Actual source code: dspacelagrange.c

  1: #include <petsc/private/petscfeimpl.h>
  2: #include <petscdmplex.h>
  3: #include <petscblaslapack.h>

  5: PetscErrorCode DMPlexGetTransitiveClosure_Internal(DM, PetscInt, PetscInt, PetscBool, PetscInt *, PetscInt *[]);

  7: struct _n_Petsc1DNodeFamily {
  8:   PetscInt        refct;
  9:   PetscDTNodeType nodeFamily;
 10:   PetscReal       gaussJacobiExp;
 11:   PetscInt        nComputed;
 12:   PetscReal     **nodesets;
 13:   PetscBool       endpoints;
 14: };

 16: /* users set node families for PETSCDUALSPACELAGRANGE with just the inputs to this function, but internally we create
 17:  * an object that can cache the computations across multiple dual spaces */
 18: static PetscErrorCode Petsc1DNodeFamilyCreate(PetscDTNodeType family, PetscReal gaussJacobiExp, PetscBool endpoints, Petsc1DNodeFamily *nf)
 19: {
 20:   Petsc1DNodeFamily f;

 22:   PetscFunctionBegin;
 23:   PetscCall(PetscNew(&f));
 24:   switch (family) {
 25:   case PETSCDTNODES_GAUSSJACOBI:
 26:   case PETSCDTNODES_EQUISPACED:
 27:     f->nodeFamily = family;
 28:     break;
 29:   default:
 30:     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Unknown 1D node family");
 31:   }
 32:   f->endpoints      = endpoints;
 33:   f->gaussJacobiExp = 0.;
 34:   if (family == PETSCDTNODES_GAUSSJACOBI) {
 35:     PetscCheck(gaussJacobiExp > -1., PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Gauss-Jacobi exponent must be > -1.");
 36:     f->gaussJacobiExp = gaussJacobiExp;
 37:   }
 38:   f->refct = 1;
 39:   *nf      = f;
 40:   PetscFunctionReturn(PETSC_SUCCESS);
 41: }

 43: static PetscErrorCode Petsc1DNodeFamilyReference(Petsc1DNodeFamily nf)
 44: {
 45:   PetscFunctionBegin;
 46:   if (nf) nf->refct++;
 47:   PetscFunctionReturn(PETSC_SUCCESS);
 48: }

 50: static PetscErrorCode Petsc1DNodeFamilyDestroy(Petsc1DNodeFamily *nf)
 51: {
 52:   PetscInt i, nc;

 54:   PetscFunctionBegin;
 55:   if (!(*nf)) PetscFunctionReturn(PETSC_SUCCESS);
 56:   if (--(*nf)->refct > 0) {
 57:     *nf = NULL;
 58:     PetscFunctionReturn(PETSC_SUCCESS);
 59:   }
 60:   nc = (*nf)->nComputed;
 61:   for (i = 0; i < nc; i++) PetscCall(PetscFree((*nf)->nodesets[i]));
 62:   PetscCall(PetscFree((*nf)->nodesets));
 63:   PetscCall(PetscFree(*nf));
 64:   *nf = NULL;
 65:   PetscFunctionReturn(PETSC_SUCCESS);
 66: }

 68: static PetscErrorCode Petsc1DNodeFamilyGetNodeSets(Petsc1DNodeFamily f, PetscInt degree, PetscReal ***nodesets)
 69: {
 70:   PetscInt nc;

 72:   PetscFunctionBegin;
 73:   nc = f->nComputed;
 74:   if (degree >= nc) {
 75:     PetscInt    i, j;
 76:     PetscReal **new_nodesets;
 77:     PetscReal  *w;

 79:     PetscCall(PetscMalloc1(degree + 1, &new_nodesets));
 80:     PetscCall(PetscArraycpy(new_nodesets, f->nodesets, nc));
 81:     PetscCall(PetscFree(f->nodesets));
 82:     f->nodesets = new_nodesets;
 83:     PetscCall(PetscMalloc1(degree + 1, &w));
 84:     for (i = nc; i < degree + 1; i++) {
 85:       PetscCall(PetscMalloc1(i + 1, &(f->nodesets[i])));
 86:       if (!i) {
 87:         f->nodesets[i][0] = 0.5;
 88:       } else {
 89:         switch (f->nodeFamily) {
 90:         case PETSCDTNODES_EQUISPACED:
 91:           if (f->endpoints) {
 92:             for (j = 0; j <= i; j++) f->nodesets[i][j] = (PetscReal)j / (PetscReal)i;
 93:           } else {
 94:             /* these nodes are at the centroids of the small simplices created by the equispaced nodes that include
 95:              * the endpoints */
 96:             for (j = 0; j <= i; j++) f->nodesets[i][j] = ((PetscReal)j + 0.5) / ((PetscReal)i + 1.);
 97:           }
 98:           break;
 99:         case PETSCDTNODES_GAUSSJACOBI:
100:           if (f->endpoints) {
101:             PetscCall(PetscDTGaussLobattoJacobiQuadrature(i + 1, 0., 1., f->gaussJacobiExp, f->gaussJacobiExp, f->nodesets[i], w));
102:           } else {
103:             PetscCall(PetscDTGaussJacobiQuadrature(i + 1, 0., 1., f->gaussJacobiExp, f->gaussJacobiExp, f->nodesets[i], w));
104:           }
105:           break;
106:         default:
107:           SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Unknown 1D node family");
108:         }
109:       }
110:     }
111:     PetscCall(PetscFree(w));
112:     f->nComputed = degree + 1;
113:   }
114:   *nodesets = f->nodesets;
115:   PetscFunctionReturn(PETSC_SUCCESS);
116: }

118: /* http://arxiv.org/abs/2002.09421 for details */
119: static PetscErrorCode PetscNodeRecursive_Internal(PetscInt dim, PetscInt degree, PetscReal **nodesets, PetscInt tup[], PetscReal node[])
120: {
121:   PetscReal w;
122:   PetscInt  i, j;

124:   PetscFunctionBeginHot;
125:   w = 0.;
126:   if (dim == 1) {
127:     node[0] = nodesets[degree][tup[0]];
128:     node[1] = nodesets[degree][tup[1]];
129:   } else {
130:     for (i = 0; i < dim + 1; i++) node[i] = 0.;
131:     for (i = 0; i < dim + 1; i++) {
132:       PetscReal wi = nodesets[degree][degree - tup[i]];

134:       for (j = 0; j < dim + 1; j++) tup[dim + 1 + j] = tup[j + (j >= i)];
135:       PetscCall(PetscNodeRecursive_Internal(dim - 1, degree - tup[i], nodesets, &tup[dim + 1], &node[dim + 1]));
136:       for (j = 0; j < dim + 1; j++) node[j + (j >= i)] += wi * node[dim + 1 + j];
137:       w += wi;
138:     }
139:     for (i = 0; i < dim + 1; i++) node[i] /= w;
140:   }
141:   PetscFunctionReturn(PETSC_SUCCESS);
142: }

144: /* compute simplex nodes for the biunit simplex from the 1D node family */
145: static PetscErrorCode Petsc1DNodeFamilyComputeSimplexNodes(Petsc1DNodeFamily f, PetscInt dim, PetscInt degree, PetscReal points[])
146: {
147:   PetscInt   *tup;
148:   PetscInt    k;
149:   PetscInt    npoints;
150:   PetscReal **nodesets = NULL;
151:   PetscInt    worksize;
152:   PetscReal  *nodework;
153:   PetscInt   *tupwork;

155:   PetscFunctionBegin;
156:   PetscCheck(dim >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Must have non-negative dimension");
157:   PetscCheck(degree >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Must have non-negative degree");
158:   if (!dim) PetscFunctionReturn(PETSC_SUCCESS);
159:   PetscCall(PetscCalloc1(dim + 2, &tup));
160:   k = 0;
161:   PetscCall(PetscDTBinomialInt(degree + dim, dim, &npoints));
162:   PetscCall(Petsc1DNodeFamilyGetNodeSets(f, degree, &nodesets));
163:   worksize = ((dim + 2) * (dim + 3)) / 2;
164:   PetscCall(PetscMalloc2(worksize, &nodework, worksize, &tupwork));
165:   /* loop over the tuples of length dim with sum at most degree */
166:   for (k = 0; k < npoints; k++) {
167:     PetscInt i;

169:     /* turn thm into tuples of length dim + 1 with sum equal to degree (barycentric indice) */
170:     tup[0] = degree;
171:     for (i = 0; i < dim; i++) tup[0] -= tup[i + 1];
172:     switch (f->nodeFamily) {
173:     case PETSCDTNODES_EQUISPACED:
174:       /* compute equispaces nodes on the unit reference triangle */
175:       if (f->endpoints) {
176:         for (i = 0; i < dim; i++) points[dim * k + i] = (PetscReal)tup[i + 1] / (PetscReal)degree;
177:       } else {
178:         for (i = 0; i < dim; i++) {
179:           /* these nodes are at the centroids of the small simplices created by the equispaced nodes that include
180:            * the endpoints */
181:           points[dim * k + i] = ((PetscReal)tup[i + 1] + 1. / (dim + 1.)) / (PetscReal)(degree + 1.);
182:         }
183:       }
184:       break;
185:     default:
186:       /* compute equispaces nodes on the barycentric reference triangle (the trace on the first dim dimensions are the
187:        * unit reference triangle nodes */
188:       for (i = 0; i < dim + 1; i++) tupwork[i] = tup[i];
189:       PetscCall(PetscNodeRecursive_Internal(dim, degree, nodesets, tupwork, nodework));
190:       for (i = 0; i < dim; i++) points[dim * k + i] = nodework[i + 1];
191:       break;
192:     }
193:     PetscCall(PetscDualSpaceLatticePointLexicographic_Internal(dim, degree, &tup[1]));
194:   }
195:   /* map from unit simplex to biunit simplex */
196:   for (k = 0; k < npoints * dim; k++) points[k] = points[k] * 2. - 1.;
197:   PetscCall(PetscFree2(nodework, tupwork));
198:   PetscCall(PetscFree(tup));
199:   PetscFunctionReturn(PETSC_SUCCESS);
200: }

202: /* If we need to get the dofs from a mesh point, or add values into dofs at a mesh point, and there is more than one dof
203:  * on that mesh point, we have to be careful about getting/adding everything in the right place.
204:  *
205:  * With nodal dofs like PETSCDUALSPACELAGRANGE makes, the general approach to calculate the value of dofs associate
206:  * with a node A is
207:  * - transform the node locations x(A) by the map that takes the mesh point to its reorientation, x' = phi(x(A))
208:  * - figure out which node was originally at the location of the transformed point, A' = idx(x')
209:  * - if the dofs are not scalars, figure out how to represent the transformed dofs in terms of the basis
210:  *   of dofs at A' (using pushforward/pullback rules)
211:  *
212:  * The one sticky point with this approach is the "A' = idx(x')" step: trying to go from real valued coordinates
213:  * back to indices.  I don't want to rely on floating point tolerances.  Additionally, PETSCDUALSPACELAGRANGE may
214:  * eventually support quasi-Lagrangian dofs, which could involve quadrature at multiple points, so the location "x(A)"
215:  * would be ambiguous.
216:  *
217:  * So each dof gets an integer value coordinate (nodeIdx in the structure below).  The choice of integer coordinates
218:  * is somewhat arbitrary, as long as all of the relevant symmetries of the mesh point correspond to *permutations* of
219:  * the integer coordinates, which do not depend on numerical precision.
220:  *
221:  * So
222:  *
223:  * - DMPlexGetTransitiveClosure_Internal() tells me how an orientation turns into a permutation of the vertices of a
224:  *   mesh point
225:  * - The permutation of the vertices, and the nodeIdx values assigned to them, tells what permutation in index space
226:  *   is associated with the orientation
227:  * - I uses that permutation to get xi' = phi(xi(A)), the integer coordinate of the transformed dof
228:  * - I can without numerical issues compute A' = idx(xi')
229:  *
230:  * Here are some examples of how the process works
231:  *
232:  * - With a triangle:
233:  *
234:  *   The triangle has the following integer coordinates for vertices, taken from the barycentric triangle
235:  *
236:  *     closure order 2
237:  *     nodeIdx (0,0,1)
238:  *      \
239:  *       +
240:  *       |\
241:  *       | \
242:  *       |  \
243:  *       |   \    closure order 1
244:  *       |    \ / nodeIdx (0,1,0)
245:  *       +-----+
246:  *        \
247:  *      closure order 0
248:  *      nodeIdx (1,0,0)
249:  *
250:  *   If I do DMPlexGetTransitiveClosure_Internal() with orientation 1, the vertices would appear
251:  *   in the order (1, 2, 0)
252:  *
253:  *   If I list the nodeIdx of each vertex in closure order for orientation 0 (0, 1, 2) and orientation 1 (1, 2, 0), I
254:  *   see
255:  *
256:  *   orientation 0  | orientation 1
257:  *
258:  *   [0] (1,0,0)      [1] (0,1,0)
259:  *   [1] (0,1,0)      [2] (0,0,1)
260:  *   [2] (0,0,1)      [0] (1,0,0)
261:  *          A                B
262:  *
263:  *   In other words, B is the result of a row permutation of A.  But, there is also
264:  *   a column permutation that accomplishes the same result, (2,0,1).
265:  *
266:  *   So if a dof has nodeIdx coordinate (a,b,c), after the transformation its nodeIdx coordinate
267:  *   is (c,a,b), and the transformed degree of freedom will be a linear combination of dofs
268:  *   that originally had coordinate (c,a,b).
269:  *
270:  * - With a quadrilateral:
271:  *
272:  *   The quadrilateral has the following integer coordinates for vertices, taken from concatenating barycentric
273:  *   coordinates for two segments:
274:  *
275:  *     closure order 3      closure order 2
276:  *     nodeIdx (1,0,0,1)    nodeIdx (0,1,0,1)
277:  *                   \      /
278:  *                    +----+
279:  *                    |    |
280:  *                    |    |
281:  *                    +----+
282:  *                   /      \
283:  *     closure order 0      closure order 1
284:  *     nodeIdx (1,0,1,0)    nodeIdx (0,1,1,0)
285:  *
286:  *   If I do DMPlexGetTransitiveClosure_Internal() with orientation 1, the vertices would appear
287:  *   in the order (1, 2, 3, 0)
288:  *
289:  *   If I list the nodeIdx of each vertex in closure order for orientation 0 (0, 1, 2, 3) and
290:  *   orientation 1 (1, 2, 3, 0), I see
291:  *
292:  *   orientation 0  | orientation 1
293:  *
294:  *   [0] (1,0,1,0)    [1] (0,1,1,0)
295:  *   [1] (0,1,1,0)    [2] (0,1,0,1)
296:  *   [2] (0,1,0,1)    [3] (1,0,0,1)
297:  *   [3] (1,0,0,1)    [0] (1,0,1,0)
298:  *          A                B
299:  *
300:  *   The column permutation that accomplishes the same result is (3,2,0,1).
301:  *
302:  *   So if a dof has nodeIdx coordinate (a,b,c,d), after the transformation its nodeIdx coordinate
303:  *   is (d,c,a,b), and the transformed degree of freedom will be a linear combination of dofs
304:  *   that originally had coordinate (d,c,a,b).
305:  *
306:  * Previously PETSCDUALSPACELAGRANGE had hardcoded symmetries for the triangle and quadrilateral,
307:  * but this approach will work for any polytope, such as the wedge (triangular prism).
308:  */
309: struct _n_PetscLagNodeIndices {
310:   PetscInt   refct;
311:   PetscInt   nodeIdxDim;
312:   PetscInt   nodeVecDim;
313:   PetscInt   nNodes;
314:   PetscInt  *nodeIdx; /* for each node an index of size nodeIdxDim */
315:   PetscReal *nodeVec; /* for each node a vector of size nodeVecDim */
316:   PetscInt  *perm;    /* if these are vertices, perm takes DMPlex point index to closure order;
317:                               if these are nodes, perm lists nodes in index revlex order */
318: };

320: /* this is just here so I can access the values in tests/ex1.c outside the library */
321: PetscErrorCode PetscLagNodeIndicesGetData_Internal(PetscLagNodeIndices ni, PetscInt *nodeIdxDim, PetscInt *nodeVecDim, PetscInt *nNodes, const PetscInt *nodeIdx[], const PetscReal *nodeVec[])
322: {
323:   PetscFunctionBegin;
324:   *nodeIdxDim = ni->nodeIdxDim;
325:   *nodeVecDim = ni->nodeVecDim;
326:   *nNodes     = ni->nNodes;
327:   *nodeIdx    = ni->nodeIdx;
328:   *nodeVec    = ni->nodeVec;
329:   PetscFunctionReturn(PETSC_SUCCESS);
330: }

332: static PetscErrorCode PetscLagNodeIndicesReference(PetscLagNodeIndices ni)
333: {
334:   PetscFunctionBegin;
335:   if (ni) ni->refct++;
336:   PetscFunctionReturn(PETSC_SUCCESS);
337: }

339: static PetscErrorCode PetscLagNodeIndicesDuplicate(PetscLagNodeIndices ni, PetscLagNodeIndices *niNew)
340: {
341:   PetscFunctionBegin;
342:   PetscCall(PetscNew(niNew));
343:   (*niNew)->refct      = 1;
344:   (*niNew)->nodeIdxDim = ni->nodeIdxDim;
345:   (*niNew)->nodeVecDim = ni->nodeVecDim;
346:   (*niNew)->nNodes     = ni->nNodes;
347:   PetscCall(PetscMalloc1(ni->nNodes * ni->nodeIdxDim, &((*niNew)->nodeIdx)));
348:   PetscCall(PetscArraycpy((*niNew)->nodeIdx, ni->nodeIdx, ni->nNodes * ni->nodeIdxDim));
349:   PetscCall(PetscMalloc1(ni->nNodes * ni->nodeVecDim, &((*niNew)->nodeVec)));
350:   PetscCall(PetscArraycpy((*niNew)->nodeVec, ni->nodeVec, ni->nNodes * ni->nodeVecDim));
351:   (*niNew)->perm = NULL;
352:   PetscFunctionReturn(PETSC_SUCCESS);
353: }

355: static PetscErrorCode PetscLagNodeIndicesDestroy(PetscLagNodeIndices *ni)
356: {
357:   PetscFunctionBegin;
358:   if (!(*ni)) PetscFunctionReturn(PETSC_SUCCESS);
359:   if (--(*ni)->refct > 0) {
360:     *ni = NULL;
361:     PetscFunctionReturn(PETSC_SUCCESS);
362:   }
363:   PetscCall(PetscFree((*ni)->nodeIdx));
364:   PetscCall(PetscFree((*ni)->nodeVec));
365:   PetscCall(PetscFree((*ni)->perm));
366:   PetscCall(PetscFree(*ni));
367:   *ni = NULL;
368:   PetscFunctionReturn(PETSC_SUCCESS);
369: }

371: /* The vertices are given nodeIdx coordinates (e.g. the corners of the barycentric triangle).  Those coordinates are
372:  * in some other order, and to understand the effect of different symmetries, we need them to be in closure order.
373:  *
374:  * If sortIdx is PETSC_FALSE, the coordinates are already in revlex order, otherwise we must sort them
375:  * to that order before we do the real work of this function, which is
376:  *
377:  * - mark the vertices in closure order
378:  * - sort them in revlex order
379:  * - use the resulting permutation to list the vertex coordinates in closure order
380:  */
381: static PetscErrorCode PetscLagNodeIndicesComputeVertexOrder(DM dm, PetscLagNodeIndices ni, PetscBool sortIdx)
382: {
383:   PetscInt           v, w, vStart, vEnd, c, d;
384:   PetscInt           nVerts;
385:   PetscInt           closureSize = 0;
386:   PetscInt          *closure     = NULL;
387:   PetscInt          *closureOrder;
388:   PetscInt          *invClosureOrder;
389:   PetscInt          *revlexOrder;
390:   PetscInt          *newNodeIdx;
391:   PetscInt           dim;
392:   Vec                coordVec;
393:   const PetscScalar *coords;

395:   PetscFunctionBegin;
396:   PetscCall(DMGetDimension(dm, &dim));
397:   PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
398:   nVerts = vEnd - vStart;
399:   PetscCall(PetscMalloc1(nVerts, &closureOrder));
400:   PetscCall(PetscMalloc1(nVerts, &invClosureOrder));
401:   PetscCall(PetscMalloc1(nVerts, &revlexOrder));
402:   if (sortIdx) { /* bubble sort nodeIdx into revlex order */
403:     PetscInt  nodeIdxDim = ni->nodeIdxDim;
404:     PetscInt *idxOrder;

406:     PetscCall(PetscMalloc1(nVerts * nodeIdxDim, &newNodeIdx));
407:     PetscCall(PetscMalloc1(nVerts, &idxOrder));
408:     for (v = 0; v < nVerts; v++) idxOrder[v] = v;
409:     for (v = 0; v < nVerts; v++) {
410:       for (w = v + 1; w < nVerts; w++) {
411:         const PetscInt *iv   = &(ni->nodeIdx[idxOrder[v] * nodeIdxDim]);
412:         const PetscInt *iw   = &(ni->nodeIdx[idxOrder[w] * nodeIdxDim]);
413:         PetscInt        diff = 0;

415:         for (d = nodeIdxDim - 1; d >= 0; d--)
416:           if ((diff = (iv[d] - iw[d]))) break;
417:         if (diff > 0) {
418:           PetscInt swap = idxOrder[v];

420:           idxOrder[v] = idxOrder[w];
421:           idxOrder[w] = swap;
422:         }
423:       }
424:     }
425:     for (v = 0; v < nVerts; v++) {
426:       for (d = 0; d < nodeIdxDim; d++) newNodeIdx[v * ni->nodeIdxDim + d] = ni->nodeIdx[idxOrder[v] * nodeIdxDim + d];
427:     }
428:     PetscCall(PetscFree(ni->nodeIdx));
429:     ni->nodeIdx = newNodeIdx;
430:     newNodeIdx  = NULL;
431:     PetscCall(PetscFree(idxOrder));
432:   }
433:   PetscCall(DMPlexGetTransitiveClosure(dm, 0, PETSC_TRUE, &closureSize, &closure));
434:   c = closureSize - nVerts;
435:   for (v = 0; v < nVerts; v++) closureOrder[v] = closure[2 * (c + v)] - vStart;
436:   for (v = 0; v < nVerts; v++) invClosureOrder[closureOrder[v]] = v;
437:   PetscCall(DMPlexRestoreTransitiveClosure(dm, 0, PETSC_TRUE, &closureSize, &closure));
438:   PetscCall(DMGetCoordinatesLocal(dm, &coordVec));
439:   PetscCall(VecGetArrayRead(coordVec, &coords));
440:   /* bubble sort closure vertices by coordinates in revlex order */
441:   for (v = 0; v < nVerts; v++) revlexOrder[v] = v;
442:   for (v = 0; v < nVerts; v++) {
443:     for (w = v + 1; w < nVerts; w++) {
444:       const PetscScalar *cv   = &coords[closureOrder[revlexOrder[v]] * dim];
445:       const PetscScalar *cw   = &coords[closureOrder[revlexOrder[w]] * dim];
446:       PetscReal          diff = 0;

448:       for (d = dim - 1; d >= 0; d--)
449:         if ((diff = PetscRealPart(cv[d] - cw[d])) != 0.) break;
450:       if (diff > 0.) {
451:         PetscInt swap = revlexOrder[v];

