xref: /libCEED/interface/ceed-preconditioning.c (revision 290fc47b5baa6f633b0072e77241e8667e9a8675)
1 // Copyright (c) 2017-2024, Lawrence Livermore National Security, LLC and other CEED contributors.
2 // All Rights Reserved. See the top-level LICENSE and NOTICE files for details.
3 //
4 // SPDX-License-Identifier: BSD-2-Clause
5 //
6 // This file is part of CEED:  http://github.com/ceed
7 
8 #include <ceed-impl.h>
9 #include <ceed.h>
10 #include <ceed/backend.h>
11 #include <assert.h>
12 #include <math.h>
13 #include <stdbool.h>
14 #include <stdio.h>
15 #include <string.h>
16 
17 /// @file
18 /// Implementation of CeedOperator preconditioning interfaces
19 
20 /// ----------------------------------------------------------------------------
21 /// CeedOperator Library Internal Preconditioning Functions
22 /// ----------------------------------------------------------------------------
23 /// @addtogroup CeedOperatorDeveloper
24 /// @{
25 
26 /**
27   @brief Duplicate a `CeedQFunction` with a reference `Ceed` to fallback for advanced `CeedOperator` functionality
28 
29   @param[in]  fallback_ceed `Ceed` on which to create fallback `CeedQFunction`
30   @param[in]  qf            `CeedQFunction` to create fallback for
31   @param[out] qf_fallback   Fallback `CeedQFunction`
32 
33   @return An error code: 0 - success, otherwise - failure
34 
35   @ref Developer
36 **/
37 static int CeedQFunctionCreateFallback(Ceed fallback_ceed, CeedQFunction qf, CeedQFunction *qf_fallback) {
38   char               *source_path_with_name = NULL;
39   CeedInt             num_input_fields, num_output_fields;
40   CeedQFunctionField *input_fields, *output_fields;
41 
42   // Check if NULL qf passed in
43   if (!qf) return CEED_ERROR_SUCCESS;
44 
45   CeedDebug256(CeedQFunctionReturnCeed(qf), 1, "---------- CeedOperator Fallback ----------\n");
46   CeedDebug(CeedQFunctionReturnCeed(qf), "Creating fallback CeedQFunction\n");
47 
48   if (qf->source_path) {
49     size_t path_len = strlen(qf->source_path), name_len = strlen(qf->kernel_name);
50 
51     CeedCall(CeedCalloc(path_len + name_len + 2, &source_path_with_name));
52     memcpy(source_path_with_name, qf->source_path, path_len);
53     memcpy(&source_path_with_name[path_len], ":", 1);
54     memcpy(&source_path_with_name[path_len + 1], qf->kernel_name, name_len);
55   } else if (qf->user_source) {
56     CeedCall(CeedStringAllocCopy(qf->user_source, &source_path_with_name));
57   } else {
58     CeedCall(CeedCalloc(1, &source_path_with_name));
59   }
60 
61   {
62     CeedInt           vec_length;
63     CeedQFunctionUser f;
64 
65     CeedCall(CeedQFunctionGetVectorLength(qf, &vec_length));
66     CeedCall(CeedQFunctionGetUserFunction(qf, &f));
67     CeedCall(CeedQFunctionCreateInterior(fallback_ceed, vec_length, f, source_path_with_name, qf_fallback));
68   }
69   {
70     CeedQFunctionContext ctx;
71 
72     CeedCall(CeedQFunctionGetContext(qf, &ctx));
73     CeedCall(CeedQFunctionSetContext(*qf_fallback, ctx));
74     CeedCall(CeedQFunctionContextDestroy(&ctx));
75   }
76   CeedCall(CeedQFunctionGetFields(qf, &num_input_fields, &input_fields, &num_output_fields, &output_fields));
77   for (CeedInt i = 0; i < num_input_fields; i++) {
78     const char  *field_name;
79     CeedInt      size;
80     CeedEvalMode eval_mode;
81 
82     CeedCall(CeedQFunctionFieldGetData(input_fields[i], &field_name, &size, &eval_mode));
83     CeedCall(CeedQFunctionAddInput(*qf_fallback, field_name, size, eval_mode));
84   }
85   for (CeedInt i = 0; i < num_output_fields; i++) {
86     const char  *field_name;
87     CeedInt      size;
88     CeedEvalMode eval_mode;
89 
90     CeedCall(CeedQFunctionFieldGetData(output_fields[i], &field_name, &size, &eval_mode));
91     CeedCall(CeedQFunctionAddOutput(*qf_fallback, field_name, size, eval_mode));
92   }
93   CeedCall(CeedFree(&source_path_with_name));
94   return CEED_ERROR_SUCCESS;
95 }
96 
97 /**
98   @brief Duplicate a `CeedOperator` with a reference `Ceed` to fallback for advanced `CeedOperator` functionality
99 
100   @param[in,out] op `CeedOperator` to create fallback for
101 
102   @return An error code: 0 - success, otherwise - failure
103 
104   @ref Developer
105 **/
106 static int CeedOperatorCreateFallback(CeedOperator op) {
107   bool         is_composite;
108   Ceed         ceed, ceed_fallback;
109   CeedOperator op_fallback;
110 
111   // Check not already created
112   if (op->op_fallback) return CEED_ERROR_SUCCESS;
113 
114   // Fallback Ceed
115   CeedCall(CeedOperatorGetCeed(op, &ceed));
116   CeedCall(CeedGetOperatorFallbackCeed(ceed, &ceed_fallback));
117   CeedCall(CeedDestroy(&ceed));
118   if (!ceed_fallback) return CEED_ERROR_SUCCESS;
119 
120   CeedDebug256(CeedOperatorReturnCeed(op), 1, "---------- CeedOperator Fallback ----------\n");
121   CeedDebug(CeedOperatorReturnCeed(op), "Creating fallback CeedOperator\n");
122 
123   // Clone Op
124   CeedCall(CeedOperatorIsComposite(op, &is_composite));
125   if (is_composite) {
126     CeedInt       num_suboperators;
127     CeedOperator *sub_operators;
128 
129     CeedCall(CeedCompositeOperatorCreate(ceed_fallback, &op_fallback));
130     CeedCall(CeedCompositeOperatorGetNumSub(op, &num_suboperators));
131     CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
132     for (CeedInt i = 0; i < num_suboperators; i++) {
133       CeedOperator op_sub_fallback;
134 
135       CeedCall(CeedOperatorGetFallback(sub_operators[i], &op_sub_fallback));
136       CeedCall(CeedCompositeOperatorAddSub(op_fallback, op_sub_fallback));
137     }
138   } else {
139     CeedInt            num_input_fields, num_output_fields;
140     CeedQFunction      qf_fallback = NULL, dqf_fallback = NULL, dqfT_fallback = NULL;
141     CeedOperatorField *input_fields, *output_fields;
142 
143     CeedCall(CeedQFunctionCreateFallback(ceed_fallback, op->qf, &qf_fallback));
144     CeedCall(CeedQFunctionCreateFallback(ceed_fallback, op->dqf, &dqf_fallback));
145     CeedCall(CeedQFunctionCreateFallback(ceed_fallback, op->dqfT, &dqfT_fallback));
146     CeedCall(CeedOperatorCreate(ceed_fallback, qf_fallback, dqf_fallback, dqfT_fallback, &op_fallback));
147     CeedCall(CeedOperatorGetFields(op, &num_input_fields, &input_fields, &num_output_fields, &output_fields));
148     for (CeedInt i = 0; i < num_input_fields; i++) {
149       const char         *field_name;
150       CeedVector          vec;
151       CeedElemRestriction rstr;
152       CeedBasis           basis;
153 
154       CeedCall(CeedOperatorFieldGetData(input_fields[i], &field_name, &rstr, &basis, &vec));
155       CeedCall(CeedOperatorSetField(op_fallback, field_name, rstr, basis, vec));
156       CeedCall(CeedVectorDestroy(&vec));
157       CeedCall(CeedElemRestrictionDestroy(&rstr));
158       CeedCall(CeedBasisDestroy(&basis));
159     }
160     for (CeedInt i = 0; i < num_output_fields; i++) {
161       const char         *field_name;
162       CeedVector          vec;
163       CeedElemRestriction rstr;
164       CeedBasis           basis;
165 
166       CeedCall(CeedOperatorFieldGetData(output_fields[i], &field_name, &rstr, &basis, &vec));
167       CeedCall(CeedOperatorSetField(op_fallback, field_name, rstr, basis, vec));
168       CeedCall(CeedVectorDestroy(&vec));
169       CeedCall(CeedElemRestrictionDestroy(&rstr));
170       CeedCall(CeedBasisDestroy(&basis));
171     }
172     {
173       CeedQFunctionAssemblyData data;
174 
175       CeedCall(CeedOperatorGetQFunctionAssemblyData(op, &data));
176       CeedCall(CeedQFunctionAssemblyDataReferenceCopy(data, &op_fallback->qf_assembled));
177     }
178     // Cleanup
179     CeedCall(CeedQFunctionDestroy(&qf_fallback));
180     CeedCall(CeedQFunctionDestroy(&dqf_fallback));
181     CeedCall(CeedQFunctionDestroy(&dqfT_fallback));
182   }
183   CeedCall(CeedOperatorSetName(op_fallback, op->name));
184   CeedCall(CeedOperatorCheckReady(op_fallback));
185   // Note: No ref-counting here so we don't get caught in a reference loop.
186   //       The op holds the only reference to op_fallback and is responsible for deleting itself and op_fallback.
187   op->op_fallback                 = op_fallback;
188   op_fallback->op_fallback_parent = op;
189   CeedCall(CeedDestroy(&ceed_fallback));
190   return CEED_ERROR_SUCCESS;
191 }
192 
193 /**
194   @brief Core logic for assembling operator diagonal or point block diagonal
195 
196   @param[in]  op             `CeedOperator` to assemble diagonal or point block diagonal
197   @param[in]  request        Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
198   @param[in]  is_point_block Boolean flag to assemble diagonal or point block diagonal
199   @param[out] assembled      `CeedVector` to store assembled diagonal
200 
201   @return An error code: 0 - success, otherwise - failure
202 
203   @ref Developer
204 **/
205 static inline int CeedSingleOperatorLinearAssembleAddDiagonal_Mesh(CeedOperator op, CeedRequest *request, const bool is_point_block,
206                                                                    CeedVector assembled) {
207   bool is_composite;
208 
209   CeedCall(CeedOperatorIsComposite(op, &is_composite));
210   CeedCheck(!is_composite, CeedOperatorReturnCeed(op), CEED_ERROR_UNSUPPORTED, "Composite operator not supported");
211 
212   // Assemble QFunction
213   CeedInt             layout_qf[3];
214   const CeedScalar   *assembled_qf_array;
215   CeedVector          assembled_qf        = NULL;
216   CeedElemRestriction assembled_elem_rstr = NULL;
217 
218   CeedCall(CeedOperatorLinearAssembleQFunctionBuildOrUpdate(op, &assembled_qf, &assembled_elem_rstr, request));
219   CeedCall(CeedElemRestrictionGetELayout(assembled_elem_rstr, layout_qf));
220   CeedCall(CeedElemRestrictionDestroy(&assembled_elem_rstr));
221   CeedCall(CeedVectorGetArrayRead(assembled_qf, CEED_MEM_HOST, &assembled_qf_array));
222 
223   // Get assembly data
224   const CeedEvalMode     **eval_modes_in, **eval_modes_out;
225   CeedInt                  num_active_bases_in, *num_eval_modes_in, num_active_bases_out, *num_eval_modes_out;
226   CeedSize               **eval_mode_offsets_in, **eval_mode_offsets_out, num_output_components;
227   CeedBasis               *active_bases_in, *active_bases_out;
228   CeedElemRestriction     *active_elem_rstrs_in, *active_elem_rstrs_out;
229   CeedOperatorAssemblyData data;
230 
231   CeedCall(CeedOperatorGetOperatorAssemblyData(op, &data));
232   CeedCall(CeedOperatorAssemblyDataGetEvalModes(data, &num_active_bases_in, &num_eval_modes_in, &eval_modes_in, &eval_mode_offsets_in,
233                                                 &num_active_bases_out, &num_eval_modes_out, &eval_modes_out, &eval_mode_offsets_out,
234                                                 &num_output_components));
235   CeedCall(CeedOperatorAssemblyDataGetBases(data, NULL, &active_bases_in, NULL, NULL, &active_bases_out, NULL));
236   CeedCall(CeedOperatorAssemblyDataGetElemRestrictions(data, NULL, &active_elem_rstrs_in, NULL, &active_elem_rstrs_out));
237 
238   // Loop over all active bases (find matching input/output pairs)
239   for (CeedInt b = 0; b < CeedIntMin(num_active_bases_in, num_active_bases_out); b++) {
240     CeedInt             b_in, b_out, num_elem, num_nodes, num_qpts, num_comp;
241     bool                has_eval_none = false;
242     CeedScalar         *elem_diag_array, *identity = NULL;
243     CeedVector          elem_diag;
244     CeedElemRestriction diag_elem_rstr;
245 
246     if (num_active_bases_in <= num_active_bases_out) {
247       b_in = b;
248       for (b_out = 0; b_out < num_active_bases_out; b_out++) {
249         if (active_bases_in[b_in] == active_bases_out[b_out]) {
250           break;
251         }
252       }
253       if (b_out == num_active_bases_out) {
254         continue;
255       }  // No matching output basis found
256     } else {
257       b_out = b;
258       for (b_in = 0; b_in < num_active_bases_in; b_in++) {
259         if (active_bases_in[b_in] == active_bases_out[b_out]) {
260           break;
261         }
262       }
263       if (b_in == num_active_bases_in) {
264         continue;
265       }  // No matching output basis found
266     }
267     CeedCheck(active_elem_rstrs_in[b_in] == active_elem_rstrs_out[b_out], CeedOperatorReturnCeed(op), CEED_ERROR_UNSUPPORTED,
268               "Cannot assemble operator diagonal with different input and output active element restrictions");
269 
270     // Assemble point block diagonal restriction, if needed
271     if (is_point_block) {
272       CeedCall(CeedOperatorCreateActivePointBlockRestriction(active_elem_rstrs_in[b_in], &diag_elem_rstr));
273     } else {
274       CeedCall(CeedElemRestrictionCreateUnsignedCopy(active_elem_rstrs_in[b_in], &diag_elem_rstr));
275     }
276 
277     // Create diagonal vector
278     CeedCall(CeedElemRestrictionCreateVector(diag_elem_rstr, NULL, &elem_diag));
279 
280     // Assemble element operator diagonals
281     CeedCall(CeedVectorSetValue(elem_diag, 0.0));
282     CeedCall(CeedVectorGetArray(elem_diag, CEED_MEM_HOST, &elem_diag_array));
283     CeedCall(CeedElemRestrictionGetNumElements(diag_elem_rstr, &num_elem));
284     CeedCall(CeedBasisGetNumNodes(active_bases_in[b_in], &num_nodes));
285     CeedCall(CeedBasisGetNumComponents(active_bases_in[b_in], &num_comp));
286     if (active_bases_in[b_in] == CEED_BASIS_NONE) num_qpts = num_nodes;
287     else CeedCall(CeedBasisGetNumQuadraturePoints(active_bases_in[b_in], &num_qpts));
288 
289     // Construct identity matrix for basis if required
290     for (CeedInt i = 0; i < num_eval_modes_in[b_in]; i++) {
291       has_eval_none = has_eval_none || (eval_modes_in[b_in][i] == CEED_EVAL_NONE);
292     }
293     for (CeedInt i = 0; i < num_eval_modes_out[b_out]; i++) {
294       has_eval_none = has_eval_none || (eval_modes_out[b_out][i] == CEED_EVAL_NONE);
295     }
296     if (has_eval_none) {
297       CeedCall(CeedCalloc(num_qpts * num_nodes, &identity));
298       for (CeedInt i = 0; i < (num_nodes < num_qpts ? num_nodes : num_qpts); i++) identity[i * num_nodes + i] = 1.0;
299     }
300 
301     // Compute the diagonal of B^T D B
302     // Each element
303     for (CeedSize e = 0; e < num_elem; e++) {
304       // Each basis eval mode pair
305       CeedInt      d_out              = 0, q_comp_out;
306       CeedEvalMode eval_mode_out_prev = CEED_EVAL_NONE;
307 
308       for (CeedInt e_out = 0; e_out < num_eval_modes_out[b_out]; e_out++) {
309         CeedInt           d_in              = 0, q_comp_in;
310         const CeedScalar *B_t               = NULL;
311         CeedEvalMode      eval_mode_in_prev = CEED_EVAL_NONE;
312 
313         CeedCall(CeedOperatorGetBasisPointer(active_bases_out[b_out], eval_modes_out[b_out][e_out], identity, &B_t));
314         CeedCall(CeedBasisGetNumQuadratureComponents(active_bases_out[b_out], eval_modes_out[b_out][e_out], &q_comp_out));
315         if (q_comp_out > 1) {
316           if (e_out == 0 || eval_modes_out[b_out][e_out] != eval_mode_out_prev) d_out = 0;
317           else B_t = &B_t[(++d_out) * num_qpts * num_nodes];
318         }
319         eval_mode_out_prev = eval_modes_out[b_out][e_out];
320 
321         for (CeedInt e_in = 0; e_in < num_eval_modes_in[b_in]; e_in++) {
322           const CeedScalar *B = NULL;
323 
324           CeedCall(CeedOperatorGetBasisPointer(active_bases_in[b_in], eval_modes_in[b_in][e_in], identity, &B));
325           CeedCall(CeedBasisGetNumQuadratureComponents(active_bases_in[b_in], eval_modes_in[b_in][e_in], &q_comp_in));
326           if (q_comp_in > 1) {
327             if (e_in == 0 || eval_modes_in[b_in][e_in] != eval_mode_in_prev) d_in = 0;
328             else B = &B[(++d_in) * num_qpts * num_nodes];
329           }
330           eval_mode_in_prev = eval_modes_in[b_in][e_in];
331 
332           // Each component
333           for (CeedInt c_out = 0; c_out < num_comp; c_out++) {
334             // Each qpt/node pair
335             for (CeedInt q = 0; q < num_qpts; q++) {
336               if (is_point_block) {
337                 // Point Block Diagonal
338                 for (CeedInt c_in = 0; c_in < num_comp; c_in++) {
339                   const CeedSize c_offset =
340                       (eval_mode_offsets_in[b_in][e_in] + c_in) * num_output_components + eval_mode_offsets_out[b_out][e_out] + c_out;
341                   const CeedScalar qf_value = assembled_qf_array[q * layout_qf[0] + c_offset * layout_qf[1] + e * layout_qf[2]];
342 
343                   for (CeedInt n = 0; n < num_nodes; n++) {
344                     elem_diag_array[((e * num_comp + c_out) * num_comp + c_in) * num_nodes + n] +=
345                         B_t[q * num_nodes + n] * qf_value * B[q * num_nodes + n];
346                   }
347                 }
348               } else {
349                 // Diagonal Only
350                 const CeedInt c_offset =
351                     (eval_mode_offsets_in[b_in][e_in] + c_out) * num_output_components + eval_mode_offsets_out[b_out][e_out] + c_out;
352                 const CeedScalar qf_value = assembled_qf_array[q * layout_qf[0] + c_offset * layout_qf[1] + e * layout_qf[2]];
353 
354                 for (CeedInt n = 0; n < num_nodes; n++) {
355                   elem_diag_array[(e * num_comp + c_out) * num_nodes + n] += B_t[q * num_nodes + n] * qf_value * B[q * num_nodes + n];
356                 }
357               }
358             }
359           }
360         }
361       }
362     }
363     CeedCall(CeedVectorRestoreArray(elem_diag, &elem_diag_array));
364 
365     // Assemble local operator diagonal
366     CeedCall(CeedElemRestrictionApply(diag_elem_rstr, CEED_TRANSPOSE, elem_diag, assembled, request));
367 
368     // Cleanup
369     CeedCall(CeedElemRestrictionDestroy(&diag_elem_rstr));
370     CeedCall(CeedVectorDestroy(&elem_diag));
371     CeedCall(CeedFree(&identity));
372   }
373   CeedCall(CeedVectorRestoreArrayRead(assembled_qf, &assembled_qf_array));
374   CeedCall(CeedVectorDestroy(&assembled_qf));
375   return CEED_ERROR_SUCCESS;
376 }
377 
378 /**
379   @brief Core logic for assembling operator diagonal or point block diagonal
380 
381   @param[in]  op             `CeedOperator` to assemble diagonal or point block diagonal
382   @param[in]  request        Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
383   @param[in]  is_point_block Boolean flag to assemble diagonal or point block diagonal
384   @param[out] assembled      `CeedVector` to store assembled diagonal
385 
386   @return An error code: 0 - success, otherwise - failure
387 
388   @ref Developer
389 **/
390 static inline int CeedSingleOperatorLinearAssembleAddDiagonal(CeedOperator op, CeedRequest *request, const bool is_point_block,
391                                                               CeedVector assembled) {
392   bool is_at_points;
393 
394   CeedCall(CeedOperatorIsAtPoints(op, &is_at_points));
395   CeedCheck(!is_at_points, CeedOperatorReturnCeed(op), CEED_ERROR_UNSUPPORTED, "AtPoints operator not supported");
396   CeedCall(CeedSingleOperatorLinearAssembleAddDiagonal_Mesh(op, request, is_point_block, assembled));
397   return CEED_ERROR_SUCCESS;
398 }
399 
400 /**
401   @brief Core logic for assembling composite operator diagonal
402 
403   @param[in]  op             `CeedOperator` to assemble point block diagonal
404   @param[in]  request        Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
405   @param[in]  is_point_block Boolean flag to assemble diagonal or point block diagonal
406   @param[out] assembled      `CeedVector` to store assembled diagonal
407 
408   @return An error code: 0 - success, otherwise - failure
409 
410   @ref Developer
411 **/
412 static inline int CeedCompositeOperatorLinearAssembleAddDiagonal(CeedOperator op, CeedRequest *request, const bool is_point_block,
413                                                                  CeedVector assembled) {
414   CeedInt       num_sub;
415   CeedOperator *suboperators;
416 
417   CeedCall(CeedCompositeOperatorGetNumSub(op, &num_sub));
418   CeedCall(CeedCompositeOperatorGetSubList(op, &suboperators));
419   for (CeedInt i = 0; i < num_sub; i++) {
420     if (is_point_block) {
421       CeedCall(CeedOperatorLinearAssembleAddPointBlockDiagonal(suboperators[i], assembled, request));
422     } else {
423       CeedCall(CeedOperatorLinearAssembleAddDiagonal(suboperators[i], assembled, request));
424     }
425   }
426   return CEED_ERROR_SUCCESS;
427 }
428 
429 /**
430   @brief Build nonzero pattern for non-composite CeedOperator`.
