527   }
2528   ierr = PetscSFGatherBegin(sf, MPIU_INT, points, remoteLocalPointOfLeafs);CHKERRQ(ierr);
2529   ierr = PetscSFGatherEnd(sf, MPIU_INT, points, remoteLocalPointOfLeafs);CHKERRQ(ierr);
2530   ierr = PetscFree(points);CHKERRQ(ierr);
2531 
2532   /* send the global numbers of vertices I own to the leafs so that they know to connect to it */
2533   ierr = PetscMalloc1(pEnd-pStart, &leafGlobalNumbers);CHKERRQ(ierr);
2534   ierr = PetscSFBcastBegin(sf, MPIU_INT, globalNumbersOfLocalOwnedVertices, leafGlobalNumbers);CHKERRQ(ierr);
2535   ierr = PetscSFBcastEnd(sf, MPIU_INT, globalNumbersOfLocalOwnedVertices, leafGlobalNumbers);CHKERRQ(ierr);
2536 
2537   /* Now start building the data structur for ParMETIS */
2538   /* vtxdist = cum_sum_vertices */
2539 
2540   numNonExclusivelyOwnedConnectTo = 0;
2541   numLeafs = 0;
2542   for (i=0; i<pEnd-pStart; i++) {
2543     if (toBalance[i]) {
2544       if (isNonExclusivelyOwned[i]) {
2545         numNonExclusivelyOwnedConnectTo += 1 + degree[i];
2546       }
2547       if (isLeaf[i]) {
2548         numLeafs++;
2549       }
2550     }
2551   }
2552 
2553 
2554   ierr = MatCreate(comm, &Apre);CHKERRQ(ierr);
2555   ierr = MatSetType(Apre, MATPREALLOCATOR);CHKERRQ(ierr);
2556   ierr = MatSetSizes(Apre, 1+numNonExclusivelyOwned, 1+numNonExclusivelyOwned, cumSumVertices[size], cumSumVertices[size]);CHKERRQ(ierr);
2557   ierr = MatSetUp(Apre);CHKERRQ(ierr);
2558 
2559   for (i=0; i<pEnd-pStart; i++) {
2560     if (toBalance[i]) {
2561       if (isNonExclusivelyOwned[i]) {
2562         ierr = MatSetValues(Apre, 1, &(cumSumVertices[rank]), 1, &(globalNumbersOfLocalOwnedVertices[i]), &one, INSERT_VALUES);CHKERRQ(ierr);
2563         ierr = MatSetValues(Apre, 1, &(globalNumbersOfLocalOwnedVertices[i]), 1, &(cumSumVertices[rank]), &one, INSERT_VALUES);CHKERRQ(ierr);
2564       } else if (isLeaf[i]) {
2565         ierr = MatSetValues(Apre, 1, &(cumSumVertices[rank]), 1, &(leafGlobalNumbers[i]), &one, INSERT_VALUES);CHKERRQ(ierr);
2566         ierr = MatSetValues(Apre, 1, &(leafGlobalNumbers[i]), 1, &(cumSumVertices[rank]), &one, INSERT_VALUES);CHKERRQ(ierr);
2567       }
2568     }
2569   }
2570 
2571   ierr = MatAssemblyBegin(Apre, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2572   ierr = MatAssemblyEnd(Apre, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2573 
2574   ierr = MatCreate(comm, &A);CHKERRQ(ierr);
2575   ierr = MatSetType(A, MATMPIAIJ);CHKERRQ(ierr);
2576   ierr = MatSetSizes(A, 1+numNonExclusivelyOwned, 1+numNonExclusivelyOwned, cumSumVertices[size], cumSumVertices[size]);CHKERRQ(ierr);
2577   ierr = MatPreallocatorPreallocate(Apre, PETSC_FALSE, A);CHKERRQ(ierr);
2578   ierr = MatDestroy(&Apre);CHKERRQ(ierr);
2579 
2580   for (i=0; i<pEnd-pStart; i++) {
2581     if (toBalance[i]) {
2582       if (isNonExclusivelyOwned[i]) {
2583         ierr = MatSetValue(A, cumSumVertices[rank], globalNumbersOfLocalOwnedVertices[i], 1, INSERT_VALUES);CHKERRQ(ierr);
2584         ierr = MatSetValue(A, globalNumbersOfLocalOwnedVertices[i], cumSumVertices[rank], 1, INSERT_VALUES);CHKERRQ(ierr);
2585       } else if (isLeaf[i]) {
