xref: /libCEED/rust/libceed-sys/c-src/interface/ceed-preconditioning.c (revision f3bd9308d5a5e31ba13aa386c05e834a5d373929)
1 // Copyright (c) 2017-2022, 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   Ceed                ceed;
41   CeedQFunctionField *input_fields, *output_fields;
42 
43   // Check if NULL qf passed in
44   if (!qf) return CEED_ERROR_SUCCESS;
45 
46   CeedCall(CeedQFunctionGetCeed(qf, &ceed));
47   CeedDebug256(ceed, 1, "---------- CeedOperator Fallback ----------\n");
48   CeedDebug(ceed, "Creating fallback CeedQFunction\n");
49 
50   if (qf->source_path) {
51     size_t path_len = strlen(qf->source_path), name_len = strlen(qf->kernel_name);
52     CeedCall(CeedCalloc(path_len + name_len + 2, &source_path_with_name));
53     memcpy(source_path_with_name, qf->source_path, path_len);
54     memcpy(&source_path_with_name[path_len], ":", 1);
55     memcpy(&source_path_with_name[path_len + 1], qf->kernel_name, name_len);
56   } else {
57     CeedCall(CeedCalloc(1, &source_path_with_name));
58   }
59 
60   {
61     CeedInt           vec_length;
62     CeedQFunctionUser f;
63 
64     CeedCall(CeedQFunctionGetVectorLength(qf, &vec_length));
65     CeedCall(CeedQFunctionGetUserFunction(qf, &f));
66     CeedCall(CeedQFunctionCreateInterior(fallback_ceed, vec_length, f, source_path_with_name, qf_fallback));
67   }
68   {
69     CeedQFunctionContext ctx;
70 
71     CeedCall(CeedQFunctionGetContext(qf, &ctx));
72     CeedCall(CeedQFunctionSetContext(*qf_fallback, ctx));
73   }
74   CeedCall(CeedQFunctionGetFields(qf, &num_input_fields, &input_fields, &num_output_fields, &output_fields));
75   for (CeedInt i = 0; i < num_input_fields; i++) {
76     const char  *field_name;
77     CeedInt      size;
78     CeedEvalMode eval_mode;
79 
80     CeedCall(CeedQFunctionFieldGetData(input_fields[i], &field_name, &size, &eval_mode));
81     CeedCall(CeedQFunctionAddInput(*qf_fallback, field_name, size, eval_mode));
82   }
83   for (CeedInt i = 0; i < num_output_fields; i++) {
84     const char  *field_name;
85     CeedInt      size;
86     CeedEvalMode eval_mode;
87 
88     CeedCall(CeedQFunctionFieldGetData(output_fields[i], &field_name, &size, &eval_mode));
89     CeedCall(CeedQFunctionAddOutput(*qf_fallback, field_name, size, eval_mode));
90   }
91   CeedCall(CeedFree(&source_path_with_name));
92   return CEED_ERROR_SUCCESS;
93 }
94 
95 /**
96   @brief Duplicate a `CeedOperator` with a reference `Ceed` to fallback for advanced `CeedOperator` functionality
97 
98   @param[in,out] op `CeedOperator` to create fallback for
99 
100   @return An error code: 0 - success, otherwise - failure
101 
102   @ref Developer
103 **/
104 static int CeedOperatorCreateFallback(CeedOperator op) {
105   bool         is_composite;
106   Ceed         ceed, ceed_fallback;
107   CeedOperator op_fallback;
108 
109   // Check not already created
110   if (op->op_fallback) return CEED_ERROR_SUCCESS;
111 
112   // Fallback Ceed
113   CeedCall(CeedOperatorGetCeed(op, &ceed));