431 
432   Users should generally use @ref CeedOperatorLinearAssembleSymbolic().
433 
434   @param[in]  op     `CeedOperator` to assemble nonzero pattern
435   @param[in]  offset Offset for number of entries
436   @param[out] rows   Row number for each entry
437   @param[out] cols   Column number for each entry
438 
439   @return An error code: 0 - success, otherwise - failure
440 
441   @ref Developer
442 **/
443 static int CeedSingleOperatorAssembleSymbolic(CeedOperator op, CeedInt offset, CeedInt *rows, CeedInt *cols) {
444   Ceed                ceed;
445   bool                is_composite;
446   CeedSize            num_nodes_in, num_nodes_out, local_num_entries, count = 0;
447   CeedInt             num_elem_in, elem_size_in, num_comp_in, layout_er_in[3];
448   CeedInt             num_elem_out, elem_size_out, num_comp_out, layout_er_out[3];
449   CeedScalar         *array;
450   const CeedScalar   *elem_dof_a_in, *elem_dof_a_out;
451   CeedVector          index_vec_in, index_vec_out, elem_dof_in, elem_dof_out;
452   CeedElemRestriction elem_rstr_in, elem_rstr_out, index_elem_rstr_in, index_elem_rstr_out;
453 
454   CeedCall(CeedOperatorIsComposite(op, &is_composite));
455   CeedCall(CeedOperatorGetCeed(op, &ceed));
456   CeedCheck(!is_composite, ceed, CEED_ERROR_UNSUPPORTED, "Composite operator not supported");
457 
458   CeedCall(CeedOperatorGetActiveVectorLengths(op, &num_nodes_in, &num_nodes_out));
459   CeedCall(CeedOperatorGetActiveElemRestrictions(op, &elem_rstr_in, &elem_rstr_out));
460   CeedCall(CeedElemRestrictionGetNumElements(elem_rstr_in, &num_elem_in));
461   CeedCall(CeedElemRestrictionGetElementSize(elem_rstr_in, &elem_size_in));
462   CeedCall(CeedElemRestrictionGetNumComponents(elem_rstr_in, &num_comp_in));
463   CeedCall(CeedElemRestrictionGetELayout(elem_rstr_in, layout_er_in));
464 
465   // Determine elem_dof relation for input
466   CeedCall(CeedVectorCreate(ceed, num_nodes_in, &index_vec_in));
467   CeedCall(CeedVectorGetArrayWrite(index_vec_in, CEED_MEM_HOST, &array));
468   for (CeedSize i = 0; i < num_nodes_in; i++) array[i] = i;
469   CeedCall(CeedVectorRestoreArray(index_vec_in, &array));
470   CeedCall(CeedVectorCreate(ceed, num_elem_in * elem_size_in * num_comp_in, &elem_dof_in));
471   CeedCall(CeedVectorSetValue(elem_dof_in, 0.0));
472   CeedCall(CeedElemRestrictionCreateUnorientedCopy(elem_rstr_in, &index_elem_rstr_in));
473   CeedCall(CeedElemRestrictionApply(index_elem_rstr_in, CEED_NOTRANSPOSE, index_vec_in, elem_dof_in, CEED_REQUEST_IMMEDIATE));
474   CeedCall(CeedVectorGetArrayRead(elem_dof_in, CEED_MEM_HOST, &elem_dof_a_in));
475   CeedCall(CeedVectorDestroy(&index_vec_in));
476   CeedCall(CeedElemRestrictionDestroy(&index_elem_rstr_in));
477 
478   if (elem_rstr_in != elem_rstr_out) {
479     CeedCall(CeedElemRestrictionGetNumElements(elem_rstr_out, &num_elem_out));
480     CeedCheck(num_elem_in == num_elem_out, ceed, CEED_ERROR_UNSUPPORTED,
481               "Active input and output operator restrictions must have the same number of elements."
482               " Input has %" CeedInt_FMT " elements; output has %" CeedInt_FMT "elements.",
483               num_elem_in, num_elem_out);
484     CeedCall(CeedElemRestrictionGetElementSize(elem_rstr_out, &elem_size_out));
485     CeedCall(CeedElemRestrictionGetNumComponents(elem_rstr_out, &num_comp_out));
486     CeedCall(CeedElemRestrictionGetELayout(elem_rstr_out, layout_er_out));
487 
488     // Determine elem_dof relation for output
489     CeedCall(CeedVectorCreate(ceed, num_nodes_out, &index_vec_out));
490     CeedCall(CeedVectorGetArrayWrite(index_vec_out, CEED_MEM_HOST, &array));
491     for (CeedSize i = 0; i < num_nodes_out; i++) array[i] = i;
492     CeedCall(CeedVectorRestoreArray(index_vec_out, &array));
493     CeedCall(CeedVectorCreate(ceed, num_elem_out * elem_size_out * num_comp_out, &elem_dof_out));
494     CeedCall(CeedVectorSetValue(elem_dof_out, 0.0));
495     CeedCall(CeedElemRestrictionCreateUnorientedCopy(elem_rstr_out, &index_elem_rstr_out));
496     CeedCall(CeedElemRestrictionApply(index_elem_rstr_out, CEED_NOTRANSPOSE, index_vec_out, elem_dof_out, CEED_REQUEST_IMMEDIATE));
497     CeedCall(CeedVectorGetArrayRead(elem_dof_out, CEED_MEM_HOST, &elem_dof_a_out));
498     CeedCall(CeedVectorDestroy(&index_vec_out));
499     CeedCall(CeedElemRestrictionDestroy(&index_elem_rstr_out));
500   } else {
501     num_elem_out     = num_elem_in;
502     elem_size_out    = elem_size_in;
503     num_comp_out     = num_comp_in;
504     layout_er_out[0] = layout_er_in[0];
505     layout_er_out[1] = layout_er_in[1];
506     layout_er_out[2] = layout_er_in[2];
507     elem_dof_a_out   = elem_dof_a_in;
508   }
509   local_num_entries = (CeedSize)elem_size_out * num_comp_out * elem_size_in * num_comp_in * num_elem_in;
510 
511   // Determine i, j locations for element matrices
512   for (CeedInt e = 0; e < num_elem_in; e++) {
513     for (CeedInt comp_in = 0; comp_in < num_comp_in; comp_in++) {
514       for (CeedInt comp_out = 0; comp_out < num_comp_out; comp_out++) {
515         for (CeedInt i = 0; i < elem_size_out; i++) {
516           for (CeedInt j = 0; j < elem_size_in; j++) {
517             const CeedInt elem_dof_index_row = i * layout_er_out[0] + comp_out * layout_er_out[1] + e * layout_er_out[2];
518             const CeedInt elem_dof_index_col = j * layout_er_in[0] + comp_in * layout_er_in[1] + e * layout_er_in[2];
519             const CeedInt row                = elem_dof_a_out[elem_dof_index_row];
520             const CeedInt col                = elem_dof_a_in[elem_dof_index_col];
521 
522             rows[offset + count] = row;
523             cols[offset + count] = col;
524             count++;
525           }
526         }
527       }
528     }
529   }
530   CeedCheck(count == local_num_entries, ceed, CEED_ERROR_MAJOR, "Error computing assembled entries");
531   CeedCall(CeedVectorRestoreArrayRead(elem_dof_in, &elem_dof_a_in));
532   CeedCall(CeedVectorDestroy(&elem_dof_in));
533   if (elem_rstr_in != elem_rstr_out) {
534     CeedCall(CeedVectorRestoreArrayRead(elem_dof_out, &elem_dof_a_out));
535     CeedCall(CeedVectorDestroy(&elem_dof_out));
536   }
537   CeedCall(CeedElemRestrictionDestroy(&elem_rstr_in));
538   CeedCall(CeedElemRestrictionDestroy(&elem_rstr_out));
539   CeedCall(CeedDestroy(&ceed));
540   return CEED_ERROR_SUCCESS;
541 }
542 
543 /**
544   @brief Assemble nonzero entries for non-composite `CeedOperator`.
545 
546   Users should generally use @ref CeedOperatorLinearAssemble().
547 
548   @param[in]  op     `CeedOperator` to assemble
549   @param[in]  offset Offset for number of entries
550   @param[out] values Values to assemble into matrix
551 
552   @return An error code: 0 - success, otherwise - failure
553 
554   @ref Developer
555 **/
556 static int CeedSingleOperatorAssemble(CeedOperator op, CeedInt offset, CeedVector values) {
557   bool is_composite;
558 
559   CeedCall(CeedOperatorIsComposite(op, &is_composite));
560   CeedCheck(!is_composite, CeedOperatorReturnCeed(op), CEED_ERROR_UNSUPPORTED, "Composite operator not supported");
561 
562   // Early exit for empty operator
563   {
564     CeedInt num_elem = 0;
565 
566     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
567     if (num_elem == 0) return CEED_ERROR_SUCCESS;
568   }
569 
570   if (op->LinearAssembleSingle) {
571     // Backend version
572     CeedCall(op->LinearAssembleSingle(op, offset, values));
573     return CEED_ERROR_SUCCESS;
574   } else {
575     // Operator fallback
576     CeedOperator op_fallback;
577 
578     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
579     if (op_fallback) {
580       CeedCall(CeedSingleOperatorAssemble(op_fallback, offset, values));
581       return CEED_ERROR_SUCCESS;
582     }
583   }
584 
585   // Assemble QFunction
586   CeedInt             layout_qf[3];
587   const CeedScalar   *assembled_qf_array;
588   CeedVector          assembled_qf        = NULL;
589   CeedElemRestriction assembled_elem_rstr = NULL;
590 
591   CeedCall(CeedOperatorLinearAssembleQFunctionBuildOrUpdate(op, &assembled_qf, &assembled_elem_rstr, CEED_REQUEST_IMMEDIATE));
592   CeedCall(CeedElemRestrictionGetELayout(assembled_elem_rstr, layout_qf));
593   CeedCall(CeedElemRestrictionDestroy(&assembled_elem_rstr));
594   CeedCall(CeedVectorGetArrayRead(assembled_qf, CEED_MEM_HOST, &assembled_qf_array));
595 
596   // Get assembly data
597   CeedInt                  num_elem_in, elem_size_in, num_comp_in, num_qpts_in;
598   CeedInt                  num_elem_out, elem_size_out, num_comp_out, num_qpts_out;
599   CeedSize                 local_num_entries, count = 0;
600   const CeedEvalMode     **eval_modes_in, **eval_modes_out;
601   CeedInt                  num_active_bases_in, *num_eval_modes_in, num_active_bases_out, *num_eval_modes_out;
602   CeedBasis               *active_bases_in, *active_bases_out, basis_in, basis_out;
603   const CeedScalar       **B_mats_in, **B_mats_out, *B_mat_in, *B_mat_out;
604   CeedElemRestriction      elem_rstr_in, elem_rstr_out;
605   CeedRestrictionType      elem_rstr_type_in, elem_rstr_type_out;
606   const bool              *elem_rstr_orients_in = NULL, *elem_rstr_orients_out = NULL;
607   const CeedInt8          *elem_rstr_curl_orients_in = NULL, *elem_rstr_curl_orients_out = NULL;
608   CeedOperatorAssemblyData data;
609 
610   CeedCall(CeedOperatorGetOperatorAssemblyData(op, &data));
611   CeedCall(CeedOperatorAssemblyDataGetEvalModes(data, &num_active_bases_in, &num_eval_modes_in, &eval_modes_in, NULL, &num_active_bases_out,
612                                                 &num_eval_modes_out, &eval_modes_out, NULL, NULL));
613 
614   CeedCheck(num_active_bases_in == 1 && num_active_bases_out == 1, CeedOperatorReturnCeed(op), CEED_ERROR_UNSUPPORTED,
615             "Cannot assemble operator with multiple active bases");
616   CeedCheck(num_eval_modes_in[0] > 0 && num_eval_modes_out[0] > 0, CeedOperatorReturnCeed(op), CEED_ERROR_UNSUPPORTED,
617             "Cannot assemble operator without inputs/outputs");
618 
619   CeedCall(CeedOperatorAssemblyDataGetBases(data, NULL, &active_bases_in, &B_mats_in, NULL, &active_bases_out, &B_mats_out));
620   CeedCall(CeedOperatorGetActiveElemRestrictions(op, &elem_rstr_in, &elem_rstr_out));
621   basis_in  = active_bases_in[0];
622   basis_out = active_bases_out[0];
623   B_mat_in  = B_mats_in[0];
624   B_mat_out = B_mats_out[0];
625 
626   CeedCall(CeedElemRestrictionGetNumElements(elem_rstr_in, &num_elem_in));
627   CeedCall(CeedElemRestrictionGetElementSize(elem_rstr_in, &elem_size_in));
628   CeedCall(CeedElemRestrictionGetNumComponents(elem_rstr_in, &num_comp_in));
629   if (basis_in == CEED_BASIS_NONE) num_qpts_in = elem_size_in;
630   else CeedCall(CeedBasisGetNumQuadraturePoints(basis_in, &num_qpts_in));
631 
632   CeedCall(CeedElemRestrictionGetType(elem_rstr_in, &elem_rstr_type_in));
633   if (elem_rstr_type_in == CEED_RESTRICTION_ORIENTED) {
634     CeedCall(CeedElemRestrictionGetOrientations(elem_rstr_in, CEED_MEM_HOST, &elem_rstr_orients_in));
635   } else if (elem_rstr_type_in == CEED_RESTRICTION_CURL_ORIENTED) {
636     CeedCall(CeedElemRestrictionGetCurlOrientations(elem_rstr_in, CEED_MEM_HOST, &elem_rstr_curl_orients_in));
637   }
638 
639   if (elem_rstr_in != elem_rstr_out) {
640     CeedCall(CeedElemRestrictionGetNumElements(elem_rstr_out, &num_elem_out));
641     CeedCheck(num_elem_in == num_elem_out, CeedOperatorReturnCeed(op), CEED_ERROR_UNSUPPORTED,
642               "Active input and output operator restrictions must have the same number of elements."
643               " Input has %" CeedInt_FMT " elements; output has %" CeedInt_FMT "elements.",
644               num_elem_in, num_elem_out);
645     CeedCall(CeedElemRestrictionGetElementSize(elem_rstr_out, &elem_size_out));
646     CeedCall(CeedElemRestrictionGetNumComponents(elem_rstr_out, &num_comp_out));
647     if (basis_out == CEED_BASIS_NONE) num_qpts_out = elem_size_out;
648     else CeedCall(CeedBasisGetNumQuadraturePoints(basis_out, &num_qpts_out));
649     CeedCheck(num_qpts_in == num_qpts_out, CeedOperatorReturnCeed(op), CEED_ERROR_UNSUPPORTED,
650               "Active input and output bases must have the same number of quadrature points."