2586         ierr = MatSetValue(A, cumSumVertices[rank], leafGlobalNumbers[i], 1, INSERT_VALUES);CHKERRQ(ierr);
2587         ierr = MatSetValue(A, leafGlobalNumbers[i], cumSumVertices[rank], 1, INSERT_VALUES);CHKERRQ(ierr);
2588       }
2589     }
2590   }
2591 
2592   ierr = MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2593   ierr = MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2594   ierr = PetscFree(leafGlobalNumbers);CHKERRQ(ierr);
2595   ierr = PetscFree(globalNumbersOfLocalOwnedVertices);CHKERRQ(ierr);
2596 
2597   nparts = size;
2598   wgtflag = 2;
2599 
2600   numflag = 0;
2601   ncon = 2;
2602   real_t *tpwgts;
2603   ierr = PetscMalloc1(ncon * nparts, &tpwgts);CHKERRQ(ierr);
2604 
2605   for (i=0; i<ncon*nparts; i++) {
2606     tpwgts[i] = 1./(nparts);
2607   }
2608 
2609 
2610   ierr = PetscMalloc1(ncon, &ubvec);CHKERRQ(ierr);
2611   ubvec[0] = 1.01;
2612   if (ncon>1) ubvec[1] = 1.01;
2613   ierr = PetscMalloc1(1, &options);CHKERRQ(ierr);
2614   options[0] = 0;
2615     lenadjncy = 0;
2616     for (i=0; i<1+numNonExclusivelyOwned; i++) {
2617       PetscInt temp=0;
2618       ierr = MatGetRow(A, cumSumVertices[rank] + i, &temp, NULL, NULL);CHKERRQ(ierr);
2619       lenadjncy += temp;
2620       ierr = MatRestoreRow(A, cumSumVertices[rank] + i, &temp, NULL, NULL);CHKERRQ(ierr);
2621     }
2622     ierr = PetscMalloc1(lenadjncy, &adjncy);CHKERRQ(ierr);
2623     lenxadj = 2 + numNonExclusivelyOwned;
2624     ierr = PetscMalloc1(lenxadj, &xadj);CHKERRQ(ierr);
2625     xadj[0] = 0;
2626     counter = 0;
2627     for (i=0; i<1+numNonExclusivelyOwned; i++) {
2628       PetscInt        temp=0;
2629       const PetscInt *cols;
2630       ierr = MatGetRow(A, cumSumVertices[rank] + i, &temp, &cols, NULL);CHKERRQ(ierr);
2631       ierr = PetscMemcpy(&adjncy[counter], cols, temp*sizeof(PetscInt));CHKERRQ(ierr);
2632       counter += temp;
2633       xadj[i+1] = counter;
2634       ierr = MatRestoreRow(A, cumSumVertices[rank] + i, &temp, &cols, NULL);CHKERRQ(ierr);
2635     }
2636 
2637 
2638   ierr = PetscMalloc1(cumSumVertices[rank+1]-cumSumVertices[rank], &part);CHKERRQ(ierr);
2639   ierr = PetscMalloc1(ncon*(1 + numNonExclusivelyOwned), &vtxwgt);CHKERRQ(ierr);
2640   vtxwgt[0] = numExclusivelyOwned;
2641   if (ncon>1) vtxwgt[1] = 1;
2642   for (i=0; i<numNonExclusivelyOwned; i++) {
2643     vtxwgt[ncon*(i+1)] = 1;
2644     if (ncon>1) vtxwgt[ncon*(i+1)+1] = 0;
2645   }
2646 
2647   if (flg) {
2648     ierr = PetscViewerASCIIPrintf(viewer, "Attempt rebalancing of shared points of depth %D on interface of mesh distribution.\n", entityDepth);CHKERRQ(ierr);
2649     ierr = PetscViewerASCIIPrintf(viewer, "Size of generated auxiliary graph: %D\n", cumSumVertices[size]);CHKERRQ(ierr);
2650   }
2651   if (parallel) {
2652     if (flg) { ierr = PetscViewerASCIIPrintf(viewer, "Using ParMETIS to partition graph.\n");CHKERRQ(ierr); }
2653     if (useInitialGuess) {
2654       if (flg) { ierr = PetscViewerASCIIPrintf(viewer, "Using current distribution of points as initial guess.\n");CHKERRQ(ierr); }
2655       PetscStackPush("ParMETIS_V3_RefineKway");