114   CeedCall(CeedGetOperatorFallbackCeed(ceed, &ceed_fallback));
115   if (!ceed_fallback) return CEED_ERROR_SUCCESS;
116 
117   CeedDebug256(ceed, 1, "---------- CeedOperator Fallback ----------\n");
118   CeedDebug(ceed, "Creating fallback CeedOperator\n");
119 
120   // Clone Op
121   CeedCall(CeedOperatorIsComposite(op, &is_composite));
122   if (is_composite) {
123     CeedInt       num_suboperators;
124     CeedOperator *sub_operators;
125 
126     CeedCall(CeedCompositeOperatorCreate(ceed_fallback, &op_fallback));
127     CeedCall(CeedCompositeOperatorGetNumSub(op, &num_suboperators));
128     CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
129     for (CeedInt i = 0; i < num_suboperators; i++) {
130       CeedOperator op_sub_fallback;
131 
132       CeedCall(CeedOperatorGetFallback(sub_operators[i], &op_sub_fallback));
133       CeedCall(CeedCompositeOperatorAddSub(op_fallback, op_sub_fallback));
134     }
135   } else {
136     CeedInt            num_input_fields, num_output_fields;
137     CeedQFunction      qf_fallback = NULL, dqf_fallback = NULL, dqfT_fallback = NULL;
138     CeedOperatorField *input_fields, *output_fields;
139 
140     CeedCall(CeedQFunctionCreateFallback(ceed_fallback, op->qf, &qf_fallback));
141     CeedCall(CeedQFunctionCreateFallback(ceed_fallback, op->dqf, &dqf_fallback));
142     CeedCall(CeedQFunctionCreateFallback(ceed_fallback, op->dqfT, &dqfT_fallback));
143     CeedCall(CeedOperatorCreate(ceed_fallback, qf_fallback, dqf_fallback, dqfT_fallback, &op_fallback));
144     CeedCall(CeedOperatorGetFields(op, &num_input_fields, &input_fields, &num_output_fields, &output_fields));
145     for (CeedInt i = 0; i < num_input_fields; i++) {
146       const char         *field_name;
147       CeedVector          vec;
148       CeedElemRestriction rstr;
149       CeedBasis           basis;
150 
151       CeedCall(CeedOperatorFieldGetData(input_fields[i], &field_name, &rstr, &basis, &vec));
152       CeedCall(CeedOperatorSetField(op_fallback, field_name, rstr, basis, vec));
153     }
154     for (CeedInt i = 0; i < num_output_fields; i++) {
155       const char         *field_name;
156       CeedVector          vec;
157       CeedElemRestriction rstr;
158       CeedBasis           basis;
159 
160       CeedCall(CeedOperatorFieldGetData(output_fields[i], &field_name, &rstr, &basis, &vec));
161       CeedCall(CeedOperatorSetField(op_fallback, field_name, rstr, basis, vec));
162     }
163     CeedCall(CeedQFunctionAssemblyDataReferenceCopy(op->qf_assembled, &op_fallback->qf_assembled));
164     // Cleanup
165     CeedCall(CeedQFunctionDestroy(&qf_fallback));
166     CeedCall(CeedQFunctionDestroy(&dqf_fallback));
167     CeedCall(CeedQFunctionDestroy(&dqfT_fallback));
168   }
169   CeedCall(CeedOperatorSetName(op_fallback, op->name));
170   CeedCall(CeedOperatorCheckReady(op_fallback));
171   // Note: No ref-counting here so we don't get caught in a reference loop.
172   //       The op holds the only reference to op_fallback and is responsible for deleting itself and op_fallback.
