xref: /petsc/src/dm/impls/plex/plextree.c (revision 2b8d69ca7ea5fe9190df62c1dce3bbd66fce84dd)
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__ "DMPlexCreateReferenceTree_Union"
225 PetscErrorCode DMPlexCreateReferenceTree_Union(DM K, DM Kref, const char *labelName, DM *ref)
226 {
227   MPI_Comm       comm;
228   PetscInt       dim, p, pStart, pEnd, pRefStart, pRefEnd, d, offset, parentSize, *parents, *childIDs;
229   PetscInt      *permvals, *unionCones, *coneSizes, *unionOrientations, numUnionPoints, *numDimPoints, numCones, numVerts;
230   DMLabel        identity, identityRef;
231   PetscSection   unionSection, unionConeSection, parentSection;
232   PetscScalar   *unionCoords;
233   IS             perm;
234   PetscErrorCode ierr;
235 
236   PetscFunctionBegin;
237   comm = PetscObjectComm((PetscObject)K);
238   ierr = DMGetDimension(K, &dim);CHKERRQ(ierr);
239   ierr = DMPlexGetChart(K, &pStart, &pEnd);CHKERRQ(ierr);
240   ierr = DMGetLabel(K, labelName, &identity);CHKERRQ(ierr);
241   ierr = DMGetLabel(Kref, labelName, &identityRef);CHKERRQ(ierr);
242   ierr = DMPlexGetChart(Kref, &pRefStart, &pRefEnd);CHKERRQ(ierr);
243   ierr = PetscSectionCreate(comm, &unionSection);CHKERRQ(ierr);
244   ierr = PetscSectionSetChart(unionSection, 0, (pEnd - pStart) + (pRefEnd - pRefStart));CHKERRQ(ierr);
245   /* count points that will go in the union */
246   for (p = pStart; p < pEnd; p++) {
247     ierr = PetscSectionSetDof(unionSection, p - pStart, 1);CHKERRQ(ierr);
248   }
249   for (p = pRefStart; p < pRefEnd; p++) {
250     PetscInt q, qSize;
251     ierr = DMLabelGetValue(identityRef, p, &q);CHKERRQ(ierr);
252     ierr = DMLabelGetStratumSize(identityRef, q, &qSize);CHKERRQ(ierr);
253     if (qSize > 1) {
254       ierr = PetscSectionSetDof(unionSection, p - pRefStart + (pEnd - pStart), 1);CHKERRQ(ierr);
255     }
256   }
257   ierr = PetscMalloc1(pEnd - pStart + pRefEnd - pRefStart,&permvals);CHKERRQ(ierr);
258   offset = 0;
259   /* stratify points in the union by topological dimension */
260   for (d = 0; d <= dim; d++) {
261     PetscInt cStart, cEnd, c;
262 
263     ierr = DMPlexGetHeightStratum(K, d, &cStart, &cEnd);CHKERRQ(ierr);
264     for (c = cStart; c < cEnd; c++) {
265       permvals[offset++] = c;
266     }
267 
268     ierr = DMPlexGetHeightStratum(Kref, d, &cStart, &cEnd);CHKERRQ(ierr);
269     for (c = cStart; c < cEnd; c++) {
270       permvals[offset++] = c + (pEnd - pStart);
271     }
272   }
273   ierr = ISCreateGeneral(comm, (pEnd - pStart) + (pRefEnd - pRefStart), permvals, PETSC_OWN_POINTER, &perm);CHKERRQ(ierr);
274   ierr = PetscSectionSetPermutation(unionSection,perm);CHKERRQ(ierr);
275   ierr = PetscSectionSetUp(unionSection);CHKERRQ(ierr);
276   ierr = PetscSectionGetStorageSize(unionSection,&numUnionPoints);CHKERRQ(ierr);
277   ierr = PetscMalloc2(numUnionPoints,&coneSizes,dim+1,&numDimPoints);CHKERRQ(ierr);
278   /* count dimension points */
279   for (d = 0; d <= dim; d++) {
280     PetscInt cStart, cOff, cOff2;
281     ierr = DMPlexGetHeightStratum(K,d,&cStart,NULL);CHKERRQ(ierr);
282     ierr = PetscSectionGetOffset(unionSection,cStart-pStart,&cOff);CHKERRQ(ierr);
283     if (d < dim) {
284       ierr = DMPlexGetHeightStratum(K,d+1,&cStart,NULL);CHKERRQ(ierr);
285       ierr = PetscSectionGetOffset(unionSection,cStart-pStart,&cOff2);CHKERRQ(ierr);
286     }
287     else {
288       cOff2 = numUnionPoints;
289     }
290     numDimPoints[dim - d] = cOff2 - cOff;
291   }
292   ierr = PetscSectionCreate(comm, &unionConeSection);CHKERRQ(ierr);
293   ierr = PetscSectionSetChart(unionConeSection, 0, numUnionPoints);CHKERRQ(ierr);
294   /* count the cones in the union */
295   for (p = pStart; p < pEnd; p++) {
296     PetscInt dof, uOff;
297 
298     ierr = DMPlexGetConeSize(K, p, &dof);CHKERRQ(ierr);
299     ierr = PetscSectionGetOffset(unionSection, p - pStart,&uOff);CHKERRQ(ierr);
300     ierr = PetscSectionSetDof(unionConeSection, uOff, dof);CHKERRQ(ierr);
301     coneSizes[uOff] = dof;
302   }
303   for (p = pRefStart; p < pRefEnd; p++) {
304     PetscInt dof, uDof, uOff;
305 
306     ierr = DMPlexGetConeSize(Kref, p, &dof);CHKERRQ(ierr);
307     ierr = PetscSectionGetDof(unionSection, p - pRefStart + (pEnd - pStart),&uDof);CHKERRQ(ierr);
308     ierr = PetscSectionGetOffset(unionSection, p - pRefStart + (pEnd - pStart),&uOff);CHKERRQ(ierr);
309     if (uDof) {
310       ierr = PetscSectionSetDof(unionConeSection, uOff, dof);CHKERRQ(ierr);
311       coneSizes[uOff] = dof;
312     }
313   }
314   ierr = PetscSectionSetUp(unionConeSection);CHKERRQ(ierr);
315   ierr = PetscSectionGetStorageSize(unionConeSection,&numCones);CHKERRQ(ierr);
316   ierr = PetscMalloc2(numCones,&unionCones,numCones,&unionOrientations);CHKERRQ(ierr);
317   /* write the cones in the union */
318   for (p = pStart; p < pEnd; p++) {
319     PetscInt dof, uOff, c, cOff;
320     const PetscInt *cone, *orientation;
321 
322     ierr = DMPlexGetConeSize(K, p, &dof);CHKERRQ(ierr);
323     ierr = DMPlexGetCone(K, p, &cone);CHKERRQ(ierr);
324     ierr = DMPlexGetConeOrientation(K, p, &orientation);CHKERRQ(ierr);
325     ierr = PetscSectionGetOffset(unionSection, p - pStart,&uOff);CHKERRQ(ierr);
326     ierr = PetscSectionGetOffset(unionConeSection,uOff,&cOff);CHKERRQ(ierr);
327     for (c = 0; c < dof; c++) {
328       PetscInt e, eOff;
329       e                           = cone[c];
330       ierr                        = PetscSectionGetOffset(unionSection, e - pStart, &eOff);CHKERRQ(ierr);
331       unionCones[cOff + c]        = eOff;
332       unionOrientations[cOff + c] = orientation[c];
333     }
334   }
335   for (p = pRefStart; p < pRefEnd; p++) {
336     PetscInt dof, uDof, uOff, c, cOff;
337     const PetscInt *cone, *orientation;
338 
339     ierr = DMPlexGetConeSize(Kref, p, &dof);CHKERRQ(ierr);
340     ierr = DMPlexGetCone(Kref, p, &cone);CHKERRQ(ierr);
341     ierr = DMPlexGetConeOrientation(Kref, p, &orientation);CHKERRQ(ierr);
342     ierr = PetscSectionGetDof(unionSection, p - pRefStart + (pEnd - pStart),&uDof);CHKERRQ(ierr);
343     ierr = PetscSectionGetOffset(unionSection, p - pRefStart + (pEnd - pStart),&uOff);CHKERRQ(ierr);
344     if (uDof) {
345       ierr = PetscSectionGetOffset(unionConeSection,uOff,&cOff);CHKERRQ(ierr);
346       for (c = 0; c < dof; c++) {
347         PetscInt e, eOff, eDof;
348 
349         e    = cone[c];
350         ierr = PetscSectionGetDof(unionSection, e - pRefStart + (pEnd - pStart),&eDof);CHKERRQ(ierr);
351         if (eDof) {
352           ierr = PetscSectionGetOffset(unionSection, e - pRefStart + (pEnd - pStart), &eOff);CHKERRQ(ierr);
353         }
354         else {
355           ierr = DMLabelGetValue(identityRef, e, &e);CHKERRQ(ierr);
356           ierr = PetscSectionGetOffset(unionSection, e - pStart, &eOff);CHKERRQ(ierr);
357         }
358         unionCones[cOff + c]        = eOff;
359         unionOrientations[cOff + c] = orientation[c];
360       }
361     }
362   }
363   /* get the coordinates */
364   {
365     PetscInt vStart, vEnd, vRefStart, vRefEnd, v, vDof, vOff;
366     PetscSection KcoordsSec, KrefCoordsSec;
367     Vec      KcoordsVec, KrefCoordsVec;
368     PetscScalar *Kcoords;
369 
370     DMGetCoordinateSection(K, &KcoordsSec);CHKERRQ(ierr);
371     DMGetCoordinatesLocal(K, &KcoordsVec);CHKERRQ(ierr);
372     DMGetCoordinateSection(Kref, &KrefCoordsSec);CHKERRQ(ierr);
373     DMGetCoordinatesLocal(Kref, &KrefCoordsVec);CHKERRQ(ierr);
374 
375     numVerts = numDimPoints[0];
376     ierr     = PetscMalloc1(numVerts * dim,&unionCoords);CHKERRQ(ierr);
377     ierr     = DMPlexGetDepthStratum(K,0,&vStart,&vEnd);CHKERRQ(ierr);
378 
379     offset = 0;
380     for (v = vStart; v < vEnd; v++) {
381       ierr = PetscSectionGetOffset(unionSection,v - pStart,&vOff);CHKERRQ(ierr);
382       ierr = VecGetValuesSection(KcoordsVec, KcoordsSec, v, &Kcoords);CHKERRQ(ierr);
383       for (d = 0; d < dim; d++) {
384         unionCoords[offset * dim + d] = Kcoords[d];
385       }
386       offset++;
387     }
388     ierr = DMPlexGetDepthStratum(Kref,0,&vRefStart,&vRefEnd);CHKERRQ(ierr);
389     for (v = vRefStart; v < vRefEnd; v++) {
390       ierr = PetscSectionGetDof(unionSection,v - pRefStart + (pEnd - pStart),&vDof);CHKERRQ(ierr);
391       ierr = PetscSectionGetOffset(unionSection,v - pRefStart + (pEnd - pStart),&vOff);CHKERRQ(ierr);
392       ierr = VecGetValuesSection(KrefCoordsVec, KrefCoordsSec, v, &Kcoords);CHKERRQ(ierr);
393       if (vDof) {
394         for (d = 0; d < dim; d++) {
395           unionCoords[offset * dim + d] = Kcoords[d];
396         }
397         offset++;
398       }
399     }
400   }
401   ierr = DMCreate(comm,ref);CHKERRQ(ierr);
402   ierr = DMSetType(*ref,DMPLEX);CHKERRQ(ierr);
403   ierr = DMSetDimension(*ref,dim);CHKERRQ(ierr);
404   ierr = DMPlexCreateFromDAG(*ref,dim,numDimPoints,coneSizes,unionCones,unionOrientations,unionCoords);CHKERRQ(ierr);
405   /* set the tree */
406   ierr = PetscSectionCreate(comm,&parentSection);CHKERRQ(ierr);
407   ierr = PetscSectionSetChart(parentSection,0,numUnionPoints);CHKERRQ(ierr);
408   for (p = pRefStart; p < pRefEnd; p++) {
409     PetscInt uDof, uOff;
410 
411     ierr = PetscSectionGetDof(unionSection, p - pRefStart + (pEnd - pStart),&uDof);CHKERRQ(ierr);
412     ierr = PetscSectionGetOffset(unionSection, p - pRefStart + (pEnd - pStart),&uOff);CHKERRQ(ierr);
413     if (uDof) {
414       PetscSectionSetDof(parentSection,uOff,1);CHKERRQ(ierr);
415     }
416   }
417   ierr = PetscSectionSetUp(parentSection);CHKERRQ(ierr);
418   ierr = PetscSectionGetStorageSize(parentSection,&parentSize);CHKERRQ(ierr);
419   ierr = PetscMalloc2(parentSize,&parents,parentSize,&childIDs);CHKERRQ(ierr);
420   for (p = pRefStart; p < pRefEnd; p++) {
421     PetscInt uDof, uOff;
422 
423     ierr = PetscSectionGetDof(unionSection, p - pRefStart + (pEnd - pStart),&uDof);CHKERRQ(ierr);
424     ierr = PetscSectionGetOffset(unionSection, p - pRefStart + (pEnd - pStart),&uOff);CHKERRQ(ierr);
425     if (uDof) {
426       PetscInt pOff, parent, parentU;
427       PetscSectionGetOffset(parentSection,uOff,&pOff);CHKERRQ(ierr);
428       DMLabelGetValue(identityRef,p,&parent);CHKERRQ(ierr);
429       ierr = PetscSectionGetOffset(unionSection, parent - pStart,&parentU);CHKERRQ(ierr);
430       parents[pOff] = parentU;
431       childIDs[pOff] = uOff;
432     }
433   }
434   ierr = DMPlexSetTree_Internal(*ref,parentSection,parents,childIDs,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
435   ierr = PetscSectionDestroy(&parentSection);CHKERRQ(ierr);
436   ierr = PetscFree2(parents,childIDs);CHKERRQ(ierr);
437 
438   /* clean up */
439   ierr = PetscSectionDestroy(&unionSection);CHKERRQ(ierr);
440   ierr = PetscSectionDestroy(&unionConeSection);CHKERRQ(ierr);
441   ierr = ISDestroy(&perm);CHKERRQ(ierr);
442   ierr = PetscFree(unionCoords);CHKERRQ(ierr);
443   ierr = PetscFree2(unionCones,unionOrientations);CHKERRQ(ierr);
444   ierr = PetscFree2(coneSizes,numDimPoints);CHKERRQ(ierr);
445   PetscFunctionReturn(0);
446 }
447 
448 #undef __FUNCT__
449 #define __FUNCT__ "DMPlexCreateDefaultReferenceTree"