2656       ierr = ParMETIS_V3_RefineKway(cumSumVertices, xadj, adjncy, vtxwgt, adjwgt, &wgtflag, &numflag, &ncon, &nparts, tpwgts, ubvec, options, &edgecut, part, &comm);
2657       PetscStackPop;
2658     } else {
2659       PetscStackPush("ParMETIS_V3_PartKway");
2660       ierr = ParMETIS_V3_PartKway(cumSumVertices, xadj, adjncy, vtxwgt, adjwgt, &wgtflag, &numflag, &ncon, &nparts, tpwgts, ubvec, options, &edgecut, part, &comm);
2661       PetscStackPop;
2662     }
2663   } else {
2664     if (flg) { ierr = PetscViewerASCIIPrintf(viewer, "Using METIS to partition graph.\n");CHKERRQ(ierr); }
2665     Mat As;
2666     PetscInt numRows;
2667     PetscInt *partGlobal;
2668     ierr = MatCreateRedundantMatrix(A, size, MPI_COMM_NULL, MAT_INITIAL_MATRIX, &As);CHKERRQ(ierr);
2669 
2670     PetscInt *numExclusivelyOwnedAll;
2671     ierr = PetscMalloc1(size, &numExclusivelyOwnedAll);CHKERRQ(ierr);
2672     numExclusivelyOwnedAll[rank] = numExclusivelyOwned;
2673     ierr = MPI_Allgather(MPI_IN_PLACE,0,MPI_DATATYPE_NULL,numExclusivelyOwnedAll,1,MPIU_INT,comm);CHKERRQ(ierr);
2674 
2675     ierr = MatGetSize(As, &numRows, NULL);CHKERRQ(ierr);
2676     ierr = PetscMalloc1(numRows, &partGlobal);CHKERRQ(ierr);
2677     if (rank == 0) {
2678       PetscInt *adjncy_g, *xadj_g, *vtxwgt_g;
2679       lenadjncy = 0;
2680 
2681       for (i=0; i<numRows; i++) {
2682         PetscInt temp=0;
2683         ierr = MatGetRow(As, i, &temp, NULL, NULL);CHKERRQ(ierr);
2684         lenadjncy += temp;
2685         ierr = MatRestoreRow(As, i, &temp, NULL, NULL);CHKERRQ(ierr);
2686       }
2687       ierr = PetscMalloc1(lenadjncy, &adjncy_g);CHKERRQ(ierr);
2688       lenxadj = 1 + numRows;
2689       ierr = PetscMalloc1(lenxadj, &xadj_g);CHKERRQ(ierr);
2690       xadj_g[0] = 0;
2691       counter = 0;
2692       for (i=0; i<numRows; i++) {
2693         PetscInt        temp=0;
2694         const PetscInt *cols;
2695         ierr = MatGetRow(As, i, &temp, &cols, NULL);CHKERRQ(ierr);
2696         ierr = PetscMemcpy(&adjncy_g[counter], cols, temp*sizeof(PetscInt));CHKERRQ(ierr);
2697         counter += temp;
2698         xadj_g[i+1] = counter;
2699         ierr = MatRestoreRow(As, i, &temp, &cols, NULL);CHKERRQ(ierr);
2700       }
2701       ierr = PetscMalloc1(2*numRows, &vtxwgt_g);CHKERRQ(ierr);
2702       for (i=0; i<size; i++){
2703         vtxwgt_g[ncon*cumSumVertices[i]] = numExclusivelyOwnedAll[i];
2704         if (ncon>1) vtxwgt_g[ncon*cumSumVertices[i]+1] = 1;
2705         for (j=cumSumVertices[i]+1; j<cumSumVertices[i+1]; j++) {
2706           vtxwgt_g[ncon*j] = 1;
2707           if (ncon>1) vtxwgt_g[2*j+1] = 0;
2708         }
2709       }
2710       ierr = PetscMalloc1(64, &options);CHKERRQ(ierr);
2711       ierr = METIS_SetDefaultOptions(options); /* initialize all defaults */
2712       options[METIS_OPTION_CONTIG]  = 1;
2713       PetscStackPush("METIS_PartGraphKway");
2714       METIS_PartGraphKway(&numRows, &ncon, xadj_g, adjncy_g, vtxwgt_g, NULL, NULL, &nparts, tpwgts, ubvec, options, &edgecut, partGlobal);
2715       PetscStackPop;
2716       ierr = PetscFree(xadj_g);CHKERRQ(ierr);
2717       ierr = PetscFree(adjncy_g);CHKERRQ(ierr);
