xref: /petsc/src/dm/impls/plex/plextree.c (revision f7c74593e9ac83520f541ace019715ad58c6995b)
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   if (ref) {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 = DMSetDimension(*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__ "DMPlexCreateAnchors_Tree"
691 static PetscErrorCode DMPlexCreateAnchors_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 = DMPlexSetAnchors(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 static PetscErrorCode DMPlexComputeAnchorMatrix_Tree_Direct(DM,PetscSection,PetscSection,Mat);
882 static PetscErrorCode DMPlexComputeAnchorMatrix_Tree_FromReference(DM,PetscSection,PetscSection,Mat);
883 
884 #undef __FUNCT__
885 #define __FUNCT__ "DMPlexSetTree_Internal"
886 static PetscErrorCode DMPlexSetTree_Internal(DM dm, PetscSection parentSection, PetscInt *parents, PetscInt *childIDs, PetscBool computeCanonical, PetscBool exchangeSupports)
887 {
888   DM_Plex       *mesh = (DM_Plex *)dm->data;
889   DM             refTree;
890   PetscInt       size;
891   PetscErrorCode ierr;
892 
893   PetscFunctionBegin;
894   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
895   PetscValidHeaderSpecific(parentSection, PETSC_SECTION_CLASSID, 2);
896   ierr = PetscObjectReference((PetscObject)parentSection);CHKERRQ(ierr);
897   ierr = PetscSectionDestroy(&mesh->parentSection);CHKERRQ(ierr);
898   mesh->parentSection = parentSection;
899   ierr = PetscSectionGetStorageSize(parentSection,&size);CHKERRQ(ierr);
900   if (parents != mesh->parents) {
901     ierr = PetscFree(mesh->parents);CHKERRQ(ierr);
902     ierr = PetscMalloc1(size,&mesh->parents);CHKERRQ(ierr);
903     ierr = PetscMemcpy(mesh->parents, parents, size * sizeof(*parents));CHKERRQ(ierr);
904   }
905   if (childIDs != mesh->childIDs) {
906     ierr = PetscFree(mesh->childIDs);CHKERRQ(ierr);
907     ierr = PetscMalloc1(size,&mesh->childIDs);CHKERRQ(ierr);
908     ierr = PetscMemcpy(mesh->childIDs, childIDs, size * sizeof(*childIDs));CHKERRQ(ierr);
909   }
910   ierr = DMPlexGetReferenceTree(dm,&refTree);CHKERRQ(ierr);
911   if (refTree) {
912     DMLabel canonLabel;
913 
914     ierr = DMPlexGetLabel(refTree,"canonical",&canonLabel);CHKERRQ(ierr);
915     if (canonLabel) {
916       PetscInt i;
917 
918       for (i = 0; i < size; i++) {
919         PetscInt canon;
920         ierr = DMLabelGetValue(canonLabel, mesh->childIDs[i], &canon);CHKERRQ(ierr);
921         if (canon >= 0) {
922           mesh->childIDs[i] = canon;
923         }
924       }
925     }
926     mesh->computeanchormatrix = DMPlexComputeAnchorMatrix_Tree_FromReference;
927   }
928   else {
929     mesh->computeanchormatrix = DMPlexComputeAnchorMatrix_Tree_Direct;
930   }
931   ierr = DMPlexTreeSymmetrize(dm);CHKERRQ(ierr);
932   if (computeCanonical) {
933     PetscInt d, dim;
934 
935     /* add the canonical label */
936     ierr = DMGetDimension(dm,&dim);CHKERRQ(ierr);
937     ierr = DMPlexCreateLabel(dm,"canonical");CHKERRQ(ierr);
938     for (d = 0; d <= dim; d++) {
939       PetscInt p, dStart, dEnd, canon = -1, cNumChildren;
940       const PetscInt *cChildren;
941 
942       ierr = DMPlexGetDepthStratum(dm,d,&dStart,&dEnd);CHKERRQ(ierr);
943       for (p = dStart; p < dEnd; p++) {
944         ierr = DMPlexGetTreeChildren(dm,p,&cNumChildren,&cChildren);CHKERRQ(ierr);
945         if (cNumChildren) {
946           canon = p;
947           break;
948         }
949       }
950       if (canon == -1) continue;
951       for (p = dStart; p < dEnd; p++) {
952         PetscInt numChildren, i;
953         const PetscInt *children;
954 
955         ierr = DMPlexGetTreeChildren(dm,p,&numChildren,&children);CHKERRQ(ierr);
956         if (numChildren) {
957           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);
958           ierr = DMPlexSetLabelValue(dm,"canonical",p,canon);CHKERRQ(ierr);
959           for (i = 0; i < numChildren; i++) {
960             ierr = DMPlexSetLabelValue(dm,"canonical",children[i],cChildren[i]);CHKERRQ(ierr);
961           }
962         }
963       }
964     }
965   }
966   if (exchangeSupports) {
967     ierr = DMPlexTreeExchangeSupports(dm);CHKERRQ(ierr);
968   }
969   mesh->createanchors = DMPlexCreateAnchors_Tree;
970   /* reset anchors */
971   ierr = DMPlexSetAnchors(dm,NULL,NULL);CHKERRQ(ierr);
972   PetscFunctionReturn(0);
973 }
974 
975 #undef __FUNCT__
976 #define __FUNCT__ "DMPlexSetTree"
977 /*@
978   DMPlexSetTree - set the tree that describes the hierarchy of non-conforming mesh points.  This routine also creates
979   the point-to-point constraints determined by the tree: a point is constained to the points in the closure of its
980   tree root.
