xref: /petsc/src/dm/impls/plex/plexpartition.c (revision a685ae26bbf9fb229cf02e15e73d16b8a9cd69e6)
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   ierr = SCOTCH_dgraphMapCompute(&grafdat, &mappdat, &stradat);CHKERRPTSCOTCH(ierr);
1755   SCOTCH_dgraphMapExit(&grafdat, &mappdat);
1756   SCOTCH_archExit(&archdat);
1757   SCOTCH_stratExit(&stradat);
1758   SCOTCH_dgraphExit(&grafdat);
1759   PetscFunctionReturn(0);
1760 }
1761 
1762 #endif /* PETSC_HAVE_PTSCOTCH */
1763 
1764 static PetscErrorCode PetscPartitionerDestroy_PTScotch(PetscPartitioner part)
1765 {
1766   PetscPartitioner_PTScotch *p = (PetscPartitioner_PTScotch *) part->data;
1767   PetscErrorCode             ierr;
1768 
1769   PetscFunctionBegin;
1770   ierr = PetscFree(p);CHKERRQ(ierr);
1771   PetscFunctionReturn(0);
1772 }
1773 
1774 static PetscErrorCode PetscPartitionerView_PTScotch_Ascii(PetscPartitioner part, PetscViewer viewer)
1775 {
1776   PetscPartitioner_PTScotch *p = (PetscPartitioner_PTScotch *) part->data;
1777   PetscErrorCode            ierr;
1778 
1779   PetscFunctionBegin;
1780   ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
1781   ierr = PetscViewerASCIIPrintf(viewer, "using partitioning strategy %s\n",PTScotchStrategyList[p->strategy]);CHKERRQ(ierr);
1782   ierr = PetscViewerASCIIPrintf(viewer, "using load imbalance ratio %g\n",(double)p->imbalance);CHKERRQ(ierr);
1783   ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
1784   PetscFunctionReturn(0);
1785 }
1786 
1787 static PetscErrorCode PetscPartitionerView_PTScotch(PetscPartitioner part, PetscViewer viewer)
1788 {
1789   PetscBool      iascii;
1790   PetscErrorCode ierr;
1791 
1792   PetscFunctionBegin;
1793   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
1794   PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
1795   ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);CHKERRQ(ierr);
1796   if (iascii) {ierr = PetscPartitionerView_PTScotch_Ascii(part, viewer);CHKERRQ(ierr);}
1797   PetscFunctionReturn(0);
1798 }
1799 
1800 static PetscErrorCode PetscPartitionerSetFromOptions_PTScotch(PetscOptionItems *PetscOptionsObject, PetscPartitioner part)
1801 {
1802   PetscPartitioner_PTScotch *p = (PetscPartitioner_PTScotch *) part->data;
1803   const char *const         *slist = PTScotchStrategyList;
1804   PetscInt                  nlist = (PetscInt)(sizeof(PTScotchStrategyList)/sizeof(PTScotchStrategyList[0]));
1805   PetscBool                 flag;
1806   PetscErrorCode            ierr;
1807 
1808   PetscFunctionBegin;
1809   ierr = PetscOptionsHead(PetscOptionsObject, "PetscPartitioner PTScotch Options");CHKERRQ(ierr);
1810   ierr = PetscOptionsEList("-petscpartitioner_ptscotch_strategy","Partitioning strategy","",slist,nlist,slist[p->strategy],&p->strategy,&flag);CHKERRQ(ierr);
1811   ierr = PetscOptionsReal("-petscpartitioner_ptscotch_imbalance","Load imbalance ratio","",p->imbalance,&p->imbalance,&flag);CHKERRQ(ierr);
1812   ierr = PetscOptionsTail();CHKERRQ(ierr);
1813   PetscFunctionReturn(0);
1814 }
1815 