173   op->op_fallback                 = op_fallback;
174   op_fallback->op_fallback_parent = op;
175   return CEED_ERROR_SUCCESS;
176 }
177 
178 /**
179   @brief Core logic for assembling operator diagonal or point block diagonal
180 
181   @param[in]  op             `CeedOperator` to assemble point block diagonal
182   @param[in]  request        Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
183   @param[in]  is_point_block Boolean flag to assemble diagonal or point block diagonal
184   @param[out] assembled      `CeedVector` to store assembled diagonal
185 
186   @return An error code: 0 - success, otherwise - failure
187 
188   @ref Developer
189 **/
190 static inline int CeedSingleOperatorLinearAssembleAddDiagonal(CeedOperator op, CeedRequest *request, const bool is_point_block,
191                                                               CeedVector assembled) {
192   Ceed ceed;
193   bool is_composite;
194 
195   CeedCall(CeedOperatorGetCeed(op, &ceed));
196   CeedCall(CeedOperatorIsComposite(op, &is_composite));
197   CeedCheck(!is_composite, ceed, CEED_ERROR_UNSUPPORTED, "Composite operator not supported");
198 
199   // Assemble QFunction
200   CeedInt             layout_qf[3];
201   const CeedScalar   *assembled_qf_array;
202   CeedVector          assembled_qf        = NULL;
203   CeedElemRestriction assembled_elem_rstr = NULL;
204 
205   CeedCall(CeedOperatorLinearAssembleQFunctionBuildOrUpdate(op, &assembled_qf, &assembled_elem_rstr, request));
206   CeedCall(CeedElemRestrictionGetELayout(assembled_elem_rstr, layout_qf));
207   CeedCall(CeedElemRestrictionDestroy(&assembled_elem_rstr));
208   CeedCall(CeedVectorGetArrayRead(assembled_qf, CEED_MEM_HOST, &assembled_qf_array));
209 
210   // Get assembly data
211   const CeedEvalMode     **eval_modes_in, **eval_modes_out;
212   CeedInt                  num_active_bases_in, *num_eval_modes_in, num_active_bases_out, *num_eval_modes_out;
213   CeedSize               **eval_mode_offsets_in, **eval_mode_offsets_out, num_output_components;
214   CeedBasis               *active_bases_in, *active_bases_out;
215   CeedElemRestriction     *active_elem_rstrs_in, *active_elem_rstrs_out;
216   CeedOperatorAssemblyData data;
217 
218   CeedCall(CeedOperatorGetOperatorAssemblyData(op, &data));
219   CeedCall(CeedOperatorAssemblyDataGetEvalModes(data, &num_active_bases_in, &num_eval_modes_in, &eval_modes_in, &eval_mode_offsets_in,
220                                                 &num_active_bases_out, &num_eval_modes_out, &eval_modes_out, &eval_mode_offsets_out,
221                                                 &num_output_components));
222   CeedCall(CeedOperatorAssemblyDataGetBases(data, NULL, &active_bases_in, NULL, NULL, &active_bases_out, NULL));
223   CeedCall(CeedOperatorAssemblyDataGetElemRestrictions(data, NULL, &active_elem_rstrs_in, NULL, &active_elem_rstrs_out));
224 
225   // Loop over all active bases (find matching input/output pairs)
226   for (CeedInt b = 0; b < CeedIntMin(num_active_bases_in, num_active_bases_out); b++) {
227     CeedInt             b_in, b_out, num_elem, num_nodes, num_qpts, num_comp;
228     bool                has_eval_none = false;
229     CeedScalar         *elem_diag_array, *identity = NULL;
230     CeedVector          elem_diag;
231     CeedElemRestriction diag_elem_rstr;
232 
233     if (num_active_bases_in <= num_active_bases_out) {
234       b_in = b;
235       for (b_out = 0; b_out < num_active_bases_out; b_out++) {
236         if (active_bases_in[b_in] == active_bases_out[b_out]) {
237           break;
238         }
239       }
240       if (b_out == num_active_bases_out) {
241         continue;
242       }  // No matching output basis found
243     } else {
244       b_out = b;