651               " Input has %" CeedInt_FMT " points; output has %" CeedInt_FMT "points.",
652               num_qpts_in, num_qpts_out);
653 
654     CeedCall(CeedElemRestrictionGetType(elem_rstr_out, &elem_rstr_type_out));
655     if (elem_rstr_type_out == CEED_RESTRICTION_ORIENTED) {
656       CeedCall(CeedElemRestrictionGetOrientations(elem_rstr_out, CEED_MEM_HOST, &elem_rstr_orients_out));
657     } else if (elem_rstr_type_out == CEED_RESTRICTION_CURL_ORIENTED) {
658       CeedCall(CeedElemRestrictionGetCurlOrientations(elem_rstr_out, CEED_MEM_HOST, &elem_rstr_curl_orients_out));
659     }
660   } else {
661     num_elem_out  = num_elem_in;
662     elem_size_out = elem_size_in;
663     num_comp_out  = num_comp_in;
664     num_qpts_out  = num_qpts_in;
665 
666     elem_rstr_orients_out      = elem_rstr_orients_in;
667     elem_rstr_curl_orients_out = elem_rstr_curl_orients_in;
668   }
669   local_num_entries = (CeedSize)elem_size_out * num_comp_out * elem_size_in * num_comp_in * num_elem_in;
670 
671   // Loop over elements and put in data structure
672   // We store B_mat_in, B_mat_out, BTD, elem_mat in row-major order
673   CeedTensorContract contract;
674   CeedScalar        *vals, *BTD_mat = NULL, *elem_mat = NULL, *elem_mat_b = NULL;
675 
676   CeedCall(CeedBasisGetTensorContract(basis_in, &contract));
677   CeedCall(CeedCalloc(elem_size_out * num_qpts_in * num_eval_modes_in[0], &BTD_mat));
678   CeedCall(CeedCalloc(elem_size_out * elem_size_in, &elem_mat));
679   if (elem_rstr_curl_orients_in || elem_rstr_curl_orients_out) CeedCall(CeedCalloc(elem_size_out * elem_size_in, &elem_mat_b));
680 
681   CeedCall(CeedVectorGetArray(values, CEED_MEM_HOST, &vals));
682   for (CeedSize e = 0; e < num_elem_in; e++) {
683     for (CeedInt comp_in = 0; comp_in < num_comp_in; comp_in++) {
684       for (CeedInt comp_out = 0; comp_out < num_comp_out; comp_out++) {
685         // Compute B^T*D
686         for (CeedSize n = 0; n < elem_size_out; n++) {
687           for (CeedSize q = 0; q < num_qpts_in; q++) {
688             for (CeedInt e_in = 0; e_in < num_eval_modes_in[0]; e_in++) {
689               const CeedSize btd_index = n * (num_qpts_in * num_eval_modes_in[0]) + q * num_eval_modes_in[0] + e_in;
690               CeedScalar     sum       = 0.0;
691 
692               for (CeedInt e_out = 0; e_out < num_eval_modes_out[0]; e_out++) {
693                 const CeedSize b_out_index     = (q * num_eval_modes_out[0] + e_out) * elem_size_out + n;
694                 const CeedSize eval_mode_index = ((e_in * num_comp_in + comp_in) * num_eval_modes_out[0] + e_out) * num_comp_out + comp_out;
695                 const CeedSize qf_index        = q * layout_qf[0] + eval_mode_index * layout_qf[1] + e * layout_qf[2];
696 
697                 sum += B_mat_out[b_out_index] * assembled_qf_array[qf_index];
698               }
699               BTD_mat[btd_index] = sum;
700             }
701           }
702         }
703 
704         // Form element matrix itself (for each block component)
705         if (contract) {
706           CeedCall(CeedTensorContractApply(contract, 1, num_qpts_in * num_eval_modes_in[0], elem_size_in, elem_size_out, BTD_mat, CEED_NOTRANSPOSE,
707                                            false, B_mat_in, elem_mat));
708         } else {
709           Ceed ceed;
710 
711           CeedCall(CeedOperatorGetCeed(op, &ceed));
712           CeedCall(CeedMatrixMatrixMultiply(ceed, BTD_mat, B_mat_in, elem_mat, elem_size_out, elem_size_in, num_qpts_in * num_eval_modes_in[0]));
713           CeedCall(CeedDestroy(&ceed));
714         }
715 
716         // Transform the element matrix if required
717         if (elem_rstr_orients_out) {
718           const bool *elem_orients = &elem_rstr_orients_out[e * elem_size_out];
719 
720           for (CeedInt i = 0; i < elem_size_out; i++) {
721             const double orient = elem_orients[i] ? -1.0 : 1.0;
722 
723             for (CeedInt j = 0; j < elem_size_in; j++) {
724               elem_mat[i * elem_size_in + j] *= orient;
725             }
726           }
727         } else if (elem_rstr_curl_orients_out) {
728           const CeedInt8 *elem_curl_orients = &elem_rstr_curl_orients_out[e * 3 * elem_size_out];
729 
730           // T^T*(B^T*D*B)
731           memcpy(elem_mat_b, elem_mat, elem_size_out * elem_size_in * sizeof(CeedScalar));
732           for (CeedInt i = 0; i < elem_size_out; i++) {
733             for (CeedInt j = 0; j < elem_size_in; j++) {
734               elem_mat[i * elem_size_in + j] = elem_mat_b[i * elem_size_in + j] * elem_curl_orients[3 * i + 1] +
735                                                (i > 0 ? elem_mat_b[(i - 1) * elem_size_in + j] * elem_curl_orients[3 * i - 1] : 0.0) +
736                                                (i < elem_size_out - 1 ? elem_mat_b[(i + 1) * elem_size_in + j] * elem_curl_orients[3 * i + 3] : 0.0);
737             }
738           }
739         }
740         if (elem_rstr_orients_in) {
741           const bool *elem_orients = &elem_rstr_orients_in[e * elem_size_in];
742 
743           for (CeedInt i = 0; i < elem_size_out; i++) {
744             for (CeedInt j = 0; j < elem_size_in; j++) {
745               elem_mat[i * elem_size_in + j] *= elem_orients[j] ? -1.0 : 1.0;
746             }
747           }
748         } else if (elem_rstr_curl_orients_in) {
749           const CeedInt8 *elem_curl_orients = &elem_rstr_curl_orients_in[e * 3 * elem_size_in];
750 
751           // (B^T*D*B)*T
752           memcpy(elem_mat_b, elem_mat, elem_size_out * elem_size_in * sizeof(CeedScalar));
753           for (CeedInt i = 0; i < elem_size_out; i++) {
754             for (CeedInt j = 0; j < elem_size_in; j++) {
755               elem_mat[i * elem_size_in + j] = elem_mat_b[i * elem_size_in + j] * elem_curl_orients[3 * j + 1] +
756                                                (j > 0 ? elem_mat_b[i * elem_size_in + j - 1] * elem_curl_orients[3 * j - 1] : 0.0) +
757                                                (j < elem_size_in - 1 ? elem_mat_b[i * elem_size_in + j + 1] * elem_curl_orients[3 * j + 3] : 0.0);
758             }
759           }
760         }
761 
762         // Put element matrix in coordinate data structure
763         for (CeedInt i = 0; i < elem_size_out; i++) {
764           for (CeedInt j = 0; j < elem_size_in; j++) {
765             vals[offset + count] = elem_mat[i * elem_size_in + j];
766             count++;
767           }
768         }
769       }
770     }
771   }
772   CeedCheck(count == local_num_entries, CeedOperatorReturnCeed(op), CEED_ERROR_MAJOR, "Error computing entries");
773   CeedCall(CeedVectorRestoreArray(values, &vals));
774 
775   // Cleanup
776   CeedCall(CeedFree(&BTD_mat));
777   CeedCall(CeedFree(&elem_mat));
778   CeedCall(CeedFree(&elem_mat_b));
779   if (elem_rstr_type_in == CEED_RESTRICTION_ORIENTED) {
780     CeedCall(CeedElemRestrictionRestoreOrientations(elem_rstr_in, &elem_rstr_orients_in));
781   } else if (elem_rstr_type_in == CEED_RESTRICTION_CURL_ORIENTED) {
782     CeedCall(CeedElemRestrictionRestoreCurlOrientations(elem_rstr_in, &elem_rstr_curl_orients_in));
783   }
784   if (elem_rstr_in != elem_rstr_out) {
785     if (elem_rstr_type_out == CEED_RESTRICTION_ORIENTED) {
786       CeedCall(CeedElemRestrictionRestoreOrientations(elem_rstr_out, &elem_rstr_orients_out));
787     } else if (elem_rstr_type_out == CEED_RESTRICTION_CURL_ORIENTED) {
788       CeedCall(CeedElemRestrictionRestoreCurlOrientations(elem_rstr_out, &elem_rstr_curl_orients_out));
789     }
790   }
791   CeedCall(CeedVectorRestoreArrayRead(assembled_qf, &assembled_qf_array));
792   CeedCall(CeedVectorDestroy(&assembled_qf));
793   CeedCall(CeedElemRestrictionDestroy(&elem_rstr_in));
794   CeedCall(CeedElemRestrictionDestroy(&elem_rstr_out));
795   return CEED_ERROR_SUCCESS;
796 }
797 
798 /**
799   @brief Count number of entries for assembled `CeedOperator`
800 
801   @param[in]  op          `CeedOperator` to assemble
802   @param[out] num_entries Number of entries in assembled representation
803 
804   @return An error code: 0 - success, otherwise - failure
805 
806   @ref Utility
807 **/
808 static int CeedSingleOperatorAssemblyCountEntries(CeedOperator op, CeedSize *num_entries) {
809   bool                is_composite;
810   CeedInt             num_elem_in, elem_size_in, num_comp_in, num_elem_out, elem_size_out, num_comp_out;
811   CeedElemRestriction rstr_in, rstr_out;
812 
813   CeedCall(CeedOperatorIsComposite(op, &is_composite));
814   CeedCheck(!is_composite, CeedOperatorReturnCeed(op), CEED_ERROR_UNSUPPORTED, "Composite operator not supported");
815 
816   CeedCall(CeedOperatorGetActiveElemRestrictions(op, &rstr_in, &rstr_out));
817   CeedCall(CeedElemRestrictionGetNumElements(rstr_in, &num_elem_in));
818   CeedCall(CeedElemRestrictionGetElementSize(rstr_in, &elem_size_in));
819   CeedCall(CeedElemRestrictionGetNumComponents(rstr_in, &num_comp_in));
820   if (rstr_in != rstr_out) {
821     CeedCall(CeedElemRestrictionGetNumElements(rstr_out, &num_elem_out));
822     CeedCheck(num_elem_in == num_elem_out, CeedOperatorReturnCeed(op), CEED_ERROR_UNSUPPORTED,
823               "Active input and output operator restrictions must have the same number of elements."
824               " Input has %" CeedInt_FMT " elements; output has %" CeedInt_FMT "elements.",
825               num_elem_in, num_elem_out);
826     CeedCall(CeedElemRestrictionGetElementSize(rstr_out, &elem_size_out));
827     CeedCall(CeedElemRestrictionGetNumComponents(rstr_out, &num_comp_out));
828   } else {
829     num_elem_out  = num_elem_in;
830     elem_size_out = elem_size_in;
831     num_comp_out  = num_comp_in;
832   }
833   CeedCall(CeedElemRestrictionDestroy(&rstr_in));
834   CeedCall(CeedElemRestrictionDestroy(&rstr_out));
835   *num_entries = (CeedSize)elem_size_in * num_comp_in * elem_size_out * num_comp_out * num_elem_in;
836   return CEED_ERROR_SUCCESS;
837 }
838 
839 /**
840   @brief Common code for creating a multigrid coarse `CeedOperator` and level transfer `CeedOperator` for a `CeedOperator`
841 
842   @param[in]  op_fine      Fine grid `CeedOperator`
843   @param[in]  p_mult_fine  L-vector multiplicity in parallel gather/scatter, or `NULL` if not creating prolongation/restriction `CeedOperator`
844   @param[in]  rstr_coarse  Coarse grid `CeedElemRestriction`
845   @param[in]  basis_coarse Coarse grid active vector `CeedBasis`
846   @param[in]  basis_c_to_f `CeedBasis` for coarse to fine interpolation, or `NULL` if not creating prolongation/restriction operators
847   @param[out] op_coarse    Coarse grid `CeedOperator`
848   @param[out] op_prolong   Coarse to fine `CeedOperator`, or `NULL`
849   @param[out] op_restrict  Fine to coarse `CeedOperator`, or `NULL`
850 
851   @return An error code: 0 - success, otherwise - failure
852 
853   @ref Developer
854 **/
855 static int CeedSingleOperatorMultigridLevel(CeedOperator op_fine, CeedVector p_mult_fine, CeedElemRestriction rstr_coarse, CeedBasis basis_coarse,
856                                             CeedBasis basis_c_to_f, CeedOperator *op_coarse, CeedOperator *op_prolong, CeedOperator *op_restrict) {
857   bool                is_composite;
858   Ceed                ceed;
859   CeedInt             num_comp, num_input_fields, num_output_fields;
860   CeedVector          mult_vec         = NULL;
861   CeedElemRestriction rstr_p_mult_fine = NULL, rstr_fine = NULL;
862   CeedOperatorField  *input_fields, *output_fields;
863 
864   CeedCall(CeedOperatorGetCeed(op_fine, &ceed));
865 
866   // Check for composite operator
867   CeedCall(CeedOperatorIsComposite(op_fine, &is_composite));
868   CeedCheck(!is_composite, ceed, CEED_ERROR_UNSUPPORTED, "Automatic multigrid setup for composite operators not supported");
869 
870   // Coarse Grid
871   CeedCall(CeedOperatorCreate(ceed, op_fine->qf, op_fine->dqf, op_fine->dqfT, op_coarse));
872   CeedCall(CeedOperatorGetFields(op_fine, &num_input_fields, &input_fields, &num_output_fields, &output_fields));
873   // -- Clone input fields
874   for (CeedInt i = 0; i < num_input_fields; i++) {
875     const char         *field_name;
876     CeedVector          vec;
877     CeedElemRestriction rstr  = NULL;
878     CeedBasis           basis = NULL;
879 
880     CeedCall(CeedOperatorFieldGetName(input_fields[i], &field_name));
881     CeedCall(CeedOperatorFieldGetVector(input_fields[i], &vec));
882     if (vec == CEED_VECTOR_ACTIVE) {
883       CeedCall(CeedElemRestrictionReferenceCopy(rstr_coarse, &rstr));
884       CeedCall(CeedBasisReferenceCopy(basis_coarse, &basis));
885       if (!rstr_fine) CeedCall(CeedOperatorFieldGetElemRestriction(input_fields[i], &rstr_fine));
886     } else {
887       CeedCall(CeedOperatorFieldGetElemRestriction(input_fields[i], &rstr));
888       CeedCall(CeedOperatorFieldGetBasis(input_fields[i], &basis));
889     }
890     CeedCall(CeedOperatorSetField(*op_coarse, field_name, rstr, basis, vec));
891     CeedCall(CeedVectorDestroy(&vec));
892     CeedCall(CeedElemRestrictionDestroy(&rstr));
893     CeedCall(CeedBasisDestroy(&basis));
894   }
895   // -- Clone output fields
896   for (CeedInt i = 0; i < num_output_fields; i++) {
897     const char         *field_name;
898     CeedVector          vec;
899     CeedElemRestriction rstr  = NULL;
900     CeedBasis           basis = NULL;
901 
902     CeedCall(CeedOperatorFieldGetName(output_fields[i], &field_name));
903     CeedCall(CeedOperatorFieldGetVector(output_fields[i], &vec));
904     if (vec == CEED_VECTOR_ACTIVE) {
905       CeedCall(CeedElemRestrictionReferenceCopy(rstr_coarse, &rstr));
906       CeedCall(CeedBasisReferenceCopy(basis_coarse, &basis));
907       if (!rstr_fine) CeedCall(CeedOperatorFieldGetElemRestriction(output_fields[i], &rstr_fine));
908     } else {
909       CeedCall(CeedOperatorFieldGetElemRestriction(output_fields[i], &rstr));
910       CeedCall(CeedOperatorFieldGetBasis(output_fields[i], &basis));
911     }
912     CeedCall(CeedOperatorSetField(*op_coarse, field_name, rstr, basis, vec));
913     CeedCall(CeedVectorDestroy(&vec));
914     CeedCall(CeedElemRestrictionDestroy(&rstr));
915     CeedCall(CeedBasisDestroy(&basis));
916   }
917   // -- Clone QFunctionAssemblyData
918   {
919     CeedQFunctionAssemblyData fine_data;
920 
921     CeedCall(CeedOperatorGetQFunctionAssemblyData(op_fine, &fine_data));
922     CeedCall(CeedQFunctionAssemblyDataReferenceCopy(fine_data, &(*op_coarse)->qf_assembled));
923   }
924 
925   // Multiplicity vector
926   if (op_restrict || op_prolong) {
927     CeedVector          mult_e_vec;
928     CeedRestrictionType rstr_type;
929 
930     CeedCall(CeedElemRestrictionGetType(rstr_fine, &rstr_type));
931     CeedCheck(rstr_type != CEED_RESTRICTION_CURL_ORIENTED, ceed, CEED_ERROR_UNSUPPORTED,
932               "Element restrictions created with CeedElemRestrictionCreateCurlOriented are not supported");
933     CeedCheck(p_mult_fine, ceed, CEED_ERROR_INCOMPATIBLE, "Prolongation or restriction operator creation requires fine grid multiplicity vector");
934     CeedCall(CeedElemRestrictionCreateUnsignedCopy(rstr_fine, &rstr_p_mult_fine));
935     CeedCall(CeedElemRestrictionCreateVector(rstr_fine, &mult_vec, &mult_e_vec));
936     CeedCall(CeedVectorSetValue(mult_e_vec, 0.0));
937     CeedCall(CeedElemRestrictionApply(rstr_p_mult_fine, CEED_NOTRANSPOSE, p_mult_fine, mult_e_vec, CEED_REQUEST_IMMEDIATE));
938     CeedCall(CeedVectorSetValue(mult_vec, 0.0));
939     CeedCall(CeedElemRestrictionApply(rstr_p_mult_fine, CEED_TRANSPOSE, mult_e_vec, mult_vec, CEED_REQUEST_IMMEDIATE));
940     CeedCall(CeedVectorDestroy(&mult_e_vec));
941     CeedCall(CeedVectorReciprocal(mult_vec));
942   }
943 
944   // Clone name
945   bool   has_name = op_fine->name;
946   size_t name_len = op_fine->name ? strlen(op_fine->name) : 0;
947   CeedCall(CeedOperatorSetName(*op_coarse, op_fine->name));
948 
949   // Check that coarse to fine basis is provided if prolong/restrict operators are requested
950   CeedCheck(basis_c_to_f || (!op_restrict && !op_prolong), ceed, CEED_ERROR_INCOMPATIBLE,
951             "Prolongation or restriction operator creation requires coarse-to-fine basis");
952 
953   // Restriction/Prolongation Operators
954   CeedCall(CeedBasisGetNumComponents(basis_coarse, &num_comp));
955 
956   // Restriction
957   if (op_restrict) {
958     CeedInt             *num_comp_r_data;
959     CeedQFunctionContext ctx_r;
960     CeedQFunction        qf_restrict;
961 
962     CeedCall(CeedQFunctionCreateInteriorByName(ceed, "Scale", &qf_restrict));
963     CeedCall(CeedCalloc(1, &num_comp_r_data));
964     num_comp_r_data[0] = num_comp;
965     CeedCall(CeedQFunctionContextCreate(ceed, &ctx_r));
966     CeedCall(CeedQFunctionContextSetData(ctx_r, CEED_MEM_HOST, CEED_OWN_POINTER, sizeof(*num_comp_r_data), num_comp_r_data));
967     CeedCall(CeedQFunctionSetContext(qf_restrict, ctx_r));
968     CeedCall(CeedQFunctionContextDestroy(&ctx_r));
969     CeedCall(CeedQFunctionAddInput(qf_restrict, "input", num_comp, CEED_EVAL_NONE));
970     CeedCall(CeedQFunctionAddInput(qf_restrict, "scale", num_comp, CEED_EVAL_NONE));
971     CeedCall(CeedQFunctionAddOutput(qf_restrict, "output", num_comp, CEED_EVAL_INTERP));
972     CeedCall(CeedQFunctionSetUserFlopsEstimate(qf_restrict, num_comp));
973 
974     CeedCall(CeedOperatorCreate(ceed, qf_restrict, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, op_restrict));