1816 static PetscErrorCode PetscPartitionerPartition_PTScotch(PetscPartitioner part, DM dm, PetscInt nparts, PetscInt numVertices, PetscInt start[], PetscInt adjacency[], PetscSection partSection, IS *partition)
1817 {
1818 #if defined(PETSC_HAVE_PTSCOTCH)
1819   MPI_Comm       comm       = PetscObjectComm((PetscObject)part);
1820   PetscInt       nvtxs      = numVertices; /* The number of vertices in full graph */
1821   PetscInt      *vtxdist;                  /* Distribution of vertices across processes */
1822   PetscInt      *xadj       = start;       /* Start of edge list for each vertex */
1823   PetscInt      *adjncy     = adjacency;   /* Edge lists for all vertices */
1824   PetscInt      *vwgt       = NULL;        /* Vertex weights */
1825   PetscInt      *adjwgt     = NULL;        /* Edge weights */
1826   PetscInt       v, i, *assignment, *points;
1827   PetscMPIInt    size, rank, p;
1828   PetscErrorCode ierr;
1829 
1830   PetscFunctionBegin;
1831   ierr = MPI_Comm_size(comm, &size);CHKERRQ(ierr);
1832   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
1833   ierr = PetscMalloc2(nparts+1,&vtxdist,PetscMax(nvtxs,1),&assignment);CHKERRQ(ierr);
1834 
1835   /* Calculate vertex distribution */
1836   vtxdist[0] = 0;
1837   ierr = MPI_Allgather(&nvtxs, 1, MPIU_INT, &vtxdist[1], 1, MPIU_INT, comm);CHKERRQ(ierr);
1838   for (p = 2; p <= size; ++p) {
1839     vtxdist[p] += vtxdist[p-1];
1840   }
1841 
1842   if (nparts == 1) {
1843     ierr = PetscMemzero(assignment, nvtxs * sizeof(PetscInt));CHKERRQ(ierr);
1844   } else {
1845     PetscSection section;
1846     /* Weight cells by dofs on cell by default */
1847     ierr = PetscMalloc1(PetscMax(nvtxs,1),&vwgt);CHKERRQ(ierr);
1848     ierr = DMGetSection(dm, &section);CHKERRQ(ierr);
1849     if (section) {
1850       PetscInt vStart, vEnd, dof;
1851       ierr = DMPlexGetHeightStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
1852       for (v = vStart; v < vEnd; ++v) {
1853         ierr = PetscSectionGetDof(section, v, &dof);CHKERRQ(ierr);
1854         /* WARNING: Assumes that meshes with overlap have the overlapped cells at the end of the stratum. */
1855         /* To do this properly, we should use the cell numbering created in DMPlexCreatePartitionerGraph. */
1856         if (v-vStart < numVertices) vwgt[v-vStart] = PetscMax(dof, 1);
1857       }
1858     } else {
1859       for (v = 0; v < nvtxs; ++v) vwgt[v] = 1;
1860     }
1861     {
1862       PetscPartitioner_PTScotch *pts = (PetscPartitioner_PTScotch *) part->data;
1863       int                       strat = PTScotch_Strategy(pts->strategy);
1864       double                    imbal = (double)pts->imbalance;
1865 
1866       for (p = 0; !vtxdist[p+1] && p < size; ++p);
1867       if (vtxdist[p+1] == vtxdist[size]) {
1868         if (rank == p) {
1869           ierr = PTScotch_PartGraph_Seq(strat, imbal, nvtxs, xadj, adjncy, vwgt, adjwgt, nparts, assignment);CHKERRQ(ierr);
1870         }
1871       } else {
1872         ierr = PTScotch_PartGraph_MPI(strat, imbal, vtxdist, xadj, adjncy, vwgt, adjwgt, nparts, assignment, comm);CHKERRQ(ierr);
1873       }
1874     }
