xref: /petsc/src/dm/impls/plex/plextree.c (revision 776742ed8f85e16ccc3b8279c9c8abdfe252f86f)
1 #include <petsc-private/dmpleximpl.h>   /*I      "petscdmplex.h"   I*/
2 #include <../src/sys/utils/hash.h>
3 #include <petsc-private/isimpl.h>
4 #include <petsc-private/petscfeimpl.h>
5 #include <petscsf.h>
6 #include <petscds.h>
7 
8 /** hierarchy routines */
9 
10 #undef __FUNCT__
11 #define __FUNCT__ "DMPlexSetReferenceTree"
12 /*@
13   DMPlexSetReferenceTree - set the reference tree for hierarchically non-conforming meshes.
14 
15   Not collective
16 
17   Input Parameters:
18 + dm - The DMPlex object
19 - ref - The reference tree DMPlex object
20 
21   Level: intermediate
22 
23 .seealso: DMPlexGetReferenceTree(), DMPlexCreateDefaultReferenceTree()
24 @*/
25 PetscErrorCode DMPlexSetReferenceTree(DM dm, DM ref)
26 {
27   DM_Plex        *mesh = (DM_Plex *)dm->data;
28   PetscErrorCode  ierr;
29 
30   PetscFunctionBegin;
31   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
32   PetscValidHeaderSpecific(ref, DM_CLASSID, 2);
33   ierr = PetscObjectReference((PetscObject)ref);CHKERRQ(ierr);
34   ierr = DMDestroy(&mesh->referenceTree);CHKERRQ(ierr);
35   mesh->referenceTree = ref;
36   PetscFunctionReturn(0);
37 }
38 
39 #undef __FUNCT__
40 #define __FUNCT__ "DMPlexGetReferenceTree"
41 /*@
42   DMPlexGetReferenceTree - get the reference tree for hierarchically non-conforming meshes.
43 
44   Not collective
45 
46   Input Parameters:
47 . dm - The DMPlex object
48 
49   Output Parameters
50 . ref - The reference tree DMPlex object
51 
52   Level: intermediate
53 
54 .seealso: DMPlexSetReferenceTree(), DMPlexCreateDefaultReferenceTree()
55 @*/
56 PetscErrorCode DMPlexGetReferenceTree(DM dm, DM *ref)
57 {
58   DM_Plex        *mesh = (DM_Plex *)dm->data;
59 
60   PetscFunctionBegin;
61   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
62   PetscValidPointer(ref,2);
63   *ref = mesh->referenceTree;
64   PetscFunctionReturn(0);
65 }
66 
67 #undef __FUNCT__
68 #define __FUNCT__ "DMPlexReferenceTreeGetChildSymmetry_Default"
69 static PetscErrorCode DMPlexReferenceTreeGetChildSymmetry_Default(DM dm, PetscInt parent, PetscInt parentOrientA, PetscInt childOrientA, PetscInt childA, PetscInt parentOrientB, PetscInt *childOrientB, PetscInt *childB)
70 {
71   PetscInt       coneSize, dStart, dEnd, dim, ABswap, oAvert, oBvert, ABswapVert;
72   PetscErrorCode ierr;
73 
74   PetscFunctionBegin;
75   if (parentOrientA == parentOrientB) {
76     if (childOrientB) *childOrientB = childOrientA;
77     if (childB) *childB = childA;
78     PetscFunctionReturn(0);
79   }
80   for (dim = 0; dim < 3; dim++) {
81     ierr = DMPlexGetDepthStratum(dm,dim,&dStart,&dEnd);CHKERRQ(ierr);
82     if (parent >= dStart && parent <= dEnd) {
83       break;
84     }
85   }
86   if (dim > 2) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Cannot perform child symmetry for %d-cells",dim);
87   if (!dim) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"A vertex has no children");
88   if (childA < dStart || childA >= dEnd) {
89     /* this is a lower-dimensional child: bootstrap */
90     PetscInt size, i, sA = -1, sB, sOrientB, sConeSize;
91     const PetscInt *supp, *coneA, *coneB, *oA, *oB;
92 
93     ierr = DMPlexGetSupportSize(dm,childA,&size);CHKERRQ(ierr);
94     ierr = DMPlexGetSupport(dm,childA,&supp);CHKERRQ(ierr);
95 
96     /* find a point sA in supp(childA) that has the same parent */
97     for (i = 0; i < size; i++) {
98       PetscInt sParent;
99 
100       sA   = supp[i];
101       if (sA == parent) continue;
102       ierr = DMPlexGetTreeParent(dm,sA,&sParent,NULL);CHKERRQ(ierr);
103       if (sParent == parent) {
104         break;
105       }
106     }
107     if (i == size) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"could not find support in children");
108     /* find out which point sB is in an equivalent position to sA under
109      * parentOrientB */
110     ierr = DMPlexReferenceTreeGetChildSymmetry_Default(dm,parent,parentOrientA,0,sA,parentOrientB,&sOrientB,&sB);CHKERRQ(ierr);
111     ierr = DMPlexGetConeSize(dm,sA,&sConeSize);CHKERRQ(ierr);
112     ierr = DMPlexGetCone(dm,sA,&coneA);CHKERRQ(ierr);
113     ierr = DMPlexGetCone(dm,sB,&coneB);CHKERRQ(ierr);
114     ierr = DMPlexGetConeOrientation(dm,sA,&oA);CHKERRQ(ierr);
115     ierr = DMPlexGetConeOrientation(dm,sB,&oB);CHKERRQ(ierr);
116     /* step through the cone of sA in natural order */
117     for (i = 0; i < sConeSize; i++) {
118       if (coneA[i] == childA) {
119         /* if childA is at position i in coneA,
120          * then we want the point that is at sOrientB*i in coneB */
121         PetscInt j = (sOrientB >= 0) ? ((sOrientB + i) % sConeSize) : ((sConeSize -(sOrientB+1) - i) % sConeSize);
122         if (childB) *childB = coneB[j];
123         if (childOrientB) {
124           PetscInt oBtrue;
125 
126           ierr          = DMPlexGetConeSize(dm,childA,&coneSize);CHKERRQ(ierr);
127           /* compose sOrientB and oB[j] */
128           if (coneSize != 0 && coneSize != 2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Expected a vertex or an edge");
129           /* we may have to flip an edge */
130           oBtrue        = coneSize ? ((sOrientB >= 0) ? oB[j] : -(oB[j] + 2)) : 0;
131           ABswap        = DihedralSwap(coneSize,oA[i],oBtrue);CHKERRQ(ierr);
132           *childOrientB = DihedralCompose(coneSize,childOrientA,ABswap);
133         }
134         break;
135       }
136     }
137     if (i == sConeSize) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"support cone mismatch");
138     PetscFunctionReturn(0);
139   }
140   /* get the cone size and symmetry swap */
141   ierr   = DMPlexGetConeSize(dm,parent,&coneSize);CHKERRQ(ierr);
142   ABswap = DihedralSwap(coneSize, parentOrientA, parentOrientB);
143   if (dim == 2) {
144     /* orientations refer to cones: we want them to refer to vertices:
145      * if it's a rotation, they are the same, but if the order is reversed, a
146      * permutation that puts side i first does *not* put vertex i first */
147     oAvert     = (parentOrientA >= 0) ? parentOrientA : -((-parentOrientA % coneSize) + 1);
148     oBvert     = (parentOrientB >= 0) ? parentOrientB : -((-parentOrientB % coneSize) + 1);
149     ABswapVert = DihedralSwap(coneSize, oAvert, oBvert);
150   }
151   else {
152     oAvert     = parentOrientA;
153     oBvert     = parentOrientB;
154     ABswapVert = ABswap;
155   }
156   if (childB) {
157     /* assume that each child corresponds to a vertex, in the same order */
158     PetscInt p, posA = -1, numChildren, i;
159     const PetscInt *children;
160 
161     /* count which position the child is in */
162     ierr = DMPlexGetTreeChildren(dm,parent,&numChildren,&children);CHKERRQ(ierr);
163     for (i = 0; i < numChildren; i++) {
164       p = children[i];
165       if (p == childA) {
166         posA = i;
167         break;
168       }
169     }
170     if (posA >= coneSize) {
171       /* this is the triangle in the middle of a uniformly refined triangle: it
172        * is invariant */
173       if (dim != 2 || posA != 3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Expected a middle triangle, got something else");
174       *childB = childA;
175     }
176     else {
177       /* figure out position B by applying ABswapVert */
178       PetscInt posB;
179 
180       posB = (ABswapVert >= 0) ? ((ABswapVert + posA) % coneSize) : ((coneSize -(ABswapVert + 1) - posA) % coneSize);
181       if (childB) *childB = children[posB];
182     }
183   }
184   if (childOrientB) *childOrientB = DihedralCompose(coneSize,childOrientA,ABswap);
185   PetscFunctionReturn(0);
186 }
187 
188 #undef __FUNCT__
189 #define __FUNCT__ "DMPlexReferenceTreeGetChildSymmetry"
190 /*@
191   DMPlexReferenceTreeGetChildSymmetry - Given a reference tree, transform a childid and orientation from one parent frame to another
192 
193   Input Parameters:
194 + dm - the reference tree DMPlex object
195 . parent - the parent point
196 . parentOrientA - the reference orientation for describing the parent
197 . childOrientA - the reference orientation for describing the child
198 . childA - the reference childID for describing the child
199 - parentOrientB - the new orientation for describing the parent
200 
201   Output Parameters:
202 + childOrientB - if not NULL, set to the new oreintation for describing the child
203 . childB - if not NULL, the new childID for describing the child
204 
205   Level: developer
206 
207 .seealso: DMPlexGetReferenceTree(), DMPlexSetReferenceTree(), DMPlexSetTree()
208 @*/
209 PetscErrorCode DMPlexReferenceTreeGetChildSymmetry(DM dm, PetscInt parent, PetscInt parentOrientA, PetscInt childOrientA, PetscInt childA, PetscInt parentOrientB, PetscInt *childOrientB, PetscInt *childB)
210 {
211   DM_Plex        *mesh = (DM_Plex *)dm->data;
212   PetscErrorCode ierr;
213 
214   PetscFunctionBegin;
215   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
216   if (!mesh->getchildsymmetry) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"DMPlexReferenceTreeGetChildSymmetry not implemented");
217   ierr = mesh->getchildsymmetry(dm,parent,parentOrientA,childOrientA,childA,parentOrientB,childOrientB,childB);CHKERRQ(ierr);
218   PetscFunctionReturn(0);
219 }
220 
221 static PetscErrorCode DMPlexSetTree_Internal(DM,PetscSection,PetscInt*,PetscInt*,PetscBool,PetscBool);
222 
223 #undef __FUNCT__
224 #define __FUNCT__ "DMPlexCreateDefaultReferenceTree"