975     CeedCall(CeedOperatorSetField(*op_restrict, "input", rstr_fine, CEED_BASIS_NONE, CEED_VECTOR_ACTIVE));
976     CeedCall(CeedOperatorSetField(*op_restrict, "scale", rstr_p_mult_fine, CEED_BASIS_NONE, mult_vec));
977     CeedCall(CeedOperatorSetField(*op_restrict, "output", rstr_coarse, basis_c_to_f, CEED_VECTOR_ACTIVE));
978 
979     // Set name
980     char *restriction_name;
981 
982     CeedCall(CeedCalloc(17 + name_len, &restriction_name));
983     sprintf(restriction_name, "restriction%s%s", has_name ? " for " : "", has_name ? op_fine->name : "");
984     CeedCall(CeedOperatorSetName(*op_restrict, restriction_name));
985     CeedCall(CeedFree(&restriction_name));
986 
987     // Check
988     CeedCall(CeedOperatorCheckReady(*op_restrict));
989 
990     // Cleanup
991     CeedCall(CeedQFunctionDestroy(&qf_restrict));
992   }
993 
994   // Prolongation
995   if (op_prolong) {
996     CeedInt             *num_comp_p_data;
997     CeedQFunctionContext ctx_p;
998     CeedQFunction        qf_prolong;
999 
1000     CeedCall(CeedQFunctionCreateInteriorByName(ceed, "Scale", &qf_prolong));
1001     CeedCall(CeedCalloc(1, &num_comp_p_data));
1002     num_comp_p_data[0] = num_comp;
1003     CeedCall(CeedQFunctionContextCreate(ceed, &ctx_p));
1004     CeedCall(CeedQFunctionContextSetData(ctx_p, CEED_MEM_HOST, CEED_OWN_POINTER, sizeof(*num_comp_p_data), num_comp_p_data));
1005     CeedCall(CeedQFunctionSetContext(qf_prolong, ctx_p));
1006     CeedCall(CeedQFunctionContextDestroy(&ctx_p));
1007     CeedCall(CeedQFunctionAddInput(qf_prolong, "input", num_comp, CEED_EVAL_INTERP));
1008     CeedCall(CeedQFunctionAddInput(qf_prolong, "scale", num_comp, CEED_EVAL_NONE));
1009     CeedCall(CeedQFunctionAddOutput(qf_prolong, "output", num_comp, CEED_EVAL_NONE));
1010     CeedCall(CeedQFunctionSetUserFlopsEstimate(qf_prolong, num_comp));
1011 
1012     CeedCall(CeedOperatorCreate(ceed, qf_prolong, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, op_prolong));
1013     CeedCall(CeedOperatorSetField(*op_prolong, "input", rstr_coarse, basis_c_to_f, CEED_VECTOR_ACTIVE));
1014     CeedCall(CeedOperatorSetField(*op_prolong, "scale", rstr_p_mult_fine, CEED_BASIS_NONE, mult_vec));
1015     CeedCall(CeedOperatorSetField(*op_prolong, "output", rstr_fine, CEED_BASIS_NONE, CEED_VECTOR_ACTIVE));
1016 
1017     // Set name
1018     char *prolongation_name;
1019 
1020     CeedCall(CeedCalloc(18 + name_len, &prolongation_name));
1021     sprintf(prolongation_name, "prolongation%s%s", has_name ? " for " : "", has_name ? op_fine->name : "");
1022     CeedCall(CeedOperatorSetName(*op_prolong, prolongation_name));
1023     CeedCall(CeedFree(&prolongation_name));
1024 
1025     // Check
1026     CeedCall(CeedOperatorCheckReady(*op_prolong));
1027 
1028     // Cleanup
1029     CeedCall(CeedQFunctionDestroy(&qf_prolong));
1030   }
1031 
1032   // Check
1033   CeedCall(CeedOperatorCheckReady(*op_coarse));
1034 
1035   // Cleanup
1036   CeedCall(CeedDestroy(&ceed));
1037   CeedCall(CeedVectorDestroy(&mult_vec));
1038   CeedCall(CeedElemRestrictionDestroy(&rstr_fine));
1039   CeedCall(CeedElemRestrictionDestroy(&rstr_p_mult_fine));
1040   CeedCall(CeedBasisDestroy(&basis_c_to_f));
1041   return CEED_ERROR_SUCCESS;
1042 }
1043 
1044 /**
1045   @brief Build 1D mass matrix and Laplacian with perturbation
1046 
1047   @param[in]  interp_1d   Interpolation matrix in one dimension
1048   @param[in]  grad_1d     Gradient matrix in one dimension
1049   @param[in]  q_weight_1d Quadrature weights in one dimension
1050   @param[in]  P_1d        Number of basis nodes in one dimension
1051   @param[in]  Q_1d        Number of quadrature points in one dimension
1052   @param[in]  dim         Dimension of basis
1053   @param[out] mass        Assembled mass matrix in one dimension
1054   @param[out] laplace     Assembled perturbed Laplacian in one dimension
1055 
1056   @return An error code: 0 - success, otherwise - failure
1057 
1058   @ref Developer
1059 **/
1060 CeedPragmaOptimizeOff
1061 static int CeedBuildMassLaplace(const CeedScalar *interp_1d, const CeedScalar *grad_1d, const CeedScalar *q_weight_1d, CeedInt P_1d, CeedInt Q_1d,
1062                                 CeedInt dim, CeedScalar *mass, CeedScalar *laplace) {
1063   for (CeedInt i = 0; i < P_1d; i++) {
1064     for (CeedInt j = 0; j < P_1d; j++) {
1065       CeedScalar sum = 0.0;
1066       for (CeedInt k = 0; k < Q_1d; k++) sum += interp_1d[k * P_1d + i] * q_weight_1d[k] * interp_1d[k * P_1d + j];
1067       mass[i + j * P_1d] = sum;
1068     }
1069   }
1070   // -- Laplacian
1071   for (CeedInt i = 0; i < P_1d; i++) {
1072     for (CeedInt j = 0; j < P_1d; j++) {
1073       CeedScalar sum = 0.0;
1074 
1075       for (CeedInt k = 0; k < Q_1d; k++) sum += grad_1d[k * P_1d + i] * q_weight_1d[k] * grad_1d[k * P_1d + j];
1076       laplace[i + j * P_1d] = sum;
1077     }
1078   }
1079   CeedScalar perturbation = dim > 2 ? 1e-6 : 1e-4;
1080   for (CeedInt i = 0; i < P_1d; i++) laplace[i + P_1d * i] += perturbation;
1081   return CEED_ERROR_SUCCESS;
1082 }
1083 CeedPragmaOptimizeOn
1084 
1085 /// @}
1086 
1087 /// ----------------------------------------------------------------------------
1088 /// CeedOperator Backend API
1089 /// ----------------------------------------------------------------------------
1090 /// @addtogroup CeedOperatorBackend
1091 /// @{
1092 
1093 /**
1094   @brief Select correct basis matrix pointer based on @ref CeedEvalMode
1095 
1096   @param[in]  basis     `CeedBasis` from which to get the basis matrix
1097   @param[in]  eval_mode Current basis evaluation mode
1098   @param[in]  identity  Pointer to identity matrix
1099   @param[out] basis_ptr `CeedBasis` pointer to set
1100 
1101   @ref Backend
1102 **/
1103 int CeedOperatorGetBasisPointer(CeedBasis basis, CeedEvalMode eval_mode, const CeedScalar *identity, const CeedScalar **basis_ptr) {
1104   switch (eval_mode) {
1105     case CEED_EVAL_NONE:
1106       *basis_ptr = identity;
1107       break;
1108     case CEED_EVAL_INTERP:
1109       CeedCall(CeedBasisGetInterp(basis, basis_ptr));
1110       break;
1111     case CEED_EVAL_GRAD:
1112       CeedCall(CeedBasisGetGrad(basis, basis_ptr));
1113       break;
1114     case CEED_EVAL_DIV:
1115       CeedCall(CeedBasisGetDiv(basis, basis_ptr));
1116       break;
1117     case CEED_EVAL_CURL:
1118       CeedCall(CeedBasisGetCurl(basis, basis_ptr));
1119       break;
1120     case CEED_EVAL_WEIGHT:
1121       break;  // Caught by QF Assembly
1122   }
1123   assert(*basis_ptr != NULL);
1124   return CEED_ERROR_SUCCESS;
1125 }
1126 
1127 /**
1128   @brief Create point block restriction for active `CeedOperatorField`
1129 
1130   @param[in]  rstr             Original `CeedElemRestriction` for active field
1131   @param[out] point_block_rstr Address of the variable where the newly created `CeedElemRestriction` will be stored
1132 
1133   @return An error code: 0 - success, otherwise - failure
1134 
1135   @ref Backend
1136 **/
1137 int CeedOperatorCreateActivePointBlockRestriction(CeedElemRestriction rstr, CeedElemRestriction *point_block_rstr) {
1138   Ceed           ceed;
1139   CeedInt        num_elem, num_comp, shift, elem_size, comp_stride, *point_block_offsets;
1140   CeedSize       l_size;
1141   const CeedInt *offsets;
1142 
1143   CeedCall(CeedElemRestrictionGetCeed(rstr, &ceed));
1144   CeedCall(CeedElemRestrictionGetOffsets(rstr, CEED_MEM_HOST, &offsets));
1145 
1146   // Expand offsets
1147   CeedCall(CeedElemRestrictionGetNumElements(rstr, &num_elem));
1148   CeedCall(CeedElemRestrictionGetNumComponents(rstr, &num_comp));
1149   CeedCall(CeedElemRestrictionGetElementSize(rstr, &elem_size));
1150   CeedCall(CeedElemRestrictionGetCompStride(rstr, &comp_stride));
1151   CeedCall(CeedElemRestrictionGetLVectorSize(rstr, &l_size));
1152   shift = num_comp;
1153   if (comp_stride != 1) shift *= num_comp;
1154   CeedCall(CeedCalloc(num_elem * elem_size, &point_block_offsets));
1155   for (CeedInt i = 0; i < num_elem * elem_size; i++) {
1156     point_block_offsets[i] = offsets[i] * shift;
1157   }
1158 
1159   // Create new restriction
1160   CeedCall(CeedElemRestrictionCreate(ceed, num_elem, elem_size, num_comp * num_comp, 1, l_size * num_comp, CEED_MEM_HOST, CEED_OWN_POINTER,
1161                                      point_block_offsets, point_block_rstr));
1162 
1163   // Cleanup
1164   CeedCall(CeedElemRestrictionRestoreOffsets(rstr, &offsets));
1165   CeedCall(CeedDestroy(&ceed));
1166   return CEED_ERROR_SUCCESS;
1167 }
1168 
1169 /**
1170   @brief Get `CeedQFunctionAssemblyData`
1171 
1172   @param[in]  op   `CeedOperator` to assemble
1173   @param[out] data `CeedQFunctionAssemblyData`
1174 
1175   @return An error code: 0 - success, otherwise - failure
1176 
1177   @ref Backend
1178 **/
1179 int CeedOperatorGetQFunctionAssemblyData(CeedOperator op, CeedQFunctionAssemblyData *data) {
1180   if (!op->qf_assembled) {
1181     CeedQFunctionAssemblyData data;
1182 
1183     CeedCall(CeedQFunctionAssemblyDataCreate(op->ceed, &data));
1184     op->qf_assembled = data;
1185   }
1186   *data = op->qf_assembled;
1187   return CEED_ERROR_SUCCESS;
1188 }
1189 
1190 /**
1191   @brief Create object holding `CeedQFunction` assembly data for `CeedOperator`
1192 
1193   @param[in]  ceed `Ceed` object used to create the `CeedQFunctionAssemblyData`
1194   @param[out] data Address of the variable where the newly created `CeedQFunctionAssemblyData` will be stored
1195 
1196   @return An error code: 0 - success, otherwise - failure
1197 
1198   @ref Backend
1199 **/
1200 int CeedQFunctionAssemblyDataCreate(Ceed ceed, CeedQFunctionAssemblyData *data) {
1201   CeedCall(CeedCalloc(1, data));
1202   (*data)->ref_count = 1;
1203   (*data)->ceed      = ceed;
1204   CeedCall(CeedReference(ceed));
1205   return CEED_ERROR_SUCCESS;
1206 }
1207 
1208 /**
1209   @brief Increment the reference counter for a `CeedQFunctionAssemblyData`
1210 
1211   @param[in,out] data `CeedQFunctionAssemblyData` to increment the reference counter
1212 
1213   @return An error code: 0 - success, otherwise - failure
1214 
1215   @ref Backend
1216 **/
1217 int CeedQFunctionAssemblyDataReference(CeedQFunctionAssemblyData data) {
1218   data->ref_count++;
1219   return CEED_ERROR_SUCCESS;
1220 }
1221 
1222 /**
1223   @brief Set re-use of `CeedQFunctionAssemblyData`
1224 
1225   @param[in,out] data       `CeedQFunctionAssemblyData` to mark for reuse
1226   @param[in]     reuse_data Boolean flag indicating data re-use
1227 
1228   @return An error code: 0 - success, otherwise - failure
1229 
1230   @ref Backend
1231 **/
1232 int CeedQFunctionAssemblyDataSetReuse(CeedQFunctionAssemblyData data, bool reuse_data) {
1233   data->reuse_data        = reuse_data;
1234   data->needs_data_update = true;
1235   return CEED_ERROR_SUCCESS;
1236 }
1237 
1238 /**
1239   @brief Mark `CeedQFunctionAssemblyData` as stale
1240 
1241   @param[in,out] data              `CeedQFunctionAssemblyData` to mark as stale
1242   @param[in]     needs_data_update Boolean flag indicating if update is needed or completed
1243 
1244   @return An error code: 0 - success, otherwise - failure
1245 
1246   @ref Backend
1247 **/
1248 int CeedQFunctionAssemblyDataSetUpdateNeeded(CeedQFunctionAssemblyData data, bool needs_data_update) {
1249   data->needs_data_update = needs_data_update;
1250   return CEED_ERROR_SUCCESS;
1251 }
1252 
1253 /**
1254   @brief Determine if `CeedQFunctionAssemblyData` needs update
1255 
1256   @param[in]  data             `CeedQFunctionAssemblyData` to mark as stale
1257   @param[out] is_update_needed Boolean flag indicating if re-assembly is required
1258 
1259   @return An error code: 0 - success, otherwise - failure
1260 
1261   @ref Backend
1262 **/
1263 int CeedQFunctionAssemblyDataIsUpdateNeeded(CeedQFunctionAssemblyData data, bool *is_update_needed) {
1264   *is_update_needed = !data->reuse_data || data->needs_data_update;
1265   return CEED_ERROR_SUCCESS;
1266 }
1267 
1268 /**
1269   @brief Copy the pointer to a `CeedQFunctionAssemblyData`.
1270 
1271   Both pointers should be destroyed with @ref CeedQFunctionAssemblyDataDestroy().
1272 
1273   Note: If the value of ` *data_copy` passed to this function is non-`NULL` , then it is assumed that ` *data_copy` is a pointer to a `CeedQFunctionAssemblyData`.
1274         This `CeedQFunctionAssemblyData` will be destroyed if ` *data_copy` is the only reference to this `CeedQFunctionAssemblyData`.
1275 
1276   @param[in]     data      `CeedQFunctionAssemblyData` to copy reference to
1277   @param[in,out] data_copy Variable to store copied reference
1278 
1279   @return An error code: 0 - success, otherwise - failure
1280 
1281   @ref Backend
1282 **/
1283 int CeedQFunctionAssemblyDataReferenceCopy(CeedQFunctionAssemblyData data, CeedQFunctionAssemblyData *data_copy) {
1284   CeedCall(CeedQFunctionAssemblyDataReference(data));
1285   CeedCall(CeedQFunctionAssemblyDataDestroy(data_copy));
1286   *data_copy = data;
1287   return CEED_ERROR_SUCCESS;
1288 }
1289 
1290 /**
1291   @brief Get setup status for internal objects for `CeedQFunctionAssemblyData`
1292 
1293   @param[in]  data     `CeedQFunctionAssemblyData` to retrieve status
1294   @param[out] is_setup Boolean flag for setup status
1295 
1296   @return An error code: 0 - success, otherwise - failure
1297 
1298   @ref Backend
1299 **/
1300 int CeedQFunctionAssemblyDataIsSetup(CeedQFunctionAssemblyData data, bool *is_setup) {
1301   *is_setup = data->is_setup;
1302   return CEED_ERROR_SUCCESS;
1303 }
1304 
1305 /**
1306   @brief Set internal objects for `CeedQFunctionAssemblyData`
1307 
1308   @param[in,out] data `CeedQFunctionAssemblyData` to set objects
1309   @param[in]     vec  `CeedVector` to store assembled `CeedQFunction` at quadrature points
1310   @param[in]     rstr `CeedElemRestriction` for `CeedVector` containing assembled `CeedQFunction`
1311 
1312   @return An error code: 0 - success, otherwise - failure
1313 
1314   @ref Backend
1315 **/
1316 int CeedQFunctionAssemblyDataSetObjects(CeedQFunctionAssemblyData data, CeedVector vec, CeedElemRestriction rstr) {
1317   CeedCall(CeedVectorReferenceCopy(vec, &data->vec));
1318   CeedCall(CeedElemRestrictionReferenceCopy(rstr, &data->rstr));
1319 
1320   data->is_setup = true;
1321   return CEED_ERROR_SUCCESS;
1322 }
1323 
1324 /**
1325   @brief Get internal objects for `CeedQFunctionAssemblyData`
1326 
1327   @param[in,out] data `CeedQFunctionAssemblyData` to set objects
1328   @param[out]    vec  `CeedVector` to store assembled `CeedQFunction` at quadrature points
1329   @param[out]    rstr `CeedElemRestriction` for `CeedVector` containing assembled `CeedQFunction`
1330 
1331   @return An error code: 0 - success, otherwise - failure
1332 
1333   @ref Backend
1334 **/
1335 int CeedQFunctionAssemblyDataGetObjects(CeedQFunctionAssemblyData data, CeedVector *vec, CeedElemRestriction *rstr) {
1336   CeedCheck(data->is_setup, data->ceed, CEED_ERROR_INCOMPLETE, "Internal objects not set; must call CeedQFunctionAssemblyDataSetObjects first.");
1337 
1338   CeedCall(CeedVectorReferenceCopy(data->vec, vec));
1339   CeedCall(CeedElemRestrictionReferenceCopy(data->rstr, rstr));
1340   return CEED_ERROR_SUCCESS;
1341 }
1342 
1343 /**
1344   @brief Destroy `CeedQFunctionAssemblyData`
1345 
1346   @param[in,out] data  `CeedQFunctionAssemblyData` to destroy
1347 
1348   @return An error code: 0 - success, otherwise - failure
1349 
1350   @ref Backend
1351 **/
1352 int CeedQFunctionAssemblyDataDestroy(CeedQFunctionAssemblyData *data) {
1353   if (!*data || --(*data)->ref_count > 0) {
1354     *data = NULL;
1355     return CEED_ERROR_SUCCESS;
1356   }
1357   CeedCall(CeedDestroy(&(*data)->ceed));
1358   CeedCall(CeedVectorDestroy(&(*data)->vec));
1359   CeedCall(CeedElemRestrictionDestroy(&(*data)->rstr));
1360 
1361   CeedCall(CeedFree(data));
1362   return CEED_ERROR_SUCCESS;
1363 }
1364 
1365 /**
1366   @brief Get `CeedOperatorAssemblyData`
1367 
1368   @param[in]  op   `CeedOperator` to assemble
1369   @param[out] data `CeedOperatorAssemblyData`
1370 
1371   @return An error code: 0 - success, otherwise - failure
1372 
1373   @ref Backend
1374 **/
1375 int CeedOperatorGetOperatorAssemblyData(CeedOperator op, CeedOperatorAssemblyData *data) {
1376   if (!op->op_assembled) {
1377     CeedOperatorAssemblyData data;
1378 
1379     CeedCall(CeedOperatorAssemblyDataCreate(op->ceed, op, &data));
1380     op->op_assembled = data;
1381   }
1382   *data = op->op_assembled;
1383   return CEED_ERROR_SUCCESS;
1384 }
1385 
1386 /**
1387   @brief Create object holding `CeedOperator` assembly data.
1388 
1389   The `CeedOperatorAssemblyData` holds an array with references to every active `CeedBasis` used in the `CeedOperator`.
1390   An array with references to the corresponding active `CeedElemRestriction` is also stored.
1391   For each active `CeedBasis, the `CeedOperatorAssemblyData` holds an array of all input and output @ref CeedEvalMode for this `CeedBasis`.
1392   The `CeedOperatorAssemblyData` holds an array of offsets for indexing into the assembled `CeedQFunction` arrays to the row representing each @ref CeedEvalMode.
1393   The number of input columns across all active bases for the assembled `CeedQFunction` is also stored.
1394   Lastly, the `CeedOperatorAssembly` data holds assembled matrices representing the full action of the `CeedBasis` for all @ref CeedEvalMode.