450 /*@
451   DMPlexCreateDefaultReferenceTree - create a reference tree for isotropic hierarchical mesh refinement.
452 
453   Collective on comm
454 
455   Input Parameters:
456 + comm    - the MPI communicator
457 . dim     - the spatial dimension
458 - simplex - Flag for simplex, otherwise use a tensor-product cell
459 
460   Output Parameters:
461 . ref     - the reference tree DMPlex object
462 
463   Level: intermediate
464 
465 .keywords: reference cell
466 .seealso: DMPlexSetReferenceTree(), DMPlexGetReferenceTree()
467 @*/
468 PetscErrorCode DMPlexCreateDefaultReferenceTree(MPI_Comm comm, PetscInt dim, PetscBool simplex, DM *ref)
469 {
470   DM_Plex       *mesh;
471   DM             K, Kref;
472   PetscInt       p, pStart, pEnd;
473   DMLabel        identity;
474   PetscErrorCode ierr;
475 
476   PetscFunctionBegin;
477 #if 1
478   comm = PETSC_COMM_SELF;
479 #endif
480   /* create a reference element */
481   ierr = DMPlexCreateReferenceCell(comm, dim, simplex, &K);CHKERRQ(ierr);
482   ierr = DMCreateLabel(K, "identity");CHKERRQ(ierr);
483   ierr = DMGetLabel(K, "identity", &identity);CHKERRQ(ierr);
484   ierr = DMPlexGetChart(K, &pStart, &pEnd);CHKERRQ(ierr);
485   for (p = pStart; p < pEnd; p++) {
486     ierr = DMLabelSetValue(identity, p, p);CHKERRQ(ierr);
487   }
488   /* refine it */
489   ierr = DMRefine(K,comm,&Kref);CHKERRQ(ierr);
490 
491   /* the reference tree is the union of these two, without duplicating
492    * points that appear in both */
493   ierr = DMPlexCreateReferenceTree_Union(K, Kref, "identity", ref);CHKERRQ(ierr);
494   mesh = (DM_Plex *) (*ref)->data;
495   mesh->getchildsymmetry = DMPlexReferenceTreeGetChildSymmetry_Default;
496   ierr = DMDestroy(&K);CHKERRQ(ierr);
497   ierr = DMDestroy(&Kref);CHKERRQ(ierr);
498   PetscFunctionReturn(0);
499 }
500 
501 #undef __FUNCT__
502 #define __FUNCT__ "DMPlexTreeSymmetrize"
503 static PetscErrorCode DMPlexTreeSymmetrize(DM dm)
504 {
505   DM_Plex        *mesh = (DM_Plex *)dm->data;
506   PetscSection   childSec, pSec;
507   PetscInt       p, pSize, cSize, parMax = PETSC_MIN_INT, parMin = PETSC_MAX_INT;
508   PetscInt       *offsets, *children, pStart, pEnd;
509   PetscErrorCode ierr;
510 
511   PetscFunctionBegin;
512   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
513   ierr = PetscSectionDestroy(&mesh->childSection);CHKERRQ(ierr);
514   ierr = PetscFree(mesh->children);CHKERRQ(ierr);
515   pSec = mesh->parentSection;
516   if (!pSec) PetscFunctionReturn(0);
517   ierr = PetscSectionGetStorageSize(pSec,&pSize);CHKERRQ(ierr);
518   for (p = 0; p < pSize; p++) {
519     PetscInt par = mesh->parents[p];
520 
521     parMax = PetscMax(parMax,par+1);
522     parMin = PetscMin(parMin,par);
523   }
524   if (parMin > parMax) {
525     parMin = -1;
526     parMax = -1;
527   }
528   ierr = PetscSectionCreate(PetscObjectComm((PetscObject)pSec),&childSec);CHKERRQ(ierr);
529   ierr = PetscSectionSetChart(childSec,parMin,parMax);CHKERRQ(ierr);
530   for (p = 0; p < pSize; p++) {
531     PetscInt par = mesh->parents[p];
532 
533     ierr = PetscSectionAddDof(childSec,par,1);CHKERRQ(ierr);
534   }
535   ierr = PetscSectionSetUp(childSec);CHKERRQ(ierr);
536   ierr = PetscSectionGetStorageSize(childSec,&cSize);CHKERRQ(ierr);
537   ierr = PetscMalloc1(cSize,&children);CHKERRQ(ierr);
538   ierr = PetscCalloc1(parMax-parMin,&offsets);CHKERRQ(ierr);
539   ierr = PetscSectionGetChart(pSec,&pStart,&pEnd);CHKERRQ(ierr);
540   for (p = pStart; p < pEnd; p++) {
541     PetscInt dof, off, i;
542 
543     ierr = PetscSectionGetDof(pSec,p,&dof);CHKERRQ(ierr);
544     ierr = PetscSectionGetOffset(pSec,p,&off);CHKERRQ(ierr);
545     for (i = 0; i < dof; i++) {
546       PetscInt par = mesh->parents[off + i], cOff;
547 
548       ierr = PetscSectionGetOffset(childSec,par,&cOff);CHKERRQ(ierr);
549       children[cOff + offsets[par-parMin]++] = p;
550     }
551   }
552   mesh->childSection = childSec;
553   mesh->children = children;
554   ierr = PetscFree(offsets);CHKERRQ(ierr);
555   PetscFunctionReturn(0);
556 }
557 
558 #undef __FUNCT__
559 #define __FUNCT__ "AnchorsFlatten"
560 static PetscErrorCode AnchorsFlatten (PetscSection section, IS is, PetscSection *sectionNew, IS *isNew)
561 {
562   PetscInt       pStart, pEnd, size, sizeNew, i, p, *valsNew = NULL;
563   const PetscInt *vals;
564   PetscSection   secNew;
565   PetscBool      anyNew, globalAnyNew;
566   PetscBool      compress;
567   PetscErrorCode ierr;
568 
569   PetscFunctionBegin;
570   ierr = PetscSectionGetChart(section,&pStart,&pEnd);CHKERRQ(ierr);
571   ierr = ISGetLocalSize(is,&size);CHKERRQ(ierr);
572   ierr = ISGetIndices(is,&vals);CHKERRQ(ierr);
573   ierr = PetscSectionCreate(PetscObjectComm((PetscObject)section),&secNew);CHKERRQ(ierr);
574   ierr = PetscSectionSetChart(secNew,pStart,pEnd);CHKERRQ(ierr);
575   for (i = 0; i < size; i++) {
576     PetscInt dof;
577 
578     p = vals[i];
579     if (p < pStart || p >= pEnd) continue;
580     ierr = PetscSectionGetDof(section, p, &dof);CHKERRQ(ierr);
581     if (dof) break;
582   }
583   if (i == size) {
584     ierr     = PetscSectionSetUp(secNew);CHKERRQ(ierr);
585     anyNew   = PETSC_FALSE;
586     compress = PETSC_FALSE;
587     sizeNew  = 0;
588   }
589   else {
590     anyNew = PETSC_TRUE;
591     for (p = pStart; p < pEnd; p++) {
592       PetscInt dof, off;
593 
594       ierr = PetscSectionGetDof(section, p, &dof);CHKERRQ(ierr);
595       ierr = PetscSectionGetOffset(section, p, &off);CHKERRQ(ierr);
596       for (i = 0; i < dof; i++) {
597         PetscInt q = vals[off + i], qDof = 0;
598 
599         if (q >= pStart && q < pEnd) {
600           ierr = PetscSectionGetDof(section, q, &qDof);CHKERRQ(ierr);
601         }
602         if (qDof) {
603           ierr = PetscSectionAddDof(secNew, p, qDof);CHKERRQ(ierr);
604         }
605         else {
606           ierr = PetscSectionAddDof(secNew, p, 1);CHKERRQ(ierr);
607         }
608       }
609     }
610     ierr = PetscSectionSetUp(secNew);CHKERRQ(ierr);
611     ierr = PetscSectionGetStorageSize(secNew,&sizeNew);CHKERRQ(ierr);
612     ierr = PetscMalloc1(sizeNew,&valsNew);CHKERRQ(ierr);
613     compress = PETSC_FALSE;
614     for (p = pStart; p < pEnd; p++) {
615       PetscInt dof, off, count, offNew, dofNew;
616 
617       ierr  = PetscSectionGetDof(section, p, &dof);CHKERRQ(ierr);
618       ierr  = PetscSectionGetOffset(section, p, &off);CHKERRQ(ierr);
619       ierr  = PetscSectionGetDof(secNew, p, &dofNew);CHKERRQ(ierr);
620       ierr  = PetscSectionGetOffset(secNew, p, &offNew);CHKERRQ(ierr);
621       count = 0;
622       for (i = 0; i < dof; i++) {
623         PetscInt q = vals[off + i], qDof = 0, qOff = 0, j;
624 
625         if (q >= pStart && q < pEnd) {
626           ierr = PetscSectionGetDof(section, q, &qDof);CHKERRQ(ierr);
627           ierr = PetscSectionGetOffset(section, q, &qOff);CHKERRQ(ierr);
628         }
629         if (qDof) {
630           PetscInt oldCount = count;
631 
632           for (j = 0; j < qDof; j++) {
633             PetscInt k, r = vals[qOff + j];
634 
635             for (k = 0; k < oldCount; k++) {
636               if (valsNew[offNew + k] == r) {
637                 break;
638               }
639             }
640             if (k == oldCount) {
641               valsNew[offNew + count++] = r;
642             }
643           }
644         }
645         else {
646           PetscInt k, oldCount = count;
647 
648           for (k = 0; k < oldCount; k++) {
649             if (valsNew[offNew + k] == q) {
650               break;
651             }
652           }
653           if (k == oldCount) {
654             valsNew[offNew + count++] = q;
655           }
656         }
657       }
658       if (count < dofNew) {
659         ierr = PetscSectionSetDof(secNew, p, count);CHKERRQ(ierr);
660         compress = PETSC_TRUE;
661       }
662     }
663   }
664   ierr = ISRestoreIndices(is,&vals);CHKERRQ(ierr);
665   ierr = MPIU_Allreduce(&anyNew,&globalAnyNew,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)secNew));CHKERRQ(ierr);
666   if (!globalAnyNew) {
667     ierr = PetscSectionDestroy(&secNew);CHKERRQ(ierr);
668     *sectionNew = NULL;
669     *isNew = NULL;
670   }
671   else {
672     PetscBool globalCompress;
673 
674     ierr = MPIU_Allreduce(&compress,&globalCompress,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)secNew));CHKERRQ(ierr);
675     if (compress) {
676       PetscSection secComp;
677       PetscInt *valsComp = NULL;
678 
679       ierr = PetscSectionCreate(PetscObjectComm((PetscObject)section),&secComp);CHKERRQ(ierr);
680       ierr = PetscSectionSetChart(secComp,pStart,pEnd);CHKERRQ(ierr);
681       for (p = pStart; p < pEnd; p++) {
682         PetscInt dof;
683 
684         ierr = PetscSectionGetDof(secNew, p, &dof);CHKERRQ(ierr);
685         ierr = PetscSectionSetDof(secComp, p, dof);CHKERRQ(ierr);
686       }
687       ierr = PetscSectionSetUp(secComp);CHKERRQ(ierr);
688       ierr = PetscSectionGetStorageSize(secComp,&sizeNew);CHKERRQ(ierr);
689       ierr = PetscMalloc1(sizeNew,&valsComp);CHKERRQ(ierr);
690       for (p = pStart; p < pEnd; p++) {
691         PetscInt dof, off, offNew, j;
692 
693         ierr = PetscSectionGetDof(secNew, p, &dof);CHKERRQ(ierr);
694         ierr = PetscSectionGetOffset(secNew, p, &off);CHKERRQ(ierr);
695         ierr = PetscSectionGetOffset(secComp, p, &offNew);CHKERRQ(ierr);
696         for (j = 0; j < dof; j++) {
697           valsComp[offNew + j] = valsNew[off + j];
698         }
699       }
700       ierr    = PetscSectionDestroy(&secNew);CHKERRQ(ierr);
701       secNew  = secComp;
702       ierr    = PetscFree(valsNew);CHKERRQ(ierr);
703       valsNew = valsComp;
704     }
705     ierr = ISCreateGeneral(PetscObjectComm((PetscObject)is),sizeNew,valsNew,PETSC_OWN_POINTER,isNew);CHKERRQ(ierr);
706   }
707   PetscFunctionReturn(0);
708 }
709 
710 #undef __FUNCT__
711 #define __FUNCT__ "DMPlexCreateAnchors_Tree"
712 static PetscErrorCode DMPlexCreateAnchors_Tree(DM dm)
713 {
714   PetscInt       p, pStart, pEnd, *anchors, size;
715   PetscInt       aMin = PETSC_MAX_INT, aMax = PETSC_MIN_INT;
716   PetscSection   aSec;
717   DMLabel        canonLabel;
718   IS             aIS;
719   PetscErrorCode ierr;
720 
721   PetscFunctionBegin;
722   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
723   ierr = DMPlexGetChart(dm,&pStart,&pEnd);CHKERRQ(ierr);
724   ierr = DMGetLabel(dm,"canonical",&canonLabel);CHKERRQ(ierr);
725   for (p = pStart; p < pEnd; p++) {
726     PetscInt parent;
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     if (parent != p) {
736       aMin = PetscMin(aMin,p);
737       aMax = PetscMax(aMax,p+1);
738     }
739   }
740   if (aMin > aMax) {
741     aMin = -1;
742     aMax = -1;
743   }
744   ierr = PetscSectionCreate(PETSC_COMM_SELF,&aSec);CHKERRQ(ierr);
745   ierr = PetscSectionSetChart(aSec,aMin,aMax);CHKERRQ(ierr);
746   for (p = aMin; p < aMax; p++) {
747     PetscInt parent, ancestor = p;
748 
749     if (canonLabel) {
750       PetscInt canon;
751 
752       ierr = DMLabelGetValue(canonLabel,p,&canon);CHKERRQ(ierr);
753       if (p != canon) continue;
754     }
755     ierr = DMPlexGetTreeParent(dm,p,&parent,NULL);CHKERRQ(ierr);
756     while (parent != ancestor) {
757       ancestor = parent;
758       ierr     = DMPlexGetTreeParent(dm,ancestor,&parent,NULL);CHKERRQ(ierr);
759     }
760     if (ancestor != p) {
761       PetscInt closureSize, *closure = NULL;
762 
763       ierr = DMPlexGetTransitiveClosure(dm,ancestor,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
764       ierr = PetscSectionSetDof(aSec,p,closureSize);CHKERRQ(ierr);
765       ierr = DMPlexRestoreTransitiveClosure(dm,ancestor,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
766     }
767   }
768   ierr = PetscSectionSetUp(aSec);CHKERRQ(ierr);
769   ierr = PetscSectionGetStorageSize(aSec,&size);CHKERRQ(ierr);
770   ierr = PetscMalloc1(size,&anchors);CHKERRQ(ierr);
771   for (p = aMin; p < aMax; p++) {
772     PetscInt parent, ancestor = p;
773 
774     if (canonLabel) {
775       PetscInt canon;
776 
777       ierr = DMLabelGetValue(canonLabel,p,&canon);CHKERRQ(ierr);
778       if (p != canon) continue;
779     }
780     ierr = DMPlexGetTreeParent(dm,p,&parent,NULL);CHKERRQ(ierr);
781     while (parent != ancestor) {
782       ancestor = parent;
783       ierr     = DMPlexGetTreeParent(dm,ancestor,&parent,NULL);CHKERRQ(ierr);
784     }
785     if (ancestor != p) {
786       PetscInt j, closureSize, *closure = NULL, aOff;
787 
788       ierr = PetscSectionGetOffset(aSec,p,&aOff);CHKERRQ(ierr);
789 
790       ierr = DMPlexGetTransitiveClosure(dm,ancestor,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
791       for (j = 0; j < closureSize; j++) {
792         anchors[aOff + j] = closure[2*j];
793       }
794       ierr = DMPlexRestoreTransitiveClosure(dm,ancestor,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
795     }
796   }
797   ierr = ISCreateGeneral(PETSC_COMM_SELF,size,anchors,PETSC_OWN_POINTER,&aIS);CHKERRQ(ierr);
798   {
799     PetscSection aSecNew = aSec;
800     IS           aISNew  = aIS;
801 
802     ierr = PetscObjectReference((PetscObject)aSec);CHKERRQ(ierr);
803     ierr = PetscObjectReference((PetscObject)aIS);CHKERRQ(ierr);
804     while (aSecNew) {
805       ierr    = PetscSectionDestroy(&aSec);CHKERRQ(ierr);
806       ierr    = ISDestroy(&aIS);CHKERRQ(ierr);
807       aSec    = aSecNew;
808       aIS     = aISNew;
809       aSecNew = NULL;
810       aISNew  = NULL;
811       ierr    = AnchorsFlatten(aSec,aIS,&aSecNew,&aISNew);CHKERRQ(ierr);
812     }
813   }
814   ierr = DMPlexSetAnchors(dm,aSec,aIS);CHKERRQ(ierr);
815   ierr = PetscSectionDestroy(&aSec);CHKERRQ(ierr);
816   ierr = ISDestroy(&aIS);CHKERRQ(ierr);
817   PetscFunctionReturn(0);
818 }
819 
820 #undef __FUNCT__
821 #define __FUNCT__ "DMPlexGetTrueSupportSize"
822 static PetscErrorCode DMPlexGetTrueSupportSize(DM dm,PetscInt p,PetscInt *dof,PetscInt *numTrueSupp)
823 {
824   PetscErrorCode ierr;
825 
826   PetscFunctionBegin;
827   if (numTrueSupp[p] == -1) {
828     PetscInt i, alldof;
829     const PetscInt *supp;
830     PetscInt count = 0;
831 
832     ierr = DMPlexGetSupportSize(dm,p,&alldof);CHKERRQ(ierr);
833     ierr = DMPlexGetSupport(dm,p,&supp);CHKERRQ(ierr);
834     for (i = 0; i < alldof; i++) {
835       PetscInt q = supp[i], numCones, j;
836       const PetscInt *cone;
837 
838       ierr = DMPlexGetConeSize(dm,q,&numCones);CHKERRQ(ierr);
839       ierr = DMPlexGetCone(dm,q,&cone);CHKERRQ(ierr);
840       for (j = 0; j < numCones; j++) {
841         if (cone[j] == p) break;
842       }
843       if (j < numCones) count++;
844     }
845     numTrueSupp[p] = count;
846   }
847   *dof = numTrueSupp[p];
848   PetscFunctionReturn(0);
849 }
850 
851 #undef __FUNCT__
852 #define __FUNCT__ "DMPlexTreeExchangeSupports"
853 static PetscErrorCode DMPlexTreeExchangeSupports(DM dm)
854 {
855   DM_Plex *mesh = (DM_Plex *)dm->data;
856   PetscSection newSupportSection;
857   PetscInt newSize, *newSupports, pStart, pEnd, p, d, depth;
858   PetscInt *numTrueSupp;
859   PetscInt *offsets;
860   PetscErrorCode ierr;
861 
862   PetscFunctionBegin;
863   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
864   /* symmetrize the hierarchy */
865   ierr = DMPlexGetDepth(dm,&depth);CHKERRQ(ierr);
866   ierr = PetscSectionCreate(PetscObjectComm((PetscObject)(mesh->supportSection)),&newSupportSection);CHKERRQ(ierr);
867   ierr = DMPlexGetChart(dm,&pStart,&pEnd);CHKERRQ(ierr);
868   ierr = PetscSectionSetChart(newSupportSection,pStart,pEnd);CHKERRQ(ierr);
869   ierr = PetscCalloc1(pEnd,&offsets);CHKERRQ(ierr);
870   ierr = PetscMalloc1(pEnd,&numTrueSupp);CHKERRQ(ierr);
871   for (p = 0; p < pEnd; p++) numTrueSupp[p] = -1;
872   /* if a point is in the (true) support of q, it should be in the support of
873    * parent(q) */
874   for (d = 0; d <= depth; d++) {
875     ierr = DMPlexGetHeightStratum(dm,d,&pStart,&pEnd);CHKERRQ(ierr);
876     for (p = pStart; p < pEnd; ++p) {
877       PetscInt dof, q, qdof, parent;
878 
879       ierr = DMPlexGetTrueSupportSize(dm,p,&dof,numTrueSupp);CHKERRQ(ierr);
880       ierr = PetscSectionAddDof(newSupportSection, p, dof);CHKERRQ(ierr);
881       q    = p;
882       ierr = DMPlexGetTreeParent(dm,q,&parent,NULL);CHKERRQ(ierr);
883       while (parent != q && parent >= pStart && parent < pEnd) {
884         q = parent;
885 
886         ierr = DMPlexGetTrueSupportSize(dm,q,&qdof,numTrueSupp);CHKERRQ(ierr);
887         ierr = PetscSectionAddDof(newSupportSection,p,qdof);CHKERRQ(ierr);
888         ierr = PetscSectionAddDof(newSupportSection,q,dof);CHKERRQ(ierr);
889         ierr = DMPlexGetTreeParent(dm,q,&parent,NULL);CHKERRQ(ierr);
890       }
891     }
892   }
893   ierr = PetscSectionSetUp(newSupportSection);CHKERRQ(ierr);
894   ierr = PetscSectionGetStorageSize(newSupportSection,&newSize);CHKERRQ(ierr);
895   ierr = PetscMalloc1(newSize,&newSupports);CHKERRQ(ierr);
896   for (d = 0; d <= depth; d++) {
897     ierr = DMPlexGetHeightStratum(dm,d,&pStart,&pEnd);CHKERRQ(ierr);
898     for (p = pStart; p < pEnd; p++) {
899       PetscInt dof, off, q, qdof, qoff, newDof, newOff, newqOff, i, parent;
900 
901       ierr = PetscSectionGetDof(mesh->supportSection, p, &dof);CHKERRQ(ierr);
902       ierr = PetscSectionGetOffset(mesh->supportSection, p, &off);CHKERRQ(ierr);
903       ierr = PetscSectionGetDof(newSupportSection, p, &newDof);CHKERRQ(ierr);
904       ierr = PetscSectionGetOffset(newSupportSection, p, &newOff);CHKERRQ(ierr);
905       for (i = 0; i < dof; i++) {
906         PetscInt numCones, j;
907         const PetscInt *cone;
908         PetscInt q = mesh->supports[off + i];
909 
910         ierr = DMPlexGetConeSize(dm,q,&numCones);CHKERRQ(ierr);
911         ierr = DMPlexGetCone(dm,q,&cone);CHKERRQ(ierr);
912         for (j = 0; j < numCones; j++) {
913           if (cone[j] == p) break;
914         }