1875     ierr = PetscFree(vwgt);CHKERRQ(ierr);
1876   }
1877 
1878   /* Convert to PetscSection+IS */
1879   ierr = PetscSectionSetChart(partSection, 0, nparts);CHKERRQ(ierr);
1880   for (v = 0; v < nvtxs; ++v) {ierr = PetscSectionAddDof(partSection, assignment[v], 1);CHKERRQ(ierr);}
1881   ierr = PetscSectionSetUp(partSection);CHKERRQ(ierr);
1882   ierr = PetscMalloc1(nvtxs, &points);CHKERRQ(ierr);
1883   for (p = 0, i = 0; p < nparts; ++p) {
1884     for (v = 0; v < nvtxs; ++v) {
1885       if (assignment[v] == p) points[i++] = v;
1886     }
1887   }
1888   if (i != nvtxs) SETERRQ2(comm, PETSC_ERR_PLIB, "Number of points %D should be %D", i, nvtxs);
1889   ierr = ISCreateGeneral(comm, nvtxs, points, PETSC_OWN_POINTER, partition);CHKERRQ(ierr);
1890 
1891   ierr = PetscFree2(vtxdist,assignment);CHKERRQ(ierr);
1892   PetscFunctionReturn(0);
1893 #else
1894   SETERRQ(PetscObjectComm((PetscObject) part), PETSC_ERR_SUP, "Mesh partitioning needs external package support.\nPlease reconfigure with --download-ptscotch.");
1895 #endif
1896 }
1897 
1898 static PetscErrorCode PetscPartitionerInitialize_PTScotch(PetscPartitioner part)
1899 {
1900   PetscFunctionBegin;
1901   part->ops->view           = PetscPartitionerView_PTScotch;
1902   part->ops->destroy        = PetscPartitionerDestroy_PTScotch;
1903   part->ops->partition      = PetscPartitionerPartition_PTScotch;
1904   part->ops->setfromoptions = PetscPartitionerSetFromOptions_PTScotch;
1905   PetscFunctionReturn(0);
1906 }
1907 
1908 /*MC
1909   PETSCPARTITIONERPTSCOTCH = "ptscotch" - A PetscPartitioner object using the PT-Scotch library
1910 
1911   Level: intermediate
1912 
1913 .seealso: PetscPartitionerType, PetscPartitionerCreate(), PetscPartitionerSetType()
1914 M*/
1915 
1916 PETSC_EXTERN PetscErrorCode PetscPartitionerCreate_PTScotch(PetscPartitioner part)
1917 {
1918   PetscPartitioner_PTScotch *p;
1919   PetscErrorCode          ierr;
1920 
1921   PetscFunctionBegin;
1922   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
1923   ierr = PetscNewLog(part, &p);CHKERRQ(ierr);
1924   part->data = p;
1925 
1926   p->strategy  = 0;
1927   p->imbalance = 0.01;
1928 
1929   ierr = PetscPartitionerInitialize_PTScotch(part);CHKERRQ(ierr);
1930   ierr = PetscCitationsRegister(PTScotchPartitionerCitation, &PTScotchPartitionercite);CHKERRQ(ierr);
1931   PetscFunctionReturn(0);
1932 }
1933 
1934 
1935 /*@
1936   DMPlexGetPartitioner - Get the mesh partitioner
1937 
1938   Not collective
1939 
1940   Input Parameter:
1941 . dm - The DM
1942 
1943   Output Parameter:
1944 . part - The PetscPartitioner
1945 
1946   Level: developer
1947 
1948   Note: This gets a borrowed reference, so the user should not destroy this PetscPartitioner.
1949 
1950 .seealso DMPlexDistribute(), DMPlexSetPartitioner(), PetscPartitionerCreate()
1951 @*/
1952 PetscErrorCode DMPlexGetPartitioner(DM dm, PetscPartitioner *part)
1953 {
1954   DM_Plex       *mesh = (DM_Plex *) dm->data;
1955 
1956   PetscFunctionBegin;
1957   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1958   PetscValidPointer(part, 2);
1959   *part = mesh->partitioner;