981 
982   Collective on dm
983 
984   Input Parameters:
985 + dm - the DMPlex object
986 . parentSection - a section describing the tree: a point has a parent if it has 1 dof in the section; the section
987                   offset indexes the parent and childID list; the reference count of parentSection is incremented
988 . parents - a list of the point parents; copied, can be destroyed
989 - childIDs - identifies the relationship of the child point to the parent point; if there is a reference tree, then
990              the child corresponds to the point in the reference tree with index childIDs; copied, can be destroyed
991 
992   Level: intermediate
993 
994 .seealso: DMPlexGetTree(), DMPlexSetReferenceTree(), DMPlexSetAnchors(), DMPlexGetTreeParent(), DMPlexGetTreeChildren()
995 @*/
996 PetscErrorCode DMPlexSetTree(DM dm, PetscSection parentSection, PetscInt parents[], PetscInt childIDs[])
997 {
998   PetscErrorCode ierr;
999 
1000   PetscFunctionBegin;
1001   ierr = DMPlexSetTree_Internal(dm,parentSection,parents,childIDs,PETSC_FALSE,PETSC_TRUE);CHKERRQ(ierr);
1002   PetscFunctionReturn(0);
1003 }
1004 
1005 #undef __FUNCT__
1006 #define __FUNCT__ "DMPlexGetTree"
1007 /*@
1008   DMPlexGetTree - get the tree that describes the hierarchy of non-conforming mesh points.
1009   Collective on dm
1010 
1011   Input Parameters:
1012 . dm - the DMPlex object
1013 
1014   Output Parameters:
1015 + parentSection - a section describing the tree: a point has a parent if it has 1 dof in the section; the section
1016                   offset indexes the parent and childID list
1017 . parents - a list of the point parents
1018 . childIDs - identifies the relationship of the child point to the parent point; if there is a reference tree, then
1019              the child corresponds to the point in the reference tree with index childID
1020 . childSection - the inverse of the parent section
1021 - children - a list of the point children
1022 
1023   Level: intermediate
1024 
1025 .seealso: DMPlexSetTree(), DMPlexSetReferenceTree(), DMPlexSetAnchors(), DMPlexGetTreeParent(), DMPlexGetTreeChildren()
1026 @*/
1027 PetscErrorCode DMPlexGetTree(DM dm, PetscSection *parentSection, PetscInt *parents[], PetscInt *childIDs[], PetscSection *childSection, PetscInt *children[])
1028 {
1029   DM_Plex        *mesh = (DM_Plex *)dm->data;
1030 
1031   PetscFunctionBegin;
1032   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1033   if (parentSection) *parentSection = mesh->parentSection;
1034   if (parents)       *parents       = mesh->parents;
1035   if (childIDs)      *childIDs      = mesh->childIDs;
1036   if (childSection)  *childSection  = mesh->childSection;
1037   if (children)      *children      = mesh->children;
1038   PetscFunctionReturn(0);
1039 }
1040 
1041 #undef __FUNCT__
1042 #define __FUNCT__ "DMPlexGetTreeParent"
1043 /*@
1044   DMPlexGetTreeParent - get the parent of a point in the tree describing the point hierarchy (not the Sieve DAG)
1045 
1046   Input Parameters:
1047 + dm - the DMPlex object
1048 - point - the query point
1049 
1050   Output Parameters:
1051 + parent - if not NULL, set to the parent of the point, or the point itself if the point does not have a parent
1052 - childID - if not NULL, set to the child ID of the point with respect to its parent, or 0 if the point
1053             does not have a parent
1054 
1055   Level: intermediate
1056 
1057 .seealso: DMPlexSetTree(), DMPlexGetTree(), DMPlexGetTreeChildren()
1058 @*/
1059 PetscErrorCode DMPlexGetTreeParent(DM dm, PetscInt point, PetscInt *parent, PetscInt *childID)
1060 {
1061   DM_Plex       *mesh = (DM_Plex *)dm->data;
1062   PetscSection   pSec;
1063   PetscErrorCode ierr;
1064 
1065   PetscFunctionBegin;
1066   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1067   pSec = mesh->parentSection;
1068   if (pSec && point >= pSec->pStart && point < pSec->pEnd) {
1069     PetscInt dof;
1070 
1071     ierr = PetscSectionGetDof (pSec, point, &dof);CHKERRQ(ierr);
1072     if (dof) {
1073       PetscInt off;
1074 
1075       ierr = PetscSectionGetOffset (pSec, point, &off);CHKERRQ(ierr);
1076       if (parent)  *parent = mesh->parents[off];
1077       if (childID) *childID = mesh->childIDs[off];
1078       PetscFunctionReturn(0);
1079     }
1080   }
1081   if (parent) {
1082     *parent = point;
1083   }
1084   if (childID) {
1085     *childID = 0;
1086   }
1087   PetscFunctionReturn(0);
1088 }
1089 
1090 #undef __FUNCT__
1091 #define __FUNCT__ "DMPlexGetTreeChildren"
1092 /*@C
1093   DMPlexGetTreeChildren - get the children of a point in the tree describing the point hierarchy (not the Sieve DAG)
1094 
1095   Input Parameters:
1096 + dm - the DMPlex object
1097 - point - the query point
1098 
1099   Output Parameters:
1100 + numChildren - if not NULL, set to the number of children
1101 - children - if not NULL, set to a list children, or set to NULL if the point has no children
1102 
1103   Level: intermediate
1104 
1105   Fortran Notes:
1106   Since it returns an array, this routine is only available in Fortran 90, and you must
1107   include petsc.h90 in your code.
