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    npoints;
149:   PetscReal **nodesets = NULL;
150:   PetscInt    worksize;
151:   PetscReal  *nodework;
152:   PetscInt   *tupwork;

154:   PetscFunctionBegin;
155:   PetscCheck(dim >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Must have non-negative dimension");
156:   PetscCheck(degree >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Must have non-negative degree");
157:   if (!dim) PetscFunctionReturn(PETSC_SUCCESS);
158:   PetscCall(PetscCalloc1(dim + 2, &tup));
159:   PetscCall(PetscDTBinomialInt(degree + dim, dim, &npoints));
160:   PetscCall(Petsc1DNodeFamilyGetNodeSets(f, degree, &nodesets));
161:   worksize = ((dim + 2) * (dim + 3)) / 2;
162:   PetscCall(PetscCalloc2(worksize, &nodework, worksize, &tupwork));
163:   /* loop over the tuples of length dim with sum at most degree */
164:   for (PetscInt k = 0; k < npoints; k++) {
165:     PetscInt i;

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

201: /* 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
202:  * on that mesh point, we have to be careful about getting/adding everything in the right place.
203:  *
204:  * With nodal dofs like PETSCDUALSPACELAGRANGE makes, the general approach to calculate the value of dofs associate
205:  * with a node A is
206:  * - transform the node locations x(A) by the map that takes the mesh point to its reorientation, x' = phi(x(A))
207:  * - figure out which node was originally at the location of the transformed point, A' = idx(x')
208:  * - if the dofs are not scalars, figure out how to represent the transformed dofs in terms of the basis
209:  *   of dofs at A' (using pushforward/pullback rules)
210:  *
211:  * The one sticky point with this approach is the "A' = idx(x')" step: trying to go from real valued coordinates
212:  * back to indices.  I don't want to rely on floating point tolerances.  Additionally, PETSCDUALSPACELAGRANGE may
213:  * eventually support quasi-Lagrangian dofs, which could involve quadrature at multiple points, so the location "x(A)"
214:  * would be ambiguous.
215:  *
216:  * So each dof gets an integer value coordinate (nodeIdx in the structure below).  The choice of integer coordinates
217:  * is somewhat arbitrary, as long as all of the relevant symmetries of the mesh point correspond to *permutations* of
218:  * the integer coordinates, which do not depend on numerical precision.
219:  *
220:  * So
221:  *
222:  * - DMPlexGetTransitiveClosure_Internal() tells me how an orientation turns into a permutation of the vertices of a
223:  *   mesh point
224:  * - The permutation of the vertices, and the nodeIdx values assigned to them, tells what permutation in index space
225:  *   is associated with the orientation
226:  * - I uses that permutation to get xi' = phi(xi(A)), the integer coordinate of the transformed dof
227:  * - I can without numerical issues compute A' = idx(xi')
228:  *
229:  * Here are some examples of how the process works
230:  *
231:  * - With a triangle:
232:  *
233:  *   The triangle has the following integer coordinates for vertices, taken from the barycentric triangle
234:  *
235:  *     closure order 2
236:  *     nodeIdx (0,0,1)
237:  *      \
238:  *       +
239:  *       |\
240:  *       | \
241:  *       |  \
242:  *       |   \    closure order 1
243:  *       |    \ / nodeIdx (0,1,0)
244:  *       +-----+
245:  *        \
246:  *      closure order 0
247:  *      nodeIdx (1,0,0)
248:  *
249:  *   If I do DMPlexGetTransitiveClosure_Internal() with orientation 1, the vertices would appear
250:  *   in the order (1, 2, 0)
251:  *
252:  *   If I list the nodeIdx of each vertex in closure order for orientation 0 (0, 1, 2) and orientation 1 (1, 2, 0), I
253:  *   see
254:  *
255:  *   orientation 0  | orientation 1
256:  *
257:  *   [0] (1,0,0)      [1] (0,1,0)
258:  *   [1] (0,1,0)      [2] (0,0,1)
259:  *   [2] (0,0,1)      [0] (1,0,0)
260:  *          A                B
261:  *
262:  *   In other words, B is the result of a row permutation of A.  But, there is also
263:  *   a column permutation that accomplishes the same result, (2,0,1).
264:  *
265:  *   So if a dof has nodeIdx coordinate (a,b,c), after the transformation its nodeIdx coordinate
266:  *   is (c,a,b), and the transformed degree of freedom will be a linear combination of dofs
267:  *   that originally had coordinate (c,a,b).
268:  *
269:  * - With a quadrilateral:
270:  *
271:  *   The quadrilateral has the following integer coordinates for vertices, taken from concatenating barycentric
272:  *   coordinates for two segments:
273:  *
274:  *     closure order 3      closure order 2
275:  *     nodeIdx (1,0,0,1)    nodeIdx (0,1,0,1)
276:  *                   \      /
277:  *                    +----+
278:  *                    |    |
279:  *                    |    |
280:  *                    +----+
281:  *                   /      \
282:  *     closure order 0      closure order 1
283:  *     nodeIdx (1,0,1,0)    nodeIdx (0,1,1,0)
284:  *
285:  *   If I do DMPlexGetTransitiveClosure_Internal() with orientation 1, the vertices would appear
286:  *   in the order (1, 2, 3, 0)
287:  *
288:  *   If I list the nodeIdx of each vertex in closure order for orientation 0 (0, 1, 2, 3) and
289:  *   orientation 1 (1, 2, 3, 0), I see
290:  *
291:  *   orientation 0  | orientation 1
292:  *
293:  *   [0] (1,0,1,0)    [1] (0,1,1,0)
294:  *   [1] (0,1,1,0)    [2] (0,1,0,1)
295:  *   [2] (0,1,0,1)    [3] (1,0,0,1)
296:  *   [3] (1,0,0,1)    [0] (1,0,1,0)
297:  *          A                B
298:  *
299:  *   The column permutation that accomplishes the same result is (3,2,0,1).
300:  *
301:  *   So if a dof has nodeIdx coordinate (a,b,c,d), after the transformation its nodeIdx coordinate
302:  *   is (d,c,a,b), and the transformed degree of freedom will be a linear combination of dofs
303:  *   that originally had coordinate (d,c,a,b).
304:  *
305:  * Previously PETSCDUALSPACELAGRANGE had hardcoded symmetries for the triangle and quadrilateral,
306:  * but this approach will work for any polytope, such as the wedge (triangular prism).
307:  */
308: struct _n_PetscLagNodeIndices {
309:   PetscInt   refct;
310:   PetscInt   nodeIdxDim;
311:   PetscInt   nodeVecDim;
312:   PetscInt   nNodes;
313:   PetscInt  *nodeIdx; /* for each node an index of size nodeIdxDim */
314:   PetscReal *nodeVec; /* for each node a vector of size nodeVecDim */
315:   PetscInt  *perm;    /* if these are vertices, perm takes DMPlex point index to closure order;
316:                               if these are nodes, perm lists nodes in index revlex order */
317: };

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

1007: /* just the points, weights aren't handled */
1008: static PetscErrorCode PetscQuadratureCreateTensor(PetscQuadrature trace, PetscQuadrature fiber, PetscQuadrature *product)
1009: {
1010:   PetscInt         dimTrace, dimFiber;
1011:   PetscInt         numPointsTrace, numPointsFiber;
1012:   PetscInt         dim, numPoints;
1013:   const PetscReal *pointsTrace;
1014:   const PetscReal *pointsFiber;
1015:   PetscReal       *points;
1016:   PetscInt         i, j, k, p;

1018:   PetscFunctionBegin;
1019:   PetscCall(PetscQuadratureGetData(trace, &dimTrace, NULL, &numPointsTrace, &pointsTrace, NULL));
1020:   PetscCall(PetscQuadratureGetData(fiber, &dimFiber, NULL, &numPointsFiber, &pointsFiber, NULL));
1021:   dim       = dimTrace + dimFiber;
1022:   numPoints = numPointsFiber * numPointsTrace;
1023:   PetscCall(PetscMalloc1(numPoints * dim, &points));
1024:   for (p = 0, j = 0; j < numPointsFiber; j++) {
1025:     for (i = 0; i < numPointsTrace; i++, p++) {
1026:       for (k = 0; k < dimTrace; k++) points[p * dim + k] = pointsTrace[i * dimTrace + k];
1027:       for (k = 0; k < dimFiber; k++) points[p * dim + dimTrace + k] = pointsFiber[j * dimFiber + k];
1028:     }
1029:   }
1030:   PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, product));
1031:   PetscCall(PetscQuadratureSetData(*product, dim, 0, numPoints, points, NULL));
1032:   PetscFunctionReturn(PETSC_SUCCESS);
1033: }

1035: /* Kronecker tensor product where matrix is considered a matrix of k-forms, so that
1036:  * the entries in the product matrix are wedge products of the entries in the original matrices */
1037: static PetscErrorCode MatTensorAltV(Mat trace, Mat fiber, PetscInt dimTrace, PetscInt kTrace, PetscInt dimFiber, PetscInt kFiber, Mat *product)
1038: {
1039:   PetscInt     mTrace, nTrace, mFiber, nFiber, m, n, k, i, j, l;
1040:   PetscInt     dim, NkTrace, NkFiber, Nk;
1041:   PetscInt     dT, dF;
1042:   PetscInt    *nnzTrace, *nnzFiber, *nnz;
1043:   PetscInt     iT, iF, jT, jF, il, jl;
1044:   PetscReal   *workT, *workT2, *workF, *workF2, *work, *workstar;
1045:   PetscReal   *projT, *projF;
1046:   PetscReal   *projTstar, *projFstar;
1047:   PetscReal   *wedgeMat;
1048:   PetscReal    sign;
1049:   PetscScalar *workS;
1050:   Mat          prod;
1051:   /* this produces dof groups that look like the identity */

1053:   PetscFunctionBegin;
1054:   PetscCall(MatGetSize(trace, &mTrace, &nTrace));
1055:   PetscCall(PetscDTBinomialInt(dimTrace, PetscAbsInt(kTrace), &NkTrace));
1056:   PetscCheck(nTrace % NkTrace == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "point value space of trace matrix is not a multiple of k-form size");
1057:   PetscCall(MatGetSize(fiber, &mFiber, &nFiber));
1058:   PetscCall(PetscDTBinomialInt(dimFiber, PetscAbsInt(kFiber), &NkFiber));
1059:   PetscCheck(nFiber % NkFiber == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "point value space of fiber matrix is not a multiple of k-form size");
1060:   PetscCall(PetscMalloc2(mTrace, &nnzTrace, mFiber, &nnzFiber));
1061:   for (i = 0; i < mTrace; i++) {
1062:     PetscCall(MatGetRow(trace, i, &nnzTrace[i], NULL, NULL));
1063:     PetscCheck(nnzTrace[i] % NkTrace == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in trace matrix are not in k-form size blocks");
1064:   }
1065:   for (i = 0; i < mFiber; i++) {
1066:     PetscCall(MatGetRow(fiber, i, &nnzFiber[i], NULL, NULL));
1067:     PetscCheck(nnzFiber[i] % NkFiber == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in fiber matrix are not in k-form size blocks");
1068:   }
1069:   dim = dimTrace + dimFiber;
1070:   k   = kFiber + kTrace;
1071:   PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk));
1072:   m = mTrace * mFiber;
1073:   PetscCall(PetscMalloc1(m, &nnz));
1074:   for (l = 0, j = 0; j < mFiber; j++)
1075:     for (i = 0; i < mTrace; i++, l++) nnz[l] = (nnzTrace[i] / NkTrace) * (nnzFiber[j] / NkFiber) * Nk;
1076:   n = (nTrace / NkTrace) * (nFiber / NkFiber) * Nk;
1077:   PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, m, n, 0, nnz, &prod));
1078:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)prod, "altv_"));
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 common 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(PetscObjectSetOptionsPrefix((PetscObject)M, "altv_"));
1255:   PetscCall(PetscFree(nnz));
1256:   /* reasoning about which points each dof needs depends on having zeros computed at points preserved */
1257:   PetscCall(MatSetOption(M, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE));
1258:   PetscCall(PetscMalloc1(maxnnz, &work));
1259:   for (i = 0; i < mA; i++) {
1260:     const PetscInt    *cols;
1261:     const PetscScalar *vals;
1262:     PetscInt           nCols;
1263:     PetscCall(MatGetRow(matA, i, &nCols, &cols, &vals));
1264:     for (j = 0; j < nCols / Nk; j++) {
1265:       PetscInt newCol = aToMerged[cols[j * Nk] / Nk];
1266:       for (l = 0; l < Nk; l++) work[j * Nk + l] = newCol * Nk + l;
1267:     }
1268:     PetscCall(MatSetValuesBlocked(M, 1, &i, nCols, work, vals, INSERT_VALUES));
1269:     PetscCall(MatRestoreRow(matA, i, &nCols, &cols, &vals));
1270:   }
1271:   for (i = 0; i < mB; i++) {
1272:     const PetscInt    *cols;
1273:     const PetscScalar *vals;

1275:     PetscInt row = i + mA;
1276:     PetscInt nCols;
1277:     PetscCall(MatGetRow(matB, i, &nCols, &cols, &vals));
1278:     for (j = 0; j < nCols / Nk; j++) {
1279:       PetscInt newCol = bToMerged[cols[j * Nk] / Nk];
1280:       for (l = 0; l < Nk; l++) work[j * Nk + l] = newCol * Nk + l;
1281:     }
1282:     PetscCall(MatSetValuesBlocked(M, 1, &row, nCols, work, vals, INSERT_VALUES));
1283:     PetscCall(MatRestoreRow(matB, i, &nCols, &cols, &vals));
1284:   }
1285:   PetscCall(PetscFree(work));
1286:   PetscCall(MatAssemblyBegin(M, MAT_FINAL_ASSEMBLY));
1287:   PetscCall(MatAssemblyEnd(M, MAT_FINAL_ASSEMBLY));
1288:   *matMerged = M;
1289:   PetscFunctionReturn(PETSC_SUCCESS);
1290: }

1292: /* Take a dual space and product a segment space that has all the same specifications (trimmed, continuous, order,
1293:  * node set), except for the form degree.  For computing boundary dofs and for making tensor product spaces */
1294: static PetscErrorCode PetscDualSpaceCreateFacetSubspace_Lagrange(PetscDualSpace sp, DM K, PetscInt f, PetscInt k, PetscInt Ncopies, PetscBool interiorOnly, PetscDualSpace *bdsp)
1295: {
1296:   PetscInt            Nknew, Ncnew;
1297:   PetscInt            dim, pointDim = -1;
1298:   PetscInt            depth;
1299:   DM                  dm;
1300:   PetscDualSpace_Lag *newlag;

1302:   PetscFunctionBegin;
1303:   PetscCall(PetscDualSpaceGetDM(sp, &dm));
1304:   PetscCall(DMGetDimension(dm, &dim));
1305:   PetscCall(DMPlexGetDepth(dm, &depth));
1306:   PetscCall(PetscDualSpaceDuplicate(sp, bdsp));
1307:   PetscCall(PetscDualSpaceSetFormDegree(*bdsp, k));
1308:   if (!K) {
1309:     if (depth == dim) {
1310:       DMPolytopeType ct;