1960   PetscFunctionReturn(0);
1961 }
1962 
1963 /*@
1964   DMPlexSetPartitioner - Set the mesh partitioner
1965 
1966   logically collective on dm and part
1967 
1968   Input Parameters:
1969 + dm - The DM
1970 - part - The partitioner
1971 
1972   Level: developer
1973 
1974   Note: Any existing PetscPartitioner will be destroyed.
1975 
1976 .seealso DMPlexDistribute(), DMPlexGetPartitioner(), PetscPartitionerCreate()
1977 @*/
1978 PetscErrorCode DMPlexSetPartitioner(DM dm, PetscPartitioner part)
1979 {
1980   DM_Plex       *mesh = (DM_Plex *) dm->data;
1981   PetscErrorCode ierr;
1982 
1983   PetscFunctionBegin;
1984   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1985   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 2);
1986   ierr = PetscObjectReference((PetscObject)part);CHKERRQ(ierr);
1987   ierr = PetscPartitionerDestroy(&mesh->partitioner);CHKERRQ(ierr);
1988   mesh->partitioner = part;
1989   PetscFunctionReturn(0);
1990 }
1991 
1992 static PetscErrorCode DMPlexAddClosure_Tree(DM dm, PetscHSetI ht, PetscInt point, PetscBool up, PetscBool down)
1993 {
1994   PetscErrorCode ierr;
1995 
1996   PetscFunctionBegin;
1997   if (up) {
1998     PetscInt parent;
1999 
2000     ierr = DMPlexGetTreeParent(dm,point,&parent,NULL);CHKERRQ(ierr);
2001     if (parent != point) {
2002       PetscInt closureSize, *closure = NULL, i;
2003 
2004       ierr = DMPlexGetTransitiveClosure(dm,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
2005       for (i = 0; i < closureSize; i++) {
2006         PetscInt cpoint = closure[2*i];
2007 
2008         ierr = PetscHSetIAdd(ht, cpoint);CHKERRQ(ierr);
2009         ierr = DMPlexAddClosure_Tree(dm,ht,cpoint,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
2010       }
2011       ierr = DMPlexRestoreTransitiveClosure(dm,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
2012     }
2013   }
2014   if (down) {
2015     PetscInt numChildren;
2016     const PetscInt *children;
2017 
2018     ierr = DMPlexGetTreeChildren(dm,point,&numChildren,&children);CHKERRQ(ierr);
2019     if (numChildren) {
2020       PetscInt i;
2021 
2022       for (i = 0; i < numChildren; i++) {
2023         PetscInt cpoint = children[i];
2024 
2025         ierr = PetscHSetIAdd(ht, cpoint);CHKERRQ(ierr);
2026         ierr = DMPlexAddClosure_Tree(dm,ht,cpoint,PETSC_FALSE,PETSC_TRUE);CHKERRQ(ierr);
2027       }
2028     }
2029   }
2030   PetscFunctionReturn(0);
2031 }
2032 
2033 /*@
2034   DMPlexPartitionLabelClosure - Add the closure of all points to the partition label
2035 
2036   Input Parameters:
2037 + dm     - The DM
2038 - label  - DMLabel assinging ranks to remote roots
2039 
2040   Level: developer
2041 
2042 .seealso: DMPlexPartitionLabelCreateSF, DMPlexDistribute(), DMPlexCreateOverlap
2043 @*/
2044 PetscErrorCode DMPlexPartitionLabelClosure(DM dm, DMLabel label)
2045 {
2046   IS              rankIS,   pointIS;
2047   const PetscInt *ranks,   *points;
2048   PetscInt        numRanks, numPoints, r, p, c, closureSize;
2049   PetscInt       *closure = NULL;
2050   DM_Plex        *mesh    = (DM_Plex *)dm->data;
2051   PetscBool       hasTree = (mesh->parentSection || mesh->childSection) ? PETSC_TRUE : PETSC_FALSE;
2052   PetscErrorCode  ierr;
2053 
2054   PetscFunctionBegin;
2055   ierr = DMLabelGetValueIS(label, &rankIS);CHKERRQ(ierr);
2056   ierr = ISGetLocalSize(rankIS, &numRanks);CHKERRQ(ierr);
2057   ierr = ISGetIndices(rankIS, &ranks);CHKERRQ(ierr);
2058 
2059   for (r = 0; r < numRanks; ++r) {
2060     const PetscInt rank = ranks[r];
2061     PetscHSetI     ht;
2062     PetscInt       nelems, *elems, off = 0;
2063 
2064     ierr = DMLabelGetStratumIS(label, rank, &pointIS);CHKERRQ(ierr);