225 /*@
226   DMPlexCreateDefaultReferenceTree - create a reference tree for isotropic hierarchical mesh refinement.
227 
228   Collective on comm
229 
230   Input Parameters:
231 + comm    - the MPI communicator
232 . dim     - the spatial dimension
233 - simplex - Flag for simplex, otherwise use a tensor-product cell
234 
235   Output Parameters:
236 . ref     - the reference tree DMPlex object
237 
238   Level: intermediate
239 
240 .keywords: reference cell
241 .seealso: DMPlexSetReferenceTree(), DMPlexGetReferenceTree()
242 @*/
243 PetscErrorCode DMPlexCreateDefaultReferenceTree(MPI_Comm comm, PetscInt dim, PetscBool simplex, DM *ref)
244 {
245   DM_Plex       *mesh;
246   DM             K, Kref;
247   PetscInt       p, pStart, pEnd, pRefStart, pRefEnd, d, offset, parentSize, *parents, *childIDs;
248   PetscInt      *permvals, *unionCones, *coneSizes, *unionOrientations, numUnionPoints, *numDimPoints, numCones, numVerts;
249   DMLabel        identity, identityRef;
250   PetscSection   unionSection, unionConeSection, parentSection;
251   PetscScalar   *unionCoords;
252   IS             perm;
253   PetscErrorCode ierr;
254 
255   PetscFunctionBegin;
256   /* create a reference element */
257   ierr = DMPlexCreateReferenceCell(comm, dim, simplex, &K);CHKERRQ(ierr);
258   ierr = DMPlexCreateLabel(K, "identity");CHKERRQ(ierr);
259   ierr = DMPlexGetLabel(K, "identity", &identity);CHKERRQ(ierr);
260   ierr = DMPlexGetChart(K, &pStart, &pEnd);CHKERRQ(ierr);
261   for (p = pStart; p < pEnd; p++) {
262     ierr = DMLabelSetValue(identity, p, p);CHKERRQ(ierr);
263   }
264   /* refine it */
265   ierr = DMRefine(K,comm,&Kref);CHKERRQ(ierr);
266 
267   /* the reference tree is the union of these two, without duplicating
268    * points that appear in both */
269   ierr = DMPlexGetLabel(Kref, "identity", &identityRef);CHKERRQ(ierr);
270   ierr = DMPlexGetChart(Kref, &pRefStart, &pRefEnd);CHKERRQ(ierr);
271   ierr = PetscSectionCreate(comm, &unionSection);CHKERRQ(ierr);
272   ierr = PetscSectionSetChart(unionSection, 0, (pEnd - pStart) + (pRefEnd - pRefStart));CHKERRQ(ierr);
273   /* count points that will go in the union */
274   for (p = pStart; p < pEnd; p++) {
275     ierr = PetscSectionSetDof(unionSection, p - pStart, 1);CHKERRQ(ierr);
276   }
277   for (p = pRefStart; p < pRefEnd; p++) {
278     PetscInt q, qSize;
279     ierr = DMLabelGetValue(identityRef, p, &q);CHKERRQ(ierr);
280     ierr = DMLabelGetStratumSize(identityRef, q, &qSize);CHKERRQ(ierr);
281     if (qSize > 1) {
282       ierr = PetscSectionSetDof(unionSection, p - pRefStart + (pEnd - pStart), 1);CHKERRQ(ierr);
283     }
284   }
285   ierr = PetscMalloc1((pEnd - pStart) + (pRefEnd - pRefStart),&permvals);CHKERRQ(ierr);
286   offset = 0;
287   /* stratify points in the union by topological dimension */
288   for (d = 0; d <= dim; d++) {
289     PetscInt cStart, cEnd, c;
290 
291     ierr = DMPlexGetHeightStratum(K, d, &cStart, &cEnd);CHKERRQ(ierr);
292     for (c = cStart; c < cEnd; c++) {
293       permvals[offset++] = c;
294     }
295 
296     ierr = DMPlexGetHeightStratum(Kref, d, &cStart, &cEnd);CHKERRQ(ierr);
297     for (c = cStart; c < cEnd; c++) {
298       permvals[offset++] = c + (pEnd - pStart);
299     }
300   }
301   ierr = ISCreateGeneral(comm, (pEnd - pStart) + (pRefEnd - pRefStart), permvals, PETSC_OWN_POINTER, &perm);CHKERRQ(ierr);
302   ierr = PetscSectionSetPermutation(unionSection,perm);CHKERRQ(ierr);
303   ierr = PetscSectionSetUp(unionSection);CHKERRQ(ierr);
304   ierr = PetscSectionGetStorageSize(unionSection,&numUnionPoints);CHKERRQ(ierr);
305   ierr = PetscMalloc2(numUnionPoints,&coneSizes,dim+1,&numDimPoints);CHKERRQ(ierr);
306   /* count dimension points */
307   for (d = 0; d <= dim; d++) {
308     PetscInt cStart, cOff, cOff2;
309     ierr = DMPlexGetHeightStratum(K,d,&cStart,NULL);CHKERRQ(ierr);
310     ierr = PetscSectionGetOffset(unionSection,cStart-pStart,&cOff);CHKERRQ(ierr);
311     if (d < dim) {
312       ierr = DMPlexGetHeightStratum(K,d+1,&cStart,NULL);CHKERRQ(ierr);
313       ierr = PetscSectionGetOffset(unionSection,cStart-pStart,&cOff2);CHKERRQ(ierr);
314     }
315     else {
316       cOff2 = numUnionPoints;
317     }
318     numDimPoints[dim - d] = cOff2 - cOff;
319   }
320   ierr = PetscSectionCreate(comm, &unionConeSection);CHKERRQ(ierr);
321   ierr = PetscSectionSetChart(unionConeSection, 0, numUnionPoints);CHKERRQ(ierr);
322   /* count the cones in the union */
323   for (p = pStart; p < pEnd; p++) {
324     PetscInt dof, uOff;
325 
326     ierr = DMPlexGetConeSize(K, p, &dof);CHKERRQ(ierr);
327     ierr = PetscSectionGetOffset(unionSection, p - pStart,&uOff);CHKERRQ(ierr);
328     ierr = PetscSectionSetDof(unionConeSection, uOff, dof);CHKERRQ(ierr);
329     coneSizes[uOff] = dof;
330   }
331   for (p = pRefStart; p < pRefEnd; p++) {
332     PetscInt dof, uDof, uOff;
333 
334     ierr = DMPlexGetConeSize(Kref, p, &dof);CHKERRQ(ierr);
335     ierr = PetscSectionGetDof(unionSection, p - pRefStart + (pEnd - pStart),&uDof);CHKERRQ(ierr);
336     ierr = PetscSectionGetOffset(unionSection, p - pRefStart + (pEnd - pStart),&uOff);CHKERRQ(ierr);
337     if (uDof) {
338       ierr = PetscSectionSetDof(unionConeSection, uOff, dof);CHKERRQ(ierr);
339       coneSizes[uOff] = dof;
340     }
341   }
342   ierr = PetscSectionSetUp(unionConeSection);CHKERRQ(ierr);
343   ierr = PetscSectionGetStorageSize(unionConeSection,&numCones);CHKERRQ(ierr);
344   ierr = PetscMalloc2(numCones,&unionCones,numCones,&unionOrientations);CHKERRQ(ierr);
345   /* write the cones in the union */
346   for (p = pStart; p < pEnd; p++) {
347     PetscInt dof, uOff, c, cOff;
348     const PetscInt *cone, *orientation;
349 
350     ierr = DMPlexGetConeSize(K, p, &dof);CHKERRQ(ierr);
351     ierr = DMPlexGetCone(K, p, &cone);CHKERRQ(ierr);
352     ierr = DMPlexGetConeOrientation(K, p, &orientation);CHKERRQ(ierr);
353     ierr = PetscSectionGetOffset(unionSection, p - pStart,&uOff);CHKERRQ(ierr);
354     ierr = PetscSectionGetOffset(unionConeSection,uOff,&cOff);CHKERRQ(ierr);
355     for (c = 0; c < dof; c++) {
356       PetscInt e, eOff;
357       e                           = cone[c];
358       ierr                        = PetscSectionGetOffset(unionSection, e - pStart, &eOff);CHKERRQ(ierr);
359       unionCones[cOff + c]        = eOff;
360       unionOrientations[cOff + c] = orientation[c];
361     }
362   }
363   for (p = pRefStart; p < pRefEnd; p++) {
364     PetscInt dof, uDof, uOff, c, cOff;
365     const PetscInt *cone, *orientation;
366 
367     ierr = DMPlexGetConeSize(Kref, p, &dof);CHKERRQ(ierr);
368     ierr = DMPlexGetCone(Kref, p, &cone);CHKERRQ(ierr);
369     ierr = DMPlexGetConeOrientation(Kref, p, &orientation);CHKERRQ(ierr);
370     ierr = PetscSectionGetDof(unionSection, p - pRefStart + (pEnd - pStart),&uDof);CHKERRQ(ierr);
371     ierr = PetscSectionGetOffset(unionSection, p - pRefStart + (pEnd - pStart),&uOff);CHKERRQ(ierr);
372     if (uDof) {
373       ierr = PetscSectionGetOffset(unionConeSection,uOff,&cOff);CHKERRQ(ierr);
374       for (c = 0; c < dof; c++) {
375         PetscInt e, eOff, eDof;
376 
377         e    = cone[c];
378         ierr = PetscSectionGetDof(unionSection, e - pRefStart + (pEnd - pStart),&eDof);CHKERRQ(ierr);
379         if (eDof) {
380           ierr = PetscSectionGetOffset(unionSection, e - pRefStart + (pEnd - pStart), &eOff);CHKERRQ(ierr);
381         }
382         else {
383           ierr = DMLabelGetValue(identityRef, e, &e);CHKERRQ(ierr);
384           ierr = PetscSectionGetOffset(unionSection, e - pStart, &eOff);CHKERRQ(ierr);
385         }
386         unionCones[cOff + c]        = eOff;
387         unionOrientations[cOff + c] = orientation[c];
388       }
389     }
390   }
391   /* get the coordinates */
392   {
393     PetscInt vStart, vEnd, vRefStart, vRefEnd, v, vDof, vOff;
394     PetscSection KcoordsSec, KrefCoordsSec;
395     Vec      KcoordsVec, KrefCoordsVec;
396     PetscScalar *Kcoords;
397 
398     DMGetCoordinateSection(K, &KcoordsSec);CHKERRQ(ierr);
399     DMGetCoordinatesLocal(K, &KcoordsVec);CHKERRQ(ierr);
400     DMGetCoordinateSection(Kref, &KrefCoordsSec);CHKERRQ(ierr);
401     DMGetCoordinatesLocal(Kref, &KrefCoordsVec);CHKERRQ(ierr);
402 
403     numVerts = numDimPoints[0];
404     ierr     = PetscMalloc1(numVerts * dim,&unionCoords);CHKERRQ(ierr);
405     ierr     = DMPlexGetDepthStratum(K,0,&vStart,&vEnd);CHKERRQ(ierr);
406 
407     offset = 0;
408     for (v = vStart; v < vEnd; v++) {
409       ierr = PetscSectionGetOffset(unionSection,v - pStart,&vOff);CHKERRQ(ierr);
410       ierr = VecGetValuesSection(KcoordsVec, KcoordsSec, v, &Kcoords);CHKERRQ(ierr);
411       for (d = 0; d < dim; d++) {
412         unionCoords[offset * dim + d] = Kcoords[d];
413       }
414       offset++;
415     }
416     ierr = DMPlexGetDepthStratum(Kref,0,&vRefStart,&vRefEnd);CHKERRQ(ierr);
417     for (v = vRefStart; v < vRefEnd; v++) {
418       ierr = PetscSectionGetDof(unionSection,v - pRefStart + (pEnd - pStart),&vDof);CHKERRQ(ierr);
419       ierr = PetscSectionGetOffset(unionSection,v - pRefStart + (pEnd - pStart),&vOff);CHKERRQ(ierr);
420       ierr = VecGetValuesSection(KrefCoordsVec, KrefCoordsSec, v, &Kcoords);CHKERRQ(ierr);
421       if (vDof) {
422         for (d = 0; d < dim; d++) {
423           unionCoords[offset * dim + d] = Kcoords[d];
424         }
425         offset++;
426       }
427     }
428   }
429   ierr = DMCreate(comm,ref);CHKERRQ(ierr);
430   ierr = DMSetType(*ref,DMPLEX);CHKERRQ(ierr);
431   ierr = DMPlexSetDimension(*ref,dim);CHKERRQ(ierr);
432   ierr = DMPlexCreateFromDAG(*ref,dim,numDimPoints,coneSizes,unionCones,unionOrientations,unionCoords);CHKERRQ(ierr);
433   /* set the tree */
434   ierr = PetscSectionCreate(comm,&parentSection);CHKERRQ(ierr);
435   ierr = PetscSectionSetChart(parentSection,0,numUnionPoints);CHKERRQ(ierr);
436   for (p = pRefStart; p < pRefEnd; p++) {
437     PetscInt uDof, uOff;
438 
439     ierr = PetscSectionGetDof(unionSection, p - pRefStart + (pEnd - pStart),&uDof);CHKERRQ(ierr);
440     ierr = PetscSectionGetOffset(unionSection, p - pRefStart + (pEnd - pStart),&uOff);CHKERRQ(ierr);
441     if (uDof) {
442       PetscSectionSetDof(parentSection,uOff,1);CHKERRQ(ierr);
443     }
444   }
445   ierr = PetscSectionSetUp(parentSection);CHKERRQ(ierr);
446   ierr = PetscSectionGetStorageSize(parentSection,&parentSize);CHKERRQ(ierr);
447   ierr = PetscMalloc2(parentSize,&parents,parentSize,&childIDs);CHKERRQ(ierr);
448   for (p = pRefStart; p < pRefEnd; p++) {
449     PetscInt uDof, uOff;
450 
451     ierr = PetscSectionGetDof(unionSection, p - pRefStart + (pEnd - pStart),&uDof);CHKERRQ(ierr);
452     ierr = PetscSectionGetOffset(unionSection, p - pRefStart + (pEnd - pStart),&uOff);CHKERRQ(ierr);
453     if (uDof) {
454       PetscInt pOff, parent, parentU;
455       PetscSectionGetOffset(parentSection,uOff,&pOff);CHKERRQ(ierr);
456       DMLabelGetValue(identityRef,p,&parent);CHKERRQ(ierr);
457       ierr = PetscSectionGetOffset(unionSection, parent - pStart,&parentU);CHKERRQ(ierr);