1395 
1396   @param[in]  ceed `Ceed` object used to create the `CeedOperatorAssemblyData`
1397   @param[in]  op   `CeedOperator` to be assembled
1398   @param[out] data Address of the variable where the newly created `CeedOperatorAssemblyData` will be stored
1399 
1400   @return An error code: 0 - success, otherwise - failure
1401 
1402   @ref Backend
1403 **/
1404 int CeedOperatorAssemblyDataCreate(Ceed ceed, CeedOperator op, CeedOperatorAssemblyData *data) {
1405   CeedInt             num_active_bases_in = 0, num_active_bases_out = 0, offset = 0;
1406   CeedInt             num_input_fields, *num_eval_modes_in = NULL, num_output_fields, *num_eval_modes_out = NULL;
1407   CeedSize          **eval_mode_offsets_in = NULL, **eval_mode_offsets_out = NULL;
1408   CeedEvalMode      **eval_modes_in = NULL, **eval_modes_out = NULL;
1409   CeedQFunctionField *qf_fields;
1410   CeedQFunction       qf;
1411   CeedOperatorField  *op_fields;
1412   bool                is_composite;
1413 
1414   CeedCall(CeedOperatorIsComposite(op, &is_composite));
1415   CeedCheck(!is_composite, ceed, CEED_ERROR_INCOMPATIBLE, "Can only create CeedOperator assembly data for non-composite operators.");
1416 
1417   // Allocate
1418   CeedCall(CeedCalloc(1, data));
1419   (*data)->ceed = ceed;
1420   CeedCall(CeedReference(ceed));
1421 
1422   // Build OperatorAssembly data
1423   CeedCall(CeedOperatorGetQFunction(op, &qf));
1424 
1425   // Determine active input basis
1426   CeedCall(CeedQFunctionGetFields(qf, &num_input_fields, &qf_fields, NULL, NULL));
1427   CeedCall(CeedOperatorGetFields(op, NULL, &op_fields, NULL, NULL));
1428   for (CeedInt i = 0; i < num_input_fields; i++) {
1429     CeedVector vec;
1430 
1431     CeedCall(CeedOperatorFieldGetVector(op_fields[i], &vec));
1432     if (vec == CEED_VECTOR_ACTIVE) {
1433       CeedInt      index = -1, num_comp, q_comp;
1434       CeedEvalMode eval_mode;
1435       CeedBasis    basis_in = NULL;
1436 
1437       CeedCall(CeedOperatorFieldGetBasis(op_fields[i], &basis_in));
1438       CeedCall(CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode));
1439       CeedCall(CeedBasisGetNumComponents(basis_in, &num_comp));
1440       CeedCall(CeedBasisGetNumQuadratureComponents(basis_in, eval_mode, &q_comp));
1441       for (CeedInt i = 0; i < num_active_bases_in; i++) {
1442         if ((*data)->active_bases_in[i] == basis_in) index = i;
1443       }
1444       if (index == -1) {
1445         CeedElemRestriction elem_rstr_in;
1446 
1447         index = num_active_bases_in;
1448         CeedCall(CeedRealloc(num_active_bases_in + 1, &(*data)->active_bases_in));
1449         (*data)->active_bases_in[num_active_bases_in] = NULL;
1450         CeedCall(CeedBasisReferenceCopy(basis_in, &(*data)->active_bases_in[num_active_bases_in]));
1451         CeedCall(CeedRealloc(num_active_bases_in + 1, &(*data)->active_elem_rstrs_in));
1452         (*data)->active_elem_rstrs_in[num_active_bases_in] = NULL;
1453         CeedCall(CeedOperatorFieldGetElemRestriction(op_fields[i], &elem_rstr_in));
1454         CeedCall(CeedElemRestrictionReferenceCopy(elem_rstr_in, &(*data)->active_elem_rstrs_in[num_active_bases_in]));
1455         CeedCall(CeedElemRestrictionDestroy(&elem_rstr_in));
1456         CeedCall(CeedRealloc(num_active_bases_in + 1, &num_eval_modes_in));
1457         num_eval_modes_in[index] = 0;
1458         CeedCall(CeedRealloc(num_active_bases_in + 1, &eval_modes_in));
1459         eval_modes_in[index] = NULL;
1460         CeedCall(CeedRealloc(num_active_bases_in + 1, &eval_mode_offsets_in));
1461         eval_mode_offsets_in[index] = NULL;
1462         CeedCall(CeedRealloc(num_active_bases_in + 1, &(*data)->assembled_bases_in));
1463         (*data)->assembled_bases_in[index] = NULL;
1464         num_active_bases_in++;
1465       }
1466       if (eval_mode != CEED_EVAL_WEIGHT) {
1467         // q_comp = 1 if CEED_EVAL_NONE, CEED_EVAL_WEIGHT caught by QF Assembly
1468         CeedCall(CeedRealloc(num_eval_modes_in[index] + q_comp, &eval_modes_in[index]));
1469         CeedCall(CeedRealloc(num_eval_modes_in[index] + q_comp, &eval_mode_offsets_in[index]));
1470         for (CeedInt d = 0; d < q_comp; d++) {
1471           eval_modes_in[index][num_eval_modes_in[index] + d]        = eval_mode;
1472           eval_mode_offsets_in[index][num_eval_modes_in[index] + d] = offset;
1473           offset += num_comp;
1474         }
1475         num_eval_modes_in[index] += q_comp;
1476       }
1477       CeedCall(CeedBasisDestroy(&basis_in));
1478     }
1479     CeedCall(CeedVectorDestroy(&vec));
1480   }
1481 
1482   // Determine active output basis
1483   CeedCall(CeedQFunctionGetFields(qf, NULL, NULL, &num_output_fields, &qf_fields));
1484   CeedCall(CeedOperatorGetFields(op, NULL, NULL, NULL, &op_fields));
1485   offset = 0;
1486   for (CeedInt i = 0; i < num_output_fields; i++) {
1487     CeedVector vec;
1488 
1489     CeedCall(CeedOperatorFieldGetVector(op_fields[i], &vec));
1490     if (vec == CEED_VECTOR_ACTIVE) {
1491       CeedInt      index = -1, num_comp, q_comp;
1492       CeedEvalMode eval_mode;
1493       CeedBasis    basis_out = NULL;
1494 
1495       CeedCall(CeedOperatorFieldGetBasis(op_fields[i], &basis_out));
1496       CeedCall(CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode));
1497       CeedCall(CeedBasisGetNumComponents(basis_out, &num_comp));
1498       CeedCall(CeedBasisGetNumQuadratureComponents(basis_out, eval_mode, &q_comp));
1499       for (CeedInt i = 0; i < num_active_bases_out; i++) {
1500         if ((*data)->active_bases_out[i] == basis_out) index = i;
1501       }
1502       if (index == -1) {
1503         CeedElemRestriction elem_rstr_out;
1504 
1505         index = num_active_bases_out;
1506         CeedCall(CeedRealloc(num_active_bases_out + 1, &(*data)->active_bases_out));
1507         (*data)->active_bases_out[num_active_bases_out] = NULL;
1508         CeedCall(CeedBasisReferenceCopy(basis_out, &(*data)->active_bases_out[num_active_bases_out]));
1509         CeedCall(CeedRealloc(num_active_bases_out + 1, &(*data)->active_elem_rstrs_out));
1510         (*data)->active_elem_rstrs_out[num_active_bases_out] = NULL;
1511         CeedCall(CeedOperatorFieldGetElemRestriction(op_fields[i], &elem_rstr_out));
1512         CeedCall(CeedElemRestrictionReferenceCopy(elem_rstr_out, &(*data)->active_elem_rstrs_out[num_active_bases_out]));
1513         CeedCall(CeedElemRestrictionDestroy(&elem_rstr_out));
1514         CeedCall(CeedRealloc(num_active_bases_out + 1, &num_eval_modes_out));
1515         num_eval_modes_out[index] = 0;
1516         CeedCall(CeedRealloc(num_active_bases_out + 1, &eval_modes_out));
1517         eval_modes_out[index] = NULL;
1518         CeedCall(CeedRealloc(num_active_bases_out + 1, &eval_mode_offsets_out));
1519         eval_mode_offsets_out[index] = NULL;
1520         CeedCall(CeedRealloc(num_active_bases_out + 1, &(*data)->assembled_bases_out));
1521         (*data)->assembled_bases_out[index] = NULL;
1522         num_active_bases_out++;
1523       }
1524       if (eval_mode != CEED_EVAL_WEIGHT) {
1525         // q_comp = 1 if CEED_EVAL_NONE, CEED_EVAL_WEIGHT caught by QF Assembly
1526         CeedCall(CeedRealloc(num_eval_modes_out[index] + q_comp, &eval_modes_out[index]));
1527         CeedCall(CeedRealloc(num_eval_modes_out[index] + q_comp, &eval_mode_offsets_out[index]));
1528         for (CeedInt d = 0; d < q_comp; d++) {
1529           eval_modes_out[index][num_eval_modes_out[index] + d]        = eval_mode;
1530           eval_mode_offsets_out[index][num_eval_modes_out[index] + d] = offset;
1531           offset += num_comp;
1532         }
1533         num_eval_modes_out[index] += q_comp;
1534       }
1535       CeedCall(CeedBasisDestroy(&basis_out));
1536     }
1537     CeedCall(CeedVectorDestroy(&vec));
1538   }
1539   CeedCall(CeedQFunctionDestroy(&qf));
1540   (*data)->num_active_bases_in   = num_active_bases_in;
1541   (*data)->num_eval_modes_in     = num_eval_modes_in;
1542   (*data)->eval_modes_in         = eval_modes_in;
1543   (*data)->eval_mode_offsets_in  = eval_mode_offsets_in;
1544   (*data)->num_active_bases_out  = num_active_bases_out;
1545   (*data)->num_eval_modes_out    = num_eval_modes_out;
1546   (*data)->eval_modes_out        = eval_modes_out;
1547   (*data)->eval_mode_offsets_out = eval_mode_offsets_out;
1548   (*data)->num_output_components = offset;
1549   return CEED_ERROR_SUCCESS;
1550 }
1551 
1552 /**
1553   @brief Get `CeedOperator` @ref CeedEvalMode for assembly.
1554 
1555   Note: See @ref CeedOperatorAssemblyDataCreate() for a full description of the data stored in this object.
1556 
1557   @param[in]  data                  `CeedOperatorAssemblyData`
1558   @param[out] num_active_bases_in   Total number of active bases for input
1559   @param[out] num_eval_modes_in     Pointer to hold array of numbers of input @ref CeedEvalMode, or `NULL`.
1560                                       `eval_modes_in[0]` holds an array of eval modes for the first active `CeedBasis`.
1561   @param[out] eval_modes_in         Pointer to hold arrays of input @ref CeedEvalMode, or `NULL`
1562   @param[out] eval_mode_offsets_in  Pointer to hold arrays of input offsets at each quadrature point
1563   @param[out] num_active_bases_out  Total number of active bases for output
1564   @param[out] num_eval_modes_out    Pointer to hold array of numbers of output @ref CeedEvalMode, or `NULL`
1565   @param[out] eval_modes_out        Pointer to hold arrays of output @ref CeedEvalMode, or `NULL`
1566   @param[out] eval_mode_offsets_out Pointer to hold arrays of output offsets at each quadrature point
1567   @param[out] num_output_components The number of columns in the assembled `CeedQFunction` matrix for each quadrature point, including contributions of all active bases
1568 
1569   @return An error code: 0 - success, otherwise - failure
1570 
1571   @ref Backend
1572 **/
1573 int CeedOperatorAssemblyDataGetEvalModes(CeedOperatorAssemblyData data, CeedInt *num_active_bases_in, CeedInt **num_eval_modes_in,
1574                                          const CeedEvalMode ***eval_modes_in, CeedSize ***eval_mode_offsets_in, CeedInt *num_active_bases_out,
1575                                          CeedInt **num_eval_modes_out, const CeedEvalMode ***eval_modes_out, CeedSize ***eval_mode_offsets_out,
1576                                          CeedSize *num_output_components) {
1577   if (num_active_bases_in) *num_active_bases_in = data->num_active_bases_in;
1578   if (num_eval_modes_in) *num_eval_modes_in = data->num_eval_modes_in;
1579   if (eval_modes_in) *eval_modes_in = (const CeedEvalMode **)data->eval_modes_in;
1580   if (eval_mode_offsets_in) *eval_mode_offsets_in = data->eval_mode_offsets_in;
1581   if (num_active_bases_out) *num_active_bases_out = data->num_active_bases_out;
1582   if (num_eval_modes_out) *num_eval_modes_out = data->num_eval_modes_out;
1583   if (eval_modes_out) *eval_modes_out = (const CeedEvalMode **)data->eval_modes_out;
1584   if (eval_mode_offsets_out) *eval_mode_offsets_out = data->eval_mode_offsets_out;
1585   if (num_output_components) *num_output_components = data->num_output_components;
1586   return CEED_ERROR_SUCCESS;
1587 }
1588 
1589 /**
1590   @brief Get `CeedOperator` `CeedBasis` data for assembly.
1591 
1592   Note: See @ref CeedOperatorAssemblyDataCreate() for a full description of the data stored in this object.
1593 
1594   @param[in]  data                 `CeedOperatorAssemblyData`
1595   @param[out] num_active_bases_in  Number of active input bases, or `NULL`
1596   @param[out] active_bases_in      Pointer to hold active input `CeedBasis`, or `NULL`
1597   @param[out] assembled_bases_in   Pointer to hold assembled active input `B` , or `NULL`
1598   @param[out] num_active_bases_out Number of active output bases, or `NULL`
1599   @param[out] active_bases_out     Pointer to hold active output `CeedBasis`, or `NULL`
1600   @param[out] assembled_bases_out  Pointer to hold assembled active output `B` , or `NULL`
1601 
1602   @return An error code: 0 - success, otherwise - failure
1603 
1604   @ref Backend
1605 **/
1606 int CeedOperatorAssemblyDataGetBases(CeedOperatorAssemblyData data, CeedInt *num_active_bases_in, CeedBasis **active_bases_in,
1607                                      const CeedScalar ***assembled_bases_in, CeedInt *num_active_bases_out, CeedBasis **active_bases_out,
1608                                      const CeedScalar ***assembled_bases_out) {
1609   // Assemble B_in, B_out if needed
1610   if (assembled_bases_in && !data->assembled_bases_in[0]) {
1611     CeedInt num_qpts;
1612 
1613     if (data->active_bases_in[0] == CEED_BASIS_NONE) CeedCall(CeedElemRestrictionGetElementSize(data->active_elem_rstrs_in[0], &num_qpts));
1614     else CeedCall(CeedBasisGetNumQuadraturePoints(data->active_bases_in[0], &num_qpts));
1615     for (CeedInt b = 0; b < data->num_active_bases_in; b++) {
1616       bool        has_eval_none = false;
1617       CeedInt     num_nodes;
1618       CeedScalar *B_in = NULL, *identity = NULL;
1619 
1620       CeedCall(CeedElemRestrictionGetElementSize(data->active_elem_rstrs_in[b], &num_nodes));
1621       CeedCall(CeedCalloc(num_qpts * num_nodes * data->num_eval_modes_in[b], &B_in));
1622 
1623       for (CeedInt i = 0; i < data->num_eval_modes_in[b]; i++) {
1624         has_eval_none = has_eval_none || (data->eval_modes_in[b][i] == CEED_EVAL_NONE);
1625       }
1626       if (has_eval_none) {
1627         CeedCall(CeedCalloc(num_qpts * num_nodes, &identity));
1628         for (CeedInt i = 0; i < (num_nodes < num_qpts ? num_nodes : num_qpts); i++) {
1629           identity[i * num_nodes + i] = 1.0;
1630         }
1631       }
1632 
1633       for (CeedInt q = 0; q < num_qpts; q++) {
1634         for (CeedInt n = 0; n < num_nodes; n++) {
1635           CeedInt      d_in              = 0, q_comp_in;
1636           CeedEvalMode eval_mode_in_prev = CEED_EVAL_NONE;
1637 
1638           for (CeedInt e_in = 0; e_in < data->num_eval_modes_in[b]; e_in++) {
1639             const CeedInt     qq = data->num_eval_modes_in[b] * q;
1640             const CeedScalar *B  = NULL;
1641 
1642             CeedCall(CeedOperatorGetBasisPointer(data->active_bases_in[b], data->eval_modes_in[b][e_in], identity, &B));
1643             CeedCall(CeedBasisGetNumQuadratureComponents(data->active_bases_in[b], data->eval_modes_in[b][e_in], &q_comp_in));
1644             if (q_comp_in > 1) {
1645               if (e_in == 0 || data->eval_modes_in[b][e_in] != eval_mode_in_prev) d_in = 0;
1646               else B = &B[(++d_in) * num_qpts * num_nodes];
1647             }
1648             eval_mode_in_prev                 = data->eval_modes_in[b][e_in];
1649             B_in[(qq + e_in) * num_nodes + n] = B[q * num_nodes + n];
1650           }
1651         }
1652       }
1653       if (identity) CeedCall(CeedFree(&identity));
1654       data->assembled_bases_in[b] = B_in;
1655     }
1656   }
1657 
1658   if (assembled_bases_out && !data->assembled_bases_out[0]) {
1659     CeedInt num_qpts;
1660 
1661     if (data->active_bases_out[0] == CEED_BASIS_NONE) CeedCall(CeedElemRestrictionGetElementSize(data->active_elem_rstrs_out[0], &num_qpts));
1662     else CeedCall(CeedBasisGetNumQuadraturePoints(data->active_bases_out[0], &num_qpts));
1663     for (CeedInt b = 0; b < data->num_active_bases_out; b++) {
1664       bool        has_eval_none = false;
1665       CeedInt     num_nodes;
1666       CeedScalar *B_out = NULL, *identity = NULL;
1667 
1668       CeedCall(CeedElemRestrictionGetElementSize(data->active_elem_rstrs_out[b], &num_nodes));
1669       CeedCall(CeedCalloc(num_qpts * num_nodes * data->num_eval_modes_out[b], &B_out));
1670 
1671       for (CeedInt i = 0; i < data->num_eval_modes_out[b]; i++) {
1672         has_eval_none = has_eval_none || (data->eval_modes_out[b][i] == CEED_EVAL_NONE);
1673       }
1674       if (has_eval_none) {
1675         CeedCall(CeedCalloc(num_qpts * num_nodes, &identity));
1676         for (CeedInt i = 0; i < (num_nodes < num_qpts ? num_nodes : num_qpts); i++) {
1677           identity[i * num_nodes + i] = 1.0;
1678         }
1679       }
1680 
1681       for (CeedInt q = 0; q < num_qpts; q++) {
1682         for (CeedInt n = 0; n < num_nodes; n++) {
1683           CeedInt      d_out              = 0, q_comp_out;
1684           CeedEvalMode eval_mode_out_prev = CEED_EVAL_NONE;
1685 
1686           for (CeedInt e_out = 0; e_out < data->num_eval_modes_out[b]; e_out++) {
1687             const CeedInt     qq = data->num_eval_modes_out[b] * q;
1688             const CeedScalar *B  = NULL;
1689 
1690             CeedCall(CeedOperatorGetBasisPointer(data->active_bases_out[b], data->eval_modes_out[b][e_out], identity, &B));
1691             CeedCall(CeedBasisGetNumQuadratureComponents(data->active_bases_out[b], data->eval_modes_out[b][e_out], &q_comp_out));
1692             if (q_comp_out > 1) {
1693               if (e_out == 0 || data->eval_modes_out[b][e_out] != eval_mode_out_prev) d_out = 0;
1694               else B = &B[(++d_out) * num_qpts * num_nodes];
1695             }
1696             eval_mode_out_prev                  = data->eval_modes_out[b][e_out];
1697             B_out[(qq + e_out) * num_nodes + n] = B[q * num_nodes + n];
1698           }
1699         }
1700       }
1701       if (identity) CeedCall(CeedFree(&identity));
1702       data->assembled_bases_out[b] = B_out;
1703     }
1704   }
1705 
1706   // Pass out assembled data
1707   if (num_active_bases_in) *num_active_bases_in = data->num_active_bases_in;
1708   if (active_bases_in) *active_bases_in = data->active_bases_in;
1709   if (assembled_bases_in) *assembled_bases_in = (const CeedScalar **)data->assembled_bases_in;
1710   if (num_active_bases_out) *num_active_bases_out = data->num_active_bases_out;
1711   if (active_bases_out) *active_bases_out = data->active_bases_out;
1712   if (assembled_bases_out) *assembled_bases_out = (const CeedScalar **)data->assembled_bases_out;
1713   return CEED_ERROR_SUCCESS;
1714 }
1715 
1716 /**
1717   @brief Get `CeedOperator` `CeedBasis` data for assembly.
1718 
1719   Note: See @ref CeedOperatorAssemblyDataCreate() for a full description of the data stored in this object.
1720 
1721   @param[in]  data                      `CeedOperatorAssemblyData`
1722   @param[out] num_active_elem_rstrs_in  Number of active input element restrictions, or `NULL`
1723   @param[out] active_elem_rstrs_in      Pointer to hold active input `CeedElemRestriction`, or `NULL`
1724   @param[out] num_active_elem_rstrs_out Number of active output element restrictions, or `NULL`
1725   @param[out] active_elem_rstrs_out     Pointer to hold active output `CeedElemRestriction`, or `NULL`
1726 
1727   @return An error code: 0 - success, otherwise - failure
1728 
1729   @ref Backend
1730 **/
1731 int CeedOperatorAssemblyDataGetElemRestrictions(CeedOperatorAssemblyData data, CeedInt *num_active_elem_rstrs_in,
1732                                                 CeedElemRestriction **active_elem_rstrs_in, CeedInt *num_active_elem_rstrs_out,
1733                                                 CeedElemRestriction **active_elem_rstrs_out) {
1734   if (num_active_elem_rstrs_in) *num_active_elem_rstrs_in = data->num_active_bases_in;
1735   if (active_elem_rstrs_in) *active_elem_rstrs_in = data->active_elem_rstrs_in;
1736   if (num_active_elem_rstrs_out) *num_active_elem_rstrs_out = data->num_active_bases_out;
1737   if (active_elem_rstrs_out) *active_elem_rstrs_out = data->active_elem_rstrs_out;
1738   return CEED_ERROR_SUCCESS;
1739 }
1740 
1741 /**
1742   @brief Destroy `CeedOperatorAssemblyData`
1743 
1744   @param[in,out] data `CeedOperatorAssemblyData` to destroy
1745 
1746   @return An error code: 0 - success, otherwise - failure
1747 
1748   @ref Backend
1749 **/
1750 int CeedOperatorAssemblyDataDestroy(CeedOperatorAssemblyData *data) {
1751   if (!*data) {
1752     *data = NULL;
1753     return CEED_ERROR_SUCCESS;
1754   }
1755   CeedCall(CeedDestroy(&(*data)->ceed));
1756   for (CeedInt b = 0; b < (*data)->num_active_bases_in; b++) {
1757     CeedCall(CeedBasisDestroy(&(*data)->active_bases_in[b]));
1758     CeedCall(CeedElemRestrictionDestroy(&(*data)->active_elem_rstrs_in[b]));
1759     CeedCall(CeedFree(&(*data)->eval_modes_in[b]));
1760     CeedCall(CeedFree(&(*data)->eval_mode_offsets_in[b]));
1761     CeedCall(CeedFree(&(*data)->assembled_bases_in[b]));
1762   }
1763   for (CeedInt b = 0; b < (*data)->num_active_bases_out; b++) {
1764     CeedCall(CeedBasisDestroy(&(*data)->active_bases_out[b]));
1765     CeedCall(CeedElemRestrictionDestroy(&(*data)->active_elem_rstrs_out[b]));
1766     CeedCall(CeedFree(&(*data)->eval_modes_out[b]));
1767     CeedCall(CeedFree(&(*data)->eval_mode_offsets_out[b]));
1768     CeedCall(CeedFree(&(*data)->assembled_bases_out[b]));
1769   }
1770   CeedCall(CeedFree(&(*data)->active_bases_in));
1771   CeedCall(CeedFree(&(*data)->active_bases_out));
1772   CeedCall(CeedFree(&(*data)->active_elem_rstrs_in));
1773   CeedCall(CeedFree(&(*data)->active_elem_rstrs_out));
1774   CeedCall(CeedFree(&(*data)->num_eval_modes_in));
1775   CeedCall(CeedFree(&(*data)->num_eval_modes_out));
1776   CeedCall(CeedFree(&(*data)->eval_modes_in));
1777   CeedCall(CeedFree(&(*data)->eval_modes_out));
1778   CeedCall(CeedFree(&(*data)->eval_mode_offsets_in));
1779   CeedCall(CeedFree(&(*data)->eval_mode_offsets_out));
1780   CeedCall(CeedFree(&(*data)->assembled_bases_in));
1781   CeedCall(CeedFree(&(*data)->assembled_bases_out));
1782 
1783   CeedCall(CeedFree(data));
1784   return CEED_ERROR_SUCCESS;
1785 }
1786 
1787 /**
1788   @brief Retrieve fallback `CeedOperator` with a reference `Ceed` for advanced `CeedOperator` functionality
1789 
1790   @param[in]  op          `CeedOperator` to retrieve fallback for
1791   @param[out] op_fallback Fallback `CeedOperator`
1792 
1793   @return An error code: 0 - success, otherwise - failure
1794 
1795   @ref Backend
1796 **/
1797 int CeedOperatorGetFallback(CeedOperator op, CeedOperator *op_fallback) {
1798   // Create if needed
1799   if (!op->op_fallback) CeedCall(CeedOperatorCreateFallback(op));
1800   if (op->op_fallback) {
1801     bool is_debug;
1802     Ceed ceed;
1803 
1804     CeedCall(CeedOperatorGetCeed(op, &ceed));
1805     CeedCall(CeedIsDebug(ceed, &is_debug));
1806     if (is_debug) {
1807       Ceed        ceed_fallback;
1808       const char *resource, *resource_fallback;
1809 
1810       CeedCall(CeedGetOperatorFallbackCeed(ceed, &ceed_fallback));
1811       CeedCall(CeedGetResource(ceed, &resource));
1812       CeedCall(CeedGetResource(ceed_fallback, &resource_fallback));
1813 
1814       CeedDebug256(ceed, CEED_DEBUG_COLOR_SUCCESS, "---------- CeedOperator Fallback ----------\n");
1815       CeedDebug(ceed, "Falling back from %s operator at address %p to %s operator at address %p\n", resource, op, resource_fallback, op->op_fallback);
1816       CeedCall(CeedDestroy(&ceed_fallback));
1817     }
1818     CeedCall(CeedDestroy(&ceed));
1819   }
1820   *op_fallback = op->op_fallback;
1821   return CEED_ERROR_SUCCESS;
1822 }
1823 
1824 /**
1825   @brief Get the parent `CeedOperator` for a fallback `CeedOperator`
1826 
1827   @param[in]  op     `CeedOperator` context
1828   @param[out] parent Variable to store parent `CeedOperator` context
1829 
1830   @return An error code: 0 - success, otherwise - failure
1831 
1832   @ref Backend
1833 **/
1834 int CeedOperatorGetFallbackParent(CeedOperator op, CeedOperator *parent) {
1835   *parent = op->op_fallback_parent ? op->op_fallback_parent : NULL;
1836   return CEED_ERROR_SUCCESS;
1837 }
1838 
1839 /**
1840   @brief Get the `Ceed` context of the parent `CeedOperator` for a fallback `CeedOperator`
1841 
1842   @param[in]  op     `CeedOperator` context
1843   @param[out] parent Variable to store parent `Ceed` context
1844 
1845   @return An error code: 0 - success, otherwise - failure
1846 
1847   @ref Backend
1848 **/
1849 int CeedOperatorGetFallbackParentCeed(CeedOperator op, Ceed *parent) {
1850   *parent = NULL;
1851   if (op->op_fallback_parent) CeedCall(CeedReferenceCopy(op->op_fallback_parent->ceed, parent));
1852   else CeedCall(CeedReferenceCopy(CeedOperatorReturnCeed(op), parent));
1853   return CEED_ERROR_SUCCESS;
1854 }
1855 
1856 /// @}
1857 
1858 /// ----------------------------------------------------------------------------
1859 /// CeedOperator Public API
1860 /// ----------------------------------------------------------------------------
1861 /// @addtogroup CeedOperatorUser
1862 /// @{
1863 
1864 /**
1865   @brief Assemble a linear `CeedQFunction` associated with a `CeedOperator`.