245       for (b_in = 0; b_in < num_active_bases_in; b_in++) {
246         if (active_bases_in[b_in] == active_bases_out[b_out]) {
247           break;
248         }
249       }
250       if (b_in == num_active_bases_in) {
251         continue;
252       }  // No matching output basis found
253     }
254     CeedCheck(active_elem_rstrs_in[b_in] == active_elem_rstrs_out[b_out], ceed, CEED_ERROR_UNSUPPORTED,
255               "Cannot assemble operator diagonal with different input and output active element restrictions");
256 
257     // Assemble point block diagonal restriction, if needed
258     if (is_point_block) {
259       CeedCall(CeedOperatorCreateActivePointBlockRestriction(active_elem_rstrs_in[b_in], &diag_elem_rstr));
260     } else {
261       CeedCall(CeedElemRestrictionCreateUnsignedCopy(active_elem_rstrs_in[b_in], &diag_elem_rstr));
262     }
263 
264     // Create diagonal vector
265     CeedCall(CeedElemRestrictionCreateVector(diag_elem_rstr, NULL, &elem_diag));
266 
267     // Assemble element operator diagonals
268     CeedCall(CeedVectorSetValue(elem_diag, 0.0));
269     CeedCall(CeedVectorGetArray(elem_diag, CEED_MEM_HOST, &elem_diag_array));
270     CeedCall(CeedElemRestrictionGetNumElements(diag_elem_rstr, &num_elem));
271     CeedCall(CeedBasisGetNumNodes(active_bases_in[b_in], &num_nodes));
272     CeedCall(CeedBasisGetNumComponents(active_bases_in[b_in], &num_comp));
273     if (active_bases_in[b_in] == CEED_BASIS_NONE) num_qpts = num_nodes;
274     else CeedCall(CeedBasisGetNumQuadraturePoints(active_bases_in[b_in], &num_qpts));
275 
276     // Construct identity matrix for basis if required
277     for (CeedInt i = 0; i < num_eval_modes_in[b_in]; i++) {
278       has_eval_none = has_eval_none || (eval_modes_in[b_in][i] == CEED_EVAL_NONE);
279     }
280     for (CeedInt i = 0; i < num_eval_modes_out[b_out]; i++) {
281       has_eval_none = has_eval_none || (eval_modes_out[b_out][i] == CEED_EVAL_NONE);
282     }
283     if (has_eval_none) {
284       CeedCall(CeedCalloc(num_qpts * num_nodes, &identity));
285       for (CeedInt i = 0; i < (num_nodes < num_qpts ? num_nodes : num_qpts); i++) identity[i * num_nodes + i] = 1.0;
286     }
287 
288     // Compute the diagonal of B^T D B
289     // Each element
290     for (CeedSize e = 0; e < num_elem; e++) {
291       // Each basis eval mode pair
292       CeedInt      d_out              = 0, q_comp_out;
293       CeedEvalMode eval_mode_out_prev = CEED_EVAL_NONE;
294 
295       for (CeedInt e_out = 0; e_out < num_eval_modes_out[b_out]; e_out++) {
296         CeedInt           d_in              = 0, q_comp_in;
297         const CeedScalar *B_t               = NULL;
298         CeedEvalMode      eval_mode_in_prev = CEED_EVAL_NONE;
299 
300         CeedCall(CeedOperatorGetBasisPointer(active_bases_out[b_out], eval_modes_out[b_out][e_out], identity, &B_t));
301         CeedCall(CeedBasisGetNumQuadratureComponents(active_bases_out[b_out], eval_modes_out[b_out][e_out], &q_comp_out));
302         if (q_comp_out > 1) {
303           if (e_out == 0 || eval_modes_out[b_out][e_out] != eval_mode_out_prev) d_out = 0;
304           else B_t = &B_t[(++d_out) * num_qpts * num_nodes];
305         }
306         eval_mode_out_prev = eval_modes_out[b_out][e_out];
307 
308         for (CeedInt e_in = 0; e_in < num_eval_modes_in[b_in]; e_in++) {
309           const CeedScalar *B = NULL;
310 
311           CeedCall(CeedOperatorGetBasisPointer(active_bases_in[b_in], eval_modes_in[b_in][e_in], identity, &B));
312           CeedCall(CeedBasisGetNumQuadratureComponents(active_bases_in[b_in], eval_modes_in[b_in][e_in], &q_comp_in));
313           if (q_comp_in > 1) {
314             if (e_in == 0 || eval_modes_in[b_in][e_in] != eval_mode_in_prev) d_in = 0;