458       parents[pOff] = parentU;
459       childIDs[pOff] = uOff;
460     }
461   }
462   ierr = DMPlexSetTree_Internal(*ref,parentSection,parents,childIDs,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
463   mesh = (DM_Plex *) (*ref)->data;
464   mesh->getchildsymmetry = DMPlexReferenceTreeGetChildSymmetry_Default;
465   ierr = PetscSectionDestroy(&parentSection);CHKERRQ(ierr);
466   ierr = PetscFree2(parents,childIDs);CHKERRQ(ierr);
467 
468   /* clean up */
469   ierr = PetscSectionDestroy(&unionSection);CHKERRQ(ierr);
470   ierr = PetscSectionDestroy(&unionConeSection);CHKERRQ(ierr);
471   ierr = ISDestroy(&perm);CHKERRQ(ierr);
472   ierr = PetscFree(unionCoords);CHKERRQ(ierr);
473   ierr = PetscFree2(unionCones,unionOrientations);CHKERRQ(ierr);
474   ierr = PetscFree2(coneSizes,numDimPoints);CHKERRQ(ierr);
475   ierr = DMDestroy(&K);CHKERRQ(ierr);
476   ierr = DMDestroy(&Kref);CHKERRQ(ierr);
477   PetscFunctionReturn(0);
478 }
479 
480 #undef __FUNCT__
481 #define __FUNCT__ "DMPlexTreeSymmetrize"
482 static PetscErrorCode DMPlexTreeSymmetrize(DM dm)
483 {
484   DM_Plex        *mesh = (DM_Plex *)dm->data;
485   PetscSection   childSec, pSec;
486   PetscInt       p, pSize, cSize, parMax = PETSC_MIN_INT, parMin = PETSC_MAX_INT;
487   PetscInt       *offsets, *children, pStart, pEnd;
488   PetscErrorCode ierr;
489 
490   PetscFunctionBegin;
491   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
492   ierr = PetscSectionDestroy(&mesh->childSection);CHKERRQ(ierr);
493   ierr = PetscFree(mesh->children);CHKERRQ(ierr);
494   pSec = mesh->parentSection;
495   if (!pSec) PetscFunctionReturn(0);
496   ierr = PetscSectionGetStorageSize(pSec,&pSize);CHKERRQ(ierr);
497   for (p = 0; p < pSize; p++) {
498     PetscInt par = mesh->parents[p];
499 
500     parMax = PetscMax(parMax,par+1);
501     parMin = PetscMin(parMin,par);
502   }
503   if (parMin > parMax) {
504     parMin = -1;
505     parMax = -1;
506   }
507   ierr = PetscSectionCreate(PetscObjectComm((PetscObject)pSec),&childSec);CHKERRQ(ierr);
508   ierr = PetscSectionSetChart(childSec,parMin,parMax);CHKERRQ(ierr);
509   for (p = 0; p < pSize; p++) {
510     PetscInt par = mesh->parents[p];
511 
512     ierr = PetscSectionAddDof(childSec,par,1);CHKERRQ(ierr);
513   }
514   ierr = PetscSectionSetUp(childSec);CHKERRQ(ierr);
515   ierr = PetscSectionGetStorageSize(childSec,&cSize);CHKERRQ(ierr);
516   ierr = PetscMalloc1(cSize,&children);CHKERRQ(ierr);
517   ierr = PetscCalloc1(parMax-parMin,&offsets);CHKERRQ(ierr);
518   ierr = PetscSectionGetChart(pSec,&pStart,&pEnd);CHKERRQ(ierr);
519   for (p = pStart; p < pEnd; p++) {
520     PetscInt dof, off, i;
521 
522     ierr = PetscSectionGetDof(pSec,p,&dof);CHKERRQ(ierr);
523     ierr = PetscSectionGetOffset(pSec,p,&off);CHKERRQ(ierr);
524     for (i = 0; i < dof; i++) {
525       PetscInt par = mesh->parents[off + i], cOff;
526 
527       ierr = PetscSectionGetOffset(childSec,par,&cOff);CHKERRQ(ierr);
528       children[cOff + offsets[par-parMin]++] = p;
529     }
530   }
531   mesh->childSection = childSec;
532   mesh->children = children;
533   ierr = PetscFree(offsets);CHKERRQ(ierr);
534   PetscFunctionReturn(0);
535 }
536 
537 #undef __FUNCT__
538 #define __FUNCT__ "AnchorsFlatten"
539 static PetscErrorCode AnchorsFlatten (PetscSection section, IS is, PetscSection *sectionNew, IS *isNew)
540 {
541   PetscInt       pStart, pEnd, size, sizeNew, i, p, *valsNew = NULL;
542   const PetscInt *vals;
543   PetscSection   secNew;
544   PetscBool      anyNew, globalAnyNew;
545   PetscBool      compress;
546   PetscErrorCode ierr;
547 
548   PetscFunctionBegin;
549   ierr = PetscSectionGetChart(section,&pStart,&pEnd);CHKERRQ(ierr);
550   ierr = ISGetLocalSize(is,&size);CHKERRQ(ierr);
551   ierr = ISGetIndices(is,&vals);CHKERRQ(ierr);
552   ierr = PetscSectionCreate(PetscObjectComm((PetscObject)section),&secNew);CHKERRQ(ierr);
553   ierr = PetscSectionSetChart(secNew,pStart,pEnd);CHKERRQ(ierr);
554   for (i = 0; i < size; i++) {
555     PetscInt dof;
556 
557     p = vals[i];
558     if (p < pStart || p >= pEnd) continue;
559     ierr = PetscSectionGetDof(section, p, &dof);CHKERRQ(ierr);
560     if (dof) break;
561   }
562   if (i == size) {
563     ierr     = PetscSectionSetUp(secNew);CHKERRQ(ierr);
564     anyNew   = PETSC_FALSE;
565     compress = PETSC_FALSE;
566     sizeNew  = 0;
567   }
568   else {
569     anyNew = PETSC_TRUE;
570     for (p = pStart; p < pEnd; p++) {
571       PetscInt dof, off;
572 
573       ierr = PetscSectionGetDof(section, p, &dof);CHKERRQ(ierr);
574       ierr = PetscSectionGetOffset(section, p, &off);CHKERRQ(ierr);
575       for (i = 0; i < dof; i++) {
576         PetscInt q = vals[off + i], qDof = 0;
577 
578         if (q >= pStart && q < pEnd) {
579           ierr = PetscSectionGetDof(section, q, &qDof);CHKERRQ(ierr);
580         }
581         if (qDof) {
582           ierr = PetscSectionAddDof(secNew, p, qDof);CHKERRQ(ierr);
583         }
584         else {
585           ierr = PetscSectionAddDof(secNew, p, 1);CHKERRQ(ierr);
586         }
587       }
588     }
589     ierr = PetscSectionSetUp(secNew);CHKERRQ(ierr);
590     ierr = PetscSectionGetStorageSize(secNew,&sizeNew);CHKERRQ(ierr);
591     ierr = PetscMalloc1(sizeNew,&valsNew);CHKERRQ(ierr);
592     compress = PETSC_FALSE;
593     for (p = pStart; p < pEnd; p++) {
594       PetscInt dof, off, count, offNew, dofNew;
595 
596       ierr  = PetscSectionGetDof(section, p, &dof);CHKERRQ(ierr);
597       ierr  = PetscSectionGetOffset(section, p, &off);CHKERRQ(ierr);
598       ierr  = PetscSectionGetDof(secNew, p, &dofNew);CHKERRQ(ierr);
599       ierr  = PetscSectionGetOffset(secNew, p, &offNew);CHKERRQ(ierr);
600       count = 0;
601       for (i = 0; i < dof; i++) {
602         PetscInt q = vals[off + i], qDof = 0, qOff = 0, j;
603 
604         if (q >= pStart && q < pEnd) {
605           ierr = PetscSectionGetDof(section, q, &qDof);CHKERRQ(ierr);
606           ierr = PetscSectionGetOffset(section, q, &qOff);CHKERRQ(ierr);
607         }
608         if (qDof) {
609           PetscInt oldCount = count;
610 
611           for (j = 0; j < qDof; j++) {
612             PetscInt k, r = vals[qOff + j];
613 
614             for (k = 0; k < oldCount; k++) {
615               if (valsNew[offNew + k] == r) {
616                 break;
617               }
618             }
619             if (k == oldCount) {
620               valsNew[offNew + count++] = r;
621             }
622           }
623         }
624         else {
625           PetscInt k, oldCount = count;
626 
627           for (k = 0; k < oldCount; k++) {
628             if (valsNew[offNew + k] == q) {
629               break;
630             }
631           }
632           if (k == oldCount) {
633             valsNew[offNew + count++] = q;
634           }
635         }
636       }
637       if (count < dofNew) {
638         ierr = PetscSectionSetDof(secNew, p, count);CHKERRQ(ierr);
639         compress = PETSC_TRUE;
640       }
641     }
642   }
643   ierr = ISRestoreIndices(is,&vals);CHKERRQ(ierr);
644   ierr = MPI_Allreduce(&anyNew,&globalAnyNew,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)secNew));CHKERRQ(ierr);
645   if (!globalAnyNew) {
646     ierr = PetscSectionDestroy(&secNew);CHKERRQ(ierr);
647     *sectionNew = NULL;
648     *isNew = NULL;
649   }
650   else {
651     PetscBool globalCompress;
652 
653     ierr = MPI_Allreduce(&compress,&globalCompress,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)secNew));CHKERRQ(ierr);
654     if (compress) {
655       PetscSection secComp;
656       PetscInt *valsComp = NULL;
657 
658       ierr = PetscSectionCreate(PetscObjectComm((PetscObject)section),&secComp);CHKERRQ(ierr);
659       ierr = PetscSectionSetChart(secComp,pStart,pEnd);CHKERRQ(ierr);
660       for (p = pStart; p < pEnd; p++) {
661         PetscInt dof;
662 
663         ierr = PetscSectionGetDof(secNew, p, &dof);CHKERRQ(ierr);
664         ierr = PetscSectionSetDof(secComp, p, dof);CHKERRQ(ierr);
665       }
666       ierr = PetscSectionSetUp(secComp);CHKERRQ(ierr);
667       ierr = PetscSectionGetStorageSize(secComp,&sizeNew);CHKERRQ(ierr);
668       ierr = PetscMalloc1(sizeNew,&valsComp);CHKERRQ(ierr);
669       for (p = pStart; p < pEnd; p++) {
670         PetscInt dof, off, offNew, j;
671 
672         ierr = PetscSectionGetDof(secNew, p, &dof);CHKERRQ(ierr);
673         ierr = PetscSectionGetOffset(secNew, p, &off);CHKERRQ(ierr);
674         ierr = PetscSectionGetOffset(secComp, p, &offNew);CHKERRQ(ierr);
675         for (j = 0; j < dof; j++) {
676           valsComp[offNew + j] = valsNew[off + j];
677         }
678       }
679       ierr    = PetscSectionDestroy(&secNew);CHKERRQ(ierr);
680       secNew  = secComp;
681       ierr    = PetscFree(valsNew);CHKERRQ(ierr);
682       valsNew = valsComp;
683     }
684     ierr = ISCreateGeneral(PetscObjectComm((PetscObject)is),sizeNew,valsNew,PETSC_OWN_POINTER,isNew);CHKERRQ(ierr);
685   }
686   PetscFunctionReturn(0);
687 }
688 
689 #undef __FUNCT__
690 #define __FUNCT__ "DMPlexComputeConstraints_Tree"
691 static PetscErrorCode DMPlexComputeConstraints_Tree(DM dm)
692 {
693   PetscInt       p, pStart, pEnd, *anchors, size;
694   PetscInt       aMin = PETSC_MAX_INT, aMax = PETSC_MIN_INT;
695   PetscSection   aSec;
696   DMLabel        canonLabel;
697   IS             aIS;
698   PetscErrorCode ierr;
699 
700   PetscFunctionBegin;
701   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
702   ierr = DMPlexGetChart(dm,&pStart,&pEnd);CHKERRQ(ierr);
703   ierr = DMPlexGetLabel(dm,"canonical",&canonLabel);CHKERRQ(ierr);
704   for (p = pStart; p < pEnd; p++) {
705     PetscInt parent;
706 
707     if (canonLabel) {
708       PetscInt canon;
709 
710       ierr = DMLabelGetValue(canonLabel,p,&canon);CHKERRQ(ierr);
711       if (p != canon) continue;
712     }
713     ierr = DMPlexGetTreeParent(dm,p,&parent,NULL);CHKERRQ(ierr);
714     if (parent != p) {
715       aMin = PetscMin(aMin,p);
716       aMax = PetscMax(aMax,p+1);
717     }
718   }
719   if (aMin > aMax) {
720     aMin = -1;
721     aMax = -1;
722   }
723   ierr = PetscSectionCreate(PetscObjectComm((PetscObject)dm),&aSec);CHKERRQ(ierr);
724   ierr = PetscSectionSetChart(aSec,aMin,aMax);CHKERRQ(ierr);
725   for (p = aMin; p < aMax; p++) {
726     PetscInt parent, ancestor = p;
727 
728     if (canonLabel) {
729       PetscInt canon;
730 
731       ierr = DMLabelGetValue(canonLabel,p,&canon);CHKERRQ(ierr);
732       if (p != canon) continue;
733     }
734     ierr = DMPlexGetTreeParent(dm,p,&parent,NULL);CHKERRQ(ierr);
735     while (parent != ancestor) {
736       ancestor = parent;
737       ierr     = DMPlexGetTreeParent(dm,ancestor,&parent,NULL);CHKERRQ(ierr);
738     }
739     if (ancestor != p) {
740       PetscInt closureSize, *closure = NULL;
741 
742       ierr = DMPlexGetTransitiveClosure(dm,ancestor,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
743       ierr = PetscSectionSetDof(aSec,p,closureSize);CHKERRQ(ierr);
744       ierr = DMPlexRestoreTransitiveClosure(dm,ancestor,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