1866 
1867   This returns a `CeedVector` containing a matrix at each quadrature point providing the action of the `CeedQFunction` associated with the `CeedOperator`.
1868   The vector `assembled` is of shape `[num_elements, num_input_fields, num_output_fields, num_quad_points]` and contains column-major matrices representing the action of the `CeedQFunction` for a corresponding quadrature point on an element.
1869 
1870   Inputs and outputs are in the order provided by the user when adding `CeedOperator` fields.
1871   For example, a `CeedQFunction` with inputs `u` and `gradu` and outputs `gradv` and `v` , provided in that order, would result in an assembled `CeedQFunction` that consists of `(1 + dim) x (dim + 1)` matrices at each quadrature point acting on the input ` [u, du_0, du_1]` and producing the output `[dv_0, dv_1, v]`.
1872 
1873   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
1874 
1875   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
1876   @param[out] assembled `CeedVector` to store assembled `CeedQFunction` at quadrature points
1877   @param[out] rstr      `CeedElemRestriction` for `CeedVector` containing assembled `CeedQFunction`
1878   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
1879 
1880   @return An error code: 0 - success, otherwise - failure
1881 
1882   @ref User
1883 **/
1884 int CeedOperatorLinearAssembleQFunction(CeedOperator op, CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
1885   CeedCall(CeedOperatorCheckReady(op));
1886 
1887   if (op->LinearAssembleQFunction) {
1888     // Backend version
1889     CeedCall(op->LinearAssembleQFunction(op, assembled, rstr, request));
1890   } else {
1891     // Operator fallback
1892     CeedOperator op_fallback;
1893 
1894     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
1895     if (op_fallback) CeedCall(CeedOperatorLinearAssembleQFunction(op_fallback, assembled, rstr, request));
1896     else return CeedError(CeedOperatorReturnCeed(op), CEED_ERROR_UNSUPPORTED, "Backend does not support CeedOperatorLinearAssembleQFunction");
1897   }
1898   return CEED_ERROR_SUCCESS;
1899 }
1900 
1901 /**
1902   @brief Assemble `CeedQFunction` and store result internally.
1903 
1904   Return copied references of stored data to the caller.
1905   Caller is responsible for ownership and destruction of the copied references.
1906   See also @ref CeedOperatorLinearAssembleQFunction().
1907 
1908   Note: If the value of `assembled` or `rstr` passed to this function are non-`NULL` , then it is assumed that they hold valid pointers.
1909         These objects will be destroyed if `*assembled` or `*rstr` is the only reference to the object.
1910 
1911   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
1912   @param[out] assembled `CeedVector` to store assembled `CeedQFunction` at quadrature points
1913   @param[out] rstr      `CeedElemRestriction` for `CeedVector` containing assembled `CeedQFunction`
1914   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
1915 
1916   @return An error code: 0 - success, otherwise - failure
1917 
1918   @ref User
1919 **/
1920 int CeedOperatorLinearAssembleQFunctionBuildOrUpdate(CeedOperator op, CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
1921   int (*LinearAssembleQFunctionUpdate)(CeedOperator, CeedVector, CeedElemRestriction, CeedRequest *) = NULL;
1922   CeedOperator op_assemble                                                                           = NULL;
1923   CeedOperator op_fallback_parent                                                                    = NULL;
1924 
1925   CeedCall(CeedOperatorCheckReady(op));
1926 
1927   // Determine if fallback parent or operator has implementation
1928   CeedCall(CeedOperatorGetFallbackParent(op, &op_fallback_parent));
1929   if (op_fallback_parent && op_fallback_parent->LinearAssembleQFunctionUpdate) {
1930     // -- Backend version for op fallback parent is faster, if it exists
1931     LinearAssembleQFunctionUpdate = op_fallback_parent->LinearAssembleQFunctionUpdate;
1932     op_assemble                   = op_fallback_parent;
1933   } else if (op->LinearAssembleQFunctionUpdate) {
1934     // -- Backend version for op
1935     LinearAssembleQFunctionUpdate = op->LinearAssembleQFunctionUpdate;
1936     op_assemble                   = op;
1937   }
1938 
1939   // Assemble QFunction
1940   if (LinearAssembleQFunctionUpdate) {
1941     // Backend or fallback parent version
1942     CeedQFunctionAssemblyData data;
1943     bool                      data_is_setup;
1944     CeedVector                assembled_vec  = NULL;
1945     CeedElemRestriction       assembled_rstr = NULL;
1946 
1947     CeedCall(CeedOperatorGetQFunctionAssemblyData(op, &data));
1948     CeedCall(CeedQFunctionAssemblyDataIsSetup(data, &data_is_setup));
1949     if (data_is_setup) {
1950       bool update_needed;
1951 
1952       CeedCall(CeedQFunctionAssemblyDataGetObjects(data, &assembled_vec, &assembled_rstr));
1953       CeedCall(CeedQFunctionAssemblyDataIsUpdateNeeded(data, &update_needed));
1954       if (update_needed) CeedCall(LinearAssembleQFunctionUpdate(op_assemble, assembled_vec, assembled_rstr, request));
1955     } else {
1956       CeedCall(CeedOperatorLinearAssembleQFunction(op_assemble, &assembled_vec, &assembled_rstr, request));
1957       CeedCall(CeedQFunctionAssemblyDataSetObjects(data, assembled_vec, assembled_rstr));
1958     }
1959     CeedCall(CeedQFunctionAssemblyDataSetUpdateNeeded(data, false));
1960 
1961     // Copy reference from internally held copy
1962     CeedCall(CeedVectorReferenceCopy(assembled_vec, assembled));
1963     CeedCall(CeedElemRestrictionReferenceCopy(assembled_rstr, rstr));
1964     CeedCall(CeedVectorDestroy(&assembled_vec));
1965     CeedCall(CeedElemRestrictionDestroy(&assembled_rstr));
1966   } else {
1967     // Operator fallback
1968     CeedOperator op_fallback;
1969 
1970     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
1971     if (op_fallback) CeedCall(CeedOperatorLinearAssembleQFunctionBuildOrUpdate(op_fallback, assembled, rstr, request));
1972     else return CeedError(CeedOperatorReturnCeed(op), CEED_ERROR_UNSUPPORTED, "Backend does not support CeedOperatorLinearAssembleQFunctionUpdate");
1973   }
1974   return CEED_ERROR_SUCCESS;
1975 }
1976 
1977 /**
1978   @brief Assemble the diagonal of a square linear `CeedOperator`
1979 
1980   This overwrites a `CeedVector` with the diagonal of a linear `CeedOperator`.
1981 
1982   Note: Currently only non-composite `CeedOperator` with a single field and composite `CeedOperator` with single field sub-operators are supported.
1983 
1984   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
1985 
1986   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
1987   @param[out] assembled `CeedVector` to store assembled `CeedOperator` diagonal
1988   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
1989 
1990   @return An error code: 0 - success, otherwise - failure
1991 
1992   @ref User
1993 **/
1994 int CeedOperatorLinearAssembleDiagonal(CeedOperator op, CeedVector assembled, CeedRequest *request) {
1995   bool     is_composite;
1996   CeedSize input_size = 0, output_size = 0;
1997 
1998   CeedCall(CeedOperatorCheckReady(op));
1999   CeedCall(CeedOperatorIsComposite(op, &is_composite));
2000 
2001   CeedCall(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
2002   CeedCheck(input_size == output_size, CeedOperatorReturnCeed(op), CEED_ERROR_DIMENSION, "Operator must be square");
2003 
2004   // Early exit for empty operator
2005   if (!is_composite) {
2006     CeedInt num_elem = 0;
2007 
2008     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
2009     if (num_elem == 0) return CEED_ERROR_SUCCESS;
2010   }
2011 
2012   if (op->LinearAssembleDiagonal) {
2013     // Backend version
2014     CeedCall(op->LinearAssembleDiagonal(op, assembled, request));
2015     return CEED_ERROR_SUCCESS;
2016   } else if (op->LinearAssembleAddDiagonal) {
2017     // Backend version with zeroing first
2018     CeedCall(CeedVectorSetValue(assembled, 0.0));
2019     CeedCall(op->LinearAssembleAddDiagonal(op, assembled, request));
2020     return CEED_ERROR_SUCCESS;
2021   } else {
2022     // Operator fallback
2023     CeedOperator op_fallback;
2024 
2025     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
2026     if (op_fallback) {
2027       CeedCall(CeedOperatorLinearAssembleDiagonal(op_fallback, assembled, request));
2028       return CEED_ERROR_SUCCESS;
2029     }
2030   }
2031   // Default interface implementation
2032   CeedCall(CeedVectorSetValue(assembled, 0.0));
2033   CeedCall(CeedOperatorLinearAssembleAddDiagonal(op, assembled, request));
2034   return CEED_ERROR_SUCCESS;
2035 }
2036 
2037 /**
2038   @brief Assemble the diagonal of a square linear `CeedOperator`.
2039 
2040   This sums into a `CeedVector` the diagonal of a linear `CeedOperator`.
2041 
2042   Note: Currently only non-composite `CeedOperator` with a single field and composite `CeedOperator` with single field sub-operators are supported.
2043 
2044   Note: Calling this function asserts that setup is complete and sets the CeedOperator as immutable.
2045 
2046   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
2047   @param[out] assembled `CeedVector` to store assembled `CeedOperator` diagonal
2048   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
2049 
2050   @return An error code: 0 - success, otherwise - failure
2051 
2052   @ref User
2053 **/
2054 int CeedOperatorLinearAssembleAddDiagonal(CeedOperator op, CeedVector assembled, CeedRequest *request) {
2055   bool     is_composite;
2056   CeedSize input_size = 0, output_size = 0;
2057 
2058   CeedCall(CeedOperatorCheckReady(op));
2059   CeedCall(CeedOperatorIsComposite(op, &is_composite));
2060 
2061   CeedCall(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
2062   CeedCheck(input_size == output_size, CeedOperatorReturnCeed(op), CEED_ERROR_DIMENSION, "Operator must be square");
2063 
2064   // Early exit for empty operator
2065   if (!is_composite) {
2066     CeedInt num_elem = 0;
2067 
2068     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
2069     if (num_elem == 0) return CEED_ERROR_SUCCESS;
2070   }
2071 
2072   if (op->LinearAssembleAddDiagonal) {
2073     // Backend version
2074     CeedCall(op->LinearAssembleAddDiagonal(op, assembled, request));
2075     return CEED_ERROR_SUCCESS;
2076   } else {
2077     // Operator fallback
2078     CeedOperator op_fallback;
2079 
2080     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
2081     if (op_fallback) {
2082       CeedCall(CeedOperatorLinearAssembleAddDiagonal(op_fallback, assembled, request));
2083       return CEED_ERROR_SUCCESS;
2084     }
2085   }
2086   // Default interface implementation
2087   if (is_composite) {
2088     CeedCall(CeedCompositeOperatorLinearAssembleAddDiagonal(op, request, false, assembled));
2089   } else {
2090     CeedCall(CeedSingleOperatorLinearAssembleAddDiagonal(op, request, false, assembled));
2091   }
2092   return CEED_ERROR_SUCCESS;
2093 }
2094 
2095 /**
2096    @brief Fully assemble the point-block diagonal pattern of a linear `CeedOperator`.
2097 
2098    Expected to be used in conjunction with @ref CeedOperatorLinearAssemblePointBlockDiagonal().
2099 
2100    The assembly routines use coordinate format, with `num_entries` tuples of the form `(i, j, value)` which indicate that value should be added to the matrix in entry `(i, j)`.
2101    Note that the `(i, j)` pairs are unique.
2102    This function returns the number of entries and their `(i, j)` locations, while @ref CeedOperatorLinearAssemblePointBlockDiagonal() provides the values in the same ordering.
2103 
2104    This will generally be slow unless your operator is low-order.
2105 
2106    Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2107 
2108    @param[in]  op          `CeedOperator` to assemble
2109    @param[out] num_entries Number of entries in coordinate nonzero pattern
2110    @param[out] rows        Row number for each entry
2111    @param[out] cols        Column number for each entry
2112 
2113    @ref User
2114 **/
2115 int CeedOperatorLinearAssemblePointBlockDiagonalSymbolic(CeedOperator op, CeedSize *num_entries, CeedInt **rows, CeedInt **cols) {
2116   bool          is_composite;
2117   CeedInt       num_active_components, num_sub_operators;
2118   CeedOperator *sub_operators;
2119 
2120   CeedCall(CeedOperatorIsComposite(op, &is_composite));
2121 
2122   CeedSize input_size = 0, output_size = 0;
2123   CeedCall(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
2124   CeedCheck(input_size == output_size, CeedOperatorReturnCeed(op), CEED_ERROR_DIMENSION, "Operator must be square");
2125 
2126   if (is_composite) {
2127     CeedCall(CeedCompositeOperatorGetNumSub(op, &num_sub_operators));
2128     CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
2129   } else {
2130     sub_operators     = &op;
2131     num_sub_operators = 1;
2132   }
2133 
2134   // Verify operator can be assembled correctly
2135   {
2136     CeedOperatorAssemblyData data;
2137     CeedInt                  num_active_elem_rstrs, comp_stride;
2138     CeedElemRestriction     *active_elem_rstrs;
2139 
2140     // Get initial values to check against
2141     CeedCall(CeedOperatorGetOperatorAssemblyData(sub_operators[0], &data));
2142     CeedCall(CeedOperatorAssemblyDataGetElemRestrictions(data, &num_active_elem_rstrs, &active_elem_rstrs, NULL, NULL));
2143     CeedCall(CeedElemRestrictionGetCompStride(active_elem_rstrs[0], &comp_stride));
2144     CeedCall(CeedElemRestrictionGetNumComponents(active_elem_rstrs[0], &num_active_components));
2145 
2146     // Verify that all active element restrictions have same component stride and number of components
2147     for (CeedInt k = 0; k < num_sub_operators; k++) {
2148       CeedCall(CeedOperatorGetOperatorAssemblyData(sub_operators[k], &data));
2149       CeedCall(CeedOperatorAssemblyDataGetElemRestrictions(data, &num_active_elem_rstrs, &active_elem_rstrs, NULL, NULL));
2150       for (CeedInt i = 0; i < num_active_elem_rstrs; i++) {
2151         CeedInt comp_stride_sub, num_active_components_sub;
2152 
2153         CeedCall(CeedElemRestrictionGetCompStride(active_elem_rstrs[i], &comp_stride_sub));
2154         CeedCheck(comp_stride == comp_stride_sub, CeedOperatorReturnCeed(op), CEED_ERROR_DIMENSION,
2155                   "Active element restrictions must have the same component stride: %d vs %d", comp_stride, comp_stride_sub);
2156         CeedCall(CeedElemRestrictionGetNumComponents(active_elem_rstrs[i], &num_active_components_sub));
2157         CeedCheck(num_active_components == num_active_components_sub, CeedOperatorReturnCeed(op), CEED_ERROR_INCOMPATIBLE,
2158                   "All suboperators must have the same number of output components."
2159                   " Previous: %" CeedInt_FMT " Current: %" CeedInt_FMT,
2160                   num_active_components, num_active_components_sub);
2161       }
2162     }
2163   }
2164   *num_entries = input_size * num_active_components;
2165   CeedCall(CeedCalloc(*num_entries, rows));
2166   CeedCall(CeedCalloc(*num_entries, cols));
2167 
2168   for (CeedInt o = 0; o < num_sub_operators; o++) {
2169     CeedElemRestriction active_elem_rstr, point_block_active_elem_rstr;
2170     CeedInt             comp_stride, num_elem, elem_size;
2171     const CeedInt      *offsets, *point_block_offsets;
2172 
2173     CeedCall(CeedOperatorGetActiveElemRestriction(sub_operators[o], &active_elem_rstr));
2174     CeedCall(CeedElemRestrictionGetCompStride(active_elem_rstr, &comp_stride));
2175     CeedCall(CeedElemRestrictionGetNumElements(active_elem_rstr, &num_elem));
2176     CeedCall(CeedElemRestrictionGetElementSize(active_elem_rstr, &elem_size));
2177     CeedCall(CeedElemRestrictionGetOffsets(active_elem_rstr, CEED_MEM_HOST, &offsets));
2178 
2179     CeedCall(CeedOperatorCreateActivePointBlockRestriction(active_elem_rstr, &point_block_active_elem_rstr));
2180     CeedCall(CeedElemRestrictionGetOffsets(point_block_active_elem_rstr, CEED_MEM_HOST, &point_block_offsets));
2181 
2182     for (CeedSize i = 0; i < num_elem * elem_size; i++) {
2183       for (CeedInt c_out = 0; c_out < num_active_components; c_out++) {
2184         for (CeedInt c_in = 0; c_in < num_active_components; c_in++) {
2185           (*rows)[point_block_offsets[i] + c_out * num_active_components + c_in] = offsets[i] + c_out * comp_stride;
2186           (*cols)[point_block_offsets[i] + c_out * num_active_components + c_in] = offsets[i] + c_in * comp_stride;
2187         }
2188       }
2189     }
2190 
2191     CeedCall(CeedElemRestrictionRestoreOffsets(active_elem_rstr, &offsets));
2192     CeedCall(CeedElemRestrictionRestoreOffsets(point_block_active_elem_rstr, &point_block_offsets));
2193     CeedCall(CeedElemRestrictionDestroy(&active_elem_rstr));
2194     CeedCall(CeedElemRestrictionDestroy(&point_block_active_elem_rstr));
2195   }
2196   return CEED_ERROR_SUCCESS;
2197 }
2198 
2199 /**
2200   @brief Assemble the point block diagonal of a square linear `CeedOperator`.