453:         revlexOrder[v] = revlexOrder[w];
454:         revlexOrder[w] = swap;
455:       }
456:     }
457:   }
458:   PetscCall(VecRestoreArrayRead(coordVec, &coords));
459:   PetscCall(PetscMalloc1(ni->nodeIdxDim * nVerts, &newNodeIdx));
460:   /* reorder nodeIdx to be in closure order */
461:   for (v = 0; v < nVerts; v++) {
462:     for (d = 0; d < ni->nodeIdxDim; d++) newNodeIdx[revlexOrder[v] * ni->nodeIdxDim + d] = ni->nodeIdx[v * ni->nodeIdxDim + d];
463:   }
464:   PetscCall(PetscFree(ni->nodeIdx));
465:   ni->nodeIdx = newNodeIdx;
466:   ni->perm    = invClosureOrder;
467:   PetscCall(PetscFree(revlexOrder));
468:   PetscCall(PetscFree(closureOrder));
469:   PetscFunctionReturn(PETSC_SUCCESS);
470: }

472: /* the coordinates of the simplex vertices are the corners of the barycentric simplex.
473:  * When we stack them on top of each other in revlex order, they look like the identity matrix */
474: static PetscErrorCode PetscLagNodeIndicesCreateSimplexVertices(DM dm, PetscLagNodeIndices *nodeIndices)
475: {
476:   PetscLagNodeIndices ni;
477:   PetscInt            dim, d;

479:   PetscFunctionBegin;
480:   PetscCall(PetscNew(&ni));
481:   PetscCall(DMGetDimension(dm, &dim));
482:   ni->nodeIdxDim = dim + 1;
483:   ni->nodeVecDim = 0;
484:   ni->nNodes     = dim + 1;
485:   ni->refct      = 1;
486:   PetscCall(PetscCalloc1((dim + 1) * (dim + 1), &(ni->nodeIdx)));
487:   for (d = 0; d < dim + 1; d++) ni->nodeIdx[d * (dim + 2)] = 1;
488:   PetscCall(PetscLagNodeIndicesComputeVertexOrder(dm, ni, PETSC_FALSE));
489:   *nodeIndices = ni;
490:   PetscFunctionReturn(PETSC_SUCCESS);
491: }

493: /* A polytope that is a tensor product of a facet and a segment.
494:  * We take whatever coordinate system was being used for the facet
495:  * and we concatenate the barycentric coordinates for the vertices
496:  * at the end of the segment, (1,0) and (0,1), to get a coordinate
497:  * system for the tensor product element */
498: static PetscErrorCode PetscLagNodeIndicesCreateTensorVertices(DM dm, PetscLagNodeIndices facetni, PetscLagNodeIndices *nodeIndices)
499: {
500:   PetscLagNodeIndices ni;
501:   PetscInt            nodeIdxDim, subNodeIdxDim = facetni->nodeIdxDim;
502:   PetscInt            nVerts, nSubVerts         = facetni->nNodes;
503:   PetscInt            dim, d, e, f, g;

505:   PetscFunctionBegin;
506:   PetscCall(PetscNew(&ni));
507:   PetscCall(DMGetDimension(dm, &dim));
508:   ni->nodeIdxDim = nodeIdxDim = subNodeIdxDim + 2;
509:   ni->nodeVecDim              = 0;
510:   ni->nNodes = nVerts = 2 * nSubVerts;
511:   ni->refct           = 1;
512:   PetscCall(PetscCalloc1(nodeIdxDim * nVerts, &(ni->nodeIdx)));
513:   for (f = 0, d = 0; d < 2; d++) {
514:     for (e = 0; e < nSubVerts; e++, f++) {
515:       for (g = 0; g < subNodeIdxDim; g++) ni->nodeIdx[f * nodeIdxDim + g] = facetni->nodeIdx[e * subNodeIdxDim + g];
516:       ni->nodeIdx[f * nodeIdxDim + subNodeIdxDim]     = (1 - d);
517:       ni->nodeIdx[f * nodeIdxDim + subNodeIdxDim + 1] = d;
518:     }
519:   }
520:   PetscCall(PetscLagNodeIndicesComputeVertexOrder(dm, ni, PETSC_TRUE));
521:   *nodeIndices = ni;
522:   PetscFunctionReturn(PETSC_SUCCESS);
523: }

525: /* This helps us compute symmetries, and it also helps us compute coordinates for dofs that are being pushed
526:  * forward from a boundary mesh point.
527:  *
528:  * Input:
529:  *
530:  * dm - the target reference cell where we want new coordinates and dof directions to be valid
531:  * vert - the vertex coordinate system for the target reference cell
532:  * p - the point in the target reference cell that the dofs are coming from
533:  * vertp - the vertex coordinate system for p's reference cell
534:  * ornt - the resulting coordinates and dof vectors will be for p under this orientation
535:  * nodep - the node coordinates and dof vectors in p's reference cell
536:  * formDegree - the form degree that the dofs transform as
537:  *
538:  * Output:
539:  *
540:  * pfNodeIdx - the node coordinates for p's dofs, in the dm reference cell, from the ornt perspective
541:  * pfNodeVec - the node dof vectors for p's dofs, in the dm reference cell, from the ornt perspective
542:  */
543: static PetscErrorCode PetscLagNodeIndicesPushForward(DM dm, PetscLagNodeIndices vert, PetscInt p, PetscLagNodeIndices vertp, PetscLagNodeIndices nodep, PetscInt ornt, PetscInt formDegree, PetscInt pfNodeIdx[], PetscReal pfNodeVec[])
544: {
545:   PetscInt          *closureVerts;
546:   PetscInt           closureSize = 0;
547:   PetscInt          *closure     = NULL;
548:   PetscInt           dim, pdim, c, i, j, k, n, v, vStart, vEnd;
549:   PetscInt           nSubVert      = vertp->nNodes;
550:   PetscInt           nodeIdxDim    = vert->nodeIdxDim;
551:   PetscInt           subNodeIdxDim = vertp->nodeIdxDim;
552:   PetscInt           nNodes        = nodep->nNodes;
553:   const PetscInt    *vertIdx       = vert->nodeIdx;
554:   const PetscInt    *subVertIdx    = vertp->nodeIdx;
555:   const PetscInt    *nodeIdx       = nodep->nodeIdx;
556:   const PetscReal   *nodeVec       = nodep->nodeVec;
557:   PetscReal         *J, *Jstar;
558:   PetscReal          detJ;
559:   PetscInt           depth, pdepth, Nk, pNk;
560:   Vec                coordVec;
561:   PetscScalar       *newCoords = NULL;
562:   const PetscScalar *oldCoords = NULL;

564:   PetscFunctionBegin;
565:   PetscCall(DMGetDimension(dm, &dim));
566:   PetscCall(DMPlexGetDepth(dm, &depth));
567:   PetscCall(DMGetCoordinatesLocal(dm, &coordVec));
568:   PetscCall(DMPlexGetPointDepth(dm, p, &pdepth));
569:   pdim = pdepth != depth ? pdepth != 0 ? pdepth : 0 : dim;
570:   PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
571:   PetscCall(DMGetWorkArray(dm, nSubVert, MPIU_INT, &closureVerts));
572:   PetscCall(DMPlexGetTransitiveClosure_Internal(dm, p, ornt, PETSC_TRUE, &closureSize, &closure));
573:   c = closureSize - nSubVert;
574:   /* we want which cell closure indices the closure of this point corresponds to */
575:   for (v = 0; v < nSubVert; v++) closureVerts[v] = vert->perm[closure[2 * (c + v)] - vStart];
576:   PetscCall(DMPlexRestoreTransitiveClosure(dm, p, PETSC_TRUE, &closureSize, &closure));
577:   /* push forward indices */
578:   for (i = 0; i < nodeIdxDim; i++) { /* for every component of the target index space */
579:     /* check if this is a component that all vertices around this point have in common */
580:     for (j = 1; j < nSubVert; j++) {
581:       if (vertIdx[closureVerts[j] * nodeIdxDim + i] != vertIdx[closureVerts[0] * nodeIdxDim + i]) break;
582:     }
583:     if (j == nSubVert) { /* all vertices have this component in common, directly copy to output */
584:       PetscInt val = vertIdx[closureVerts[0] * nodeIdxDim + i];
585:       for (n = 0; n < nNodes; n++) pfNodeIdx[n * nodeIdxDim + i] = val;
586:     } else {
587:       PetscInt subi = -1;
588:       /* there must be a component in vertp that looks the same */
589:       for (k = 0; k < subNodeIdxDim; k++) {
590:         for (j = 0; j < nSubVert; j++) {
591:           if (vertIdx[closureVerts[j] * nodeIdxDim + i] != subVertIdx[j * subNodeIdxDim + k]) break;
592:         }
593:         if (j == nSubVert) {
594:           subi = k;
595:           break;
596:         }
597:       }
598:       PetscCheck(subi >= 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Did not find matching coordinate");
599:       /* that component in the vertp system becomes component i in the vert system for each dof */
600:       for (n = 0; n < nNodes; n++) pfNodeIdx[n * nodeIdxDim + i] = nodeIdx[n * subNodeIdxDim + subi];
601:     }
602:   }
603:   /* push forward vectors */
604:   PetscCall(DMGetWorkArray(dm, dim * dim, MPIU_REAL, &J));
605:   if (ornt != 0) { /* temporarily change the coordinate vector so
606:                       DMPlexComputeCellGeometryAffineFEM gives us the Jacobian we want */
607:     PetscInt  closureSize2 = 0;
608:     PetscInt *closure2     = NULL;

610:     PetscCall(DMPlexGetTransitiveClosure_Internal(dm, p, 0, PETSC_TRUE, &closureSize2, &closure2));
611:     PetscCall(PetscMalloc1(dim * nSubVert, &newCoords));
612:     PetscCall(VecGetArrayRead(coordVec, &oldCoords));
613:     for (v = 0; v < nSubVert; v++) {
614:       PetscInt d;
615:       for (d = 0; d < dim; d++) newCoords[(closure2[2 * (c + v)] - vStart) * dim + d] = oldCoords[closureVerts[v] * dim + d];
616:     }
617:     PetscCall(VecRestoreArrayRead(coordVec, &oldCoords));
618:     PetscCall(DMPlexRestoreTransitiveClosure(dm, p, PETSC_TRUE, &closureSize2, &closure2));
619:     PetscCall(VecPlaceArray(coordVec, newCoords));
620:   }
621:   PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, p, NULL, J, NULL, &detJ));
622:   if (ornt != 0) {
623:     PetscCall(VecResetArray(coordVec));
624:     PetscCall(PetscFree(newCoords));
625:   }
626:   PetscCall(DMRestoreWorkArray(dm, nSubVert, MPIU_INT, &closureVerts));
627:   /* compactify */
628:   for (i = 0; i < dim; i++)
629:     for (j = 0; j < pdim; j++) J[i * pdim + j] = J[i * dim + j];
630:   /* We have the Jacobian mapping the point's reference cell to this reference cell:
631:    * pulling back a function to the point and applying the dof is what we want,
632:    * so we get the pullback matrix and multiply the dof by that matrix on the right */
633:   PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(formDegree), &Nk));
634:   PetscCall(PetscDTBinomialInt(pdim, PetscAbsInt(formDegree), &pNk));
635:   PetscCall(DMGetWorkArray(dm, pNk * Nk, MPIU_REAL, &Jstar));
636:   PetscCall(PetscDTAltVPullbackMatrix(pdim, dim, J, formDegree, Jstar));
637:   for (n = 0; n < nNodes; n++) {
638:     for (i = 0; i < Nk; i++) {
639:       PetscReal val = 0.;
640:       for (j = 0; j < pNk; j++) val += nodeVec[n * pNk + j] * Jstar[j * Nk + i];
641:       pfNodeVec[n * Nk + i] = val;
642:     }
643:   }
644:   PetscCall(DMRestoreWorkArray(dm, pNk * Nk, MPIU_REAL, &Jstar));
645:   PetscCall(DMRestoreWorkArray(dm, dim * dim, MPIU_REAL, &J));
646:   PetscFunctionReturn(PETSC_SUCCESS);
647: }

649: /* given to sets of nodes, take the tensor product, where the product of the dof indices is concatenation and the
650:  * product of the dof vectors is the wedge product */
651: static PetscErrorCode PetscLagNodeIndicesTensor(PetscLagNodeIndices tracei, PetscInt dimT, PetscInt kT, PetscLagNodeIndices fiberi, PetscInt dimF, PetscInt kF, PetscLagNodeIndices *nodeIndices)
652: {
653:   PetscInt            dim = dimT + dimF;
654:   PetscInt            nodeIdxDim, nNodes;
655:   PetscInt            formDegree = kT + kF;
656:   PetscInt            Nk, NkT, NkF;
657:   PetscInt            MkT, MkF;
658:   PetscLagNodeIndices ni;
659:   PetscInt            i, j, l;
660:   PetscReal          *projF, *projT;
661:   PetscReal          *projFstar, *projTstar;
662:   PetscReal          *workF, *workF2, *workT, *workT2, *work, *work2;
663:   PetscReal          *wedgeMat;
664:   PetscReal           sign;

666:   PetscFunctionBegin;
667:   PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(formDegree), &Nk));
668:   PetscCall(PetscDTBinomialInt(dimT, PetscAbsInt(kT), &NkT));
669:   PetscCall(PetscDTBinomialInt(dimF, PetscAbsInt(kF), &NkF));
670:   PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(kT), &MkT));
671:   PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(kF), &MkF));
672:   PetscCall(PetscNew(&ni));
673:   ni->nodeIdxDim = nodeIdxDim = tracei->nodeIdxDim + fiberi->nodeIdxDim;
674:   ni->nodeVecDim              = Nk;
675:   ni->nNodes = nNodes = tracei->nNodes * fiberi->nNodes;
676:   ni->refct           = 1;
677:   PetscCall(PetscMalloc1(nNodes * nodeIdxDim, &(ni->nodeIdx)));
678:   /* first concatenate the indices */
679:   for (l = 0, j = 0; j < fiberi->nNodes; j++) {
680:     for (i = 0; i < tracei->nNodes; i++, l++) {
681:       PetscInt m, n = 0;

683:       for (m = 0; m < tracei->nodeIdxDim; m++) ni->nodeIdx[l * nodeIdxDim + n++] = tracei->nodeIdx[i * tracei->nodeIdxDim + m];
684:       for (m = 0; m < fiberi->nodeIdxDim; m++) ni->nodeIdx[l * nodeIdxDim + n++] = fiberi->nodeIdx[j * fiberi->nodeIdxDim + m];
685:     }
686:   }

688:   /* now wedge together the push-forward vectors */
689:   PetscCall(PetscMalloc1(nNodes * Nk, &(ni->nodeVec)));
690:   PetscCall(PetscCalloc2(dimT * dim, &projT, dimF * dim, &projF));
691:   for (i = 0; i < dimT; i++) projT[i * (dim + 1)] = 1.;
692:   for (i = 0; i < dimF; i++) projF[i * (dim + dimT + 1) + dimT] = 1.;
693:   PetscCall(PetscMalloc2(MkT * NkT, &projTstar, MkF * NkF, &projFstar));
694:   PetscCall(PetscDTAltVPullbackMatrix(dim, dimT, projT, kT, projTstar));
695:   PetscCall(PetscDTAltVPullbackMatrix(dim, dimF, projF, kF, projFstar));
696:   PetscCall(PetscMalloc6(MkT, &workT, MkT, &workT2, MkF, &workF, MkF, &workF2, Nk, &work, Nk, &work2));
697:   PetscCall(PetscMalloc1(Nk * MkT, &wedgeMat));
698:   sign = (PetscAbsInt(kT * kF) & 1) ? -1. : 1.;
699:   for (l = 0, j = 0; j < fiberi->nNodes; j++) {
700:     PetscInt d, e;

702:     /* push forward fiber k-form */
703:     for (d = 0; d < MkF; d++) {
704:       PetscReal val = 0.;
705:       for (e = 0; e < NkF; e++) val += projFstar[d * NkF + e] * fiberi->nodeVec[j * NkF + e];
706:       workF[d] = val;
707:     }
708:     /* Hodge star to proper form if necessary */
709:     if (kF < 0) {
710:       for (d = 0; d < MkF; d++) workF2[d] = workF[d];
711:       PetscCall(PetscDTAltVStar(dim, PetscAbsInt(kF), 1, workF2, workF));
712:     }
713:     /* Compute the matrix that wedges this form with one of the trace k-form */
714:     PetscCall(PetscDTAltVWedgeMatrix(dim, PetscAbsInt(kF), PetscAbsInt(kT), workF, wedgeMat));
715:     for (i = 0; i < tracei->nNodes; i++, l++) {
716:       /* push forward trace k-form */
717:       for (d = 0; d < MkT; d++) {
718:         PetscReal val = 0.;
719:         for (e = 0; e < NkT; e++) val += projTstar[d * NkT + e] * tracei->nodeVec[i * NkT + e];
720:         workT[d] = val;
721:       }
722:       /* Hodge star to proper form if necessary */
723:       if (kT < 0) {
724:         for (d = 0; d < MkT; d++) workT2[d] = workT[d];
725:         PetscCall(PetscDTAltVStar(dim, PetscAbsInt(kT), 1, workT2, workT));
726:       }
727:       /* compute the wedge product of the push-forward trace form and firer forms */
728:       for (d = 0; d < Nk; d++) {
729:         PetscReal val = 0.;
730:         for (e = 0; e < MkT; e++) val += wedgeMat[d * MkT + e] * workT[e];
731:         work[d] = val;
732:       }
733:       /* inverse Hodge star from proper form if necessary */
734:       if (formDegree < 0) {
735:         for (d = 0; d < Nk; d++) work2[d] = work[d];
736:         PetscCall(PetscDTAltVStar(dim, PetscAbsInt(formDegree), -1, work2, work));
737:       }
738:       /* insert into the array (adjusting for sign) */
739:       for (d = 0; d < Nk; d++) ni->nodeVec[l * Nk + d] = sign * work[d];
740:     }
741:   }
742:   PetscCall(PetscFree(wedgeMat));
743:   PetscCall(PetscFree6(workT, workT2, workF, workF2, work, work2));
744:   PetscCall(PetscFree2(projTstar, projFstar));
745:   PetscCall(PetscFree2(projT, projF));
746:   *nodeIndices = ni;
747:   PetscFunctionReturn(PETSC_SUCCESS);
748: }

750: /* simple union of two sets of nodes */
751: static PetscErrorCode PetscLagNodeIndicesMerge(PetscLagNodeIndices niA, PetscLagNodeIndices niB, PetscLagNodeIndices *nodeIndices)
752: {
753:   PetscLagNodeIndices ni;
754:   PetscInt            nodeIdxDim, nodeVecDim, nNodes;

756:   PetscFunctionBegin;
757:   PetscCall(PetscNew(&ni));
758:   ni->nodeIdxDim = nodeIdxDim = niA->nodeIdxDim;
759:   PetscCheck(niB->nodeIdxDim == nodeIdxDim, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Cannot merge PetscLagNodeIndices with different nodeIdxDim");
760:   ni->nodeVecDim = nodeVecDim = niA->nodeVecDim;
761:   PetscCheck(niB->nodeVecDim == nodeVecDim, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Cannot merge PetscLagNodeIndices with different nodeVecDim");
762:   ni->nNodes = nNodes = niA->nNodes + niB->nNodes;
763:   ni->refct           = 1;
764:   PetscCall(PetscMalloc1(nNodes * nodeIdxDim, &(ni->nodeIdx)));
765:   PetscCall(PetscMalloc1(nNodes * nodeVecDim, &(ni->nodeVec)));
766:   PetscCall(PetscArraycpy(ni->nodeIdx, niA->nodeIdx, niA->nNodes * nodeIdxDim));
767:   PetscCall(PetscArraycpy(ni->nodeVec, niA->nodeVec, niA->nNodes * nodeVecDim));
768:   PetscCall(PetscArraycpy(&(ni->nodeIdx[niA->nNodes * nodeIdxDim]), niB->nodeIdx, niB->nNodes * nodeIdxDim));
769:   PetscCall(PetscArraycpy(&(ni->nodeVec[niA->nNodes * nodeVecDim]), niB->nodeVec, niB->nNodes * nodeVecDim));
770:   *nodeIndices = ni;
771:   PetscFunctionReturn(PETSC_SUCCESS);
772: }

774: #define PETSCTUPINTCOMPREVLEX(N) \
775:   static int PetscConcat_(PetscTupIntCompRevlex_, N)(const void *a, const void *b) \
776:   { \
777:     const PetscInt *A = (const PetscInt *)a; \
778:     const PetscInt *B = (const PetscInt *)b; \
779:     int             i; \
780:     PetscInt        diff = 0; \
781:     for (i = 0; i < N; i++) { \
782:       diff = A[N - i] - B[N - i]; \
783:       if (diff) break; \
784:     } \
785:     return (diff <= 0) ? (diff < 0) ? -1 : 0 : 1; \
786:   }

788: PETSCTUPINTCOMPREVLEX(3)
789: PETSCTUPINTCOMPREVLEX(4)
790: PETSCTUPINTCOMPREVLEX(5)
791: PETSCTUPINTCOMPREVLEX(6)
792: PETSCTUPINTCOMPREVLEX(7)

794: static int PetscTupIntCompRevlex_N(const void *a, const void *b)
795: {
796:   const PetscInt *A = (const PetscInt *)a;
797:   const PetscInt *B = (const PetscInt *)b;
798:   int             i;
799:   int             N    = A[0];
800:   PetscInt        diff = 0;
801:   for (i = 0; i < N; i++) {
802:     diff = A[N - i] - B[N - i];
803:     if (diff) break;
804:   }
805:   return (diff <= 0) ? (diff < 0) ? -1 : 0 : 1;
806: }

808: /* The nodes are not necessarily in revlex order wrt nodeIdx: get the permutation
809:  * that puts them in that order */
810: static PetscErrorCode PetscLagNodeIndicesGetPermutation(PetscLagNodeIndices ni, PetscInt *perm[])
811: {
812:   PetscFunctionBegin;
813:   if (!(ni->perm)) {
814:     PetscInt *sorter;
815:     PetscInt  m          = ni->nNodes;
816:     PetscInt  nodeIdxDim = ni->nodeIdxDim;
817:     PetscInt  i, j, k, l;
818:     PetscInt *prm;
819:     int (*comp)(const void *, const void *);

821:     PetscCall(PetscMalloc1((nodeIdxDim + 2) * m, &sorter));
822:     for (k = 0, l = 0, i = 0; i < m; i++) {
823:       sorter[k++] = nodeIdxDim + 1;
824:       sorter[k++] = i;
825:       for (j = 0; j < nodeIdxDim; j++) sorter[k++] = ni->nodeIdx[l++];
826:     }
827:     switch (nodeIdxDim) {
828:     case 2:
829:       comp = PetscTupIntCompRevlex_3;
830:       break;
831:     case 3:
832:       comp = PetscTupIntCompRevlex_4;
833:       break;
834:     case 4:
835:       comp = PetscTupIntCompRevlex_5;
836:       break;
837:     case 5:
838:       comp = PetscTupIntCompRevlex_6;
839:       break;
840:     case 6:
841:       comp = PetscTupIntCompRevlex_7;
842:       break;
843:     default:
844:       comp = PetscTupIntCompRevlex_N;
845:       break;
846:     }
847:     qsort(sorter, m, (nodeIdxDim + 2) * sizeof(PetscInt), comp);
848:     PetscCall(PetscMalloc1(m, &prm));
849:     for (i = 0; i < m; i++) prm[i] = sorter[(nodeIdxDim + 2) * i + 1];
850:     ni->perm = prm;
851:     PetscCall(PetscFree(sorter));
852:   }
853:   *perm = ni->perm;
854:   PetscFunctionReturn(PETSC_SUCCESS);
855: }