745     }
746   }
747   ierr = PetscSectionSetUp(aSec);CHKERRQ(ierr);
748   ierr = PetscSectionGetStorageSize(aSec,&size);CHKERRQ(ierr);
749   ierr = PetscMalloc1(size,&anchors);CHKERRQ(ierr);
750   for (p = aMin; p < aMax; p++) {
751     PetscInt parent, ancestor = p;
752 
753     if (canonLabel) {
754       PetscInt canon;
755 
756       ierr = DMLabelGetValue(canonLabel,p,&canon);CHKERRQ(ierr);
757       if (p != canon) continue;
758     }
759     ierr = DMPlexGetTreeParent(dm,p,&parent,NULL);CHKERRQ(ierr);
760     while (parent != ancestor) {
761       ancestor = parent;
762       ierr     = DMPlexGetTreeParent(dm,ancestor,&parent,NULL);CHKERRQ(ierr);
763     }
764     if (ancestor != p) {
765       PetscInt j, closureSize, *closure = NULL, aOff;
766 
767       ierr = PetscSectionGetOffset(aSec,p,&aOff);CHKERRQ(ierr);
768 
769       ierr = DMPlexGetTransitiveClosure(dm,ancestor,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
770       for (j = 0; j < closureSize; j++) {
771         anchors[aOff + j] = closure[2*j];
772       }
773       ierr = DMPlexRestoreTransitiveClosure(dm,ancestor,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
774     }
775   }
776   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)dm),size,anchors,PETSC_OWN_POINTER,&aIS);CHKERRQ(ierr);
777   {
778     PetscSection aSecNew = aSec;
779     IS           aISNew  = aIS;
780 
781     ierr = PetscObjectReference((PetscObject)aSec);CHKERRQ(ierr);
782     ierr = PetscObjectReference((PetscObject)aIS);CHKERRQ(ierr);
783     while (aSecNew) {
784       ierr    = PetscSectionDestroy(&aSec);CHKERRQ(ierr);
785       ierr    = ISDestroy(&aIS);CHKERRQ(ierr);
786       aSec    = aSecNew;
787       aIS     = aISNew;
788       aSecNew = NULL;
789       aISNew  = NULL;
790       ierr    = AnchorsFlatten(aSec,aIS,&aSecNew,&aISNew);CHKERRQ(ierr);
791     }
792   }
793   ierr = DMPlexSetConstraints(dm,aSec,aIS);CHKERRQ(ierr);
794   ierr = PetscSectionDestroy(&aSec);CHKERRQ(ierr);
795   ierr = ISDestroy(&aIS);CHKERRQ(ierr);
796   PetscFunctionReturn(0);
797 }
798 
799 #undef __FUNCT__
800 #define __FUNCT__ "DMPlexTreeExchangeSupports"
801 static PetscErrorCode DMPlexTreeExchangeSupports(DM dm)
802 {
803   DM_Plex *mesh = (DM_Plex *)dm->data;
804   PetscSection newSupportSection;
805   PetscInt newSize, *newSupports, pStart, pEnd, p, d, depth;
806   PetscInt *offsets;
807   PetscErrorCode ierr;
808 
809   PetscFunctionBegin;
810   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
811   /* symmetrize the hierarchy */
812   ierr = DMPlexGetDepth(dm,&depth);CHKERRQ(ierr);
813   ierr = PetscSectionCreate(PetscObjectComm((PetscObject)dm),&newSupportSection);CHKERRQ(ierr);
814   ierr = DMPlexGetChart(dm,&pStart,&pEnd);CHKERRQ(ierr);
815   ierr = PetscSectionSetChart(newSupportSection,pStart,pEnd);CHKERRQ(ierr);
816   ierr = PetscCalloc1(pEnd,&offsets);CHKERRQ(ierr);
817   /* if a point is in the support of q, it should be in the support of
818    * parent(q) */
819   for (d = 0; d <= depth; d++) {
820     ierr = DMPlexGetHeightStratum(dm,d,&pStart,&pEnd);CHKERRQ(ierr);
821     for (p = pStart; p < pEnd; ++p) {
822       PetscInt dof, q, qdof, parent;
823 
824       ierr = PetscSectionGetDof(mesh->supportSection, p, &dof);CHKERRQ(ierr);
825       ierr = PetscSectionAddDof(newSupportSection, p, dof);CHKERRQ(ierr);
826       q    = p;
827       ierr = DMPlexGetTreeParent(dm,q,&parent,NULL);CHKERRQ(ierr);
828       while (parent != q && parent >= pStart && parent < pEnd) {
829         q = parent;
830 
831         ierr = PetscSectionGetDof(mesh->supportSection, q, &qdof);CHKERRQ(ierr);
832         ierr = PetscSectionAddDof(newSupportSection,p,qdof);CHKERRQ(ierr);
833         ierr = PetscSectionAddDof(newSupportSection,q,dof);CHKERRQ(ierr);
834         ierr = DMPlexGetTreeParent(dm,q,&parent,NULL);CHKERRQ(ierr);
835       }
836     }
837   }
838   ierr = PetscSectionSetUp(newSupportSection);CHKERRQ(ierr);
839   ierr = PetscSectionGetStorageSize(newSupportSection,&newSize);CHKERRQ(ierr);
840   ierr = PetscMalloc1(newSize,&newSupports);CHKERRQ(ierr);
841   for (d = 0; d <= depth; d++) {
842     ierr = DMPlexGetHeightStratum(dm,d,&pStart,&pEnd);CHKERRQ(ierr);
843     for (p = pStart; p < pEnd; p++) {
844       PetscInt dof, off, q, qdof, qoff, newDof, newOff, newqOff, i, parent;
845 
846       ierr = PetscSectionGetDof(mesh->supportSection, p, &dof);CHKERRQ(ierr);
847       ierr = PetscSectionGetOffset(mesh->supportSection, p, &off);CHKERRQ(ierr);
848       ierr = PetscSectionGetDof(newSupportSection, p, &newDof);CHKERRQ(ierr);
849       ierr = PetscSectionGetOffset(newSupportSection, p, &newOff);CHKERRQ(ierr);
850       for (i = 0; i < dof; i++) {
851         newSupports[newOff+offsets[p]++] = mesh->supports[off + i];
852       }
853       mesh->maxSupportSize = PetscMax(mesh->maxSupportSize,newDof);
854 
855       q    = p;
856       ierr = DMPlexGetTreeParent(dm,q,&parent,NULL);CHKERRQ(ierr);
857       while (parent != q && parent >= pStart && parent < pEnd) {
858         q = parent;
859         ierr = PetscSectionGetDof(mesh->supportSection, q, &qdof);CHKERRQ(ierr);
860         ierr = PetscSectionGetOffset(mesh->supportSection, q, &qoff);CHKERRQ(ierr);
861         ierr = PetscSectionGetOffset(newSupportSection, q, &newqOff);CHKERRQ(ierr);
862         for (i = 0; i < qdof; i++) {
863           newSupports[newOff+offsets[p]++] = mesh->supports[qoff + i];
864         }
865         for (i = 0; i < dof; i++) {
866           newSupports[newqOff+offsets[q]++] = mesh->supports[off + i];
867         }
868         ierr = DMPlexGetTreeParent(dm,q,&parent,NULL);CHKERRQ(ierr);
869       }
870     }
871   }
872   ierr = PetscSectionDestroy(&mesh->supportSection);CHKERRQ(ierr);
873   mesh->supportSection = newSupportSection;
874   ierr = PetscFree(mesh->supports);CHKERRQ(ierr);
875   mesh->supports = newSupports;
876   ierr = PetscFree(offsets);CHKERRQ(ierr);
877 
878   PetscFunctionReturn(0);
879 }
880 
881 #undef __FUNCT__
882 #define __FUNCT__ "DMPlexSetTree_Internal"
883 static PetscErrorCode DMPlexSetTree_Internal(DM dm, PetscSection parentSection, PetscInt *parents, PetscInt *childIDs, PetscBool computeCanonical, PetscBool exchangeSupports)
884 {
885   DM_Plex       *mesh = (DM_Plex *)dm->data;
886   DM             refTree;
887   PetscInt       size;
888   PetscErrorCode ierr;
889 
890   PetscFunctionBegin;
891   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
892   PetscValidHeaderSpecific(parentSection, PETSC_SECTION_CLASSID, 2);
893   ierr = PetscObjectReference((PetscObject)parentSection);CHKERRQ(ierr);
894   ierr = PetscSectionDestroy(&mesh->parentSection);CHKERRQ(ierr);
895   mesh->parentSection = parentSection;
896   ierr = PetscSectionGetStorageSize(parentSection,&size);CHKERRQ(ierr);
897   if (parents != mesh->parents) {
898     ierr = PetscFree(mesh->parents);CHKERRQ(ierr);
899     ierr = PetscMalloc1(size,&mesh->parents);CHKERRQ(ierr);
900     ierr = PetscMemcpy(mesh->parents, parents, size * sizeof(*parents));CHKERRQ(ierr);
901   }
902   if (childIDs != mesh->childIDs) {
903     ierr = PetscFree(mesh->childIDs);CHKERRQ(ierr);
904     ierr = PetscMalloc1(size,&mesh->childIDs);CHKERRQ(ierr);
905     ierr = PetscMemcpy(mesh->childIDs, childIDs, size * sizeof(*childIDs));CHKERRQ(ierr);
906   }
907   ierr = DMPlexGetReferenceTree(dm,&refTree);CHKERRQ(ierr);
908   if (refTree) {
909     DMLabel canonLabel;
910 
911     ierr = DMPlexGetLabel(refTree,"canonical",&canonLabel);CHKERRQ(ierr);
912     if (canonLabel) {
913       PetscInt i;
914 
915       for (i = 0; i < size; i++) {
916         PetscInt canon;
917         ierr = DMLabelGetValue(canonLabel, mesh->childIDs[i], &canon);CHKERRQ(ierr);
918         if (canon >= 0) {
919           mesh->childIDs[i] = canon;
920         }
921       }
922     }
923   }
924   ierr = DMPlexTreeSymmetrize(dm);CHKERRQ(ierr);
925   if (computeCanonical) {
926     PetscInt d, dim;
927 
928     /* add the canonical label */
929     ierr = DMPlexGetDimension(dm,&dim);CHKERRQ(ierr);
930     ierr = DMPlexCreateLabel(dm,"canonical");CHKERRQ(ierr);
931     for (d = 0; d <= dim; d++) {
932       PetscInt p, dStart, dEnd, canon = -1, cNumChildren;
933       const PetscInt *cChildren;
934 
935       ierr = DMPlexGetDepthStratum(dm,d,&dStart,&dEnd);CHKERRQ(ierr);
936       for (p = dStart; p < dEnd; p++) {
937         ierr = DMPlexGetTreeChildren(dm,p,&cNumChildren,&cChildren);CHKERRQ(ierr);
938         if (cNumChildren) {
939           canon = p;
940           break;
941         }
942       }
943       if (canon == -1) continue;
944       for (p = dStart; p < dEnd; p++) {
945         PetscInt numChildren, i;
946         const PetscInt *children;
947 
948         ierr = DMPlexGetTreeChildren(dm,p,&numChildren,&children);CHKERRQ(ierr);
949         if (numChildren) {
950           if (numChildren != cNumChildren) SETERRQ2(PetscObjectComm((PetscObject)dm),PETSC_ERR_PLIB,"All parent points in a stratum should have the same number of children: %d != %d", numChildren, cNumChildren);
951           ierr = DMPlexSetLabelValue(dm,"canonical",p,canon);CHKERRQ(ierr);
952           for (i = 0; i < numChildren; i++) {
953             ierr = DMPlexSetLabelValue(dm,"canonical",children[i],cChildren[i]);CHKERRQ(ierr);
954           }
955         }
956       }
957     }
958   }
959   if (exchangeSupports) {
960     ierr = DMPlexTreeExchangeSupports(dm);CHKERRQ(ierr);
961   }
962   ierr = DMPlexComputeConstraints_Tree(dm);CHKERRQ(ierr);
963   PetscFunctionReturn(0);
964 }
965 
966 #undef __FUNCT__
967 #define __FUNCT__ "DMPlexSetTree"
968 /*@
969   DMPlexSetTree - set the tree that describes the hierarchy of non-conforming mesh points.  This routine also creates
970   the point-to-point constraints determined by the tree: a point is constained to the points in the closure of its
971   tree root.
972 
973   Collective on dm
974 
975   Input Parameters:
976 + dm - the DMPlex object
977 . parentSection - a section describing the tree: a point has a parent if it has 1 dof in the section; the section
978                   offset indexes the parent and childID list; the reference count of parentSection is incremented
979 . parents - a list of the point parents; copied, can be destroyed
980 - childIDs - identifies the relationship of the child point to the parent point; if there is a reference tree, then
981              the child corresponds to the point in the reference tree with index childIDs; copied, can be destroyed
982 
983   Level: intermediate
984 
985 .seealso: DMPlexGetTree(), DMPlexSetReferenceTree(), DMPlexSetConstraints(), DMPlexGetTreeParent(), DMPlexGetTreeChildren()
986 @*/
987 PetscErrorCode DMPlexSetTree(DM dm, PetscSection parentSection, PetscInt parents[], PetscInt childIDs[])
988 {
989   PetscErrorCode ierr;
990 
991   PetscFunctionBegin;
992   ierr = DMPlexSetTree_Internal(dm,parentSection,parents,childIDs,PETSC_FALSE,PETSC_TRUE);CHKERRQ(ierr);
993   PetscFunctionReturn(0);
994 }
995 
996 #undef __FUNCT__
997 #define __FUNCT__ "DMPlexGetTree"