2201 
2202   This overwrites a `CeedVector` with the point block diagonal of a linear `CeedOperator`.
2203 
2204   Note: Currently only non-composite `CeedOperator` with a single field and composite `CeedOperator` with single field sub-operators are supported.
2205 
2206   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2207 
2208   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
2209   @param[out] assembled `CeedVector` to store assembled `CeedOperator` point block diagonal, provided in row-major form with an `num_comp * num_comp` block at each node.
2210                           The dimensions of this vector are derived from the active vector for the `CeedOperator`.
2211                           The array has shape `[nodes, component out, component in]`.
2212   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
2213 
2214   @return An error code: 0 - success, otherwise - failure
2215 
2216   @ref User
2217 **/
2218 int CeedOperatorLinearAssemblePointBlockDiagonal(CeedOperator op, CeedVector assembled, CeedRequest *request) {
2219   bool     is_composite;
2220   CeedSize input_size = 0, output_size = 0;
2221 
2222   CeedCall(CeedOperatorCheckReady(op));
2223   CeedCall(CeedOperatorIsComposite(op, &is_composite));
2224 
2225   CeedCall(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
2226   CeedCheck(input_size == output_size, CeedOperatorReturnCeed(op), CEED_ERROR_DIMENSION, "Operator must be square");
2227 
2228   // Early exit for empty operator
2229   if (!is_composite) {
2230     CeedInt num_elem = 0;
2231 
2232     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
2233     if (num_elem == 0) return CEED_ERROR_SUCCESS;
2234   }
2235 
2236   if (op->LinearAssemblePointBlockDiagonal) {
2237     // Backend version
2238     CeedCall(op->LinearAssemblePointBlockDiagonal(op, assembled, request));
2239     return CEED_ERROR_SUCCESS;
2240   } else if (op->LinearAssembleAddPointBlockDiagonal) {
2241     // Backend version with zeroing first
2242     CeedCall(CeedVectorSetValue(assembled, 0.0));
2243     CeedCall(CeedOperatorLinearAssembleAddPointBlockDiagonal(op, assembled, request));
2244     return CEED_ERROR_SUCCESS;
2245   } else {
2246     // Operator fallback
2247     CeedOperator op_fallback;
2248 
2249     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
2250     if (op_fallback) {
2251       CeedCall(CeedOperatorLinearAssemblePointBlockDiagonal(op_fallback, assembled, request));
2252       return CEED_ERROR_SUCCESS;
2253     }
2254   }
2255   // Default interface implementation
2256   CeedCall(CeedVectorSetValue(assembled, 0.0));
2257   CeedCall(CeedOperatorLinearAssembleAddPointBlockDiagonal(op, assembled, request));
2258   return CEED_ERROR_SUCCESS;
2259 }
2260 
2261 /**
2262   @brief Assemble the point block diagonal of a square linear `CeedOperator`.
2263 
2264   This sums into a `CeedVector` with the point block diagonal of a linear `CeedOperator`.
2265 
2266   Note: Currently only non-composite `CeedOperator` with a single field and composite `CeedOperator` with single field sub-operators are supported.
2267 
2268   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2269 
2270   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
2271   @param[out] assembled `CeedVector` to store assembled CeedOperator point block diagonal, provided in row-major form with an `num_comp * num_comp` block at each node.
2272                           The dimensions of this vector are derived from the active vector for the `CeedOperator`.
2273                           The array has shape `[nodes, component out, component in]`.
2274   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
2275 
2276   @return An error code: 0 - success, otherwise - failure
2277 
2278   @ref User
2279 **/
2280 int CeedOperatorLinearAssembleAddPointBlockDiagonal(CeedOperator op, CeedVector assembled, CeedRequest *request) {
2281   bool     is_composite;
2282   CeedSize input_size = 0, output_size = 0;
2283 
2284   CeedCall(CeedOperatorCheckReady(op));
2285   CeedCall(CeedOperatorIsComposite(op, &is_composite));
2286 
2287   CeedCall(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
2288   CeedCheck(input_size == output_size, CeedOperatorReturnCeed(op), CEED_ERROR_DIMENSION, "Operator must be square");
2289 
2290   // Early exit for empty operator
2291   if (!is_composite) {
2292     CeedInt num_elem = 0;
2293 
2294     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
2295     if (num_elem == 0) return CEED_ERROR_SUCCESS;
2296   }
2297 
2298   if (op->LinearAssembleAddPointBlockDiagonal) {
2299     // Backend version
2300     CeedCall(op->LinearAssembleAddPointBlockDiagonal(op, assembled, request));
2301     return CEED_ERROR_SUCCESS;
2302   } else {
2303     // Operator fallback
2304     CeedOperator op_fallback;
2305 
2306     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
2307     if (op_fallback) {
2308       CeedCall(CeedOperatorLinearAssembleAddPointBlockDiagonal(op_fallback, assembled, request));
2309       return CEED_ERROR_SUCCESS;
2310     }
2311   }
2312   // Default interface implementation
2313   if (is_composite) {
2314     CeedCall(CeedCompositeOperatorLinearAssembleAddDiagonal(op, request, true, assembled));
2315   } else {
2316     CeedCall(CeedSingleOperatorLinearAssembleAddDiagonal(op, request, true, assembled));
2317   }
2318   return CEED_ERROR_SUCCESS;
2319 }
2320 
2321 /**
2322    @brief Fully assemble the nonzero pattern of a linear `CeedOperator`.
2323 
2324    Expected to be used in conjunction with @ref CeedOperatorLinearAssemble().
2325 
2326    The assembly routines use coordinate format, with `num_entries` tuples of the form `(i, j, value)` which indicate that value should be added to the matrix in entry `(i, j)`.
2327    Note that the `(i, j)` pairs are not unique and may repeat.
2328    This function returns the number of entries and their `(i, j)` locations, while @ref CeedOperatorLinearAssemble() provides the values in the same ordering.
2329 
2330    This will generally be slow unless your operator is low-order.
2331 
2332    Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2333 
2334    @param[in]  op          `CeedOperator` to assemble
2335    @param[out] num_entries Number of entries in coordinate nonzero pattern
2336    @param[out] rows        Row number for each entry
2337    @param[out] cols        Column number for each entry
2338 
2339    @ref User
2340 **/
2341 int CeedOperatorLinearAssembleSymbolic(CeedOperator op, CeedSize *num_entries, CeedInt **rows, CeedInt **cols) {
2342   bool          is_composite;
2343   CeedInt       num_suboperators, offset = 0;
2344   CeedSize      single_entries;
2345   CeedOperator *sub_operators;
2346 
2347   CeedCall(CeedOperatorCheckReady(op));
2348   CeedCall(CeedOperatorIsComposite(op, &is_composite));
2349 
2350   if (op->LinearAssembleSymbolic) {
2351     // Backend version
2352     CeedCall(op->LinearAssembleSymbolic(op, num_entries, rows, cols));
2353     return CEED_ERROR_SUCCESS;
2354   } else {
2355     // Operator fallback
2356     CeedOperator op_fallback;
2357 
2358     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
2359     if (op_fallback) {
2360       CeedCall(CeedOperatorLinearAssembleSymbolic(op_fallback, num_entries, rows, cols));
2361       return CEED_ERROR_SUCCESS;
2362     }
2363   }
2364 
2365   // Default interface implementation
2366 
2367   // Count entries and allocate rows, cols arrays
2368   *num_entries = 0;
2369   if (is_composite) {
2370     CeedCall(CeedCompositeOperatorGetNumSub(op, &num_suboperators));
2371     CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
2372     for (CeedInt k = 0; k < num_suboperators; ++k) {
2373       CeedCall(CeedSingleOperatorAssemblyCountEntries(sub_operators[k], &single_entries));
2374       *num_entries += single_entries;
2375     }
2376   } else {
2377     CeedCall(CeedSingleOperatorAssemblyCountEntries(op, &single_entries));
2378     *num_entries += single_entries;
2379   }
2380   CeedCall(CeedCalloc(*num_entries, rows));
2381   CeedCall(CeedCalloc(*num_entries, cols));
2382 
2383   // Assemble nonzero locations
2384   if (is_composite) {
2385     CeedCall(CeedCompositeOperatorGetNumSub(op, &num_suboperators));
2386     CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
2387     for (CeedInt k = 0; k < num_suboperators; ++k) {
2388       CeedCall(CeedSingleOperatorAssembleSymbolic(sub_operators[k], offset, *rows, *cols));
2389       CeedCall(CeedSingleOperatorAssemblyCountEntries(sub_operators[k], &single_entries));
2390       offset += single_entries;
2391     }
2392   } else {
2393     CeedCall(CeedSingleOperatorAssembleSymbolic(op, offset, *rows, *cols));
2394   }
2395   return CEED_ERROR_SUCCESS;
2396 }
2397 
2398 /**
2399    @brief Fully assemble the nonzero entries of a linear operator.
2400 
2401    Expected to be used in conjunction with @ref CeedOperatorLinearAssembleSymbolic().
2402 
2403    The assembly routines use coordinate format, with `num_entries` tuples of the form `(i, j, value)` which indicate that value should be added to the matrix in entry `(i, j)`.
2404    Note that the `(i, j)` pairs are not unique and may repeat.
2405    This function returns the values of the nonzero entries to be added, their `(i, j)` locations are provided by @ref CeedOperatorLinearAssembleSymbolic().
2406 
2407    This will generally be slow unless your operator is low-order.
2408 
2409    Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2410 
2411    @param[in]  op     `CeedOperator` to assemble
2412    @param[out] values Values to assemble into matrix
2413 
2414    @ref User
2415 **/
2416 int CeedOperatorLinearAssemble(CeedOperator op, CeedVector values) {
2417   bool          is_composite;
2418   CeedInt       num_suboperators, offset = 0;
2419   CeedSize      single_entries = 0;
2420   CeedOperator *sub_operators;
2421 
2422   CeedCall(CeedOperatorCheckReady(op));
2423   CeedCall(CeedOperatorIsComposite(op, &is_composite));
2424 
2425   // Early exit for empty operator
2426   if (!is_composite) {
2427     CeedInt num_elem = 0;
2428 
2429     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
2430     if (num_elem == 0) return CEED_ERROR_SUCCESS;
2431   }
2432 
2433   if (op->LinearAssemble) {
2434     // Backend version
2435     CeedCall(op->LinearAssemble(op, values));
2436     return CEED_ERROR_SUCCESS;
2437   } else {
2438     // Operator fallback
2439     CeedOperator op_fallback;
2440 
2441     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
2442     if (op_fallback) {
2443       CeedCall(CeedOperatorLinearAssemble(op_fallback, values));
2444       return CEED_ERROR_SUCCESS;
2445     }
2446   }
2447 
2448   // Default interface implementation
2449   CeedCall(CeedVectorSetValue(values, 0.0));
2450   if (is_composite) {
2451     CeedCall(CeedCompositeOperatorGetNumSub(op, &num_suboperators));
2452     CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
2453     for (CeedInt k = 0; k < num_suboperators; k++) {
2454       CeedCall(CeedSingleOperatorAssemble(sub_operators[k], offset, values));
2455       CeedCall(CeedSingleOperatorAssemblyCountEntries(sub_operators[k], &single_entries));
2456       offset += single_entries;
2457     }
2458   } else {
2459     CeedCall(CeedSingleOperatorAssemble(op, offset, values));
2460   }
2461   return CEED_ERROR_SUCCESS;
2462 }
2463 
2464 /**
2465   @brief Get the multiplicity of nodes across sub-operators in a composite `CeedOperator`.
2466 
2467   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2468 
2469   @param[in]  op               Composite `CeedOperator`
2470   @param[in]  num_skip_indices Number of sub-operators to skip
2471   @param[in]  skip_indices     Array of indices of sub-operators to skip
2472   @param[out] mult             Vector to store multiplicity (of size `l_size` )
2473 
2474   @return An error code: 0 - success, otherwise - failure
2475 
2476   @ref User
2477 **/
2478 int CeedCompositeOperatorGetMultiplicity(CeedOperator op, CeedInt num_skip_indices, CeedInt *skip_indices, CeedVector mult) {
2479   Ceed                ceed;
2480   CeedInt             num_suboperators;
2481   CeedSize            l_vec_len;
2482   CeedScalar         *mult_array;
2483   CeedVector          ones_l_vec;
2484   CeedElemRestriction elem_rstr, mult_elem_rstr;
2485   CeedOperator       *sub_operators;
2486 
2487   CeedCall(CeedOperatorCheckReady(op));
2488 
2489   // Zero mult vector
2490   CeedCall(CeedVectorSetValue(mult, 0.0));
2491 
2492   // Get suboperators
2493   CeedCall(CeedCompositeOperatorGetNumSub(op, &num_suboperators));
2494   if (num_suboperators == 0) return CEED_ERROR_SUCCESS;
2495   CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
2496 
2497   // Work vector
2498   CeedCall(CeedVectorGetLength(mult, &l_vec_len));
2499   CeedCall(CeedOperatorGetCeed(op, &ceed));
2500   CeedCall(CeedVectorCreate(ceed, l_vec_len, &ones_l_vec));
2501   CeedCall(CeedDestroy(&ceed));
2502   CeedCall(CeedVectorSetValue(ones_l_vec, 1.0));
2503   CeedCall(CeedVectorGetArray(mult, CEED_MEM_HOST, &mult_array));
2504 
2505   // Compute multiplicity across suboperators
2506   for (CeedInt i = 0; i < num_suboperators; i++) {
2507     const CeedScalar *sub_mult_array;
2508     CeedVector        sub_mult_l_vec, ones_e_vec;
2509 
2510     // -- Check for suboperator to skip
2511     for (CeedInt j = 0; j < num_skip_indices; j++) {
2512       if (skip_indices[j] == i) continue;
2513     }
2514 
2515     // -- Sub operator multiplicity
2516     CeedCall(CeedOperatorGetActiveElemRestriction(sub_operators[i], &elem_rstr));
2517     CeedCall(CeedElemRestrictionCreateUnorientedCopy(elem_rstr, &mult_elem_rstr));
2518     CeedCall(CeedElemRestrictionDestroy(&elem_rstr));
2519     CeedCall(CeedElemRestrictionCreateVector(mult_elem_rstr, &sub_mult_l_vec, &ones_e_vec));
2520     CeedCall(CeedVectorSetValue(sub_mult_l_vec, 0.0));
2521     CeedCall(CeedElemRestrictionApply(mult_elem_rstr, CEED_NOTRANSPOSE, ones_l_vec, ones_e_vec, CEED_REQUEST_IMMEDIATE));
2522     CeedCall(CeedElemRestrictionApply(mult_elem_rstr, CEED_TRANSPOSE, ones_e_vec, sub_mult_l_vec, CEED_REQUEST_IMMEDIATE));
2523     CeedCall(CeedVectorGetArrayRead(sub_mult_l_vec, CEED_MEM_HOST, &sub_mult_array));
2524     // ---- Flag every node present in the current suboperator
2525     for (CeedSize j = 0; j < l_vec_len; j++) {
2526       if (sub_mult_array[j] > 0.0) mult_array[j] += 1.0;
2527     }
2528     CeedCall(CeedVectorRestoreArrayRead(sub_mult_l_vec, &sub_mult_array));
2529     CeedCall(CeedVectorDestroy(&sub_mult_l_vec));
2530     CeedCall(CeedVectorDestroy(&ones_e_vec));
2531     CeedCall(CeedElemRestrictionDestroy(&mult_elem_rstr));
2532   }
2533   CeedCall(CeedVectorRestoreArray(mult, &mult_array));
2534   CeedCall(CeedVectorDestroy(&ones_l_vec));
2535   return CEED_ERROR_SUCCESS;
2536 }
2537 
2538 /**
2539   @brief Create a multigrid coarse `CeedOperator` and level transfer `CeedOperator` for a `CeedOperator`, creating the prolongation basis from the fine and coarse grid interpolation.
2540 
2541   Note: Calling this function asserts that setup is complete and sets all four `CeedOperator` as immutable.
2542 
2543   @param[in]  op_fine      Fine grid `CeedOperator`
2544   @param[in]  p_mult_fine  L-vector multiplicity in parallel gather/scatter, or `NULL` if not creating prolongation/restriction `CeedOperator`
2545   @param[in]  rstr_coarse  Coarse grid `CeedElemRestriction`
2546   @param[in]  basis_coarse Coarse grid active vector `CeedBasis`
2547   @param[out] op_coarse    Coarse grid `CeedOperator`
2548   @param[out] op_prolong   Coarse to fine `CeedOperator`, or `NULL`
2549   @param[out] op_restrict  Fine to coarse `CeedOperator`, or `NULL`
2550 
2551   @return An error code: 0 - success, otherwise - failure
2552 
2553   @ref User
2554 **/
2555 int CeedOperatorMultigridLevelCreate(CeedOperator op_fine, CeedVector p_mult_fine, CeedElemRestriction rstr_coarse, CeedBasis basis_coarse,
2556                                      CeedOperator *op_coarse, CeedOperator *op_prolong, CeedOperator *op_restrict) {
2557   CeedBasis basis_c_to_f = NULL;
2558 
2559   CeedCall(CeedOperatorCheckReady(op_fine));
2560 
2561   // Build prolongation matrix, if required
2562   if (op_prolong || op_restrict) {
2563     CeedBasis basis_fine;
2564 
2565     CeedCall(CeedOperatorGetActiveBasis(op_fine, &basis_fine));
2566     CeedCall(CeedBasisCreateProjection(basis_coarse, basis_fine, &basis_c_to_f));
2567     CeedCall(CeedBasisDestroy(&basis_fine));
2568   }
2569 
2570   // Core code
2571   CeedCall(CeedSingleOperatorMultigridLevel(op_fine, p_mult_fine, rstr_coarse, basis_coarse, basis_c_to_f, op_coarse, op_prolong, op_restrict));
2572   return CEED_ERROR_SUCCESS;
2573 }
2574 
2575 /**
2576   @brief Create a multigrid coarse `CeedOperator` and level transfer `CeedOperator` for a `CeedOperator` with a tensor basis for the active basis.
2577 
2578   Note: Calling this function asserts that setup is complete and sets all four `CeedOperator` as immutable.
2579 
2580   @param[in]  op_fine       Fine grid `CeedOperator`
2581   @param[in]  p_mult_fine   L-vector multiplicity in parallel gather/scatter, or `NULL` if not creating prolongation/restriction `CeedOperator`
2582   @param[in]  rstr_coarse   Coarse grid `CeedElemRestriction`
2583   @param[in]  basis_coarse  Coarse grid active vector `CeedBasis`
2584   @param[in]  interp_c_to_f Matrix for coarse to fine interpolation, or `NULL` if not creating prolongation/restriction `CeedOperator`
2585   @param[out] op_coarse     Coarse grid `CeedOperator`
2586   @param[out] op_prolong    Coarse to fine `CeedOperator`, or `NULL`
2587   @param[out] op_restrict   Fine to coarse `CeedOperator`, or `NULL`
2588 
2589   @return An error code: 0 - success, otherwise - failure
2590 
2591   @ref User
2592 **/
2593 int CeedOperatorMultigridLevelCreateTensorH1(CeedOperator op_fine, CeedVector p_mult_fine, CeedElemRestriction rstr_coarse, CeedBasis basis_coarse,
2594                                              const CeedScalar *interp_c_to_f, CeedOperator *op_coarse, CeedOperator *op_prolong,
2595                                              CeedOperator *op_restrict) {
2596   Ceed      ceed;
2597   CeedInt   Q_f, Q_c;
2598   CeedBasis basis_fine, basis_c_to_f = NULL;
2599 
2600   CeedCall(CeedOperatorCheckReady(op_fine));
2601   CeedCall(CeedOperatorGetCeed(op_fine, &ceed));
2602 
2603   // Check for compatible quadrature spaces
2604   CeedCall(CeedOperatorGetActiveBasis(op_fine, &basis_fine));
2605   CeedCall(CeedBasisGetNumQuadraturePoints(basis_fine, &Q_f));
2606   CeedCall(CeedBasisGetNumQuadraturePoints(basis_coarse, &Q_c));
2607   CeedCheck(Q_f == Q_c, ceed, CEED_ERROR_DIMENSION,
2608             "Bases must have compatible quadrature spaces."