1312:       pointDim = dim - 1;
1313:       PetscCall(DMPlexGetCellType(dm, f, &ct));
1314:       PetscCall(DMPlexCreateReferenceCell(PETSC_COMM_SELF, ct, &K));
1315:     } else if (depth == 1) {
1316:       pointDim = 0;
1317:       PetscCall(DMPlexCreateReferenceCell(PETSC_COMM_SELF, DM_POLYTOPE_POINT, &K));
1318:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unsupported interpolation state of reference element");
1319:   } else {
1320:     PetscCall(PetscObjectReference((PetscObject)K));
1321:     PetscCall(DMGetDimension(K, &pointDim));
1322:   }
1323:   PetscCall(PetscDualSpaceSetDM(*bdsp, K));
1324:   PetscCall(DMDestroy(&K));
1325:   PetscCall(PetscDTBinomialInt(pointDim, PetscAbsInt(k), &Nknew));
1326:   Ncnew = Nknew * Ncopies;
1327:   PetscCall(PetscDualSpaceSetNumComponents(*bdsp, Ncnew));
1328:   newlag               = (PetscDualSpace_Lag *)(*bdsp)->data;
1329:   newlag->interiorOnly = interiorOnly;
1330:   PetscCall(PetscDualSpaceSetUp(*bdsp));
1331:   PetscFunctionReturn(PETSC_SUCCESS);
1332: }

1334: /* Construct simplex nodes from a nodefamily, add Nk dof vectors of length Nk at each node.
1335:  * Return the (quadrature, matrix) form of the dofs and the nodeIndices form as well.
1336:  *
1337:  * Sometimes we want a set of nodes to be contained in the interior of the element,
1338:  * even when the node scheme puts nodes on the boundaries.  numNodeSkip tells
1339:  * the routine how many "layers" of nodes need to be skipped.
1340:  * */
1341: static PetscErrorCode PetscDualSpaceLagrangeCreateSimplexNodeMat(Petsc1DNodeFamily nodeFamily, PetscInt dim, PetscInt sum, PetscInt Nk, PetscInt numNodeSkip, PetscQuadrature *iNodes, Mat *iMat, PetscLagNodeIndices *nodeIndices)
1342: {
1343:   PetscReal          *extraNodeCoords, *nodeCoords;
1344:   PetscInt            nNodes, nExtraNodes;
1345:   PetscInt            i, j, k, extraSum = sum + numNodeSkip * (1 + dim);
1346:   PetscQuadrature     intNodes;
1347:   Mat                 intMat;
1348:   PetscLagNodeIndices ni;

1350:   PetscFunctionBegin;
1351:   PetscCall(PetscDTBinomialInt(dim + sum, dim, &nNodes));
1352:   PetscCall(PetscDTBinomialInt(dim + extraSum, dim, &nExtraNodes));

1354:   PetscCall(PetscMalloc1(dim * nExtraNodes, &extraNodeCoords));
1355:   PetscCall(PetscNew(&ni));
1356:   ni->nodeIdxDim = dim + 1;
1357:   ni->nodeVecDim = Nk;
1358:   ni->nNodes     = nNodes * Nk;
1359:   ni->refct      = 1;
1360:   PetscCall(PetscMalloc1(nNodes * Nk * (dim + 1), &ni->nodeIdx));
1361:   PetscCall(PetscMalloc1(nNodes * Nk * Nk, &ni->nodeVec));
1362:   for (i = 0; i < nNodes; i++)
1363:     for (j = 0; j < Nk; j++)
1364:       for (k = 0; k < Nk; k++) ni->nodeVec[(i * Nk + j) * Nk + k] = (j == k) ? 1. : 0.;
1365:   PetscCall(Petsc1DNodeFamilyComputeSimplexNodes(nodeFamily, dim, extraSum, extraNodeCoords));
1366:   if (numNodeSkip) {
1367:     PetscInt  k;
1368:     PetscInt *tup;

1370:     PetscCall(PetscMalloc1(dim * nNodes, &nodeCoords));
1371:     PetscCall(PetscMalloc1(dim + 1, &tup));
1372:     for (k = 0; k < nNodes; k++) {
1373:       PetscInt j, c;
1374:       PetscInt index;

1376:       PetscCall(PetscDTIndexToBary(dim + 1, sum, k, tup));
1377:       for (j = 0; j < dim + 1; j++) tup[j] += numNodeSkip;
1378:       for (c = 0; c < Nk; c++) {
1379:         for (j = 0; j < dim + 1; j++) ni->nodeIdx[(k * Nk + c) * (dim + 1) + j] = tup[j] + 1;
1380:       }
1381:       PetscCall(PetscDTBaryToIndex(dim + 1, extraSum, tup, &index));
1382:       for (j = 0; j < dim; j++) nodeCoords[k * dim + j] = extraNodeCoords[index * dim + j];
1383:     }
1384:     PetscCall(PetscFree(tup));
1385:     PetscCall(PetscFree(extraNodeCoords));
1386:   } else {
1387:     PetscInt  k;
1388:     PetscInt *tup;

1390:     nodeCoords = extraNodeCoords;
1391:     PetscCall(PetscMalloc1(dim + 1, &tup));
1392:     for (k = 0; k < nNodes; k++) {
1393:       PetscInt j, c;

1395:       PetscCall(PetscDTIndexToBary(dim + 1, sum, k, tup));
1396:       for (c = 0; c < Nk; c++) {
1397:         for (j = 0; j < dim + 1; j++) {
1398:           /* barycentric indices can have zeros, but we don't want to push forward zeros because it makes it harder to
1399:            * determine which nodes correspond to which under symmetries, so we increase by 1.  This is fine
1400:            * because the nodeIdx coordinates don't have any meaning other than helping to identify symmetries */
1401:           ni->nodeIdx[(k * Nk + c) * (dim + 1) + j] = tup[j] + 1;
1402:         }
1403:       }
1404:     }
1405:     PetscCall(PetscFree(tup));
1406:   }
1407:   PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &intNodes));
1408:   PetscCall(PetscQuadratureSetData(intNodes, dim, 0, nNodes, nodeCoords, NULL));
1409:   PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, nNodes * Nk, nNodes * Nk, Nk, NULL, &intMat));
1410:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)intMat, "lag_"));
1411:   PetscCall(MatSetOption(intMat, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE));
1412:   for (j = 0; j < nNodes * Nk; j++) {
1413:     PetscInt rem = j % Nk;
1414:     PetscInt a, aprev = j - rem;
1415:     PetscInt anext = aprev + Nk;

1417:     for (a = aprev; a < anext; a++) PetscCall(MatSetValue(intMat, j, a, (a == j) ? 1. : 0., INSERT_VALUES));
1418:   }
1419:   PetscCall(MatAssemblyBegin(intMat, MAT_FINAL_ASSEMBLY));
1420:   PetscCall(MatAssemblyEnd(intMat, MAT_FINAL_ASSEMBLY));
1421:   *iNodes      = intNodes;
1422:   *iMat        = intMat;
1423:   *nodeIndices = ni;
1424:   PetscFunctionReturn(PETSC_SUCCESS);
1425: }

1427: /* once the nodeIndices have been created for the interior of the reference cell, and for all of the boundary cells,
1428:  * push forward the boundary dofs and concatenate them into the full node indices for the dual space */
1429: static PetscErrorCode PetscDualSpaceLagrangeCreateAllNodeIdx(PetscDualSpace sp)
1430: {
1431:   DM                  dm;
1432:   PetscInt            dim, nDofs;
1433:   PetscSection        section;
1434:   PetscInt            pStart, pEnd, p;
1435:   PetscInt            formDegree, Nk;
1436:   PetscInt            nodeIdxDim, spintdim;
1437:   PetscDualSpace_Lag *lag;
1438:   PetscLagNodeIndices ni, verti;

1440:   PetscFunctionBegin;
1441:   lag   = (PetscDualSpace_Lag *)sp->data;
1442:   verti = lag->vertIndices;
1443:   PetscCall(PetscDualSpaceGetDM(sp, &dm));
1444:   PetscCall(DMGetDimension(dm, &dim));
1445:   PetscCall(PetscDualSpaceGetFormDegree(sp, &formDegree));
1446:   PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(formDegree), &Nk));
1447:   PetscCall(PetscDualSpaceGetSection(sp, &section));
1448:   PetscCall(PetscSectionGetStorageSize(section, &nDofs));
1449:   PetscCall(PetscNew(&ni));
1450:   ni->nodeIdxDim = nodeIdxDim = verti->nodeIdxDim;
1451:   ni->nodeVecDim              = Nk;
1452:   ni->nNodes                  = nDofs;
1453:   ni->refct                   = 1;
1454:   PetscCall(PetscMalloc1(nodeIdxDim * nDofs, &ni->nodeIdx));
1455:   PetscCall(PetscMalloc1(Nk * nDofs, &ni->nodeVec));
1456:   PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
1457:   PetscCall(PetscSectionGetDof(section, 0, &spintdim));
1458:   if (spintdim) {
1459:     PetscCall(PetscArraycpy(ni->nodeIdx, lag->intNodeIndices->nodeIdx, spintdim * nodeIdxDim));
1460:     PetscCall(PetscArraycpy(ni->nodeVec, lag->intNodeIndices->nodeVec, spintdim * Nk));
1461:   }
1462:   for (p = pStart + 1; p < pEnd; p++) {
1463:     PetscDualSpace      psp = sp->pointSpaces[p];
1464:     PetscDualSpace_Lag *plag;
1465:     PetscInt            dof, off;

1467:     PetscCall(PetscSectionGetDof(section, p, &dof));
1468:     if (!dof) continue;
1469:     plag = (PetscDualSpace_Lag *)psp->data;
1470:     PetscCall(PetscSectionGetOffset(section, p, &off));
1471:     PetscCall(PetscLagNodeIndicesPushForward(dm, verti, p, plag->vertIndices, plag->intNodeIndices, 0, formDegree, &ni->nodeIdx[off * nodeIdxDim], &ni->nodeVec[off * Nk]));
1472:   }
1473:   lag->allNodeIndices = ni;
1474:   PetscFunctionReturn(PETSC_SUCCESS);
1475: }

1477: /* once the (quadrature, Matrix) forms of the dofs have been created for the interior of the
1478:  * reference cell and for the boundary cells, jk
1479:  * push forward the boundary data and concatenate them into the full (quadrature, matrix) data
1480:  * for the dual space */
1481: static PetscErrorCode PetscDualSpaceCreateAllDataFromInteriorData(PetscDualSpace sp)
1482: {
1483:   DM              dm;
1484:   PetscSection    section;
1485:   PetscInt        pStart, pEnd, p, k, Nk, dim, Nc;
1486:   PetscInt        nNodes;
1487:   PetscInt        countNodes;
1488:   Mat             allMat;
1489:   PetscQuadrature allNodes;
1490:   PetscInt        nDofs;
1491:   PetscInt        maxNzforms, j;
1492:   PetscScalar    *work;
1493:   PetscReal      *L, *J, *Jinv, *v0, *pv0;
1494:   PetscInt       *iwork;
1495:   PetscReal      *nodes;

1497:   PetscFunctionBegin;
1498:   PetscCall(PetscDualSpaceGetDM(sp, &dm));
1499:   PetscCall(DMGetDimension(dm, &dim));
1500:   PetscCall(PetscDualSpaceGetSection(sp, &section));
1501:   PetscCall(PetscSectionGetStorageSize(section, &nDofs));
1502:   PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
1503:   PetscCall(PetscDualSpaceGetFormDegree(sp, &k));
1504:   PetscCall(PetscDualSpaceGetNumComponents(sp, &Nc));
1505:   PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk));
1506:   for (p = pStart, nNodes = 0, maxNzforms = 0; p < pEnd; p++) {
1507:     PetscDualSpace  psp;
1508:     DM              pdm;
1509:     PetscInt        pdim, pNk;
1510:     PetscQuadrature intNodes;
1511:     Mat             intMat;

1513:     PetscCall(PetscDualSpaceGetPointSubspace(sp, p, &psp));
1514:     if (!psp) continue;
1515:     PetscCall(PetscDualSpaceGetDM(psp, &pdm));
1516:     PetscCall(DMGetDimension(pdm, &pdim));
1517:     if (pdim < PetscAbsInt(k)) continue;
1518:     PetscCall(PetscDTBinomialInt(pdim, PetscAbsInt(k), &pNk));
1519:     PetscCall(PetscDualSpaceGetInteriorData(psp, &intNodes, &intMat));
1520:     if (intNodes) {
1521:       PetscInt nNodesp;

1523:       PetscCall(PetscQuadratureGetData(intNodes, NULL, NULL, &nNodesp, NULL, NULL));
1524:       nNodes += nNodesp;
1525:     }
1526:     if (intMat) {
1527:       PetscInt maxNzsp;
1528:       PetscInt maxNzformsp;

1530:       PetscCall(MatSeqAIJGetMaxRowNonzeros(intMat, &maxNzsp));
1531:       PetscCheck(maxNzsp % pNk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "interior matrix is not laid out as blocks of k-forms");
1532:       maxNzformsp = maxNzsp / pNk;
1533:       maxNzforms  = PetscMax(maxNzforms, maxNzformsp);
1534:     }
1535:   }
1536:   PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, nDofs, nNodes * Nc, maxNzforms * Nk, NULL, &allMat));
1537:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)allMat, "ds_"));
1538:   PetscCall(MatSetOption(allMat, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE));
1539:   PetscCall(PetscMalloc7(dim, &v0, dim, &pv0, dim * dim, &J, dim * dim, &Jinv, Nk * Nk, &L, maxNzforms * Nk, &work, maxNzforms * Nk, &iwork));
1540:   for (j = 0; j < dim; j++) pv0[j] = -1.;
1541:   PetscCall(PetscMalloc1(dim * nNodes, &nodes));
1542:   for (p = pStart, countNodes = 0; p < pEnd; p++) {
1543:     PetscDualSpace  psp;
1544:     PetscQuadrature intNodes;
1545:     DM              pdm;
1546:     PetscInt        pdim, pNk;
1547:     PetscInt        countNodesIn = countNodes;
1548:     PetscReal       detJ;
1549:     Mat             intMat;

1551:     PetscCall(PetscDualSpaceGetPointSubspace(sp, p, &psp));
1552:     if (!psp) continue;
1553:     PetscCall(PetscDualSpaceGetDM(psp, &pdm));
1554:     PetscCall(DMGetDimension(pdm, &pdim));
1555:     if (pdim < PetscAbsInt(k)) continue;
1556:     PetscCall(PetscDualSpaceGetInteriorData(psp, &intNodes, &intMat));
1557:     if (intNodes == NULL && intMat == NULL) continue;
1558:     PetscCall(PetscDTBinomialInt(pdim, PetscAbsInt(k), &pNk));
1559:     if (p) {
1560:       PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, p, v0, J, Jinv, &detJ));
1561:     } else { /* identity */
1562:       PetscInt i, j;

1564:       for (i = 0; i < dim; i++)
1565:         for (j = 0; j < dim; j++) J[i * dim + j] = Jinv[i * dim + j] = 0.;
1566:       for (i = 0; i < dim; i++) J[i * dim + i] = Jinv[i * dim + i] = 1.;
1567:       for (i = 0; i < dim; i++) v0[i] = -1.;
1568:     }
1569:     if (pdim != dim) { /* compactify Jacobian */
1570:       PetscInt i, j;

1572:       for (i = 0; i < dim; i++)
1573:         for (j = 0; j < pdim; j++) J[i * pdim + j] = J[i * dim + j];
1574:     }
1575:     PetscCall(PetscDTAltVPullbackMatrix(pdim, dim, J, k, L));
1576:     if (intNodes) { /* push forward quadrature locations by the affine transformation */
1577:       PetscInt         nNodesp;
1578:       const PetscReal *nodesp;
1579:       PetscInt         j;

1581:       PetscCall(PetscQuadratureGetData(intNodes, NULL, NULL, &nNodesp, &nodesp, NULL));
1582:       for (j = 0; j < nNodesp; j++, countNodes++) {
1583:         PetscInt d, e;