915         if (j < numCones) newSupports[newOff+offsets[p]++] = q;
916       }
917       mesh->maxSupportSize = PetscMax(mesh->maxSupportSize,newDof);
918 
919       q    = p;
920       ierr = DMPlexGetTreeParent(dm,q,&parent,NULL);CHKERRQ(ierr);
921       while (parent != q && parent >= pStart && parent < pEnd) {
922         q = parent;
923         ierr = PetscSectionGetDof(mesh->supportSection, q, &qdof);CHKERRQ(ierr);
924         ierr = PetscSectionGetOffset(mesh->supportSection, q, &qoff);CHKERRQ(ierr);
925         ierr = PetscSectionGetOffset(newSupportSection, q, &newqOff);CHKERRQ(ierr);
926         for (i = 0; i < qdof; i++) {
927           PetscInt numCones, j;
928           const PetscInt *cone;
929           PetscInt r = mesh->supports[qoff + i];
930 
931           ierr = DMPlexGetConeSize(dm,r,&numCones);CHKERRQ(ierr);
932           ierr = DMPlexGetCone(dm,r,&cone);CHKERRQ(ierr);
933           for (j = 0; j < numCones; j++) {
934             if (cone[j] == q) break;
935           }
936           if (j < numCones) newSupports[newOff+offsets[p]++] = r;
937         }
938         for (i = 0; i < dof; i++) {
939           PetscInt numCones, j;
940           const PetscInt *cone;
941           PetscInt r = mesh->supports[off + i];
942 
943           ierr = DMPlexGetConeSize(dm,r,&numCones);CHKERRQ(ierr);
944           ierr = DMPlexGetCone(dm,r,&cone);CHKERRQ(ierr);
945           for (j = 0; j < numCones; j++) {
946             if (cone[j] == p) break;
947           }
948           if (j < numCones) newSupports[newqOff+offsets[q]++] = r;
949         }
950         ierr = DMPlexGetTreeParent(dm,q,&parent,NULL);CHKERRQ(ierr);
951       }
952     }
953   }
954   ierr = PetscSectionDestroy(&mesh->supportSection);CHKERRQ(ierr);
955   mesh->supportSection = newSupportSection;
956   ierr = PetscFree(mesh->supports);CHKERRQ(ierr);
957   mesh->supports = newSupports;
958   ierr = PetscFree(offsets);CHKERRQ(ierr);
959   ierr = PetscFree(numTrueSupp);CHKERRQ(ierr);
960 
961   PetscFunctionReturn(0);
962 }
963 
964 static PetscErrorCode DMPlexComputeAnchorMatrix_Tree_Direct(DM,PetscSection,PetscSection,Mat);
965 static PetscErrorCode DMPlexComputeAnchorMatrix_Tree_FromReference(DM,PetscSection,PetscSection,Mat);
966 
967 #undef __FUNCT__
968 #define __FUNCT__ "DMPlexSetTree_Internal"
969 static PetscErrorCode DMPlexSetTree_Internal(DM dm, PetscSection parentSection, PetscInt *parents, PetscInt *childIDs, PetscBool computeCanonical, PetscBool exchangeSupports)
970 {
971   DM_Plex       *mesh = (DM_Plex *)dm->data;
972   DM             refTree;
973   PetscInt       size;
974   PetscErrorCode ierr;
975 
976   PetscFunctionBegin;
977   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
978   PetscValidHeaderSpecific(parentSection, PETSC_SECTION_CLASSID, 2);
979   ierr = PetscObjectReference((PetscObject)parentSection);CHKERRQ(ierr);
980   ierr = PetscSectionDestroy(&mesh->parentSection);CHKERRQ(ierr);
981   mesh->parentSection = parentSection;
982   ierr = PetscSectionGetStorageSize(parentSection,&size);CHKERRQ(ierr);
983   if (parents != mesh->parents) {
984     ierr = PetscFree(mesh->parents);CHKERRQ(ierr);
985     ierr = PetscMalloc1(size,&mesh->parents);CHKERRQ(ierr);
986     ierr = PetscMemcpy(mesh->parents, parents, size * sizeof(*parents));CHKERRQ(ierr);
987   }
988   if (childIDs != mesh->childIDs) {
989     ierr = PetscFree(mesh->childIDs);CHKERRQ(ierr);
990     ierr = PetscMalloc1(size,&mesh->childIDs);CHKERRQ(ierr);
991     ierr = PetscMemcpy(mesh->childIDs, childIDs, size * sizeof(*childIDs));CHKERRQ(ierr);
992   }
993   ierr = DMPlexGetReferenceTree(dm,&refTree);CHKERRQ(ierr);
994   if (refTree) {
995     DMLabel canonLabel;
996 
997     ierr = DMGetLabel(refTree,"canonical",&canonLabel);CHKERRQ(ierr);
998     if (canonLabel) {
999       PetscInt i;
1000 
1001       for (i = 0; i < size; i++) {
1002         PetscInt canon;
1003         ierr = DMLabelGetValue(canonLabel, mesh->childIDs[i], &canon);CHKERRQ(ierr);
1004         if (canon >= 0) {
1005           mesh->childIDs[i] = canon;
1006         }
1007       }
1008     }
1009     mesh->computeanchormatrix = DMPlexComputeAnchorMatrix_Tree_FromReference;
1010   }
1011   else {
1012     mesh->computeanchormatrix = DMPlexComputeAnchorMatrix_Tree_Direct;
1013   }
1014   ierr = DMPlexTreeSymmetrize(dm);CHKERRQ(ierr);
1015   if (computeCanonical) {
1016     PetscInt d, dim;
1017 
1018     /* add the canonical label */
1019     ierr = DMGetDimension(dm,&dim);CHKERRQ(ierr);
1020     ierr = DMCreateLabel(dm,"canonical");CHKERRQ(ierr);
1021     for (d = 0; d <= dim; d++) {
1022       PetscInt p, dStart, dEnd, canon = -1, cNumChildren;
1023       const PetscInt *cChildren;
1024 
1025       ierr = DMPlexGetDepthStratum(dm,d,&dStart,&dEnd);CHKERRQ(ierr);
1026       for (p = dStart; p < dEnd; p++) {
1027         ierr = DMPlexGetTreeChildren(dm,p,&cNumChildren,&cChildren);CHKERRQ(ierr);
1028         if (cNumChildren) {
1029           canon = p;
1030           break;
1031         }
1032       }
1033       if (canon == -1) continue;
1034       for (p = dStart; p < dEnd; p++) {
1035         PetscInt numChildren, i;
1036         const PetscInt *children;
1037 
1038         ierr = DMPlexGetTreeChildren(dm,p,&numChildren,&children);CHKERRQ(ierr);
1039         if (numChildren) {
1040           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);
1041           ierr = DMSetLabelValue(dm,"canonical",p,canon);CHKERRQ(ierr);
1042           for (i = 0; i < numChildren; i++) {
1043             ierr = DMSetLabelValue(dm,"canonical",children[i],cChildren[i]);CHKERRQ(ierr);
1044           }
1045         }
1046       }
1047     }
1048   }
1049   if (exchangeSupports) {
1050     ierr = DMPlexTreeExchangeSupports(dm);CHKERRQ(ierr);
1051   }
1052   mesh->createanchors = DMPlexCreateAnchors_Tree;
1053   /* reset anchors */
1054   ierr = DMPlexSetAnchors(dm,NULL,NULL);CHKERRQ(ierr);
1055   PetscFunctionReturn(0);
1056 }
1057 
1058 #undef __FUNCT__
1059 #define __FUNCT__ "DMPlexSetTree"
1060 /*@
1061   DMPlexSetTree - set the tree that describes the hierarchy of non-conforming mesh points.  This routine also creates
1062   the point-to-point constraints determined by the tree: a point is constained to the points in the closure of its
1063   tree root.
1064 
1065   Collective on dm
1066 
1067   Input Parameters:
1068 + dm - the DMPlex object
1069 . parentSection - a section describing the tree: a point has a parent if it has 1 dof in the section; the section
1070                   offset indexes the parent and childID list; the reference count of parentSection is incremented
1071 . parents - a list of the point parents; copied, can be destroyed
1072 - childIDs - identifies the relationship of the child point to the parent point; if there is a reference tree, then
1073              the child corresponds to the point in the reference tree with index childIDs; copied, can be destroyed
1074 
1075   Level: intermediate
1076 
1077 .seealso: DMPlexGetTree(), DMPlexSetReferenceTree(), DMPlexSetAnchors(), DMPlexGetTreeParent(), DMPlexGetTreeChildren()
1078 @*/
1079 PetscErrorCode DMPlexSetTree(DM dm, PetscSection parentSection, PetscInt parents[], PetscInt childIDs[])
1080 {
1081   PetscErrorCode ierr;
1082 
1083   PetscFunctionBegin;
1084   ierr = DMPlexSetTree_Internal(dm,parentSection,parents,childIDs,PETSC_FALSE,PETSC_TRUE);CHKERRQ(ierr);
1085   PetscFunctionReturn(0);
1086 }
1087 
1088 #undef __FUNCT__
1089 #define __FUNCT__ "DMPlexGetTree"
1090 /*@
1091   DMPlexGetTree - get the tree that describes the hierarchy of non-conforming mesh points.
1092   Collective on dm
1093 
1094   Input Parameters:
1095 . dm - the DMPlex object
1096 
1097   Output Parameters:
1098 + parentSection - a section describing the tree: a point has a parent if it has 1 dof in the section; the section
1099                   offset indexes the parent and childID list
1100 . parents - a list of the point parents
1101 . childIDs - identifies the relationship of the child point to the parent point; if there is a reference tree, then
1102              the child corresponds to the point in the reference tree with index childID
1103 . childSection - the inverse of the parent section
1104 - children - a list of the point children
1105 
1106   Level: intermediate
1107 
1108 .seealso: DMPlexSetTree(), DMPlexSetReferenceTree(), DMPlexSetAnchors(), DMPlexGetTreeParent(), DMPlexGetTreeChildren()
1109 @*/
1110 PetscErrorCode DMPlexGetTree(DM dm, PetscSection *parentSection, PetscInt *parents[], PetscInt *childIDs[], PetscSection *childSection, PetscInt *children[])
1111 {
1112   DM_Plex        *mesh = (DM_Plex *)dm->data;
1113 
1114   PetscFunctionBegin;
1115   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1116   if (parentSection) *parentSection = mesh->parentSection;
1117   if (parents)       *parents       = mesh->parents;
1118   if (childIDs)      *childIDs      = mesh->childIDs;
1119   if (childSection)  *childSection  = mesh->childSection;
1120   if (children)      *children      = mesh->children;
1121   PetscFunctionReturn(0);
1122 }
1123 
1124 #undef __FUNCT__
1125 #define __FUNCT__ "DMPlexGetTreeParent"
1126 /*@
1127   DMPlexGetTreeParent - get the parent of a point in the tree describing the point hierarchy (not the Sieve DAG)
1128 
1129   Input Parameters:
1130 + dm - the DMPlex object
1131 - point - the query point
1132 
1133   Output Parameters:
1134 + parent - if not NULL, set to the parent of the point, or the point itself if the point does not have a parent
1135 - childID - if not NULL, set to the child ID of the point with respect to its parent, or 0 if the point
1136             does not have a parent
1137 
1138   Level: intermediate
1139 
1140 .seealso: DMPlexSetTree(), DMPlexGetTree(), DMPlexGetTreeChildren()
1141 @*/
1142 PetscErrorCode DMPlexGetTreeParent(DM dm, PetscInt point, PetscInt *parent, PetscInt *childID)
1143 {
1144   DM_Plex       *mesh = (DM_Plex *)dm->data;
1145   PetscSection   pSec;
1146   PetscErrorCode ierr;
1147 
1148   PetscFunctionBegin;
1149   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1150   pSec = mesh->parentSection;
1151   if (pSec && point >= pSec->pStart && point < pSec->pEnd) {
1152     PetscInt dof;
1153 
1154     ierr = PetscSectionGetDof (pSec, point, &dof);CHKERRQ(ierr);
1155     if (dof) {
1156       PetscInt off;
1157 
1158       ierr = PetscSectionGetOffset (pSec, point, &off);CHKERRQ(ierr);
1159       if (parent)  *parent = mesh->parents[off];
1160       if (childID) *childID = mesh->childIDs[off];
1161       PetscFunctionReturn(0);
1162     }
1163   }
1164   if (parent) {
1165     *parent = point;
1166   }
1167   if (childID) {
1168     *childID = 0;
1169   }
1170   PetscFunctionReturn(0);
1171 }
1172 
1173 #undef __FUNCT__
1174 #define __FUNCT__ "DMPlexGetTreeChildren"
1175 /*@C
1176   DMPlexGetTreeChildren - get the children of a point in the tree describing the point hierarchy (not the Sieve DAG)
1177 
1178   Input Parameters:
1179 + dm - the DMPlex object
1180 - point - the query point
1181 
1182   Output Parameters:
1183 + numChildren - if not NULL, set to the number of children
1184 - children - if not NULL, set to a list children, or set to NULL if the point has no children
1185 
1186   Level: intermediate
1187 
1188   Fortran Notes:
1189   Since it returns an array, this routine is only available in Fortran 90, and you must
1190   include petsc.h90 in your code.
1191 
1192 .seealso: DMPlexSetTree(), DMPlexGetTree(), DMPlexGetTreeParent()
1193 @*/
1194 PetscErrorCode DMPlexGetTreeChildren(DM dm, PetscInt point, PetscInt *numChildren, const PetscInt *children[])
1195 {
1196   DM_Plex       *mesh = (DM_Plex *)dm->data;
1197   PetscSection   childSec;
1198   PetscInt       dof = 0;
1199   PetscErrorCode ierr;
1200 
1201   PetscFunctionBegin;
1202   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1203   childSec = mesh->childSection;
1204   if (childSec && point >= childSec->pStart && point < childSec->pEnd) {
1205     ierr = PetscSectionGetDof (childSec, point, &dof);CHKERRQ(ierr);
1206   }
1207   if (numChildren) *numChildren = dof;
1208   if (children) {
1209     if (dof) {
1210       PetscInt off;
1211 
1212       ierr = PetscSectionGetOffset (childSec, point, &off);CHKERRQ(ierr);
1213       *children = &mesh->children[off];
1214     }
1215     else {
1216       *children = NULL;
1217     }
1218   }
1219   PetscFunctionReturn(0);
1220 }
1221 
1222 #undef __FUNCT__
1223 #define __FUNCT__ "DMPlexComputeAnchorMatrix_Tree_Direct"
1224 static PetscErrorCode DMPlexComputeAnchorMatrix_Tree_Direct(DM dm, PetscSection section, PetscSection cSec, Mat cMat)
1225 {
1226   PetscDS        ds;
1227   PetscInt       spdim;
1228   PetscInt       numFields, f, c, cStart, cEnd, pStart, pEnd, conStart, conEnd;
1229   const PetscInt *anchors;
1230   PetscSection   aSec;
1231   PetscReal      *v0, *v0parent, *vtmp, *J, *Jparent, *invJparent, detJ, detJparent;
1232   IS             aIS;
1233   PetscErrorCode ierr;
1234 
1235   PetscFunctionBegin;
1236   ierr = DMPlexGetChart(dm,&pStart,&pEnd);CHKERRQ(ierr);
1237   ierr = DMGetDS(dm,&ds);CHKERRQ(ierr);
1238   ierr = PetscDSGetNumFields(ds,&numFields);CHKERRQ(ierr);
1239   ierr = DMPlexGetHeightStratum(dm,0,&cStart,&cEnd);CHKERRQ(ierr);
1240   ierr = DMPlexGetAnchors(dm,&aSec,&aIS);CHKERRQ(ierr);
1241   ierr = ISGetIndices(aIS,&anchors);CHKERRQ(ierr);
1242   ierr = PetscSectionGetChart(cSec,&conStart,&conEnd);CHKERRQ(ierr);
1243   ierr = DMGetDimension(dm,&spdim);CHKERRQ(ierr);
1244   ierr = PetscMalloc6(spdim,&v0,spdim,&v0parent,spdim,&vtmp,spdim*spdim,&J,spdim*spdim,&Jparent,spdim*spdim,&invJparent);CHKERRQ(ierr);
1245 
1246   for (f = 0; f < numFields; f++) {
1247     PetscObject disc;
1248     PetscFE fe = NULL;
1249     PetscFV fv = NULL;
1250     PetscClassId id;
1251     PetscDualSpace space;
1252     PetscInt i, j, k, nPoints, offset;
1253     PetscInt fSize, fComp;
1254     PetscReal *B = NULL;
1255     PetscReal *weights, *pointsRef, *pointsReal;
1256     Mat Amat, Bmat, Xmat;
1257 
1258     ierr = PetscDSGetDiscretization(ds,f,&disc);CHKERRQ(ierr);
1259     ierr = PetscObjectGetClassId(disc,&id);CHKERRQ(ierr);
1260     if (id == PETSCFE_CLASSID) {
1261       fe = (PetscFE) disc;
1262       ierr = PetscFEGetDualSpace(fe,&space);CHKERRQ(ierr);
1263       ierr = PetscDualSpaceGetDimension(space,&fSize);CHKERRQ(ierr);
1264       ierr = PetscFEGetNumComponents(fe,&fComp);CHKERRQ(ierr);
1265     }
1266     else if (id == PETSCFV_CLASSID) {
1267       fv = (PetscFV) disc;
1268       ierr = PetscFVGetDualSpace(fv,&space);CHKERRQ(ierr);
1269       ierr = PetscDualSpaceGetDimension(space,&fSize);CHKERRQ(ierr);
1270       ierr = PetscFVGetNumComponents(fv,&fComp);CHKERRQ(ierr);
1271     }
1272     else SETERRQ1(PetscObjectComm(disc),PETSC_ERR_ARG_UNKNOWN_TYPE, "PetscDS discretization id %d not recognized.", id);
1273 
1274     ierr = MatCreate(PETSC_COMM_SELF,&Amat);CHKERRQ(ierr);
1275     ierr = MatSetSizes(Amat,fSize,fSize,fSize,fSize);CHKERRQ(ierr);
1276     ierr = MatSetType(Amat,MATSEQDENSE);CHKERRQ(ierr);
1277     ierr = MatSetUp(Amat);CHKERRQ(ierr);
1278     ierr = MatDuplicate(Amat,MAT_DO_NOT_COPY_VALUES,&Bmat);CHKERRQ(ierr);
1279     ierr = MatDuplicate(Amat,MAT_DO_NOT_COPY_VALUES,&Xmat);CHKERRQ(ierr);
1280     nPoints = 0;
1281     for (i = 0; i < fSize; i++) {
1282       PetscInt        qPoints;
1283       PetscQuadrature quad;
1284 
1285       ierr = PetscDualSpaceGetFunctional(space,i,&quad);CHKERRQ(ierr);
1286       ierr = PetscQuadratureGetData(quad,NULL,&qPoints,NULL,NULL);CHKERRQ(ierr);
1287       nPoints += qPoints;
1288     }
1289     ierr = PetscMalloc3(nPoints,&weights,spdim*nPoints,&pointsRef,spdim*nPoints,&pointsReal);CHKERRQ(ierr);
1290     offset = 0;
1291     for (i = 0; i < fSize; i++) {
1292       PetscInt        qPoints;
1293       const PetscReal    *p, *w;
1294       PetscQuadrature quad;
1295 
1296       ierr = PetscDualSpaceGetFunctional(space,i,&quad);CHKERRQ(ierr);
1297       ierr = PetscQuadratureGetData(quad,NULL,&qPoints,&p,&w);CHKERRQ(ierr);
1298       ierr = PetscMemcpy(weights+offset,w,qPoints*sizeof(*w));CHKERRQ(ierr);
1299       ierr = PetscMemcpy(pointsRef+spdim*offset,p,spdim*qPoints*sizeof(*p));CHKERRQ(ierr);
1300       offset += qPoints;
1301     }
1302     if (id == PETSCFE_CLASSID) {
1303       ierr = PetscFEGetTabulation(fe,nPoints,pointsRef,&B,NULL,NULL);CHKERRQ(ierr);
1304     }
1305     else {
1306       ierr = PetscFVGetTabulation(fv,nPoints,pointsRef,&B,NULL,NULL);CHKERRQ(ierr);
1307     }
1308     offset = 0;
1309     for (i = 0; i < fSize; i++) {
1310       PetscInt        qPoints;
1311       PetscQuadrature quad;
1312 
1313       ierr = PetscDualSpaceGetFunctional(space,i,&quad);CHKERRQ(ierr);
1314       ierr = PetscQuadratureGetData(quad,NULL,&qPoints,NULL,NULL);CHKERRQ(ierr);
1315       for (j = 0; j < fSize; j++) {
1316         PetscScalar val = 0.;
1317 
1318         for (k = 0; k < qPoints; k++) {
1319           val += B[((offset + k) * fSize + j) * fComp] * weights[k];
1320         }
1321         ierr = MatSetValue(Amat,i,j,val,INSERT_VALUES);CHKERRQ(ierr);
1322       }
1323       offset += qPoints;
1324     }
1325     if (id == PETSCFE_CLASSID) {
1326       ierr = PetscFERestoreTabulation(fe,nPoints,pointsRef,&B,NULL,NULL);CHKERRQ(ierr);
1327     }
1328     else {
1329       ierr = PetscFVRestoreTabulation(fv,nPoints,pointsRef,&B,NULL,NULL);CHKERRQ(ierr);
1330     }
1331     ierr = MatAssemblyBegin(Amat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1332     ierr = MatAssemblyEnd(Amat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1333     ierr = MatLUFactor(Amat,NULL,NULL,NULL);CHKERRQ(ierr);
1334     for (c = cStart; c < cEnd; c++) {
1335       PetscInt parent;
1336       PetscInt closureSize, closureSizeP, *closure = NULL, *closureP = NULL;
1337       PetscInt *childOffsets, *parentOffsets;
1338 
1339       ierr = DMPlexGetTreeParent(dm,c,&parent,NULL);CHKERRQ(ierr);