1108 
1109 .seealso: DMPlexSetTree(), DMPlexGetTree(), DMPlexGetTreeParent()
1110 @*/
1111 PetscErrorCode DMPlexGetTreeChildren(DM dm, PetscInt point, PetscInt *numChildren, const PetscInt *children[])
1112 {
1113   DM_Plex       *mesh = (DM_Plex *)dm->data;
1114   PetscSection   childSec;
1115   PetscInt       dof = 0;
1116   PetscErrorCode ierr;
1117 
1118   PetscFunctionBegin;
1119   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1120   childSec = mesh->childSection;
1121   if (childSec && point >= childSec->pStart && point < childSec->pEnd) {
1122     ierr = PetscSectionGetDof (childSec, point, &dof);CHKERRQ(ierr);
1123   }
1124   if (numChildren) *numChildren = dof;
1125   if (children) {
1126     if (dof) {
1127       PetscInt off;
1128 
1129       ierr = PetscSectionGetOffset (childSec, point, &off);CHKERRQ(ierr);
1130       *children = &mesh->children[off];
1131     }
1132     else {
1133       *children = NULL;
1134     }
1135   }
1136   PetscFunctionReturn(0);
1137 }
1138 
1139 #undef __FUNCT__
1140 #define __FUNCT__ "DMPlexComputeAnchorMatrix_Tree_Direct"
1141 static PetscErrorCode DMPlexComputeAnchorMatrix_Tree_Direct(DM dm, PetscSection section, PetscSection cSec, Mat cMat)
1142 {
1143   PetscDS        ds;
1144   PetscInt       spdim;
1145   PetscInt       numFields, f, c, cStart, cEnd, pStart, pEnd, conStart, conEnd;
1146   const PetscInt *anchors;
1147   PetscSection   aSec;
1148   PetscReal      *v0, *v0parent, *vtmp, *J, *Jparent, *invJparent, detJ, detJparent;
1149   IS             aIS;
1150   PetscErrorCode ierr;
1151 
1152   PetscFunctionBegin;
1153   ierr = DMPlexGetChart(dm,&pStart,&pEnd);CHKERRQ(ierr);
1154   ierr = DMGetDS(dm,&ds);CHKERRQ(ierr);
1155   ierr = PetscDSGetNumFields(ds,&numFields);CHKERRQ(ierr);
1156   ierr = DMPlexGetHeightStratum(dm,0,&cStart,&cEnd);CHKERRQ(ierr);
1157   ierr = DMPlexGetAnchors(dm,&aSec,&aIS);CHKERRQ(ierr);
1158   ierr = ISGetIndices(aIS,&anchors);CHKERRQ(ierr);
1159   ierr = PetscSectionGetChart(cSec,&conStart,&conEnd);CHKERRQ(ierr);
1160   ierr = DMGetDimension(dm,&spdim);CHKERRQ(ierr);
1161   ierr = PetscMalloc6(spdim,&v0,spdim,&v0parent,spdim,&vtmp,spdim*spdim,&J,spdim*spdim,&Jparent,spdim*spdim,&invJparent);CHKERRQ(ierr);
1162 
1163   for (f = 0; f < numFields; f++) {
1164     PetscFE fe;
1165     PetscDualSpace space;
1166     PetscInt i, j, k, nPoints, offset;
1167     PetscInt fSize, fComp;
1168     PetscReal *B = NULL;
1169     PetscReal *weights, *pointsRef, *pointsReal;
1170     Mat Amat, Bmat, Xmat;
1171 
1172     ierr = PetscDSGetDiscretization(ds,f,(PetscObject *)(&fe));CHKERRQ(ierr);
1173     ierr = PetscFEGetDualSpace(fe,&space);CHKERRQ(ierr);
1174     ierr = PetscDualSpaceGetDimension(space,&fSize);CHKERRQ(ierr);
1175     ierr = PetscFEGetNumComponents(fe,&fComp);CHKERRQ(ierr);
1176     ierr = MatCreate(PETSC_COMM_SELF,&Amat);CHKERRQ(ierr);
1177     ierr = MatSetSizes(Amat,fSize,fSize,fSize,fSize);CHKERRQ(ierr);
1178     ierr = MatSetType(Amat,MATSEQDENSE);CHKERRQ(ierr);
1179     ierr = MatSetUp(Amat);CHKERRQ(ierr);
1180     ierr = MatDuplicate(Amat,MAT_DO_NOT_COPY_VALUES,&Bmat);CHKERRQ(ierr);
1181     ierr = MatDuplicate(Amat,MAT_DO_NOT_COPY_VALUES,&Xmat);CHKERRQ(ierr);
1182     nPoints = 0;
1183     for (i = 0; i < fSize; i++) {
1184       PetscInt        qPoints;
1185       PetscQuadrature quad;
1186 
1187       ierr = PetscDualSpaceGetFunctional(space,i,&quad);CHKERRQ(ierr);
1188       ierr = PetscQuadratureGetData(quad,NULL,&qPoints,NULL,NULL);CHKERRQ(ierr);
1189       nPoints += qPoints;
1190     }
1191     ierr = PetscMalloc3(nPoints,&weights,spdim*nPoints,&pointsRef,spdim*nPoints,&pointsReal);CHKERRQ(ierr);
1192     offset = 0;
1193     for (i = 0; i < fSize; i++) {
1194       PetscInt        qPoints;
1195       const PetscReal    *p, *w;
1196       PetscQuadrature quad;
1197 
1198       ierr = PetscDualSpaceGetFunctional(space,i,&quad);CHKERRQ(ierr);
1199       ierr = PetscQuadratureGetData(quad,NULL,&qPoints,&p,&w);CHKERRQ(ierr);
1200       ierr = PetscMemcpy(weights+offset,w,qPoints*sizeof(*w));CHKERRQ(ierr);