2065     ierr = ISGetLocalSize(pointIS, &numPoints);CHKERRQ(ierr);
2066     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
2067     ierr = PetscHSetICreate(&ht);CHKERRQ(ierr);
2068     ierr = PetscHSetIResize(ht, numPoints*16);CHKERRQ(ierr);
2069     for (p = 0; p < numPoints; ++p) {
2070       ierr = DMPlexGetTransitiveClosure(dm, points[p], PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
2071       for (c = 0; c < closureSize*2; c += 2) {
2072         ierr = PetscHSetIAdd(ht, closure[c]);CHKERRQ(ierr);
2073         if (hasTree) {ierr = DMPlexAddClosure_Tree(dm, ht, closure[c], PETSC_TRUE, PETSC_TRUE);CHKERRQ(ierr);}
2074       }
2075     }
2076     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
2077     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2078     ierr = PetscHSetIGetSize(ht, &nelems);CHKERRQ(ierr);
2079     ierr = PetscMalloc1(nelems, &elems);CHKERRQ(ierr);
2080     ierr = PetscHSetIGetElems(ht, &off, elems);CHKERRQ(ierr);
2081     ierr = PetscHSetIDestroy(&ht);CHKERRQ(ierr);
2082     ierr = PetscSortInt(nelems, elems);CHKERRQ(ierr);
2083     ierr = ISCreateGeneral(PETSC_COMM_SELF, nelems, elems, PETSC_OWN_POINTER, &pointIS);CHKERRQ(ierr);
2084     ierr = DMLabelSetStratumIS(label, rank, pointIS);CHKERRQ(ierr);
2085     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2086   }
2087 
2088   if (closure) {ierr = DMPlexRestoreTransitiveClosure(dm, 0, PETSC_TRUE, NULL, &closure);CHKERRQ(ierr);}
2089   ierr = ISRestoreIndices(rankIS, &ranks);CHKERRQ(ierr);
2090   ierr = ISDestroy(&rankIS);CHKERRQ(ierr);
2091   PetscFunctionReturn(0);
2092 }
2093 
2094 /*@
2095   DMPlexPartitionLabelAdjacency - Add one level of adjacent points to the partition label
2096 
2097   Input Parameters:
2098 + dm     - The DM
2099 - label  - DMLabel assinging ranks to remote roots
2100 
2101   Level: developer
2102 
2103 .seealso: DMPlexPartitionLabelCreateSF, DMPlexDistribute(), DMPlexCreateOverlap
2104 @*/
2105 PetscErrorCode DMPlexPartitionLabelAdjacency(DM dm, DMLabel label)
2106 {
2107   IS              rankIS,   pointIS;
2108   const PetscInt *ranks,   *points;
2109   PetscInt        numRanks, numPoints, r, p, a, adjSize;
2110   PetscInt       *adj = NULL;
2111   PetscErrorCode  ierr;
2112 
2113   PetscFunctionBegin;
2114   ierr = DMLabelGetValueIS(label, &rankIS);CHKERRQ(ierr);
2115   ierr = ISGetLocalSize(rankIS, &numRanks);CHKERRQ(ierr);
2116   ierr = ISGetIndices(rankIS, &ranks);CHKERRQ(ierr);
2117   for (r = 0; r < numRanks; ++r) {
2118     const PetscInt rank = ranks[r];
2119 
2120     ierr = DMLabelGetStratumIS(label, rank, &pointIS);CHKERRQ(ierr);
2121     ierr = ISGetLocalSize(pointIS, &numPoints);CHKERRQ(ierr);
2122     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
2123     for (p = 0; p < numPoints; ++p) {
2124       adjSize = PETSC_DETERMINE;
2125       ierr = DMPlexGetAdjacency(dm, points[p], &adjSize, &adj);CHKERRQ(ierr);
2126       for (a = 0; a < adjSize; ++a) {ierr = DMLabelSetValue(label, adj[a], rank);CHKERRQ(ierr);}
2127     }
2128     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
2129     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2130   }
2131   ierr = ISRestoreIndices(rankIS, &ranks);CHKERRQ(ierr);
2132   ierr = ISDestroy(&rankIS);CHKERRQ(ierr);
2133   ierr = PetscFree(adj);CHKERRQ(ierr);
2134   PetscFunctionReturn(0);
2135 }
2136 
2137 /*@
2138   DMPlexPartitionLabelPropagate - Propagate points in a partition label over the point SF
2139 
2140   Input Parameters:
2141 + dm     - The DM
2142 - label  - DMLabel assinging ranks to remote roots
2143 
2144   Level: developer
2145 
2146   Note: This is required when generating multi-level overlaps to capture
2147   overlap points from non-neighbouring partitions.