1340       if (parent == c) continue;
1341       ierr = DMPlexGetTransitiveClosure(dm,c,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1342       for (i = 0; i < closureSize; i++) {
1343         PetscInt p = closure[2*i];
1344         PetscInt conDof;
1345 
1346         if (p < conStart || p >= conEnd) continue;
1347         if (numFields > 1) {
1348           ierr = PetscSectionGetFieldDof(cSec,p,f,&conDof);CHKERRQ(ierr);
1349         }
1350         else {
1351           ierr = PetscSectionGetDof(cSec,p,&conDof);CHKERRQ(ierr);
1352         }
1353         if (conDof) break;
1354       }
1355       if (i == closureSize) {
1356         ierr = DMPlexRestoreTransitiveClosure(dm,c,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1357         continue;
1358       }
1359 
1360       ierr = DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, NULL, &detJ);CHKERRQ(ierr);
1361       ierr = DMPlexComputeCellGeometryFEM(dm, parent, NULL, v0parent, Jparent, invJparent, &detJparent);CHKERRQ(ierr);
1362       for (i = 0; i < nPoints; i++) {
1363         CoordinatesRefToReal(spdim, spdim, v0, J, &pointsRef[i*spdim],vtmp);CHKERRQ(ierr);
1364         CoordinatesRealToRef(spdim, spdim, v0parent, invJparent, vtmp, &pointsReal[i*spdim]);CHKERRQ(ierr);
1365       }
1366       if (id == PETSCFE_CLASSID) {
1367         ierr = PetscFEGetTabulation(fe,nPoints,pointsReal,&B,NULL,NULL);CHKERRQ(ierr);
1368       }
1369       else {
1370         ierr = PetscFVGetTabulation(fv,nPoints,pointsReal,&B,NULL,NULL);CHKERRQ(ierr);
1371       }
1372       offset = 0;
1373       for (i = 0; i < fSize; i++) {
1374         PetscInt        qPoints;
1375         PetscQuadrature quad;
1376 
1377         ierr = PetscDualSpaceGetFunctional(space,i,&quad);CHKERRQ(ierr);
1378         ierr = PetscQuadratureGetData(quad,NULL,&qPoints,NULL,NULL);CHKERRQ(ierr);
1379         for (j = 0; j < fSize; j++) {
1380           PetscScalar val = 0.;
1381 
1382           for (k = 0; k < qPoints; k++) {
1383             val += B[((offset + k) * fSize + j) * fComp] * weights[k];
1384           }
1385           MatSetValue(Bmat,i,j,val,INSERT_VALUES);CHKERRQ(ierr);
1386         }
1387         offset += qPoints;
1388       }
1389       if (id == PETSCFE_CLASSID) {
1390         ierr = PetscFERestoreTabulation(fe,nPoints,pointsReal,&B,NULL,NULL);CHKERRQ(ierr);
1391       }
1392       else {
1393         ierr = PetscFVRestoreTabulation(fv,nPoints,pointsReal,&B,NULL,NULL);CHKERRQ(ierr);
1394       }
1395       ierr = MatAssemblyBegin(Bmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1396       ierr = MatAssemblyEnd(Bmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1397       ierr = MatMatSolve(Amat,Bmat,Xmat);CHKERRQ(ierr);
1398       ierr = DMPlexGetTransitiveClosure(dm,parent,PETSC_TRUE,&closureSizeP,&closureP);CHKERRQ(ierr);
1399       ierr = PetscMalloc2(closureSize+1,&childOffsets,closureSizeP+1,&parentOffsets);CHKERRQ(ierr);
1400       childOffsets[0] = 0;
1401       for (i = 0; i < closureSize; i++) {
1402         PetscInt p = closure[2*i];
1403         PetscInt dof;
1404 
1405         if (numFields > 1) {
1406           ierr = PetscSectionGetFieldDof(section,p,f,&dof);CHKERRQ(ierr);
1407         }
1408         else {
1409           ierr = PetscSectionGetDof(section,p,&dof);CHKERRQ(ierr);
1410         }
1411         childOffsets[i+1]=childOffsets[i]+dof / fComp;
1412       }
1413       parentOffsets[0] = 0;
1414       for (i = 0; i < closureSizeP; i++) {
1415         PetscInt p = closureP[2*i];
1416         PetscInt dof;
1417 
1418         if (numFields > 1) {
1419           ierr = PetscSectionGetFieldDof(section,p,f,&dof);CHKERRQ(ierr);
1420         }
1421         else {
1422           ierr = PetscSectionGetDof(section,p,&dof);CHKERRQ(ierr);
1423         }
1424         parentOffsets[i+1]=parentOffsets[i]+dof / fComp;
1425       }
1426       for (i = 0; i < closureSize; i++) {
1427         PetscInt conDof, conOff, aDof, aOff;
1428         PetscInt p = closure[2*i];
1429         PetscInt o = closure[2*i+1];
1430 
1431         if (p < conStart || p >= conEnd) continue;
1432         if (numFields > 1) {
1433           ierr = PetscSectionGetFieldDof(cSec,p,f,&conDof);CHKERRQ(ierr);
1434           ierr = PetscSectionGetFieldOffset(cSec,p,f,&conOff);CHKERRQ(ierr);
1435         }
1436         else {
1437           ierr = PetscSectionGetDof(cSec,p,&conDof);CHKERRQ(ierr);
1438           ierr = PetscSectionGetOffset(cSec,p,&conOff);CHKERRQ(ierr);
1439         }
1440         if (!conDof) continue;
1441         ierr = PetscSectionGetDof(aSec,p,&aDof);CHKERRQ(ierr);
1442         ierr = PetscSectionGetOffset(aSec,p,&aOff);CHKERRQ(ierr);
1443         for (k = 0; k < aDof; k++) {
1444           PetscInt a = anchors[aOff + k];
1445           PetscInt aSecDof, aSecOff;
1446 
1447           if (numFields > 1) {
1448             ierr = PetscSectionGetFieldDof(section,a,f,&aSecDof);CHKERRQ(ierr);
1449             ierr = PetscSectionGetFieldOffset(section,a,f,&aSecOff);CHKERRQ(ierr);
1450           }
1451           else {
1452             ierr = PetscSectionGetDof(section,a,&aSecDof);CHKERRQ(ierr);
1453             ierr = PetscSectionGetOffset(section,a,&aSecOff);CHKERRQ(ierr);
1454           }
1455           if (!aSecDof) continue;
1456 
1457           for (j = 0; j < closureSizeP; j++) {
1458             PetscInt q = closureP[2*j];
1459             PetscInt oq = closureP[2*j+1];
1460 
1461             if (q == a) {
1462               PetscInt r, s, t;
1463 
1464               for (r = childOffsets[i]; r < childOffsets[i+1]; r++) {
1465                 for (s = parentOffsets[j]; s < parentOffsets[j+1]; s++) {
1466                   PetscScalar val;
1467                   PetscInt insertCol, insertRow;
1468 
1469                   ierr = MatGetValue(Xmat,r,s,&val);CHKERRQ(ierr);
1470                   if (o >= 0) {
1471                     insertRow = conOff + fComp * (r - childOffsets[i]);
1472                   }
1473                   else {
1474                     insertRow = conOff + fComp * (childOffsets[i + 1] - 1 - r);
1475                   }
1476                   if (oq >= 0) {
1477                     insertCol = aSecOff + fComp * (s - parentOffsets[j]);
1478                   }
1479                   else {
1480                     insertCol = aSecOff + fComp * (parentOffsets[j + 1] - 1 - s);
1481                   }
1482                   for (t = 0; t < fComp; t++) {
1483                     ierr = MatSetValue(cMat,insertRow + t,insertCol + t,val,INSERT_VALUES);CHKERRQ(ierr);
1484                   }
1485                 }
1486               }
1487             }
1488           }
1489         }
1490       }
1491       ierr = PetscFree2(childOffsets,parentOffsets);CHKERRQ(ierr);
1492       ierr = DMPlexRestoreTransitiveClosure(dm,c,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1493       ierr = DMPlexRestoreTransitiveClosure(dm,parent,PETSC_TRUE,&closureSizeP,&closureP);CHKERRQ(ierr);
1494     }
1495     ierr = MatDestroy(&Amat);CHKERRQ(ierr);
1496     ierr = MatDestroy(&Bmat);CHKERRQ(ierr);
1497     ierr = MatDestroy(&Xmat);CHKERRQ(ierr);
1498     ierr = PetscFree3(weights,pointsRef,pointsReal);CHKERRQ(ierr);
1499   }
1500   ierr = MatAssemblyBegin(cMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1501   ierr = MatAssemblyEnd(cMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1502   ierr = PetscFree6(v0,v0parent,vtmp,J,Jparent,invJparent);CHKERRQ(ierr);
1503   ierr = ISRestoreIndices(aIS,&anchors);CHKERRQ(ierr);
1504 
1505   PetscFunctionReturn(0);
1506 }
1507 
1508 #undef __FUNCT__
1509 #define __FUNCT__ "DMPlexReferenceTreeGetChildrenMatrices"
1510 static PetscErrorCode DMPlexReferenceTreeGetChildrenMatrices(DM refTree, PetscScalar ****childrenMats, PetscInt ***childrenN)
1511 {
1512   Mat            refCmat;
1513   PetscDS        ds;
1514   PetscInt       numFields, f, pRefStart, pRefEnd, p, *rows, *cols, maxDof, maxAnDof, **refPointFieldN;
1515   PetscScalar    ***refPointFieldMats;
1516   PetscSection   refConSec, refAnSec, refSection;
1517   IS             refAnIS;
1518   const PetscInt *refAnchors;
1519   PetscErrorCode ierr;
1520 
1521   PetscFunctionBegin;
1522   ierr = DMGetDS(refTree,&ds);CHKERRQ(ierr);
1523   ierr = PetscDSGetNumFields(ds,&numFields);CHKERRQ(ierr);
1524   ierr = DMGetDefaultConstraints(refTree,&refConSec,&refCmat);CHKERRQ(ierr);
1525   ierr = DMPlexGetAnchors(refTree,&refAnSec,&refAnIS);CHKERRQ(ierr);
1526   ierr = ISGetIndices(refAnIS,&refAnchors);CHKERRQ(ierr);
1527   ierr = DMGetDefaultSection(refTree,&refSection);CHKERRQ(ierr);
1528   ierr = PetscSectionGetChart(refConSec,&pRefStart,&pRefEnd);CHKERRQ(ierr);
1529   ierr = PetscMalloc1(pRefEnd-pRefStart,&refPointFieldMats);CHKERRQ(ierr);
1530   ierr = PetscMalloc1(pRefEnd-pRefStart,&refPointFieldN);CHKERRQ(ierr);
1531   ierr = PetscSectionGetMaxDof(refConSec,&maxDof);CHKERRQ(ierr);
1532   ierr = PetscSectionGetMaxDof(refAnSec,&maxAnDof);CHKERRQ(ierr);
1533   ierr = PetscMalloc1(maxDof,&rows);CHKERRQ(ierr);
1534   ierr = PetscMalloc1(maxDof*maxAnDof,&cols);CHKERRQ(ierr);
1535   for (p = pRefStart; p < pRefEnd; p++) {
1536     PetscInt parent, closureSize, *closure = NULL, pDof;
1537 
1538     ierr = DMPlexGetTreeParent(refTree,p,&parent,NULL);CHKERRQ(ierr);
1539     ierr = PetscSectionGetDof(refConSec,p,&pDof);CHKERRQ(ierr);
1540     if (!pDof || parent == p) continue;
1541 
1542     ierr = PetscMalloc1(numFields,&refPointFieldMats[p-pRefStart]);CHKERRQ(ierr);
1543     ierr = PetscCalloc1(numFields,&refPointFieldN[p-pRefStart]);CHKERRQ(ierr);
1544     ierr = DMPlexGetTransitiveClosure(refTree,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1545     for (f = 0; f < numFields; f++) {
1546       PetscInt cDof, cOff, numCols, r, i, fComp;
1547       PetscObject disc;
1548       PetscClassId id;
1549       PetscFE fe = NULL;
1550       PetscFV fv = NULL;
1551 
1552       ierr = PetscDSGetDiscretization(ds,f,&disc);CHKERRQ(ierr);
1553       ierr = PetscObjectGetClassId(disc,&id);CHKERRQ(ierr);
1554       if (id == PETSCFE_CLASSID) {
1555         fe = (PetscFE) disc;
1556         ierr = PetscFEGetNumComponents(fe,&fComp);CHKERRQ(ierr);
1557       }
1558       else if (id == PETSCFV_CLASSID) {
1559         fv = (PetscFV) disc;
1560         ierr = PetscFVGetNumComponents(fv,&fComp);CHKERRQ(ierr);
1561       }
1562       else SETERRQ1(PetscObjectComm(disc),PETSC_ERR_ARG_UNKNOWN_TYPE, "PetscDS discretization id %d not recognized.", id);
1563 
1564       if (numFields > 1) {
1565         ierr = PetscSectionGetFieldDof(refConSec,p,f,&cDof);CHKERRQ(ierr);
1566         ierr = PetscSectionGetFieldOffset(refConSec,p,f,&cOff);CHKERRQ(ierr);
1567       }
1568       else {
1569         ierr = PetscSectionGetDof(refConSec,p,&cDof);CHKERRQ(ierr);
1570         ierr = PetscSectionGetOffset(refConSec,p,&cOff);CHKERRQ(ierr);
1571       }
1572 
1573       if (!cDof) continue;
1574       for (r = 0; r < cDof; r++) {
1575         rows[r] = cOff + r;
1576       }
1577       numCols = 0;
1578       for (i = 0; i < closureSize; i++) {
1579         PetscInt q = closure[2*i];
1580         PetscInt o = closure[2*i+1];
1581         PetscInt aDof, aOff, j;
1582 
1583         if (numFields > 1) {
1584           ierr = PetscSectionGetFieldDof(refSection,q,f,&aDof);CHKERRQ(ierr);
1585           ierr = PetscSectionGetFieldOffset(refSection,q,f,&aOff);CHKERRQ(ierr);
1586         }
1587         else {
1588           ierr = PetscSectionGetDof(refSection,q,&aDof);CHKERRQ(ierr);
1589           ierr = PetscSectionGetOffset(refSection,q,&aOff);CHKERRQ(ierr);
1590         }
1591 
1592         for (j = 0; j < aDof; j++) {
1593           PetscInt node = (o >= 0) ? (j / fComp) : ((aDof - 1 - j) / fComp);
1594           PetscInt comp = (j % fComp);
1595 
1596           cols[numCols++] = aOff + node * fComp + comp;
1597         }
1598       }
1599       refPointFieldN[p-pRefStart][f] = numCols;
1600       ierr = PetscMalloc1(cDof*numCols,&refPointFieldMats[p-pRefStart][f]);CHKERRQ(ierr);
1601       ierr = MatGetValues(refCmat,cDof,rows,numCols,cols,refPointFieldMats[p-pRefStart][f]);CHKERRQ(ierr);
1602     }
1603     ierr = DMPlexRestoreTransitiveClosure(refTree,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1604   }
1605   *childrenMats = refPointFieldMats;
1606   *childrenN = refPointFieldN;
1607   ierr = ISRestoreIndices(refAnIS,&refAnchors);CHKERRQ(ierr);
1608   ierr = PetscFree(rows);CHKERRQ(ierr);
1609   ierr = PetscFree(cols);CHKERRQ(ierr);
1610   PetscFunctionReturn(0);
1611 }
1612 
1613 #undef __FUNCT__
1614 #define __FUNCT__ "DMPlexReferenceTreeRestoreChildrenMatrices"
1615 static PetscErrorCode DMPlexReferenceTreeRestoreChildrenMatrices(DM refTree, PetscScalar ****childrenMats, PetscInt ***childrenN)
1616 {
1617   PetscDS        ds;
1618   PetscInt       **refPointFieldN;
1619   PetscScalar    ***refPointFieldMats;
1620   PetscInt       numFields, pRefStart, pRefEnd, p, f;
1621   PetscSection   refConSec;
1622   PetscErrorCode ierr;
1623 
1624   PetscFunctionBegin;
1625   refPointFieldN = *childrenN;
1626   *childrenN = NULL;
1627   refPointFieldMats = *childrenMats;
1628   *childrenMats = NULL;
1629   ierr = DMGetDS(refTree,&ds);CHKERRQ(ierr);
1630   ierr = PetscDSGetNumFields(ds,&numFields);CHKERRQ(ierr);
1631   ierr = DMGetDefaultConstraints(refTree,&refConSec,NULL);CHKERRQ(ierr);
1632   ierr = PetscSectionGetChart(refConSec,&pRefStart,&pRefEnd);CHKERRQ(ierr);
1633   for (p = pRefStart; p < pRefEnd; p++) {
1634     PetscInt parent, pDof;
1635 
1636     ierr = DMPlexGetTreeParent(refTree,p,&parent,NULL);CHKERRQ(ierr);
1637     ierr = PetscSectionGetDof(refConSec,p,&pDof);CHKERRQ(ierr);
1638     if (!pDof || parent == p) continue;
1639 
1640     for (f = 0; f < numFields; f++) {
1641       PetscInt cDof;
1642 
1643       if (numFields > 1) {
1644         ierr = PetscSectionGetFieldDof(refConSec,p,f,&cDof);CHKERRQ(ierr);
1645       }
1646       else {
1647         ierr = PetscSectionGetDof(refConSec,p,&cDof);CHKERRQ(ierr);
1648       }
1649 
1650       if (!cDof) continue;
1651       ierr = PetscFree(refPointFieldMats[p - pRefStart][f]);CHKERRQ(ierr);
1652     }
1653     ierr = PetscFree(refPointFieldMats[p - pRefStart]);CHKERRQ(ierr);
1654     ierr = PetscFree(refPointFieldN[p - pRefStart]);CHKERRQ(ierr);
1655   }
1656   ierr = PetscFree(refPointFieldMats);CHKERRQ(ierr);
1657   ierr = PetscFree(refPointFieldN);CHKERRQ(ierr);
1658   PetscFunctionReturn(0);
1659 }
1660 
1661 #undef __FUNCT__
1662 #define __FUNCT__ "DMPlexComputeAnchorMatrix_Tree_FromReference"
1663 static PetscErrorCode DMPlexComputeAnchorMatrix_Tree_FromReference(DM dm, PetscSection section, PetscSection conSec, Mat cMat)
1664 {
1665   DM             refTree;
1666   PetscDS        ds;
1667   Mat            refCmat;
1668   PetscInt       numFields, f, pRefStart, pRefEnd, p, maxDof, maxAnDof, *perm, *iperm, pStart, pEnd, conStart, conEnd, **refPointFieldN;
1669   PetscScalar ***refPointFieldMats, *pointWork;
1670   PetscSection   refConSec, refAnSec, anSec;
1671   IS             refAnIS, anIS;
1672   const PetscInt *anchors;
1673   PetscErrorCode ierr;
1674 
1675   PetscFunctionBegin;
1676   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1677   ierr = DMGetDS(dm,&ds);CHKERRQ(ierr);
1678   ierr = PetscDSGetNumFields(ds,&numFields);CHKERRQ(ierr);
1679   ierr = DMPlexGetReferenceTree(dm,&refTree);CHKERRQ(ierr);
1680   ierr = DMSetDS(refTree,ds);CHKERRQ(ierr);
1681   ierr = DMGetDefaultConstraints(refTree,&refConSec,&refCmat);CHKERRQ(ierr);
1682   ierr = DMPlexGetAnchors(refTree,&refAnSec,&refAnIS);CHKERRQ(ierr);
1683   ierr = DMPlexGetAnchors(dm,&anSec,&anIS);CHKERRQ(ierr);
1684   ierr = ISGetIndices(anIS,&anchors);CHKERRQ(ierr);
1685   ierr = PetscSectionGetChart(refConSec,&pRefStart,&pRefEnd);CHKERRQ(ierr);
1686   ierr = PetscSectionGetChart(conSec,&conStart,&conEnd);CHKERRQ(ierr);
1687   ierr = PetscSectionGetMaxDof(refConSec,&maxDof);CHKERRQ(ierr);
1688   ierr = PetscSectionGetMaxDof(refAnSec,&maxAnDof);CHKERRQ(ierr);
1689   ierr = PetscMalloc1(maxDof*maxDof*maxAnDof,&pointWork);CHKERRQ(ierr);
1690 
1691   /* step 1: get submats for every constrained point in the reference tree */
1692   ierr = DMPlexReferenceTreeGetChildrenMatrices(refTree,&refPointFieldMats,&refPointFieldN);CHKERRQ(ierr);
1693 
1694   /* step 2: compute the preorder */
1695   ierr = DMPlexGetChart(dm,&pStart,&pEnd);CHKERRQ(ierr);
1696   ierr = PetscMalloc2(pEnd-pStart,&perm,pEnd-pStart,&iperm);CHKERRQ(ierr);
1697   for (p = pStart; p < pEnd; p++) {
1698     perm[p - pStart] = p;
1699     iperm[p - pStart] = p-pStart;
1700   }
1701   for (p = 0; p < pEnd - pStart;) {
1702     PetscInt point = perm[p];
1703     PetscInt parent;
1704 
1705     ierr = DMPlexGetTreeParent(dm,point,&parent,NULL);CHKERRQ(ierr);
1706     if (parent == point) {
1707       p++;
1708     }
1709     else {
1710       PetscInt size, closureSize, *closure = NULL, i;
1711 
1712       ierr = DMPlexGetTransitiveClosure(dm,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1713       for (i = 0; i < closureSize; i++) {
1714         PetscInt q = closure[2*i];
1715         if (iperm[q-pStart] > iperm[point-pStart]) {
1716           /* swap */
1717           perm[p]               = q;
1718           perm[iperm[q-pStart]] = point;
1719           iperm[point-pStart]   = iperm[q-pStart];
1720           iperm[q-pStart]       = p;
1721           break;
1722         }
1723       }
1724       size = closureSize;
1725       ierr = DMPlexRestoreTransitiveClosure(dm,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1726       if (i == size) {
1727         p++;
1728       }
1729     }
1730   }
1731 
1732   /* step 3: fill the constraint matrix */
1733   /* we are going to use a preorder progressive fill strategy.  Mat doesn't
1734    * allow progressive fill without assembly, so we are going to set up the
1735    * values outside of the Mat first.