857: static PetscErrorCode PetscDualSpaceDestroy_Lagrange(PetscDualSpace sp)
858: {
859:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;

861:   PetscFunctionBegin;
862:   if (lag->symperms) {
863:     PetscInt **selfSyms = lag->symperms[0];

865:     if (selfSyms) {
866:       PetscInt i, **allocated = &selfSyms[-lag->selfSymOff];

868:       for (i = 0; i < lag->numSelfSym; i++) PetscCall(PetscFree(allocated[i]));
869:       PetscCall(PetscFree(allocated));
870:     }
871:     PetscCall(PetscFree(lag->symperms));
872:   }
873:   if (lag->symflips) {
874:     PetscScalar **selfSyms = lag->symflips[0];

876:     if (selfSyms) {
877:       PetscInt      i;
878:       PetscScalar **allocated = &selfSyms[-lag->selfSymOff];

880:       for (i = 0; i < lag->numSelfSym; i++) PetscCall(PetscFree(allocated[i]));
881:       PetscCall(PetscFree(allocated));
882:     }
883:     PetscCall(PetscFree(lag->symflips));
884:   }
885:   PetscCall(Petsc1DNodeFamilyDestroy(&(lag->nodeFamily)));
886:   PetscCall(PetscLagNodeIndicesDestroy(&(lag->vertIndices)));
887:   PetscCall(PetscLagNodeIndicesDestroy(&(lag->intNodeIndices)));
888:   PetscCall(PetscLagNodeIndicesDestroy(&(lag->allNodeIndices)));
889:   PetscCall(PetscFree(lag));
890:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetContinuity_C", NULL));
891:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetContinuity_C", NULL));
892:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetTensor_C", NULL));
893:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetTensor_C", NULL));
894:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetTrimmed_C", NULL));
895:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetTrimmed_C", NULL));
896:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetNodeType_C", NULL));
897:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetNodeType_C", NULL));
898:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetUseMoments_C", NULL));
899:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetUseMoments_C", NULL));
900:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetMomentOrder_C", NULL));
901:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetMomentOrder_C", NULL));
902:   PetscFunctionReturn(PETSC_SUCCESS);
903: }

905: static PetscErrorCode PetscDualSpaceLagrangeView_Ascii(PetscDualSpace sp, PetscViewer viewer)
906: {
907:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;

909:   PetscFunctionBegin;
910:   PetscCall(PetscViewerASCIIPrintf(viewer, "%s %s%sLagrange dual space\n", lag->continuous ? "Continuous" : "Discontinuous", lag->tensorSpace ? "tensor " : "", lag->trimmed ? "trimmed " : ""));
911:   PetscFunctionReturn(PETSC_SUCCESS);
912: }

914: static PetscErrorCode PetscDualSpaceView_Lagrange(PetscDualSpace sp, PetscViewer viewer)
915: {
916:   PetscBool iascii;

918:   PetscFunctionBegin;
921:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
922:   if (iascii) PetscCall(PetscDualSpaceLagrangeView_Ascii(sp, viewer));
923:   PetscFunctionReturn(PETSC_SUCCESS);
924: }

926: static PetscErrorCode PetscDualSpaceSetFromOptions_Lagrange(PetscDualSpace sp, PetscOptionItems *PetscOptionsObject)
927: {
928:   PetscBool       continuous, tensor, trimmed, flg, flg2, flg3;
929:   PetscDTNodeType nodeType;
930:   PetscReal       nodeExponent;
931:   PetscInt        momentOrder;
932:   PetscBool       nodeEndpoints, useMoments;

934:   PetscFunctionBegin;
935:   PetscCall(PetscDualSpaceLagrangeGetContinuity(sp, &continuous));
936:   PetscCall(PetscDualSpaceLagrangeGetTensor(sp, &tensor));
937:   PetscCall(PetscDualSpaceLagrangeGetTrimmed(sp, &trimmed));
938:   PetscCall(PetscDualSpaceLagrangeGetNodeType(sp, &nodeType, &nodeEndpoints, &nodeExponent));
939:   if (nodeType == PETSCDTNODES_DEFAULT) nodeType = PETSCDTNODES_GAUSSJACOBI;
940:   PetscCall(PetscDualSpaceLagrangeGetUseMoments(sp, &useMoments));
941:   PetscCall(PetscDualSpaceLagrangeGetMomentOrder(sp, &momentOrder));
942:   PetscOptionsHeadBegin(PetscOptionsObject, "PetscDualSpace Lagrange Options");
943:   PetscCall(PetscOptionsBool("-petscdualspace_lagrange_continuity", "Flag for continuous element", "PetscDualSpaceLagrangeSetContinuity", continuous, &continuous, &flg));
944:   if (flg) PetscCall(PetscDualSpaceLagrangeSetContinuity(sp, continuous));
945:   PetscCall(PetscOptionsBool("-petscdualspace_lagrange_tensor", "Flag for tensor dual space", "PetscDualSpaceLagrangeSetTensor", tensor, &tensor, &flg));
946:   if (flg) PetscCall(PetscDualSpaceLagrangeSetTensor(sp, tensor));
947:   PetscCall(PetscOptionsBool("-petscdualspace_lagrange_trimmed", "Flag for trimmed dual space", "PetscDualSpaceLagrangeSetTrimmed", trimmed, &trimmed, &flg));
948:   if (flg) PetscCall(PetscDualSpaceLagrangeSetTrimmed(sp, trimmed));
949:   PetscCall(PetscOptionsEnum("-petscdualspace_lagrange_node_type", "Lagrange node location type", "PetscDualSpaceLagrangeSetNodeType", PetscDTNodeTypes, (PetscEnum)nodeType, (PetscEnum *)&nodeType, &flg));
950:   PetscCall(PetscOptionsBool("-petscdualspace_lagrange_node_endpoints", "Flag for nodes that include endpoints", "PetscDualSpaceLagrangeSetNodeType", nodeEndpoints, &nodeEndpoints, &flg2));
951:   flg3 = PETSC_FALSE;
952:   if (nodeType == PETSCDTNODES_GAUSSJACOBI) PetscCall(PetscOptionsReal("-petscdualspace_lagrange_node_exponent", "Gauss-Jacobi weight function exponent", "PetscDualSpaceLagrangeSetNodeType", nodeExponent, &nodeExponent, &flg3));
953:   if (flg || flg2 || flg3) PetscCall(PetscDualSpaceLagrangeSetNodeType(sp, nodeType, nodeEndpoints, nodeExponent));
954:   PetscCall(PetscOptionsBool("-petscdualspace_lagrange_use_moments", "Use moments (where appropriate) for functionals", "PetscDualSpaceLagrangeSetUseMoments", useMoments, &useMoments, &flg));
955:   if (flg) PetscCall(PetscDualSpaceLagrangeSetUseMoments(sp, useMoments));
956:   PetscCall(PetscOptionsInt("-petscdualspace_lagrange_moment_order", "Quadrature order for moment functionals", "PetscDualSpaceLagrangeSetMomentOrder", momentOrder, &momentOrder, &flg));
957:   if (flg) PetscCall(PetscDualSpaceLagrangeSetMomentOrder(sp, momentOrder));
958:   PetscOptionsHeadEnd();
959:   PetscFunctionReturn(PETSC_SUCCESS);
960: }

962: static PetscErrorCode PetscDualSpaceDuplicate_Lagrange(PetscDualSpace sp, PetscDualSpace spNew)
963: {
964:   PetscBool           cont, tensor, trimmed, boundary;
965:   PetscDTNodeType     nodeType;
966:   PetscReal           exponent;
967:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;

969:   PetscFunctionBegin;
970:   PetscCall(PetscDualSpaceLagrangeGetContinuity(sp, &cont));
971:   PetscCall(PetscDualSpaceLagrangeSetContinuity(spNew, cont));
972:   PetscCall(PetscDualSpaceLagrangeGetTensor(sp, &tensor));
973:   PetscCall(PetscDualSpaceLagrangeSetTensor(spNew, tensor));
974:   PetscCall(PetscDualSpaceLagrangeGetTrimmed(sp, &trimmed));
975:   PetscCall(PetscDualSpaceLagrangeSetTrimmed(spNew, trimmed));
976:   PetscCall(PetscDualSpaceLagrangeGetNodeType(sp, &nodeType, &boundary, &exponent));
977:   PetscCall(PetscDualSpaceLagrangeSetNodeType(spNew, nodeType, boundary, exponent));
978:   if (lag->nodeFamily) {
979:     PetscDualSpace_Lag *lagnew = (PetscDualSpace_Lag *)spNew->data;

981:     PetscCall(Petsc1DNodeFamilyReference(lag->nodeFamily));
982:     lagnew->nodeFamily = lag->nodeFamily;
983:   }
984:   PetscFunctionReturn(PETSC_SUCCESS);
985: }

987: /* for making tensor product spaces: take a dual space and product a segment space that has all the same
988:  * specifications (trimmed, continuous, order, node set), except for the form degree */
989: static PetscErrorCode PetscDualSpaceCreateEdgeSubspace_Lagrange(PetscDualSpace sp, PetscInt order, PetscInt k, PetscInt Nc, PetscBool interiorOnly, PetscDualSpace *bdsp)
990: {
991:   DM                  K;
992:   PetscDualSpace_Lag *newlag;

994:   PetscFunctionBegin;
995:   PetscCall(PetscDualSpaceDuplicate(sp, bdsp));
996:   PetscCall(PetscDualSpaceSetFormDegree(*bdsp, k));
997:   PetscCall(DMPlexCreateReferenceCell(PETSC_COMM_SELF, DMPolytopeTypeSimpleShape(1, PETSC_TRUE), &K));
998:   PetscCall(PetscDualSpaceSetDM(*bdsp, K));
999:   PetscCall(DMDestroy(&K));
1000:   PetscCall(PetscDualSpaceSetOrder(*bdsp, order));
1001:   PetscCall(PetscDualSpaceSetNumComponents(*bdsp, Nc));
1002:   newlag               = (PetscDualSpace_Lag *)(*bdsp)->data;
1003:   newlag->interiorOnly = interiorOnly;
1004:   PetscCall(PetscDualSpaceSetUp(*bdsp));
1005:   PetscFunctionReturn(PETSC_SUCCESS);
1006: }

1008: /* just the points, weights aren't handled */
1009: static PetscErrorCode PetscQuadratureCreateTensor(PetscQuadrature trace, PetscQuadrature fiber, PetscQuadrature *product)
1010: {
1011:   PetscInt         dimTrace, dimFiber;
1012:   PetscInt         numPointsTrace, numPointsFiber;
1013:   PetscInt         dim, numPoints;
1014:   const PetscReal *pointsTrace;
1015:   const PetscReal *pointsFiber;
1016:   PetscReal       *points;
1017:   PetscInt         i, j, k, p;

1019:   PetscFunctionBegin;
1020:   PetscCall(PetscQuadratureGetData(trace, &dimTrace, NULL, &numPointsTrace, &pointsTrace, NULL));
1021:   PetscCall(PetscQuadratureGetData(fiber, &dimFiber, NULL, &numPointsFiber, &pointsFiber, NULL));
1022:   dim       = dimTrace + dimFiber;
1023:   numPoints = numPointsFiber * numPointsTrace;
1024:   PetscCall(PetscMalloc1(numPoints * dim, &points));
1025:   for (p = 0, j = 0; j < numPointsFiber; j++) {
1026:     for (i = 0; i < numPointsTrace; i++, p++) {
1027:       for (k = 0; k < dimTrace; k++) points[p * dim + k] = pointsTrace[i * dimTrace + k];
1028:       for (k = 0; k < dimFiber; k++) points[p * dim + dimTrace + k] = pointsFiber[j * dimFiber + k];
1029:     }
1030:   }
1031:   PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, product));
1032:   PetscCall(PetscQuadratureSetData(*product, dim, 0, numPoints, points, NULL));
1033:   PetscFunctionReturn(PETSC_SUCCESS);
1034: }

1036: /* Kronecker tensor product where matrix is considered a matrix of k-forms, so that
1037:  * the entries in the product matrix are wedge products of the entries in the original matrices */
1038: static PetscErrorCode MatTensorAltV(Mat trace, Mat fiber, PetscInt dimTrace, PetscInt kTrace, PetscInt dimFiber, PetscInt kFiber, Mat *product)
1039: {
1040:   PetscInt     mTrace, nTrace, mFiber, nFiber, m, n, k, i, j, l;
1041:   PetscInt     dim, NkTrace, NkFiber, Nk;
1042:   PetscInt     dT, dF;
1043:   PetscInt    *nnzTrace, *nnzFiber, *nnz;
1044:   PetscInt     iT, iF, jT, jF, il, jl;
1045:   PetscReal   *workT, *workT2, *workF, *workF2, *work, *workstar;
1046:   PetscReal   *projT, *projF;
1047:   PetscReal   *projTstar, *projFstar;
1048:   PetscReal   *wedgeMat;
1049:   PetscReal    sign;
1050:   PetscScalar *workS;
1051:   Mat          prod;
1052:   /* this produces dof groups that look like the identity */

1054:   PetscFunctionBegin;
1055:   PetscCall(MatGetSize(trace, &mTrace, &nTrace));
1056:   PetscCall(PetscDTBinomialInt(dimTrace, PetscAbsInt(kTrace), &NkTrace));
1057:   PetscCheck(nTrace % NkTrace == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "point value space of trace matrix is not a multiple of k-form size");
1058:   PetscCall(MatGetSize(fiber, &mFiber, &nFiber));
1059:   PetscCall(PetscDTBinomialInt(dimFiber, PetscAbsInt(kFiber), &NkFiber));
1060:   PetscCheck(nFiber % NkFiber == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "point value space of fiber matrix is not a multiple of k-form size");
1061:   PetscCall(PetscMalloc2(mTrace, &nnzTrace, mFiber, &nnzFiber));
1062:   for (i = 0; i < mTrace; i++) {
1063:     PetscCall(MatGetRow(trace, i, &(nnzTrace[i]), NULL, NULL));
1064:     PetscCheck(nnzTrace[i] % NkTrace == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in trace matrix are not in k-form size blocks");
1065:   }
1066:   for (i = 0; i < mFiber; i++) {
1067:     PetscCall(MatGetRow(fiber, i, &(nnzFiber[i]), NULL, NULL));
1068:     PetscCheck(nnzFiber[i] % NkFiber == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in fiber matrix are not in k-form size blocks");
1069:   }
1070:   dim = dimTrace + dimFiber;
1071:   k   = kFiber + kTrace;
1072:   PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk));
1073:   m = mTrace * mFiber;
1074:   PetscCall(PetscMalloc1(m, &nnz));
1075:   for (l = 0, j = 0; j < mFiber; j++)
1076:     for (i = 0; i < mTrace; i++, l++) nnz[l] = (nnzTrace[i] / NkTrace) * (nnzFiber[j] / NkFiber) * Nk;
1077:   n = (nTrace / NkTrace) * (nFiber / NkFiber) * Nk;
1078:   PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, m, n, 0, nnz, &prod));
1079:   PetscCall(PetscFree(nnz));
1080:   PetscCall(PetscFree2(nnzTrace, nnzFiber));
1081:   /* reasoning about which points each dof needs depends on having zeros computed at points preserved */
1082:   PetscCall(MatSetOption(prod, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE));
1083:   /* compute pullbacks */
1084:   PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(kTrace), &dT));
1085:   PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(kFiber), &dF));
1086:   PetscCall(PetscMalloc4(dimTrace * dim, &projT, dimFiber * dim, &projF, dT * NkTrace, &projTstar, dF * NkFiber, &projFstar));
1087:   PetscCall(PetscArrayzero(projT, dimTrace * dim));
1088:   for (i = 0; i < dimTrace; i++) projT[i * (dim + 1)] = 1.;
1089:   PetscCall(PetscArrayzero(projF, dimFiber * dim));
1090:   for (i = 0; i < dimFiber; i++) projF[i * (dim + 1) + dimTrace] = 1.;
1091:   PetscCall(PetscDTAltVPullbackMatrix(dim, dimTrace, projT, kTrace, projTstar));
1092:   PetscCall(PetscDTAltVPullbackMatrix(dim, dimFiber, projF, kFiber, projFstar));
1093:   PetscCall(PetscMalloc5(dT, &workT, dF, &workF, Nk, &work, Nk, &workstar, Nk, &workS));
1094:   PetscCall(PetscMalloc2(dT, &workT2, dF, &workF2));
1095:   PetscCall(PetscMalloc1(Nk * dT, &wedgeMat));
1096:   sign = (PetscAbsInt(kTrace * kFiber) & 1) ? -1. : 1.;
1097:   for (i = 0, iF = 0; iF < mFiber; iF++) {
1098:     PetscInt           ncolsF, nformsF;
1099:     const PetscInt    *colsF;
1100:     const PetscScalar *valsF;

1102:     PetscCall(MatGetRow(fiber, iF, &ncolsF, &colsF, &valsF));
1103:     nformsF = ncolsF / NkFiber;
1104:     for (iT = 0; iT < mTrace; iT++, i++) {
1105:       PetscInt           ncolsT, nformsT;
1106:       const PetscInt    *colsT;
1107:       const PetscScalar *valsT;

1109:       PetscCall(MatGetRow(trace, iT, &ncolsT, &colsT, &valsT));
1110:       nformsT = ncolsT / NkTrace;
1111:       for (j = 0, jF = 0; jF < nformsF; jF++) {
1112:         PetscInt colF = colsF[jF * NkFiber] / NkFiber;

1114:         for (il = 0; il < dF; il++) {
1115:           PetscReal val = 0.;
1116:           for (jl = 0; jl < NkFiber; jl++) val += projFstar[il * NkFiber + jl] * PetscRealPart(valsF[jF * NkFiber + jl]);
1117:           workF[il] = val;
1118:         }
1119:         if (kFiber < 0) {
1120:           for (il = 0; il < dF; il++) workF2[il] = workF[il];
1121:           PetscCall(PetscDTAltVStar(dim, PetscAbsInt(kFiber), 1, workF2, workF));
1122:         }
1123:         PetscCall(PetscDTAltVWedgeMatrix(dim, PetscAbsInt(kFiber), PetscAbsInt(kTrace), workF, wedgeMat));
1124:         for (jT = 0; jT < nformsT; jT++, j++) {
1125:           PetscInt           colT = colsT[jT * NkTrace] / NkTrace;
1126:           PetscInt           col  = colF * (nTrace / NkTrace) + colT;
1127:           const PetscScalar *vals;

1129:           for (il = 0; il < dT; il++) {
1130:             PetscReal val = 0.;
1131:             for (jl = 0; jl < NkTrace; jl++) val += projTstar[il * NkTrace + jl] * PetscRealPart(valsT[jT * NkTrace + jl]);
1132:             workT[il] = val;
1133:           }
1134:           if (kTrace < 0) {
1135:             for (il = 0; il < dT; il++) workT2[il] = workT[il];
1136:             PetscCall(PetscDTAltVStar(dim, PetscAbsInt(kTrace), 1, workT2, workT));
1137:           }

1139:           for (il = 0; il < Nk; il++) {
1140:             PetscReal val = 0.;
1141:             for (jl = 0; jl < dT; jl++) val += sign * wedgeMat[il * dT + jl] * workT[jl];
1142:             work[il] = val;
1143:           }
1144:           if (k < 0) {
1145:             PetscCall(PetscDTAltVStar(dim, PetscAbsInt(k), -1, work, workstar));
1146: #if defined(PETSC_USE_COMPLEX)
1147:             for (l = 0; l < Nk; l++) workS[l] = workstar[l];
1148:             vals = &workS[0];
1149: #else
1150:             vals = &workstar[0];
1151: #endif
1152:           } else {
1153: #if defined(PETSC_USE_COMPLEX)
1154:             for (l = 0; l < Nk; l++) workS[l] = work[l];
1155:             vals = &workS[0];
1156: #else
1157:             vals = &work[0];
1158: #endif
1159:           }
1160:           for (l = 0; l < Nk; l++) PetscCall(MatSetValue(prod, i, col * Nk + l, vals[l], INSERT_VALUES)); /* Nk */
1161:         }                                                                                                 /* jT */
1162:       }                                                                                                   /* jF */
1163:       PetscCall(MatRestoreRow(trace, iT, &ncolsT, &colsT, &valsT));
1164:     } /* iT */
1165:     PetscCall(MatRestoreRow(fiber, iF, &ncolsF, &colsF, &valsF));
1166:   } /* iF */
1167:   PetscCall(PetscFree(wedgeMat));
1168:   PetscCall(PetscFree4(projT, projF, projTstar, projFstar));
1169:   PetscCall(PetscFree2(workT2, workF2));
1170:   PetscCall(PetscFree5(workT, workF, work, workstar, workS));
1171:   PetscCall(MatAssemblyBegin(prod, MAT_FINAL_ASSEMBLY));
1172:   PetscCall(MatAssemblyEnd(prod, MAT_FINAL_ASSEMBLY));
1173:   *product = prod;
1174:   PetscFunctionReturn(PETSC_SUCCESS);
1175: }

1177: /* Union of quadrature points, with an attempt to identify commont points in the two sets */
1178: static PetscErrorCode PetscQuadraturePointsMerge(PetscQuadrature quadA, PetscQuadrature quadB, PetscQuadrature *quadJoint, PetscInt *aToJoint[], PetscInt *bToJoint[])
1179: {
1180:   PetscInt         dimA, dimB;
1181:   PetscInt         nA, nB, nJoint, i, j, d;
1182:   const PetscReal *pointsA;
1183:   const PetscReal *pointsB;
1184:   PetscReal       *pointsJoint;
1185:   PetscInt        *aToJ, *bToJ;
1186:   PetscQuadrature  qJ;

1188:   PetscFunctionBegin;
1189:   PetscCall(PetscQuadratureGetData(quadA, &dimA, NULL, &nA, &pointsA, NULL));
1190:   PetscCall(PetscQuadratureGetData(quadB, &dimB, NULL, &nB, &pointsB, NULL));
1191:   PetscCheck(dimA == dimB, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Quadrature points must be in the same dimension");
1192:   nJoint = nA;
1193:   PetscCall(PetscMalloc1(nA, &aToJ));
1194:   for (i = 0; i < nA; i++) aToJ[i] = i;
1195:   PetscCall(PetscMalloc1(nB, &bToJ));
1196:   for (i = 0; i < nB; i++) {
1197:     for (j = 0; j < nA; j++) {
1198:       bToJ[i] = -1;
1199:       for (d = 0; d < dimA; d++)
1200:         if (PetscAbsReal(pointsB[i * dimA + d] - pointsA[j * dimA + d]) > PETSC_SMALL) break;
1201:       if (d == dimA) {
1202:         bToJ[i] = j;
1203:         break;
1204:       }
1205:     }
1206:     if (bToJ[i] == -1) bToJ[i] = nJoint++;
1207:   }
1208:   *aToJoint = aToJ;
1209:   *bToJoint = bToJ;
1210:   PetscCall(PetscMalloc1(nJoint * dimA, &pointsJoint));
1211:   PetscCall(PetscArraycpy(pointsJoint, pointsA, nA * dimA));
1212:   for (i = 0; i < nB; i++) {
1213:     if (bToJ[i] >= nA) {
1214:       for (d = 0; d < dimA; d++) pointsJoint[bToJ[i] * dimA + d] = pointsB[i * dimA + d];
1215:     }
1216:   }
1217:   PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &qJ));
1218:   PetscCall(PetscQuadratureSetData(qJ, dimA, 0, nJoint, pointsJoint, NULL));
1219:   *quadJoint = qJ;
1220:   PetscFunctionReturn(PETSC_SUCCESS);
1221: }