2609             " Fine grid: %" CeedInt_FMT " points, Coarse grid: %" CeedInt_FMT " points",
2610             Q_f, Q_c);
2611 
2612   // Create coarse to fine basis, if required
2613   if (op_prolong || op_restrict) {
2614     CeedInt     dim, num_comp, num_nodes_c, P_1d_f, P_1d_c;
2615     CeedScalar *q_ref, *q_weight, *grad;
2616 
2617     // Check if interpolation matrix is provided
2618     CeedCheck(interp_c_to_f, ceed, CEED_ERROR_INCOMPATIBLE,
2619               "Prolongation or restriction operator creation requires coarse-to-fine interpolation matrix");
2620     CeedCall(CeedBasisGetDimension(basis_fine, &dim));
2621     CeedCall(CeedBasisGetNumComponents(basis_fine, &num_comp));
2622     CeedCall(CeedBasisGetNumNodes1D(basis_fine, &P_1d_f));
2623     CeedCall(CeedBasisDestroy(&basis_fine));
2624     CeedCall(CeedElemRestrictionGetElementSize(rstr_coarse, &num_nodes_c));
2625     P_1d_c = dim == 1 ? num_nodes_c : dim == 2 ? sqrt(num_nodes_c) : cbrt(num_nodes_c);
2626     CeedCall(CeedCalloc(P_1d_f, &q_ref));
2627     CeedCall(CeedCalloc(P_1d_f, &q_weight));
2628     CeedCall(CeedCalloc(P_1d_f * P_1d_c * dim, &grad));
2629     CeedCall(CeedBasisCreateTensorH1(ceed, dim, num_comp, P_1d_c, P_1d_f, interp_c_to_f, grad, q_ref, q_weight, &basis_c_to_f));
2630     CeedCall(CeedFree(&q_ref));
2631     CeedCall(CeedFree(&q_weight));
2632     CeedCall(CeedFree(&grad));
2633   }
2634 
2635   // Core code
2636   CeedCall(CeedSingleOperatorMultigridLevel(op_fine, p_mult_fine, rstr_coarse, basis_coarse, basis_c_to_f, op_coarse, op_prolong, op_restrict));
2637   CeedCall(CeedDestroy(&ceed));
2638   return CEED_ERROR_SUCCESS;
2639 }
2640 
2641 /**
2642   @brief Create a multigrid coarse `CeedOperator` and level transfer `CeedOperator` for a `CeedOperator` with a non-tensor basis for the active vector
2643 
2644   Note: Calling this function asserts that setup is complete and sets all four `CeedOperator` as immutable.
2645 
2646   @param[in]  op_fine       Fine grid `CeedOperator`
2647   @param[in]  p_mult_fine   L-vector multiplicity in parallel gather/scatter, or `NULL` if not creating prolongation/restriction `CeedOperator`
2648   @param[in]  rstr_coarse   Coarse grid `CeedElemRestriction`
2649   @param[in]  basis_coarse  Coarse grid active vector `CeedBasis`
2650   @param[in]  interp_c_to_f Matrix for coarse to fine interpolation, or `NULL` if not creating prolongation/restriction `CeedOperator`
2651   @param[out] op_coarse     Coarse grid `CeedOperator`
2652   @param[out] op_prolong    Coarse to fine `CeedOperator`, or `NULL`
2653   @param[out] op_restrict   Fine to coarse `CeedOperator`, or `NULL`
2654 
2655   @return An error code: 0 - success, otherwise - failure
2656 
2657   @ref User
2658 **/
2659 int CeedOperatorMultigridLevelCreateH1(CeedOperator op_fine, CeedVector p_mult_fine, CeedElemRestriction rstr_coarse, CeedBasis basis_coarse,
2660                                        const CeedScalar *interp_c_to_f, CeedOperator *op_coarse, CeedOperator *op_prolong,
2661                                        CeedOperator *op_restrict) {
2662   Ceed      ceed;
2663   CeedInt   Q_f, Q_c;
2664   CeedBasis basis_fine, basis_c_to_f = NULL;
2665 
2666   CeedCall(CeedOperatorCheckReady(op_fine));
2667   CeedCall(CeedOperatorGetCeed(op_fine, &ceed));
2668 
2669   // Check for compatible quadrature spaces
2670   CeedCall(CeedOperatorGetActiveBasis(op_fine, &basis_fine));
2671   CeedCall(CeedBasisGetNumQuadraturePoints(basis_fine, &Q_f));
2672   CeedCall(CeedBasisGetNumQuadraturePoints(basis_coarse, &Q_c));
2673   CeedCheck(Q_f == Q_c, ceed, CEED_ERROR_DIMENSION, "Bases must have compatible quadrature spaces");
2674 
2675   // Coarse to fine basis
2676   if (op_prolong || op_restrict) {
2677     CeedInt          dim, num_comp, num_nodes_c, num_nodes_f;
2678     CeedScalar      *q_ref, *q_weight, *grad;
2679     CeedElemTopology topo;
2680 
2681     // Check if interpolation matrix is provided
2682     CeedCheck(interp_c_to_f, ceed, CEED_ERROR_INCOMPATIBLE,
2683               "Prolongation or restriction operator creation requires coarse-to-fine interpolation matrix");
2684     CeedCall(CeedBasisGetTopology(basis_fine, &topo));
2685     CeedCall(CeedBasisGetDimension(basis_fine, &dim));
2686     CeedCall(CeedBasisGetNumComponents(basis_fine, &num_comp));
2687     CeedCall(CeedBasisGetNumNodes(basis_fine, &num_nodes_f));
2688     CeedCall(CeedBasisDestroy(&basis_fine));
2689     CeedCall(CeedElemRestrictionGetElementSize(rstr_coarse, &num_nodes_c));
2690     CeedCall(CeedCalloc(num_nodes_f * dim, &q_ref));
2691     CeedCall(CeedCalloc(num_nodes_f, &q_weight));
2692     CeedCall(CeedCalloc(num_nodes_f * num_nodes_c * dim, &grad));
2693     CeedCall(CeedBasisCreateH1(ceed, topo, num_comp, num_nodes_c, num_nodes_f, interp_c_to_f, grad, q_ref, q_weight, &basis_c_to_f));
2694     CeedCall(CeedFree(&q_ref));
2695     CeedCall(CeedFree(&q_weight));
2696     CeedCall(CeedFree(&grad));
2697   }
2698 
2699   // Core code
2700   CeedCall(CeedSingleOperatorMultigridLevel(op_fine, p_mult_fine, rstr_coarse, basis_coarse, basis_c_to_f, op_coarse, op_prolong, op_restrict));
2701   CeedCall(CeedDestroy(&ceed));
2702   return CEED_ERROR_SUCCESS;
2703 }
2704 
2705 /**
2706   @brief Build a FDM based approximate inverse for each element for a `CeedOperator`.
2707 
2708   This returns a `CeedOperator` and `CeedVector` to apply a Fast Diagonalization Method based approximate inverse.
2709   This function obtains the simultaneous diagonalization for the 1D mass and Laplacian operators, \f$M = V^T V, K = V^T S V\f$.
2710   The assembled `CeedQFunction` is used to modify the eigenvalues from simultaneous diagonalization and obtain an approximate inverse of the form \f$V^T \hat S V\f$.
2711   The `CeedOperator` must be linear and non-composite.
2712   The associated `CeedQFunction` must therefore also be linear.
2713 
2714   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2715 
2716   @param[in]  op      `CeedOperator` to create element inverses
2717   @param[out] fdm_inv `CeedOperator` to apply the action of a FDM based inverse for each element
2718   @param[in]  request Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
2719 
2720   @return An error code: 0 - success, otherwise - failure
2721 
2722   @ref User
2723 **/
2724 int CeedOperatorCreateFDMElementInverse(CeedOperator op, CeedOperator *fdm_inv, CeedRequest *request) {
2725   Ceed                 ceed, ceed_parent;
2726   bool                 interp = false, grad = false, is_tensor_basis = true;
2727   CeedInt              num_input_fields, P_1d, Q_1d, num_nodes, num_qpts, dim, num_comp = 1, num_elem = 1;
2728   CeedScalar          *mass, *laplace, *x, *fdm_interp, *lambda, *elem_avg;
2729   const CeedScalar    *interp_1d, *grad_1d, *q_weight_1d;
2730   CeedVector           q_data;
2731   CeedElemRestriction  rstr  = NULL, rstr_qd_i;
2732   CeedBasis            basis = NULL, fdm_basis;
2733   CeedQFunctionContext ctx_fdm;
2734   CeedQFunctionField  *qf_fields;
2735   CeedQFunction        qf, qf_fdm;
2736   CeedOperatorField   *op_fields;
2737 
2738   CeedCall(CeedOperatorCheckReady(op));
2739 
2740   if (op->CreateFDMElementInverse) {
2741     // Backend version
2742     CeedCall(op->CreateFDMElementInverse(op, fdm_inv, request));
2743     return CEED_ERROR_SUCCESS;
2744   } else {
2745     // Operator fallback
2746     CeedOperator op_fallback;
2747 
2748     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
2749     if (op_fallback) {
2750       CeedCall(CeedOperatorCreateFDMElementInverse(op_fallback, fdm_inv, request));
2751       return CEED_ERROR_SUCCESS;
2752     }
2753   }
2754 
2755   // Default interface implementation
2756   CeedCall(CeedOperatorGetCeed(op, &ceed));
2757   CeedCall(CeedOperatorGetFallbackParentCeed(op, &ceed_parent));
2758   CeedCall(CeedOperatorGetQFunction(op, &qf));
2759 
2760   // Determine active input basis
2761   CeedCall(CeedOperatorGetFields(op, &num_input_fields, &op_fields, NULL, NULL));
2762   CeedCall(CeedQFunctionGetFields(qf, NULL, &qf_fields, NULL, NULL));
2763   for (CeedInt i = 0; i < num_input_fields; i++) {
2764     CeedVector vec;
2765 
2766     CeedCall(CeedOperatorFieldGetVector(op_fields[i], &vec));
2767     if (vec == CEED_VECTOR_ACTIVE) {
2768       CeedEvalMode eval_mode;
2769 
2770       CeedCall(CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode));
2771       interp = interp || eval_mode == CEED_EVAL_INTERP;
2772       grad   = grad || eval_mode == CEED_EVAL_GRAD;
2773       if (!basis) CeedCall(CeedOperatorFieldGetBasis(op_fields[i], &basis));
2774       if (!rstr) CeedCall(CeedOperatorFieldGetElemRestriction(op_fields[i], &rstr));
2775     }
2776     CeedCall(CeedVectorDestroy(&vec));
2777   }
2778   CeedCheck(basis, ceed, CEED_ERROR_BACKEND, "No active field set");
2779   CeedCall(CeedBasisGetNumNodes1D(basis, &P_1d));
2780   CeedCall(CeedBasisGetNumNodes(basis, &num_nodes));
2781   CeedCall(CeedBasisGetNumQuadraturePoints1D(basis, &Q_1d));
2782   CeedCall(CeedBasisGetNumQuadraturePoints(basis, &num_qpts));
2783   CeedCall(CeedBasisGetDimension(basis, &dim));
2784   CeedCall(CeedBasisGetNumComponents(basis, &num_comp));
2785   CeedCall(CeedElemRestrictionGetNumElements(rstr, &num_elem));
2786 
2787   // Build and diagonalize 1D Mass and Laplacian
2788   CeedCall(CeedBasisIsTensor(basis, &is_tensor_basis));
2789   CeedCheck(is_tensor_basis, ceed, CEED_ERROR_BACKEND, "FDMElementInverse only supported for tensor bases");
2790   CeedCall(CeedCalloc(P_1d * P_1d, &mass));
2791   CeedCall(CeedCalloc(P_1d * P_1d, &laplace));
2792   CeedCall(CeedCalloc(P_1d * P_1d, &x));
2793   CeedCall(CeedCalloc(P_1d * P_1d, &fdm_interp));
2794   CeedCall(CeedCalloc(P_1d, &lambda));
2795   // -- Build matrices
2796   CeedCall(CeedBasisGetInterp1D(basis, &interp_1d));
2797   CeedCall(CeedBasisGetGrad1D(basis, &grad_1d));
2798   CeedCall(CeedBasisGetQWeights(basis, &q_weight_1d));
2799   CeedCall(CeedBuildMassLaplace(interp_1d, grad_1d, q_weight_1d, P_1d, Q_1d, dim, mass, laplace));
2800 
2801   // -- Diagonalize
2802   CeedCall(CeedSimultaneousDiagonalization(ceed, laplace, mass, x, lambda, P_1d));
2803   CeedCall(CeedFree(&mass));
2804   CeedCall(CeedFree(&laplace));
2805   for (CeedInt i = 0; i < P_1d; i++) {
2806     for (CeedInt j = 0; j < P_1d; j++) fdm_interp[i + j * P_1d] = x[j + i * P_1d];
2807   }
2808   CeedCall(CeedFree(&x));
2809 
2810   {
2811     CeedInt             layout[3], num_modes = (interp ? 1 : 0) + (grad ? dim : 0);
2812     CeedScalar          max_norm = 0;
2813     const CeedScalar   *assembled_array, *q_weight_array;
2814     CeedVector          assembled = NULL, q_weight;
2815     CeedElemRestriction rstr_qf   = NULL;
2816 
2817     // Assemble QFunction
2818     CeedCall(CeedOperatorLinearAssembleQFunctionBuildOrUpdate(op, &assembled, &rstr_qf, request));
2819     CeedCall(CeedElemRestrictionGetELayout(rstr_qf, layout));
2820     CeedCall(CeedElemRestrictionDestroy(&rstr_qf));
2821     CeedCall(CeedVectorNorm(assembled, CEED_NORM_MAX, &max_norm));
2822 
2823     // Calculate element averages
2824     CeedCall(CeedVectorCreate(ceed_parent, num_qpts, &q_weight));
2825     CeedCall(CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT, CEED_VECTOR_NONE, q_weight));
2826     CeedCall(CeedVectorGetArrayRead(assembled, CEED_MEM_HOST, &assembled_array));
2827     CeedCall(CeedVectorGetArrayRead(q_weight, CEED_MEM_HOST, &q_weight_array));
2828     CeedCall(CeedCalloc(num_elem, &elem_avg));
2829     const CeedScalar qf_value_bound = max_norm * 100 * CEED_EPSILON;
2830 
2831     for (CeedInt e = 0; e < num_elem; e++) {
2832       CeedInt count = 0;
2833 
2834       for (CeedInt q = 0; q < num_qpts; q++) {
2835         for (CeedInt i = 0; i < num_comp * num_comp * num_modes * num_modes; i++) {
2836           if (fabs(assembled_array[q * layout[0] + i * layout[1] + e * layout[2]]) > qf_value_bound) {
2837             elem_avg[e] += assembled_array[q * layout[0] + i * layout[1] + e * layout[2]] / q_weight_array[q];
2838             count++;
2839           }
2840         }
2841       }
2842       if (count) {
2843         elem_avg[e] /= count;
2844       } else {
2845         elem_avg[e] = 1.0;
2846       }
2847     }
2848     CeedCall(CeedVectorRestoreArrayRead(assembled, &assembled_array));
2849     CeedCall(CeedVectorDestroy(&assembled));
2850     CeedCall(CeedVectorRestoreArrayRead(q_weight, &q_weight_array));
2851     CeedCall(CeedVectorDestroy(&q_weight));
2852   }
2853 
2854   // Build FDM diagonal
2855   {
2856     CeedScalar *q_data_array, *fdm_diagonal;
2857 
2858     CeedCall(CeedCalloc(num_comp * num_nodes, &fdm_diagonal));
2859     const CeedScalar fdm_diagonal_bound = num_nodes * CEED_EPSILON;
2860     for (CeedInt c = 0; c < num_comp; c++) {
2861       for (CeedInt n = 0; n < num_nodes; n++) {
2862         if (interp) fdm_diagonal[c * num_nodes + n] = 1.0;
2863         if (grad) {
2864           for (CeedInt d = 0; d < dim; d++) {
2865             CeedInt i = (n / CeedIntPow(P_1d, d)) % P_1d;
2866             fdm_diagonal[c * num_nodes + n] += lambda[i];
2867           }
2868         }
2869         if (fabs(fdm_diagonal[c * num_nodes + n]) < fdm_diagonal_bound) fdm_diagonal[c * num_nodes + n] = fdm_diagonal_bound;
2870       }
2871     }
2872     CeedCall(CeedVectorCreate(ceed_parent, num_elem * num_comp * num_nodes, &q_data));
2873     CeedCall(CeedVectorSetValue(q_data, 0.0));
2874     CeedCall(CeedVectorGetArrayWrite(q_data, CEED_MEM_HOST, &q_data_array));
2875     for (CeedInt e = 0; e < num_elem; e++) {
2876       for (CeedInt c = 0; c < num_comp; c++) {
2877         for (CeedInt n = 0; n < num_nodes; n++) {
2878           q_data_array[(e * num_comp + c) * num_nodes + n] = 1. / (elem_avg[e] * fdm_diagonal[c * num_nodes + n]);
2879         }
2880       }
2881     }
2882     CeedCall(CeedFree(&elem_avg));
2883     CeedCall(CeedFree(&fdm_diagonal));
2884     CeedCall(CeedVectorRestoreArray(q_data, &q_data_array));
2885   }
2886 
2887   // Setup FDM operator
2888   // -- Basis
2889   {
2890     CeedScalar *grad_dummy, *q_ref_dummy, *q_weight_dummy;
2891 
2892     CeedCall(CeedCalloc(P_1d * P_1d, &grad_dummy));
2893     CeedCall(CeedCalloc(P_1d, &q_ref_dummy));
2894     CeedCall(CeedCalloc(P_1d, &q_weight_dummy));
2895     CeedCall(CeedBasisCreateTensorH1(ceed_parent, dim, num_comp, P_1d, P_1d, fdm_interp, grad_dummy, q_ref_dummy, q_weight_dummy, &fdm_basis));
2896     CeedCall(CeedFree(&fdm_interp));
2897     CeedCall(CeedFree(&grad_dummy));
2898     CeedCall(CeedFree(&q_ref_dummy));
2899     CeedCall(CeedFree(&q_weight_dummy));
2900     CeedCall(CeedFree(&lambda));
2901   }
2902 
2903   // -- Restriction
2904   {
2905     CeedInt strides[3] = {1, num_nodes, num_nodes * num_comp};
2906     CeedCall(CeedElemRestrictionCreateStrided(ceed_parent, num_elem, num_nodes, num_comp,
2907                                               (CeedSize)num_elem * (CeedSize)num_comp * (CeedSize)num_nodes, strides, &rstr_qd_i));
2908   }
2909 
2910   // -- QFunction
2911   CeedCall(CeedQFunctionCreateInteriorByName(ceed_parent, "Scale", &qf_fdm));
2912   CeedCall(CeedQFunctionAddInput(qf_fdm, "input", num_comp, CEED_EVAL_INTERP));
2913   CeedCall(CeedQFunctionAddInput(qf_fdm, "scale", num_comp, CEED_EVAL_NONE));
2914   CeedCall(CeedQFunctionAddOutput(qf_fdm, "output", num_comp, CEED_EVAL_INTERP));
2915   CeedCall(CeedQFunctionSetUserFlopsEstimate(qf_fdm, num_comp));
2916 
2917   // -- QFunction context
2918   {
2919     CeedInt *num_comp_data;
2920 
2921     CeedCall(CeedCalloc(1, &num_comp_data));
2922     num_comp_data[0] = num_comp;
2923     CeedCall(CeedQFunctionContextCreate(ceed, &ctx_fdm));
2924     CeedCall(CeedQFunctionContextSetData(ctx_fdm, CEED_MEM_HOST, CEED_OWN_POINTER, sizeof(*num_comp_data), num_comp_data));
2925   }
2926   CeedCall(CeedQFunctionSetContext(qf_fdm, ctx_fdm));
2927   CeedCall(CeedQFunctionContextDestroy(&ctx_fdm));
2928 
2929   // -- Operator
2930   CeedCall(CeedOperatorCreate(ceed_parent, qf_fdm, NULL, NULL, fdm_inv));
2931   CeedCall(CeedOperatorSetField(*fdm_inv, "input", rstr, fdm_basis, CEED_VECTOR_ACTIVE));
2932   CeedCall(CeedOperatorSetField(*fdm_inv, "scale", rstr_qd_i, CEED_BASIS_NONE, q_data));
2933   CeedCall(CeedOperatorSetField(*fdm_inv, "output", rstr, fdm_basis, CEED_VECTOR_ACTIVE));
2934 
2935   // Cleanup
2936   CeedCall(CeedDestroy(&ceed));
2937   CeedCall(CeedDestroy(&ceed_parent));
2938   CeedCall(CeedVectorDestroy(&q_data));
2939   CeedCall(CeedElemRestrictionDestroy(&rstr));
2940   CeedCall(CeedElemRestrictionDestroy(&rstr_qd_i));
2941   CeedCall(CeedBasisDestroy(&basis));
2942   CeedCall(CeedBasisDestroy(&fdm_basis));
2943   CeedCall(CeedQFunctionDestroy(&qf));
2944   CeedCall(CeedQFunctionDestroy(&qf_fdm));
2945   return CEED_ERROR_SUCCESS;
2946 }
2947 
2948 /// @}
2949