1736    */
1737   {
1738     PetscInt nRows, row, nnz;
1739     PetscBool done;
1740     const PetscInt *ia, *ja;
1741     PetscScalar *vals;
1742 
1743     ierr = MatGetRowIJ(cMat,0,PETSC_FALSE,PETSC_FALSE,&nRows,&ia,&ja,&done);CHKERRQ(ierr);
1744     if (!done) SETERRQ(PetscObjectComm((PetscObject)cMat),PETSC_ERR_PLIB,"Could not get RowIJ of constraint matrix");
1745     nnz  = ia[nRows];
1746     /* malloc and then zero rows right before we fill them: this way valgrind
1747      * can tell if we are doing progressive fill in the wrong order */
1748     ierr = PetscMalloc1(nnz,&vals);CHKERRQ(ierr);
1749     for (p = 0; p < pEnd - pStart; p++) {
1750       PetscInt parent, childid, closureSize, *closure = NULL;
1751       PetscInt point = perm[p], pointDof;
1752 
1753       ierr = DMPlexGetTreeParent(dm,point,&parent,&childid);CHKERRQ(ierr);
1754       if ((point < conStart) || (point >= conEnd) || (parent == point)) continue;
1755       ierr = PetscSectionGetDof(conSec,point,&pointDof);CHKERRQ(ierr);
1756       if (!pointDof) continue;
1757       ierr = DMPlexGetTransitiveClosure(dm,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1758       for (f = 0; f < numFields; f++) {
1759         PetscInt cDof, cOff, numCols, numFillCols, i, r, fComp, matOffset, offset;
1760         PetscScalar *pointMat;
1761         PetscObject disc;
1762         PetscClassId id;
1763         PetscFE fe = NULL;
1764         PetscFV fv = NULL;
1765 
1766         ierr = PetscDSGetDiscretization(ds,f,&disc);CHKERRQ(ierr);
1767         ierr = PetscObjectGetClassId(disc,&id);CHKERRQ(ierr);
1768         if (id == PETSCFE_CLASSID) {
1769           fe = (PetscFE) disc;
1770           ierr = PetscFEGetNumComponents(fe,&fComp);CHKERRQ(ierr);
1771         }
1772         else if (id == PETSCFV_CLASSID) {
1773           fv = (PetscFV) disc;
1774           ierr = PetscFVGetNumComponents(fv,&fComp);CHKERRQ(ierr);
1775         }
1776 
1777         if (numFields > 1) {
1778           ierr = PetscSectionGetFieldDof(conSec,point,f,&cDof);CHKERRQ(ierr);
1779           ierr = PetscSectionGetFieldOffset(conSec,point,f,&cOff);CHKERRQ(ierr);
1780         }
1781         else {
1782           ierr = PetscSectionGetDof(conSec,point,&cDof);CHKERRQ(ierr);
1783           ierr = PetscSectionGetOffset(conSec,point,&cOff);CHKERRQ(ierr);
1784         }
1785         if (!cDof) continue;
1786 
1787         /* make sure that every row for this point is the same size */
1788 #if defined(PETSC_USE_DEBUG)
1789         for (r = 0; r < cDof; r++) {
1790           if (cDof > 1 && r) {
1791             if ((ia[cOff+r+1]-ia[cOff+r]) != (ia[cOff+r]-ia[cOff+r-1])) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Two point rows have different nnz: %D vs. %D", (ia[cOff+r+1]-ia[cOff+r]), (ia[cOff+r]-ia[cOff+r-1]));
1792           }
1793         }
1794 #endif
1795         /* zero rows */
1796         for (i = ia[cOff] ; i< ia[cOff+cDof];i++) {
1797           vals[i] = 0.;
1798         }
1799         matOffset = ia[cOff];
1800         numFillCols = ia[cOff+1] - matOffset;
1801         pointMat = refPointFieldMats[childid-pRefStart][f];
1802         numCols = refPointFieldN[childid-pRefStart][f];
1803         offset = 0;
1804         for (i = 0; i < closureSize; i++) {
1805           PetscInt q = closure[2*i];
1806           PetscInt o = closure[2*i+1];
1807           PetscInt aDof, aOff, j, k, qConDof, qConOff;
1808 
1809           qConDof = qConOff = 0;
1810           if (numFields > 1) {
1811             ierr = PetscSectionGetFieldDof(section,q,f,&aDof);CHKERRQ(ierr);
1812             ierr = PetscSectionGetFieldOffset(section,q,f,&aOff);CHKERRQ(ierr);
1813             if (q >= conStart && q < conEnd) {
1814               ierr = PetscSectionGetFieldDof(conSec,q,f,&qConDof);CHKERRQ(ierr);
1815               ierr = PetscSectionGetFieldOffset(conSec,q,f,&qConOff);CHKERRQ(ierr);
1816             }
1817           }
1818           else {
1819             ierr = PetscSectionGetDof(section,q,&aDof);CHKERRQ(ierr);
1820             ierr = PetscSectionGetOffset(section,q,&aOff);CHKERRQ(ierr);
1821             if (q >= conStart && q < conEnd) {
1822               ierr = PetscSectionGetDof(conSec,q,&qConDof);CHKERRQ(ierr);
1823               ierr = PetscSectionGetOffset(conSec,q,&qConOff);CHKERRQ(ierr);
1824             }
1825           }
1826           if (!aDof) continue;
1827           if (qConDof) {
1828             /* this point has anchors: its rows of the matrix should already
1829              * be filled, thanks to preordering */
1830             /* first multiply into pointWork, then set in matrix */
1831             PetscInt aMatOffset = ia[qConOff];
1832             PetscInt aNumFillCols = ia[qConOff + 1] - aMatOffset;
1833             for (r = 0; r < cDof; r++) {
1834               for (j = 0; j < aNumFillCols; j++) {
1835                 PetscScalar inVal = 0;
1836                 for (k = 0; k < aDof; k++) {
1837                   PetscInt node = (o >= 0) ? (k / fComp) : ((aDof - 1 - k) / fComp);
1838                   PetscInt comp = (k % fComp);
1839                   PetscInt col  = node * fComp + comp;
1840 
1841                   inVal += pointMat[r * numCols + offset + col] * vals[aMatOffset + aNumFillCols * k + j];
1842                 }
1843                 pointWork[r * aNumFillCols + j] = inVal;
1844               }
1845             }
1846             /* assume that the columns are sorted, spend less time searching */
1847             for (j = 0, k = 0; j < aNumFillCols; j++) {
1848               PetscInt col = ja[aMatOffset + j];
1849               for (;k < numFillCols; k++) {
1850                 if (ja[matOffset + k] == col) {
1851                   break;
1852                 }
1853               }
1854               if (k == numFillCols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"No nonzero space for (%d, %d)", cOff, col);
1855               for (r = 0; r < cDof; r++) {
1856                 vals[matOffset + numFillCols * r + k] = pointWork[r * aNumFillCols + j];
1857               }
1858             }
1859           }
1860           else {
1861             /* find where to put this portion of pointMat into the matrix */
1862             for (k = 0; k < numFillCols; k++) {
1863               if (ja[matOffset + k] == aOff) {
1864                 break;
1865               }
1866             }
1867             if (k == numFillCols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"No nonzero space for (%d, %d)", cOff, aOff);
1868             for (j = 0; j < aDof; j++) {
1869               PetscInt node = (o >= 0) ? (j / fComp) : ((aDof - 1 - j) / fComp);
1870               PetscInt comp = (j % fComp);
1871               PetscInt col  = node * fComp + comp;
1872               for (r = 0; r < cDof; r++) {
1873                 vals[matOffset + numFillCols * r + k + col] += pointMat[r * numCols + offset + col];
1874               }
1875             }
1876           }
1877           offset += aDof;
1878         }
1879       }
1880       ierr = DMPlexRestoreTransitiveClosure(dm,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1881     }
1882     for (row = 0; row < nRows; row++) {
1883       ierr = MatSetValues(cMat,1,&row,ia[row+1]-ia[row],&ja[ia[row]],&vals[ia[row]],INSERT_VALUES);CHKERRQ(ierr);
1884     }
1885     ierr = MatRestoreRowIJ(cMat,0,PETSC_FALSE,PETSC_FALSE,&nRows,&ia,&ja,&done);CHKERRQ(ierr);
1886     if (!done) SETERRQ(PetscObjectComm((PetscObject)cMat),PETSC_ERR_PLIB,"Could not restore RowIJ of constraint matrix");
1887     ierr = MatAssemblyBegin(cMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1888     ierr = MatAssemblyEnd(cMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1889     ierr = PetscFree(vals);CHKERRQ(ierr);
1890   }
1891 
1892   /* clean up */
1893   ierr = ISRestoreIndices(anIS,&anchors);CHKERRQ(ierr);
1894   ierr = PetscFree2(perm,iperm);CHKERRQ(ierr);
1895   ierr = PetscFree(pointWork);CHKERRQ(ierr);
1896   ierr = DMPlexReferenceTreeRestoreChildrenMatrices(refTree,&refPointFieldMats,&refPointFieldN);CHKERRQ(ierr);
1897   PetscFunctionReturn(0);
1898 }
1899 
1900 #undef __FUNCT__
1901 #define __FUNCT__ "DMPlexTreeRefineCell"
1902 /* refine a single cell on rank 0: this is not intended to provide good local refinement, only to create an example of
1903  * a non-conforming mesh.  Local refinement comes later */
1904 PetscErrorCode DMPlexTreeRefineCell (DM dm, PetscInt cell, DM *ncdm)
1905 {
1906   DM K;
1907   PetscMPIInt rank;
1908   PetscInt dim, *pNewStart, *pNewEnd, *pNewCount, *pOldStart, *pOldEnd, offset, d, pStart, pEnd;
1909   PetscInt numNewCones, *newConeSizes, *newCones, *newOrientations;
1910   PetscInt *Kembedding;
1911   PetscInt *cellClosure=NULL, nc;
1912   PetscScalar *newVertexCoords;
1913   PetscInt numPointsWithParents, *parents, *childIDs, *perm, *iperm, *preOrient, pOffset;
1914   PetscSection parentSection;
1915   PetscErrorCode ierr;
1916 
1917   PetscFunctionBegin;
1918   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm),&rank);CHKERRQ(ierr);
1919   ierr = DMGetDimension(dm,&dim);CHKERRQ(ierr);
1920   ierr = DMPlexCreate(PetscObjectComm((PetscObject)dm), ncdm);CHKERRQ(ierr);
1921   ierr = DMSetDimension(*ncdm,dim);CHKERRQ(ierr);
1922 
1923   ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
1924   ierr = PetscSectionCreate(PetscObjectComm((PetscObject)dm),&parentSection);CHKERRQ(ierr);
1925   ierr = DMPlexGetReferenceTree(dm,&K);CHKERRQ(ierr);
1926   if (!rank) {
1927     /* compute the new charts */
1928     ierr = PetscMalloc5(dim+1,&pNewCount,dim+1,&pNewStart,dim+1,&pNewEnd,dim+1,&pOldStart,dim+1,&pOldEnd);CHKERRQ(ierr);
1929     offset = 0;
1930     for (d = 0; d <= dim; d++) {
1931       PetscInt pOldCount, kStart, kEnd, k;
1932 
1933       pNewStart[d] = offset;
1934       ierr = DMPlexGetHeightStratum(dm,d,&pOldStart[d],&pOldEnd[d]);CHKERRQ(ierr);
1935       ierr = DMPlexGetHeightStratum(K,d,&kStart,&kEnd);CHKERRQ(ierr);
1936       pOldCount = pOldEnd[d] - pOldStart[d];
1937       /* adding the new points */
1938       pNewCount[d] = pOldCount + kEnd - kStart;
1939       if (!d) {
1940         /* removing the cell */
1941         pNewCount[d]--;
1942       }
1943       for (k = kStart; k < kEnd; k++) {
1944         PetscInt parent;
1945         ierr = DMPlexGetTreeParent(K,k,&parent,NULL);CHKERRQ(ierr);
1946         if (parent == k) {
1947           /* avoid double counting points that won't actually be new */
1948           pNewCount[d]--;
1949         }
1950       }
1951       pNewEnd[d] = pNewStart[d] + pNewCount[d];
1952       offset = pNewEnd[d];
1953 
1954     }
1955     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]);
1956     /* get the current closure of the cell that we are removing */
1957     ierr = DMPlexGetTransitiveClosure(dm,cell,PETSC_TRUE,&nc,&cellClosure);CHKERRQ(ierr);
1958 
1959     ierr = PetscMalloc1(pNewEnd[dim],&newConeSizes);CHKERRQ(ierr);
1960     {
1961       PetscInt kStart, kEnd, k, closureSizeK, *closureK = NULL, j;
1962 
1963       ierr = DMPlexGetChart(K,&kStart,&kEnd);CHKERRQ(ierr);
1964       ierr = PetscMalloc4(kEnd-kStart,&Kembedding,kEnd-kStart,&perm,kEnd-kStart,&iperm,kEnd-kStart,&preOrient);CHKERRQ(ierr);
1965 
1966       for (k = kStart; k < kEnd; k++) {
1967         perm[k - kStart] = k;
1968         iperm [k - kStart] = k - kStart;
1969         preOrient[k - kStart] = 0;
1970       }
1971 
1972       ierr = DMPlexGetTransitiveClosure(K,0,PETSC_TRUE,&closureSizeK,&closureK);CHKERRQ(ierr);
1973       for (j = 1; j < closureSizeK; j++) {
1974         PetscInt parentOrientA = closureK[2*j+1];
1975         PetscInt parentOrientB = cellClosure[2*j+1];
1976         PetscInt p, q;
1977 
1978         p = closureK[2*j];
1979         q = cellClosure[2*j];
1980         for (d = 0; d <= dim; d++) {
1981           if (q >= pOldStart[d] && q < pOldEnd[d]) {
1982             Kembedding[p] = (q - pOldStart[d]) + pNewStart[d];
1983           }
1984         }
1985         if (parentOrientA != parentOrientB) {
1986           PetscInt numChildren, i;
1987           const PetscInt *children;
1988 
1989           ierr = DMPlexGetTreeChildren(K,p,&numChildren,&children);CHKERRQ(ierr);
1990           for (i = 0; i < numChildren; i++) {
1991             PetscInt kPerm, oPerm;
1992 
1993             k    = children[i];
1994             ierr = DMPlexReferenceTreeGetChildSymmetry(K,p,parentOrientA,0,k,parentOrientB,&oPerm,&kPerm);CHKERRQ(ierr);
1995             /* perm = what refTree position I'm in */
1996             perm[kPerm-kStart]      = k;
1997             /* iperm = who is at this position */
1998             iperm[k-kStart]         = kPerm-kStart;
1999             preOrient[kPerm-kStart] = oPerm;
2000           }
2001         }
2002       }
2003       ierr = DMPlexRestoreTransitiveClosure(K,0,PETSC_TRUE,&closureSizeK,&closureK);CHKERRQ(ierr);
2004     }
2005     ierr = PetscSectionSetChart(parentSection,0,pNewEnd[dim]);CHKERRQ(ierr);
2006     offset = 0;
2007     numNewCones = 0;
2008     for (d = 0; d <= dim; d++) {
2009       PetscInt kStart, kEnd, k;
2010       PetscInt p;
2011       PetscInt size;
2012 
2013       for (p = pOldStart[d]; p < pOldEnd[d]; p++) {
2014         /* skip cell 0 */
2015         if (p == cell) continue;
2016         /* old cones to new cones */
2017         ierr = DMPlexGetConeSize(dm,p,&size);CHKERRQ(ierr);
2018         newConeSizes[offset++] = size;
2019         numNewCones += size;
2020       }
2021 
2022       ierr = DMPlexGetHeightStratum(K,d,&kStart,&kEnd);CHKERRQ(ierr);
2023       for (k = kStart; k < kEnd; k++) {
2024         PetscInt kParent;
2025 
2026         ierr = DMPlexGetTreeParent(K,k,&kParent,NULL);CHKERRQ(ierr);
2027         if (kParent != k) {
2028           Kembedding[k] = offset;
2029           ierr = DMPlexGetConeSize(K,k,&size);CHKERRQ(ierr);
2030           newConeSizes[offset++] = size;
2031           numNewCones += size;
2032           if (kParent != 0) {
2033             ierr = PetscSectionSetDof(parentSection,Kembedding[k],1);CHKERRQ(ierr);
2034           }
2035         }
2036       }
2037     }
2038 
2039     ierr = PetscSectionSetUp(parentSection);CHKERRQ(ierr);
2040     ierr = PetscSectionGetStorageSize(parentSection,&numPointsWithParents);CHKERRQ(ierr);
2041     ierr = PetscMalloc2(numNewCones,&newCones,numNewCones,&newOrientations);CHKERRQ(ierr);
2042     ierr = PetscMalloc2(numPointsWithParents,&parents,numPointsWithParents,&childIDs);CHKERRQ(ierr);
2043 
2044     /* fill new cones */
2045     offset = 0;
2046     for (d = 0; d <= dim; d++) {
2047       PetscInt kStart, kEnd, k, l;
2048       PetscInt p;
2049       PetscInt size;
2050       const PetscInt *cone, *orientation;
2051 
2052       for (p = pOldStart[d]; p < pOldEnd[d]; p++) {
2053         /* skip cell 0 */
2054         if (p == cell) continue;
2055         /* old cones to new cones */
2056         ierr = DMPlexGetConeSize(dm,p,&size);CHKERRQ(ierr);
2057         ierr = DMPlexGetCone(dm,p,&cone);CHKERRQ(ierr);
2058         ierr = DMPlexGetConeOrientation(dm,p,&orientation);CHKERRQ(ierr);
2059         for (l = 0; l < size; l++) {
2060           newCones[offset]          = (cone[l] - pOldStart[d + 1]) + pNewStart[d + 1];
2061           newOrientations[offset++] = orientation[l];
2062         }
2063       }