2718       ierr = PetscFree(vtxwgt_g);CHKERRQ(ierr);
2719     }
2720     ierr = PetscFree(numExclusivelyOwnedAll);CHKERRQ(ierr);
2721 
2722     ierr = MPI_Bcast(partGlobal,numRows,MPIU_INT,0, comm);CHKERRQ(ierr);
2723     for (i=cumSumVertices[rank]; i<cumSumVertices[rank+1]; i++) {
2724       part[i-cumSumVertices[rank]] = partGlobal[i];
2725     }
2726     ierr = PetscFree(partGlobal);CHKERRQ(ierr);
2727     ierr = MatDestroy(&As);CHKERRQ(ierr);
2728   }
2729 
2730   ierr = MatDestroy(&A);CHKERRQ(ierr);
2731   ierr = PetscFree(ubvec);CHKERRQ(ierr);
2732   ierr = PetscFree(tpwgts);CHKERRQ(ierr);
2733   ierr = PetscFree(options);CHKERRQ(ierr);
2734 
2735 
2736   /* Now rename the result so that the vertex resembling the exclusively owned points stays on the same rank */
2737 
2738   ierr = PetscMalloc1(size, &firstVertices);CHKERRQ(ierr);
2739   ierr = PetscMalloc1(size, &renumbering);CHKERRQ(ierr);
2740   firstVertices[rank] = part[0];
2741   ierr = MPI_Allgather(MPI_IN_PLACE,0,MPI_DATATYPE_NULL,firstVertices,1,MPIU_INT,comm);CHKERRQ(ierr);
2742   for (i=0; i<size; i++) {
2743     renumbering[firstVertices[i]] = i;
2744   }
2745   for (i=0; i<cumSumVertices[rank+1]-cumSumVertices[rank]; i++) {
2746     part[i] = renumbering[part[i]];
2747   }
2748   /* Check if the renumbering worked (this can fail when ParMETIS gives fewer partitions than there are processes) */
2749   failed = (PetscInt)(part[0] != rank);
2750   ierr = MPI_Allreduce(&failed, &failedGlobal, 1, MPIU_INT, MPI_SUM, comm);CHKERRQ(ierr);
2751 
2752   if (failedGlobal > 0) {
2753     PetscFunctionReturn(1);
2754   }
2755 
2756 
2757   /*Let's check how well we did distributing points*/
2758   if (flg) {
2759     PetscInt *distribution, *distribution_before, min, max, min_before, max_before;
2760     ierr = PetscCalloc1(size, &distribution);CHKERRQ(ierr);
2761     ierr = PetscCalloc1(size, &distribution_before);CHKERRQ(ierr);
2762     for (i=0; i<cumSumVertices[rank+1]-cumSumVertices[rank]; i++) {
2763       distribution[part[i]] += vtxwgt[ncon*i];
2764       distribution_before[rank] += vtxwgt[ncon*i];
2765     }
2766     ierr = MPI_Allreduce(MPI_IN_PLACE, distribution, size, MPIU_INT, MPI_SUM, comm);CHKERRQ(ierr);
2767     ierr = MPI_Allreduce(MPI_IN_PLACE, distribution_before, size, MPIU_INT, MPI_SUM, comm);CHKERRQ(ierr);
2768     min = distribution[0];
2769     max = distribution[0];
2770     min_before = distribution_before[0];
2771     max_before = distribution_before[0];
2772     for (i=1; i<size; i++) {
2773       if (distribution[i]<min) min=distribution[i];
2774       if (distribution[i]>max) max=distribution[i];
2775       if (distribution_before[i]<min_before) min_before=distribution_before[i];
2776       if (distribution_before[i]>max_before) max_before=distribution_before[i];
2777     }
2778     ierr = PetscViewerASCIIPrintf(viewer, "Comparing number of owned entities of depth %D on each process before rebalancing, after rebalancing, and after consistency checks.\n", entityDepth);CHKERRQ(ierr);
2779     ierr = PetscViewerASCIIPrintf(viewer, "Initial.     Min: %D, Max: %D, Ratio: %f\n", min_before, max_before, (max_before*1.)/min_before);CHKERRQ(ierr);