2148 
2149 .seealso: DMPlexPartitionLabelCreateSF, DMPlexDistribute(), DMPlexCreateOverlap
2150 @*/
2151 PetscErrorCode DMPlexPartitionLabelPropagate(DM dm, DMLabel label)
2152 {
2153   MPI_Comm        comm;
2154   PetscMPIInt     rank;
2155   PetscSF         sfPoint;
2156   DMLabel         lblRoots, lblLeaves;
2157   IS              rankIS, pointIS;
2158   const PetscInt *ranks;
2159   PetscInt        numRanks, r;
2160   PetscErrorCode  ierr;
2161 
2162   PetscFunctionBegin;
2163   ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr);
2164   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
2165   ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);
2166   /* Pull point contributions from remote leaves into local roots */
2167   ierr = DMLabelGather(label, sfPoint, &lblLeaves);CHKERRQ(ierr);
2168   ierr = DMLabelGetValueIS(lblLeaves, &rankIS);CHKERRQ(ierr);
2169   ierr = ISGetLocalSize(rankIS, &numRanks);CHKERRQ(ierr);
2170   ierr = ISGetIndices(rankIS, &ranks);CHKERRQ(ierr);
2171   for (r = 0; r < numRanks; ++r) {
2172     const PetscInt remoteRank = ranks[r];
2173     if (remoteRank == rank) continue;
2174     ierr = DMLabelGetStratumIS(lblLeaves, remoteRank, &pointIS);CHKERRQ(ierr);
2175     ierr = DMLabelInsertIS(label, pointIS, remoteRank);CHKERRQ(ierr);
2176     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2177   }
2178   ierr = ISRestoreIndices(rankIS, &ranks);CHKERRQ(ierr);
2179   ierr = ISDestroy(&rankIS);CHKERRQ(ierr);
2180   ierr = DMLabelDestroy(&lblLeaves);CHKERRQ(ierr);
2181   /* Push point contributions from roots into remote leaves */
2182   ierr = DMLabelDistribute(label, sfPoint, &lblRoots);CHKERRQ(ierr);
2183   ierr = DMLabelGetValueIS(lblRoots, &rankIS);CHKERRQ(ierr);
2184   ierr = ISGetLocalSize(rankIS, &numRanks);CHKERRQ(ierr);
2185   ierr = ISGetIndices(rankIS, &ranks);CHKERRQ(ierr);
2186   for (r = 0; r < numRanks; ++r) {
2187     const PetscInt remoteRank = ranks[r];
2188     if (remoteRank == rank) continue;
2189     ierr = DMLabelGetStratumIS(lblRoots, remoteRank, &pointIS);CHKERRQ(ierr);
2190     ierr = DMLabelInsertIS(label, pointIS, remoteRank);CHKERRQ(ierr);
2191     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2192   }
2193   ierr = ISRestoreIndices(rankIS, &ranks);CHKERRQ(ierr);
2194   ierr = ISDestroy(&rankIS);CHKERRQ(ierr);
2195   ierr = DMLabelDestroy(&lblRoots);CHKERRQ(ierr);
2196   PetscFunctionReturn(0);
2197 }
2198 
2199 /*@
2200   DMPlexPartitionLabelInvert - Create a partition label of remote roots from a local root label
2201 
2202   Input Parameters:
2203 + dm        - The DM
2204 . rootLabel - DMLabel assinging ranks to local roots
2205 . processSF - A star forest mapping into the local index on each remote rank
2206 
2207   Output Parameter:
2208 - leafLabel - DMLabel assinging ranks to remote roots
2209 
2210   Note: The rootLabel defines a send pattern by mapping local points to remote target ranks. The
2211   resulting leafLabel is a receiver mapping of remote roots to their parent rank.