1223: /* Matrices matA and matB are both quadrature -> dof matrices: produce a matrix that is joint quadrature -> union of
1224:  * dofs, where the joint quadrature was produced by PetscQuadraturePointsMerge */
1225: static PetscErrorCode MatricesMerge(Mat matA, Mat matB, PetscInt dim, PetscInt k, PetscInt numMerged, const PetscInt aToMerged[], const PetscInt bToMerged[], Mat *matMerged)
1226: {
1227:   PetscInt  m, n, mA, nA, mB, nB, Nk, i, j, l;
1228:   Mat       M;
1229:   PetscInt *nnz;
1230:   PetscInt  maxnnz;
1231:   PetscInt *work;

1233:   PetscFunctionBegin;
1234:   PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk));
1235:   PetscCall(MatGetSize(matA, &mA, &nA));
1236:   PetscCheck(nA % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "matA column space not a multiple of k-form size");
1237:   PetscCall(MatGetSize(matB, &mB, &nB));
1238:   PetscCheck(nB % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "matB column space not a multiple of k-form size");
1239:   m = mA + mB;
1240:   n = numMerged * Nk;
1241:   PetscCall(PetscMalloc1(m, &nnz));
1242:   maxnnz = 0;
1243:   for (i = 0; i < mA; i++) {
1244:     PetscCall(MatGetRow(matA, i, &(nnz[i]), NULL, NULL));
1245:     PetscCheck(nnz[i] % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in matA are not in k-form size blocks");
1246:     maxnnz = PetscMax(maxnnz, nnz[i]);
1247:   }
1248:   for (i = 0; i < mB; i++) {
1249:     PetscCall(MatGetRow(matB, i, &(nnz[i + mA]), NULL, NULL));
1250:     PetscCheck(nnz[i + mA] % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in matB are not in k-form size blocks");
1251:     maxnnz = PetscMax(maxnnz, nnz[i + mA]);
1252:   }
1253:   PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, m, n, 0, nnz, &M));
1254:   PetscCall(PetscFree(nnz));
1255:   /* reasoning about which points each dof needs depends on having zeros computed at points preserved */
1256:   PetscCall(MatSetOption(M, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE));
1257:   PetscCall(PetscMalloc1(maxnnz, &work));
1258:   for (i = 0; i < mA; i++) {
1259:     const PetscInt    *cols;
1260:     const PetscScalar *vals;
1261:     PetscInt           nCols;
1262:     PetscCall(MatGetRow(matA, i, &nCols, &cols, &vals));
1263:     for (j = 0; j < nCols / Nk; j++) {
1264:       PetscInt newCol = aToMerged[cols[j * Nk] / Nk];
1265:       for (l = 0; l < Nk; l++) work[j * Nk + l] = newCol * Nk + l;
1266:     }
1267:     PetscCall(MatSetValuesBlocked(M, 1, &i, nCols, work, vals, INSERT_VALUES));
1268:     PetscCall(MatRestoreRow(matA, i, &nCols, &cols, &vals));
1269:   }
1270:   for (i = 0; i < mB; i++) {
1271:     const PetscInt    *cols;
1272:     const PetscScalar *vals;

1274:     PetscInt row = i + mA;
1275:     PetscInt nCols;
1276:     PetscCall(MatGetRow(matB, i, &nCols, &cols, &vals));
1277:     for (j = 0; j < nCols / Nk; j++) {
1278:       PetscInt newCol = bToMerged[cols[j * Nk] / Nk];
1279:       for (l = 0; l < Nk; l++) work[j * Nk + l] = newCol * Nk + l;
1280:     }
1281:     PetscCall(MatSetValuesBlocked(M, 1, &row, nCols, work, vals, INSERT_VALUES));
1282:     PetscCall(MatRestoreRow(matB, i, &nCols, &cols, &vals));
1283:   }
1284:   PetscCall(PetscFree(work));
1285:   PetscCall(MatAssemblyBegin(M, MAT_FINAL_ASSEMBLY));
1286:   PetscCall(MatAssemblyEnd(M, MAT_FINAL_ASSEMBLY));
1287:   *matMerged = M;
1288:   PetscFunctionReturn(PETSC_SUCCESS);
1289: }

1291: /* Take a dual space and product a segment space that has all the same specifications (trimmed, continuous, order,
1292:  * node set), except for the form degree.  For computing boundary dofs and for making tensor product spaces */
1293: static PetscErrorCode PetscDualSpaceCreateFacetSubspace_Lagrange(PetscDualSpace sp, DM K, PetscInt f, PetscInt k, PetscInt Ncopies, PetscBool interiorOnly, PetscDualSpace *bdsp)
1294: {
1295:   PetscInt            Nknew, Ncnew;
1296:   PetscInt            dim, pointDim = -1;
1297:   PetscInt            depth;
1298:   DM                  dm;
1299:   PetscDualSpace_Lag *newlag;

1301:   PetscFunctionBegin;
1302:   PetscCall(PetscDualSpaceGetDM(sp, &dm));
1303:   PetscCall(DMGetDimension(dm, &dim));
1304:   PetscCall(DMPlexGetDepth(dm, &depth));
1305:   PetscCall(PetscDualSpaceDuplicate(sp, bdsp));
1306:   PetscCall(PetscDualSpaceSetFormDegree(*bdsp, k));
1307:   if (!K) {
1308:     if (depth == dim) {
1309:       DMPolytopeType ct;

1311:       pointDim = dim - 1;
1312:       PetscCall(DMPlexGetCellType(dm, f, &ct));
1313:       PetscCall(DMPlexCreateReferenceCell(PETSC_COMM_SELF, ct, &K));
1314:     } else if (depth == 1) {
1315:       pointDim = 0;
1316:       PetscCall(DMPlexCreateReferenceCell(PETSC_COMM_SELF, DM_POLYTOPE_POINT, &K));
1317:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unsupported interpolation state of reference element");
1318:   } else {
1319:     PetscCall(PetscObjectReference((PetscObject)K));
1320:     PetscCall(DMGetDimension(K, &pointDim));
1321:   }
1322:   PetscCall(PetscDualSpaceSetDM(*bdsp, K));
1323:   PetscCall(DMDestroy(&K));
1324:   PetscCall(PetscDTBinomialInt(pointDim, PetscAbsInt(k), &Nknew));
1325:   Ncnew = Nknew * Ncopies;
1326:   PetscCall(PetscDualSpaceSetNumComponents(*bdsp, Ncnew));
1327:   newlag               = (PetscDualSpace_Lag *)(*bdsp)->data;
1328:   newlag->interiorOnly = interiorOnly;
1329:   PetscCall(PetscDualSpaceSetUp(*bdsp));
1330:   PetscFunctionReturn(PETSC_SUCCESS);
1331: }

1333: /* Construct simplex nodes from a nodefamily, add Nk dof vectors of length Nk at each node.
1334:  * Return the (quadrature, matrix) form of the dofs and the nodeIndices form as well.
1335:  *
1336:  * Sometimes we want a set of nodes to be contained in the interior of the element,
1337:  * even when the node scheme puts nodes on the boundaries.  numNodeSkip tells
1338:  * the routine how many "layers" of nodes need to be skipped.
1339:  * */
1340: static PetscErrorCode PetscDualSpaceLagrangeCreateSimplexNodeMat(Petsc1DNodeFamily nodeFamily, PetscInt dim, PetscInt sum, PetscInt Nk, PetscInt numNodeSkip, PetscQuadrature *iNodes, Mat *iMat, PetscLagNodeIndices *nodeIndices)
1341: {
1342:   PetscReal          *extraNodeCoords, *nodeCoords;
1343:   PetscInt            nNodes, nExtraNodes;
1344:   PetscInt            i, j, k, extraSum = sum + numNodeSkip * (1 + dim);
1345:   PetscQuadrature     intNodes;
1346:   Mat                 intMat;
1347:   PetscLagNodeIndices ni;

1349:   PetscFunctionBegin;
1350:   PetscCall(PetscDTBinomialInt(dim + sum, dim, &nNodes));
1351:   PetscCall(PetscDTBinomialInt(dim + extraSum, dim, &nExtraNodes));

1353:   PetscCall(PetscMalloc1(dim * nExtraNodes, &extraNodeCoords));
1354:   PetscCall(PetscNew(&ni));
1355:   ni->nodeIdxDim = dim + 1;
1356:   ni->nodeVecDim = Nk;
1357:   ni->nNodes     = nNodes * Nk;
1358:   ni->refct      = 1;
1359:   PetscCall(PetscMalloc1(nNodes * Nk * (dim + 1), &(ni->nodeIdx)));
1360:   PetscCall(PetscMalloc1(nNodes * Nk * Nk, &(ni->nodeVec)));
1361:   for (i = 0; i < nNodes; i++)
1362:     for (j = 0; j < Nk; j++)
1363:       for (k = 0; k < Nk; k++) ni->nodeVec[(i * Nk + j) * Nk + k] = (j == k) ? 1. : 0.;
1364:   PetscCall(Petsc1DNodeFamilyComputeSimplexNodes(nodeFamily, dim, extraSum, extraNodeCoords));
1365:   if (numNodeSkip) {
1366:     PetscInt  k;
1367:     PetscInt *tup;

1369:     PetscCall(PetscMalloc1(dim * nNodes, &nodeCoords));
1370:     PetscCall(PetscMalloc1(dim + 1, &tup));
1371:     for (k = 0; k < nNodes; k++) {
1372:       PetscInt j, c;
1373:       PetscInt index;

1375:       PetscCall(PetscDTIndexToBary(dim + 1, sum, k, tup));
1376:       for (j = 0; j < dim + 1; j++) tup[j] += numNodeSkip;
1377:       for (c = 0; c < Nk; c++) {
1378:         for (j = 0; j < dim + 1; j++) ni->nodeIdx[(k * Nk + c) * (dim + 1) + j] = tup[j] + 1;
1379:       }
1380:       PetscCall(PetscDTBaryToIndex(dim + 1, extraSum, tup, &index));
1381:       for (j = 0; j < dim; j++) nodeCoords[k * dim + j] = extraNodeCoords[index * dim + j];
1382:     }
1383:     PetscCall(PetscFree(tup));
1384:     PetscCall(PetscFree(extraNodeCoords));
1385:   } else {
1386:     PetscInt  k;
1387:     PetscInt *tup;

1389:     nodeCoords = extraNodeCoords;
1390:     PetscCall(PetscMalloc1(dim + 1, &tup));
1391:     for (k = 0; k < nNodes; k++) {
1392:       PetscInt j, c;

1394:       PetscCall(PetscDTIndexToBary(dim + 1, sum, k, tup));
1395:       for (c = 0; c < Nk; c++) {
1396:         for (j = 0; j < dim + 1; j++) {
1397:           /* barycentric indices can have zeros, but we don't want to push forward zeros because it makes it harder to
1398:            * determine which nodes correspond to which under symmetries, so we increase by 1.  This is fine
1399:            * because the nodeIdx coordinates don't have any meaning other than helping to identify symmetries */
1400:           ni->nodeIdx[(k * Nk + c) * (dim + 1) + j] = tup[j] + 1;
1401:         }
1402:       }
1403:     }
1404:     PetscCall(PetscFree(tup));
1405:   }
1406:   PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &intNodes));
1407:   PetscCall(PetscQuadratureSetData(intNodes, dim, 0, nNodes, nodeCoords, NULL));
1408:   PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, nNodes * Nk, nNodes * Nk, Nk, NULL, &intMat));
1409:   PetscCall(MatSetOption(intMat, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE));
1410:   for (j = 0; j < nNodes * Nk; j++) {
1411:     PetscInt rem = j % Nk;
1412:     PetscInt a, aprev = j - rem;
1413:     PetscInt anext = aprev + Nk;

1415:     for (a = aprev; a < anext; a++) PetscCall(MatSetValue(intMat, j, a, (a == j) ? 1. : 0., INSERT_VALUES));
1416:   }
1417:   PetscCall(MatAssemblyBegin(intMat, MAT_FINAL_ASSEMBLY));
1418:   PetscCall(MatAssemblyEnd(intMat, MAT_FINAL_ASSEMBLY));
1419:   *iNodes      = intNodes;
1420:   *iMat        = intMat;
1421:   *nodeIndices = ni;
1422:   PetscFunctionReturn(PETSC_SUCCESS);
1423: }

1425: /* once the nodeIndices have been created for the interior of the reference cell, and for all of the boundary cells,
1426:  * push forward the boundary dofs and concatenate them into the full node indices for the dual space */
1427: static PetscErrorCode PetscDualSpaceLagrangeCreateAllNodeIdx(PetscDualSpace sp)
1428: {
1429:   DM                  dm;
1430:   PetscInt            dim, nDofs;
1431:   PetscSection        section;
1432:   PetscInt            pStart, pEnd, p;
1433:   PetscInt            formDegree, Nk;
1434:   PetscInt            nodeIdxDim, spintdim;
1435:   PetscDualSpace_Lag *lag;
1436:   PetscLagNodeIndices ni, verti;

1438:   PetscFunctionBegin;
1439:   lag   = (PetscDualSpace_Lag *)sp->data;
1440:   verti = lag->vertIndices;
1441:   PetscCall(PetscDualSpaceGetDM(sp, &dm));
1442:   PetscCall(DMGetDimension(dm, &dim));
1443:   PetscCall(PetscDualSpaceGetFormDegree(sp, &formDegree));
1444:   PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(formDegree), &Nk));
1445:   PetscCall(PetscDualSpaceGetSection(sp, &section));
1446:   PetscCall(PetscSectionGetStorageSize(section, &nDofs));
1447:   PetscCall(PetscNew(&ni));
1448:   ni->nodeIdxDim = nodeIdxDim = verti->nodeIdxDim;
1449:   ni->nodeVecDim              = Nk;
1450:   ni->nNodes                  = nDofs;
1451:   ni->refct                   = 1;
1452:   PetscCall(PetscMalloc1(nodeIdxDim * nDofs, &(ni->nodeIdx)));
1453:   PetscCall(PetscMalloc1(Nk * nDofs, &(ni->nodeVec)));
1454:   PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
1455:   PetscCall(PetscSectionGetDof(section, 0, &spintdim));
1456:   if (spintdim) {
1457:     PetscCall(PetscArraycpy(ni->nodeIdx, lag->intNodeIndices->nodeIdx, spintdim * nodeIdxDim));
1458:     PetscCall(PetscArraycpy(ni->nodeVec, lag->intNodeIndices->nodeVec, spintdim * Nk));
1459:   }
1460:   for (p = pStart + 1; p < pEnd; p++) {
1461:     PetscDualSpace      psp = sp->pointSpaces[p];
1462:     PetscDualSpace_Lag *plag;
1463:     PetscInt            dof, off;

1465:     PetscCall(PetscSectionGetDof(section, p, &dof));
1466:     if (!dof) continue;
1467:     plag = (PetscDualSpace_Lag *)psp->data;
1468:     PetscCall(PetscSectionGetOffset(section, p, &off));
1469:     PetscCall(PetscLagNodeIndicesPushForward(dm, verti, p, plag->vertIndices, plag->intNodeIndices, 0, formDegree, &(ni->nodeIdx[off * nodeIdxDim]), &(ni->nodeVec[off * Nk])));
1470:   }
1471:   lag->allNodeIndices = ni;
1472:   PetscFunctionReturn(PETSC_SUCCESS);
1473: }

1475: /* once the (quadrature, Matrix) forms of the dofs have been created for the interior of the
1476:  * reference cell and for the boundary cells, jk
1477:  * push forward the boundary data and concatenate them into the full (quadrature, matrix) data
1478:  * for the dual space */
1479: static PetscErrorCode PetscDualSpaceCreateAllDataFromInteriorData(PetscDualSpace sp)
1480: {
1481:   DM              dm;
1482:   PetscSection    section;
1483:   PetscInt        pStart, pEnd, p, k, Nk, dim, Nc;
1484:   PetscInt        nNodes;
1485:   PetscInt        countNodes;
1486:   Mat             allMat;
1487:   PetscQuadrature allNodes;
1488:   PetscInt        nDofs;
1489:   PetscInt        maxNzforms, j;
1490:   PetscScalar    *work;
1491:   PetscReal      *L, *J, *Jinv, *v0, *pv0;
1492:   PetscInt       *iwork;
1493:   PetscReal      *nodes;

1495:   PetscFunctionBegin;
1496:   PetscCall(PetscDualSpaceGetDM(sp, &dm));
1497:   PetscCall(DMGetDimension(dm, &dim));
1498:   PetscCall(PetscDualSpaceGetSection(sp, &section));
1499:   PetscCall(PetscSectionGetStorageSize(section, &nDofs));
1500:   PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
1501:   PetscCall(PetscDualSpaceGetFormDegree(sp, &k));
1502:   PetscCall(PetscDualSpaceGetNumComponents(sp, &Nc));
1503:   PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk));
1504:   for (p = pStart, nNodes = 0, maxNzforms = 0; p < pEnd; p++) {
1505:     PetscDualSpace  psp;
1506:     DM              pdm;
1507:     PetscInt        pdim, pNk;
1508:     PetscQuadrature intNodes;
1509:     Mat             intMat;

1511:     PetscCall(PetscDualSpaceGetPointSubspace(sp, p, &psp));
1512:     if (!psp) continue;
1513:     PetscCall(PetscDualSpaceGetDM(psp, &pdm));
1514:     PetscCall(DMGetDimension(pdm, &pdim));
1515:     if (pdim < PetscAbsInt(k)) continue;
1516:     PetscCall(PetscDTBinomialInt(pdim, PetscAbsInt(k), &pNk));
1517:     PetscCall(PetscDualSpaceGetInteriorData(psp, &intNodes, &intMat));
1518:     if (intNodes) {
1519:       PetscInt nNodesp;

1521:       PetscCall(PetscQuadratureGetData(intNodes, NULL, NULL, &nNodesp, NULL, NULL));
1522:       nNodes += nNodesp;
1523:     }
1524:     if (intMat) {
1525:       PetscInt maxNzsp;
1526:       PetscInt maxNzformsp;

1528:       PetscCall(MatSeqAIJGetMaxRowNonzeros(intMat, &maxNzsp));
1529:       PetscCheck(maxNzsp % pNk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "interior matrix is not laid out as blocks of k-forms");
1530:       maxNzformsp = maxNzsp / pNk;
1531:       maxNzforms  = PetscMax(maxNzforms, maxNzformsp);
1532:     }
1533:   }
1534:   PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, nDofs, nNodes * Nc, maxNzforms * Nk, NULL, &allMat));
1535:   PetscCall(MatSetOption(allMat, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE));
1536:   PetscCall(PetscMalloc7(dim, &v0, dim, &pv0, dim * dim, &J, dim * dim, &Jinv, Nk * Nk, &L, maxNzforms * Nk, &work, maxNzforms * Nk, &iwork));
1537:   for (j = 0; j < dim; j++) pv0[j] = -1.;
1538:   PetscCall(PetscMalloc1(dim * nNodes, &nodes));
1539:   for (p = pStart, countNodes = 0; p < pEnd; p++) {
1540:     PetscDualSpace  psp;
1541:     PetscQuadrature intNodes;
1542:     DM              pdm;
1543:     PetscInt        pdim, pNk;
1544:     PetscInt        countNodesIn = countNodes;
1545:     PetscReal       detJ;
1546:     Mat             intMat;

1548:     PetscCall(PetscDualSpaceGetPointSubspace(sp, p, &psp));
1549:     if (!psp) continue;
1550:     PetscCall(PetscDualSpaceGetDM(psp, &pdm));
1551:     PetscCall(DMGetDimension(pdm, &pdim));
1552:     if (pdim < PetscAbsInt(k)) continue;
1553:     PetscCall(PetscDualSpaceGetInteriorData(psp, &intNodes, &intMat));
1554:     if (intNodes == NULL && intMat == NULL) continue;
1555:     PetscCall(PetscDTBinomialInt(pdim, PetscAbsInt(k), &pNk));
1556:     if (p) {
1557:       PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, p, v0, J, Jinv, &detJ));
1558:     } else { /* identity */
1559:       PetscInt i, j;

1561:       for (i = 0; i < dim; i++)
1562:         for (j = 0; j < dim; j++) J[i * dim + j] = Jinv[i * dim + j] = 0.;
1563:       for (i = 0; i < dim; i++) J[i * dim + i] = Jinv[i * dim + i] = 1.;
1564:       for (i = 0; i < dim; i++) v0[i] = -1.;
1565:     }
1566:     if (pdim != dim) { /* compactify Jacobian */
1567:       PetscInt i, j;

1569:       for (i = 0; i < dim; i++)
1570:         for (j = 0; j < pdim; j++) J[i * pdim + j] = J[i * dim + j];
1571:     }
1572:     PetscCall(PetscDTAltVPullbackMatrix(pdim, dim, J, k, L));
1573:     if (intNodes) { /* push forward quadrature locations by the affine transformation */
1574:       PetscInt         nNodesp;
1575:       const PetscReal *nodesp;
1576:       PetscInt         j;

1578:       PetscCall(PetscQuadratureGetData(intNodes, NULL, NULL, &nNodesp, &nodesp, NULL));
1579:       for (j = 0; j < nNodesp; j++, countNodes++) {
1580:         PetscInt d, e;

1582:         for (d = 0; d < dim; d++) {
1583:           nodes[countNodes * dim + d] = v0[d];
1584:           for (e = 0; e < pdim; e++) nodes[countNodes * dim + d] += J[d * pdim + e] * (nodesp[j * pdim + e] - pv0[e]);
1585:         }
1586:       }
1587:     }
1588:     if (intMat) {
1589:       PetscInt nrows;
1590:       PetscInt off;

1592:       PetscCall(PetscSectionGetDof(section, p, &nrows));
1593:       PetscCall(PetscSectionGetOffset(section, p, &off));
1594:       for (j = 0; j < nrows; j++) {
1595:         PetscInt           ncols;
1596:         const PetscInt    *cols;
1597:         const PetscScalar *vals;
1598:         PetscInt           l, d, e;
1599:         PetscInt           row = j + off;

1601:         PetscCall(MatGetRow(intMat, j, &ncols, &cols, &vals));
1602:         PetscCheck(ncols % pNk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "interior matrix is not laid out as blocks of k-forms");
1603:         for (l = 0; l < ncols / pNk; l++) {
1604:           PetscInt blockcol;

1606:           for (d = 0; d < pNk; d++) PetscCheck((cols[l * pNk + d] % pNk) == d, PETSC_COMM_SELF, PETSC_ERR_PLIB, "interior matrix is not laid out as blocks of k-forms");
1607:           blockcol = cols[l * pNk] / pNk;
1608:           for (d = 0; d < Nk; d++) iwork[l * Nk + d] = (blockcol + countNodesIn) * Nk + d;
1609:           for (d = 0; d < Nk; d++) work[l * Nk + d] = 0.;
1610:           for (d = 0; d < Nk; d++) {
1611:             for (e = 0; e < pNk; e++) {
1612:               /* "push forward" dof by pulling back a k-form to be evaluated on the point: multiply on the right by L */
1613:               work[l * Nk + d] += vals[l * pNk + e] * L[e * Nk + d];
1614:             }
1615:           }
1616:         }
1617:         PetscCall(MatSetValues(allMat, 1, &row, (ncols / pNk) * Nk, iwork, work, INSERT_VALUES));
1618:         PetscCall(MatRestoreRow(intMat, j, &ncols, &cols, &vals));
1619:       }
1620:     }
1621:   }
1622:   PetscCall(MatAssemblyBegin(allMat, MAT_FINAL_ASSEMBLY));
1623:   PetscCall(MatAssemblyEnd(allMat, MAT_FINAL_ASSEMBLY));
1624:   PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &allNodes));
1625:   PetscCall(PetscQuadratureSetData(allNodes, dim, 0, nNodes, nodes, NULL));
1626:   PetscCall(PetscFree7(v0, pv0, J, Jinv, L, work, iwork));
1627:   PetscCall(MatDestroy(&(sp->allMat)));
1628:   sp->allMat = allMat;
1629:   PetscCall(PetscQuadratureDestroy(&(sp->allNodes)));
1630:   sp->allNodes = allNodes;
1631:   PetscFunctionReturn(PETSC_SUCCESS);
1632: }