2780     ierr = PetscViewerASCIIPrintf(viewer, "Rebalanced.  Min: %D, Max: %D, Ratio: %f\n", min, max, (max*1.)/min);CHKERRQ(ierr);
2781     ierr = PetscFree(distribution);CHKERRQ(ierr);
2782     ierr = PetscFree(distribution_before);CHKERRQ(ierr);
2783   }
2784 
2785   /* Now check that every vertex is owned by a process that it is actually connected to. */
2786   for (i=1; i<=numNonExclusivelyOwned; i++) {
2787     PetscInt loc = 0;
2788     ierr = PetscFindInt(cumSumVertices[part[i]], xadj[i+1]-xadj[i], &adjncy[xadj[i]], &loc);CHKERRQ(ierr);
2789     /* If not, then just set the owner to the original owner (hopefully a rare event, it means that a vertex has been isolated) */
2790     if (loc<0) {
2791       part[i] = rank;
2792     }
2793   }
2794 
2795   /* Let's see how significant the influences of the previous fixing up step was.*/
2796   if (flg) {
2797     PetscInt *distribution, min, max;
2798     ierr = PetscCalloc1(size, &distribution);CHKERRQ(ierr);
2799     for (i=0; i<cumSumVertices[rank+1]-cumSumVertices[rank]; i++) {
2800       distribution[part[i]] += vtxwgt[ncon*i];
2801     }
2802     ierr = MPI_Allreduce(MPI_IN_PLACE, distribution, size, MPIU_INT, MPI_SUM, comm);CHKERRQ(ierr);
2803     min = distribution[0];
2804     max = distribution[0];
2805     for (i=1; i<size; i++) {
2806       if (distribution[i]<min) min=distribution[i];
2807       if (distribution[i]>max) max=distribution[i];
2808     }
2809     ierr = PetscViewerASCIIPrintf(viewer, "After.      Min: %D, Max: %D, Ratio: %f\n", min, max, (max*1.)/min);CHKERRQ(ierr);
2810     ierr = PetscFree(distribution);CHKERRQ(ierr);
2811   }
2812 
2813   ierr = PetscFree(cumSumVertices);CHKERRQ(ierr);
2814   ierr = PetscFree(firstVertices);CHKERRQ(ierr);
2815   ierr = PetscFree(renumbering);CHKERRQ(ierr);
2816   ierr = PetscFree(xadj);CHKERRQ(ierr);
2817   ierr = PetscFree(adjncy);CHKERRQ(ierr);
2818   ierr = PetscFree(vtxwgt);CHKERRQ(ierr);
2819 
2820 
2821   /* Figure out the new owners of the vertices that are up for grabs and their numbers on the new owners */
2822   PetscInt *newOwners, *newNumbers;
2823   ierr = PetscMalloc1(pEnd-pStart, &newOwners);CHKERRQ(ierr);
2824   ierr = PetscMalloc1(pEnd-pStart, &newNumbers);CHKERRQ(ierr);
2825   for (i=0; i<pEnd-pStart; i++) {
2826     newOwners[i] = -1;
2827     newNumbers[i] = -1;
2828   }
2829   {
2830     PetscInt oldNumber, newNumber, oldOwner, newOwner;
2831     counter = 1;
2832     for (i=0; i<pEnd-pStart; i++) {
2833       if (toBalance[i]) {
2834         if (isNonExclusivelyOwned[i]) {
2835           oldNumber = i;
2836           newNumber = -1;
2837           oldOwner = rank;
2838           newOwner = part[counter];
2839           if (oldOwner == newOwner) {
2840             newNumber = oldNumber;
2841           } else {
2842             for (j=0; j<degree[i]; j++) {
2843               if (locationsOfLeafs[cumSumDegrees[oldNumber]+j] == newOwner) {
2844                 newNumber = remoteLocalPointOfLeafs[cumSumDegrees[oldNumber]+j];
2845                 break;
2846               }