1585:         for (d = 0; d < dim; d++) {
1586:           nodes[countNodes * dim + d] = v0[d];
1587:           for (e = 0; e < pdim; e++) nodes[countNodes * dim + d] += J[d * pdim + e] * (nodesp[j * pdim + e] - pv0[e]);
1588:         }
1589:       }
1590:     }
1591:     if (intMat) {
1592:       PetscInt nrows;
1593:       PetscInt off;

1595:       PetscCall(PetscSectionGetDof(section, p, &nrows));
1596:       PetscCall(PetscSectionGetOffset(section, p, &off));
1597:       for (j = 0; j < nrows; j++) {
1598:         PetscInt           ncols;
1599:         const PetscInt    *cols;
1600:         const PetscScalar *vals;
1601:         PetscInt           l, d, e;
1602:         PetscInt           row = j + off;

1604:         PetscCall(MatGetRow(intMat, j, &ncols, &cols, &vals));
1605:         PetscCheck(ncols % pNk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "interior matrix is not laid out as blocks of k-forms");
1606:         for (l = 0; l < ncols / pNk; l++) {
1607:           PetscInt blockcol;

1609:           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");
1610:           blockcol = cols[l * pNk] / pNk;
1611:           for (d = 0; d < Nk; d++) iwork[l * Nk + d] = (blockcol + countNodesIn) * Nk + d;
1612:           for (d = 0; d < Nk; d++) work[l * Nk + d] = 0.;
1613:           for (d = 0; d < Nk; d++) {
1614:             for (e = 0; e < pNk; e++) {
1615:               /* "push forward" dof by pulling back a k-form to be evaluated on the point: multiply on the right by L */
1616:               work[l * Nk + d] += vals[l * pNk + e] * L[e * Nk + d];
1617:             }
1618:           }
1619:         }
1620:         PetscCall(MatSetValues(allMat, 1, &row, (ncols / pNk) * Nk, iwork, work, INSERT_VALUES));
1621:         PetscCall(MatRestoreRow(intMat, j, &ncols, &cols, &vals));
1622:       }
1623:     }
1624:   }
1625:   PetscCall(MatAssemblyBegin(allMat, MAT_FINAL_ASSEMBLY));
1626:   PetscCall(MatAssemblyEnd(allMat, MAT_FINAL_ASSEMBLY));
1627:   PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &allNodes));
1628:   PetscCall(PetscQuadratureSetData(allNodes, dim, 0, nNodes, nodes, NULL));
1629:   PetscCall(PetscFree7(v0, pv0, J, Jinv, L, work, iwork));
1630:   PetscCall(MatDestroy(&sp->allMat));
1631:   sp->allMat = allMat;
1632:   PetscCall(PetscQuadratureDestroy(&sp->allNodes));
1633:   sp->allNodes = allNodes;
1634:   PetscFunctionReturn(PETSC_SUCCESS);
1635: }

1637: static PetscErrorCode PetscDualSpaceComputeFunctionalsFromAllData_Moments(PetscDualSpace sp)
1638: {
1639:   Mat              allMat;
1640:   PetscInt         momentOrder, i;
1641:   PetscBool        tensor = PETSC_FALSE;
1642:   const PetscReal *weights;
1643:   PetscScalar     *array;
1644:   PetscInt         nDofs;
1645:   PetscInt         dim, Nc;
1646:   DM               dm;
1647:   PetscQuadrature  allNodes;
1648:   PetscInt         nNodes;

1650:   PetscFunctionBegin;
1651:   PetscCall(PetscDualSpaceGetDM(sp, &dm));
1652:   PetscCall(DMGetDimension(dm, &dim));
1653:   PetscCall(PetscDualSpaceGetNumComponents(sp, &Nc));
1654:   PetscCall(PetscDualSpaceGetAllData(sp, &allNodes, &allMat));
1655:   PetscCall(MatGetSize(allMat, &nDofs, NULL));
1656:   PetscCheck(nDofs == 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "We do not yet support moments beyond P0, nDofs == %" PetscInt_FMT, nDofs);
1657:   PetscCall(PetscMalloc1(nDofs, &sp->functional));
1658:   PetscCall(PetscDualSpaceLagrangeGetMomentOrder(sp, &momentOrder));
1659:   PetscCall(PetscDualSpaceLagrangeGetTensor(sp, &tensor));
1660:   if (!tensor) PetscCall(PetscDTStroudConicalQuadrature(dim, Nc, PetscMax(momentOrder + 1, 1), -1.0, 1.0, &sp->functional[0]));
1661:   else PetscCall(PetscDTGaussTensorQuadrature(dim, Nc, PetscMax(momentOrder + 1, 1), -1.0, 1.0, &sp->functional[0]));
1662:   /* Need to replace allNodes and allMat */
1663:   PetscCall(PetscObjectReference((PetscObject)sp->functional[0]));
1664:   PetscCall(PetscQuadratureDestroy(&sp->allNodes));
1665:   sp->allNodes = sp->functional[0];
1666:   PetscCall(PetscQuadratureGetData(sp->allNodes, NULL, NULL, &nNodes, NULL, &weights));
1667:   PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, nDofs, nNodes * Nc, NULL, &allMat));
1668:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)allMat, "ds_"));
1669:   PetscCall(MatDenseGetArrayWrite(allMat, &array));
1670:   for (i = 0; i < nNodes * Nc; ++i) array[i] = weights[i];
1671:   PetscCall(MatDenseRestoreArrayWrite(allMat, &array));
1672:   PetscCall(MatAssemblyBegin(allMat, MAT_FINAL_ASSEMBLY));
1673:   PetscCall(MatAssemblyEnd(allMat, MAT_FINAL_ASSEMBLY));
1674:   PetscCall(MatDestroy(&sp->allMat));
1675:   sp->allMat = allMat;
1676:   PetscFunctionReturn(PETSC_SUCCESS);
1677: }

1679: /* rather than trying to get all data from the functionals, we create
1680:  * the functionals from rows of the quadrature -> dof matrix.
1681:  *
1682:  * Ideally most of the uses of PetscDualSpace in PetscFE will switch
1683:  * to using intMat and allMat, so that the individual functionals
1684:  * don't need to be constructed at all */
1685: PETSC_INTERN PetscErrorCode PetscDualSpaceComputeFunctionalsFromAllData(PetscDualSpace sp)
1686: {
1687:   PetscQuadrature  allNodes;
1688:   Mat              allMat;
1689:   PetscInt         nDofs;
1690:   PetscInt         dim, Nc, f;
1691:   DM               dm;
1692:   PetscInt         nNodes, spdim;
1693:   const PetscReal *nodes = NULL;
1694:   PetscSection     section;
1695:   PetscBool        useMoments;

1697:   PetscFunctionBegin;
1698:   PetscCall(PetscDualSpaceGetDM(sp, &dm));
1699:   PetscCall(DMGetDimension(dm, &dim));
1700:   PetscCall(PetscDualSpaceGetNumComponents(sp, &Nc));
1701:   PetscCall(PetscDualSpaceGetAllData(sp, &allNodes, &allMat));
1702:   nNodes = 0;
1703:   if (allNodes) PetscCall(PetscQuadratureGetData(allNodes, NULL, NULL, &nNodes, &nodes, NULL));
1704:   PetscCall(MatGetSize(allMat, &nDofs, NULL));
1705:   PetscCall(PetscDualSpaceGetSection(sp, &section));
1706:   PetscCall(PetscSectionGetStorageSize(section, &spdim));
1707:   PetscCheck(spdim == nDofs, PETSC_COMM_SELF, PETSC_ERR_PLIB, "incompatible all matrix size");
1708:   PetscCall(PetscMalloc1(nDofs, &sp->functional));
1709:   PetscCall(PetscDualSpaceLagrangeGetUseMoments(sp, &useMoments));
1710:   for (f = 0; f < nDofs; f++) {
1711:     PetscInt           ncols, c;
1712:     const PetscInt    *cols;
1713:     const PetscScalar *vals;
1714:     PetscReal         *nodesf;
1715:     PetscReal         *weightsf;
1716:     PetscInt           nNodesf;
1717:     PetscInt           countNodes;

1719:     PetscCall(MatGetRow(allMat, f, &ncols, &cols, &vals));
1720:     for (c = 1, nNodesf = 1; c < ncols; c++) {
1721:       if ((cols[c] / Nc) != (cols[c - 1] / Nc)) nNodesf++;
1722:     }
1723:     PetscCall(PetscMalloc1(dim * nNodesf, &nodesf));
1724:     PetscCall(PetscMalloc1(Nc * nNodesf, &weightsf));
1725:     for (c = 0, countNodes = 0; c < ncols; c++) {
1726:       if (!c || ((cols[c] / Nc) != (cols[c - 1] / Nc))) {
1727:         PetscInt d;

1729:         for (d = 0; d < Nc; d++) weightsf[countNodes * Nc + d] = 0.;
1730:         for (d = 0; d < dim; d++) nodesf[countNodes * dim + d] = nodes[(cols[c] / Nc) * dim + d];
1731:         countNodes++;
1732:       }
1733:       weightsf[(countNodes - 1) * Nc + (cols[c] % Nc)] = PetscRealPart(vals[c]);
1734:     }
1735:     PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &sp->functional[f]));
1736:     PetscCall(PetscQuadratureSetData(sp->functional[f], dim, Nc, nNodesf, nodesf, weightsf));
1737:     PetscCall(MatRestoreRow(allMat, f, &ncols, &cols, &vals));
1738:   }
1739:   PetscFunctionReturn(PETSC_SUCCESS);
1740: }

1742: /* check if a cell is a tensor product of the segment with a facet,
1743:  * specifically checking if f and f2 can be the "endpoints" (like the triangles
1744:  * at either end of a wedge) */
1745: static PetscErrorCode DMPlexPointIsTensor_Internal_Given(DM dm, PetscInt p, PetscInt f, PetscInt f2, PetscBool *isTensor)
1746: {
1747:   PetscInt        coneSize, c;
1748:   const PetscInt *cone;
1749:   const PetscInt *fCone;
1750:   const PetscInt *f2Cone;
1751:   PetscInt        fs[2];
1752:   PetscInt        meetSize, nmeet;
1753:   const PetscInt *meet;

1755:   PetscFunctionBegin;
1756:   fs[0] = f;
1757:   fs[1] = f2;
1758:   PetscCall(DMPlexGetMeet(dm, 2, fs, &meetSize, &meet));
1759:   nmeet = meetSize;
1760:   PetscCall(DMPlexRestoreMeet(dm, 2, fs, &meetSize, &meet));
1761:   /* two points that have a non-empty meet cannot be at opposite ends of a cell */
1762:   if (nmeet) {
1763:     *isTensor = PETSC_FALSE;
1764:     PetscFunctionReturn(PETSC_SUCCESS);
1765:   }
1766:   PetscCall(DMPlexGetConeSize(dm, p, &coneSize));
1767:   PetscCall(DMPlexGetCone(dm, p, &cone));
1768:   PetscCall(DMPlexGetCone(dm, f, &fCone));
1769:   PetscCall(DMPlexGetCone(dm, f2, &f2Cone));
1770:   for (c = 0; c < coneSize; c++) {
1771:     PetscInt        e, ef;
1772:     PetscInt        d = -1, d2 = -1;
1773:     PetscInt        dcount, d2count;
1774:     PetscInt        t = cone[c];
1775:     PetscInt        tConeSize;
1776:     PetscBool       tIsTensor;
1777:     const PetscInt *tCone;

1779:     if (t == f || t == f2) continue;
1780:     /* for every other facet in the cone, check that is has
1781:      * one ridge in common with each end */
1782:     PetscCall(DMPlexGetConeSize(dm, t, &tConeSize));
1783:     PetscCall(DMPlexGetCone(dm, t, &tCone));

1785:     dcount  = 0;
1786:     d2count = 0;
1787:     for (e = 0; e < tConeSize; e++) {
1788:       PetscInt q = tCone[e];
1789:       for (ef = 0; ef < coneSize - 2; ef++) {
1790:         if (fCone[ef] == q) {
1791:           if (dcount) {
1792:             *isTensor = PETSC_FALSE;
1793:             PetscFunctionReturn(PETSC_SUCCESS);
1794:           }
1795:           d = q;
1796:           dcount++;
1797:         } else if (f2Cone[ef] == q) {
1798:           if (d2count) {
1799:             *isTensor = PETSC_FALSE;
1800:             PetscFunctionReturn(PETSC_SUCCESS);
1801:           }
1802:           d2 = q;
1803:           d2count++;
1804:         }
1805:       }
1806:     }
1807:     /* if the whole cell is a tensor with the segment, then this
1808:      * facet should be a tensor with the segment */
1809:     PetscCall(DMPlexPointIsTensor_Internal_Given(dm, t, d, d2, &tIsTensor));
1810:     if (!tIsTensor) {
1811:       *isTensor = PETSC_FALSE;
1812:       PetscFunctionReturn(PETSC_SUCCESS);
1813:     }
1814:   }
1815:   *isTensor = PETSC_TRUE;
1816:   PetscFunctionReturn(PETSC_SUCCESS);
1817: }

1819: /* determine if a cell is a tensor with a segment by looping over pairs of facets to find a pair
1820:  * that could be the opposite ends */
1821: static PetscErrorCode DMPlexPointIsTensor_Internal(DM dm, PetscInt p, PetscBool *isTensor, PetscInt *endA, PetscInt *endB)
1822: {
1823:   PetscInt        coneSize, c, c2;
1824:   const PetscInt *cone;

1826:   PetscFunctionBegin;
1827:   PetscCall(DMPlexGetConeSize(dm, p, &coneSize));
1828:   if (!coneSize) {
1829:     if (isTensor) *isTensor = PETSC_FALSE;
1830:     if (endA) *endA = -1;
1831:     if (endB) *endB = -1;
1832:   }
1833:   PetscCall(DMPlexGetCone(dm, p, &cone));
1834:   for (c = 0; c < coneSize; c++) {
1835:     PetscInt f = cone[c];
1836:     PetscInt fConeSize;

1838:     PetscCall(DMPlexGetConeSize(dm, f, &fConeSize));
1839:     if (fConeSize != coneSize - 2) continue;

1841:     for (c2 = c + 1; c2 < coneSize; c2++) {
1842:       PetscInt  f2 = cone[c2];
1843:       PetscBool isTensorff2;
1844:       PetscInt  f2ConeSize;

1846:       PetscCall(DMPlexGetConeSize(dm, f2, &f2ConeSize));
1847:       if (f2ConeSize != coneSize - 2) continue;

1849:       PetscCall(DMPlexPointIsTensor_Internal_Given(dm, p, f, f2, &isTensorff2));
1850:       if (isTensorff2) {
1851:         if (isTensor) *isTensor = PETSC_TRUE;
1852:         if (endA) *endA = f;
1853:         if (endB) *endB = f2;
1854:         PetscFunctionReturn(PETSC_SUCCESS);
1855:       }
1856:     }
1857:   }
1858:   if (isTensor) *isTensor = PETSC_FALSE;
1859:   if (endA) *endA = -1;
1860:   if (endB) *endB = -1;
1861:   PetscFunctionReturn(PETSC_SUCCESS);
1862: }

1864: /* determine if a cell is a tensor with a segment by looping over pairs of facets to find a pair
1865:  * that could be the opposite ends */
1866: static PetscErrorCode DMPlexPointIsTensor(DM dm, PetscInt p, PetscBool *isTensor, PetscInt *endA, PetscInt *endB)
1867: {
1868:   DMPlexInterpolatedFlag interpolated;