1634: /* rather than trying to get all data from the functionals, we create
1635:  * the functionals from rows of the quadrature -> dof matrix.
1636:  *
1637:  * Ideally most of the uses of PetscDualSpace in PetscFE will switch
1638:  * to using intMat and allMat, so that the individual functionals
1639:  * don't need to be constructed at all */
1640: static PetscErrorCode PetscDualSpaceComputeFunctionalsFromAllData(PetscDualSpace sp)
1641: {
1642:   PetscQuadrature  allNodes;
1643:   Mat              allMat;
1644:   PetscInt         nDofs;
1645:   PetscInt         dim, k, Nk, Nc, f;
1646:   DM               dm;
1647:   PetscInt         nNodes, spdim;
1648:   const PetscReal *nodes = NULL;
1649:   PetscSection     section;
1650:   PetscBool        useMoments;

1652:   PetscFunctionBegin;
1653:   PetscCall(PetscDualSpaceGetDM(sp, &dm));
1654:   PetscCall(DMGetDimension(dm, &dim));
1655:   PetscCall(PetscDualSpaceGetNumComponents(sp, &Nc));
1656:   PetscCall(PetscDualSpaceGetFormDegree(sp, &k));
1657:   PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk));
1658:   PetscCall(PetscDualSpaceGetAllData(sp, &allNodes, &allMat));
1659:   nNodes = 0;
1660:   if (allNodes) PetscCall(PetscQuadratureGetData(allNodes, NULL, NULL, &nNodes, &nodes, NULL));
1661:   PetscCall(MatGetSize(allMat, &nDofs, NULL));
1662:   PetscCall(PetscDualSpaceGetSection(sp, &section));
1663:   PetscCall(PetscSectionGetStorageSize(section, &spdim));
1664:   PetscCheck(spdim == nDofs, PETSC_COMM_SELF, PETSC_ERR_PLIB, "incompatible all matrix size");
1665:   PetscCall(PetscMalloc1(nDofs, &(sp->functional)));
1666:   PetscCall(PetscDualSpaceLagrangeGetUseMoments(sp, &useMoments));
1667:   if (useMoments) {
1668:     Mat              allMat;
1669:     PetscInt         momentOrder, i;
1670:     PetscBool        tensor;
1671:     const PetscReal *weights;
1672:     PetscScalar     *array;

1674:     PetscCheck(nDofs == 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "We do not yet support moments beyond P0, nDofs == %" PetscInt_FMT, nDofs);
1675:     PetscCall(PetscDualSpaceLagrangeGetMomentOrder(sp, &momentOrder));
1676:     PetscCall(PetscDualSpaceLagrangeGetTensor(sp, &tensor));
1677:     if (!tensor) PetscCall(PetscDTStroudConicalQuadrature(dim, Nc, PetscMax(momentOrder + 1, 1), -1.0, 1.0, &(sp->functional[0])));
1678:     else PetscCall(PetscDTGaussTensorQuadrature(dim, Nc, PetscMax(momentOrder + 1, 1), -1.0, 1.0, &(sp->functional[0])));
1679:     /* Need to replace allNodes and allMat */
1680:     PetscCall(PetscObjectReference((PetscObject)sp->functional[0]));
1681:     PetscCall(PetscQuadratureDestroy(&(sp->allNodes)));
1682:     sp->allNodes = sp->functional[0];
1683:     PetscCall(PetscQuadratureGetData(sp->allNodes, NULL, NULL, &nNodes, NULL, &weights));
1684:     PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, nDofs, nNodes * Nc, NULL, &allMat));
1685:     PetscCall(MatDenseGetArrayWrite(allMat, &array));
1686:     for (i = 0; i < nNodes * Nc; ++i) array[i] = weights[i];
1687:     PetscCall(MatDenseRestoreArrayWrite(allMat, &array));
1688:     PetscCall(MatAssemblyBegin(allMat, MAT_FINAL_ASSEMBLY));
1689:     PetscCall(MatAssemblyEnd(allMat, MAT_FINAL_ASSEMBLY));
1690:     PetscCall(MatDestroy(&(sp->allMat)));
1691:     sp->allMat = allMat;
1692:     PetscFunctionReturn(PETSC_SUCCESS);
1693:   }
1694:   for (f = 0; f < nDofs; f++) {
1695:     PetscInt           ncols, c;
1696:     const PetscInt    *cols;
1697:     const PetscScalar *vals;
1698:     PetscReal         *nodesf;
1699:     PetscReal         *weightsf;
1700:     PetscInt           nNodesf;
1701:     PetscInt           countNodes;

1703:     PetscCall(MatGetRow(allMat, f, &ncols, &cols, &vals));
1704:     PetscCheck(ncols % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "all matrix is not laid out as blocks of k-forms");
1705:     for (c = 1, nNodesf = 1; c < ncols; c++) {
1706:       if ((cols[c] / Nc) != (cols[c - 1] / Nc)) nNodesf++;
1707:     }
1708:     PetscCall(PetscMalloc1(dim * nNodesf, &nodesf));
1709:     PetscCall(PetscMalloc1(Nc * nNodesf, &weightsf));
1710:     for (c = 0, countNodes = 0; c < ncols; c++) {
1711:       if (!c || ((cols[c] / Nc) != (cols[c - 1] / Nc))) {
1712:         PetscInt d;

1714:         for (d = 0; d < Nc; d++) weightsf[countNodes * Nc + d] = 0.;
1715:         for (d = 0; d < dim; d++) nodesf[countNodes * dim + d] = nodes[(cols[c] / Nc) * dim + d];
1716:         countNodes++;
1717:       }
1718:       weightsf[(countNodes - 1) * Nc + (cols[c] % Nc)] = PetscRealPart(vals[c]);
1719:     }
1720:     PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &(sp->functional[f])));
1721:     PetscCall(PetscQuadratureSetData(sp->functional[f], dim, Nc, nNodesf, nodesf, weightsf));
1722:     PetscCall(MatRestoreRow(allMat, f, &ncols, &cols, &vals));
1723:   }
1724:   PetscFunctionReturn(PETSC_SUCCESS);
1725: }

1727: /* take a matrix meant for k-forms and expand it to one for Ncopies */
1728: static PetscErrorCode PetscDualSpaceLagrangeMatrixCreateCopies(Mat A, PetscInt Nk, PetscInt Ncopies, Mat *Abs)
1729: {
1730:   PetscInt m, n, i, j, k;
1731:   PetscInt maxnnz, *nnz, *iwork;
1732:   Mat      Ac;

1734:   PetscFunctionBegin;
1735:   PetscCall(MatGetSize(A, &m, &n));
1736:   PetscCheck(n % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Number of columns in A %" PetscInt_FMT " is not a multiple of Nk %" PetscInt_FMT, n, Nk);
1737:   PetscCall(PetscMalloc1(m * Ncopies, &nnz));
1738:   for (i = 0, maxnnz = 0; i < m; i++) {
1739:     PetscInt innz;
1740:     PetscCall(MatGetRow(A, i, &innz, NULL, NULL));
1741:     PetscCheck(innz % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "A row %" PetscInt_FMT " nnzs is not a multiple of Nk %" PetscInt_FMT, innz, Nk);
1742:     for (j = 0; j < Ncopies; j++) nnz[i * Ncopies + j] = innz;
1743:     maxnnz = PetscMax(maxnnz, innz);
1744:   }
1745:   PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, m * Ncopies, n * Ncopies, 0, nnz, &Ac));
1746:   PetscCall(MatSetOption(Ac, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE));
1747:   PetscCall(PetscFree(nnz));
1748:   PetscCall(PetscMalloc1(maxnnz, &iwork));
1749:   for (i = 0; i < m; i++) {
1750:     PetscInt           innz;
1751:     const PetscInt    *cols;
1752:     const PetscScalar *vals;

1754:     PetscCall(MatGetRow(A, i, &innz, &cols, &vals));
1755:     for (j = 0; j < innz; j++) iwork[j] = (cols[j] / Nk) * (Nk * Ncopies) + (cols[j] % Nk);
1756:     for (j = 0; j < Ncopies; j++) {
1757:       PetscInt row = i * Ncopies + j;

1759:       PetscCall(MatSetValues(Ac, 1, &row, innz, iwork, vals, INSERT_VALUES));
1760:       for (k = 0; k < innz; k++) iwork[k] += Nk;
1761:     }
1762:     PetscCall(MatRestoreRow(A, i, &innz, &cols, &vals));
1763:   }
1764:   PetscCall(PetscFree(iwork));
1765:   PetscCall(MatAssemblyBegin(Ac, MAT_FINAL_ASSEMBLY));
1766:   PetscCall(MatAssemblyEnd(Ac, MAT_FINAL_ASSEMBLY));
1767:   *Abs = Ac;
1768:   PetscFunctionReturn(PETSC_SUCCESS);
1769: }

1771: /* check if a cell is a tensor product of the segment with a facet,
1772:  * specifically checking if f and f2 can be the "endpoints" (like the triangles
1773:  * at either end of a wedge) */
1774: static PetscErrorCode DMPlexPointIsTensor_Internal_Given(DM dm, PetscInt p, PetscInt f, PetscInt f2, PetscBool *isTensor)
1775: {
1776:   PetscInt        coneSize, c;
1777:   const PetscInt *cone;
1778:   const PetscInt *fCone;
1779:   const PetscInt *f2Cone;
1780:   PetscInt        fs[2];
1781:   PetscInt        meetSize, nmeet;
1782:   const PetscInt *meet;

1784:   PetscFunctionBegin;
1785:   fs[0] = f;
1786:   fs[1] = f2;
1787:   PetscCall(DMPlexGetMeet(dm, 2, fs, &meetSize, &meet));
1788:   nmeet = meetSize;
1789:   PetscCall(DMPlexRestoreMeet(dm, 2, fs, &meetSize, &meet));
1790:   /* two points that have a non-empty meet cannot be at opposite ends of a cell */
1791:   if (nmeet) {
1792:     *isTensor = PETSC_FALSE;
1793:     PetscFunctionReturn(PETSC_SUCCESS);
1794:   }
1795:   PetscCall(DMPlexGetConeSize(dm, p, &coneSize));
1796:   PetscCall(DMPlexGetCone(dm, p, &cone));
1797:   PetscCall(DMPlexGetCone(dm, f, &fCone));
1798:   PetscCall(DMPlexGetCone(dm, f2, &f2Cone));
1799:   for (c = 0; c < coneSize; c++) {
1800:     PetscInt        e, ef;
1801:     PetscInt        d = -1, d2 = -1;
1802:     PetscInt        dcount, d2count;
1803:     PetscInt        t = cone[c];
1804:     PetscInt        tConeSize;
1805:     PetscBool       tIsTensor;
1806:     const PetscInt *tCone;

1808:     if (t == f || t == f2) continue;
1809:     /* for every other facet in the cone, check that is has
1810:      * one ridge in common with each end */
1811:     PetscCall(DMPlexGetConeSize(dm, t, &tConeSize));
1812:     PetscCall(DMPlexGetCone(dm, t, &tCone));

1814:     dcount  = 0;
1815:     d2count = 0;
1816:     for (e = 0; e < tConeSize; e++) {
1817:       PetscInt q = tCone[e];
1818:       for (ef = 0; ef < coneSize - 2; ef++) {
1819:         if (fCone[ef] == q) {
1820:           if (dcount) {
1821:             *isTensor = PETSC_FALSE;
1822:             PetscFunctionReturn(PETSC_SUCCESS);
1823:           }
1824:           d = q;
1825:           dcount++;
1826:         } else if (f2Cone[ef] == q) {
1827:           if (d2count) {
1828:             *isTensor = PETSC_FALSE;
1829:             PetscFunctionReturn(PETSC_SUCCESS);
1830:           }
1831:           d2 = q;
1832:           d2count++;
1833:         }
1834:       }
1835:     }
1836:     /* if the whole cell is a tensor with the segment, then this
1837:      * facet should be a tensor with the segment */
1838:     PetscCall(DMPlexPointIsTensor_Internal_Given(dm, t, d, d2, &tIsTensor));
1839:     if (!tIsTensor) {
1840:       *isTensor = PETSC_FALSE;
1841:       PetscFunctionReturn(PETSC_SUCCESS);
1842:     }
1843:   }
1844:   *isTensor = PETSC_TRUE;
1845:   PetscFunctionReturn(PETSC_SUCCESS);
1846: }

1848: /* determine if a cell is a tensor with a segment by looping over pairs of facets to find a pair
1849:  * that could be the opposite ends */
1850: static PetscErrorCode DMPlexPointIsTensor_Internal(DM dm, PetscInt p, PetscBool *isTensor, PetscInt *endA, PetscInt *endB)
1851: {
1852:   PetscInt        coneSize, c, c2;
1853:   const PetscInt *cone;

1855:   PetscFunctionBegin;
1856:   PetscCall(DMPlexGetConeSize(dm, p, &coneSize));
1857:   if (!coneSize) {
1858:     if (isTensor) *isTensor = PETSC_FALSE;
1859:     if (endA) *endA = -1;
1860:     if (endB) *endB = -1;
1861:   }
1862:   PetscCall(DMPlexGetCone(dm, p, &cone));
1863:   for (c = 0; c < coneSize; c++) {
1864:     PetscInt f = cone[c];
1865:     PetscInt fConeSize;

1867:     PetscCall(DMPlexGetConeSize(dm, f, &fConeSize));
1868:     if (fConeSize != coneSize - 2) continue;

1870:     for (c2 = c + 1; c2 < coneSize; c2++) {
1871:       PetscInt  f2 = cone[c2];
1872:       PetscBool isTensorff2;
1873:       PetscInt  f2ConeSize;

1875:       PetscCall(DMPlexGetConeSize(dm, f2, &f2ConeSize));
1876:       if (f2ConeSize != coneSize - 2) continue;

1878:       PetscCall(DMPlexPointIsTensor_Internal_Given(dm, p, f, f2, &isTensorff2));
1879:       if (isTensorff2) {
1880:         if (isTensor) *isTensor = PETSC_TRUE;
1881:         if (endA) *endA = f;
1882:         if (endB) *endB = f2;
1883:         PetscFunctionReturn(PETSC_SUCCESS);
1884:       }
1885:     }
1886:   }
1887:   if (isTensor) *isTensor = PETSC_FALSE;
1888:   if (endA) *endA = -1;
1889:   if (endB) *endB = -1;
1890:   PetscFunctionReturn(PETSC_SUCCESS);
1891: }

1893: /* determine if a cell is a tensor with a segment by looping over pairs of facets to find a pair
1894:  * that could be the opposite ends */
1895: static PetscErrorCode DMPlexPointIsTensor(DM dm, PetscInt p, PetscBool *isTensor, PetscInt *endA, PetscInt *endB)
1896: {
1897:   DMPlexInterpolatedFlag interpolated;

1899:   PetscFunctionBegin;
1900:   PetscCall(DMPlexIsInterpolated(dm, &interpolated));
1901:   PetscCheck(interpolated == DMPLEX_INTERPOLATED_FULL, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONGSTATE, "Only for interpolated DMPlex's");
1902:   PetscCall(DMPlexPointIsTensor_Internal(dm, p, isTensor, endA, endB));
1903:   PetscFunctionReturn(PETSC_SUCCESS);
1904: }

1906: /* Let k = formDegree and k' = -sign(k) * dim + k.  Transform a symmetric frame for k-forms on the biunit simplex into
1907:  * a symmetric frame for k'-forms on the biunit simplex.
1908:  *
1909:  * A frame is "symmetric" if the pullback of every symmetry of the biunit simplex is a permutation of the frame.
1910:  *
1911:  * forms in the symmetric frame are used as dofs in the untrimmed simplex spaces.  This way, symmetries of the
1912:  * reference cell result in permutations of dofs grouped by node.
1913:  *
1914:  * Use T to transform dof matrices for k'-forms into dof matrices for k-forms as a block diagonal transformation on
1915:  * the right.
1916:  */
1917: static PetscErrorCode BiunitSimplexSymmetricFormTransformation(PetscInt dim, PetscInt formDegree, PetscReal T[])
1918: {
1919:   PetscInt   k  = formDegree;
1920:   PetscInt   kd = k < 0 ? dim + k : k - dim;
1921:   PetscInt   Nk;
1922:   PetscReal *biToEq, *eqToBi, *biToEqStar, *eqToBiStar;
1923:   PetscInt   fact;

1925:   PetscFunctionBegin;
1926:   PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk));
1927:   PetscCall(PetscCalloc4(dim * dim, &biToEq, dim * dim, &eqToBi, Nk * Nk, &biToEqStar, Nk * Nk, &eqToBiStar));
1928:   /* fill in biToEq: Jacobian of the transformation from the biunit simplex to the equilateral simplex */
1929:   fact = 0;
1930:   for (PetscInt i = 0; i < dim; i++) {
1931:     biToEq[i * dim + i] = PetscSqrtReal(((PetscReal)i + 2.) / (2. * ((PetscReal)i + 1.)));
1932:     fact += 4 * (i + 1);
1933:     for (PetscInt j = i + 1; j < dim; j++) biToEq[i * dim + j] = PetscSqrtReal(1. / (PetscReal)fact);
1934:   }
1935:   /* fill in eqToBi: Jacobian of the transformation from the equilateral simplex to the biunit simplex */
1936:   fact = 0;
1937:   for (PetscInt j = 0; j < dim; j++) {
1938:     eqToBi[j * dim + j] = PetscSqrtReal(2. * ((PetscReal)j + 1.) / ((PetscReal)j + 2));
1939:     fact += j + 1;
1940:     for (PetscInt i = 0; i < j; i++) eqToBi[i * dim + j] = -PetscSqrtReal(1. / (PetscReal)fact);
1941:   }
1942:   PetscCall(PetscDTAltVPullbackMatrix(dim, dim, biToEq, kd, biToEqStar));
1943:   PetscCall(PetscDTAltVPullbackMatrix(dim, dim, eqToBi, k, eqToBiStar));
1944:   /* product of pullbacks simulates the following steps
1945:    *
1946:    * 1. start with frame W = [w_1, w_2, ..., w_m] of k forms that is symmetric on the biunit simplex:
1947:           if J is the Jacobian of a symmetry of the biunit simplex, then J_k* W = [J_k*w_1, ..., J_k*w_m]
1948:           is a permutation of W.
1949:           Even though a k' form --- a (dim - k) form represented by its Hodge star --- has the same geometric
1950:           content as a k form, W is not a symmetric frame of k' forms on the biunit simplex.  That's because,
1951:           for general Jacobian J, J_k* != J_k'*.
1952:    * 2. pullback W to the equilateral triangle using the k pullback, W_eq = eqToBi_k* W.  All symmetries of the
1953:           equilateral simplex have orthonormal Jacobians.  For an orthonormal Jacobian O, J_k* = J_k'*, so W_eq is
1954:           also a symmetric frame for k' forms on the equilateral simplex.
1955:      3. pullback W_eq back to the biunit simplex using the k' pulback, V = biToEq_k'* W_eq = biToEq_k'* eqToBi_k* W.
1956:           V is a symmetric frame for k' forms on the biunit simplex.
1957:    */
1958:   for (PetscInt i = 0; i < Nk; i++) {
1959:     for (PetscInt j = 0; j < Nk; j++) {
1960:       PetscReal val = 0.;
1961:       for (PetscInt k = 0; k < Nk; k++) val += biToEqStar[i * Nk + k] * eqToBiStar[k * Nk + j];
1962:       T[i * Nk + j] = val;
1963:     }
1964:   }
1965:   PetscCall(PetscFree4(biToEq, eqToBi, biToEqStar, eqToBiStar));
1966:   PetscFunctionReturn(PETSC_SUCCESS);
1967: }

1969: /* permute a quadrature -> dof matrix so that its rows are in revlex order by nodeIdx */
1970: static PetscErrorCode MatPermuteByNodeIdx(Mat A, PetscLagNodeIndices ni, Mat *Aperm)
1971: {
1972:   PetscInt   m, n, i, j;
1973:   PetscInt   nodeIdxDim = ni->nodeIdxDim;
1974:   PetscInt   nodeVecDim = ni->nodeVecDim;
1975:   PetscInt  *perm;
1976:   IS         permIS;
1977:   IS         id;
1978:   PetscInt  *nIdxPerm;
1979:   PetscReal *nVecPerm;

1981:   PetscFunctionBegin;
1982:   PetscCall(PetscLagNodeIndicesGetPermutation(ni, &perm));
1983:   PetscCall(MatGetSize(A, &m, &n));
1984:   PetscCall(PetscMalloc1(nodeIdxDim * m, &nIdxPerm));
1985:   PetscCall(PetscMalloc1(nodeVecDim * m, &nVecPerm));
1986:   for (i = 0; i < m; i++)
1987:     for (j = 0; j < nodeIdxDim; j++) nIdxPerm[i * nodeIdxDim + j] = ni->nodeIdx[perm[i] * nodeIdxDim + j];
1988:   for (i = 0; i < m; i++)
1989:     for (j = 0; j < nodeVecDim; j++) nVecPerm[i * nodeVecDim + j] = ni->nodeVec[perm[i] * nodeVecDim + j];
1990:   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, m, perm, PETSC_USE_POINTER, &permIS));
1991:   PetscCall(ISSetPermutation(permIS));
1992:   PetscCall(ISCreateStride(PETSC_COMM_SELF, n, 0, 1, &id));
1993:   PetscCall(ISSetPermutation(id));
1994:   PetscCall(MatPermute(A, permIS, id, Aperm));
1995:   PetscCall(ISDestroy(&permIS));
1996:   PetscCall(ISDestroy(&id));
1997:   for (i = 0; i < m; i++) perm[i] = i;
1998:   PetscCall(PetscFree(ni->nodeIdx));
1999:   PetscCall(PetscFree(ni->nodeVec));
2000:   ni->nodeIdx = nIdxPerm;
2001:   ni->nodeVec = nVecPerm;
2002:   PetscFunctionReturn(PETSC_SUCCESS);
2003: }

2005: static PetscErrorCode PetscDualSpaceSetUp_Lagrange(PetscDualSpace sp)
2006: {
2007:   PetscDualSpace_Lag    *lag   = (PetscDualSpace_Lag *)sp->data;
2008:   DM                     dm    = sp->dm;
2009:   DM                     dmint = NULL;
2010:   PetscInt               order;
2011:   PetscInt               Nc = sp->Nc;
2012:   MPI_Comm               comm;
2013:   PetscBool              continuous;
2014:   PetscSection           section;
2015:   PetscInt               depth, dim, pStart, pEnd, cStart, cEnd, p, *pStratStart, *pStratEnd, d;
2016:   PetscInt               formDegree, Nk, Ncopies;
2017:   PetscInt               tensorf = -1, tensorf2 = -1;
2018:   PetscBool              tensorCell, tensorSpace;
2019:   PetscBool              uniform, trimmed;
2020:   Petsc1DNodeFamily      nodeFamily;
2021:   PetscInt               numNodeSkip;
2022:   DMPlexInterpolatedFlag interpolated;
2023:   PetscBool              isbdm;