998 /*@
999   DMPlexGetTree - get the tree that describes the hierarchy of non-conforming mesh points.
1000   Collective on dm
1001 
1002   Input Parameters:
1003 . dm - the DMPlex object
1004 
1005   Output Parameters:
1006 + parentSection - a section describing the tree: a point has a parent if it has 1 dof in the section; the section
1007                   offset indexes the parent and childID list
1008 . parents - a list of the point parents
1009 . childIDs - identifies the relationship of the child point to the parent point; if there is a reference tree, then
1010              the child corresponds to the point in the reference tree with index childID
1011 . childSection - the inverse of the parent section
1012 - children - a list of the point children
1013 
1014   Level: intermediate
1015 
1016 .seealso: DMPlexSetTree(), DMPlexSetReferenceTree(), DMPlexSetConstraints(), DMPlexGetTreeParent(), DMPlexGetTreeChildren()
1017 @*/
1018 PetscErrorCode DMPlexGetTree(DM dm, PetscSection *parentSection, PetscInt *parents[], PetscInt *childIDs[], PetscSection *childSection, PetscInt *children[])
1019 {
1020   DM_Plex        *mesh = (DM_Plex *)dm->data;
1021 
1022   PetscFunctionBegin;
1023   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1024   if (parentSection) *parentSection = mesh->parentSection;
1025   if (parents)       *parents       = mesh->parents;
1026   if (childIDs)      *childIDs      = mesh->childIDs;
1027   if (childSection)  *childSection  = mesh->childSection;
1028   if (children)      *children      = mesh->children;
1029   PetscFunctionReturn(0);
1030 }
1031 
1032 #undef __FUNCT__
1033 #define __FUNCT__ "DMPlexGetTreeParent"
1034 /*@
1035   DMPlexGetTreeParent - get the parent of a point in the tree describing the point hierarchy (not the Sieve DAG)
1036 
1037   Input Parameters:
1038 + dm - the DMPlex object
1039 - point - the query point
1040 
1041   Output Parameters:
1042 + parent - if not NULL, set to the parent of the point, or the point itself if the point does not have a parent
1043 - childID - if not NULL, set to the child ID of the point with respect to its parent, or 0 if the point
1044             does not have a parent
1045 
1046   Level: intermediate
1047 
1048 .seealso: DMPlexSetTree(), DMPlexGetTree(), DMPlexGetTreeChildren()
1049 @*/
1050 PetscErrorCode DMPlexGetTreeParent(DM dm, PetscInt point, PetscInt *parent, PetscInt *childID)
1051 {
1052   DM_Plex       *mesh = (DM_Plex *)dm->data;
1053   PetscSection   pSec;
1054   PetscErrorCode ierr;
1055 
1056   PetscFunctionBegin;
1057   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1058   pSec = mesh->parentSection;
1059   if (pSec && point >= pSec->pStart && point < pSec->pEnd) {
1060     PetscInt dof;
1061 
1062     ierr = PetscSectionGetDof (pSec, point, &dof);CHKERRQ(ierr);
1063     if (dof) {
1064       PetscInt off;
1065 
1066       ierr = PetscSectionGetOffset (pSec, point, &off);CHKERRQ(ierr);
1067       if (parent)  *parent = mesh->parents[off];
1068       if (childID) *childID = mesh->childIDs[off];
1069       PetscFunctionReturn(0);
1070     }
1071   }
1072   if (parent) {
1073     *parent = point;
1074   }
1075   if (childID) {
1076     *childID = 0;
1077   }
1078   PetscFunctionReturn(0);
1079 }
1080 
1081 #undef __FUNCT__
1082 #define __FUNCT__ "DMPlexGetTreeChildren"
1083 /*@C
1084   DMPlexGetTreeChildren - get the children of a point in the tree describing the point hierarchy (not the Sieve DAG)
1085 
1086   Input Parameters:
1087 + dm - the DMPlex object
1088 - point - the query point
1089 
1090   Output Parameters:
1091 + numChildren - if not NULL, set to the number of children
1092 - children - if not NULL, set to a list children, or set to NULL if the point has no children
1093 
1094   Level: intermediate
1095 
1096   Fortran Notes:
1097   Since it returns an array, this routine is only available in Fortran 90, and you must
1098   include petsc.h90 in your code.
1099 
1100 .seealso: DMPlexSetTree(), DMPlexGetTree(), DMPlexGetTreeParent()
1101 @*/
1102 PetscErrorCode DMPlexGetTreeChildren(DM dm, PetscInt point, PetscInt *numChildren, const PetscInt *children[])
1103 {
1104   DM_Plex       *mesh = (DM_Plex *)dm->data;
1105   PetscSection   childSec;
1106   PetscInt       dof = 0;
1107   PetscErrorCode ierr;
1108 
1109   PetscFunctionBegin;
1110   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1111   childSec = mesh->childSection;
1112   if (childSec && point >= childSec->pStart && point < childSec->pEnd) {
1113     ierr = PetscSectionGetDof (childSec, point, &dof);CHKERRQ(ierr);
1114   }
1115   if (numChildren) *numChildren = dof;
1116   if (children) {
1117     if (dof) {
1118       PetscInt off;
1119 
1120       ierr = PetscSectionGetOffset (childSec, point, &off);CHKERRQ(ierr);
1121       *children = &mesh->children[off];
1122     }
1123     else {
1124       *children = NULL;
1125     }
1126   }
1127   PetscFunctionReturn(0);
1128 }
1129 
1130 #undef __FUNCT__
1131 #define __FUNCT__ "DMPlexComputeConstraintMatrix_ReferenceTree"
1132 static PetscErrorCode DMPlexComputeConstraintMatrix_ReferenceTree(DM dm)
1133 {
1134   PetscDS        ds;
1135   PetscInt       spdim;
1136   PetscInt       numFields, f, c, cStart, cEnd, pStart, pEnd, conStart, conEnd;
1137   const PetscInt *anchors;
1138   PetscSection   section, cSec, aSec;
1139   Mat            cMat;
1140   PetscReal      *v0, *v0parent, *vtmp, *J, *Jparent, *invJparent, detJ, detJparent;
1141   IS             aIS;
1142   PetscErrorCode ierr;
1143 
1144   PetscFunctionBegin;
1145   ierr = DMPlexGetChart(dm,&pStart,&pEnd);CHKERRQ(ierr);
1146   ierr = DMGetDS(dm,&ds);CHKERRQ(ierr);
1147   ierr = PetscDSGetNumFields(ds,&numFields);CHKERRQ(ierr);
1148   ierr = DMPlexGetHeightStratum(dm,0,&cStart,&cEnd);CHKERRQ(ierr);
1149   ierr = DMGetDefaultSection(dm,&section);CHKERRQ(ierr);
1150   ierr = DMPlexGetConstraintSection(dm,&cSec);CHKERRQ(ierr);
1151   ierr = DMPlexGetConstraints(dm,&aSec,&aIS);CHKERRQ(ierr);
1152   ierr = ISGetIndices(aIS,&anchors);CHKERRQ(ierr);
1153   ierr = PetscSectionGetChart(cSec,&conStart,&conEnd);CHKERRQ(ierr);
1154   ierr = DMPlexGetConstraintMatrix(dm,&cMat);CHKERRQ(ierr);
1155   ierr = DMPlexGetDimension(dm,&spdim);CHKERRQ(ierr);
1156   ierr = PetscMalloc6(spdim,&v0,spdim,&v0parent,spdim,&vtmp,spdim*spdim,&J,spdim*spdim,&Jparent,spdim*spdim,&invJparent);CHKERRQ(ierr);
1157 
1158   for (f = 0; f < numFields; f++) {
1159     PetscFE fe;
1160     PetscDualSpace space;
1161     PetscInt i, j, k, nPoints, offset;
1162     PetscInt fSize, fComp;
1163     PetscScalar *B = NULL;
1164     PetscReal *weights, *pointsRef, *pointsReal;
1165     Mat Amat, Bmat, Xmat;
1166 
1167     ierr = PetscDSGetDiscretization(ds,f,(PetscObject *)(&fe));CHKERRQ(ierr);
1168     ierr = PetscFEGetDualSpace(fe,&space);CHKERRQ(ierr);
1169     ierr = PetscDualSpaceGetDimension(space,&fSize);CHKERRQ(ierr);
1170     ierr = PetscFEGetNumComponents(fe,&fComp);CHKERRQ(ierr);
1171     ierr = MatCreate(PETSC_COMM_SELF,&Amat);CHKERRQ(ierr);
1172     ierr = MatSetSizes(Amat,fSize,fSize,fSize,fSize);CHKERRQ(ierr);
1173     ierr = MatSetType(Amat,MATSEQDENSE);CHKERRQ(ierr);
1174     ierr = MatSetUp(Amat);CHKERRQ(ierr);
1175     ierr = MatDuplicate(Amat,MAT_DO_NOT_COPY_VALUES,&Bmat);CHKERRQ(ierr);
1176     ierr = MatDuplicate(Amat,MAT_DO_NOT_COPY_VALUES,&Xmat);CHKERRQ(ierr);
1177     nPoints = 0;
1178     for (i = 0; i < fSize; i++) {
1179       PetscInt        qPoints;
1180       PetscQuadrature quad;
1181 
1182       ierr = PetscDualSpaceGetFunctional(space,i,&quad);CHKERRQ(ierr);
1183       ierr = PetscQuadratureGetData(quad,NULL,&qPoints,NULL,NULL);CHKERRQ(ierr);
1184       nPoints += qPoints;
1185     }
1186     ierr = PetscMalloc3(nPoints,&weights,spdim*nPoints,&pointsRef,spdim*nPoints,&pointsReal);CHKERRQ(ierr);
1187     offset = 0;
1188     for (i = 0; i < fSize; i++) {
1189       PetscInt        qPoints;
1190       const PetscReal    *p, *w;
1191       PetscQuadrature quad;
1192 
1193       ierr = PetscDualSpaceGetFunctional(space,i,&quad);CHKERRQ(ierr);
1194       ierr = PetscQuadratureGetData(quad,NULL,&qPoints,&p,&w);CHKERRQ(ierr);
1195       ierr = PetscMemcpy(weights+offset,w,qPoints*sizeof(*w));CHKERRQ(ierr);
1196       ierr = PetscMemcpy(pointsRef+spdim*offset,p,spdim*qPoints*sizeof(*p));CHKERRQ(ierr);
1197       offset += qPoints;
1198     }
1199     ierr = PetscFEGetTabulation(fe,nPoints,pointsRef,&B,NULL,NULL);CHKERRQ(ierr);
1200     offset = 0;
1201     for (i = 0; i < fSize; i++) {
1202       PetscInt        qPoints;
1203       PetscQuadrature quad;
1204 
1205       ierr = PetscDualSpaceGetFunctional(space,i,&quad);CHKERRQ(ierr);
1206       ierr = PetscQuadratureGetData(quad,NULL,&qPoints,NULL,NULL);CHKERRQ(ierr);
1207       for (j = 0; j < fSize; j++) {
1208         PetscScalar val = 0.;
1209 
1210         for (k = 0; k < qPoints; k++) {
1211           val += B[((offset + k) * fSize + j) * fComp] * weights[k];
1212         }
1213         ierr = MatSetValue(Amat,i,j,val,INSERT_VALUES);CHKERRQ(ierr);
1214       }
1215       offset += qPoints;
1216     }
1217     ierr = PetscFERestoreTabulation(fe,nPoints,pointsRef,&B,NULL,NULL);CHKERRQ(ierr);
1218     ierr = MatAssemblyBegin(Amat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1219     ierr = MatAssemblyEnd(Amat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1220     ierr = MatLUFactor(Amat,NULL,NULL,NULL);CHKERRQ(ierr);
1221     for (c = cStart; c < cEnd; c++) {
1222       PetscInt parent;
1223       PetscInt closureSize, closureSizeP, *closure = NULL, *closureP = NULL;
1224       PetscInt *childOffsets, *parentOffsets;
1225 
1226       ierr = DMPlexGetTreeParent(dm,c,&parent,NULL);CHKERRQ(ierr);
1227       if (parent == c) continue;
1228       ierr = DMPlexGetTransitiveClosure(dm,c,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1229       for (i = 0; i < closureSize; i++) {
1230         PetscInt p = closure[2*i];
1231         PetscInt conDof;
1232 
1233         if (p < conStart || p >= conEnd) continue;
1234         if (numFields > 1) {
1235           ierr = PetscSectionGetFieldDof(cSec,p,f,&conDof);CHKERRQ(ierr);
1236         }
1237         else {
1238           ierr = PetscSectionGetDof(cSec,p,&conDof);CHKERRQ(ierr);
1239         }
1240         if (conDof) break;
1241       }
1242       if (i == closureSize) {
1243         ierr = DMPlexRestoreTransitiveClosure(dm,c,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1244         continue;
1245       }
1246 
1247       ierr = DMPlexComputeCellGeometry(dm, c, v0, J, NULL, &detJ);CHKERRQ(ierr);
1248       ierr = DMPlexComputeCellGeometry(dm, parent, v0parent, Jparent, invJparent, &detJparent);CHKERRQ(ierr);
1249       for (i = 0; i < nPoints; i++) {
1250         CoordinatesRefToReal(spdim, spdim, v0, J, &pointsRef[i*spdim],vtmp);CHKERRQ(ierr);
1251         CoordinatesRealToRef(spdim, spdim, v0parent, invJparent, vtmp, &pointsReal[i*spdim]);CHKERRQ(ierr);
1252       }
1253       ierr = PetscFEGetTabulation(fe,nPoints,pointsReal,&B,NULL,NULL);CHKERRQ(ierr);
1254       offset = 0;
1255       for (i = 0; i < fSize; i++) {
1256         PetscInt        qPoints;
1257         PetscQuadrature quad;
1258 
1259         ierr = PetscDualSpaceGetFunctional(space,i,&quad);CHKERRQ(ierr);
1260         ierr = PetscQuadratureGetData(quad,NULL,&qPoints,NULL,NULL);CHKERRQ(ierr);
1261         for (j = 0; j < fSize; j++) {
1262           PetscScalar val = 0.;
1263 
1264           for (k = 0; k < qPoints; k++) {
1265             val += B[((offset + k) * fSize + j) * fComp] * weights[k];
1266           }
1267           MatSetValue(Bmat,i,j,val,INSERT_VALUES);CHKERRQ(ierr);
1268         }
1269         offset += qPoints;
1270       }
1271       ierr = PetscFERestoreTabulation(fe,nPoints,pointsReal,&B,NULL,NULL);CHKERRQ(ierr);