1870:   PetscFunctionBegin;
1871:   PetscCall(DMPlexIsInterpolated(dm, &interpolated));
1872:   PetscCheck(interpolated == DMPLEX_INTERPOLATED_FULL, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONGSTATE, "Only for interpolated DMPlex's");
1873:   PetscCall(DMPlexPointIsTensor_Internal(dm, p, isTensor, endA, endB));
1874:   PetscFunctionReturn(PETSC_SUCCESS);
1875: }

1877: /* Let k = formDegree and k' = -sign(k) * dim + k.  Transform a symmetric frame for k-forms on the biunit simplex into
1878:  * a symmetric frame for k'-forms on the biunit simplex.
1879:  *
1880:  * A frame is "symmetric" if the pullback of every symmetry of the biunit simplex is a permutation of the frame.
1881:  *
1882:  * forms in the symmetric frame are used as dofs in the untrimmed simplex spaces.  This way, symmetries of the
1883:  * reference cell result in permutations of dofs grouped by node.
1884:  *
1885:  * Use T to transform dof matrices for k'-forms into dof matrices for k-forms as a block diagonal transformation on
1886:  * the right.
1887:  */
1888: static PetscErrorCode BiunitSimplexSymmetricFormTransformation(PetscInt dim, PetscInt formDegree, PetscReal T[])
1889: {
1890:   PetscInt   k  = formDegree;
1891:   PetscInt   kd = k < 0 ? dim + k : k - dim;
1892:   PetscInt   Nk;
1893:   PetscReal *biToEq, *eqToBi, *biToEqStar, *eqToBiStar;
1894:   PetscInt   fact;

1896:   PetscFunctionBegin;
1897:   PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk));
1898:   PetscCall(PetscCalloc4(dim * dim, &biToEq, dim * dim, &eqToBi, Nk * Nk, &biToEqStar, Nk * Nk, &eqToBiStar));
1899:   /* fill in biToEq: Jacobian of the transformation from the biunit simplex to the equilateral simplex */
1900:   fact = 0;
1901:   for (PetscInt i = 0; i < dim; i++) {
1902:     biToEq[i * dim + i] = PetscSqrtReal(((PetscReal)i + 2.) / (2. * ((PetscReal)i + 1.)));
1903:     fact += 4 * (i + 1);
1904:     for (PetscInt j = i + 1; j < dim; j++) biToEq[i * dim + j] = PetscSqrtReal(1. / (PetscReal)fact);
1905:   }
1906:   /* fill in eqToBi: Jacobian of the transformation from the equilateral simplex to the biunit simplex */
1907:   fact = 0;
1908:   for (PetscInt j = 0; j < dim; j++) {
1909:     eqToBi[j * dim + j] = PetscSqrtReal(2. * ((PetscReal)j + 1.) / ((PetscReal)j + 2));
1910:     fact += j + 1;
1911:     for (PetscInt i = 0; i < j; i++) eqToBi[i * dim + j] = -PetscSqrtReal(1. / (PetscReal)fact);
1912:   }
1913:   PetscCall(PetscDTAltVPullbackMatrix(dim, dim, biToEq, kd, biToEqStar));
1914:   PetscCall(PetscDTAltVPullbackMatrix(dim, dim, eqToBi, k, eqToBiStar));
1915:   /* product of pullbacks simulates the following steps
1916:    *
1917:    * 1. start with frame W = [w_1, w_2, ..., w_m] of k forms that is symmetric on the biunit simplex:
1918:           if J is the Jacobian of a symmetry of the biunit simplex, then J_k* W = [J_k*w_1, ..., J_k*w_m]
1919:           is a permutation of W.
1920:           Even though a k' form --- a (dim - k) form represented by its Hodge star --- has the same geometric
1921:           content as a k form, W is not a symmetric frame of k' forms on the biunit simplex.  That's because,
1922:           for general Jacobian J, J_k* != J_k'*.
1923:    * 2. pullback W to the equilateral triangle using the k pullback, W_eq = eqToBi_k* W.  All symmetries of the
1924:           equilateral simplex have orthonormal Jacobians.  For an orthonormal Jacobian O, J_k* = J_k'*, so W_eq is
1925:           also a symmetric frame for k' forms on the equilateral simplex.
1926:      3. pullback W_eq back to the biunit simplex using the k' pulback, V = biToEq_k'* W_eq = biToEq_k'* eqToBi_k* W.
1927:           V is a symmetric frame for k' forms on the biunit simplex.
1928:    */
1929:   for (PetscInt i = 0; i < Nk; i++) {
1930:     for (PetscInt j = 0; j < Nk; j++) {
1931:       PetscReal val = 0.;
1932:       for (PetscInt k = 0; k < Nk; k++) val += biToEqStar[i * Nk + k] * eqToBiStar[k * Nk + j];
1933:       T[i * Nk + j] = val;
1934:     }
1935:   }
1936:   PetscCall(PetscFree4(biToEq, eqToBi, biToEqStar, eqToBiStar));
1937:   PetscFunctionReturn(PETSC_SUCCESS);
1938: }

1940: /* permute a quadrature -> dof matrix so that its rows are in revlex order by nodeIdx */
1941: static PetscErrorCode MatPermuteByNodeIdx(Mat A, PetscLagNodeIndices ni, Mat *Aperm)
1942: {
1943:   PetscInt   m, n, i, j;
1944:   PetscInt   nodeIdxDim = ni->nodeIdxDim;
1945:   PetscInt   nodeVecDim = ni->nodeVecDim;
1946:   PetscInt  *perm;
1947:   IS         permIS;
1948:   IS         id;
1949:   PetscInt  *nIdxPerm;
1950:   PetscReal *nVecPerm;

1952:   PetscFunctionBegin;
1953:   PetscCall(PetscLagNodeIndicesGetPermutation(ni, &perm));
1954:   PetscCall(MatGetSize(A, &m, &n));
1955:   PetscCall(PetscMalloc1(nodeIdxDim * m, &nIdxPerm));
1956:   PetscCall(PetscMalloc1(nodeVecDim * m, &nVecPerm));
1957:   for (i = 0; i < m; i++)
1958:     for (j = 0; j < nodeIdxDim; j++) nIdxPerm[i * nodeIdxDim + j] = ni->nodeIdx[perm[i] * nodeIdxDim + j];
1959:   for (i = 0; i < m; i++)
1960:     for (j = 0; j < nodeVecDim; j++) nVecPerm[i * nodeVecDim + j] = ni->nodeVec[perm[i] * nodeVecDim + j];
1961:   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, m, perm, PETSC_USE_POINTER, &permIS));
1962:   PetscCall(ISSetPermutation(permIS));
1963:   PetscCall(ISCreateStride(PETSC_COMM_SELF, n, 0, 1, &id));
1964:   PetscCall(ISSetPermutation(id));
1965:   PetscCall(MatPermute(A, permIS, id, Aperm));
1966:   PetscCall(ISDestroy(&permIS));
1967:   PetscCall(ISDestroy(&id));
1968:   for (i = 0; i < m; i++) perm[i] = i;
1969:   PetscCall(PetscFree(ni->nodeIdx));
1970:   PetscCall(PetscFree(ni->nodeVec));
1971:   ni->nodeIdx = nIdxPerm;
1972:   ni->nodeVec = nVecPerm;
1973:   PetscFunctionReturn(PETSC_SUCCESS);
1974: }

1976: static PetscErrorCode PetscDualSpaceSetUp_Lagrange(PetscDualSpace sp)
1977: {
1978:   PetscDualSpace_Lag    *lag   = (PetscDualSpace_Lag *)sp->data;
1979:   DM                     dm    = sp->dm;
1980:   DM                     dmint = NULL;
1981:   PetscInt               order;
1982:   PetscInt               Nc;
1983:   MPI_Comm               comm;
1984:   PetscBool              continuous;
1985:   PetscSection           section;
1986:   PetscInt               depth, dim, pStart, pEnd, cStart, cEnd, p, *pStratStart, *pStratEnd, d;
1987:   PetscInt               formDegree, Nk, Ncopies;
1988:   PetscInt               tensorf = -1, tensorf2 = -1;
1989:   PetscBool              tensorCell, tensorSpace;
1990:   PetscBool              uniform, trimmed;
1991:   Petsc1DNodeFamily      nodeFamily;
1992:   PetscInt               numNodeSkip;
1993:   DMPlexInterpolatedFlag interpolated;
1994:   PetscBool              isbdm;

1996:   PetscFunctionBegin;
1997:   /* step 1: sanitize input */
1998:   PetscCall(PetscObjectGetComm((PetscObject)sp, &comm));
1999:   PetscCall(DMGetDimension(dm, &dim));
2000:   PetscCall(PetscObjectTypeCompare((PetscObject)sp, PETSCDUALSPACEBDM, &isbdm));
2001:   if (isbdm) {
2002:     sp->k = -(dim - 1); /* form degree of H-div */
2003:     PetscCall(PetscObjectChangeTypeName((PetscObject)sp, PETSCDUALSPACELAGRANGE));
2004:   }
2005:   PetscCall(PetscDualSpaceGetFormDegree(sp, &formDegree));
2006:   PetscCheck(PetscAbsInt(formDegree) <= dim, comm, PETSC_ERR_ARG_OUTOFRANGE, "Form degree must be bounded by dimension");
2007:   PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(formDegree), &Nk));
2008:   if (sp->Nc <= 0 && lag->numCopies > 0) sp->Nc = Nk * lag->numCopies;
2009:   Nc = sp->Nc;
2010:   PetscCheck(Nc % Nk == 0, comm, PETSC_ERR_ARG_INCOMP, "Number of components is not a multiple of form degree size");
2011:   if (lag->numCopies <= 0) lag->numCopies = Nc / Nk;
2012:   Ncopies = lag->numCopies;
2013:   PetscCheck(Nc / Nk == Ncopies, comm, PETSC_ERR_ARG_INCOMP, "Number of copies * (dim choose k) != Nc");
2014:   if (!dim) sp->order = 0;
2015:   order   = sp->order;
2016:   uniform = sp->uniform;
2017:   PetscCheck(uniform, PETSC_COMM_SELF, PETSC_ERR_SUP, "Variable order not supported yet");
2018:   if (lag->trimmed && !formDegree) lag->trimmed = PETSC_FALSE; /* trimmed spaces are the same as full spaces for 0-forms */
2019:   if (lag->nodeType == PETSCDTNODES_DEFAULT) {
2020:     lag->nodeType     = PETSCDTNODES_GAUSSJACOBI;
2021:     lag->nodeExponent = 0.;
2022:     /* trimmed spaces don't include corner vertices, so don't use end nodes by default */
2023:     lag->endNodes = lag->trimmed ? PETSC_FALSE : PETSC_TRUE;
2024:   }
2025:   /* If a trimmed space and the user did choose nodes with endpoints, skip them by default */
2026:   if (lag->numNodeSkip < 0) lag->numNodeSkip = (lag->trimmed && lag->endNodes) ? 1 : 0;
2027:   numNodeSkip = lag->numNodeSkip;
2028:   PetscCheck(!lag->trimmed || order, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot have zeroth order trimmed elements");
2029:   if (lag->trimmed && PetscAbsInt(formDegree) == dim) { /* convert trimmed n-forms to untrimmed of one polynomial order less */
2030:     sp->order--;
2031:     order--;
2032:     lag->trimmed = PETSC_FALSE;
2033:   }
2034:   trimmed = lag->trimmed;
2035:   if (!order || PetscAbsInt(formDegree) == dim) lag->continuous = PETSC_FALSE;
2036:   continuous = lag->continuous;
2037:   PetscCall(DMPlexGetDepth(dm, &depth));
2038:   PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
2039:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
2040:   PetscCheck(pStart == 0 && cStart == 0, PetscObjectComm((PetscObject)sp), PETSC_ERR_ARG_WRONGSTATE, "Expect DM with chart starting at zero and cells first");
2041:   PetscCheck(cEnd == 1, PetscObjectComm((PetscObject)sp), PETSC_ERR_ARG_WRONGSTATE, "Use PETSCDUALSPACEREFINED for multi-cell reference meshes");
2042:   PetscCall(DMPlexIsInterpolated(dm, &interpolated));
2043:   if (interpolated != DMPLEX_INTERPOLATED_FULL) {
2044:     PetscCall(DMPlexInterpolate(dm, &dmint));
2045:   } else {
2046:     PetscCall(PetscObjectReference((PetscObject)dm));
2047:     dmint = dm;
2048:   }
2049:   tensorCell = PETSC_FALSE;
2050:   if (dim > 1) PetscCall(DMPlexPointIsTensor(dmint, 0, &tensorCell, &tensorf, &tensorf2));
2051:   lag->tensorCell = tensorCell;
2052:   if (dim < 2 || !lag->tensorCell) lag->tensorSpace = PETSC_FALSE;
2053:   tensorSpace = lag->tensorSpace;
2054:   if (!lag->nodeFamily) PetscCall(Petsc1DNodeFamilyCreate(lag->nodeType, lag->nodeExponent, lag->endNodes, &lag->nodeFamily));
2055:   nodeFamily = lag->nodeFamily;
2056:   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");

2058:   if (Ncopies > 1) {
2059:     PetscDualSpace scalarsp;

2061:     PetscCall(PetscDualSpaceDuplicate(sp, &scalarsp));
2062:     /* Setting the number of components to Nk is a space with 1 copy of each k-form */
2063:     sp->setupcalled = PETSC_FALSE;
2064:     PetscCall(PetscDualSpaceSetNumComponents(scalarsp, Nk));
2065:     PetscCall(PetscDualSpaceSetUp(scalarsp));
2066:     PetscCall(PetscDualSpaceSetType(sp, PETSCDUALSPACESUM));
2067:     PetscCall(PetscDualSpaceSumSetNumSubspaces(sp, Ncopies));
2068:     PetscCall(PetscDualSpaceSumSetConcatenate(sp, PETSC_TRUE));
2069:     PetscCall(PetscDualSpaceSumSetInterleave(sp, PETSC_TRUE, PETSC_FALSE));
2070:     for (PetscInt i = 0; i < Ncopies; i++) PetscCall(PetscDualSpaceSumSetSubspace(sp, i, scalarsp));
2071:     PetscCall(PetscDualSpaceSetUp(sp));
2072:     PetscCall(PetscDualSpaceDestroy(&scalarsp));
2073:     PetscCall(DMDestroy(&dmint));
2074:     PetscFunctionReturn(PETSC_SUCCESS);
2075:   }

2077:   /* step 2: construct the boundary spaces */
2078:   PetscCall(PetscMalloc2(depth + 1, &pStratStart, depth + 1, &pStratEnd));
2079:   PetscCall(PetscCalloc1(pEnd, &sp->pointSpaces));
2080:   for (d = 0; d <= depth; ++d) PetscCall(DMPlexGetDepthStratum(dm, d, &pStratStart[d], &pStratEnd[d]));
2081:   PetscCall(PetscDualSpaceSectionCreate_Internal(sp, &section));
2082:   sp->pointSection = section;
2083:   if (continuous && !lag->interiorOnly) {
2084:     PetscInt h;

2086:     for (p = pStratStart[depth - 1]; p < pStratEnd[depth - 1]; p++) { /* calculate the facet dual spaces */
2087:       PetscReal      v0[3];
2088:       DMPolytopeType ptype;
2089:       PetscReal      J[9], detJ;
2090:       PetscInt       q;

2092:       PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, p, v0, J, NULL, &detJ));
2093:       PetscCall(DMPlexGetCellType(dm, p, &ptype));

2095:       /* compare to previous facets: if computed, reference that dualspace */
2096:       for (q = pStratStart[depth - 1]; q < p; q++) {
2097:         DMPolytopeType qtype;