315             else B = &B[(++d_in) * num_qpts * num_nodes];
316           }
317           eval_mode_in_prev = eval_modes_in[b_in][e_in];
318 
319           // Each component
320           for (CeedInt c_out = 0; c_out < num_comp; c_out++) {
321             // Each qpt/node pair
322             for (CeedInt q = 0; q < num_qpts; q++) {
323               if (is_point_block) {
324                 // Point Block Diagonal
325                 for (CeedInt c_in = 0; c_in < num_comp; c_in++) {
326                   const CeedSize c_offset =
327                       (eval_mode_offsets_in[b_in][e_in] + c_in) * num_output_components + eval_mode_offsets_out[b_out][e_out] + c_out;
328                   const CeedScalar qf_value = assembled_qf_array[q * layout_qf[0] + c_offset * layout_qf[1] + e * layout_qf[2]];
329 
330                   for (CeedInt n = 0; n < num_nodes; n++) {
331                     elem_diag_array[((e * num_comp + c_out) * num_comp + c_in) * num_nodes + n] +=
332                         B_t[q * num_nodes + n] * qf_value * B[q * num_nodes + n];
333                   }
334                 }
335               } else {
336                 // Diagonal Only
337                 const CeedInt c_offset =
338                     (eval_mode_offsets_in[b_in][e_in] + c_out) * num_output_components + eval_mode_offsets_out[b_out][e_out] + c_out;
339                 const CeedScalar qf_value = assembled_qf_array[q * layout_qf[0] + c_offset * layout_qf[1] + e * layout_qf[2]];
340 
341                 for (CeedInt n = 0; n < num_nodes; n++) {
342                   elem_diag_array[(e * num_comp + c_out) * num_nodes + n] += B_t[q * num_nodes + n] * qf_value * B[q * num_nodes + n];
343                 }
344               }
345             }
346           }
347         }
348       }
349     }
350     CeedCall(CeedVectorRestoreArray(elem_diag, &elem_diag_array));
351 
352     // Assemble local operator diagonal
353     CeedCall(CeedElemRestrictionApply(diag_elem_rstr, CEED_TRANSPOSE, elem_diag, assembled, request));
354 
355     // Cleanup
356     CeedCall(CeedElemRestrictionDestroy(&diag_elem_rstr));
357     CeedCall(CeedVectorDestroy(&elem_diag));
358     CeedCall(CeedFree(&identity));
359   }
360   CeedCall(CeedVectorRestoreArrayRead(assembled_qf, &assembled_qf_array));
361   CeedCall(CeedVectorDestroy(&assembled_qf));
362   return CEED_ERROR_SUCCESS;
363 }
364 
365 /**
366   @brief Core logic for assembling composite operator diagonal
367 
368   @param[in]  op             `CeedOperator` to assemble point block diagonal
369   @param[in]  request        Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
370   @param[in]  is_point_block Boolean flag to assemble diagonal or point block diagonal
371   @param[out] assembled      `CeedVector` to store assembled diagonal
372 
373   @return An error code: 0 - success, otherwise - failure
374 
375   @ref Developer
376 **/
377 static inline int CeedCompositeOperatorLinearAssembleAddDiagonal(CeedOperator op, CeedRequest *request, const bool is_point_block,
378                                                                  CeedVector assembled) {
379   CeedInt       num_sub;
380   CeedOperator *suboperators;
381 
382   CeedCall(CeedCompositeOperatorGetNumSub(op, &num_sub));
383   CeedCall(CeedCompositeOperatorGetSubList(op, &suboperators));
384   for (CeedInt i = 0; i < num_sub; i++) {
385     if (is_point_block) {
386       CeedCall(CeedOperatorLinearAssembleAddPointBlockDiagonal(suboperators[i], assembled, request));
387     } else {
388       CeedCall(CeedOperatorLinearAssembleAddDiagonal(suboperators[i], assembled, request));
389     }
390   }
391   return CEED_ERROR_SUCCESS;
392 }
393 
394 /**
395   @brief Build nonzero pattern for non-composite CeedOperator`.