1272       ierr = MatAssemblyBegin(Bmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1273       ierr = MatAssemblyEnd(Bmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1274       ierr = MatMatSolve(Amat,Bmat,Xmat);CHKERRQ(ierr);
1275       ierr = DMPlexGetTransitiveClosure(dm,parent,PETSC_TRUE,&closureSizeP,&closureP);CHKERRQ(ierr);
1276       ierr = PetscMalloc2(closureSize+1,&childOffsets,closureSizeP+1,&parentOffsets);CHKERRQ(ierr);
1277       childOffsets[0] = 0;
1278       for (i = 0; i < closureSize; i++) {
1279         PetscInt p = closure[2*i];
1280         PetscInt dof;
1281 
1282         if (numFields > 1) {
1283           ierr = PetscSectionGetFieldDof(section,p,f,&dof);CHKERRQ(ierr);
1284         }
1285         else {
1286           ierr = PetscSectionGetDof(section,p,&dof);CHKERRQ(ierr);
1287         }
1288         childOffsets[i+1]=childOffsets[i]+dof / fComp;
1289       }
1290       parentOffsets[0] = 0;
1291       for (i = 0; i < closureSizeP; i++) {
1292         PetscInt p = closureP[2*i];
1293         PetscInt dof;
1294 
1295         if (numFields > 1) {
1296           ierr = PetscSectionGetFieldDof(section,p,f,&dof);CHKERRQ(ierr);
1297         }
1298         else {
1299           ierr = PetscSectionGetDof(section,p,&dof);CHKERRQ(ierr);
1300         }
1301         parentOffsets[i+1]=parentOffsets[i]+dof / fComp;
1302       }
1303       for (i = 0; i < closureSize; i++) {
1304         PetscInt conDof, conOff, aDof, aOff;
1305         PetscInt p = closure[2*i];
1306         PetscInt o = closure[2*i+1];
1307 
1308         if (p < conStart || p >= conEnd) continue;
1309         if (numFields > 1) {
1310           ierr = PetscSectionGetFieldDof(cSec,p,f,&conDof);CHKERRQ(ierr);
1311           ierr = PetscSectionGetFieldOffset(cSec,p,f,&conOff);CHKERRQ(ierr);
1312         }
1313         else {
1314           ierr = PetscSectionGetDof(cSec,p,&conDof);CHKERRQ(ierr);
1315           ierr = PetscSectionGetOffset(cSec,p,&conOff);CHKERRQ(ierr);
1316         }
1317         if (!conDof) continue;
1318         ierr = PetscSectionGetDof(aSec,p,&aDof);CHKERRQ(ierr);
1319         ierr = PetscSectionGetOffset(aSec,p,&aOff);CHKERRQ(ierr);
1320         for (k = 0; k < aDof; k++) {
1321           PetscInt a = anchors[aOff + k];
1322           PetscInt aSecDof, aSecOff;
1323 
1324           if (numFields > 1) {
1325             ierr = PetscSectionGetFieldDof(section,a,f,&aSecDof);CHKERRQ(ierr);
1326             ierr = PetscSectionGetFieldOffset(section,a,f,&aSecOff);CHKERRQ(ierr);
1327           }
1328           else {
1329             ierr = PetscSectionGetDof(section,a,&aSecDof);CHKERRQ(ierr);
1330             ierr = PetscSectionGetOffset(section,a,&aSecOff);CHKERRQ(ierr);
1331           }
1332           if (!aSecDof) continue;
1333 
1334           for (j = 0; j < closureSizeP; j++) {
1335             PetscInt q = closureP[2*j];
1336             PetscInt oq = closureP[2*j+1];
1337 
1338             if (q == a) {
1339               PetscInt r, s, t;
1340 
1341               for (r = childOffsets[i]; r < childOffsets[i+1]; r++) {
1342                 for (s = parentOffsets[j]; s < parentOffsets[j+1]; s++) {
1343                   PetscScalar val;
1344                   PetscInt insertCol, insertRow;
1345 
1346                   ierr = MatGetValue(Xmat,r,s,&val);CHKERRQ(ierr);
1347                   if (o >= 0) {
1348                     insertRow = conOff + fComp * (r - childOffsets[i]);
1349                   }
1350                   else {
1351                     insertRow = conOff + fComp * (childOffsets[i + 1] - 1 - r);
1352                   }
1353                   if (oq >= 0) {
1354                     insertCol = aSecOff + fComp * (s - parentOffsets[j]);
1355                   }
1356                   else {
1357                     insertCol = aSecOff + fComp * (parentOffsets[j + 1] - 1 - s);
1358                   }
1359                   for (t = 0; t < fComp; t++) {
1360                     ierr = MatSetValue(cMat,insertRow + t,insertCol + t,val,INSERT_VALUES);CHKERRQ(ierr);
1361                   }
1362                 }
1363               }
1364             }
1365           }
1366         }
1367       }
1368       ierr = PetscFree2(childOffsets,parentOffsets);CHKERRQ(ierr);
1369       ierr = DMPlexRestoreTransitiveClosure(dm,c,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1370       ierr = DMPlexRestoreTransitiveClosure(dm,parent,PETSC_TRUE,&closureSizeP,&closureP);CHKERRQ(ierr);
1371     }
1372     ierr = MatDestroy(&Amat);CHKERRQ(ierr);
1373     ierr = MatDestroy(&Bmat);CHKERRQ(ierr);
1374     ierr = MatDestroy(&Xmat);CHKERRQ(ierr);
1375     ierr = PetscFree3(weights,pointsRef,pointsReal);CHKERRQ(ierr);
1376   }
1377   ierr = MatAssemblyBegin(cMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1378   ierr = MatAssemblyEnd(cMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1379   ierr = PetscFree6(v0,v0parent,vtmp,J,Jparent,invJparent);CHKERRQ(ierr);
1380   ierr = ISRestoreIndices(aIS,&anchors);CHKERRQ(ierr);
1381 
1382   PetscFunctionReturn(0);
1383 }
1384 
1385 #undef __FUNCT__
1386 #define __FUNCT__ "DMPlexComputeConstraintMatrix_Tree"
1387 PetscErrorCode DMPlexComputeConstraintMatrix_Tree(DM dm)
1388 {
1389   DM             refTree;
1390   PetscDS        ds;
1391   Mat            refCmat, cMat;
1392   PetscInt       numFields, f, pRefStart, pRefEnd, p, *rows, *cols, maxDof, maxAnDof, *perm, *iperm, pStart, pEnd, conStart, conEnd, **refPointFieldN;
1393   PetscScalar ***refPointFieldMats, *pointWork;
1394   PetscSection   refConSec, conSec, refAnSec, anSec, section, refSection;
1395   IS             refAnIS, anIS;
1396   const PetscInt *refAnchors, *anchors;
1397   PetscErrorCode ierr;
1398 
1399   PetscFunctionBegin;
1400   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1401   ierr = DMGetDS(dm,&ds);CHKERRQ(ierr);
1402   ierr = PetscDSGetNumFields(ds,&numFields);CHKERRQ(ierr);
1403   ierr = DMPlexGetReferenceTree(dm,&refTree);CHKERRQ(ierr);
1404   ierr = DMSetDS(refTree,ds);CHKERRQ(ierr);
1405   ierr = DMPlexComputeConstraintMatrix_ReferenceTree(refTree);CHKERRQ(ierr);
1406   ierr = DMPlexGetConstraintMatrix(refTree,&refCmat);CHKERRQ(ierr);
1407   ierr = DMPlexGetChart(refTree,&pRefStart,&pRefEnd);CHKERRQ(ierr);
1408   ierr = DMPlexGetConstraints(refTree,&refAnSec,&refAnIS);CHKERRQ(ierr);
1409   ierr = DMPlexGetConstraints(dm,&anSec,&anIS);CHKERRQ(ierr);
1410   ierr = ISGetIndices(refAnIS,&refAnchors);CHKERRQ(ierr);
1411   ierr = ISGetIndices(anIS,&anchors);CHKERRQ(ierr);
1412   ierr = DMPlexGetConstraintSection(refTree,&refConSec);CHKERRQ(ierr);
1413   ierr = DMPlexGetConstraintSection(dm,&conSec);CHKERRQ(ierr);
1414   ierr = DMGetDefaultSection(refTree,&refSection);CHKERRQ(ierr);
1415   ierr = DMGetDefaultSection(dm,&section);CHKERRQ(ierr);
1416   ierr = PetscSectionGetChart(refConSec,&pRefStart,&pRefEnd);CHKERRQ(ierr);
1417   ierr = PetscSectionGetChart(conSec,&conStart,&conEnd);CHKERRQ(ierr);
1418   ierr = PetscMalloc1(pRefEnd-pRefStart,&refPointFieldMats);CHKERRQ(ierr);
1419   ierr = PetscMalloc1(pRefEnd-pRefStart,&refPointFieldN);CHKERRQ(ierr);
1420   ierr = PetscSectionGetMaxDof(refConSec,&maxDof);CHKERRQ(ierr);
1421   ierr = PetscSectionGetMaxDof(refAnSec,&maxAnDof);CHKERRQ(ierr);
1422   ierr = PetscMalloc1(maxDof,&rows);CHKERRQ(ierr);
1423   ierr = PetscMalloc1(maxDof*maxAnDof,&cols);CHKERRQ(ierr);
1424   ierr = PetscMalloc1(maxDof*maxDof*maxAnDof,&pointWork);CHKERRQ(ierr);
1425 
1426   /* step 1: get submats for every constrained point in the reference tree */
1427   for (p = pRefStart; p < pRefEnd; p++) {
1428     PetscInt parent, closureSize, *closure = NULL, pDof;
1429 
1430     ierr = DMPlexGetTreeParent(refTree,p,&parent,NULL);CHKERRQ(ierr);
1431     ierr = PetscSectionGetDof(refConSec,p,&pDof);CHKERRQ(ierr);
1432     if (!pDof || parent == p) continue;
1433 
1434     ierr = PetscMalloc1(numFields,&refPointFieldMats[p-pRefStart]);CHKERRQ(ierr);
1435     ierr = PetscCalloc1(numFields,&refPointFieldN[p-pRefStart]);CHKERRQ(ierr);
1436     ierr = DMPlexGetTransitiveClosure(refTree,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1437     for (f = 0; f < numFields; f++) {
1438       PetscInt cDof, cOff, numCols, r, i, fComp;
1439       PetscFE fe;
1440 
1441       ierr = PetscDSGetDiscretization(ds,f,(PetscObject *) &fe);CHKERRQ(ierr);
1442       ierr = PetscFEGetNumComponents(fe,&fComp);CHKERRQ(ierr);
1443 
1444       if (numFields > 1) {
1445         ierr = PetscSectionGetFieldDof(refConSec,p,f,&cDof);CHKERRQ(ierr);
1446         ierr = PetscSectionGetFieldOffset(refConSec,p,f,&cOff);CHKERRQ(ierr);
1447       }
1448       else {
1449         ierr = PetscSectionGetDof(refConSec,p,&cDof);CHKERRQ(ierr);
1450         ierr = PetscSectionGetOffset(refConSec,p,&cOff);CHKERRQ(ierr);
1451       }
1452 
1453       if (!cDof) continue;
1454       for (r = 0; r < cDof; r++) {
1455         rows[r] = cOff + r;
1456       }
1457       numCols = 0;
1458       for (i = 0; i < closureSize; i++) {
1459         PetscInt q = closure[2*i];
1460         PetscInt o = closure[2*i+1];
1461         PetscInt aDof, aOff, j;
1462 
1463         if (numFields > 1) {
1464           ierr = PetscSectionGetFieldDof(refSection,q,f,&aDof);CHKERRQ(ierr);
1465           ierr = PetscSectionGetFieldOffset(refSection,q,f,&aOff);CHKERRQ(ierr);
1466         }
1467         else {
1468           ierr = PetscSectionGetDof(refSection,q,&aDof);CHKERRQ(ierr);
1469           ierr = PetscSectionGetOffset(refSection,q,&aOff);CHKERRQ(ierr);
1470         }
1471 
1472         for (j = 0; j < aDof; j++) {
1473           PetscInt node = (o >= 0) ? (j / fComp) : ((aDof - 1 - j) / fComp);
1474           PetscInt comp = (j % fComp);
1475 
1476           cols[numCols++] = aOff + node * fComp + comp;
1477         }
1478       }
1479       refPointFieldN[p-pRefStart][f] = numCols;
1480       ierr = PetscMalloc1(cDof*numCols,&refPointFieldMats[p-pRefStart][f]);CHKERRQ(ierr);
1481       ierr = MatGetValues(refCmat,cDof,rows,numCols,cols,refPointFieldMats[p-pRefStart][f]);CHKERRQ(ierr);
1482     }
1483     ierr = DMPlexRestoreTransitiveClosure(refTree,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1484   }
1485 
1486   /* step 2: compute the preorder */
1487   ierr = DMPlexGetChart(dm,&pStart,&pEnd);CHKERRQ(ierr);
1488   ierr = PetscMalloc2(pEnd-pStart,&perm,pEnd-pStart,&iperm);CHKERRQ(ierr);
1489   for (p = pStart; p < pEnd; p++) {
1490     perm[p - pStart] = p;
1491     iperm[p - pStart] = p-pStart;
1492   }
1493   for (p = 0; p < pEnd - pStart;) {
1494     PetscInt point = perm[p];
1495     PetscInt parent;
1496 
1497     ierr = DMPlexGetTreeParent(dm,point,&parent,NULL);CHKERRQ(ierr);
1498     if (parent == point) {
1499       p++;
1500     }
1501     else {
1502       PetscInt size, closureSize, *closure = NULL, i;
1503 
1504       ierr = DMPlexGetTransitiveClosure(dm,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1505       for (i = 0; i < closureSize; i++) {
1506         PetscInt q = closure[2*i];
1507         if (iperm[q-pStart] > iperm[point-pStart]) {
1508           /* swap */
1509           perm[p]               = q;
1510           perm[iperm[q-pStart]] = point;
1511           iperm[point-pStart]   = iperm[q-pStart];
1512           iperm[q-pStart]       = p;
1513           break;
1514         }
1515       }
1516       size = closureSize;
1517       ierr = DMPlexRestoreTransitiveClosure(dm,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1518       if (i == size) {
1519         p++;
1520       }
1521     }
1522   }
1523 
1524   /* step 3: fill the constraint matrix */
1525   /* we are going to use a preorder progressive fill strategy.  Mat doesn't
1526    * allow progressive fill without assembly, so we are going to set up the
1527    * values outside of the Mat first.