1201       ierr = PetscMemcpy(pointsRef+spdim*offset,p,spdim*qPoints*sizeof(*p));CHKERRQ(ierr);
1202       offset += qPoints;
1203     }
1204     ierr = PetscFEGetTabulation(fe,nPoints,pointsRef,&B,NULL,NULL);CHKERRQ(ierr);
1205     offset = 0;
1206     for (i = 0; i < fSize; i++) {
1207       PetscInt        qPoints;
1208       PetscQuadrature quad;
1209 
1210       ierr = PetscDualSpaceGetFunctional(space,i,&quad);CHKERRQ(ierr);
1211       ierr = PetscQuadratureGetData(quad,NULL,&qPoints,NULL,NULL);CHKERRQ(ierr);
1212       for (j = 0; j < fSize; j++) {
1213         PetscScalar val = 0.;
1214 
1215         for (k = 0; k < qPoints; k++) {
1216           val += B[((offset + k) * fSize + j) * fComp] * weights[k];
1217         }
1218         ierr = MatSetValue(Amat,i,j,val,INSERT_VALUES);CHKERRQ(ierr);
1219       }
1220       offset += qPoints;
1221     }
1222     ierr = PetscFERestoreTabulation(fe,nPoints,pointsRef,&B,NULL,NULL);CHKERRQ(ierr);
1223     ierr = MatAssemblyBegin(Amat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1224     ierr = MatAssemblyEnd(Amat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1225     ierr = MatLUFactor(Amat,NULL,NULL,NULL);CHKERRQ(ierr);
1226     for (c = cStart; c < cEnd; c++) {
1227       PetscInt parent;
1228       PetscInt closureSize, closureSizeP, *closure = NULL, *closureP = NULL;
1229       PetscInt *childOffsets, *parentOffsets;
1230 
1231       ierr = DMPlexGetTreeParent(dm,c,&parent,NULL);CHKERRQ(ierr);
1232       if (parent == c) continue;
1233       ierr = DMPlexGetTransitiveClosure(dm,c,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1234       for (i = 0; i < closureSize; i++) {
1235         PetscInt p = closure[2*i];
1236         PetscInt conDof;
1237 
1238         if (p < conStart || p >= conEnd) continue;
1239         if (numFields > 1) {
1240           ierr = PetscSectionGetFieldDof(cSec,p,f,&conDof);CHKERRQ(ierr);
1241         }
1242         else {
1243           ierr = PetscSectionGetDof(cSec,p,&conDof);CHKERRQ(ierr);
1244         }
1245         if (conDof) break;
1246       }
1247       if (i == closureSize) {
1248         ierr = DMPlexRestoreTransitiveClosure(dm,c,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1249         continue;
1250       }
1251 
1252       ierr = DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, NULL, &detJ);CHKERRQ(ierr);
1253       ierr = DMPlexComputeCellGeometryFEM(dm, parent, NULL, v0parent, Jparent, invJparent, &detJparent);CHKERRQ(ierr);
1254       for (i = 0; i < nPoints; i++) {
1255         CoordinatesRefToReal(spdim, spdim, v0, J, &pointsRef[i*spdim],vtmp);CHKERRQ(ierr);
1256         CoordinatesRealToRef(spdim, spdim, v0parent, invJparent, vtmp, &pointsReal[i*spdim]);CHKERRQ(ierr);
1257       }
1258       ierr = PetscFEGetTabulation(fe,nPoints,pointsReal,&B,NULL,NULL);CHKERRQ(ierr);
1259       offset = 0;
1260       for (i = 0; i < fSize; i++) {
1261         PetscInt        qPoints;
1262         PetscQuadrature quad;
1263 
1264         ierr = PetscDualSpaceGetFunctional(space,i,&quad);CHKERRQ(ierr);
1265         ierr = PetscQuadratureGetData(quad,NULL,&qPoints,NULL,NULL);CHKERRQ(ierr);
1266         for (j = 0; j < fSize; j++) {
1267           PetscScalar val = 0.;
1268 
1269           for (k = 0; k < qPoints; k++) {
1270             val += B[((offset + k) * fSize + j) * fComp] * weights[k];
1271           }
1272           MatSetValue(Bmat,i,j,val,INSERT_VALUES);CHKERRQ(ierr);
1273         }
1274         offset += qPoints;
1275       }
1276       ierr = PetscFERestoreTabulation(fe,nPoints,pointsReal,&B,NULL,NULL);CHKERRQ(ierr);
1277       ierr = MatAssemblyBegin(Bmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1278       ierr = MatAssemblyEnd(Bmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1279       ierr = MatMatSolve(Amat,Bmat,Xmat);CHKERRQ(ierr);
1280       ierr = DMPlexGetTransitiveClosure(dm,parent,PETSC_TRUE,&closureSizeP,&closureP);CHKERRQ(ierr);
1281       ierr = PetscMalloc2(closureSize+1,&childOffsets,closureSizeP+1,&parentOffsets);CHKERRQ(ierr);
1282       childOffsets[0] = 0;
1283       for (i = 0; i < closureSize; i++) {
1284         PetscInt p = closure[2*i];