2064 
2065       ierr = DMPlexGetHeightStratum(K,d,&kStart,&kEnd);CHKERRQ(ierr);
2066       for (k = kStart; k < kEnd; k++) {
2067         PetscInt kPerm = perm[k], kParent;
2068         PetscInt preO  = preOrient[k];
2069 
2070         ierr = DMPlexGetTreeParent(K,k,&kParent,NULL);CHKERRQ(ierr);
2071         if (kParent != k) {
2072           /* embed new cones */
2073           ierr = DMPlexGetConeSize(K,k,&size);CHKERRQ(ierr);
2074           ierr = DMPlexGetCone(K,kPerm,&cone);CHKERRQ(ierr);
2075           ierr = DMPlexGetConeOrientation(K,kPerm,&orientation);CHKERRQ(ierr);
2076           for (l = 0; l < size; l++) {
2077             PetscInt q, m = (preO >= 0) ? ((preO + l) % size) : ((size -(preO + 1) - l) % size);
2078             PetscInt newO, lSize, oTrue;
2079 
2080             q                         = iperm[cone[m]];
2081             newCones[offset]          = Kembedding[q];
2082             ierr                      = DMPlexGetConeSize(K,q,&lSize);CHKERRQ(ierr);
2083             oTrue                     = orientation[m];
2084             oTrue                     = ((!lSize) || (preOrient[k] >= 0)) ? oTrue : -(oTrue + 2);
2085             newO                      = DihedralCompose(lSize,oTrue,preOrient[q]);
2086             newOrientations[offset++] = newO;
2087           }
2088           if (kParent != 0) {
2089             PetscInt newPoint = Kembedding[kParent];
2090             ierr              = PetscSectionGetOffset(parentSection,Kembedding[k],&pOffset);CHKERRQ(ierr);
2091             parents[pOffset]  = newPoint;
2092             childIDs[pOffset] = k;
2093           }
2094         }
2095       }
2096     }
2097 
2098     ierr = PetscMalloc1(dim*(pNewEnd[dim]-pNewStart[dim]),&newVertexCoords);CHKERRQ(ierr);
2099 
2100     /* fill coordinates */
2101     offset = 0;
2102     {
2103       PetscInt kStart, kEnd, l;
2104       PetscSection vSection;
2105       PetscInt v;
2106       Vec coords;
2107       PetscScalar *coordvals;
2108       PetscInt dof, off;
2109       PetscReal v0[3], J[9], detJ;
2110 
2111 #if defined(PETSC_USE_DEBUG)
2112       {
2113         PetscInt k;
2114         ierr = DMPlexGetHeightStratum(K,0,&kStart,&kEnd);CHKERRQ(ierr);
2115         for (k = kStart; k < kEnd; k++) {
2116           ierr = DMPlexComputeCellGeometryFEM(K, k, NULL, v0, J, NULL, &detJ);CHKERRQ(ierr);
2117           if (detJ <= 0.) SETERRQ1 (PETSC_COMM_SELF,PETSC_ERR_PLIB,"reference tree cell %d has bad determinant",k);
2118         }
2119       }
2120 #endif
2121       ierr = DMPlexComputeCellGeometryFEM(dm, cell, NULL, v0, J, NULL, &detJ);CHKERRQ(ierr);
2122       ierr = DMGetCoordinateSection(dm,&vSection);CHKERRQ(ierr);
2123       ierr = DMGetCoordinatesLocal(dm,&coords);CHKERRQ(ierr);
2124       ierr = VecGetArray(coords,&coordvals);CHKERRQ(ierr);
2125       for (v = pOldStart[dim]; v < pOldEnd[dim]; v++) {
2126 
2127         ierr = PetscSectionGetDof(vSection,v,&dof);CHKERRQ(ierr);
2128         ierr = PetscSectionGetOffset(vSection,v,&off);CHKERRQ(ierr);
2129         for (l = 0; l < dof; l++) {
2130           newVertexCoords[offset++] = coordvals[off + l];
2131         }
2132       }
2133       ierr = VecRestoreArray(coords,&coordvals);CHKERRQ(ierr);
2134 
2135       ierr = DMGetCoordinateSection(K,&vSection);CHKERRQ(ierr);
2136       ierr = DMGetCoordinatesLocal(K,&coords);CHKERRQ(ierr);
2137       ierr = VecGetArray(coords,&coordvals);CHKERRQ(ierr);
2138       ierr = DMPlexGetDepthStratum(K,0,&kStart,&kEnd);CHKERRQ(ierr);
2139       for (v = kStart; v < kEnd; v++) {
2140         PetscReal coord[3], newCoord[3];
2141         PetscInt  vPerm = perm[v];
2142         PetscInt  kParent;
2143 
2144         ierr = DMPlexGetTreeParent(K,v,&kParent,NULL);CHKERRQ(ierr);
2145         if (kParent != v) {
2146           /* this is a new vertex */
2147           ierr = PetscSectionGetOffset(vSection,vPerm,&off);CHKERRQ(ierr);
2148           for (l = 0; l < dim; ++l) coord[l] = PetscRealPart(coordvals[off+l]);
2149           CoordinatesRefToReal(dim, dim, v0, J, coord, newCoord);CHKERRQ(ierr);
2150           for (l = 0; l < dim; ++l) newVertexCoords[offset+l] = newCoord[l];
2151           offset += dim;
2152         }
2153       }
2154       ierr = VecRestoreArray(coords,&coordvals);CHKERRQ(ierr);
2155     }
2156 
2157     /* need to reverse the order of pNewCount: vertices first, cells last */
2158     for (d = 0; d < (dim + 1) / 2; d++) {
2159       PetscInt tmp;
2160 
2161       tmp = pNewCount[d];
2162       pNewCount[d] = pNewCount[dim - d];
2163       pNewCount[dim - d] = tmp;
2164     }
2165 
2166     ierr = DMPlexCreateFromDAG(*ncdm,dim,pNewCount,newConeSizes,newCones,newOrientations,newVertexCoords);CHKERRQ(ierr);
2167     ierr = DMPlexSetReferenceTree(*ncdm,K);CHKERRQ(ierr);
2168     ierr = DMPlexSetTree(*ncdm,parentSection,parents,childIDs);CHKERRQ(ierr);
2169 
2170     /* clean up */
2171     ierr = DMPlexRestoreTransitiveClosure(dm,cell,PETSC_TRUE,&nc,&cellClosure);CHKERRQ(ierr);
2172     ierr = PetscFree5(pNewCount,pNewStart,pNewEnd,pOldStart,pOldEnd);CHKERRQ(ierr);
2173     ierr = PetscFree(newConeSizes);CHKERRQ(ierr);
2174     ierr = PetscFree2(newCones,newOrientations);CHKERRQ(ierr);
2175     ierr = PetscFree(newVertexCoords);CHKERRQ(ierr);
2176     ierr = PetscFree2(parents,childIDs);CHKERRQ(ierr);
2177     ierr = PetscFree4(Kembedding,perm,iperm,preOrient);CHKERRQ(ierr);
2178   }
2179   else {
2180     PetscInt    p, counts[4];
2181     PetscInt    *coneSizes, *cones, *orientations;
2182     Vec         coordVec;
2183     PetscScalar *coords;
2184 
2185     for (d = 0; d <= dim; d++) {
2186       PetscInt dStart, dEnd;
2187 
2188       ierr = DMPlexGetDepthStratum(dm,d,&dStart,&dEnd);CHKERRQ(ierr);
2189       counts[d] = dEnd - dStart;
2190     }
2191     ierr = PetscMalloc1(pEnd-pStart,&coneSizes);CHKERRQ(ierr);
2192     for (p = pStart; p < pEnd; p++) {
2193       ierr = DMPlexGetConeSize(dm,p,&coneSizes[p-pStart]);CHKERRQ(ierr);
2194     }
2195     ierr = DMPlexGetCones(dm, &cones);CHKERRQ(ierr);
2196     ierr = DMPlexGetConeOrientations(dm, &orientations);CHKERRQ(ierr);
2197     ierr = DMGetCoordinatesLocal(dm,&coordVec);CHKERRQ(ierr);
2198     ierr = VecGetArray(coordVec,&coords);CHKERRQ(ierr);
2199 
2200     ierr = PetscSectionSetChart(parentSection,pStart,pEnd);CHKERRQ(ierr);
2201     ierr = PetscSectionSetUp(parentSection);CHKERRQ(ierr);
2202     ierr = DMPlexCreateFromDAG(*ncdm,dim,counts,coneSizes,cones,orientations,NULL);CHKERRQ(ierr);
2203     ierr = DMPlexSetReferenceTree(*ncdm,K);CHKERRQ(ierr);
2204     ierr = DMPlexSetTree(*ncdm,parentSection,NULL,NULL);CHKERRQ(ierr);
2205     ierr = VecRestoreArray(coordVec,&coords);CHKERRQ(ierr);
2206   }
2207   ierr = PetscSectionDestroy(&parentSection);CHKERRQ(ierr);
2208 
2209   PetscFunctionReturn(0);
2210 }
2211 
2212 PETSC_EXTERN PetscErrorCode indicesPointFields_private(PetscSection,PetscInt,PetscInt,PetscInt[],PetscBool,PetscInt,PetscInt[]);
2213 PETSC_EXTERN PetscErrorCode indicesPoint_private(PetscSection,PetscInt,PetscInt,PetscInt *,PetscBool,PetscInt,PetscInt[]);
2214 
2215 #undef __FUNCT__
2216 #define __FUNCT__ "DMPlexComputeInterpolatorTree"
2217 PetscErrorCode DMPlexComputeInterpolatorTree(DM coarse, DM fine, PetscSF coarseToFine, PetscInt *childIds, Mat mat)
2218 {
2219   PetscSF        coarseToFineEmbedded;
2220   PetscSection   globalCoarse, globalFine;
2221   PetscSection   localCoarse, localFine;
2222   PetscSection   aSec, cSec;
2223   PetscSection   rootIndicesSec, rootMatricesSec;
2224   PetscSection   leafIndicesSec, leafMatricesSec;
2225   PetscInt       *rootIndices, *leafIndices;
2226   PetscScalar    *rootMatrices, *leafMatrices;
2227   IS             aIS;
2228   const PetscInt *anchors;
2229   Mat            cMat;
2230   PetscInt       numFields;
2231   PetscInt       pStartC, pEndC, pStartF, pEndF, p;
2232   PetscInt       aStart, aEnd, cStart, cEnd;
2233   PetscInt       *maxChildIds;
2234   PetscInt       *offsets, *newOffsets, *offsetsCopy, *newOffsetsCopy, *rowOffsets, *numD, *numO;
2235   PetscErrorCode ierr;
2236 
2237   PetscFunctionBegin;
2238   ierr = DMPlexGetChart(coarse,&pStartC,&pEndC);CHKERRQ(ierr);
2239   ierr = DMPlexGetChart(fine,&pStartF,&pEndF);CHKERRQ(ierr);
2240   ierr = DMGetDefaultGlobalSection(fine,&globalFine);CHKERRQ(ierr);
2241   { /* winnow fine points that don't have global dofs out of the sf */
2242     PetscInt dof, cdof, numPointsWithDofs, offset, *pointsWithDofs;
2243 
2244     for (p = pStartF, numPointsWithDofs = 0; p < pEndF; p++) {
2245       ierr = PetscSectionGetDof(globalFine,p,&dof);CHKERRQ(ierr);
2246       ierr = PetscSectionGetConstraintDof(globalFine,p,&cdof);CHKERRQ(ierr);
2247       if ((dof - cdof) > 0) {
2248         numPointsWithDofs++;
2249       }
2250     }
2251     ierr = PetscMalloc1(numPointsWithDofs,&pointsWithDofs);CHKERRQ(ierr);
2252     for (p = pStartF, offset = 0; p < pEndF; p++) {
2253       ierr = PetscSectionGetDof(globalFine,p,&dof);CHKERRQ(ierr);
2254       ierr = PetscSectionGetConstraintDof(globalFine,p,&cdof);CHKERRQ(ierr);
2255       if ((dof - cdof) > 0) {
2256         pointsWithDofs[offset++] = p - pStartF;
2257       }
2258     }
2259     ierr = PetscSFCreateEmbeddedLeafSF(coarseToFine, numPointsWithDofs, pointsWithDofs, &coarseToFineEmbedded);CHKERRQ(ierr);
2260   }
2261   /* communicate back to the coarse mesh which coarse points have children (that may require interpolation) */
2262   ierr = PetscMalloc1(pEndC-pStartC,&maxChildIds);CHKERRQ(ierr);
2263   for (p = pStartC; p < pEndC; p++) {
2264     maxChildIds[p - pStartC] = -1;
2265   }
2266   ierr = PetscSFReduceBegin(coarseToFineEmbedded,MPIU_INT,childIds,maxChildIds,MPIU_MAX);CHKERRQ(ierr);
2267   ierr = PetscSFReduceEnd(coarseToFineEmbedded,MPIU_INT,childIds,maxChildIds,MPIU_MAX);CHKERRQ(ierr);
2268 
2269   ierr = DMGetDefaultSection(coarse,&localCoarse);CHKERRQ(ierr);
2270   ierr = DMGetDefaultGlobalSection(coarse,&globalCoarse);CHKERRQ(ierr);
2271 
2272   ierr = DMPlexGetAnchors(coarse,&aSec,&aIS);CHKERRQ(ierr);
2273   ierr = ISGetIndices(aIS,&anchors);CHKERRQ(ierr);
2274   ierr = PetscSectionGetChart(aSec,&aStart,&aEnd);CHKERRQ(ierr);
2275 
2276   ierr = DMGetDefaultConstraints(coarse,&cSec,&cMat);CHKERRQ(ierr);
2277   ierr = PetscSectionGetChart(cSec,&cStart,&cEnd);CHKERRQ(ierr);
2278 
2279   /* create sections that will send to children the indices and matrices they will need to construct the interpolator */
2280   ierr = PetscSectionCreate(PetscObjectComm((PetscObject)coarse),&rootIndicesSec);CHKERRQ(ierr);
2281   ierr = PetscSectionCreate(PetscObjectComm((PetscObject)coarse),&rootMatricesSec);CHKERRQ(ierr);
2282   ierr = PetscSectionSetChart(rootIndicesSec,pStartC,pEndC);CHKERRQ(ierr);
2283   ierr = PetscSectionSetChart(rootMatricesSec,pStartC,pEndC);CHKERRQ(ierr);
2284   ierr = PetscSectionGetNumFields(globalCoarse,&numFields);CHKERRQ(ierr);
2285   {
2286     PetscInt maxFields = PetscMax(1,numFields);CHKERRQ(ierr);
2287     ierr = PetscMalloc7(maxFields,&offsets,maxFields,&offsetsCopy,maxFields,&newOffsets,maxFields,&newOffsetsCopy,maxFields,&rowOffsets,maxFields,&numD,maxFields,&numO);CHKERRQ(ierr);
2288   }
2289 
2290   for (p = pStartC; p < pEndC; p++) { /* count the sizes of the indices and matrices */
2291     PetscInt dof, matSize;
2292     PetscInt aDof           = 0;
2293     PetscInt cDof           = 0;
2294     PetscInt maxChildId     = maxChildIds[p - pStartC];
2295     PetscInt numRowIndices  = 0;
2296     PetscInt numColIndices  = 0;
2297 
2298     ierr = PetscSectionGetDof(globalCoarse,p,&dof);CHKERRQ(ierr);
2299     if (p >= aStart && p < aEnd) {
2300       ierr = PetscSectionGetDof(aSec,p,&aDof);CHKERRQ(ierr);
2301     }
2302     if (p >= cStart && p < cEnd) {
2303       ierr = PetscSectionGetDof(cSec,p,&cDof);CHKERRQ(ierr);
2304     }
2305     offsets[0]    = 0;
2306     newOffsets[0] = 0;
2307     if (maxChildId >= 0) { /* this point has children (with dofs) that will need to be interpolated from the closure of p */
2308       PetscInt *closure = NULL, closureSize, cl, f;
2309 
2310       ierr = DMPlexGetTransitiveClosure(coarse,p,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
2311       for (cl = 0; cl < closureSize; cl++) { /* get the closure */
2312         PetscInt c = closure[2 * cl], clDof;
2313 
2314         ierr = PetscSectionGetDof(localCoarse,c,&clDof);CHKERRQ(ierr);
2315         numRowIndices += clDof;
2316         for (f = 0; f < numFields; f++) {
2317           ierr = PetscSectionGetFieldDof(localCoarse,c,f,&clDof);CHKERRQ(ierr);
2318           offsets[f + 1] += clDof;
2319         }
2320       }
2321       for (f = 0; f < numFields; f++) {
2322         offsets[f + 1]   += offsets[f];
2323         newOffsets[f + 1] = offsets[f + 1];
2324       }
2325       /* get the number of indices needed and their field offsets */
2326       ierr = DMPlexAnchorsModifyMat(coarse,localCoarse,closureSize,numRowIndices,closure,NULL,NULL,&numColIndices,NULL,NULL,newOffsets,PETSC_FALSE);CHKERRQ(ierr);
2327       ierr = DMPlexRestoreTransitiveClosure(coarse,p,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
2328       if (!numColIndices) { /* there are no hanging constraint modifications, so the matrix is just the identity: do not send it */
2329         numColIndices = numRowIndices;
2330         matSize = 0;
2331       }
2332       else if (numFields) { /* we send one submat for each field: sum their sizes */
2333         matSize = 0;
2334         for (f = 0; f < numFields; f++) {
2335           PetscInt numRow, numCol;
2336 
2337           numRow = offsets[f + 1] - offsets[f];
2338           numCol = newOffsets[f + 1] - newOffsets[f + 1];
2339           matSize += numRow * numCol;
2340         }
2341       }
2342       else {
2343         matSize = numRowIndices * numColIndices;
2344       }
2345     }
2346     else if (cDof > 0) { /* this point's dofs are interpolated via cMat: get the submatrix of cMat */
2347       PetscInt aOff, a, f;
2348 
2349       ierr = PetscSectionGetOffset(aSec,p,&aOff);CHKERRQ(ierr);
2350       for (f = 0; f < numFields; f++) {
2351         PetscInt fDof;
2352 
2353         ierr = PetscSectionGetFieldDof(localCoarse,p,f,&fDof);CHKERRQ(ierr);
2354         offsets[f+1] = fDof;
2355       }
2356       for (a = 0; a < aDof; a++) {
2357         PetscInt anchor = anchors[a + aOff], aLocalDof;
2358 
2359         ierr = PetscSectionGetDof(localCoarse,anchor,&aLocalDof);CHKERRQ(ierr);
2360         numColIndices += aLocalDof;
2361         for (f = 0; f < numFields; f++) {
2362           PetscInt fDof;
2363 
2364           ierr = PetscSectionGetFieldDof(localCoarse,anchor,f,&fDof);CHKERRQ(ierr);
2365           newOffsets[f+1] += fDof;
2366         }
2367       }
2368       if (numFields) {
2369         matSize = 0;
2370         for (f = 0; f < numFields; f++) {
2371           matSize += offsets[f+1] * newOffsets[f+1];
2372         }
2373       }
2374       else {
2375         matSize = numColIndices * dof;
2376       }
2377     }
2378     else { /* no children, and no constraints on dofs: just get the global indices */
2379       numColIndices = dof;
2380       matSize       = 0;
2381     }
2382     /* we will pack the column indices with the field offsets */