1528    */
1529   {
1530     PetscInt nRows, row, nnz;
1531     PetscBool done;
1532     const PetscInt *ia, *ja;
1533     PetscScalar *vals;
1534 
1535     ierr = DMPlexGetConstraintMatrix(dm,&cMat);CHKERRQ(ierr);
1536     ierr = MatGetRowIJ(cMat,0,PETSC_FALSE,PETSC_FALSE,&nRows,&ia,&ja,&done);CHKERRQ(ierr);
1537     if (!done) SETERRQ(PetscObjectComm((PetscObject)cMat),PETSC_ERR_PLIB,"Could not get RowIJ of constraint matrix");
1538     nnz  = ia[nRows];
1539     /* malloc and then zero rows right before we fill them: this way valgrind
1540      * can tell if we are doing progressive fill in the wrong order */
1541     ierr = PetscMalloc1(nnz,&vals);CHKERRQ(ierr);
1542     for (p = 0; p < pEnd - pStart; p++) {
1543       PetscInt parent, childid, closureSize, *closure = NULL;
1544       PetscInt point = perm[p], pointDof;
1545 
1546       ierr = DMPlexGetTreeParent(dm,point,&parent,&childid);CHKERRQ(ierr);
1547       if ((point < conStart) || (point >= conEnd) || (parent == point)) continue;
1548       ierr = PetscSectionGetDof(conSec,point,&pointDof);CHKERRQ(ierr);
1549       if (!pointDof) continue;
1550       ierr = DMPlexGetTransitiveClosure(dm,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1551       for (f = 0; f < numFields; f++) {
1552         PetscInt cDof, cOff, numCols, numFillCols, i, r, fComp, matOffset, offset;
1553         PetscScalar *pointMat;
1554         PetscFE fe;
1555 
1556         ierr = PetscDSGetDiscretization(ds,f,(PetscObject *) &fe);CHKERRQ(ierr);
1557         ierr = PetscFEGetNumComponents(fe,&fComp);CHKERRQ(ierr);
1558 
1559         if (numFields > 1) {
1560           ierr = PetscSectionGetFieldDof(conSec,point,f,&cDof);CHKERRQ(ierr);
1561           ierr = PetscSectionGetFieldOffset(conSec,point,f,&cOff);CHKERRQ(ierr);
1562         }
1563         else {
1564           ierr = PetscSectionGetDof(conSec,point,&cDof);CHKERRQ(ierr);
1565           ierr = PetscSectionGetOffset(conSec,point,&cOff);CHKERRQ(ierr);
1566         }
1567         if (!cDof) continue;
1568 
1569         /* make sure that every row for this point is the same size */
1570 #if defined(PETSC_USE_DEBUG)
1571         for (r = 0; r < cDof; r++) {
1572           if (cDof > 1 && r) {
1573             if ((ia[cOff+r+1]-ia[cOff+r]) != (ia[cOff+r]-ia[cOff+r-1])) {
1574               SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Two point rows have different nnz: %d vs. %d", (ia[rows[r]+1]-ia[rows[r]]), (ia[rows[r]]-ia[rows[r]-1]));
1575             }
1576           }
1577         }
1578 #endif
1579         /* zero rows */
1580         for (i = ia[cOff] ; i< ia[cOff+cDof];i++) {
1581           vals[i] = 0.;
1582         }
1583         matOffset = ia[cOff];
1584         numFillCols = ia[cOff+1] - matOffset;
1585         pointMat = refPointFieldMats[childid-pRefStart][f];
1586         numCols = refPointFieldN[childid-pRefStart][f];
1587         offset = 0;
1588         for (i = 0; i < closureSize; i++) {
1589           PetscInt q = closure[2*i];
1590           PetscInt o = closure[2*i+1];
1591           PetscInt aDof, aOff, j, k, qConDof, qConOff;
1592 
1593           qConDof = qConOff = 0;
1594           if (numFields > 1) {
1595             ierr = PetscSectionGetFieldDof(section,q,f,&aDof);CHKERRQ(ierr);
1596             ierr = PetscSectionGetFieldOffset(section,q,f,&aOff);CHKERRQ(ierr);
1597             if (q >= conStart && q < conEnd) {
1598               ierr = PetscSectionGetFieldDof(conSec,q,f,&qConDof);CHKERRQ(ierr);
1599               ierr = PetscSectionGetFieldOffset(conSec,q,f,&qConOff);CHKERRQ(ierr);
1600             }
1601           }
1602           else {
1603             ierr = PetscSectionGetDof(section,q,&aDof);CHKERRQ(ierr);
1604             ierr = PetscSectionGetOffset(section,q,&aOff);CHKERRQ(ierr);
1605             if (q >= conStart && q < conEnd) {
1606               ierr = PetscSectionGetDof(conSec,q,&qConDof);CHKERRQ(ierr);
1607               ierr = PetscSectionGetOffset(conSec,q,&qConOff);CHKERRQ(ierr);
1608             }
1609           }
1610           if (!aDof) continue;
1611           if (qConDof) {
1612             /* this point has anchors: its rows of the matrix should already
1613              * be filled, thanks to preordering */
1614             /* first multiply into pointWork, then set in matrix */
1615             PetscInt aMatOffset = ia[qConOff];
1616             PetscInt aNumFillCols = ia[qConOff + 1] - aMatOffset;
1617             for (r = 0; r < cDof; r++) {
1618               for (j = 0; j < aNumFillCols; j++) {
1619                 PetscScalar inVal = 0;
1620                 for (k = 0; k < aDof; k++) {
1621                   PetscInt node = (o >= 0) ? (k / fComp) : ((aDof - 1 - k) / fComp);
1622                   PetscInt comp = (k % fComp);
1623                   PetscInt col  = node * fComp + comp;
1624 
1625                   inVal += pointMat[r * numCols + offset + col] * vals[aMatOffset + aNumFillCols * k + j];
1626                 }
1627                 pointWork[r * aNumFillCols + j] = inVal;
1628               }
1629             }
1630             /* assume that the columns are sorted, spend less time searching */
1631             for (j = 0, k = 0; j < aNumFillCols; j++) {
1632               PetscInt col = ja[aMatOffset + j];
1633               for (;k < numFillCols; k++) {
1634                 if (ja[matOffset + k] == col) {
1635                   break;
1636                 }
1637               }
1638               if (k == numFillCols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"No nonzero space for (%d, %d)", cOff, col);
1639               for (r = 0; r < cDof; r++) {
1640                 vals[matOffset + numFillCols * r + k] = pointWork[r * aNumFillCols + j];
1641               }
1642             }
1643           }
1644           else {
1645             /* find where to put this portion of pointMat into the matrix */
1646             for (k = 0; k < numFillCols; k++) {
1647               if (ja[matOffset + k] == aOff) {
1648                 break;
1649               }
1650             }
1651             if (k == numFillCols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"No nonzero space for (%d, %d)", cOff, aOff);
1652             for (j = 0; j < aDof; j++) {
1653               PetscInt node = (o >= 0) ? (j / fComp) : ((aDof - 1 - j) / fComp);
1654               PetscInt comp = (j % fComp);
1655               PetscInt col  = node * fComp + comp;
1656               for (r = 0; r < cDof; r++) {
1657                 vals[matOffset + numFillCols * r + k + col] += pointMat[r * numCols + offset + col];
1658               }
1659             }
1660           }
1661           offset += aDof;
1662         }
1663       }
1664       ierr = DMPlexRestoreTransitiveClosure(dm,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1665     }
1666     for (row = 0; row < nRows; row++) {
1667       ierr = MatSetValues(cMat,1,&row,ia[row+1]-ia[row],&ja[ia[row]],&vals[ia[row]],INSERT_VALUES);CHKERRQ(ierr);
1668     }
1669     ierr = MatRestoreRowIJ(cMat,0,PETSC_FALSE,PETSC_FALSE,&nRows,&ia,&ja,&done);CHKERRQ(ierr);
1670     if (!done) SETERRQ(PetscObjectComm((PetscObject)cMat),PETSC_ERR_PLIB,"Could not restore RowIJ of constraint matrix");
1671     ierr = MatAssemblyBegin(cMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1672     ierr = MatAssemblyEnd(cMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1673     ierr = PetscFree(vals);CHKERRQ(ierr);
1674   }
1675 
1676   /* clean up */
1677   ierr = ISRestoreIndices(refAnIS,&refAnchors);CHKERRQ(ierr);
1678   ierr = ISRestoreIndices(anIS,&anchors);CHKERRQ(ierr);
1679   ierr = PetscFree2(perm,iperm);CHKERRQ(ierr);
1680   ierr = PetscFree(rows);CHKERRQ(ierr);
1681   ierr = PetscFree(cols);CHKERRQ(ierr);
1682   ierr = PetscFree(pointWork);CHKERRQ(ierr);
1683   for (p = pRefStart; p < pRefEnd; p++) {
1684     PetscInt parent, pDof;
1685 
1686     ierr = DMPlexGetTreeParent(refTree,p,&parent,NULL);CHKERRQ(ierr);
1687     ierr = PetscSectionGetDof(refConSec,p,&pDof);CHKERRQ(ierr);
1688     if (!pDof || parent == p) continue;
1689 
1690     for (f = 0; f < numFields; f++) {
1691       PetscInt cDof;
1692 
1693       if (numFields > 1) {
1694         ierr = PetscSectionGetFieldDof(refConSec,p,f,&cDof);CHKERRQ(ierr);
1695       }
1696       else {
1697         ierr = PetscSectionGetDof(refConSec,p,&cDof);CHKERRQ(ierr);
1698       }
1699 
1700       if (!cDof) continue;
1701       ierr = PetscFree(refPointFieldMats[p - pRefStart][f]);CHKERRQ(ierr);
1702     }
1703     ierr = PetscFree(refPointFieldMats[p - pRefStart]);CHKERRQ(ierr);
1704     ierr = PetscFree(refPointFieldN[p - pRefStart]);CHKERRQ(ierr);
1705   }
1706   ierr = PetscFree(refPointFieldMats);CHKERRQ(ierr);
1707   ierr = PetscFree(refPointFieldN);CHKERRQ(ierr);
1708   PetscFunctionReturn(0);
1709 }
1710 
1711 #undef __FUNCT__
1712 #define __FUNCT__ "DMPlexTreeRefineCell"
1713 /* refine a single cell on rank 0: this is not intended to provide good local refinement, only to create an example of
1714  * a non-conforming mesh.  Local refinement comes later */
1715 PetscErrorCode DMPlexTreeRefineCell (DM dm, PetscInt cell, DM *ncdm)
1716 {
1717   DM K;
1718   PetscInt rank;
1719   PetscInt dim, *pNewStart, *pNewEnd, *pNewCount, *pOldStart, *pOldEnd, offset, d, pStart, pEnd;
1720   PetscInt numNewCones, *newConeSizes, *newCones, *newOrientations;
1721   PetscInt *Kembedding;
1722   PetscInt *cellClosure=NULL, nc;
1723   PetscScalar *newVertexCoords;
1724   PetscInt numPointsWithParents, *parents, *childIDs, *perm, *iperm, *preOrient, pOffset;
1725   PetscSection parentSection;
1726   PetscErrorCode ierr;
1727 
1728   PetscFunctionBegin;
1729   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm),&rank);CHKERRQ(ierr);
1730   ierr = DMPlexGetDimension(dm,&dim);CHKERRQ(ierr);
1731   ierr = DMPlexCreate(PetscObjectComm((PetscObject)dm), ncdm);CHKERRQ(ierr);
1732   ierr = DMPlexSetDimension(*ncdm,dim);CHKERRQ(ierr);
1733 
1734   ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
1735   ierr = PetscSectionCreate(PetscObjectComm((PetscObject)dm),&parentSection);CHKERRQ(ierr);
1736   ierr = DMPlexGetReferenceTree(dm,&K);CHKERRQ(ierr);
1737   if (!rank) {
1738     /* compute the new charts */
1739     ierr = PetscMalloc5(dim+1,&pNewCount,dim+1,&pNewStart,dim+1,&pNewEnd,dim+1,&pOldStart,dim+1,&pOldEnd);CHKERRQ(ierr);
1740     offset = 0;
1741     for (d = 0; d <= dim; d++) {
1742       PetscInt pOldCount, kStart, kEnd, k;
1743 
1744       pNewStart[d] = offset;
1745       ierr = DMPlexGetHeightStratum(dm,d,&pOldStart[d],&pOldEnd[d]);CHKERRQ(ierr);
1746       ierr = DMPlexGetHeightStratum(K,d,&kStart,&kEnd);CHKERRQ(ierr);
1747       pOldCount = pOldEnd[d] - pOldStart[d];
1748       /* adding the new points */
1749       pNewCount[d] = pOldCount + kEnd - kStart;
1750       if (!d) {
1751         /* removing the cell */
1752         pNewCount[d]--;
1753       }
1754       for (k = kStart; k < kEnd; k++) {
1755         PetscInt parent;
1756         ierr = DMPlexGetTreeParent(K,k,&parent,NULL);CHKERRQ(ierr);
1757         if (parent == k) {
1758           /* avoid double counting points that won't actually be new */
1759           pNewCount[d]--;
1760         }
1761       }
1762       pNewEnd[d] = pNewStart[d] + pNewCount[d];
1763       offset = pNewEnd[d];
1764 
1765     }