1285         PetscInt dof;
1286 
1287         if (numFields > 1) {
1288           ierr = PetscSectionGetFieldDof(section,p,f,&dof);CHKERRQ(ierr);
1289         }
1290         else {
1291           ierr = PetscSectionGetDof(section,p,&dof);CHKERRQ(ierr);
1292         }
1293         childOffsets[i+1]=childOffsets[i]+dof / fComp;
1294       }
1295       parentOffsets[0] = 0;
1296       for (i = 0; i < closureSizeP; i++) {
1297         PetscInt p = closureP[2*i];
1298         PetscInt dof;
1299 
1300         if (numFields > 1) {
1301           ierr = PetscSectionGetFieldDof(section,p,f,&dof);CHKERRQ(ierr);
1302         }
1303         else {
1304           ierr = PetscSectionGetDof(section,p,&dof);CHKERRQ(ierr);
1305         }
1306         parentOffsets[i+1]=parentOffsets[i]+dof / fComp;
1307       }
1308       for (i = 0; i < closureSize; i++) {
1309         PetscInt conDof, conOff, aDof, aOff;
1310         PetscInt p = closure[2*i];
1311         PetscInt o = closure[2*i+1];
1312 
1313         if (p < conStart || p >= conEnd) continue;
1314         if (numFields > 1) {
1315           ierr = PetscSectionGetFieldDof(cSec,p,f,&conDof);CHKERRQ(ierr);
1316           ierr = PetscSectionGetFieldOffset(cSec,p,f,&conOff);CHKERRQ(ierr);
1317         }
1318         else {
1319           ierr = PetscSectionGetDof(cSec,p,&conDof);CHKERRQ(ierr);
1320           ierr = PetscSectionGetOffset(cSec,p,&conOff);CHKERRQ(ierr);
1321         }
1322         if (!conDof) continue;
1323         ierr = PetscSectionGetDof(aSec,p,&aDof);CHKERRQ(ierr);
1324         ierr = PetscSectionGetOffset(aSec,p,&aOff);CHKERRQ(ierr);
1325         for (k = 0; k < aDof; k++) {
1326           PetscInt a = anchors[aOff + k];
1327           PetscInt aSecDof, aSecOff;
1328 
1329           if (numFields > 1) {
1330             ierr = PetscSectionGetFieldDof(section,a,f,&aSecDof);CHKERRQ(ierr);
1331             ierr = PetscSectionGetFieldOffset(section,a,f,&aSecOff);CHKERRQ(ierr);
1332           }
1333           else {
1334             ierr = PetscSectionGetDof(section,a,&aSecDof);CHKERRQ(ierr);
1335             ierr = PetscSectionGetOffset(section,a,&aSecOff);CHKERRQ(ierr);
1336           }
1337           if (!aSecDof) continue;
1338 
1339           for (j = 0; j < closureSizeP; j++) {
1340             PetscInt q = closureP[2*j];
1341             PetscInt oq = closureP[2*j+1];
1342 
1343             if (q == a) {
1344               PetscInt r, s, t;
1345 
1346               for (r = childOffsets[i]; r < childOffsets[i+1]; r++) {
1347                 for (s = parentOffsets[j]; s < parentOffsets[j+1]; s++) {
1348                   PetscScalar val;
1349                   PetscInt insertCol, insertRow;
1350 
1351                   ierr = MatGetValue(Xmat,r,s,&val);CHKERRQ(ierr);
1352                   if (o >= 0) {
1353                     insertRow = conOff + fComp * (r - childOffsets[i]);
1354                   }
1355                   else {
1356                     insertRow = conOff + fComp * (childOffsets[i + 1] - 1 - r);
1357                   }
1358                   if (oq >= 0) {
1359                     insertCol = aSecOff + fComp * (s - parentOffsets[j]);
1360                   }
1361                   else {
1362                     insertCol = aSecOff + fComp * (parentOffsets[j + 1] - 1 - s);
1363                   }
1364                   for (t = 0; t < fComp; t++) {
1365                     ierr = MatSetValue(cMat,insertRow + t,insertCol + t,val,INSERT_VALUES);CHKERRQ(ierr);
1366                   }
1367                 }
1368               }
1369             }
1370           }
1371         }
1372       }
1373       ierr = PetscFree2(childOffsets,parentOffsets);CHKERRQ(ierr);
1374       ierr = DMPlexRestoreTransitiveClosure(dm,c,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1375       ierr = DMPlexRestoreTransitiveClosure(dm,parent,PETSC_TRUE,&closureSizeP,&closureP);CHKERRQ(ierr);
1376     }
1377     ierr = MatDestroy(&Amat);CHKERRQ(ierr);
1378     ierr = MatDestroy(&Bmat);CHKERRQ(ierr);
1379     ierr = MatDestroy(&Xmat);CHKERRQ(ierr);