2383     ierr = PetscSectionSetDof(rootIndicesSec,p,numColIndices ? numColIndices+2*numFields : 0);CHKERRQ(ierr);
2384     ierr = PetscSectionSetDof(rootMatricesSec,p,matSize);CHKERRQ(ierr);
2385   }
2386   ierr = PetscSectionSetUp(rootIndicesSec);CHKERRQ(ierr);
2387   ierr = PetscSectionSetUp(rootMatricesSec);CHKERRQ(ierr);
2388   {
2389     PetscInt    numRootIndices, numRootMatrices;
2390 
2391     ierr = PetscSectionGetStorageSize(rootIndicesSec,&numRootIndices);CHKERRQ(ierr);
2392     ierr = PetscSectionGetStorageSize(rootMatricesSec,&numRootMatrices);CHKERRQ(ierr);
2393     ierr = PetscMalloc2(numRootIndices,&rootIndices,numRootMatrices,&rootMatrices);CHKERRQ(ierr);
2394     for (p = pStartC; p < pEndC; p++) {
2395       PetscInt    numRowIndices, numColIndices, matSize, dof;
2396       PetscInt    pIndOff, pMatOff;
2397       PetscInt    *pInd;
2398       PetscInt    maxChildId = maxChildIds[p - pStartC];
2399       PetscScalar *pMat = NULL;
2400 
2401       ierr = PetscSectionGetDof(rootIndicesSec,p,&numColIndices);CHKERRQ(ierr);
2402       if (!numColIndices) {
2403         continue;
2404       }
2405       offsets[0]        = 0;
2406       newOffsets[0]     = 0;
2407       offsetsCopy[0]    = 0;
2408       newOffsetsCopy[0] = 0;
2409       numColIndices -= 2 * numFields;
2410       ierr = PetscSectionGetOffset(rootIndicesSec,p,&pIndOff);CHKERRQ(ierr);
2411       pInd = &(rootIndices[pIndOff]);
2412       ierr = PetscSectionGetDof(rootMatricesSec,p,&matSize);CHKERRQ(ierr);
2413       if (matSize) {
2414         ierr = PetscSectionGetOffset(rootMatricesSec,p,&pMatOff);CHKERRQ(ierr);
2415         pMat = &rootMatrices[pMatOff];
2416       }
2417       ierr = PetscSectionGetDof(globalCoarse,p,&dof);CHKERRQ(ierr);
2418       if (maxChildId >= 0) { /* build an identity matrix, apply matrix constraints on the right */
2419         PetscInt i, j;
2420         PetscInt numRowIndices = matSize / numColIndices;
2421 
2422         if (!numRowIndices) { /* don't need to calculate the mat, just the indices */
2423           PetscInt numIndices, *indices;
2424           ierr = DMPlexGetClosureIndices(coarse,localCoarse,globalCoarse,p,&numIndices,&indices,offsets);CHKERRQ(ierr);
2425           if (numIndices != numColIndices) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"mismatching constraint indices calculations");
2426           for (i = 0; i < numColIndices; i++) {
2427             pInd[i] = indices[i];
2428           }
2429           for (i = 0; i < numFields; i++) {
2430             pInd[numColIndices + i]             = offsets[i+1];
2431             pInd[numColIndices + numFields + i] = offsets[i+1];
2432           }
2433           ierr = DMPlexRestoreClosureIndices(coarse,localCoarse,globalCoarse,p,&numIndices,&indices,offsets);CHKERRQ(ierr);
2434         }
2435         else {
2436           PetscInt closureSize, *closure = NULL, cl;
2437           PetscScalar *pMatIn, *pMatModified;
2438           PetscInt numPoints,*points;
2439 
2440           ierr = DMGetWorkArray(coarse,numRowIndices * numRowIndices,PETSC_SCALAR,&pMatIn);CHKERRQ(ierr);
2441           for (i = 0; i < numRowIndices; i++) { /* initialize to the identity */
2442             for (j = 0; j < numRowIndices; j++) {
2443               pMatIn[i * numRowIndices + j] = (i == j) ? 1. : 0.;
2444             }
2445           }
2446           ierr = DMPlexGetTransitiveClosure(coarse, p, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
2447           if (numFields) {
2448             PetscInt f;
2449 
2450             for (cl = 0; cl < closureSize; cl++) {
2451               PetscInt c = closure[2 * cl];
2452 
2453               for (f = 0; f < numFields; f++) {
2454                 PetscInt fDof;
2455 
2456                 ierr = PetscSectionGetFieldDof(localCoarse,c,f,&fDof);CHKERRQ(ierr);
2457                 offsets[f + 1] += fDof;
2458               }
2459             }
2460             for (f = 0; f < numFields; f++) {
2461               offsets[f + 1]   += offsets[f];
2462               newOffsets[f + 1] = offsets[f + 1];
2463             }
2464           }
2465           /* apply hanging node constraints on the right, get the new points and the new offsets */
2466           ierr = DMPlexAnchorsModifyMat(coarse,localCoarse,closureSize,numRowIndices,closure,pMat,&numPoints,NULL,&points,&pMatModified,newOffsets,PETSC_FALSE);CHKERRQ(ierr);
2467           if (!numFields) {
2468             for (i = 0; i < numRowIndices * numColIndices; i++) {
2469               pMat[i] = pMatModified[i];
2470             }
2471           }
2472           else {
2473             PetscInt f, i, j, count;
2474             for (f = 0, count = 0; f < numFields; f++) {
2475               for (i = offsets[f]; i < offsets[f+1]; i++) {
2476                 for (j = newOffsets[f]; j < newOffsets[f+1]; j++, count++) {
2477                   pMat[count] = pMatModified[i * numColIndices + j];
2478                 }
2479               }
2480             }
2481           }
2482           ierr = DMRestoreWorkArray(coarse,numRowIndices * numColIndices,PETSC_SCALAR,&pMatModified);CHKERRQ(ierr);
2483           ierr = DMPlexRestoreTransitiveClosure(coarse, p, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
2484           ierr = DMRestoreWorkArray(coarse,numRowIndices * numColIndices,PETSC_SCALAR,&pMatIn);CHKERRQ(ierr);
2485           if (numFields) {
2486             PetscInt f;
2487             for (f = 0; f < numFields; f++) {
2488               pInd[numColIndices + f]             = offsets[f+1];
2489               pInd[numColIndices + numFields + f] = newOffsets[f+1];
2490             }
2491             for (cl = 0; cl < numPoints*2; cl += 2) {
2492               PetscInt o = points[cl+1], globalOff, c = points[cl];
2493               ierr = PetscSectionGetOffset(globalCoarse, c, &globalOff);CHKERRQ(ierr);
2494               indicesPointFields_private(localCoarse, c, globalOff < 0 ? -(globalOff+1) : globalOff, newOffsets, PETSC_FALSE, o, pInd);
2495             }
2496           } else {
2497             for (cl = 0; cl < numPoints*2; cl += 2) {
2498               PetscInt o = points[cl+1], c = points[cl], globalOff;
2499               ierr = PetscSectionGetOffset(globalCoarse, c, &globalOff);CHKERRQ(ierr);
2500               indicesPoint_private(localCoarse, c, globalOff < 0 ? -(globalOff+1) : globalOff, newOffsets, PETSC_FALSE, o, pInd);
2501             }
2502           }
2503         }
2504       }
2505       else if (matSize) {
2506         PetscInt cOff;
2507         PetscInt *rowIndices, *colIndices, a, aDof, aOff;
2508 
2509         numRowIndices = matSize / numColIndices;
2510         if (numRowIndices != dof) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Miscounted dofs");
2511         ierr = DMGetWorkArray(coarse,numRowIndices,PETSC_INT,&rowIndices);CHKERRQ(ierr);
2512         ierr = DMGetWorkArray(coarse,numColIndices,PETSC_INT,&colIndices);CHKERRQ(ierr);
2513         ierr = PetscSectionGetOffset(cSec,p,&cOff);CHKERRQ(ierr);
2514         ierr = PetscSectionGetDof(aSec,p,&aDof);CHKERRQ(ierr);
2515         ierr = PetscSectionGetOffset(aSec,p,&aOff);CHKERRQ(ierr);
2516         if (numFields) {
2517           PetscInt f;
2518 
2519           for (f = 0; f < numFields; f++) {
2520             PetscInt fDof;
2521             ierr = PetscSectionGetFieldDof(cSec,p,f,&fDof);CHKERRQ(ierr);
2522             offsets[f + 1] = fDof;
2523             for (a = 0; a < aDof; a++) {
2524               PetscInt anchor = anchors[a + aOff];
2525               ierr = PetscSectionGetFieldDof(localCoarse,anchor,f,&fDof);CHKERRQ(ierr);
2526               newOffsets[f + 1] += fDof;
2527             }
2528           }
2529           for (f = 0; f < numFields; f++) {
2530             offsets[f + 1]       += offsets[f];
2531             offsetsCopy[f + 1]    = offsets[f + 1];
2532             newOffsets[f + 1]    += newOffsets[f];
2533             newOffsetsCopy[f + 1] = newOffsets[f + 1];
2534           }
2535           indicesPointFields_private(cSec,p,cOff,offsetsCopy,PETSC_TRUE,0,rowIndices);CHKERRQ(ierr);
2536           for (a = 0; a < aDof; a++) {
2537             PetscInt anchor = anchors[a + aOff], lOff;
2538             ierr = PetscSectionGetOffset(localCoarse,anchor,&lOff);CHKERRQ(ierr);
2539             indicesPointFields_private(localCoarse,anchor,lOff,newOffsetsCopy,PETSC_TRUE,0,colIndices);CHKERRQ(ierr);
2540           }
2541         }
2542         else {
2543           indicesPoint_private(cSec,p,cOff,offsets,PETSC_TRUE,0,rowIndices);CHKERRQ(ierr);
2544           for (a = 0; a < aDof; a++) {
2545             PetscInt anchor = anchors[a + aOff], lOff;
2546             ierr = PetscSectionGetOffset(localCoarse,anchor,&lOff);CHKERRQ(ierr);
2547             indicesPoint_private(localCoarse,anchor,lOff,newOffsets,PETSC_TRUE,0,colIndices);CHKERRQ(ierr);
2548           }
2549         }
2550         if (numFields) {
2551           PetscInt count, f, a;
2552           for (f = 0, count = 0; f < numFields; f++) {
2553             PetscInt iSize = offsets[f + 1] - offsets[f];
2554             PetscInt jSize = newOffsets[f + 1] - newOffsets[f];
2555             ierr = MatGetValues(cMat,iSize,&rowIndices[offsets[f]],jSize,&colIndices[newOffsets[f]],&pMat[count]);CHKERRQ(ierr);
2556             count += iSize * jSize;
2557             pInd[numColIndices + f]             = offsets[f+1];
2558             pInd[numColIndices + numFields + f] = newOffsets[f+1];
2559           }
2560           for (a = 0; a < aDof; a++) {
2561             PetscInt anchor = anchors[a + aOff];
2562             PetscInt gOff;
2563             ierr = PetscSectionGetOffset(globalCoarse,anchor,&gOff);CHKERRQ(ierr);
2564             indicesPointFields_private(localCoarse,anchor,gOff < 0 ? -(gOff + 1) : gOff,newOffsets,PETSC_FALSE,0,pInd);CHKERRQ(ierr);
2565           }
2566         }
2567         else {
2568           PetscInt a;
2569           ierr = MatGetValues(cMat,numRowIndices,rowIndices,numColIndices,colIndices,pMat);CHKERRQ(ierr);
2570           for (a = 0; a < aDof; a++) {
2571             PetscInt anchor = anchors[a + aOff];
2572             PetscInt gOff;
2573             ierr = PetscSectionGetOffset(globalCoarse,anchor,&gOff);CHKERRQ(ierr);
2574             indicesPoint_private(localCoarse,anchor,gOff < 0 ? -(gOff + 1) : gOff,newOffsets,PETSC_FALSE,0,pInd);CHKERRQ(ierr);
2575           }
2576         }
2577         ierr = DMRestoreWorkArray(coarse,numColIndices,PETSC_INT,&colIndices);CHKERRQ(ierr);
2578         ierr = DMRestoreWorkArray(coarse,numRowIndices,PETSC_INT,&rowIndices);CHKERRQ(ierr);
2579       }
2580       else {
2581         PetscInt gOff;
2582 
2583         ierr = PetscSectionGetOffset(globalCoarse,p,&gOff);CHKERRQ(ierr);
2584         if (numFields) {
2585           PetscInt f;
2586 
2587           for (f = 0; f < numFields; f++) {
2588             PetscInt fDof;
2589             ierr = PetscSectionGetFieldDof(localCoarse,p,f,&fDof);CHKERRQ(ierr);
2590             offsets[f + 1] = fDof + offsets[f];
2591           }
2592           for (f = 0; f < numFields; f++) {
2593             pInd[numColIndices + f]             = offsets[f+1];
2594             pInd[numColIndices + numFields + f] = offsets[f+1];
2595           }
2596           indicesPointFields_private(localCoarse,p,gOff < 0 ? -(gOff + 1) : gOff,offsets,PETSC_FALSE,0,pInd);CHKERRQ(ierr);
2597         }
2598         else {
2599           indicesPoint_private(localCoarse,p,gOff < 0 ? -(gOff + 1) : gOff,offsets,PETSC_FALSE,0,pInd);CHKERRQ(ierr);
2600         }
2601       }
2602     }
2603     ierr = PetscFree(maxChildIds);CHKERRQ(ierr);
2604   }
2605   {
2606     PetscSF  indicesSF, matricesSF;
2607     PetscInt *remoteOffsetsIndices, *remoteOffsetsMatrices, numLeafIndices, numLeafMatrices;
2608 
2609     ierr = PetscSectionCreate(PetscObjectComm((PetscObject)fine),&leafIndicesSec);CHKERRQ(ierr);
2610     ierr = PetscSectionCreate(PetscObjectComm((PetscObject)fine),&leafMatricesSec);CHKERRQ(ierr);
2611     ierr = PetscSFDistributeSection(coarseToFineEmbedded,rootIndicesSec,&remoteOffsetsIndices,leafIndicesSec);CHKERRQ(ierr);
2612     ierr = PetscSFDistributeSection(coarseToFineEmbedded,rootMatricesSec,&remoteOffsetsMatrices,leafMatricesSec);CHKERRQ(ierr);
2613     ierr = PetscSFCreateSectionSF(coarseToFineEmbedded,rootIndicesSec,remoteOffsetsIndices,leafIndicesSec,&indicesSF);CHKERRQ(ierr);
2614     ierr = PetscSFCreateSectionSF(coarseToFineEmbedded,rootMatricesSec,remoteOffsetsMatrices,leafMatricesSec,&matricesSF);CHKERRQ(ierr);
2615     ierr = PetscSFDestroy(&coarseToFineEmbedded);CHKERRQ(ierr);
2616     ierr = PetscFree(remoteOffsetsIndices);CHKERRQ(ierr);
2617     ierr = PetscFree(remoteOffsetsMatrices);CHKERRQ(ierr);
2618     ierr = PetscSectionGetStorageSize(leafIndicesSec,&numLeafIndices);CHKERRQ(ierr);
2619     ierr = PetscSectionGetStorageSize(leafMatricesSec,&numLeafMatrices);CHKERRQ(ierr);
2620     ierr = PetscMalloc2(numLeafIndices,&leafIndices,numLeafMatrices,&leafMatrices);CHKERRQ(ierr);
2621     ierr = PetscSFBcastBegin(indicesSF,MPIU_INT,rootIndices,leafIndices);CHKERRQ(ierr);
2622     ierr = PetscSFBcastBegin(matricesSF,MPIU_INT,rootMatrices,leafMatrices);CHKERRQ(ierr);
2623     ierr = PetscSFBcastEnd(indicesSF,MPIU_INT,rootIndices,leafIndices);CHKERRQ(ierr);
2624     ierr = PetscSFBcastEnd(matricesSF,MPIU_INT,rootMatrices,leafMatrices);CHKERRQ(ierr);
2625     ierr = PetscSFDestroy(&matricesSF);CHKERRQ(ierr);
2626     ierr = PetscSFDestroy(&indicesSF);CHKERRQ(ierr);
2627     ierr = PetscFree2(rootIndices,rootMatrices);CHKERRQ(ierr);
2628     ierr = PetscSectionDestroy(&rootIndicesSec);CHKERRQ(ierr);
2629     ierr = PetscSectionDestroy(&rootMatricesSec);CHKERRQ(ierr);
2630   }
2631   /* count to preallocate */
2632   ierr = DMGetDefaultSection(fine,&localFine);CHKERRQ(ierr);
2633   {
2634     PetscInt    nGlobal;
2635     PetscInt    *dnnz, *onnz;
2636     PetscLayout colMap;
2637     PetscInt    colStart, colEnd;
2638     PetscInt    maxDof;
2639     PetscInt    *rowIndices;
2640     DM           refTree;
2641     PetscInt     **refPointFieldN;
2642     PetscScalar  ***refPointFieldMats;
2643     PetscSection refConSec, refAnSec;
2644     PetscInt     pRefStart,pRefEnd,maxConDof,maxAnDof;
2645     PetscScalar  *pointWork;
2646 
2647     ierr = PetscSectionGetConstrainedStorageSize(globalFine,&nGlobal);CHKERRQ(ierr);
2648     ierr = PetscCalloc2(nGlobal,&dnnz,nGlobal,&onnz);CHKERRQ(ierr);
2649     ierr = MatGetLayouts(mat,NULL,&colMap);CHKERRQ(ierr);
2650     ierr = PetscLayoutSetUp(colMap);CHKERRQ(ierr);
2651     ierr = PetscLayoutGetRange(colMap,&colStart,&colEnd);CHKERRQ(ierr);
2652     ierr = PetscSectionGetMaxDof(globalFine,&maxDof);CHKERRQ(ierr);
2653     ierr = DMGetWorkArray(fine,maxDof,PETSC_INT,&rowIndices);CHKERRQ(ierr);
2654     for (p = pStartF; p < pEndF; p++) {
2655       PetscInt    gDof, gcDof, gOff;
2656       PetscInt    numColIndices, pIndOff, *pInd;
2657       PetscInt    matSize;
2658       PetscInt    i;
2659 
2660       ierr = PetscSectionGetDof(globalFine,p,&gDof);CHKERRQ(ierr);
2661       ierr = PetscSectionGetConstraintDof(globalFine,p,&gcDof);CHKERRQ(ierr);
2662       if ((gDof - gcDof) <= 0) {
2663         continue;
2664       }
2665       ierr = PetscSectionGetOffset(globalFine,p,&gOff);CHKERRQ(ierr);