1766     if (cell < pOldStart[0] || cell >= pOldEnd[0]) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"%d not in cell range [%d, %d)", cell, pOldStart[0], pOldEnd[0]);
1767     /* get the current closure of the cell that we are removing */
1768     ierr = DMPlexGetTransitiveClosure(dm,cell,PETSC_TRUE,&nc,&cellClosure);CHKERRQ(ierr);
1769 
1770     ierr = PetscMalloc1(pNewEnd[dim],&newConeSizes);CHKERRQ(ierr);
1771     {
1772       PetscInt kStart, kEnd, k, closureSizeK, *closureK = NULL, j;
1773 
1774       ierr = DMPlexGetChart(K,&kStart,&kEnd);CHKERRQ(ierr);
1775       ierr = PetscMalloc4(kEnd-kStart,&Kembedding,kEnd-kStart,&perm,kEnd-kStart,&iperm,kEnd-kStart,&preOrient);CHKERRQ(ierr);
1776 
1777       for (k = kStart; k < kEnd; k++) {
1778         perm[k - kStart] = k;
1779         iperm [k - kStart] = k - kStart;
1780         preOrient[k - kStart] = 0;
1781       }
1782 
1783       ierr = DMPlexGetTransitiveClosure(K,0,PETSC_TRUE,&closureSizeK,&closureK);CHKERRQ(ierr);
1784       for (j = 1; j < closureSizeK; j++) {
1785         PetscInt parentOrientA = closureK[2*j+1];
1786         PetscInt parentOrientB = cellClosure[2*j+1];
1787         PetscInt p, q;
1788 
1789         p = closureK[2*j];
1790         q = cellClosure[2*j];
1791         for (d = 0; d <= dim; d++) {
1792           if (q >= pOldStart[d] && q < pOldEnd[d]) {
1793             Kembedding[p] = (q - pOldStart[d]) + pNewStart[d];
1794           }
1795         }
1796         if (parentOrientA != parentOrientB) {
1797           PetscInt numChildren, i;
1798           const PetscInt *children;
1799 
1800           ierr = DMPlexGetTreeChildren(K,p,&numChildren,&children);CHKERRQ(ierr);
1801           for (i = 0; i < numChildren; i++) {
1802             PetscInt kPerm, oPerm;
1803 
1804             k    = children[i];
1805             ierr = DMPlexReferenceTreeGetChildSymmetry(K,p,parentOrientA,0,k,parentOrientB,&oPerm,&kPerm);CHKERRQ(ierr);
1806             /* perm = what refTree position I'm in */
1807             perm[kPerm-kStart]      = k;
1808             /* iperm = who is at this position */
1809             iperm[k-kStart]         = kPerm-kStart;
1810             preOrient[kPerm-kStart] = oPerm;
1811           }
1812         }
1813       }
1814       ierr = DMPlexRestoreTransitiveClosure(K,0,PETSC_TRUE,&closureSizeK,&closureK);CHKERRQ(ierr);
1815     }
1816     ierr = PetscSectionSetChart(parentSection,0,pNewEnd[dim]);CHKERRQ(ierr);
1817     offset = 0;
1818     numNewCones = 0;
1819     for (d = 0; d <= dim; d++) {
1820       PetscInt kStart, kEnd, k;
1821       PetscInt p;
1822       PetscInt size;
1823 
1824       for (p = pOldStart[d]; p < pOldEnd[d]; p++) {
1825         /* skip cell 0 */
1826         if (p == cell) continue;
1827         /* old cones to new cones */
1828         ierr = DMPlexGetConeSize(dm,p,&size);CHKERRQ(ierr);
1829         newConeSizes[offset++] = size;
1830         numNewCones += size;
1831       }
1832 
1833       ierr = DMPlexGetHeightStratum(K,d,&kStart,&kEnd);CHKERRQ(ierr);
1834       for (k = kStart; k < kEnd; k++) {
1835         PetscInt kParent;
1836 
1837         ierr = DMPlexGetTreeParent(K,k,&kParent,NULL);CHKERRQ(ierr);
1838         if (kParent != k) {
1839           Kembedding[k] = offset;
1840           ierr = DMPlexGetConeSize(K,k,&size);CHKERRQ(ierr);
1841           newConeSizes[offset++] = size;
1842           numNewCones += size;
1843           if (kParent != 0) {
1844             ierr = PetscSectionSetDof(parentSection,Kembedding[k],1);CHKERRQ(ierr);
1845           }
1846         }
1847       }
1848     }
1849 
1850     ierr = PetscSectionSetUp(parentSection);CHKERRQ(ierr);
1851     ierr = PetscSectionGetStorageSize(parentSection,&numPointsWithParents);CHKERRQ(ierr);
1852     ierr = PetscMalloc2(numNewCones,&newCones,numNewCones,&newOrientations);CHKERRQ(ierr);
1853     ierr = PetscMalloc2(numPointsWithParents,&parents,numPointsWithParents,&childIDs);CHKERRQ(ierr);
1854 
1855     /* fill new cones */
1856     offset = 0;
1857     for (d = 0; d <= dim; d++) {
1858       PetscInt kStart, kEnd, k, l;
1859       PetscInt p;
1860       PetscInt size;
1861       const PetscInt *cone, *orientation;
1862 
1863       for (p = pOldStart[d]; p < pOldEnd[d]; p++) {
1864         /* skip cell 0 */
1865         if (p == cell) continue;
1866         /* old cones to new cones */
1867         ierr = DMPlexGetConeSize(dm,p,&size);CHKERRQ(ierr);
1868         ierr = DMPlexGetCone(dm,p,&cone);CHKERRQ(ierr);
1869         ierr = DMPlexGetConeOrientation(dm,p,&orientation);CHKERRQ(ierr);
1870         for (l = 0; l < size; l++) {
1871           newCones[offset]          = (cone[l] - pOldStart[d + 1]) + pNewStart[d + 1];
1872           newOrientations[offset++] = orientation[l];
1873         }
1874       }
1875 
1876       ierr = DMPlexGetHeightStratum(K,d,&kStart,&kEnd);CHKERRQ(ierr);
1877       for (k = kStart; k < kEnd; k++) {
1878         PetscInt kPerm = perm[k], kParent;
1879         PetscInt preO  = preOrient[k];
1880 
1881         ierr = DMPlexGetTreeParent(K,k,&kParent,NULL);CHKERRQ(ierr);
1882         if (kParent != k) {
1883           /* embed new cones */
1884           ierr = DMPlexGetConeSize(K,k,&size);CHKERRQ(ierr);
1885           ierr = DMPlexGetCone(K,kPerm,&cone);CHKERRQ(ierr);
1886           ierr = DMPlexGetConeOrientation(K,kPerm,&orientation);CHKERRQ(ierr);
1887           for (l = 0; l < size; l++) {
1888             PetscInt q, m = (preO >= 0) ? ((preO + l) % size) : ((size -(preO + 1) - l) % size);
1889             PetscInt newO, lSize, oTrue;
1890 
1891             q                         = iperm[cone[m]];
1892             newCones[offset]          = Kembedding[q];
1893             ierr                      = DMPlexGetConeSize(K,q,&lSize);CHKERRQ(ierr);
1894             oTrue                     = orientation[m];
1895             oTrue                     = ((!lSize) || (preOrient[k] >= 0)) ? oTrue : -(oTrue + 2);
1896             newO                      = DihedralCompose(lSize,oTrue,preOrient[q]);
1897             newOrientations[offset++] = newO;
1898           }
1899           if (kParent != 0) {
1900             PetscInt newPoint = Kembedding[kParent];
1901             ierr              = PetscSectionGetOffset(parentSection,Kembedding[k],&pOffset);CHKERRQ(ierr);
1902             parents[pOffset]  = newPoint;
1903             childIDs[pOffset] = k;
1904           }
1905         }
1906       }
1907     }
1908 
1909     ierr = PetscMalloc1(dim*(pNewEnd[dim]-pNewStart[dim]),&newVertexCoords);CHKERRQ(ierr);
1910 
1911     /* fill coordinates */
1912     offset = 0;
1913     {
1914       PetscInt k, kStart, kEnd, l;
1915       PetscSection vSection;
1916       PetscInt v;
1917       Vec coords;
1918       PetscScalar *coordvals;
1919       PetscInt dof, off;
1920       PetscScalar v0[3], J[9], detJ;
1921 
1922 #if defined(PETSC_USE_DEBUG)
1923       ierr = DMPlexGetHeightStratum(K,0,&kStart,&kEnd);CHKERRQ(ierr);
1924       for (k = kStart; k < kEnd; k++) {
1925         ierr = DMPlexComputeCellGeometry(K, k, v0, J, NULL, &detJ);CHKERRQ(ierr);
1926         if (detJ <= 0.) SETERRQ1 (PETSC_COMM_SELF,PETSC_ERR_PLIB,"reference tree cell %d has bad determinant",k);
1927       }
1928 #endif
1929       ierr = DMPlexComputeCellGeometry(dm, cell, v0, J, NULL, &detJ);CHKERRQ(ierr);
1930       ierr = DMGetCoordinateSection(dm,&vSection);CHKERRQ(ierr);
1931       ierr = DMGetCoordinatesLocal(dm,&coords);CHKERRQ(ierr);
1932       ierr = VecGetArray(coords,&coordvals);CHKERRQ(ierr);
1933       for (v = pOldStart[dim]; v < pOldEnd[dim]; v++) {
1934 
1935         ierr = PetscSectionGetDof(vSection,v,&dof);CHKERRQ(ierr);
1936         ierr = PetscSectionGetOffset(vSection,v,&off);CHKERRQ(ierr);
1937         for (l = 0; l < dof; l++) {
1938           newVertexCoords[offset++] = coordvals[off + l];
1939         }
1940       }
1941       ierr = VecRestoreArray(coords,&coordvals);CHKERRQ(ierr);
1942 
1943       ierr = DMGetCoordinateSection(K,&vSection);CHKERRQ(ierr);
1944       ierr = DMGetCoordinatesLocal(K,&coords);CHKERRQ(ierr);
1945       ierr = VecGetArray(coords,&coordvals);CHKERRQ(ierr);
1946       ierr = DMPlexGetDepthStratum(K,0,&kStart,&kEnd);CHKERRQ(ierr);
1947       for (v = kStart; v < kEnd; v++) {
1948         PetscInt vPerm = perm[v];
1949         PetscInt kParent;
1950 
1951         ierr = DMPlexGetTreeParent(K,v,&kParent,NULL);CHKERRQ(ierr);
1952         if (kParent != v) {
1953           /* this is a new vertex */
1954           ierr = PetscSectionGetOffset(vSection,vPerm,&off);CHKERRQ(ierr);
1955           CoordinatesRefToReal(dim, dim, v0, J, &coordvals[off],&newVertexCoords[offset]);CHKERRQ(ierr);
1956           offset += dim;
1957         }
1958       }
1959       ierr = VecRestoreArray(coords,&coordvals);CHKERRQ(ierr);
1960     }
1961 
1962     /* need to reverse the order of pNewCount: vertices first, cells last */
1963     for (d = 0; d < (dim + 1) / 2; d++) {
1964       PetscInt tmp;
1965 
1966       tmp = pNewCount[d];
1967       pNewCount[d] = pNewCount[dim - d];
1968       pNewCount[dim - d] = tmp;
1969     }
1970 
1971     ierr = DMPlexCreateFromDAG(*ncdm,dim,pNewCount,newConeSizes,newCones,newOrientations,newVertexCoords);CHKERRQ(ierr);
1972     ierr = DMPlexSetReferenceTree(*ncdm,K);CHKERRQ(ierr);
1973     ierr = DMPlexSetTree(*ncdm,parentSection,parents,childIDs);CHKERRQ(ierr);
1974 
1975     /* clean up */
1976     ierr = DMPlexRestoreTransitiveClosure(dm,cell,PETSC_TRUE,&nc,&cellClosure);CHKERRQ(ierr);
1977     ierr = PetscFree5(pNewCount,pNewStart,pNewEnd,pOldStart,pOldEnd);CHKERRQ(ierr);
1978     ierr = PetscFree(newConeSizes);CHKERRQ(ierr);
1979     ierr = PetscFree2(newCones,newOrientations);CHKERRQ(ierr);
1980     ierr = PetscFree(newVertexCoords);CHKERRQ(ierr);
1981     ierr = PetscFree2(parents,childIDs);CHKERRQ(ierr);
1982     ierr = PetscFree4(Kembedding,perm,iperm,preOrient);CHKERRQ(ierr);
1983   }
1984   else {
1985     PetscInt    p, counts[4];
1986     PetscInt    *coneSizes, *cones, *orientations;
1987     Vec         coordVec;
1988     PetscScalar *coords;
1989 
1990     for (d = 0; d <= dim; d++) {
1991       PetscInt dStart, dEnd;
1992 
1993       ierr = DMPlexGetDepthStratum(dm,d,&dStart,&dEnd);CHKERRQ(ierr);
1994       counts[d] = dEnd - dStart;
1995     }
1996     ierr = PetscMalloc1(pEnd-pStart,&coneSizes);CHKERRQ(ierr);
1997     for (p = pStart; p < pEnd; p++) {
1998       ierr = DMPlexGetConeSize(dm,p,&coneSizes[p-pStart]);CHKERRQ(ierr);
1999     }
2000     ierr = DMPlexGetCones(dm, &cones);CHKERRQ(ierr);
2001     ierr = DMPlexGetConeOrientations(dm, &orientations);CHKERRQ(ierr);
2002     ierr = DMGetCoordinatesLocal(dm,&coordVec);CHKERRQ(ierr);
2003     ierr = VecGetArray(coordVec,&coords);CHKERRQ(ierr);
2004 
2005     ierr = PetscSectionSetChart(parentSection,pStart,pEnd);CHKERRQ(ierr);
2006     ierr = PetscSectionSetUp(parentSection);CHKERRQ(ierr);
2007     ierr = DMPlexCreateFromDAG(*ncdm,dim,counts,coneSizes,cones,orientations,NULL);CHKERRQ(ierr);
2008     ierr = DMPlexSetReferenceTree(*ncdm,K);CHKERRQ(ierr);
2009     ierr = DMPlexSetTree(*ncdm,parentSection,NULL,NULL);CHKERRQ(ierr);
2010     ierr = VecRestoreArray(coordVec,&coords);CHKERRQ(ierr);
2011   }
2012   ierr = PetscSectionDestroy(&parentSection);CHKERRQ(ierr);
2013 
2014   PetscFunctionReturn(0);
2015 }
2016