1380     ierr = PetscFree3(weights,pointsRef,pointsReal);CHKERRQ(ierr);
1381   }
1382   ierr = MatAssemblyBegin(cMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1383   ierr = MatAssemblyEnd(cMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1384   ierr = PetscFree6(v0,v0parent,vtmp,J,Jparent,invJparent);CHKERRQ(ierr);
1385   ierr = ISRestoreIndices(aIS,&anchors);CHKERRQ(ierr);
1386 
1387   PetscFunctionReturn(0);
1388 }
1389 
1390 #undef __FUNCT__
1391 #define __FUNCT__ "DMPlexComputeAnchorMatrix_Tree_FromReference"
1392 static PetscErrorCode DMPlexComputeAnchorMatrix_Tree_FromReference(DM dm, PetscSection section, PetscSection conSec, Mat cMat)
1393 {
1394   DM             refTree;
1395   PetscDS        ds;
1396   Mat            refCmat;
1397   PetscInt       numFields, f, pRefStart, pRefEnd, p, *rows, *cols, maxDof, maxAnDof, *perm, *iperm, pStart, pEnd, conStart, conEnd, **refPointFieldN;
1398   PetscScalar ***refPointFieldMats, *pointWork;
1399   PetscSection   refConSec, refAnSec, anSec, refSection;
1400   IS             refAnIS, anIS;
1401   const PetscInt *refAnchors, *anchors;
1402   PetscErrorCode ierr;
1403 
1404   PetscFunctionBegin;
1405   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1406   ierr = DMGetDS(dm,&ds);CHKERRQ(ierr);
1407   ierr = PetscDSGetNumFields(ds,&numFields);CHKERRQ(ierr);
1408   ierr = DMPlexGetReferenceTree(dm,&refTree);CHKERRQ(ierr);
1409   ierr = DMSetDS(refTree,ds);CHKERRQ(ierr);
1410   ierr = DMGetDefaultConstraints(refTree,&refConSec,&refCmat);CHKERRQ(ierr);
1411   ierr = DMPlexGetChart(refTree,&pRefStart,&pRefEnd);CHKERRQ(ierr);
1412   ierr = DMPlexGetAnchors(refTree,&refAnSec,&refAnIS);CHKERRQ(ierr);
1413   ierr = DMPlexGetAnchors(dm,&anSec,&anIS);CHKERRQ(ierr);
1414   ierr = ISGetIndices(refAnIS,&refAnchors);CHKERRQ(ierr);
1415   ierr = ISGetIndices(anIS,&anchors);CHKERRQ(ierr);
1416   ierr = DMGetDefaultSection(refTree,&refSection);CHKERRQ(ierr);
1417   ierr = PetscSectionGetChart(refConSec,&pRefStart,&pRefEnd);CHKERRQ(ierr);
1418   ierr = PetscSectionGetChart(conSec,&conStart,&conEnd);CHKERRQ(ierr);
1419   ierr = PetscMalloc1(pRefEnd-pRefStart,&refPointFieldMats);CHKERRQ(ierr);
1420   ierr = PetscMalloc1(pRefEnd-pRefStart,&refPointFieldN);CHKERRQ(ierr);
1421   ierr = PetscSectionGetMaxDof(refConSec,&maxDof);CHKERRQ(ierr);
1422   ierr = PetscSectionGetMaxDof(refAnSec,&maxAnDof);CHKERRQ(ierr);
1423   ierr = PetscMalloc1(maxDof,&rows);CHKERRQ(ierr);
1424   ierr = PetscMalloc1(maxDof*maxAnDof,&cols);CHKERRQ(ierr);
1425   ierr = PetscMalloc1(maxDof*maxDof*maxAnDof,&pointWork);CHKERRQ(ierr);
1426 
1427   /* step 1: get submats for every constrained point in the reference tree */
1428   for (p = pRefStart; p < pRefEnd; p++) {
1429     PetscInt parent, closureSize, *closure = NULL, pDof;
1430 
1431     ierr = DMPlexGetTreeParent(refTree,p,&parent,NULL);CHKERRQ(ierr);
1432     ierr = PetscSectionGetDof(refConSec,p,&pDof);CHKERRQ(ierr);
1433     if (!pDof || parent == p) continue;
1434 
1435     ierr = PetscMalloc1(numFields,&refPointFieldMats[p-pRefStart]);CHKERRQ(ierr);
1436     ierr = PetscCalloc1(numFields,&refPointFieldN[p-pRefStart]);CHKERRQ(ierr);
1437     ierr = DMPlexGetTransitiveClosure(refTree,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1438     for (f = 0; f < numFields; f++) {
1439       PetscInt cDof, cOff, numCols, r, i, fComp;
1440       PetscFE fe;
1441 
1442       ierr = PetscDSGetDiscretization(ds,f,(PetscObject *) &fe);CHKERRQ(ierr);
1443       ierr = PetscFEGetNumComponents(fe,&fComp);CHKERRQ(ierr);
1444 
1445       if (numFields > 1) {
1446         ierr = PetscSectionGetFieldDof(refConSec,p,f,&cDof);CHKERRQ(ierr);
1447         ierr = PetscSectionGetFieldOffset(refConSec,p,f,&cOff);CHKERRQ(ierr);
1448       }
1449       else {
1450         ierr = PetscSectionGetDof(refConSec,p,&cDof);CHKERRQ(ierr);
1451         ierr = PetscSectionGetOffset(refConSec,p,&cOff);CHKERRQ(ierr);
1452       }
1453 
1454       if (!cDof) continue;
1455       for (r = 0; r < cDof; r++) {
1456         rows[r] = cOff + r;
1457       }
1458       numCols = 0;
1459       for (i = 0; i < closureSize; i++) {