2666       if (gOff < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"I though having global dofs meant a non-negative offset");
2667       ierr = PetscSectionGetDof(leafIndicesSec,p,&numColIndices);CHKERRQ(ierr);
2668       ierr = PetscSectionGetOffset(leafIndicesSec,p,&pIndOff);CHKERRQ(ierr);
2669       numColIndices -= 2 * numFields;
2670       if (numColIndices <= 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"global fine dof with no dofs to interpolate from");
2671       pInd = &leafIndices[pIndOff];
2672       offsets[0]        = 0;
2673       offsetsCopy[0]    = 0;
2674       newOffsets[0]     = 0;
2675       newOffsetsCopy[0] = 0;
2676       if (numFields) {
2677         PetscInt f;
2678         for (f = 0; f < numFields; f++) {
2679           PetscInt rowDof;
2680 
2681           ierr = PetscSectionGetFieldDof(localFine,p,f,&rowDof);CHKERRQ(ierr);
2682           offsets[f + 1]        = offsets[f] + rowDof;
2683           offsetsCopy[f + 1]    = offsets[f + 1];
2684           newOffsets[f + 1]     = pInd[numColIndices + numFields + f];
2685           numD[f] = 0;
2686           numO[f] = 0;
2687         }
2688         ierr = indicesPointFields_private(localFine,p,gOff,offsetsCopy,PETSC_FALSE,0,rowIndices);CHKERRQ(ierr);
2689         for (f = 0; f < numFields; f++) {
2690           PetscInt colOffset    = newOffsets[f];
2691           PetscInt numFieldCols = newOffsets[f + 1] - newOffsets[f];
2692 
2693           for (i = 0; i < numFieldCols; i++) {
2694             PetscInt gInd = pInd[i + colOffset];
2695 
2696             if (gInd >= colStart && gInd < colEnd) {
2697               numD[f]++;
2698             }
2699             else if (gInd >= 0) { /* negative means non-entry */
2700               numO[f]++;
2701             }
2702           }
2703         }
2704       }
2705       else {
2706         ierr = indicesPoint_private(localFine,p,gOff,offsetsCopy,PETSC_FALSE,0,rowIndices);CHKERRQ(ierr);
2707         numD[0] = 0;
2708         numO[0] = 0;
2709         for (i = 0; i < numColIndices; i++) {
2710           PetscInt gInd = pInd[i];
2711 
2712           if (gInd >= colStart && gInd < colEnd) {
2713             numD[0]++;
2714           }
2715           else if (gInd >= 0) { /* negative means non-entry */
2716             numO[0]++;
2717           }
2718         }
2719       }
2720       ierr = PetscSectionGetDof(leafMatricesSec,p,&matSize);CHKERRQ(ierr);
2721       if (!matSize) { /* incoming matrix is identity */
2722         PetscInt childId;
2723 
2724         childId = childIds[p-pStartF];
2725         if (childId < 0) { /* no child interpolation: one nnz per */
2726           if (numFields) {
2727             PetscInt f, count;
2728             for (f = 0, count = 0; f < numFields; f++) {
2729               PetscInt numRows = offsets[f+1] - offsets[f], row;
2730               for (row = 0; row < numRows; row++) {
2731                 PetscInt gIndCoarse = pInd[newOffsets[f] + row];
2732                 PetscInt gIndFine   = rowIndices[offsets[f] + row];
2733                 if (gIndCoarse >= colStart && gIndCoarse < colEnd) { /* local */
2734                   if (gIndFine < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Mismatched number of constrained dofs");
2735                   dnnz[gOff + count++] = 1;
2736                 }
2737                 else if (gIndCoarse >= 0) { /* remote */
2738                   if (gIndFine < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Mismatched number of constrained dofs");
2739                   onnz[gOff + count++] = 1;
2740                 }
2741                 else { /* constrained */
2742                   if (gIndFine >= 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Mismatched number of constrained dofs");
2743                 }
2744               }
2745             }
2746           }
2747           else {
2748             PetscInt count, i;
2749             for (i = 0, count = 0; i < gDof; i++) {
2750               PetscInt gIndCoarse = pInd[i];
2751               PetscInt gIndFine   = rowIndices[i];
2752               if (gIndCoarse >= colStart && gIndCoarse < colEnd) { /* local */
2753                 if (gIndFine < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Mismatched number of constrained dofs");
2754                 dnnz[gOff + count++] = 1;
2755               }
2756               else if (gIndCoarse >= 0) { /* remote */
2757                 if (gIndFine < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Mismatched number of constrained dofs");
2758                 onnz[gOff + count++] = 1;
2759               }
2760               else { /* constrained */
2761                 if (gIndFine >= 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Mismatched number of constrained dofs");
2762               }
2763             }
2764           }
2765         }
2766         else { /* interpolate from all */
2767           if (numFields) {
2768             PetscInt f, count;
2769             for (f = 0, count = 0; f < numFields; f++) {
2770               PetscInt numRows = offsets[f+1] - offsets[f], row;
2771               for (row = 0; row < numRows; row++) {
2772                 PetscInt gIndFine = rowIndices[offsets[f] + row];
2773                 if (gIndFine >= 0) {
2774                   dnnz[gOff + count] = numD[f];
2775                   onnz[gOff + count++] = numO[f];
2776                 }
2777               }
2778             }
2779           }
2780           else {
2781             PetscInt count, i;
2782             for (i = 0, count = 0; i < gDof; i++) {
2783               PetscInt gIndFine = rowIndices[i];
2784               if (gIndFine >= 0) {
2785                 dnnz[gOff + count] = numD[0];
2786                 onnz[gOff + count++] = numO[0];
2787               }
2788             }
2789           }
2790         }
2791       }
2792       else { /* interpolate from all */
2793         if (numFields) {
2794           PetscInt f, count;
2795           for (f = 0, count = 0; f < numFields; f++) {
2796             PetscInt numRows = offsets[f+1] - offsets[f], row;
2797             for (row = 0; row < numRows; row++) {
2798               PetscInt gIndFine = rowIndices[offsets[f] + row];
2799               if (gIndFine >= 0) {
2800                 dnnz[gOff + count] = numD[f];
2801                 onnz[gOff + count++] = numO[f];
2802               }
2803             }
2804           }
2805         }
2806         else { /* every dof get a full row */
2807           PetscInt count, i;
2808           for (i = 0, count = 0; i < gDof; i++) {
2809             PetscInt gIndFine = rowIndices[i];
2810             if (gIndFine >= 0) {
2811               dnnz[gOff + count] = numD[0];
2812               onnz[gOff + count++] = numO[0];
2813             }
2814           }
2815         }
2816       }
2817     }
2818     ierr = MatXAIJSetPreallocation(mat,1,dnnz,onnz,NULL,NULL);CHKERRQ(ierr);
2819     ierr = PetscFree2(dnnz,onnz);CHKERRQ(ierr);
2820 
2821     ierr = DMPlexGetReferenceTree(fine,&refTree);CHKERRQ(ierr);
2822     ierr = DMPlexReferenceTreeGetChildrenMatrices(refTree,&refPointFieldMats,&refPointFieldN);CHKERRQ(ierr);
2823     ierr = DMGetDefaultConstraints(refTree,&refConSec,NULL);CHKERRQ(ierr);
2824     ierr = DMPlexGetAnchors(refTree,&refAnSec,NULL);CHKERRQ(ierr);
2825     ierr = PetscSectionGetChart(refConSec,&pRefStart,&pRefEnd);CHKERRQ(ierr);
2826     ierr = PetscSectionGetMaxDof(refConSec,&maxConDof);CHKERRQ(ierr);
2827     ierr = PetscSectionGetMaxDof(refAnSec,&maxAnDof);CHKERRQ(ierr);
2828     ierr = PetscMalloc1(maxConDof*maxConDof*maxAnDof,&pointWork);CHKERRQ(ierr);
2829     for (p = pStartF; p < pEndF; p++) {
2830       PetscInt    gDof, gcDof, gOff;
2831       PetscInt    numColIndices, pIndOff, *pInd;
2832       PetscInt    matSize;
2833       PetscInt    childId;
2834 
2835 
2836       ierr = PetscSectionGetDof(globalFine,p,&gDof);CHKERRQ(ierr);
2837       ierr = PetscSectionGetConstraintDof(globalFine,p,&gcDof);CHKERRQ(ierr);
2838       if ((gDof - gcDof) <= 0) {
2839         continue;
2840       }
2841       childId = childIds[p-pStartF];
2842       ierr = PetscSectionGetOffset(globalFine,p,&gOff);CHKERRQ(ierr);
2843       ierr = PetscSectionGetDof(leafIndicesSec,p,&numColIndices);CHKERRQ(ierr);
2844       ierr = PetscSectionGetOffset(leafIndicesSec,p,&pIndOff);CHKERRQ(ierr);
2845       numColIndices -= 2 * numFields;
2846       pInd = &leafIndices[pIndOff];
2847       offsets[0]        = 0;
2848       offsetsCopy[0]    = 0;
2849       newOffsets[0]     = 0;
2850       newOffsetsCopy[0] = 0;
2851       rowOffsets[0]     = 0;
2852       if (numFields) {
2853         PetscInt f;
2854         for (f = 0; f < numFields; f++) {
2855           PetscInt rowDof;
2856 
2857           ierr = PetscSectionGetFieldDof(localFine,p,f,&rowDof);CHKERRQ(ierr);
2858           offsets[f + 1]     = offsets[f] + rowDof;
2859           offsetsCopy[f + 1] = offsets[f + 1];
2860           rowOffsets[f + 1]  = pInd[numColIndices + f];
2861           newOffsets[f + 1]  = pInd[numColIndices + numFields + f];
2862         }
2863         ierr = indicesPointFields_private(localFine,p,gOff,offsetsCopy,PETSC_FALSE,0,rowIndices);CHKERRQ(ierr);
2864       }
2865       else {
2866         ierr = indicesPoint_private(localFine,p,gOff,offsetsCopy,PETSC_FALSE,0,rowIndices);CHKERRQ(ierr);
2867       }
2868       ierr = PetscSectionGetDof(leafMatricesSec,p,&matSize);CHKERRQ(ierr);
2869       if (!matSize) { /* incoming matrix is identity */
2870         if (childId < 0) { /* no child interpolation: scatter */
2871           if (numFields) {
2872             PetscInt f;
2873             for (f = 0; f < numFields; f++) {
2874               PetscInt numRows = offsets[f+1] - offsets[f], row;
2875               for (row = 0; row < numRows; row++) {
2876                 ierr = MatSetValue(mat,rowIndices[offsets[f]+row],pInd[newOffsets[f]+row],1.,INSERT_VALUES);CHKERRQ(ierr);
2877               }
2878             }
2879           }
2880           else {
2881             PetscInt numRows = gDof, row;
2882             for (row = 0; row < numRows; row++) {
2883               ierr = MatSetValue(mat,rowIndices[row],pInd[row],1.,INSERT_VALUES);CHKERRQ(ierr);
2884             }
2885           }
2886         }
2887         else { /* interpolate from all */
2888           if (numFields) {
2889             PetscInt f;
2890             for (f = 0; f < numFields; f++) {
2891               PetscInt numRows = offsets[f+1] - offsets[f];
2892               PetscInt numCols = newOffsets[f + 1] - newOffsets[f];
2893               ierr = MatSetValues(mat,numRows,&rowIndices[offsets[f]],numCols,&pInd[newOffsets[f]],refPointFieldMats[childId - pRefStart][f],INSERT_VALUES);CHKERRQ(ierr);
2894             }
2895           }
2896           else {
2897             ierr = MatSetValues(mat,gDof,rowIndices,numColIndices,pInd,refPointFieldMats[childId - pRefStart][0],INSERT_VALUES);CHKERRQ(ierr);
2898           }
2899         }
2900       }
2901       else { /* interpolate from all */
2902         PetscInt    pMatOff;
2903         PetscScalar *pMat;
2904 
2905         ierr = PetscSectionGetOffset(leafMatricesSec,p,&pMatOff);CHKERRQ(ierr);
2906         pMat = &leafMatrices[pMatOff];
2907         if (childId < 0) { /* copy the incoming matrix */
2908           if (numFields) {
2909             PetscInt f, count;
2910             for (f = 0, count = 0; f < numFields; f++) {
2911               PetscInt numRows = offsets[f+1]-offsets[f];
2912               PetscInt numCols = newOffsets[f+1]-newOffsets[f];
2913               PetscInt numInRows = rowOffsets[f+1]-rowOffsets[f];
2914               PetscScalar *inMat = &pMat[count];
2915 
2916               ierr = MatSetValues(mat,numRows,&rowIndices[offsets[f]],numCols,&pInd[newOffsets[f]],inMat,INSERT_VALUES);CHKERRQ(ierr);
2917               count += numCols * numInRows;
2918             }
2919           }
2920           else {
2921             ierr = MatSetValues(mat,gDof,rowIndices,numColIndices,pInd,pMat,INSERT_VALUES);CHKERRQ(ierr);
2922           }
2923         }
2924         else { /* multiply the incoming matrix by the child interpolation */
2925           if (numFields) {
2926             PetscInt f, count;
2927             for (f = 0, count = 0; f < numFields; f++) {
2928               PetscInt numRows = offsets[f+1]-offsets[f];
2929               PetscInt numCols = newOffsets[f+1]-newOffsets[f];
2930               PetscInt numInRows = rowOffsets[f+1]-rowOffsets[f];
2931               PetscScalar *inMat = &pMat[count];
2932               PetscInt i, j, k;
2933               if (refPointFieldN[childId - pRefStart][f] != numInRows) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Point constraint matrix multiply dimension mismatch");
2934               for (i = 0; i < numRows; i++) {
2935                 for (j = 0; j < numCols; j++) {
2936                   PetscScalar val = 0.;
2937                   for (k = 0; k < numInRows; k++) {
2938                     val += refPointFieldMats[childId - pRefStart][f][i * numInRows + k] * inMat[k * numCols + j];
2939                   }
2940                   pointWork[i * numCols + j] = val;
2941                 }
2942               }
2943               ierr = MatSetValues(mat,numRows,&rowIndices[offsets[f]],numCols,&pInd[newOffsets[f]],pointWork,INSERT_VALUES);CHKERRQ(ierr);
2944               count += numCols * numInRows;
2945             }
2946           }
2947           else { /* every dof get a full row */
2948             PetscInt numRows   = gDof;
2949             PetscInt numCols   = numColIndices;
2950             PetscInt numInRows = matSize / numColIndices;
2951             PetscInt i, j, k;
2952             if (refPointFieldN[childId - pRefStart][0] != numInRows) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Point constraint matrix multiply dimension mismatch");
2953             for (i = 0; i < numRows; i++) {
2954               for (j = 0; j < numCols; j++) {
2955                 PetscScalar val = 0.;
2956                 for (k = 0; k < numInRows; k++) {
2957                   val += refPointFieldMats[childId - pRefStart][0][i * numInRows + k] * pMat[k * numCols + j];
2958                 }
2959                 pointWork[i * numCols + j] = val;
2960               }
2961             }
2962             ierr = MatSetValues(mat,numRows,rowIndices,numCols,pInd,pointWork,INSERT_VALUES);CHKERRQ(ierr);
2963           }
2964         }
2965       }
2966     }
2967     ierr = DMPlexReferenceTreeRestoreChildrenMatrices(refTree,&refPointFieldMats,&refPointFieldN);CHKERRQ(ierr);
2968     ierr = DMRestoreWorkArray(fine,maxDof,PETSC_INT,&rowIndices);CHKERRQ(ierr);
2969     ierr = PetscFree(pointWork);CHKERRQ(ierr);
2970   }
2971   ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2972   ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2973   ierr = PetscSectionDestroy(&leafIndicesSec);CHKERRQ(ierr);
2974   ierr = PetscSectionDestroy(&leafMatricesSec);CHKERRQ(ierr);
2975   ierr = PetscFree2(leafIndices,leafMatrices);CHKERRQ(ierr);
2976   ierr = PetscFree7(offsets,offsetsCopy,newOffsets,newOffsetsCopy,rowOffsets,numD,numO);CHKERRQ(ierr);
2977   ierr = ISRestoreIndices(aIS,&anchors);CHKERRQ(ierr);
2978   PetscFunctionReturn(0);
2979 }
2980