2025:   PetscFunctionBegin;
2026:   /* step 1: sanitize input */
2027:   PetscCall(PetscObjectGetComm((PetscObject)sp, &comm));
2028:   PetscCall(DMGetDimension(dm, &dim));
2029:   PetscCall(PetscObjectTypeCompare((PetscObject)sp, PETSCDUALSPACEBDM, &isbdm));
2030:   if (isbdm) {
2031:     sp->k = -(dim - 1); /* form degree of H-div */
2032:     PetscCall(PetscObjectChangeTypeName((PetscObject)sp, PETSCDUALSPACELAGRANGE));
2033:   }
2034:   PetscCall(PetscDualSpaceGetFormDegree(sp, &formDegree));
2035:   PetscCheck(PetscAbsInt(formDegree) <= dim, comm, PETSC_ERR_ARG_OUTOFRANGE, "Form degree must be bounded by dimension");
2036:   PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(formDegree), &Nk));
2037:   if (sp->Nc <= 0 && lag->numCopies > 0) sp->Nc = Nk * lag->numCopies;
2038:   Nc = sp->Nc;
2039:   PetscCheck(Nc % Nk == 0, comm, PETSC_ERR_ARG_INCOMP, "Number of components is not a multiple of form degree size");
2040:   if (lag->numCopies <= 0) lag->numCopies = Nc / Nk;
2041:   Ncopies = lag->numCopies;
2042:   PetscCheck(Nc / Nk == Ncopies, comm, PETSC_ERR_ARG_INCOMP, "Number of copies * (dim choose k) != Nc");
2043:   if (!dim) sp->order = 0;
2044:   order   = sp->order;
2045:   uniform = sp->uniform;
2046:   PetscCheck(uniform, PETSC_COMM_SELF, PETSC_ERR_SUP, "Variable order not supported yet");
2047:   if (lag->trimmed && !formDegree) lag->trimmed = PETSC_FALSE; /* trimmed spaces are the same as full spaces for 0-forms */
2048:   if (lag->nodeType == PETSCDTNODES_DEFAULT) {
2049:     lag->nodeType     = PETSCDTNODES_GAUSSJACOBI;
2050:     lag->nodeExponent = 0.;
2051:     /* trimmed spaces don't include corner vertices, so don't use end nodes by default */
2052:     lag->endNodes = lag->trimmed ? PETSC_FALSE : PETSC_TRUE;
2053:   }
2054:   /* If a trimmed space and the user did choose nodes with endpoints, skip them by default */
2055:   if (lag->numNodeSkip < 0) lag->numNodeSkip = (lag->trimmed && lag->endNodes) ? 1 : 0;
2056:   numNodeSkip = lag->numNodeSkip;
2057:   PetscCheck(!lag->trimmed || order, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot have zeroth order trimmed elements");
2058:   if (lag->trimmed && PetscAbsInt(formDegree) == dim) { /* convert trimmed n-forms to untrimmed of one polynomial order less */
2059:     sp->order--;
2060:     order--;
2061:     lag->trimmed = PETSC_FALSE;
2062:   }
2063:   trimmed = lag->trimmed;
2064:   if (!order || PetscAbsInt(formDegree) == dim) lag->continuous = PETSC_FALSE;
2065:   continuous = lag->continuous;
2066:   PetscCall(DMPlexGetDepth(dm, &depth));
2067:   PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
2068:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
2069:   PetscCheck(pStart == 0 && cStart == 0, PetscObjectComm((PetscObject)sp), PETSC_ERR_ARG_WRONGSTATE, "Expect DM with chart starting at zero and cells first");
2070:   PetscCheck(cEnd == 1, PetscObjectComm((PetscObject)sp), PETSC_ERR_ARG_WRONGSTATE, "Use PETSCDUALSPACEREFINED for multi-cell reference meshes");
2071:   PetscCall(DMPlexIsInterpolated(dm, &interpolated));
2072:   if (interpolated != DMPLEX_INTERPOLATED_FULL) {
2073:     PetscCall(DMPlexInterpolate(dm, &dmint));
2074:   } else {
2075:     PetscCall(PetscObjectReference((PetscObject)dm));
2076:     dmint = dm;
2077:   }
2078:   tensorCell = PETSC_FALSE;
2079:   if (dim > 1) PetscCall(DMPlexPointIsTensor(dmint, 0, &tensorCell, &tensorf, &tensorf2));
2080:   lag->tensorCell = tensorCell;
2081:   if (dim < 2 || !lag->tensorCell) lag->tensorSpace = PETSC_FALSE;
2082:   tensorSpace = lag->tensorSpace;
2083:   if (!lag->nodeFamily) PetscCall(Petsc1DNodeFamilyCreate(lag->nodeType, lag->nodeExponent, lag->endNodes, &lag->nodeFamily));
2084:   nodeFamily = lag->nodeFamily;
2085:   PetscCheck(interpolated == DMPLEX_INTERPOLATED_FULL || !continuous || (PetscAbsInt(formDegree) <= 0 && order <= 1), PETSC_COMM_SELF, PETSC_ERR_PLIB, "Reference element won't support all boundary nodes");

2087:   /* step 2: construct the boundary spaces */
2088:   PetscCall(PetscMalloc2(depth + 1, &pStratStart, depth + 1, &pStratEnd));
2089:   PetscCall(PetscCalloc1(pEnd, &(sp->pointSpaces)));
2090:   for (d = 0; d <= depth; ++d) PetscCall(DMPlexGetDepthStratum(dm, d, &pStratStart[d], &pStratEnd[d]));
2091:   PetscCall(PetscDualSpaceSectionCreate_Internal(sp, &section));
2092:   sp->pointSection = section;
2093:   if (continuous && !(lag->interiorOnly)) {
2094:     PetscInt h;

2096:     for (p = pStratStart[depth - 1]; p < pStratEnd[depth - 1]; p++) { /* calculate the facet dual spaces */
2097:       PetscReal      v0[3];
2098:       DMPolytopeType ptype;
2099:       PetscReal      J[9], detJ;
2100:       PetscInt       q;

2102:       PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, p, v0, J, NULL, &detJ));
2103:       PetscCall(DMPlexGetCellType(dm, p, &ptype));

2105:       /* compare to previous facets: if computed, reference that dualspace */
2106:       for (q = pStratStart[depth - 1]; q < p; q++) {
2107:         DMPolytopeType qtype;

2109:         PetscCall(DMPlexGetCellType(dm, q, &qtype));
2110:         if (qtype == ptype) break;
2111:       }
2112:       if (q < p) { /* this facet has the same dual space as that one */
2113:         PetscCall(PetscObjectReference((PetscObject)sp->pointSpaces[q]));
2114:         sp->pointSpaces[p] = sp->pointSpaces[q];
2115:         continue;
2116:       }
2117:       /* if not, recursively compute this dual space */
2118:       PetscCall(PetscDualSpaceCreateFacetSubspace_Lagrange(sp, NULL, p, formDegree, Ncopies, PETSC_FALSE, &sp->pointSpaces[p]));
2119:     }
2120:     for (h = 2; h <= depth; h++) { /* get the higher subspaces from the facet subspaces */
2121:       PetscInt hd   = depth - h;
2122:       PetscInt hdim = dim - h;

2124:       if (hdim < PetscAbsInt(formDegree)) break;
2125:       for (p = pStratStart[hd]; p < pStratEnd[hd]; p++) {
2126:         PetscInt        suppSize, s;
2127:         const PetscInt *supp;

2129:         PetscCall(DMPlexGetSupportSize(dm, p, &suppSize));
2130:         PetscCall(DMPlexGetSupport(dm, p, &supp));
2131:         for (s = 0; s < suppSize; s++) {
2132:           DM              qdm;
2133:           PetscDualSpace  qsp, psp;
2134:           PetscInt        c, coneSize, q;
2135:           const PetscInt *cone;
2136:           const PetscInt *refCone;

2138:           q   = supp[0];
2139:           qsp = sp->pointSpaces[q];
2140:           PetscCall(DMPlexGetConeSize(dm, q, &coneSize));
2141:           PetscCall(DMPlexGetCone(dm, q, &cone));
2142:           for (c = 0; c < coneSize; c++)
2143:             if (cone[c] == p) break;
2144:           PetscCheck(c != coneSize, PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "cone/support mismatch");
2145:           PetscCall(PetscDualSpaceGetDM(qsp, &qdm));
2146:           PetscCall(DMPlexGetCone(qdm, 0, &refCone));
2147:           /* get the equivalent dual space from the support dual space */
2148:           PetscCall(PetscDualSpaceGetPointSubspace(qsp, refCone[c], &psp));
2149:           if (!s) {
2150:             PetscCall(PetscObjectReference((PetscObject)psp));
2151:             sp->pointSpaces[p] = psp;
2152:           }
2153:         }
2154:       }
2155:     }
2156:     for (p = 1; p < pEnd; p++) {
2157:       PetscInt pspdim;
2158:       if (!sp->pointSpaces[p]) continue;
2159:       PetscCall(PetscDualSpaceGetInteriorDimension(sp->pointSpaces[p], &pspdim));
2160:       PetscCall(PetscSectionSetDof(section, p, pspdim));
2161:     }
2162:   }

2164:   if (Ncopies > 1) {
2165:     Mat                 intMatScalar, allMatScalar;
2166:     PetscDualSpace      scalarsp;
2167:     PetscDualSpace_Lag *scalarlag;

2169:     PetscCall(PetscDualSpaceDuplicate(sp, &scalarsp));
2170:     /* Setting the number of components to Nk is a space with 1 copy of each k-form */
2171:     PetscCall(PetscDualSpaceSetNumComponents(scalarsp, Nk));
2172:     PetscCall(PetscDualSpaceSetUp(scalarsp));
2173:     PetscCall(PetscDualSpaceGetInteriorData(scalarsp, &(sp->intNodes), &intMatScalar));
2174:     PetscCall(PetscObjectReference((PetscObject)(sp->intNodes)));
2175:     if (intMatScalar) PetscCall(PetscDualSpaceLagrangeMatrixCreateCopies(intMatScalar, Nk, Ncopies, &(sp->intMat)));
2176:     PetscCall(PetscDualSpaceGetAllData(scalarsp, &(sp->allNodes), &allMatScalar));
2177:     PetscCall(PetscObjectReference((PetscObject)(sp->allNodes)));
2178:     PetscCall(PetscDualSpaceLagrangeMatrixCreateCopies(allMatScalar, Nk, Ncopies, &(sp->allMat)));
2179:     sp->spdim    = scalarsp->spdim * Ncopies;
2180:     sp->spintdim = scalarsp->spintdim * Ncopies;
2181:     scalarlag    = (PetscDualSpace_Lag *)scalarsp->data;
2182:     PetscCall(PetscLagNodeIndicesReference(scalarlag->vertIndices));
2183:     lag->vertIndices = scalarlag->vertIndices;
2184:     PetscCall(PetscLagNodeIndicesReference(scalarlag->intNodeIndices));
2185:     lag->intNodeIndices = scalarlag->intNodeIndices;
2186:     PetscCall(PetscLagNodeIndicesReference(scalarlag->allNodeIndices));
2187:     lag->allNodeIndices = scalarlag->allNodeIndices;
2188:     PetscCall(PetscDualSpaceDestroy(&scalarsp));
2189:     PetscCall(PetscSectionSetDof(section, 0, sp->spintdim));
2190:     PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2191:     PetscCall(PetscDualSpaceComputeFunctionalsFromAllData(sp));
2192:     PetscCall(PetscFree2(pStratStart, pStratEnd));
2193:     PetscCall(DMDestroy(&dmint));
2194:     PetscFunctionReturn(PETSC_SUCCESS);
2195:   }

2197:   if (trimmed && !continuous) {
2198:     /* the dofs of a trimmed space don't have a nice tensor/lattice structure:
2199:      * just construct the continuous dual space and copy all of the data over,
2200:      * allocating it all to the cell instead of splitting it up between the boundaries */
2201:     PetscDualSpace      spcont;
2202:     PetscInt            spdim, f;
2203:     PetscQuadrature     allNodes;
2204:     PetscDualSpace_Lag *lagc;
2205:     Mat                 allMat;

2207:     PetscCall(PetscDualSpaceDuplicate(sp, &spcont));
2208:     PetscCall(PetscDualSpaceLagrangeSetContinuity(spcont, PETSC_TRUE));
2209:     PetscCall(PetscDualSpaceSetUp(spcont));
2210:     PetscCall(PetscDualSpaceGetDimension(spcont, &spdim));
2211:     sp->spdim = sp->spintdim = spdim;
2212:     PetscCall(PetscSectionSetDof(section, 0, spdim));
2213:     PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2214:     PetscCall(PetscMalloc1(spdim, &(sp->functional)));
2215:     for (f = 0; f < spdim; f++) {
2216:       PetscQuadrature fn;

2218:       PetscCall(PetscDualSpaceGetFunctional(spcont, f, &fn));
2219:       PetscCall(PetscObjectReference((PetscObject)fn));
2220:       sp->functional[f] = fn;
2221:     }
2222:     PetscCall(PetscDualSpaceGetAllData(spcont, &allNodes, &allMat));
2223:     PetscCall(PetscObjectReference((PetscObject)allNodes));
2224:     PetscCall(PetscObjectReference((PetscObject)allNodes));
2225:     sp->allNodes = sp->intNodes = allNodes;
2226:     PetscCall(PetscObjectReference((PetscObject)allMat));
2227:     PetscCall(PetscObjectReference((PetscObject)allMat));
2228:     sp->allMat = sp->intMat = allMat;
2229:     lagc                    = (PetscDualSpace_Lag *)spcont->data;
2230:     PetscCall(PetscLagNodeIndicesReference(lagc->vertIndices));
2231:     lag->vertIndices = lagc->vertIndices;
2232:     PetscCall(PetscLagNodeIndicesReference(lagc->allNodeIndices));
2233:     PetscCall(PetscLagNodeIndicesReference(lagc->allNodeIndices));
2234:     lag->intNodeIndices = lagc->allNodeIndices;
2235:     lag->allNodeIndices = lagc->allNodeIndices;
2236:     PetscCall(PetscDualSpaceDestroy(&spcont));
2237:     PetscCall(PetscFree2(pStratStart, pStratEnd));
2238:     PetscCall(DMDestroy(&dmint));
2239:     PetscFunctionReturn(PETSC_SUCCESS);
2240:   }

2242:   /* step 3: construct intNodes, and intMat, and combine it with boundray data to make allNodes and allMat */
2243:   if (!tensorSpace) {
2244:     if (!tensorCell) PetscCall(PetscLagNodeIndicesCreateSimplexVertices(dm, &(lag->vertIndices)));

2246:     if (trimmed) {
2247:       /* there is one dof in the interior of the a trimmed element for each full polynomial of with degree at most
2248:        * order + k - dim - 1 */
2249:       if (order + PetscAbsInt(formDegree) > dim) {
2250:         PetscInt sum = order + PetscAbsInt(formDegree) - dim - 1;
2251:         PetscInt nDofs;

2253:         PetscCall(PetscDualSpaceLagrangeCreateSimplexNodeMat(nodeFamily, dim, sum, Nk, numNodeSkip, &sp->intNodes, &sp->intMat, &(lag->intNodeIndices)));
2254:         PetscCall(MatGetSize(sp->intMat, &nDofs, NULL));
2255:         PetscCall(PetscSectionSetDof(section, 0, nDofs));
2256:       }
2257:       PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2258:       PetscCall(PetscDualSpaceCreateAllDataFromInteriorData(sp));
2259:       PetscCall(PetscDualSpaceLagrangeCreateAllNodeIdx(sp));
2260:     } else {
2261:       if (!continuous) {
2262:         /* if discontinuous just construct one node for each set of dofs (a set of dofs is a basis for the k-form
2263:          * space) */
2264:         PetscInt sum = order;
2265:         PetscInt nDofs;

2267:         PetscCall(PetscDualSpaceLagrangeCreateSimplexNodeMat(nodeFamily, dim, sum, Nk, numNodeSkip, &sp->intNodes, &sp->intMat, &(lag->intNodeIndices)));
2268:         PetscCall(MatGetSize(sp->intMat, &nDofs, NULL));
2269:         PetscCall(PetscSectionSetDof(section, 0, nDofs));
2270:         PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2271:         PetscCall(PetscObjectReference((PetscObject)(sp->intNodes)));
2272:         sp->allNodes = sp->intNodes;
2273:         PetscCall(PetscObjectReference((PetscObject)(sp->intMat)));
2274:         sp->allMat = sp->intMat;
2275:         PetscCall(PetscLagNodeIndicesReference(lag->intNodeIndices));
2276:         lag->allNodeIndices = lag->intNodeIndices;
2277:       } else {
2278:         /* there is one dof in the interior of the a full element for each trimmed polynomial of with degree at most
2279:          * order + k - dim, but with complementary form degree */
2280:         if (order + PetscAbsInt(formDegree) > dim) {
2281:           PetscDualSpace      trimmedsp;
2282:           PetscDualSpace_Lag *trimmedlag;
2283:           PetscQuadrature     intNodes;
2284:           PetscInt            trFormDegree = formDegree >= 0 ? formDegree - dim : dim - PetscAbsInt(formDegree);
2285:           PetscInt            nDofs;
2286:           Mat                 intMat;

2288:           PetscCall(PetscDualSpaceDuplicate(sp, &trimmedsp));
2289:           PetscCall(PetscDualSpaceLagrangeSetTrimmed(trimmedsp, PETSC_TRUE));
2290:           PetscCall(PetscDualSpaceSetOrder(trimmedsp, order + PetscAbsInt(formDegree) - dim));
2291:           PetscCall(PetscDualSpaceSetFormDegree(trimmedsp, trFormDegree));
2292:           trimmedlag              = (PetscDualSpace_Lag *)trimmedsp->data;
2293:           trimmedlag->numNodeSkip = numNodeSkip + 1;
2294:           PetscCall(PetscDualSpaceSetUp(trimmedsp));
2295:           PetscCall(PetscDualSpaceGetAllData(trimmedsp, &intNodes, &intMat));
2296:           PetscCall(PetscObjectReference((PetscObject)intNodes));
2297:           sp->intNodes = intNodes;
2298:           PetscCall(PetscLagNodeIndicesReference(trimmedlag->allNodeIndices));
2299:           lag->intNodeIndices = trimmedlag->allNodeIndices;
2300:           PetscCall(PetscObjectReference((PetscObject)intMat));
2301:           if (PetscAbsInt(formDegree) > 0 && PetscAbsInt(formDegree) < dim) {
2302:             PetscReal   *T;
2303:             PetscScalar *work;
2304:             PetscInt     nCols, nRows;
2305:             Mat          intMatT;

2307:             PetscCall(MatDuplicate(intMat, MAT_COPY_VALUES, &intMatT));
2308:             PetscCall(MatGetSize(intMat, &nRows, &nCols));
2309:             PetscCall(PetscMalloc2(Nk * Nk, &T, nCols, &work));
2310:             PetscCall(BiunitSimplexSymmetricFormTransformation(dim, formDegree, T));
2311:             for (PetscInt row = 0; row < nRows; row++) {
2312:               PetscInt           nrCols;
2313:               const PetscInt    *rCols;
2314:               const PetscScalar *rVals;

2316:               PetscCall(MatGetRow(intMat, row, &nrCols, &rCols, &rVals));
2317:               PetscCheck(nrCols % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in intMat matrix are not in k-form size blocks");
2318:               for (PetscInt b = 0; b < nrCols; b += Nk) {
2319:                 const PetscScalar *v = &rVals[b];
2320:                 PetscScalar       *w = &work[b];
2321:                 for (PetscInt j = 0; j < Nk; j++) {
2322:                   w[j] = 0.;
2323:                   for (PetscInt i = 0; i < Nk; i++) w[j] += v[i] * T[i * Nk + j];
2324:                 }
2325:               }
2326:               PetscCall(MatSetValuesBlocked(intMatT, 1, &row, nrCols, rCols, work, INSERT_VALUES));
2327:               PetscCall(MatRestoreRow(intMat, row, &nrCols, &rCols, &rVals));
2328:             }
2329:             PetscCall(MatAssemblyBegin(intMatT, MAT_FINAL_ASSEMBLY));
2330:             PetscCall(MatAssemblyEnd(intMatT, MAT_FINAL_ASSEMBLY));
2331:             PetscCall(MatDestroy(&intMat));
2332:             intMat = intMatT;
2333:             PetscCall(PetscLagNodeIndicesDestroy(&(lag->intNodeIndices)));
2334:             PetscCall(PetscLagNodeIndicesDuplicate(trimmedlag->allNodeIndices, &(lag->intNodeIndices)));
2335:             {
2336:               PetscInt         nNodes     = lag->intNodeIndices->nNodes;
2337:               PetscReal       *newNodeVec = lag->intNodeIndices->nodeVec;
2338:               const PetscReal *oldNodeVec = trimmedlag->allNodeIndices->nodeVec;

2340:               for (PetscInt n = 0; n < nNodes; n++) {
2341:                 PetscReal       *w = &newNodeVec[n * Nk];
2342:                 const PetscReal *v = &oldNodeVec[n * Nk];

2344:                 for (PetscInt j = 0; j < Nk; j++) {
2345:                   w[j] = 0.;
2346:                   for (PetscInt i = 0; i < Nk; i++) w[j] += v[i] * T[i * Nk + j];
2347:                 }
2348:               }
2349:             }
2350:             PetscCall(PetscFree2(T, work));
2351:           }
2352:           sp->intMat = intMat;
2353:           PetscCall(MatGetSize(sp->intMat, &nDofs, NULL));
2354:           PetscCall(PetscDualSpaceDestroy(&trimmedsp));
2355:           PetscCall(PetscSectionSetDof(section, 0, nDofs));
2356:         }
2357:         PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2358:         PetscCall(PetscDualSpaceCreateAllDataFromInteriorData(sp));
2359:         PetscCall(PetscDualSpaceLagrangeCreateAllNodeIdx(sp));
2360:       }
2361:     }
2362:   } else {
2363:     PetscQuadrature     intNodesTrace  = NULL;
2364:     PetscQuadrature     intNodesFiber  = NULL;
2365:     PetscQuadrature     intNodes       = NULL;
2366:     PetscLagNodeIndices intNodeIndices = NULL;
2367:     Mat                 intMat         = NULL;

2369:     if (PetscAbsInt(formDegree) < dim) { /* get the trace k-forms on the first facet, and the 0-forms on the edge,
2370:                                             and wedge them together to create some of the k-form dofs */
2371:       PetscDualSpace      trace, fiber;
2372:       PetscDualSpace_Lag *tracel, *fiberl;
2373:       Mat                 intMatTrace, intMatFiber;