2099:         PetscCall(DMPlexGetCellType(dm, q, &qtype));
2100:         if (qtype == ptype) break;
2101:       }
2102:       if (q < p) { /* this facet has the same dual space as that one */
2103:         PetscCall(PetscObjectReference((PetscObject)sp->pointSpaces[q]));
2104:         sp->pointSpaces[p] = sp->pointSpaces[q];
2105:         continue;
2106:       }
2107:       /* if not, recursively compute this dual space */
2108:       PetscCall(PetscDualSpaceCreateFacetSubspace_Lagrange(sp, NULL, p, formDegree, Ncopies, PETSC_FALSE, &sp->pointSpaces[p]));
2109:     }
2110:     for (h = 2; h <= depth; h++) { /* get the higher subspaces from the facet subspaces */
2111:       PetscInt hd   = depth - h;
2112:       PetscInt hdim = dim - h;

2114:       if (hdim < PetscAbsInt(formDegree)) break;
2115:       for (p = pStratStart[hd]; p < pStratEnd[hd]; p++) {
2116:         PetscInt        suppSize, s;
2117:         const PetscInt *supp;

2119:         PetscCall(DMPlexGetSupportSize(dm, p, &suppSize));
2120:         PetscCall(DMPlexGetSupport(dm, p, &supp));
2121:         for (s = 0; s < suppSize; s++) {
2122:           DM              qdm;
2123:           PetscDualSpace  qsp, psp;
2124:           PetscInt        c, coneSize, q;
2125:           const PetscInt *cone;
2126:           const PetscInt *refCone;

2128:           q   = supp[s];
2129:           qsp = sp->pointSpaces[q];
2130:           PetscCall(DMPlexGetConeSize(dm, q, &coneSize));
2131:           PetscCall(DMPlexGetCone(dm, q, &cone));
2132:           for (c = 0; c < coneSize; c++)
2133:             if (cone[c] == p) break;
2134:           PetscCheck(c != coneSize, PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "cone/support mismatch");
2135:           PetscCall(PetscDualSpaceGetDM(qsp, &qdm));
2136:           PetscCall(DMPlexGetCone(qdm, 0, &refCone));
2137:           /* get the equivalent dual space from the support dual space */
2138:           PetscCall(PetscDualSpaceGetPointSubspace(qsp, refCone[c], &psp));
2139:           if (!s) {
2140:             PetscCall(PetscObjectReference((PetscObject)psp));
2141:             sp->pointSpaces[p] = psp;
2142:           }
2143:         }
2144:       }
2145:     }
2146:     for (p = 1; p < pEnd; p++) {
2147:       PetscInt pspdim;
2148:       if (!sp->pointSpaces[p]) continue;
2149:       PetscCall(PetscDualSpaceGetInteriorDimension(sp->pointSpaces[p], &pspdim));
2150:       PetscCall(PetscSectionSetDof(section, p, pspdim));
2151:     }
2152:   }

2154:   if (trimmed && !continuous) {
2155:     /* the dofs of a trimmed space don't have a nice tensor/lattice structure:
2156:      * just construct the continuous dual space and copy all of the data over,
2157:      * allocating it all to the cell instead of splitting it up between the boundaries */
2158:     PetscDualSpace      spcont;
2159:     PetscInt            spdim, f;
2160:     PetscQuadrature     allNodes;
2161:     PetscDualSpace_Lag *lagc;
2162:     Mat                 allMat;

2164:     PetscCall(PetscDualSpaceDuplicate(sp, &spcont));
2165:     PetscCall(PetscDualSpaceLagrangeSetContinuity(spcont, PETSC_TRUE));
2166:     PetscCall(PetscDualSpaceSetUp(spcont));
2167:     PetscCall(PetscDualSpaceGetDimension(spcont, &spdim));
2168:     sp->spdim = sp->spintdim = spdim;
2169:     PetscCall(PetscSectionSetDof(section, 0, spdim));
2170:     PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2171:     PetscCall(PetscMalloc1(spdim, &sp->functional));
2172:     for (f = 0; f < spdim; f++) {
2173:       PetscQuadrature fn;

2175:       PetscCall(PetscDualSpaceGetFunctional(spcont, f, &fn));
2176:       PetscCall(PetscObjectReference((PetscObject)fn));
2177:       sp->functional[f] = fn;
2178:     }
2179:     PetscCall(PetscDualSpaceGetAllData(spcont, &allNodes, &allMat));
2180:     PetscCall(PetscObjectReference((PetscObject)allNodes));
2181:     PetscCall(PetscObjectReference((PetscObject)allNodes));
2182:     sp->allNodes = sp->intNodes = allNodes;
2183:     PetscCall(PetscObjectReference((PetscObject)allMat));
2184:     PetscCall(PetscObjectReference((PetscObject)allMat));
2185:     sp->allMat = sp->intMat = allMat;
2186:     lagc                    = (PetscDualSpace_Lag *)spcont->data;
2187:     PetscCall(PetscLagNodeIndicesReference(lagc->vertIndices));
2188:     lag->vertIndices = lagc->vertIndices;
2189:     PetscCall(PetscLagNodeIndicesReference(lagc->allNodeIndices));
2190:     PetscCall(PetscLagNodeIndicesReference(lagc->allNodeIndices));
2191:     lag->intNodeIndices = lagc->allNodeIndices;
2192:     lag->allNodeIndices = lagc->allNodeIndices;
2193:     PetscCall(PetscDualSpaceDestroy(&spcont));
2194:     PetscCall(PetscFree2(pStratStart, pStratEnd));
2195:     PetscCall(DMDestroy(&dmint));
2196:     PetscFunctionReturn(PETSC_SUCCESS);
2197:   }

2199:   /* step 3: construct intNodes, and intMat, and combine it with boundray data to make allNodes and allMat */
2200:   if (!tensorSpace) {
2201:     if (!tensorCell) PetscCall(PetscLagNodeIndicesCreateSimplexVertices(dm, &lag->vertIndices));

2203:     if (trimmed) {
2204:       /* there is one dof in the interior of the a trimmed element for each full polynomial of with degree at most
2205:        * order + k - dim - 1 */
2206:       if (order + PetscAbsInt(formDegree) > dim) {
2207:         PetscInt sum = order + PetscAbsInt(formDegree) - dim - 1;
2208:         PetscInt nDofs;

2210:         PetscCall(PetscDualSpaceLagrangeCreateSimplexNodeMat(nodeFamily, dim, sum, Nk, numNodeSkip, &sp->intNodes, &sp->intMat, &lag->intNodeIndices));
2211:         PetscCall(MatGetSize(sp->intMat, &nDofs, NULL));
2212:         PetscCall(PetscSectionSetDof(section, 0, nDofs));
2213:       }
2214:       PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2215:       PetscCall(PetscDualSpaceCreateAllDataFromInteriorData(sp));
2216:       PetscCall(PetscDualSpaceLagrangeCreateAllNodeIdx(sp));
2217:     } else {
2218:       if (!continuous) {
2219:         /* if discontinuous just construct one node for each set of dofs (a set of dofs is a basis for the k-form
2220:          * space) */
2221:         PetscInt sum = order;
2222:         PetscInt nDofs;

2224:         PetscCall(PetscDualSpaceLagrangeCreateSimplexNodeMat(nodeFamily, dim, sum, Nk, numNodeSkip, &sp->intNodes, &sp->intMat, &lag->intNodeIndices));
2225:         PetscCall(MatGetSize(sp->intMat, &nDofs, NULL));
2226:         PetscCall(PetscSectionSetDof(section, 0, nDofs));
2227:         PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2228:         PetscCall(PetscObjectReference((PetscObject)sp->intNodes));
2229:         sp->allNodes = sp->intNodes;
2230:         PetscCall(PetscObjectReference((PetscObject)sp->intMat));
2231:         sp->allMat = sp->intMat;
2232:         PetscCall(PetscLagNodeIndicesReference(lag->intNodeIndices));
2233:         lag->allNodeIndices = lag->intNodeIndices;
2234:       } else {
2235:         /* there is one dof in the interior of the a full element for each trimmed polynomial of with degree at most
2236:          * order + k - dim, but with complementary form degree */
2237:         if (order + PetscAbsInt(formDegree) > dim) {
2238:           PetscDualSpace      trimmedsp;
2239:           PetscDualSpace_Lag *trimmedlag;
2240:           PetscQuadrature     intNodes;
2241:           PetscInt            trFormDegree = formDegree >= 0 ? formDegree - dim : dim - PetscAbsInt(formDegree);
2242:           PetscInt            nDofs;
2243:           Mat                 intMat;

2245:           PetscCall(PetscDualSpaceDuplicate(sp, &trimmedsp));
2246:           PetscCall(PetscDualSpaceLagrangeSetTrimmed(trimmedsp, PETSC_TRUE));
2247:           PetscCall(PetscDualSpaceSetOrder(trimmedsp, order + PetscAbsInt(formDegree) - dim));
2248:           PetscCall(PetscDualSpaceSetFormDegree(trimmedsp, trFormDegree));
2249:           trimmedlag              = (PetscDualSpace_Lag *)trimmedsp->data;
2250:           trimmedlag->numNodeSkip = numNodeSkip + 1;
2251:           PetscCall(PetscDualSpaceSetUp(trimmedsp));
2252:           PetscCall(PetscDualSpaceGetAllData(trimmedsp, &intNodes, &intMat));
2253:           PetscCall(PetscObjectReference((PetscObject)intNodes));
2254:           sp->intNodes = intNodes;
2255:           PetscCall(PetscLagNodeIndicesReference(trimmedlag->allNodeIndices));
2256:           lag->intNodeIndices = trimmedlag->allNodeIndices;
2257:           PetscCall(PetscObjectReference((PetscObject)intMat));
2258:           if (PetscAbsInt(formDegree) > 0 && PetscAbsInt(formDegree) < dim) {
2259:             PetscReal   *T;
2260:             PetscScalar *work;
2261:             PetscInt     nCols, nRows;
2262:             Mat          intMatT;

2264:             PetscCall(MatDuplicate(intMat, MAT_COPY_VALUES, &intMatT));
2265:             PetscCall(MatGetSize(intMat, &nRows, &nCols));
2266:             PetscCall(PetscMalloc2(Nk * Nk, &T, nCols, &work));
2267:             PetscCall(BiunitSimplexSymmetricFormTransformation(dim, formDegree, T));
2268:             for (PetscInt row = 0; row < nRows; row++) {
2269:               PetscInt           nrCols;
2270:               const PetscInt    *rCols;
2271:               const PetscScalar *rVals;

2273:               PetscCall(MatGetRow(intMat, row, &nrCols, &rCols, &rVals));
2274:               PetscCheck(nrCols % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in intMat matrix are not in k-form size blocks");
2275:               for (PetscInt b = 0; b < nrCols; b += Nk) {
2276:                 const PetscScalar *v = &rVals[b];
2277:                 PetscScalar       *w = &work[b];
2278:                 for (PetscInt j = 0; j < Nk; j++) {
2279:                   w[j] = 0.;
2280:                   for (PetscInt i = 0; i < Nk; i++) w[j] += v[i] * T[i * Nk + j];
2281:                 }
2282:               }
2283:               PetscCall(MatSetValuesBlocked(intMatT, 1, &row, nrCols, rCols, work, INSERT_VALUES));
2284:               PetscCall(MatRestoreRow(intMat, row, &nrCols, &rCols, &rVals));
2285:             }
2286:             PetscCall(MatAssemblyBegin(intMatT, MAT_FINAL_ASSEMBLY));
2287:             PetscCall(MatAssemblyEnd(intMatT, MAT_FINAL_ASSEMBLY));
2288:             PetscCall(MatDestroy(&intMat));
2289:             intMat = intMatT;
2290:             PetscCall(PetscLagNodeIndicesDestroy(&lag->intNodeIndices));
2291:             PetscCall(PetscLagNodeIndicesDuplicate(trimmedlag->allNodeIndices, &lag->intNodeIndices));
2292:             {
2293:               PetscInt         nNodes     = lag->intNodeIndices->nNodes;
2294:               PetscReal       *newNodeVec = lag->intNodeIndices->nodeVec;
2295:               const PetscReal *oldNodeVec = trimmedlag->allNodeIndices->nodeVec;

2297:               for (PetscInt n = 0; n < nNodes; n++) {
2298:                 PetscReal       *w = &newNodeVec[n * Nk];
2299:                 const PetscReal *v = &oldNodeVec[n * Nk];

2301:                 for (PetscInt j = 0; j < Nk; j++) {
2302:                   w[j] = 0.;
2303:                   for (PetscInt i = 0; i < Nk; i++) w[j] += v[i] * T[i * Nk + j];
2304:                 }
2305:               }
2306:             }
2307:             PetscCall(PetscFree2(T, work));
2308:           }
2309:           sp->intMat = intMat;
2310:           PetscCall(MatGetSize(sp->intMat, &nDofs, NULL));
2311:           PetscCall(PetscDualSpaceDestroy(&trimmedsp));
2312:           PetscCall(PetscSectionSetDof(section, 0, nDofs));
2313:         }
2314:         PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2315:         PetscCall(PetscDualSpaceCreateAllDataFromInteriorData(sp));
2316:         PetscCall(PetscDualSpaceLagrangeCreateAllNodeIdx(sp));
2317:       }
2318:     }
2319:   } else {
2320:     PetscQuadrature     intNodesTrace  = NULL;
2321:     PetscQuadrature     intNodesFiber  = NULL;
2322:     PetscQuadrature     intNodes       = NULL;
2323:     PetscLagNodeIndices intNodeIndices = NULL;
2324:     Mat                 intMat         = NULL;

2326:     if (PetscAbsInt(formDegree) < dim) { /* get the trace k-forms on the first facet, and the 0-forms on the edge,
2327:                                             and wedge them together to create some of the k-form dofs */
2328:       PetscDualSpace      trace, fiber;
2329:       PetscDualSpace_Lag *tracel, *fiberl;
2330:       Mat                 intMatTrace, intMatFiber;

2332:       if (sp->pointSpaces[tensorf]) {
2333:         PetscCall(PetscObjectReference((PetscObject)sp->pointSpaces[tensorf]));
2334:         trace = sp->pointSpaces[tensorf];
2335:       } else {
2336:         PetscCall(PetscDualSpaceCreateFacetSubspace_Lagrange(sp, NULL, tensorf, formDegree, Ncopies, PETSC_TRUE, &trace));
2337:       }
2338:       PetscCall(PetscDualSpaceCreateEdgeSubspace_Lagrange(sp, order, 0, 1, PETSC_TRUE, &fiber));
2339:       tracel = (PetscDualSpace_Lag *)trace->data;
2340:       fiberl = (PetscDualSpace_Lag *)fiber->data;
2341:       PetscCall(PetscLagNodeIndicesCreateTensorVertices(dm, tracel->vertIndices, &lag->vertIndices));
2342:       PetscCall(PetscDualSpaceGetInteriorData(trace, &intNodesTrace, &intMatTrace));
2343:       PetscCall(PetscDualSpaceGetInteriorData(fiber, &intNodesFiber, &intMatFiber));
2344:       if (intNodesTrace && intNodesFiber) {
2345:         PetscCall(PetscQuadratureCreateTensor(intNodesTrace, intNodesFiber, &intNodes));
2346:         PetscCall(MatTensorAltV(intMatTrace, intMatFiber, dim - 1, formDegree, 1, 0, &intMat));
2347:         PetscCall(PetscLagNodeIndicesTensor(tracel->intNodeIndices, dim - 1, formDegree, fiberl->intNodeIndices, 1, 0, &intNodeIndices));
2348:       }
2349:       PetscCall(PetscObjectReference((PetscObject)intNodesTrace));
2350:       PetscCall(PetscObjectReference((PetscObject)intNodesFiber));
2351:       PetscCall(PetscDualSpaceDestroy(&fiber));
2352:       PetscCall(PetscDualSpaceDestroy(&trace));
2353:     }
2354:     if (PetscAbsInt(formDegree) > 0) { /* get the trace (k-1)-forms on the first facet, and the 1-forms on the edge,
2355:                                           and wedge them together to create the remaining k-form dofs */
2356:       PetscDualSpace      trace, fiber;
2357:       PetscDualSpace_Lag *tracel, *fiberl;
2358:       PetscQuadrature     intNodesTrace2, intNodesFiber2, intNodes2;
2359:       PetscLagNodeIndices intNodeIndices2;
2360:       Mat                 intMatTrace, intMatFiber, intMat2;
2361:       PetscInt            traceDegree = formDegree > 0 ? formDegree - 1 : formDegree + 1;
2362:       PetscInt            fiberDegree = formDegree > 0 ? 1 : -1;