2212 
2213   Level: developer
2214 
2215 .seealso: DMPlexPartitionLabelCreateSF, DMPlexDistribute(), DMPlexCreateOverlap
2216 @*/
2217 PetscErrorCode DMPlexPartitionLabelInvert(DM dm, DMLabel rootLabel, PetscSF processSF, DMLabel leafLabel)
2218 {
2219   MPI_Comm           comm;
2220   PetscMPIInt        rank, size;
2221   PetscInt           p, n, numNeighbors, ssize, l, nleaves;
2222   PetscSF            sfPoint;
2223   PetscSFNode       *rootPoints, *leafPoints;
2224   PetscSection       rootSection, leafSection;
2225   const PetscSFNode *remote;
2226   const PetscInt    *local, *neighbors;
2227   IS                 valueIS;
2228   PetscErrorCode     ierr;
2229 
2230   PetscFunctionBegin;
2231   ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr);
2232   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
2233   ierr = MPI_Comm_size(comm, &size);CHKERRQ(ierr);
2234   ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);
2235 
2236   /* Convert to (point, rank) and use actual owners */
2237   ierr = PetscSectionCreate(comm, &rootSection);CHKERRQ(ierr);
2238   ierr = PetscSectionSetChart(rootSection, 0, size);CHKERRQ(ierr);
2239   ierr = DMLabelGetValueIS(rootLabel, &valueIS);CHKERRQ(ierr);
2240   ierr = ISGetLocalSize(valueIS, &numNeighbors);CHKERRQ(ierr);
2241   ierr = ISGetIndices(valueIS, &neighbors);CHKERRQ(ierr);
2242   for (n = 0; n < numNeighbors; ++n) {
2243     PetscInt numPoints;
2244 
2245     ierr = DMLabelGetStratumSize(rootLabel, neighbors[n], &numPoints);CHKERRQ(ierr);
2246     ierr = PetscSectionAddDof(rootSection, neighbors[n], numPoints);CHKERRQ(ierr);
2247   }
2248   ierr = PetscSectionSetUp(rootSection);CHKERRQ(ierr);
2249   ierr = PetscSectionGetStorageSize(rootSection, &ssize);CHKERRQ(ierr);
2250   ierr = PetscMalloc1(ssize, &rootPoints);CHKERRQ(ierr);
2251   ierr = PetscSFGetGraph(sfPoint, NULL, &nleaves, &local, &remote);CHKERRQ(ierr);
2252   for (n = 0; n < numNeighbors; ++n) {
2253     IS              pointIS;
2254     const PetscInt *points;
2255     PetscInt        off, numPoints, p;
2256 
2257     ierr = PetscSectionGetOffset(rootSection, neighbors[n], &off);CHKERRQ(ierr);
2258     ierr = DMLabelGetStratumIS(rootLabel, neighbors[n], &pointIS);CHKERRQ(ierr);
2259     ierr = ISGetLocalSize(pointIS, &numPoints);CHKERRQ(ierr);
2260     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
2261     for (p = 0; p < numPoints; ++p) {
2262       if (local) {ierr = PetscFindInt(points[p], nleaves, local, &l);CHKERRQ(ierr);}
2263       else       {l = -1;}
2264       if (l >= 0) {rootPoints[off+p] = remote[l];}
2265       else        {rootPoints[off+p].index = points[p]; rootPoints[off+p].rank = rank;}
2266     }
2267     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
2268     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2269   }
2270   ierr = ISRestoreIndices(valueIS, &neighbors);CHKERRQ(ierr);
2271   ierr = ISDestroy(&valueIS);CHKERRQ(ierr);
2272   /* Communicate overlap */
2273   ierr = PetscSectionCreate(comm, &leafSection);CHKERRQ(ierr);
2274   ierr = DMPlexDistributeData(dm, processSF, rootSection, MPIU_2INT, rootPoints, leafSection, (void**) &leafPoints);CHKERRQ(ierr);
2275   /* Filter remote contributions (ovLeafPoints) into the overlapSF */
2276   ierr = PetscSectionGetStorageSize(leafSection, &ssize);CHKERRQ(ierr);
2277   for (p = 0; p < ssize; p++) {
2278     ierr = DMLabelSetValue(leafLabel, leafPoints[p].index, leafPoints[p].rank);CHKERRQ(ierr);
2279   }
2280   ierr = PetscFree(rootPoints);CHKERRQ(ierr);
2281   ierr = PetscSectionDestroy(&rootSection);CHKERRQ(ierr);
2282   ierr = PetscFree(leafPoints);CHKERRQ(ierr);
2283   ierr = PetscSectionDestroy(&leafSection);CHKERRQ(ierr);
2284   PetscFunctionReturn(0);
2285 }
2286 
2287 /*@
2288   DMPlexPartitionLabelCreateSF - Create a star forest from a label that assigns ranks to points
2289 
2290   Input Parameters:
2291 + dm    - The DM
2292 . label - DMLabel assinging ranks to remote roots
2293 
2294   Output Parameter:
2295 - sf    - The star forest communication context encapsulating the defined mapping