1460         PetscInt q = closure[2*i];
1461         PetscInt o = closure[2*i+1];
1462         PetscInt aDof, aOff, j;
1463 
1464         if (numFields > 1) {
1465           ierr = PetscSectionGetFieldDof(refSection,q,f,&aDof);CHKERRQ(ierr);
1466           ierr = PetscSectionGetFieldOffset(refSection,q,f,&aOff);CHKERRQ(ierr);
1467         }
1468         else {
1469           ierr = PetscSectionGetDof(refSection,q,&aDof);CHKERRQ(ierr);
1470           ierr = PetscSectionGetOffset(refSection,q,&aOff);CHKERRQ(ierr);
1471         }
1472 
1473         for (j = 0; j < aDof; j++) {
1474           PetscInt node = (o >= 0) ? (j / fComp) : ((aDof - 1 - j) / fComp);
1475           PetscInt comp = (j % fComp);
1476 
1477           cols[numCols++] = aOff + node * fComp + comp;
1478         }
1479       }
1480       refPointFieldN[p-pRefStart][f] = numCols;
1481       ierr = PetscMalloc1(cDof*numCols,&refPointFieldMats[p-pRefStart][f]);CHKERRQ(ierr);
1482       ierr = MatGetValues(refCmat,cDof,rows,numCols,cols,refPointFieldMats[p-pRefStart][f]);CHKERRQ(ierr);
1483     }
1484     ierr = DMPlexRestoreTransitiveClosure(refTree,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1485   }
1486 
1487   /* step 2: compute the preorder */
1488   ierr = DMPlexGetChart(dm,&pStart,&pEnd);CHKERRQ(ierr);
1489   ierr = PetscMalloc2(pEnd-pStart,&perm,pEnd-pStart,&iperm);CHKERRQ(ierr);
1490   for (p = pStart; p < pEnd; p++) {
1491     perm[p - pStart] = p;
1492     iperm[p - pStart] = p-pStart;
1493   }
1494   for (p = 0; p < pEnd - pStart;) {
1495     PetscInt point = perm[p];
1496     PetscInt parent;
1497 
1498     ierr = DMPlexGetTreeParent(dm,point,&parent,NULL);CHKERRQ(ierr);
1499     if (parent == point) {
1500       p++;
1501     }
1502     else {
1503       PetscInt size, closureSize, *closure = NULL, i;
1504 
1505       ierr = DMPlexGetTransitiveClosure(dm,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1506       for (i = 0; i < closureSize; i++) {
1507         PetscInt q = closure[2*i];
1508         if (iperm[q-pStart] > iperm[point-pStart]) {
1509           /* swap */
1510           perm[p]               = q;
1511           perm[iperm[q-pStart]] = point;
1512           iperm[point-pStart]   = iperm[q-pStart];
1513           iperm[q-pStart]       = p;
1514           break;
1515         }
1516       }
1517       size = closureSize;
1518       ierr = DMPlexRestoreTransitiveClosure(dm,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1519       if (i == size) {
1520         p++;
1521       }
1522     }
1523   }
1524 
1525   /* step 3: fill the constraint matrix */
1526   /* we are going to use a preorder progressive fill strategy.  Mat doesn't
1527    * allow progressive fill without assembly, so we are going to set up the
1528    * values outside of the Mat first.
1529    */
1530   {
1531     PetscInt nRows, row, nnz;
1532     PetscBool done;
1533     const PetscInt *ia, *ja;
1534     PetscScalar *vals;
1535 
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   PetscMPIInt 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 = DMGetDimension(dm,&dim);CHKERRQ(ierr);
1731   ierr = DMPlexCreate(PetscObjectComm((PetscObject)dm), ncdm);CHKERRQ(ierr);
1732   ierr = DMSetDimension(*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 kStart, kEnd, l;
1915       PetscSection vSection;
1916       PetscInt v;
1917       Vec coords;
1918       PetscScalar *coordvals;
1919       PetscInt dof, off;
1920       PetscReal v0[3], J[9], detJ;
1921 
1922 #if defined(PETSC_USE_DEBUG)
1923       {
1924         PetscInt k;
1925         ierr = DMPlexGetHeightStratum(K,0,&kStart,&kEnd);CHKERRQ(ierr);
1926         for (k = kStart; k < kEnd; k++) {
1927           ierr = DMPlexComputeCellGeometryFEM(K, k, NULL, v0, J, NULL, &detJ);CHKERRQ(ierr);
1928           if (detJ <= 0.) SETERRQ1 (PETSC_COMM_SELF,PETSC_ERR_PLIB,"reference tree cell %d has bad determinant",k);
1929         }
1930       }
1931 #endif
1932       ierr = DMPlexComputeCellGeometryFEM(dm, cell, NULL, v0, J, NULL, &detJ);CHKERRQ(ierr);
1933       ierr = DMGetCoordinateSection(dm,&vSection);CHKERRQ(ierr);