2364:       PetscCall(PetscDualSpaceCreateFacetSubspace_Lagrange(sp, NULL, tensorf, traceDegree, Ncopies, PETSC_TRUE, &trace));
2365:       PetscCall(PetscDualSpaceCreateEdgeSubspace_Lagrange(sp, order, fiberDegree, 1, PETSC_TRUE, &fiber));
2366:       tracel = (PetscDualSpace_Lag *)trace->data;
2367:       fiberl = (PetscDualSpace_Lag *)fiber->data;
2368:       if (!lag->vertIndices) PetscCall(PetscLagNodeIndicesCreateTensorVertices(dm, tracel->vertIndices, &lag->vertIndices));
2369:       PetscCall(PetscDualSpaceGetInteriorData(trace, &intNodesTrace2, &intMatTrace));
2370:       PetscCall(PetscDualSpaceGetInteriorData(fiber, &intNodesFiber2, &intMatFiber));
2371:       if (intNodesTrace2 && intNodesFiber2) {
2372:         PetscCall(PetscQuadratureCreateTensor(intNodesTrace2, intNodesFiber2, &intNodes2));
2373:         PetscCall(MatTensorAltV(intMatTrace, intMatFiber, dim - 1, traceDegree, 1, fiberDegree, &intMat2));
2374:         PetscCall(PetscLagNodeIndicesTensor(tracel->intNodeIndices, dim - 1, traceDegree, fiberl->intNodeIndices, 1, fiberDegree, &intNodeIndices2));
2375:         if (!intMat) {
2376:           intMat         = intMat2;
2377:           intNodes       = intNodes2;
2378:           intNodeIndices = intNodeIndices2;
2379:         } else {
2380:           /* merge the matrices, quadrature points, and nodes */
2381:           PetscInt            nM;
2382:           PetscInt            nDof, nDof2;
2383:           PetscInt           *toMerged = NULL, *toMerged2 = NULL;
2384:           PetscQuadrature     merged               = NULL;
2385:           PetscLagNodeIndices intNodeIndicesMerged = NULL;
2386:           Mat                 matMerged            = NULL;

2388:           PetscCall(MatGetSize(intMat, &nDof, NULL));
2389:           PetscCall(MatGetSize(intMat2, &nDof2, NULL));
2390:           PetscCall(PetscQuadraturePointsMerge(intNodes, intNodes2, &merged, &toMerged, &toMerged2));
2391:           PetscCall(PetscQuadratureGetData(merged, NULL, NULL, &nM, NULL, NULL));
2392:           PetscCall(MatricesMerge(intMat, intMat2, dim, formDegree, nM, toMerged, toMerged2, &matMerged));
2393:           PetscCall(PetscLagNodeIndicesMerge(intNodeIndices, intNodeIndices2, &intNodeIndicesMerged));
2394:           PetscCall(PetscFree(toMerged));
2395:           PetscCall(PetscFree(toMerged2));
2396:           PetscCall(MatDestroy(&intMat));
2397:           PetscCall(MatDestroy(&intMat2));
2398:           PetscCall(PetscQuadratureDestroy(&intNodes));
2399:           PetscCall(PetscQuadratureDestroy(&intNodes2));
2400:           PetscCall(PetscLagNodeIndicesDestroy(&intNodeIndices));
2401:           PetscCall(PetscLagNodeIndicesDestroy(&intNodeIndices2));
2402:           intNodes       = merged;
2403:           intMat         = matMerged;
2404:           intNodeIndices = intNodeIndicesMerged;
2405:           if (!trimmed) {
2406:             /* I think users expect that, when a node has a full basis for the k-forms,
2407:              * they should be consecutive dofs.  That isn't the case for trimmed spaces,
2408:              * but is for some of the nodes in untrimmed spaces, so in that case we
2409:              * sort them to group them by node */
2410:             Mat intMatPerm;

2412:             PetscCall(MatPermuteByNodeIdx(intMat, intNodeIndices, &intMatPerm));
2413:             PetscCall(MatDestroy(&intMat));
2414:             intMat = intMatPerm;
2415:           }
2416:         }
2417:       }
2418:       PetscCall(PetscDualSpaceDestroy(&fiber));
2419:       PetscCall(PetscDualSpaceDestroy(&trace));
2420:     }
2421:     PetscCall(PetscQuadratureDestroy(&intNodesTrace));
2422:     PetscCall(PetscQuadratureDestroy(&intNodesFiber));
2423:     sp->intNodes        = intNodes;
2424:     sp->intMat          = intMat;
2425:     lag->intNodeIndices = intNodeIndices;
2426:     {
2427:       PetscInt nDofs = 0;

2429:       if (intMat) PetscCall(MatGetSize(intMat, &nDofs, NULL));
2430:       PetscCall(PetscSectionSetDof(section, 0, nDofs));
2431:     }
2432:     PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2433:     if (continuous) {
2434:       PetscCall(PetscDualSpaceCreateAllDataFromInteriorData(sp));
2435:       PetscCall(PetscDualSpaceLagrangeCreateAllNodeIdx(sp));
2436:     } else {
2437:       PetscCall(PetscObjectReference((PetscObject)intNodes));
2438:       sp->allNodes = intNodes;
2439:       PetscCall(PetscObjectReference((PetscObject)intMat));
2440:       sp->allMat = intMat;
2441:       PetscCall(PetscLagNodeIndicesReference(intNodeIndices));
2442:       lag->allNodeIndices = intNodeIndices;
2443:     }
2444:   }
2445:   PetscCall(PetscSectionGetStorageSize(section, &sp->spdim));
2446:   PetscCall(PetscSectionGetConstrainedStorageSize(section, &sp->spintdim));
2447:   // TODO: fix this, computing functionals from moments should be no different for nodal vs modal
2448:   if (lag->useMoments) {
2449:     PetscCall(PetscDualSpaceComputeFunctionalsFromAllData_Moments(sp));
2450:   } else {
2451:     PetscCall(PetscDualSpaceComputeFunctionalsFromAllData(sp));
2452:   }
2453:   PetscCall(PetscFree2(pStratStart, pStratEnd));
2454:   PetscCall(DMDestroy(&dmint));
2455:   PetscFunctionReturn(PETSC_SUCCESS);
2456: }

2458: /* Create a matrix that represents the transformation that DMPlexVecGetClosure() would need
2459:  * to get the representation of the dofs for a mesh point if the mesh point had this orientation
2460:  * relative to the cell */
2461: PetscErrorCode PetscDualSpaceCreateInteriorSymmetryMatrix_Lagrange(PetscDualSpace sp, PetscInt ornt, Mat *symMat)
2462: {
2463:   PetscDualSpace_Lag *lag;
2464:   DM                  dm;
2465:   PetscLagNodeIndices vertIndices, intNodeIndices;
2466:   PetscLagNodeIndices ni;
2467:   PetscInt            nodeIdxDim, nodeVecDim, nNodes;
2468:   PetscInt            formDegree;
2469:   PetscInt           *perm, *permOrnt;
2470:   PetscInt           *nnz;
2471:   PetscInt            n;
2472:   PetscInt            maxGroupSize;
2473:   PetscScalar        *V, *W, *work;
2474:   Mat                 A;

2476:   PetscFunctionBegin;
2477:   if (!sp->spintdim) {
2478:     *symMat = NULL;
2479:     PetscFunctionReturn(PETSC_SUCCESS);
2480:   }
2481:   lag            = (PetscDualSpace_Lag *)sp->data;
2482:   vertIndices    = lag->vertIndices;
2483:   intNodeIndices = lag->intNodeIndices;
2484:   PetscCall(PetscDualSpaceGetDM(sp, &dm));
2485:   PetscCall(PetscDualSpaceGetFormDegree(sp, &formDegree));
2486:   PetscCall(PetscNew(&ni));
2487:   ni->refct      = 1;
2488:   ni->nodeIdxDim = nodeIdxDim = intNodeIndices->nodeIdxDim;
2489:   ni->nodeVecDim = nodeVecDim = intNodeIndices->nodeVecDim;
2490:   ni->nNodes = nNodes = intNodeIndices->nNodes;
2491:   PetscCall(PetscMalloc1(nNodes * nodeIdxDim, &ni->nodeIdx));
2492:   PetscCall(PetscMalloc1(nNodes * nodeVecDim, &ni->nodeVec));
2493:   /* push forward the dofs by the symmetry of the reference element induced by ornt */
2494:   PetscCall(PetscLagNodeIndicesPushForward(dm, vertIndices, 0, vertIndices, intNodeIndices, ornt, formDegree, ni->nodeIdx, ni->nodeVec));
2495:   /* get the revlex order for both the original and transformed dofs */
2496:   PetscCall(PetscLagNodeIndicesGetPermutation(intNodeIndices, &perm));
2497:   PetscCall(PetscLagNodeIndicesGetPermutation(ni, &permOrnt));
2498:   PetscCall(PetscMalloc1(nNodes, &nnz));
2499:   for (n = 0, maxGroupSize = 0; n < nNodes;) { /* incremented in the loop */
2500:     PetscInt *nind = &(ni->nodeIdx[permOrnt[n] * nodeIdxDim]);
2501:     PetscInt  m, nEnd;
2502:     PetscInt  groupSize;
2503:     /* for each group of dofs that have the same nodeIdx coordinate */
2504:     for (nEnd = n + 1; nEnd < nNodes; nEnd++) {
2505:       PetscInt *mind = &(ni->nodeIdx[permOrnt[nEnd] * nodeIdxDim]);
2506:       PetscInt  d;

2508:       /* compare the oriented permutation indices */
2509:       for (d = 0; d < nodeIdxDim; d++)
2510:         if (mind[d] != nind[d]) break;
2511:       if (d < nodeIdxDim) break;
2512:     }
2513:     /* permOrnt[[n, nEnd)] is a group of dofs that, under the symmetry are at the same location */

2515:     /* the symmetry had better map the group of dofs with the same permuted nodeIdx
2516:      * to a group of dofs with the same size, otherwise we messed up */
2517:     if (PetscDefined(USE_DEBUG)) {
2518:       PetscInt  m;
2519:       PetscInt *nind = &(intNodeIndices->nodeIdx[perm[n] * nodeIdxDim]);

2521:       for (m = n + 1; m < nEnd; m++) {
2522:         PetscInt *mind = &(intNodeIndices->nodeIdx[perm[m] * nodeIdxDim]);
2523:         PetscInt  d;

2525:         /* compare the oriented permutation indices */
2526:         for (d = 0; d < nodeIdxDim; d++)
2527:           if (mind[d] != nind[d]) break;
2528:         if (d < nodeIdxDim) break;
2529:       }
2530:       PetscCheck(m >= nEnd, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Dofs with same index after symmetry not same block size");
2531:     }
2532:     groupSize = nEnd - n;
2533:     /* each pushforward dof vector will be expressed in a basis of the unpermuted dofs */
2534:     for (m = n; m < nEnd; m++) nnz[permOrnt[m]] = groupSize;

2536:     maxGroupSize = PetscMax(maxGroupSize, nEnd - n);
2537:     n            = nEnd;
2538:   }
2539:   PetscCheck(maxGroupSize <= nodeVecDim, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Dofs are not in blocks that can be solved");
2540:   PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, nNodes, nNodes, 0, nnz, &A));
2541:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)A, "lag_"));
2542:   PetscCall(PetscFree(nnz));
2543:   PetscCall(PetscMalloc3(maxGroupSize * nodeVecDim, &V, maxGroupSize * nodeVecDim, &W, nodeVecDim * 2, &work));
2544:   for (n = 0; n < nNodes;) { /* incremented in the loop */
2545:     PetscInt *nind = &(ni->nodeIdx[permOrnt[n] * nodeIdxDim]);
2546:     PetscInt  nEnd;
2547:     PetscInt  m;
2548:     PetscInt  groupSize;
2549:     for (nEnd = n + 1; nEnd < nNodes; nEnd++) {
2550:       PetscInt *mind = &(ni->nodeIdx[permOrnt[nEnd] * nodeIdxDim]);
2551:       PetscInt  d;

2553:       /* compare the oriented permutation indices */
2554:       for (d = 0; d < nodeIdxDim; d++)
2555:         if (mind[d] != nind[d]) break;
2556:       if (d < nodeIdxDim) break;
2557:     }
2558:     groupSize = nEnd - n;
2559:     /* get all of the vectors from the original and all of the pushforward vectors */
2560:     for (m = n; m < nEnd; m++) {
2561:       PetscInt d;

2563:       for (d = 0; d < nodeVecDim; d++) {
2564:         V[(m - n) * nodeVecDim + d] = intNodeIndices->nodeVec[perm[m] * nodeVecDim + d];
2565:         W[(m - n) * nodeVecDim + d] = ni->nodeVec[permOrnt[m] * nodeVecDim + d];
2566:       }
2567:     }
2568:     /* now we have to solve for W in terms of V: the systems isn't always square, but the span
2569:      * of V and W should always be the same, so the solution of the normal equations works */
2570:     {
2571:       char         transpose = 'N';
2572:       PetscBLASInt bm, bn, bnrhs, blda, bldb, blwork, info;

2574:       PetscCall(PetscBLASIntCast(nodeVecDim, &bm));
2575:       PetscCall(PetscBLASIntCast(groupSize, &bn));
2576:       PetscCall(PetscBLASIntCast(groupSize, &bnrhs));
2577:       PetscCall(PetscBLASIntCast(bm, &blda));
2578:       PetscCall(PetscBLASIntCast(bm, &bldb));
2579:       PetscCall(PetscBLASIntCast(2 * nodeVecDim, &blwork));
2580:       PetscCallBLAS("LAPACKgels", LAPACKgels_(&transpose, &bm, &bn, &bnrhs, V, &blda, W, &bldb, work, &blwork, &info));
2581:       PetscCheck(info == 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Bad argument to GELS");
2582:       /* repack */
2583:       {
2584:         PetscInt i, j;

2586:         for (i = 0; i < groupSize; i++) {
2587:           for (j = 0; j < groupSize; j++) {
2588:             /* notice the different leading dimension */
2589:             V[i * groupSize + j] = W[i * nodeVecDim + j];
2590:           }
2591:         }
2592:       }
2593:       if (PetscDefined(USE_DEBUG)) {
2594:         PetscReal res;

2596:         /* check that the normal error is 0 */
2597:         for (m = n; m < nEnd; m++) {
2598:           PetscInt d;