2847             }
2848           }
2849           if (newNumber == -1) SETERRQ(PetscObjectComm((PetscObject) part), PETSC_ERR_SUP, "Couldn't find the new owner of vertex.");
2850 
2851           newOwners[oldNumber] = newOwner;
2852           newNumbers[oldNumber] = newNumber;
2853           counter++;
2854         }
2855       }
2856     }
2857   }
2858   ierr = PetscFree(cumSumDegrees);CHKERRQ(ierr);
2859   ierr = PetscFree(locationsOfLeafs);CHKERRQ(ierr);
2860   ierr = PetscFree(remoteLocalPointOfLeafs);CHKERRQ(ierr);
2861 
2862   ierr = PetscSFBcastBegin(sf, MPIU_INT, newOwners, newOwners);CHKERRQ(ierr);
2863   ierr = PetscSFBcastEnd(sf, MPIU_INT, newOwners, newOwners);CHKERRQ(ierr);
2864   ierr = PetscSFBcastBegin(sf, MPIU_INT, newNumbers, newNumbers);CHKERRQ(ierr);
2865   ierr = PetscSFBcastEnd(sf, MPIU_INT, newNumbers, newNumbers);CHKERRQ(ierr);
2866 
2867   /* Now count how many leafs we have on each processor. */
2868   leafCounter=0;
2869   for (i=0; i<pEnd-pStart; i++) {
2870     if (toBalance[i]){
2871       if (newOwners[i] >= 0 && newOwners[i] != rank) {
2872         leafCounter++;
2873       }
2874     } else {
2875       if (isLeaf[i]) {
2876         leafCounter++;
2877       }
2878     }
2879   }
2880 
2881   /* Now set up the new sf by creating the leaf arrays */
2882   ierr = PetscMalloc1(leafCounter, &leafsNew);CHKERRQ(ierr);
2883   ierr = PetscMalloc1(leafCounter, &leafLocationsNew);CHKERRQ(ierr);
2884 
2885   counter = 0;
2886   leafCounter = 0;
2887   for (i=0; i<pEnd-pStart; i++) {
2888     if (toBalance[i]){
2889       if (isLeaf[i]) {
2890         counter++;
2891       }
2892       if (newOwners[i] >= 0 && newOwners[i] != rank) {
2893         leafsNew[leafCounter] = i;
2894         leafLocationsNew[leafCounter].rank = newOwners[i];
2895         leafLocationsNew[leafCounter].index = newNumbers[i];
2896         leafCounter++;
2897       }
2898     } else {
2899       if (isLeaf[i]) {
2900         leafsNew[leafCounter] = i;
2901         leafLocationsNew[leafCounter].rank = iremote[counter].rank;
2902         leafLocationsNew[leafCounter].index = iremote[counter].index;
2903         leafCounter++;
2904         counter++;
2905       }
2906     }
2907   }
2908 
2909   ierr = PetscSFSetGraph(sf, nroots, leafCounter, leafsNew, PETSC_OWN_POINTER, leafLocationsNew, PETSC_OWN_POINTER);CHKERRQ(ierr);
2910 
2911 
2912   ierr = PetscFree(toBalance);CHKERRQ(ierr);
2913   ierr = PetscFree(isLeaf);CHKERRQ(ierr);
2914   ierr = PetscFree(isNonExclusivelyOwned);CHKERRQ(ierr);
2915   ierr = PetscFree(isExclusivelyOwned);CHKERRQ(ierr);
2916   ierr = PetscFree(newOwners);CHKERRQ(ierr);
2917   ierr = PetscFree(newNumbers);CHKERRQ(ierr);
2918   if (flg) {
2919     ierr = PetscViewerPopFormat(viewer);
2920     ierr = PetscViewerDestroy(&viewer);
2921   }
2922   ierr = PetscLogEventEnd(DMPLEX_RebalanceSharedPoints, dm, 0, 0, 0);CHKERRQ(ierr);
2923 #else
2924   SETERRQ(PetscObjectComm((PetscObject) part), PETSC_ERR_SUP, "Mesh partitioning needs external package support.\nPlease reconfigure with --download-parmetis.");
2925 #endif
2926   PetscFunctionReturn(0);
2927 }
2928