1934       ierr = DMGetCoordinatesLocal(dm,&coords);CHKERRQ(ierr);
1935       ierr = VecGetArray(coords,&coordvals);CHKERRQ(ierr);
1936       for (v = pOldStart[dim]; v < pOldEnd[dim]; v++) {
1937 
1938         ierr = PetscSectionGetDof(vSection,v,&dof);CHKERRQ(ierr);
1939         ierr = PetscSectionGetOffset(vSection,v,&off);CHKERRQ(ierr);
1940         for (l = 0; l < dof; l++) {
1941           newVertexCoords[offset++] = coordvals[off + l];
1942         }
1943       }
1944       ierr = VecRestoreArray(coords,&coordvals);CHKERRQ(ierr);
1945 
1946       ierr = DMGetCoordinateSection(K,&vSection);CHKERRQ(ierr);
1947       ierr = DMGetCoordinatesLocal(K,&coords);CHKERRQ(ierr);
1948       ierr = VecGetArray(coords,&coordvals);CHKERRQ(ierr);
1949       ierr = DMPlexGetDepthStratum(K,0,&kStart,&kEnd);CHKERRQ(ierr);
1950       for (v = kStart; v < kEnd; v++) {
1951         PetscReal coord[3], newCoord[3];
1952         PetscInt  vPerm = perm[v];
1953         PetscInt  kParent;
1954 
1955         ierr = DMPlexGetTreeParent(K,v,&kParent,NULL);CHKERRQ(ierr);
1956         if (kParent != v) {
1957           /* this is a new vertex */
1958           ierr = PetscSectionGetOffset(vSection,vPerm,&off);CHKERRQ(ierr);
1959           for (l = 0; l < dim; ++l) coord[l] = PetscRealPart(coordvals[off+l]);
1960           CoordinatesRefToReal(dim, dim, v0, J, coord, newCoord);CHKERRQ(ierr);
1961           for (l = 0; l < dim; ++l) newVertexCoords[offset+l] = newCoord[l];
1962           offset += dim;
1963         }
1964       }
1965       ierr = VecRestoreArray(coords,&coordvals);CHKERRQ(ierr);
1966     }
1967 
1968     /* need to reverse the order of pNewCount: vertices first, cells last */
1969     for (d = 0; d < (dim + 1) / 2; d++) {
1970       PetscInt tmp;
1971 
1972       tmp = pNewCount[d];
1973       pNewCount[d] = pNewCount[dim - d];
1974       pNewCount[dim - d] = tmp;
1975     }
1976 
1977     ierr = DMPlexCreateFromDAG(*ncdm,dim,pNewCount,newConeSizes,newCones,newOrientations,newVertexCoords);CHKERRQ(ierr);
1978     ierr = DMPlexSetReferenceTree(*ncdm,K);CHKERRQ(ierr);
1979     ierr = DMPlexSetTree(*ncdm,parentSection,parents,childIDs);CHKERRQ(ierr);
1980 
1981     /* clean up */
1982     ierr = DMPlexRestoreTransitiveClosure(dm,cell,PETSC_TRUE,&nc,&cellClosure);CHKERRQ(ierr);
1983     ierr = PetscFree5(pNewCount,pNewStart,pNewEnd,pOldStart,pOldEnd);CHKERRQ(ierr);
1984     ierr = PetscFree(newConeSizes);CHKERRQ(ierr);
1985     ierr = PetscFree2(newCones,newOrientations);CHKERRQ(ierr);
1986     ierr = PetscFree(newVertexCoords);CHKERRQ(ierr);
1987     ierr = PetscFree2(parents,childIDs);CHKERRQ(ierr);
1988     ierr = PetscFree4(Kembedding,perm,iperm,preOrient);CHKERRQ(ierr);
1989   }
1990   else {
1991     PetscInt    p, counts[4];
1992     PetscInt    *coneSizes, *cones, *orientations;
1993     Vec         coordVec;
1994     PetscScalar *coords;
1995 
1996     for (d = 0; d <= dim; d++) {
1997       PetscInt dStart, dEnd;
1998 
1999       ierr = DMPlexGetDepthStratum(dm,d,&dStart,&dEnd);CHKERRQ(ierr);
2000       counts[d] = dEnd - dStart;
2001     }
2002     ierr = PetscMalloc1(pEnd-pStart,&coneSizes);CHKERRQ(ierr);
2003     for (p = pStart; p < pEnd; p++) {
2004       ierr = DMPlexGetConeSize(dm,p,&coneSizes[p-pStart]);CHKERRQ(ierr);
2005     }
2006     ierr = DMPlexGetCones(dm, &cones);CHKERRQ(ierr);
2007     ierr = DMPlexGetConeOrientations(dm, &orientations);CHKERRQ(ierr);
2008     ierr = DMGetCoordinatesLocal(dm,&coordVec);CHKERRQ(ierr);
2009     ierr = VecGetArray(coordVec,&coords);CHKERRQ(ierr);
2010 
2011     ierr = PetscSectionSetChart(parentSection,pStart,pEnd);CHKERRQ(ierr);
2012     ierr = PetscSectionSetUp(parentSection);CHKERRQ(ierr);
2013     ierr = DMPlexCreateFromDAG(*ncdm,dim,counts,coneSizes,cones,orientations,NULL);CHKERRQ(ierr);
2014     ierr = DMPlexSetReferenceTree(*ncdm,K);CHKERRQ(ierr);
2015     ierr = DMPlexSetTree(*ncdm,parentSection,NULL,NULL);CHKERRQ(ierr);
2016     ierr = VecRestoreArray(coordVec,&coords);CHKERRQ(ierr);
2017   }
2018   ierr = PetscSectionDestroy(&parentSection);CHKERRQ(ierr);
2019 
2020   PetscFunctionReturn(0);
2021 }
2022