2600:           for (d = 0; d < nodeVecDim; d++) W[(m - n) * nodeVecDim + d] = ni->nodeVec[permOrnt[m] * nodeVecDim + d];
2601:         }
2602:         res = 0.;
2603:         for (PetscInt i = 0; i < groupSize; i++) {
2604:           for (PetscInt j = 0; j < nodeVecDim; j++) {
2605:             for (PetscInt k = 0; k < groupSize; k++) W[i * nodeVecDim + j] -= V[i * groupSize + k] * intNodeIndices->nodeVec[perm[n + k] * nodeVecDim + j];
2606:             res += PetscAbsScalar(W[i * nodeVecDim + j]);
2607:           }
2608:         }
2609:         PetscCheck(res <= PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_LIB, "Dof block did not solve");
2610:       }
2611:     }
2612:     PetscCall(MatSetValues(A, groupSize, &permOrnt[n], groupSize, &perm[n], V, INSERT_VALUES));
2613:     n = nEnd;
2614:   }
2615:   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
2616:   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
2617:   *symMat = A;
2618:   PetscCall(PetscFree3(V, W, work));
2619:   PetscCall(PetscLagNodeIndicesDestroy(&ni));
2620:   PetscFunctionReturn(PETSC_SUCCESS);
2621: }

2623: // get the symmetries of closure points
2624: PETSC_INTERN PetscErrorCode PetscDualSpaceGetBoundarySymmetries_Internal(PetscDualSpace sp, PetscInt ***symperms, PetscScalar ***symflips)
2625: {
2626:   PetscInt  closureSize = 0;
2627:   PetscInt *closure     = NULL;
2628:   PetscInt  r;

2630:   PetscFunctionBegin;
2631:   PetscCall(DMPlexGetTransitiveClosure(sp->dm, 0, PETSC_TRUE, &closureSize, &closure));
2632:   for (r = 0; r < closureSize; r++) {
2633:     PetscDualSpace       psp;
2634:     PetscInt             point = closure[2 * r];
2635:     PetscInt             pspintdim;
2636:     const PetscInt    ***psymperms = NULL;
2637:     const PetscScalar ***psymflips = NULL;

2639:     if (!point) continue;
2640:     PetscCall(PetscDualSpaceGetPointSubspace(sp, point, &psp));
2641:     if (!psp) continue;
2642:     PetscCall(PetscDualSpaceGetInteriorDimension(psp, &pspintdim));
2643:     if (!pspintdim) continue;
2644:     PetscCall(PetscDualSpaceGetSymmetries(psp, &psymperms, &psymflips));
2645:     symperms[r] = (PetscInt **)(psymperms ? psymperms[0] : NULL);
2646:     symflips[r] = (PetscScalar **)(psymflips ? psymflips[0] : NULL);
2647:   }
2648:   PetscCall(DMPlexRestoreTransitiveClosure(sp->dm, 0, PETSC_TRUE, &closureSize, &closure));
2649:   PetscFunctionReturn(PETSC_SUCCESS);
2650: }

2652: #define BaryIndex(perEdge, a, b, c) (((b) * (2 * perEdge + 1 - (b))) / 2) + (c)

2654: #define CartIndex(perEdge, a, b) (perEdge * (a) + b)

2656: /* the existing interface for symmetries is insufficient for all cases:
2657:  * - it should be sufficient for form degrees that are scalar (0 and n)
2658:  * - it should be sufficient for hypercube dofs
2659:  * - it isn't sufficient for simplex cells with non-scalar form degrees if
2660:  *   there are any dofs in the interior
2661:  *
2662:  * We compute the general transformation matrices, and if they fit, we return them,
2663:  * otherwise we error (but we should probably change the interface to allow for
2664:  * these symmetries)
2665:  */
2666: static PetscErrorCode PetscDualSpaceGetSymmetries_Lagrange(PetscDualSpace sp, const PetscInt ****perms, const PetscScalar ****flips)
2667: {
2668:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2669:   PetscInt            dim, order, Nc;

2671:   PetscFunctionBegin;
2672:   PetscCall(PetscDualSpaceGetOrder(sp, &order));
2673:   PetscCall(PetscDualSpaceGetNumComponents(sp, &Nc));
2674:   PetscCall(DMGetDimension(sp->dm, &dim));
2675:   if (!lag->symComputed) { /* store symmetries */
2676:     PetscInt       pStart, pEnd, p;
2677:     PetscInt       numPoints;
2678:     PetscInt       numFaces;
2679:     PetscInt       spintdim;
2680:     PetscInt    ***symperms;
2681:     PetscScalar ***symflips;

2683:     PetscCall(DMPlexGetChart(sp->dm, &pStart, &pEnd));
2684:     numPoints = pEnd - pStart;
2685:     {
2686:       DMPolytopeType ct;
2687:       /* The number of arrangements is no longer based on the number of faces */
2688:       PetscCall(DMPlexGetCellType(sp->dm, 0, &ct));
2689:       numFaces = DMPolytopeTypeGetNumArrangements(ct) / 2;
2690:     }
2691:     PetscCall(PetscCalloc1(numPoints, &symperms));
2692:     PetscCall(PetscCalloc1(numPoints, &symflips));
2693:     spintdim = sp->spintdim;
2694:     /* The nodal symmetry behavior is not present when tensorSpace != tensorCell: someone might want this for the "S"
2695:      * family of FEEC spaces.  Most used in particular are discontinuous polynomial L2 spaces in tensor cells, where
2696:      * the symmetries are not necessary for FE assembly.  So for now we assume this is the case and don't return
2697:      * symmetries if tensorSpace != tensorCell */
2698:     if (spintdim && 0 < dim && dim < 3 && (lag->tensorSpace == lag->tensorCell)) { /* compute self symmetries */
2699:       PetscInt    **cellSymperms;
2700:       PetscScalar **cellSymflips;
2701:       PetscInt      ornt;
2702:       PetscInt      nCopies = Nc / lag->intNodeIndices->nodeVecDim;
2703:       PetscInt      nNodes  = lag->intNodeIndices->nNodes;

2705:       lag->numSelfSym = 2 * numFaces;
2706:       lag->selfSymOff = numFaces;
2707:       PetscCall(PetscCalloc1(2 * numFaces, &cellSymperms));
2708:       PetscCall(PetscCalloc1(2 * numFaces, &cellSymflips));
2709:       /* we want to be able to index symmetries directly with the orientations, which range from [-numFaces,numFaces) */
2710:       symperms[0] = &cellSymperms[numFaces];
2711:       symflips[0] = &cellSymflips[numFaces];
2712:       PetscCheck(lag->intNodeIndices->nodeVecDim * nCopies == Nc, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Node indices incompatible with dofs");
2713:       PetscCheck(nNodes * nCopies == spintdim, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Node indices incompatible with dofs");
2714:       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 */
2715:         Mat          symMat;
2716:         PetscInt    *perm;
2717:         PetscScalar *flips;
2718:         PetscInt     i;

2720:         if (!ornt) continue;
2721:         PetscCall(PetscMalloc1(spintdim, &perm));
2722:         PetscCall(PetscCalloc1(spintdim, &flips));
2723:         for (i = 0; i < spintdim; i++) perm[i] = -1;
2724:         PetscCall(PetscDualSpaceCreateInteriorSymmetryMatrix_Lagrange(sp, ornt, &symMat));
2725:         for (i = 0; i < nNodes; i++) {
2726:           PetscInt           ncols;
2727:           PetscInt           j, k;
2728:           const PetscInt    *cols;
2729:           const PetscScalar *vals;
2730:           PetscBool          nz_seen = PETSC_FALSE;

2732:           PetscCall(MatGetRow(symMat, i, &ncols, &cols, &vals));
2733:           for (j = 0; j < ncols; j++) {
2734:             if (PetscAbsScalar(vals[j]) > PETSC_SMALL) {
2735:               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");
2736:               nz_seen = PETSC_TRUE;
2737:               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");
2738:               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");
2739:               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");
2740:               for (k = 0; k < nCopies; k++) perm[cols[j] * nCopies + k] = i * nCopies + k;
2741:               if (PetscRealPart(vals[j]) < 0.) {
2742:                 for (k = 0; k < nCopies; k++) flips[i * nCopies + k] = -1.;
2743:               } else {
2744:                 for (k = 0; k < nCopies; k++) flips[i * nCopies + k] = 1.;
2745:               }
2746:             }
2747:           }
2748:           PetscCall(MatRestoreRow(symMat, i, &ncols, &cols, &vals));
2749:         }
2750:         PetscCall(MatDestroy(&symMat));
2751:         /* if there were no sign flips, keep NULL */
2752:         for (i = 0; i < spintdim; i++)
2753:           if (flips[i] != 1.) break;
2754:         if (i == spintdim) {
2755:           PetscCall(PetscFree(flips));
2756:           flips = NULL;
2757:         }
2758:         /* if the permutation is identity, keep NULL */
2759:         for (i = 0; i < spintdim; i++)
2760:           if (perm[i] != i) break;
2761:         if (i == spintdim) {
2762:           PetscCall(PetscFree(perm));
2763:           perm = NULL;
2764:         }
2765:         symperms[0][ornt] = perm;
2766:         symflips[0][ornt] = flips;
2767:       }
2768:       /* if no orientations produced non-identity permutations, keep NULL */
2769:       for (ornt = -numFaces; ornt < numFaces; ornt++)
2770:         if (symperms[0][ornt]) break;
2771:       if (ornt == numFaces) {
2772:         PetscCall(PetscFree(cellSymperms));
2773:         symperms[0] = NULL;
2774:       }
2775:       /* if no orientations produced sign flips, keep NULL */
2776:       for (ornt = -numFaces; ornt < numFaces; ornt++)
2777:         if (symflips[0][ornt]) break;
2778:       if (ornt == numFaces) {
2779:         PetscCall(PetscFree(cellSymflips));
2780:         symflips[0] = NULL;
2781:       }
2782:     }
2783:     PetscCall(PetscDualSpaceGetBoundarySymmetries_Internal(sp, symperms, symflips));
2784:     for (p = 0; p < pEnd; p++)
2785:       if (symperms[p]) break;
2786:     if (p == pEnd) {
2787:       PetscCall(PetscFree(symperms));
2788:       symperms = NULL;
2789:     }
2790:     for (p = 0; p < pEnd; p++)
2791:       if (symflips[p]) break;
2792:     if (p == pEnd) {
2793:       PetscCall(PetscFree(symflips));
2794:       symflips = NULL;
2795:     }
2796:     lag->symperms    = symperms;
2797:     lag->symflips    = symflips;
2798:     lag->symComputed = PETSC_TRUE;
2799:   }
2800:   if (perms) *perms = (const PetscInt ***)lag->symperms;
2801:   if (flips) *flips = (const PetscScalar ***)lag->symflips;
2802:   PetscFunctionReturn(PETSC_SUCCESS);
2803: }

2805: static PetscErrorCode PetscDualSpaceLagrangeGetContinuity_Lagrange(PetscDualSpace sp, PetscBool *continuous)
2806: {
2807:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;

2809:   PetscFunctionBegin;
2811:   PetscAssertPointer(continuous, 2);
2812:   *continuous = lag->continuous;
2813:   PetscFunctionReturn(PETSC_SUCCESS);
2814: }

2816: static PetscErrorCode PetscDualSpaceLagrangeSetContinuity_Lagrange(PetscDualSpace sp, PetscBool continuous)
2817: {
2818:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;

2820:   PetscFunctionBegin;
2822:   lag->continuous = continuous;
2823:   PetscFunctionReturn(PETSC_SUCCESS);
2824: }

2826: /*@
2827:   PetscDualSpaceLagrangeGetContinuity - Retrieves the flag for element continuity

2829:   Not Collective

2831:   Input Parameter:
2832: . sp - the `PetscDualSpace`

2834:   Output Parameter:
2835: . continuous - flag for element continuity

2837:   Level: intermediate

2839: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeSetContinuity()`
2840: @*/
2841: PetscErrorCode PetscDualSpaceLagrangeGetContinuity(PetscDualSpace sp, PetscBool *continuous)
2842: {
2843:   PetscFunctionBegin;
2845:   PetscAssertPointer(continuous, 2);
2846:   PetscTryMethod(sp, "PetscDualSpaceLagrangeGetContinuity_C", (PetscDualSpace, PetscBool *), (sp, continuous));
2847:   PetscFunctionReturn(PETSC_SUCCESS);
2848: }

2850: /*@
2851:   PetscDualSpaceLagrangeSetContinuity - Indicate whether the element is continuous

2853:   Logically Collective

2855:   Input Parameters:
2856: + sp         - the `PetscDualSpace`
2857: - continuous - flag for element continuity

2859:   Options Database Key:
2860: . -petscdualspace_lagrange_continuity <bool> - use a continuous element

2862:   Level: intermediate

2864: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeGetContinuity()`
2865: @*/
2866: PetscErrorCode PetscDualSpaceLagrangeSetContinuity(PetscDualSpace sp, PetscBool continuous)
2867: {
2868:   PetscFunctionBegin;
2871:   PetscTryMethod(sp, "PetscDualSpaceLagrangeSetContinuity_C", (PetscDualSpace, PetscBool), (sp, continuous));
2872:   PetscFunctionReturn(PETSC_SUCCESS);
2873: }

2875: static PetscErrorCode PetscDualSpaceLagrangeGetTensor_Lagrange(PetscDualSpace sp, PetscBool *tensor)
2876: {
2877:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;

2879:   PetscFunctionBegin;
2880:   *tensor = lag->tensorSpace;
2881:   PetscFunctionReturn(PETSC_SUCCESS);
2882: }

2884: static PetscErrorCode PetscDualSpaceLagrangeSetTensor_Lagrange(PetscDualSpace sp, PetscBool tensor)
2885: {
2886:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;

2888:   PetscFunctionBegin;
2889:   lag->tensorSpace = tensor;
2890:   PetscFunctionReturn(PETSC_SUCCESS);
2891: }

2893: static PetscErrorCode PetscDualSpaceLagrangeGetTrimmed_Lagrange(PetscDualSpace sp, PetscBool *trimmed)
2894: {
2895:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;

2897:   PetscFunctionBegin;
2898:   *trimmed = lag->trimmed;
2899:   PetscFunctionReturn(PETSC_SUCCESS);
2900: }

2902: static PetscErrorCode PetscDualSpaceLagrangeSetTrimmed_Lagrange(PetscDualSpace sp, PetscBool trimmed)
2903: {
2904:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;

2906:   PetscFunctionBegin;
2907:   lag->trimmed = trimmed;
2908:   PetscFunctionReturn(PETSC_SUCCESS);
2909: }

2911: static PetscErrorCode PetscDualSpaceLagrangeGetNodeType_Lagrange(PetscDualSpace sp, PetscDTNodeType *nodeType, PetscBool *boundary, PetscReal *exponent)
2912: {
2913:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;

2915:   PetscFunctionBegin;
2916:   if (nodeType) *nodeType = lag->nodeType;
2917:   if (boundary) *boundary = lag->endNodes;
2918:   if (exponent) *exponent = lag->nodeExponent;
2919:   PetscFunctionReturn(PETSC_SUCCESS);
2920: }

2922: static PetscErrorCode PetscDualSpaceLagrangeSetNodeType_Lagrange(PetscDualSpace sp, PetscDTNodeType nodeType, PetscBool boundary, PetscReal exponent)
2923: {
2924:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;

2926:   PetscFunctionBegin;
2927:   PetscCheck(nodeType != PETSCDTNODES_GAUSSJACOBI || exponent > -1., PetscObjectComm((PetscObject)sp), PETSC_ERR_ARG_OUTOFRANGE, "Exponent must be > -1");
2928:   lag->nodeType     = nodeType;
2929:   lag->endNodes     = boundary;
2930:   lag->nodeExponent = exponent;
2931:   PetscFunctionReturn(PETSC_SUCCESS);
2932: }

2934: static PetscErrorCode PetscDualSpaceLagrangeGetUseMoments_Lagrange(PetscDualSpace sp, PetscBool *useMoments)
2935: {
2936:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;

2938:   PetscFunctionBegin;
2939:   *useMoments = lag->useMoments;
2940:   PetscFunctionReturn(PETSC_SUCCESS);
2941: }