2296 
2297   Note: The incoming label is a receiver mapping of remote points to their parent rank.
2298 
2299   Level: developer
2300 
2301 .seealso: DMPlexDistribute(), DMPlexCreateOverlap
2302 @*/
2303 PetscErrorCode DMPlexPartitionLabelCreateSF(DM dm, DMLabel label, PetscSF *sf)
2304 {
2305   PetscMPIInt     rank, size;
2306   PetscInt        n, numRemote, p, numPoints, pStart, pEnd, idx = 0;
2307   PetscSFNode    *remotePoints;
2308   IS              remoteRootIS;
2309   const PetscInt *remoteRoots;
2310   PetscErrorCode ierr;
2311 
2312   PetscFunctionBegin;
2313   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRQ(ierr);
2314   ierr = MPI_Comm_size(PetscObjectComm((PetscObject) dm), &size);CHKERRQ(ierr);
2315 
2316   for (numRemote = 0, n = 0; n < size; ++n) {
2317     ierr = DMLabelGetStratumSize(label, n, &numPoints);CHKERRQ(ierr);
2318     numRemote += numPoints;
2319   }
2320   ierr = PetscMalloc1(numRemote, &remotePoints);CHKERRQ(ierr);
2321   /* Put owned points first */
2322   ierr = DMLabelGetStratumSize(label, rank, &numPoints);CHKERRQ(ierr);
2323   if (numPoints > 0) {
2324     ierr = DMLabelGetStratumIS(label, rank, &remoteRootIS);CHKERRQ(ierr);
2325     ierr = ISGetIndices(remoteRootIS, &remoteRoots);CHKERRQ(ierr);
2326     for (p = 0; p < numPoints; p++) {
2327       remotePoints[idx].index = remoteRoots[p];
2328       remotePoints[idx].rank = rank;
2329       idx++;
2330     }
2331     ierr = ISRestoreIndices(remoteRootIS, &remoteRoots);CHKERRQ(ierr);
2332     ierr = ISDestroy(&remoteRootIS);CHKERRQ(ierr);
2333   }
2334   /* Now add remote points */
2335   for (n = 0; n < size; ++n) {
2336     ierr = DMLabelGetStratumSize(label, n, &numPoints);CHKERRQ(ierr);
2337     if (numPoints <= 0 || n == rank) continue;
2338     ierr = DMLabelGetStratumIS(label, n, &remoteRootIS);CHKERRQ(ierr);
2339     ierr = ISGetIndices(remoteRootIS, &remoteRoots);CHKERRQ(ierr);
2340     for (p = 0; p < numPoints; p++) {
2341       remotePoints[idx].index = remoteRoots[p];
2342       remotePoints[idx].rank = n;
2343       idx++;
2344     }
2345     ierr = ISRestoreIndices(remoteRootIS, &remoteRoots);CHKERRQ(ierr);
2346     ierr = ISDestroy(&remoteRootIS);CHKERRQ(ierr);
2347   }
2348   ierr = PetscSFCreate(PetscObjectComm((PetscObject) dm), sf);CHKERRQ(ierr);
2349   ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
2350   ierr = PetscSFSetGraph(*sf, pEnd-pStart, numRemote, NULL, PETSC_OWN_POINTER, remotePoints, PETSC_OWN_POINTER);CHKERRQ(ierr);
2351   PetscFunctionReturn(0);
2352 }
2353