2375:       if (sp->pointSpaces[tensorf]) {
2376:         PetscCall(PetscObjectReference((PetscObject)(sp->pointSpaces[tensorf])));
2377:         trace = sp->pointSpaces[tensorf];
2378:       } else {
2379:         PetscCall(PetscDualSpaceCreateFacetSubspace_Lagrange(sp, NULL, tensorf, formDegree, Ncopies, PETSC_TRUE, &trace));
2380:       }
2381:       PetscCall(PetscDualSpaceCreateEdgeSubspace_Lagrange(sp, order, 0, 1, PETSC_TRUE, &fiber));
2382:       tracel = (PetscDualSpace_Lag *)trace->data;
2383:       fiberl = (PetscDualSpace_Lag *)fiber->data;
2384:       PetscCall(PetscLagNodeIndicesCreateTensorVertices(dm, tracel->vertIndices, &(lag->vertIndices)));
2385:       PetscCall(PetscDualSpaceGetInteriorData(trace, &intNodesTrace, &intMatTrace));
2386:       PetscCall(PetscDualSpaceGetInteriorData(fiber, &intNodesFiber, &intMatFiber));
2387:       if (intNodesTrace && intNodesFiber) {
2388:         PetscCall(PetscQuadratureCreateTensor(intNodesTrace, intNodesFiber, &intNodes));
2389:         PetscCall(MatTensorAltV(intMatTrace, intMatFiber, dim - 1, formDegree, 1, 0, &intMat));
2390:         PetscCall(PetscLagNodeIndicesTensor(tracel->intNodeIndices, dim - 1, formDegree, fiberl->intNodeIndices, 1, 0, &intNodeIndices));
2391:       }
2392:       PetscCall(PetscObjectReference((PetscObject)intNodesTrace));
2393:       PetscCall(PetscObjectReference((PetscObject)intNodesFiber));
2394:       PetscCall(PetscDualSpaceDestroy(&fiber));
2395:       PetscCall(PetscDualSpaceDestroy(&trace));
2396:     }
2397:     if (PetscAbsInt(formDegree) > 0) { /* get the trace (k-1)-forms on the first facet, and the 1-forms on the edge,
2398:                                           and wedge them together to create the remaining k-form dofs */
2399:       PetscDualSpace      trace, fiber;
2400:       PetscDualSpace_Lag *tracel, *fiberl;
2401:       PetscQuadrature     intNodesTrace2, intNodesFiber2, intNodes2;
2402:       PetscLagNodeIndices intNodeIndices2;
2403:       Mat                 intMatTrace, intMatFiber, intMat2;
2404:       PetscInt            traceDegree = formDegree > 0 ? formDegree - 1 : formDegree + 1;
2405:       PetscInt            fiberDegree = formDegree > 0 ? 1 : -1;

2407:       PetscCall(PetscDualSpaceCreateFacetSubspace_Lagrange(sp, NULL, tensorf, traceDegree, Ncopies, PETSC_TRUE, &trace));
2408:       PetscCall(PetscDualSpaceCreateEdgeSubspace_Lagrange(sp, order, fiberDegree, 1, PETSC_TRUE, &fiber));
2409:       tracel = (PetscDualSpace_Lag *)trace->data;
2410:       fiberl = (PetscDualSpace_Lag *)fiber->data;
2411:       if (!lag->vertIndices) PetscCall(PetscLagNodeIndicesCreateTensorVertices(dm, tracel->vertIndices, &(lag->vertIndices)));
2412:       PetscCall(PetscDualSpaceGetInteriorData(trace, &intNodesTrace2, &intMatTrace));
2413:       PetscCall(PetscDualSpaceGetInteriorData(fiber, &intNodesFiber2, &intMatFiber));
2414:       if (intNodesTrace2 && intNodesFiber2) {
2415:         PetscCall(PetscQuadratureCreateTensor(intNodesTrace2, intNodesFiber2, &intNodes2));
2416:         PetscCall(MatTensorAltV(intMatTrace, intMatFiber, dim - 1, traceDegree, 1, fiberDegree, &intMat2));
2417:         PetscCall(PetscLagNodeIndicesTensor(tracel->intNodeIndices, dim - 1, traceDegree, fiberl->intNodeIndices, 1, fiberDegree, &intNodeIndices2));
2418:         if (!intMat) {
2419:           intMat         = intMat2;
2420:           intNodes       = intNodes2;
2421:           intNodeIndices = intNodeIndices2;
2422:         } else {
2423:           /* merge the matrices, quadrature points, and nodes */
2424:           PetscInt            nM;
2425:           PetscInt            nDof, nDof2;
2426:           PetscInt           *toMerged = NULL, *toMerged2 = NULL;
2427:           PetscQuadrature     merged               = NULL;
2428:           PetscLagNodeIndices intNodeIndicesMerged = NULL;
2429:           Mat                 matMerged            = NULL;

2431:           PetscCall(MatGetSize(intMat, &nDof, NULL));
2432:           PetscCall(MatGetSize(intMat2, &nDof2, NULL));
2433:           PetscCall(PetscQuadraturePointsMerge(intNodes, intNodes2, &merged, &toMerged, &toMerged2));
2434:           PetscCall(PetscQuadratureGetData(merged, NULL, NULL, &nM, NULL, NULL));
2435:           PetscCall(MatricesMerge(intMat, intMat2, dim, formDegree, nM, toMerged, toMerged2, &matMerged));
2436:           PetscCall(PetscLagNodeIndicesMerge(intNodeIndices, intNodeIndices2, &intNodeIndicesMerged));
2437:           PetscCall(PetscFree(toMerged));
2438:           PetscCall(PetscFree(toMerged2));
2439:           PetscCall(MatDestroy(&intMat));
2440:           PetscCall(MatDestroy(&intMat2));
2441:           PetscCall(PetscQuadratureDestroy(&intNodes));
2442:           PetscCall(PetscQuadratureDestroy(&intNodes2));
2443:           PetscCall(PetscLagNodeIndicesDestroy(&intNodeIndices));
2444:           PetscCall(PetscLagNodeIndicesDestroy(&intNodeIndices2));
2445:           intNodes       = merged;
2446:           intMat         = matMerged;
2447:           intNodeIndices = intNodeIndicesMerged;
2448:           if (!trimmed) {
2449:             /* I think users expect that, when a node has a full basis for the k-forms,
2450:              * they should be consecutive dofs.  That isn't the case for trimmed spaces,
2451:              * but is for some of the nodes in untrimmed spaces, so in that case we
2452:              * sort them to group them by node */
2453:             Mat intMatPerm;

2455:             PetscCall(MatPermuteByNodeIdx(intMat, intNodeIndices, &intMatPerm));
2456:             PetscCall(MatDestroy(&intMat));
2457:             intMat = intMatPerm;
2458:           }
2459:         }
2460:       }
2461:       PetscCall(PetscDualSpaceDestroy(&fiber));
2462:       PetscCall(PetscDualSpaceDestroy(&trace));
2463:     }
2464:     PetscCall(PetscQuadratureDestroy(&intNodesTrace));
2465:     PetscCall(PetscQuadratureDestroy(&intNodesFiber));
2466:     sp->intNodes        = intNodes;
2467:     sp->intMat          = intMat;
2468:     lag->intNodeIndices = intNodeIndices;
2469:     {
2470:       PetscInt nDofs = 0;

2472:       if (intMat) PetscCall(MatGetSize(intMat, &nDofs, NULL));
2473:       PetscCall(PetscSectionSetDof(section, 0, nDofs));
2474:     }
2475:     PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2476:     if (continuous) {
2477:       PetscCall(PetscDualSpaceCreateAllDataFromInteriorData(sp));
2478:       PetscCall(PetscDualSpaceLagrangeCreateAllNodeIdx(sp));
2479:     } else {
2480:       PetscCall(PetscObjectReference((PetscObject)intNodes));
2481:       sp->allNodes = intNodes;
2482:       PetscCall(PetscObjectReference((PetscObject)intMat));
2483:       sp->allMat = intMat;
2484:       PetscCall(PetscLagNodeIndicesReference(intNodeIndices));
2485:       lag->allNodeIndices = intNodeIndices;
2486:     }
2487:   }
2488:   PetscCall(PetscSectionGetStorageSize(section, &sp->spdim));
2489:   PetscCall(PetscSectionGetConstrainedStorageSize(section, &sp->spintdim));
2490:   PetscCall(PetscDualSpaceComputeFunctionalsFromAllData(sp));
2491:   PetscCall(PetscFree2(pStratStart, pStratEnd));
2492:   PetscCall(DMDestroy(&dmint));
2493:   PetscFunctionReturn(PETSC_SUCCESS);
2494: }

2496: /* Create a matrix that represents the transformation that DMPlexVecGetClosure() would need
2497:  * to get the representation of the dofs for a mesh point if the mesh point had this orientation
2498:  * relative to the cell */
2499: PetscErrorCode PetscDualSpaceCreateInteriorSymmetryMatrix_Lagrange(PetscDualSpace sp, PetscInt ornt, Mat *symMat)
2500: {
2501:   PetscDualSpace_Lag *lag;
2502:   DM                  dm;
2503:   PetscLagNodeIndices vertIndices, intNodeIndices;
2504:   PetscLagNodeIndices ni;
2505:   PetscInt            nodeIdxDim, nodeVecDim, nNodes;
2506:   PetscInt            formDegree;
2507:   PetscInt           *perm, *permOrnt;
2508:   PetscInt           *nnz;
2509:   PetscInt            n;
2510:   PetscInt            maxGroupSize;
2511:   PetscScalar        *V, *W, *work;
2512:   Mat                 A;

2514:   PetscFunctionBegin;
2515:   if (!sp->spintdim) {
2516:     *symMat = NULL;
2517:     PetscFunctionReturn(PETSC_SUCCESS);
2518:   }
2519:   lag            = (PetscDualSpace_Lag *)sp->data;
2520:   vertIndices    = lag->vertIndices;
2521:   intNodeIndices = lag->intNodeIndices;
2522:   PetscCall(PetscDualSpaceGetDM(sp, &dm));
2523:   PetscCall(PetscDualSpaceGetFormDegree(sp, &formDegree));
2524:   PetscCall(PetscNew(&ni));
2525:   ni->refct      = 1;
2526:   ni->nodeIdxDim = nodeIdxDim = intNodeIndices->nodeIdxDim;
2527:   ni->nodeVecDim = nodeVecDim = intNodeIndices->nodeVecDim;
2528:   ni->nNodes = nNodes = intNodeIndices->nNodes;
2529:   PetscCall(PetscMalloc1(nNodes * nodeIdxDim, &(ni->nodeIdx)));
2530:   PetscCall(PetscMalloc1(nNodes * nodeVecDim, &(ni->nodeVec)));
2531:   /* push forward the dofs by the symmetry of the reference element induced by ornt */
2532:   PetscCall(PetscLagNodeIndicesPushForward(dm, vertIndices, 0, vertIndices, intNodeIndices, ornt, formDegree, ni->nodeIdx, ni->nodeVec));
2533:   /* get the revlex order for both the original and transformed dofs */
2534:   PetscCall(PetscLagNodeIndicesGetPermutation(intNodeIndices, &perm));
2535:   PetscCall(PetscLagNodeIndicesGetPermutation(ni, &permOrnt));
2536:   PetscCall(PetscMalloc1(nNodes, &nnz));
2537:   for (n = 0, maxGroupSize = 0; n < nNodes;) { /* incremented in the loop */
2538:     PetscInt *nind = &(ni->nodeIdx[permOrnt[n] * nodeIdxDim]);
2539:     PetscInt  m, nEnd;
2540:     PetscInt  groupSize;
2541:     /* for each group of dofs that have the same nodeIdx coordinate */
2542:     for (nEnd = n + 1; nEnd < nNodes; nEnd++) {
2543:       PetscInt *mind = &(ni->nodeIdx[permOrnt[nEnd] * nodeIdxDim]);
2544:       PetscInt  d;

2546:       /* compare the oriented permutation indices */
2547:       for (d = 0; d < nodeIdxDim; d++)
2548:         if (mind[d] != nind[d]) break;
2549:       if (d < nodeIdxDim) break;
2550:     }
2551:     /* permOrnt[[n, nEnd)] is a group of dofs that, under the symmetry are at the same location */

2553:     /* the symmetry had better map the group of dofs with the same permuted nodeIdx
2554:      * to a group of dofs with the same size, otherwise we messed up */
2555:     if (PetscDefined(USE_DEBUG)) {
2556:       PetscInt  m;
2557:       PetscInt *nind = &(intNodeIndices->nodeIdx[perm[n] * nodeIdxDim]);

2559:       for (m = n + 1; m < nEnd; m++) {
2560:         PetscInt *mind = &(intNodeIndices->nodeIdx[perm[m] * nodeIdxDim]);
2561:         PetscInt  d;

2563:         /* compare the oriented permutation indices */
2564:         for (d = 0; d < nodeIdxDim; d++)
2565:           if (mind[d] != nind[d]) break;
2566:         if (d < nodeIdxDim) break;
2567:       }
2568:       PetscCheck(m >= nEnd, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Dofs with same index after symmetry not same block size");
2569:     }
2570:     groupSize = nEnd - n;
2571:     /* each pushforward dof vector will be expressed in a basis of the unpermuted dofs */
2572:     for (m = n; m < nEnd; m++) nnz[permOrnt[m]] = groupSize;

2574:     maxGroupSize = PetscMax(maxGroupSize, nEnd - n);
2575:     n            = nEnd;
2576:   }
2577:   PetscCheck(maxGroupSize <= nodeVecDim, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Dofs are not in blocks that can be solved");
2578:   PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, nNodes, nNodes, 0, nnz, &A));
2579:   PetscCall(PetscFree(nnz));
2580:   PetscCall(PetscMalloc3(maxGroupSize * nodeVecDim, &V, maxGroupSize * nodeVecDim, &W, nodeVecDim * 2, &work));
2581:   for (n = 0; n < nNodes;) { /* incremented in the loop */
2582:     PetscInt *nind = &(ni->nodeIdx[permOrnt[n] * nodeIdxDim]);
2583:     PetscInt  nEnd;
2584:     PetscInt  m;
2585:     PetscInt  groupSize;
2586:     for (nEnd = n + 1; nEnd < nNodes; nEnd++) {
2587:       PetscInt *mind = &(ni->nodeIdx[permOrnt[nEnd] * nodeIdxDim]);
2588:       PetscInt  d;

2590:       /* compare the oriented permutation indices */
2591:       for (d = 0; d < nodeIdxDim; d++)
2592:         if (mind[d] != nind[d]) break;
2593:       if (d < nodeIdxDim) break;
2594:     }
2595:     groupSize = nEnd - n;
2596:     /* get all of the vectors from the original and all of the pushforward vectors */
2597:     for (m = n; m < nEnd; m++) {
2598:       PetscInt d;

2600:       for (d = 0; d < nodeVecDim; d++) {
2601:         V[(m - n) * nodeVecDim + d] = intNodeIndices->nodeVec[perm[m] * nodeVecDim + d];
2602:         W[(m - n) * nodeVecDim + d] = ni->nodeVec[permOrnt[m] * nodeVecDim + d];
2603:       }
2604:     }
2605:     /* now we have to solve for W in terms of V: the systems isn't always square, but the span
2606:      * of V and W should always be the same, so the solution of the normal equations works */
2607:     {
2608:       char         transpose = 'N';
2609:       PetscBLASInt bm        = nodeVecDim;
2610:       PetscBLASInt bn        = groupSize;
2611:       PetscBLASInt bnrhs     = groupSize;
2612:       PetscBLASInt blda      = bm;
2613:       PetscBLASInt bldb      = bm;
2614:       PetscBLASInt blwork    = 2 * nodeVecDim;
2615:       PetscBLASInt info;

2617:       PetscCallBLAS("LAPACKgels", LAPACKgels_(&transpose, &bm, &bn, &bnrhs, V, &blda, W, &bldb, work, &blwork, &info));
2618:       PetscCheck(info == 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Bad argument to GELS");
2619:       /* repack */
2620:       {
2621:         PetscInt i, j;

2623:         for (i = 0; i < groupSize; i++) {
2624:           for (j = 0; j < groupSize; j++) {
2625:             /* notice the different leading dimension */
2626:             V[i * groupSize + j] = W[i * nodeVecDim + j];
2627:           }
2628:         }
2629:       }
2630:       if (PetscDefined(USE_DEBUG)) {
2631:         PetscReal res;

2633:         /* check that the normal error is 0 */
2634:         for (m = n; m < nEnd; m++) {
2635:           PetscInt d;

2637:           for (d = 0; d < nodeVecDim; d++) W[(m - n) * nodeVecDim + d] = ni->nodeVec[permOrnt[m] * nodeVecDim + d];
2638:         }
2639:         res = 0.;
2640:         for (PetscInt i = 0; i < groupSize; i++) {
2641:           for (PetscInt j = 0; j < nodeVecDim; j++) {
2642:             for (PetscInt k = 0; k < groupSize; k++) W[i * nodeVecDim + j] -= V[i * groupSize + k] * intNodeIndices->nodeVec[perm[n + k] * nodeVecDim + j];
2643:             res += PetscAbsScalar(W[i * nodeVecDim + j]);
2644:           }
2645:         }
2646:         PetscCheck(res <= PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_LIB, "Dof block did not solve");
2647:       }
2648:     }
2649:     PetscCall(MatSetValues(A, groupSize, &permOrnt[n], groupSize, &perm[n], V, INSERT_VALUES));
2650:     n = nEnd;
2651:   }
2652:   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
2653:   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
2654:   *symMat = A;
2655:   PetscCall(PetscFree3(V, W, work));
2656:   PetscCall(PetscLagNodeIndicesDestroy(&ni));
2657:   PetscFunctionReturn(PETSC_SUCCESS);
2658: }

2660: #define BaryIndex(perEdge, a, b, c) (((b) * (2 * perEdge + 1 - (b))) / 2) + (c)

2662: #define CartIndex(perEdge, a, b) (perEdge * (a) + b)

2664: /* the existing interface for symmetries is insufficient for all cases:
2665:  * - it should be sufficient for form degrees that are scalar (0 and n)
2666:  * - it should be sufficient for hypercube dofs
2667:  * - it isn't sufficient for simplex cells with non-scalar form degrees if
2668:  *   there are any dofs in the interior
2669:  *
2670:  * We compute the general transformation matrices, and if they fit, we return them,
2671:  * otherwise we error (but we should probably change the interface to allow for
2672:  * these symmetries)
2673:  */
2674: static PetscErrorCode PetscDualSpaceGetSymmetries_Lagrange(PetscDualSpace sp, const PetscInt ****perms, const PetscScalar ****flips)
2675: {
2676:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2677:   PetscInt            dim, order, Nc;

2679:   PetscFunctionBegin;
2680:   PetscCall(PetscDualSpaceGetOrder(sp, &order));
2681:   PetscCall(PetscDualSpaceGetNumComponents(sp, &Nc));
2682:   PetscCall(DMGetDimension(sp->dm, &dim));
2683:   if (!lag->symComputed) { /* store symmetries */
2684:     PetscInt       pStart, pEnd, p;
2685:     PetscInt       numPoints;
2686:     PetscInt       numFaces;
2687:     PetscInt       spintdim;
2688:     PetscInt    ***symperms;
2689:     PetscScalar ***symflips;

2691:     PetscCall(DMPlexGetChart(sp->dm, &pStart, &pEnd));
2692:     numPoints = pEnd - pStart;
2693:     {
2694:       DMPolytopeType ct;
2695:       /* The number of arrangements is no longer based on the number of faces */
2696:       PetscCall(DMPlexGetCellType(sp->dm, 0, &ct));
2697:       numFaces = DMPolytopeTypeGetNumArrangments(ct) / 2;
2698:     }
2699:     PetscCall(PetscCalloc1(numPoints, &symperms));
2700:     PetscCall(PetscCalloc1(numPoints, &symflips));
2701:     spintdim = sp->spintdim;
2702:     /* The nodal symmetry behavior is not present when tensorSpace != tensorCell: someone might want this for the "S"
2703:      * family of FEEC spaces.  Most used in particular are discontinuous polynomial L2 spaces in tensor cells, where
2704:      * the symmetries are not necessary for FE assembly.  So for now we assume this is the case and don't return
2705:      * symmetries if tensorSpace != tensorCell */
2706:     if (spintdim && 0 < dim && dim < 3 && (lag->tensorSpace == lag->tensorCell)) { /* compute self symmetries */
2707:       PetscInt    **cellSymperms;
2708:       PetscScalar **cellSymflips;
2709:       PetscInt      ornt;
2710:       PetscInt      nCopies = Nc / lag->intNodeIndices->nodeVecDim;
2711:       PetscInt      nNodes  = lag->intNodeIndices->nNodes;

2713:       lag->numSelfSym = 2 * numFaces;
2714:       lag->selfSymOff = numFaces;
2715:       PetscCall(PetscCalloc1(2 * numFaces, &cellSymperms));
2716:       PetscCall(PetscCalloc1(2 * numFaces, &cellSymflips));
2717:       /* we want to be able to index symmetries directly with the orientations, which range from [-numFaces,numFaces) */
2718:       symperms[0] = &cellSymperms[numFaces];
2719:       symflips[0] = &cellSymflips[numFaces];
2720:       PetscCheck(lag->intNodeIndices->nodeVecDim * nCopies == Nc, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Node indices incompatible with dofs");
2721:       PetscCheck(nNodes * nCopies == spintdim, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Node indices incompatible with dofs");
2722:       for (ornt = -numFaces; ornt < numFaces; ornt++) { /* for every symmetry, compute the symmetry matrix, and extract rows to see if it fits in the perm + flip framework */
2723:         Mat          symMat;
2724:         PetscInt    *perm;
2725:         PetscScalar *flips;
2726:         PetscInt     i;

2728:         if (!ornt) continue;
2729:         PetscCall(PetscMalloc1(spintdim, &perm));
2730:         PetscCall(PetscCalloc1(spintdim, &flips));
2731:         for (i = 0; i < spintdim; i++) perm[i] = -1;
2732:         PetscCall(PetscDualSpaceCreateInteriorSymmetryMatrix_Lagrange(sp, ornt, &symMat));
2733:         for (i = 0; i < nNodes; i++) {
2734:           PetscInt           ncols;
2735:           PetscInt           j, k;
2736:           const PetscInt    *cols;
2737:           const PetscScalar *vals;
2738:           PetscBool          nz_seen = PETSC_FALSE;

2740:           PetscCall(MatGetRow(symMat, i, &ncols, &cols, &vals));
2741:           for (j = 0; j < ncols; j++) {
2742:             if (PetscAbsScalar(vals[j]) > PETSC_SMALL) {
2743:               PetscCheck(!nz_seen, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "This dual space has symmetries that can't be described as a permutation + sign flips");
2744:               nz_seen = PETSC_TRUE;
2745:               PetscCheck(PetscAbsReal(PetscAbsScalar(vals[j]) - PetscRealConstant(1.)) <= PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "This dual space has symmetries that can't be described as a permutation + sign flips");
2746:               PetscCheck(PetscAbsReal(PetscImaginaryPart(vals[j])) <= PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "This dual space has symmetries that can't be described as a permutation + sign flips");
2747:               PetscCheck(perm[cols[j] * nCopies] < 0, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "This dual space has symmetries that can't be described as a permutation + sign flips");
2748:               for (k = 0; k < nCopies; k++) perm[cols[j] * nCopies + k] = i * nCopies + k;
2749:               if (PetscRealPart(vals[j]) < 0.) {
2750:                 for (k = 0; k < nCopies; k++) flips[i * nCopies + k] = -1.;
2751:               } else {
2752:                 for (k = 0; k < nCopies; k++) flips[i * nCopies + k] = 1.;
2753:               }
2754:             }
2755:           }
2756:           PetscCall(MatRestoreRow(symMat, i, &ncols, &cols, &vals));
2757:         }
2758:         PetscCall(MatDestroy(&symMat));
2759:         /* if there were no sign flips, keep NULL */
2760:         for (i = 0; i < spintdim; i++)
2761:           if (flips[i] != 1.) break;
2762:         if (i == spintdim) {
2763:           PetscCall(PetscFree(flips));
2764:           flips = NULL;
2765:         }
2766:         /* if the permutation is identity, keep NULL */
2767:         for (i = 0; i < spintdim; i++)
2768:           if (perm[i] != i) break;
2769:         if (i == spintdim) {
2770:           PetscCall(PetscFree(perm));
2771:           perm = NULL;
2772:         }
2773:         symperms[0][ornt] = perm;
2774:         symflips[0][ornt] = flips;
2775:       }
2776:       /* if no orientations produced non-identity permutations, keep NULL */
2777:       for (ornt = -numFaces; ornt < numFaces; ornt++)
2778:         if (symperms[0][ornt]) break;
2779:       if (ornt == numFaces) {
2780:         PetscCall(PetscFree(cellSymperms));
2781:         symperms[0] = NULL;
2782:       }
2783:       /* if no orientations produced sign flips, keep NULL */
2784:       for (ornt = -numFaces; ornt < numFaces; ornt++)
2785:         if (symflips[0][ornt]) break;
2786:       if (ornt == numFaces) {
2787:         PetscCall(PetscFree(cellSymflips));
2788:         symflips[0] = NULL;
2789:       }
2790:     }
2791:     { /* get the symmetries of closure points */
2792:       PetscInt  closureSize = 0;
2793:       PetscInt *closure     = NULL;
2794:       PetscInt  r;