2943: static PetscErrorCode PetscDualSpaceLagrangeSetUseMoments_Lagrange(PetscDualSpace sp, PetscBool useMoments)
2944: {
2945:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;

2947:   PetscFunctionBegin;
2948:   lag->useMoments = useMoments;
2949:   PetscFunctionReturn(PETSC_SUCCESS);
2950: }

2952: static PetscErrorCode PetscDualSpaceLagrangeGetMomentOrder_Lagrange(PetscDualSpace sp, PetscInt *momentOrder)
2953: {
2954:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;

2956:   PetscFunctionBegin;
2957:   *momentOrder = lag->momentOrder;
2958:   PetscFunctionReturn(PETSC_SUCCESS);
2959: }

2961: static PetscErrorCode PetscDualSpaceLagrangeSetMomentOrder_Lagrange(PetscDualSpace sp, PetscInt momentOrder)
2962: {
2963:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;

2965:   PetscFunctionBegin;
2966:   lag->momentOrder = momentOrder;
2967:   PetscFunctionReturn(PETSC_SUCCESS);
2968: }

2970: /*@
2971:   PetscDualSpaceLagrangeGetTensor - Get the tensor nature of the dual space

2973:   Not Collective

2975:   Input Parameter:
2976: . sp - The `PetscDualSpace`

2978:   Output Parameter:
2979: . tensor - Whether the dual space has tensor layout (vs. simplicial)

2981:   Level: intermediate

2983: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeSetTensor()`, `PetscDualSpaceCreate()`
2984: @*/
2985: PetscErrorCode PetscDualSpaceLagrangeGetTensor(PetscDualSpace sp, PetscBool *tensor)
2986: {
2987:   PetscFunctionBegin;
2989:   PetscAssertPointer(tensor, 2);
2990:   PetscTryMethod(sp, "PetscDualSpaceLagrangeGetTensor_C", (PetscDualSpace, PetscBool *), (sp, tensor));
2991:   PetscFunctionReturn(PETSC_SUCCESS);
2992: }

2994: /*@
2995:   PetscDualSpaceLagrangeSetTensor - Set the tensor nature of the dual space

2997:   Not Collective

2999:   Input Parameters:
3000: + sp     - The `PetscDualSpace`
3001: - tensor - Whether the dual space has tensor layout (vs. simplicial)

3003:   Level: intermediate

3005: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeGetTensor()`, `PetscDualSpaceCreate()`
3006: @*/
3007: PetscErrorCode PetscDualSpaceLagrangeSetTensor(PetscDualSpace sp, PetscBool tensor)
3008: {
3009:   PetscFunctionBegin;
3011:   PetscTryMethod(sp, "PetscDualSpaceLagrangeSetTensor_C", (PetscDualSpace, PetscBool), (sp, tensor));
3012:   PetscFunctionReturn(PETSC_SUCCESS);
3013: }

3015: /*@
3016:   PetscDualSpaceLagrangeGetTrimmed - Get the trimmed nature of the dual space

3018:   Not Collective

3020:   Input Parameter:
3021: . sp - The `PetscDualSpace`

3023:   Output Parameter:
3024: . 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)

3026:   Level: intermediate

3028: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeSetTrimmed()`, `PetscDualSpaceCreate()`
3029: @*/
3030: PetscErrorCode PetscDualSpaceLagrangeGetTrimmed(PetscDualSpace sp, PetscBool *trimmed)
3031: {
3032:   PetscFunctionBegin;
3034:   PetscAssertPointer(trimmed, 2);
3035:   PetscTryMethod(sp, "PetscDualSpaceLagrangeGetTrimmed_C", (PetscDualSpace, PetscBool *), (sp, trimmed));
3036:   PetscFunctionReturn(PETSC_SUCCESS);
3037: }

3039: /*@
3040:   PetscDualSpaceLagrangeSetTrimmed - Set the trimmed nature of the dual space

3042:   Not Collective

3044:   Input Parameters:
3045: + sp      - The `PetscDualSpace`
3046: - 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)

3048:   Level: intermediate

3050: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeGetTrimmed()`, `PetscDualSpaceCreate()`
3051: @*/
3052: PetscErrorCode PetscDualSpaceLagrangeSetTrimmed(PetscDualSpace sp, PetscBool trimmed)
3053: {
3054:   PetscFunctionBegin;
3056:   PetscTryMethod(sp, "PetscDualSpaceLagrangeSetTrimmed_C", (PetscDualSpace, PetscBool), (sp, trimmed));
3057:   PetscFunctionReturn(PETSC_SUCCESS);
3058: }

3060: /*@
3061:   PetscDualSpaceLagrangeGetNodeType - Get a description of how nodes are laid out for Lagrange polynomials in this
3062:   dual space

3064:   Not Collective

3066:   Input Parameter:
3067: . sp - The `PetscDualSpace`

3069:   Output Parameters:
3070: + nodeType - The type of nodes
3071: . boundary - Whether the node type is one that includes endpoints (if nodeType is `PETSCDTNODES_GAUSSJACOBI`, nodes that
3072:              include the boundary are Gauss-Lobatto-Jacobi nodes)
3073: - exponent - If nodeType is `PETSCDTNODES_GAUSJACOBI`, indicates the exponent used for both ends of the 1D Jacobi weight function
3074:              '0' is Gauss-Legendre, '-0.5' is Gauss-Chebyshev of the first type, '0.5' is Gauss-Chebyshev of the second type

3076:   Level: advanced

3078: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDTNodeType`, `PetscDualSpaceLagrangeSetNodeType()`
3079: @*/
3080: PetscErrorCode PetscDualSpaceLagrangeGetNodeType(PetscDualSpace sp, PetscDTNodeType *nodeType, PetscBool *boundary, PetscReal *exponent)
3081: {
3082:   PetscFunctionBegin;
3084:   if (nodeType) PetscAssertPointer(nodeType, 2);
3085:   if (boundary) PetscAssertPointer(boundary, 3);
3086:   if (exponent) PetscAssertPointer(exponent, 4);
3087:   PetscTryMethod(sp, "PetscDualSpaceLagrangeGetNodeType_C", (PetscDualSpace, PetscDTNodeType *, PetscBool *, PetscReal *), (sp, nodeType, boundary, exponent));
3088:   PetscFunctionReturn(PETSC_SUCCESS);
3089: }

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

3095:   Logically Collective

3097:   Input Parameters:
3098: + sp       - The `PetscDualSpace`
3099: . nodeType - The type of nodes
3100: . boundary - Whether the node type is one that includes endpoints (if nodeType is `PETSCDTNODES_GAUSSJACOBI`, nodes that
3101:              include the boundary are Gauss-Lobatto-Jacobi nodes)
3102: - exponent - If nodeType is `PETSCDTNODES_GAUSJACOBI`, indicates the exponent used for both ends of the 1D Jacobi weight function
3103:              '0' is Gauss-Legendre, '-0.5' is Gauss-Chebyshev of the first type, '0.5' is Gauss-Chebyshev of the second type

3105:   Level: advanced

3107: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDTNodeType`, `PetscDualSpaceLagrangeGetNodeType()`
3108: @*/
3109: PetscErrorCode PetscDualSpaceLagrangeSetNodeType(PetscDualSpace sp, PetscDTNodeType nodeType, PetscBool boundary, PetscReal exponent)
3110: {
3111:   PetscFunctionBegin;
3113:   PetscTryMethod(sp, "PetscDualSpaceLagrangeSetNodeType_C", (PetscDualSpace, PetscDTNodeType, PetscBool, PetscReal), (sp, nodeType, boundary, exponent));
3114:   PetscFunctionReturn(PETSC_SUCCESS);
3115: }

3117: /*@
3118:   PetscDualSpaceLagrangeGetUseMoments - Get the flag for using moment functionals

3120:   Not Collective

3122:   Input Parameter:
3123: . sp - The `PetscDualSpace`

3125:   Output Parameter:
3126: . useMoments - Moment flag

3128:   Level: advanced

3130: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeSetUseMoments()`
3131: @*/
3132: PetscErrorCode PetscDualSpaceLagrangeGetUseMoments(PetscDualSpace sp, PetscBool *useMoments)
3133: {
3134:   PetscFunctionBegin;
3136:   PetscAssertPointer(useMoments, 2);
3137:   PetscUseMethod(sp, "PetscDualSpaceLagrangeGetUseMoments_C", (PetscDualSpace, PetscBool *), (sp, useMoments));
3138:   PetscFunctionReturn(PETSC_SUCCESS);
3139: }

3141: /*@
3142:   PetscDualSpaceLagrangeSetUseMoments - Set the flag for moment functionals

3144:   Logically Collective

3146:   Input Parameters:
3147: + sp         - The `PetscDualSpace`
3148: - useMoments - The flag for moment functionals

3150:   Level: advanced

3152: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeGetUseMoments()`
3153: @*/
3154: PetscErrorCode PetscDualSpaceLagrangeSetUseMoments(PetscDualSpace sp, PetscBool useMoments)
3155: {
3156:   PetscFunctionBegin;
3158:   PetscTryMethod(sp, "PetscDualSpaceLagrangeSetUseMoments_C", (PetscDualSpace, PetscBool), (sp, useMoments));
3159:   PetscFunctionReturn(PETSC_SUCCESS);
3160: }

3162: /*@
3163:   PetscDualSpaceLagrangeGetMomentOrder - Get the order for moment integration

3165:   Not Collective

3167:   Input Parameter:
3168: . sp - The `PetscDualSpace`

3170:   Output Parameter:
3171: . order - Moment integration order

3173:   Level: advanced

3175: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeSetMomentOrder()`
3176: @*/
3177: PetscErrorCode PetscDualSpaceLagrangeGetMomentOrder(PetscDualSpace sp, PetscInt *order)
3178: {
3179:   PetscFunctionBegin;
3181:   PetscAssertPointer(order, 2);
3182:   PetscUseMethod(sp, "PetscDualSpaceLagrangeGetMomentOrder_C", (PetscDualSpace, PetscInt *), (sp, order));
3183:   PetscFunctionReturn(PETSC_SUCCESS);
3184: }

3186: /*@
3187:   PetscDualSpaceLagrangeSetMomentOrder - Set the order for moment integration

3189:   Logically Collective

3191:   Input Parameters:
3192: + sp    - The `PetscDualSpace`
3193: - order - The order for moment integration

3195:   Level: advanced

3197: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeGetMomentOrder()`
3198: @*/
3199: PetscErrorCode PetscDualSpaceLagrangeSetMomentOrder(PetscDualSpace sp, PetscInt order)
3200: {
3201:   PetscFunctionBegin;
3203:   PetscTryMethod(sp, "PetscDualSpaceLagrangeSetMomentOrder_C", (PetscDualSpace, PetscInt), (sp, order));
3204:   PetscFunctionReturn(PETSC_SUCCESS);
3205: }

3207: static PetscErrorCode PetscDualSpaceInitialize_Lagrange(PetscDualSpace sp)
3208: {
3209:   PetscFunctionBegin;
3210:   sp->ops->destroy              = PetscDualSpaceDestroy_Lagrange;
3211:   sp->ops->view                 = PetscDualSpaceView_Lagrange;
3212:   sp->ops->setfromoptions       = PetscDualSpaceSetFromOptions_Lagrange;
3213:   sp->ops->duplicate            = PetscDualSpaceDuplicate_Lagrange;
3214:   sp->ops->setup                = PetscDualSpaceSetUp_Lagrange;
3215:   sp->ops->createheightsubspace = NULL;
3216:   sp->ops->createpointsubspace  = NULL;
3217:   sp->ops->getsymmetries        = PetscDualSpaceGetSymmetries_Lagrange;
3218:   sp->ops->apply                = PetscDualSpaceApplyDefault;
3219:   sp->ops->applyall             = PetscDualSpaceApplyAllDefault;
3220:   sp->ops->applyint             = PetscDualSpaceApplyInteriorDefault;
3221:   sp->ops->createalldata        = PetscDualSpaceCreateAllDataDefault;
3222:   sp->ops->createintdata        = PetscDualSpaceCreateInteriorDataDefault;
3223:   PetscFunctionReturn(PETSC_SUCCESS);
3224: }

3226: /*MC
3227:   PETSCDUALSPACELAGRANGE = "lagrange" - A `PetscDualSpaceType` that encapsulates a dual space of pointwise evaluation functionals

3229:   Level: intermediate

3231:   Developer Note:
3232:   This `PetscDualSpace` seems to manage directly trimmed and untrimmed polynomials as well as tensor and non-tensor polynomials while for `PetscSpace` there seems to
3233:   be different `PetscSpaceType` for them.

3235: .seealso: `PetscDualSpace`, `PetscDualSpaceType`, `PetscDualSpaceCreate()`, `PetscDualSpaceSetType()`,
3236:           `PetscDualSpaceLagrangeSetMomentOrder()`, `PetscDualSpaceLagrangeGetMomentOrder()`, `PetscDualSpaceLagrangeSetUseMoments()`, `PetscDualSpaceLagrangeGetUseMoments()`,
3237:           `PetscDualSpaceLagrangeSetNodeType, PetscDualSpaceLagrangeGetNodeType, PetscDualSpaceLagrangeGetContinuity, PetscDualSpaceLagrangeSetContinuity,
3238:           `PetscDualSpaceLagrangeGetTensor()`, `PetscDualSpaceLagrangeSetTensor()`, `PetscDualSpaceLagrangeGetTrimmed()`, `PetscDualSpaceLagrangeSetTrimmed()`
3239: M*/
3240: PETSC_EXTERN PetscErrorCode PetscDualSpaceCreate_Lagrange(PetscDualSpace sp)
3241: {
3242:   PetscDualSpace_Lag *lag;

3244:   PetscFunctionBegin;
3246:   PetscCall(PetscNew(&lag));
3247:   sp->data = lag;

3249:   lag->tensorCell  = PETSC_FALSE;
3250:   lag->tensorSpace = PETSC_FALSE;
3251:   lag->continuous  = PETSC_TRUE;
3252:   lag->numCopies   = PETSC_DEFAULT;
3253:   lag->numNodeSkip = PETSC_DEFAULT;
3254:   lag->nodeType    = PETSCDTNODES_DEFAULT;
3255:   lag->useMoments  = PETSC_FALSE;
3256:   lag->momentOrder = 0;

3258:   PetscCall(PetscDualSpaceInitialize_Lagrange(sp));
3259:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetContinuity_C", PetscDualSpaceLagrangeGetContinuity_Lagrange));
3260:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetContinuity_C", PetscDualSpaceLagrangeSetContinuity_Lagrange));
3261:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetTensor_C", PetscDualSpaceLagrangeGetTensor_Lagrange));
3262:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetTensor_C", PetscDualSpaceLagrangeSetTensor_Lagrange));
3263:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetTrimmed_C", PetscDualSpaceLagrangeGetTrimmed_Lagrange));
3264:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetTrimmed_C", PetscDualSpaceLagrangeSetTrimmed_Lagrange));
3265:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetNodeType_C", PetscDualSpaceLagrangeGetNodeType_Lagrange));
3266:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetNodeType_C", PetscDualSpaceLagrangeSetNodeType_Lagrange));
3267:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetUseMoments_C", PetscDualSpaceLagrangeGetUseMoments_Lagrange));
3268:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetUseMoments_C", PetscDualSpaceLagrangeSetUseMoments_Lagrange));
3269:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetMomentOrder_C", PetscDualSpaceLagrangeGetMomentOrder_Lagrange));
3270:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetMomentOrder_C", PetscDualSpaceLagrangeSetMomentOrder_Lagrange));
3271:   PetscFunctionReturn(PETSC_SUCCESS);
3272: }