2796:       PetscCall(DMPlexGetTransitiveClosure(sp->dm, 0, PETSC_TRUE, &closureSize, &closure));
2797:       for (r = 0; r < closureSize; r++) {
2798:         PetscDualSpace       psp;
2799:         PetscInt             point = closure[2 * r];
2800:         PetscInt             pspintdim;
2801:         const PetscInt    ***psymperms = NULL;
2802:         const PetscScalar ***psymflips = NULL;

2804:         if (!point) continue;
2805:         PetscCall(PetscDualSpaceGetPointSubspace(sp, point, &psp));
2806:         if (!psp) continue;
2807:         PetscCall(PetscDualSpaceGetInteriorDimension(psp, &pspintdim));
2808:         if (!pspintdim) continue;
2809:         PetscCall(PetscDualSpaceGetSymmetries(psp, &psymperms, &psymflips));
2810:         symperms[r] = (PetscInt **)(psymperms ? psymperms[0] : NULL);
2811:         symflips[r] = (PetscScalar **)(psymflips ? psymflips[0] : NULL);
2812:       }
2813:       PetscCall(DMPlexRestoreTransitiveClosure(sp->dm, 0, PETSC_TRUE, &closureSize, &closure));
2814:     }
2815:     for (p = 0; p < pEnd; p++)
2816:       if (symperms[p]) break;
2817:     if (p == pEnd) {
2818:       PetscCall(PetscFree(symperms));
2819:       symperms = NULL;
2820:     }
2821:     for (p = 0; p < pEnd; p++)
2822:       if (symflips[p]) break;
2823:     if (p == pEnd) {
2824:       PetscCall(PetscFree(symflips));
2825:       symflips = NULL;
2826:     }
2827:     lag->symperms    = symperms;
2828:     lag->symflips    = symflips;
2829:     lag->symComputed = PETSC_TRUE;
2830:   }
2831:   if (perms) *perms = (const PetscInt ***)lag->symperms;
2832:   if (flips) *flips = (const PetscScalar ***)lag->symflips;
2833:   PetscFunctionReturn(PETSC_SUCCESS);
2834: }

2836: static PetscErrorCode PetscDualSpaceLagrangeGetContinuity_Lagrange(PetscDualSpace sp, PetscBool *continuous)
2837: {
2838:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;

2840:   PetscFunctionBegin;
2843:   *continuous = lag->continuous;
2844:   PetscFunctionReturn(PETSC_SUCCESS);
2845: }

2847: static PetscErrorCode PetscDualSpaceLagrangeSetContinuity_Lagrange(PetscDualSpace sp, PetscBool continuous)
2848: {
2849:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;

2851:   PetscFunctionBegin;
2853:   lag->continuous = continuous;
2854:   PetscFunctionReturn(PETSC_SUCCESS);
2855: }

2857: /*@
2858:   PetscDualSpaceLagrangeGetContinuity - Retrieves the flag for element continuity

2860:   Not Collective

2862:   Input Parameter:
2863: . sp         - the `PetscDualSpace`

2865:   Output Parameter:
2866: . continuous - flag for element continuity

2868:   Level: intermediate

2870: .seealso: `PetscDualSpace`, `PetscDualSpaceLagrangeSetContinuity()`
2871: @*/
2872: PetscErrorCode PetscDualSpaceLagrangeGetContinuity(PetscDualSpace sp, PetscBool *continuous)
2873: {
2874:   PetscFunctionBegin;
2877:   PetscTryMethod(sp, "PetscDualSpaceLagrangeGetContinuity_C", (PetscDualSpace, PetscBool *), (sp, continuous));
2878:   PetscFunctionReturn(PETSC_SUCCESS);
2879: }

2881: /*@
2882:   PetscDualSpaceLagrangeSetContinuity - Indicate whether the element is continuous

2884:   Logically Collective on sp

2886:   Input Parameters:
2887: + sp         - the `PetscDualSpace`
2888: - continuous - flag for element continuity

2890:   Options Database:
2891: . -petscdualspace_lagrange_continuity <bool> - use a continuous element

2893:   Level: intermediate

2895: .seealso: `PetscDualSpace`, `PetscDualSpaceLagrangeGetContinuity()`
2896: @*/
2897: PetscErrorCode PetscDualSpaceLagrangeSetContinuity(PetscDualSpace sp, PetscBool continuous)
2898: {
2899:   PetscFunctionBegin;
2902:   PetscTryMethod(sp, "PetscDualSpaceLagrangeSetContinuity_C", (PetscDualSpace, PetscBool), (sp, continuous));
2903:   PetscFunctionReturn(PETSC_SUCCESS);
2904: }

2906: static PetscErrorCode PetscDualSpaceLagrangeGetTensor_Lagrange(PetscDualSpace sp, PetscBool *tensor)
2907: {
2908:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;

2910:   PetscFunctionBegin;
2911:   *tensor = lag->tensorSpace;
2912:   PetscFunctionReturn(PETSC_SUCCESS);
2913: }

2915: static PetscErrorCode PetscDualSpaceLagrangeSetTensor_Lagrange(PetscDualSpace sp, PetscBool tensor)
2916: {
2917:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;

2919:   PetscFunctionBegin;
2920:   lag->tensorSpace = tensor;
2921:   PetscFunctionReturn(PETSC_SUCCESS);
2922: }

2924: static PetscErrorCode PetscDualSpaceLagrangeGetTrimmed_Lagrange(PetscDualSpace sp, PetscBool *trimmed)
2925: {
2926:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;

2928:   PetscFunctionBegin;
2929:   *trimmed = lag->trimmed;
2930:   PetscFunctionReturn(PETSC_SUCCESS);
2931: }

2933: static PetscErrorCode PetscDualSpaceLagrangeSetTrimmed_Lagrange(PetscDualSpace sp, PetscBool trimmed)
2934: {
2935:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;

2937:   PetscFunctionBegin;
2938:   lag->trimmed = trimmed;
2939:   PetscFunctionReturn(PETSC_SUCCESS);
2940: }

2942: static PetscErrorCode PetscDualSpaceLagrangeGetNodeType_Lagrange(PetscDualSpace sp, PetscDTNodeType *nodeType, PetscBool *boundary, PetscReal *exponent)
2943: {
2944:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;

2946:   PetscFunctionBegin;
2947:   if (nodeType) *nodeType = lag->nodeType;
2948:   if (boundary) *boundary = lag->endNodes;
2949:   if (exponent) *exponent = lag->nodeExponent;
2950:   PetscFunctionReturn(PETSC_SUCCESS);
2951: }

2953: static PetscErrorCode PetscDualSpaceLagrangeSetNodeType_Lagrange(PetscDualSpace sp, PetscDTNodeType nodeType, PetscBool boundary, PetscReal exponent)
2954: {
2955:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;

2957:   PetscFunctionBegin;
2958:   PetscCheck(nodeType != PETSCDTNODES_GAUSSJACOBI || exponent > -1., PetscObjectComm((PetscObject)sp), PETSC_ERR_ARG_OUTOFRANGE, "Exponent must be > -1");
2959:   lag->nodeType     = nodeType;
2960:   lag->endNodes     = boundary;
2961:   lag->nodeExponent = exponent;
2962:   PetscFunctionReturn(PETSC_SUCCESS);
2963: }

2965: static PetscErrorCode PetscDualSpaceLagrangeGetUseMoments_Lagrange(PetscDualSpace sp, PetscBool *useMoments)
2966: {
2967:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;

2969:   PetscFunctionBegin;
2970:   *useMoments = lag->useMoments;
2971:   PetscFunctionReturn(PETSC_SUCCESS);
2972: }

2974: static PetscErrorCode PetscDualSpaceLagrangeSetUseMoments_Lagrange(PetscDualSpace sp, PetscBool useMoments)
2975: {
2976:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;

2978:   PetscFunctionBegin;
2979:   lag->useMoments = useMoments;
2980:   PetscFunctionReturn(PETSC_SUCCESS);
2981: }

2983: static PetscErrorCode PetscDualSpaceLagrangeGetMomentOrder_Lagrange(PetscDualSpace sp, PetscInt *momentOrder)
2984: {
2985:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;

2987:   PetscFunctionBegin;
2988:   *momentOrder = lag->momentOrder;
2989:   PetscFunctionReturn(PETSC_SUCCESS);
2990: }

2992: static PetscErrorCode PetscDualSpaceLagrangeSetMomentOrder_Lagrange(PetscDualSpace sp, PetscInt momentOrder)
2993: {
2994:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;

2996:   PetscFunctionBegin;
2997:   lag->momentOrder = momentOrder;
2998:   PetscFunctionReturn(PETSC_SUCCESS);
2999: }

3001: /*@
3002:   PetscDualSpaceLagrangeGetTensor - Get the tensor nature of the dual space

3004:   Not collective

3006:   Input Parameter:
3007: . sp - The `PetscDualSpace`

3009:   Output Parameter:
3010: . tensor - Whether the dual space has tensor layout (vs. simplicial)

3012:   Level: intermediate

3014: .seealso: `PetscDualSpace`, `PetscDualSpaceLagrangeSetTensor()`, `PetscDualSpaceCreate()`
3015: @*/
3016: PetscErrorCode PetscDualSpaceLagrangeGetTensor(PetscDualSpace sp, PetscBool *tensor)
3017: {
3018:   PetscFunctionBegin;
3021:   PetscTryMethod(sp, "PetscDualSpaceLagrangeGetTensor_C", (PetscDualSpace, PetscBool *), (sp, tensor));
3022:   PetscFunctionReturn(PETSC_SUCCESS);
3023: }

3025: /*@
3026:   PetscDualSpaceLagrangeSetTensor - Set the tensor nature of the dual space

3028:   Not collective

3030:   Input Parameters:
3031: + sp - The `PetscDualSpace`
3032: - tensor - Whether the dual space has tensor layout (vs. simplicial)

3034:   Level: intermediate

3036: .seealso: `PetscDualSpace`, `PetscDualSpaceLagrangeGetTensor()`, `PetscDualSpaceCreate()`
3037: @*/
3038: PetscErrorCode PetscDualSpaceLagrangeSetTensor(PetscDualSpace sp, PetscBool tensor)
3039: {
3040:   PetscFunctionBegin;
3042:   PetscTryMethod(sp, "PetscDualSpaceLagrangeSetTensor_C", (PetscDualSpace, PetscBool), (sp, tensor));
3043:   PetscFunctionReturn(PETSC_SUCCESS);
3044: }

3046: /*@
3047:   PetscDualSpaceLagrangeGetTrimmed - Get the trimmed nature of the dual space

3049:   Not collective

3051:   Input Parameter:
3052: . sp - The `PetscDualSpace`

3054:   Output Parameter:
3055: . trimmed - Whether the dual space represents to dual basis of a trimmed polynomial space (e.g. Raviart-Thomas and higher order / other form degree variants)

3057:   Level: intermediate

3059: .seealso: `PetscDualSpace`, `PetscDualSpaceLagrangeSetTrimmed()`, `PetscDualSpaceCreate()`
3060: @*/
3061: PetscErrorCode PetscDualSpaceLagrangeGetTrimmed(PetscDualSpace sp, PetscBool *trimmed)
3062: {
3063:   PetscFunctionBegin;
3066:   PetscTryMethod(sp, "PetscDualSpaceLagrangeGetTrimmed_C", (PetscDualSpace, PetscBool *), (sp, trimmed));
3067:   PetscFunctionReturn(PETSC_SUCCESS);
3068: }

3070: /*@
3071:   PetscDualSpaceLagrangeSetTrimmed - Set the trimmed nature of the dual space

3073:   Not collective

3075:   Input Parameters:
3076: + sp - The `PetscDualSpace`
3077: - trimmed - Whether the dual space represents to dual basis of a trimmed polynomial space (e.g. Raviart-Thomas and higher order / other form degree variants)

3079:   Level: intermediate

3081: .seealso: `PetscDualSpace`, `PetscDualSpaceLagrangeGetTrimmed()`, `PetscDualSpaceCreate()`
3082: @*/
3083: PetscErrorCode PetscDualSpaceLagrangeSetTrimmed(PetscDualSpace sp, PetscBool trimmed)
3084: {
3085:   PetscFunctionBegin;
3087:   PetscTryMethod(sp, "PetscDualSpaceLagrangeSetTrimmed_C", (PetscDualSpace, PetscBool), (sp, trimmed));
3088:   PetscFunctionReturn(PETSC_SUCCESS);
3089: }

3091: /*@
3092:   PetscDualSpaceLagrangeGetNodeType - Get a description of how nodes are laid out for Lagrange polynomials in this
3093:   dual space

3095:   Not collective

3097:   Input Parameter:
3098: . sp - The `PetscDualSpace`

3100:   Output Parameters:
3101: + nodeType - The type of nodes
3102: . boundary - Whether the node type is one that includes endpoints (if nodeType is `PETSCDTNODES_GAUSSJACOBI`, nodes that
3103:              include the boundary are Gauss-Lobatto-Jacobi nodes)
3104: - exponent - If nodeType is `PETSCDTNODES_GAUSJACOBI`, indicates the exponent used for both ends of the 1D Jacobi weight function
3105:              '0' is Gauss-Legendre, '-0.5' is Gauss-Chebyshev of the first type, '0.5' is Gauss-Chebyshev of the second type

3107:   Level: advanced

3109: .seealso: `PetscDualSpace`, `PetscDTNodeType`, `PetscDualSpaceLagrangeSetNodeType()`
3110: @*/
3111: PetscErrorCode PetscDualSpaceLagrangeGetNodeType(PetscDualSpace sp, PetscDTNodeType *nodeType, PetscBool *boundary, PetscReal *exponent)
3112: {
3113:   PetscFunctionBegin;
3118:   PetscTryMethod(sp, "PetscDualSpaceLagrangeGetNodeType_C", (PetscDualSpace, PetscDTNodeType *, PetscBool *, PetscReal *), (sp, nodeType, boundary, exponent));
3119:   PetscFunctionReturn(PETSC_SUCCESS);
3120: }

3122: /*@
3123:   PetscDualSpaceLagrangeSetNodeType - Set a description of how nodes are laid out for Lagrange polynomials in this
3124:   dual space

3126:   Logically collective

3128:   Input Parameters:
3129: + sp - The `PetscDualSpace`
3130: . nodeType - The type of nodes
3131: . boundary - Whether the node type is one that includes endpoints (if nodeType is `PETSCDTNODES_GAUSSJACOBI`, nodes that
3132:              include the boundary are Gauss-Lobatto-Jacobi nodes)
3133: - exponent - If nodeType is `PETSCDTNODES_GAUSJACOBI`, indicates the exponent used for both ends of the 1D Jacobi weight function
3134:              '0' is Gauss-Legendre, '-0.5' is Gauss-Chebyshev of the first type, '0.5' is Gauss-Chebyshev of the second type

3136:   Level: advanced

3138: .seealso: `PetscDualSpace`, `PetscDTNodeType`, `PetscDualSpaceLagrangeGetNodeType()`
3139: @*/
3140: PetscErrorCode PetscDualSpaceLagrangeSetNodeType(PetscDualSpace sp, PetscDTNodeType nodeType, PetscBool boundary, PetscReal exponent)
3141: {
3142:   PetscFunctionBegin;
3144:   PetscTryMethod(sp, "PetscDualSpaceLagrangeSetNodeType_C", (PetscDualSpace, PetscDTNodeType, PetscBool, PetscReal), (sp, nodeType, boundary, exponent));
3145:   PetscFunctionReturn(PETSC_SUCCESS);
3146: }

3148: /*@
3149:   PetscDualSpaceLagrangeGetUseMoments - Get the flag for using moment functionals

3151:   Not collective

3153:   Input Parameter:
3154: . sp - The `PetscDualSpace`

3156:   Output Parameter:
3157: . useMoments - Moment flag

3159:   Level: advanced

3161: .seealso: `PetscDualSpace`, `PetscDualSpaceLagrangeSetUseMoments()`
3162: @*/
3163: PetscErrorCode PetscDualSpaceLagrangeGetUseMoments(PetscDualSpace sp, PetscBool *useMoments)
3164: {
3165:   PetscFunctionBegin;
3168:   PetscUseMethod(sp, "PetscDualSpaceLagrangeGetUseMoments_C", (PetscDualSpace, PetscBool *), (sp, useMoments));
3169:   PetscFunctionReturn(PETSC_SUCCESS);
3170: }

3172: /*@
3173:   PetscDualSpaceLagrangeSetUseMoments - Set the flag for moment functionals

3175:   Logically collective

3177:   Input Parameters:
3178: + sp - The `PetscDualSpace`
3179: - useMoments - The flag for moment functionals

3181:   Level: advanced

3183: .seealso: `PetscDualSpace`, `PetscDualSpaceLagrangeGetUseMoments()`
3184: @*/
3185: PetscErrorCode PetscDualSpaceLagrangeSetUseMoments(PetscDualSpace sp, PetscBool useMoments)
3186: {
3187:   PetscFunctionBegin;
3189:   PetscTryMethod(sp, "PetscDualSpaceLagrangeSetUseMoments_C", (PetscDualSpace, PetscBool), (sp, useMoments));
3190:   PetscFunctionReturn(PETSC_SUCCESS);
3191: }

3193: /*@
3194:   PetscDualSpaceLagrangeGetMomentOrder - Get the order for moment integration

3196:   Not collective

3198:   Input Parameter:
3199: . sp - The `PetscDualSpace`

3201:   Output Parameter:
3202: . order - Moment integration order

3204:   Level: advanced

3206: .seealso: `PetscDualSpace`, `PetscDualSpaceLagrangeSetMomentOrder()`
3207: @*/
3208: PetscErrorCode PetscDualSpaceLagrangeGetMomentOrder(PetscDualSpace sp, PetscInt *order)
3209: {
3210:   PetscFunctionBegin;
3213:   PetscUseMethod(sp, "PetscDualSpaceLagrangeGetMomentOrder_C", (PetscDualSpace, PetscInt *), (sp, order));
3214:   PetscFunctionReturn(PETSC_SUCCESS);
3215: }

3217: /*@
3218:   PetscDualSpaceLagrangeSetMomentOrder - Set the order for moment integration

3220:   Logically collective

3222:   Input Parameters:
3223: + sp - The `PetscDualSpace`
3224: - order - The order for moment integration

3226:   Level: advanced

3228: .seealso: `PetscDualSpace`, `PetscDualSpaceLagrangeGetMomentOrder()`
3229: @*/
3230: PetscErrorCode PetscDualSpaceLagrangeSetMomentOrder(PetscDualSpace sp, PetscInt order)
3231: {
3232:   PetscFunctionBegin;
3234:   PetscTryMethod(sp, "PetscDualSpaceLagrangeSetMomentOrder_C", (PetscDualSpace, PetscInt), (sp, order));
3235:   PetscFunctionReturn(PETSC_SUCCESS);
3236: }

3238: static PetscErrorCode PetscDualSpaceInitialize_Lagrange(PetscDualSpace sp)
3239: {
3240:   PetscFunctionBegin;
3241:   sp->ops->destroy              = PetscDualSpaceDestroy_Lagrange;
3242:   sp->ops->view                 = PetscDualSpaceView_Lagrange;
3243:   sp->ops->setfromoptions       = PetscDualSpaceSetFromOptions_Lagrange;
3244:   sp->ops->duplicate            = PetscDualSpaceDuplicate_Lagrange;
3245:   sp->ops->setup                = PetscDualSpaceSetUp_Lagrange;
3246:   sp->ops->createheightsubspace = NULL;
3247:   sp->ops->createpointsubspace  = NULL;
3248:   sp->ops->getsymmetries        = PetscDualSpaceGetSymmetries_Lagrange;
3249:   sp->ops->apply                = PetscDualSpaceApplyDefault;
3250:   sp->ops->applyall             = PetscDualSpaceApplyAllDefault;
3251:   sp->ops->applyint             = PetscDualSpaceApplyInteriorDefault;
3252:   sp->ops->createalldata        = PetscDualSpaceCreateAllDataDefault;
3253:   sp->ops->createintdata        = PetscDualSpaceCreateInteriorDataDefault;
3254:   PetscFunctionReturn(PETSC_SUCCESS);
3255: }

3257: /*MC
3258:   PETSCDUALSPACELAGRANGE = "lagrange" - A `PetscDualSpaceType` that encapsulates a dual space of pointwise evaluation functionals

3260:   Level: intermediate

3262: .seealso: `PetscDualSpace`, `PetscDualSpaceType`, `PetscDualSpaceCreate()`, `PetscDualSpaceSetType()`
3263: M*/
3264: PETSC_EXTERN PetscErrorCode PetscDualSpaceCreate_Lagrange(PetscDualSpace sp)
3265: {
3266:   PetscDualSpace_Lag *lag;

3268:   PetscFunctionBegin;
3270:   PetscCall(PetscNew(&lag));
3271:   sp->data = lag;

3273:   lag->tensorCell  = PETSC_FALSE;
3274:   lag->tensorSpace = PETSC_FALSE;
3275:   lag->continuous  = PETSC_TRUE;
3276:   lag->numCopies   = PETSC_DEFAULT;
3277:   lag->numNodeSkip = PETSC_DEFAULT;
3278:   lag->nodeType    = PETSCDTNODES_DEFAULT;
3279:   lag->useMoments  = PETSC_FALSE;
3280:   lag->momentOrder = 0;

3282:   PetscCall(PetscDualSpaceInitialize_Lagrange(sp));
3283:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetContinuity_C", PetscDualSpaceLagrangeGetContinuity_Lagrange));
3284:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetContinuity_C", PetscDualSpaceLagrangeSetContinuity_Lagrange));
3285:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetTensor_C", PetscDualSpaceLagrangeGetTensor_Lagrange));
3286:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetTensor_C", PetscDualSpaceLagrangeSetTensor_Lagrange));
3287:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetTrimmed_C", PetscDualSpaceLagrangeGetTrimmed_Lagrange));
3288:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetTrimmed_C", PetscDualSpaceLagrangeSetTrimmed_Lagrange));
3289:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetNodeType_C", PetscDualSpaceLagrangeGetNodeType_Lagrange));
3290:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetNodeType_C", PetscDualSpaceLagrangeSetNodeType_Lagrange));
3291:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetUseMoments_C", PetscDualSpaceLagrangeGetUseMoments_Lagrange));
3292:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetUseMoments_C", PetscDualSpaceLagrangeSetUseMoments_Lagrange));
3293:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetMomentOrder_C", PetscDualSpaceLagrangeGetMomentOrder_Lagrange));
3294:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetMomentOrder_C", PetscDualSpaceLagrangeSetMomentOrder_Lagrange));
3295:   PetscFunctionReturn(PETSC_SUCCESS);
3296: }