396 
397   Users should generally use @ref CeedOperatorLinearAssembleSymbolic().
398 
399   @param[in]  op     `CeedOperator` to assemble nonzero pattern
400   @param[in]  offset Offset for number of entries
401   @param[out] rows   Row number for each entry
402   @param[out] cols   Column number for each entry
403 
404   @return An error code: 0 - success, otherwise - failure
405 
406   @ref Developer
407 **/
408 static int CeedSingleOperatorAssembleSymbolic(CeedOperator op, CeedInt offset, CeedInt *rows, CeedInt *cols) {
409   Ceed                ceed;
410   bool                is_composite;
411   CeedSize            num_nodes_in, num_nodes_out, local_num_entries, count = 0;
412   CeedInt             num_elem_in, elem_size_in, num_comp_in, layout_er_in[3];
413   CeedInt             num_elem_out, elem_size_out, num_comp_out, layout_er_out[3];
414   CeedScalar         *array;
415   const CeedScalar   *elem_dof_a_in, *elem_dof_a_out;
416   CeedVector          index_vec_in, index_vec_out, elem_dof_in, elem_dof_out;
417   CeedElemRestriction elem_rstr_in, elem_rstr_out, index_elem_rstr_in, index_elem_rstr_out;
418 
419   CeedCall(CeedOperatorGetCeed(op, &ceed));
420   CeedCall(CeedOperatorIsComposite(op, &is_composite));
421   CeedCheck(!is_composite, ceed, CEED_ERROR_UNSUPPORTED, "Composite operator not supported");
422 
423   CeedCall(CeedOperatorGetActiveVectorLengths(op, &num_nodes_in, &num_nodes_out));
424   CeedCall(CeedOperatorGetActiveElemRestrictions(op, &elem_rstr_in, &elem_rstr_out));
425   CeedCall(CeedElemRestrictionGetNumElements(elem_rstr_in, &num_elem_in));
426   CeedCall(CeedElemRestrictionGetElementSize(elem_rstr_in, &elem_size_in));
427   CeedCall(CeedElemRestrictionGetNumComponents(elem_rstr_in, &num_comp_in));
428   CeedCall(CeedElemRestrictionGetELayout(elem_rstr_in, layout_er_in));
429 
430   // Determine elem_dof relation for input
431   CeedCall(CeedVectorCreate(ceed, num_nodes_in, &index_vec_in));
432   CeedCall(CeedVectorGetArrayWrite(index_vec_in, CEED_MEM_HOST, &array));
433   for (CeedInt i = 0; i < num_nodes_in; i++) array[i] = i;
434   CeedCall(CeedVectorRestoreArray(index_vec_in, &array));
435   CeedCall(CeedVectorCreate(ceed, num_elem_in * elem_size_in * num_comp_in, &elem_dof_in));
436   CeedCall(CeedVectorSetValue(elem_dof_in, 0.0));
437   CeedCall(CeedElemRestrictionCreateUnorientedCopy(elem_rstr_in, &index_elem_rstr_in));
438   CeedCall(CeedElemRestrictionApply(index_elem_rstr_in, CEED_NOTRANSPOSE, index_vec_in, elem_dof_in, CEED_REQUEST_IMMEDIATE));
439   CeedCall(CeedVectorGetArrayRead(elem_dof_in, CEED_MEM_HOST, &elem_dof_a_in));
440   CeedCall(CeedVectorDestroy(&index_vec_in));
441   CeedCall(CeedElemRestrictionDestroy(&index_elem_rstr_in));
442 
443   if (elem_rstr_in != elem_rstr_out) {
444     CeedCall(CeedElemRestrictionGetNumElements(elem_rstr_out, &num_elem_out));
445     CeedCheck(num_elem_in == num_elem_out, ceed, CEED_ERROR_UNSUPPORTED,
446               "Active input and output operator restrictions must have the same number of elements");
447     CeedCall(CeedElemRestrictionGetElementSize(elem_rstr_out, &elem_size_out));
448     CeedCall(CeedElemRestrictionGetNumComponents(elem_rstr_out, &num_comp_out));
449     CeedCall(CeedElemRestrictionGetELayout(elem_rstr_out, layout_er_out));
450 
451     // Determine elem_dof relation for output
452     CeedCall(CeedVectorCreate(ceed, num_nodes_out, &index_vec_out));
453     CeedCall(CeedVectorGetArrayWrite(index_vec_out, CEED_MEM_HOST, &array));
454     for (CeedInt i = 0; i < num_nodes_out; i++) array[i] = i;
455     CeedCall(CeedVectorRestoreArray(index_vec_out, &array));
456     CeedCall(CeedVectorCreate(ceed, num_elem_out * elem_size_out * num_comp_out, &elem_dof_out));
457     CeedCall(CeedVectorSetValue(elem_dof_out, 0.0));
458     CeedCall(CeedElemRestrictionCreateUnorientedCopy(elem_rstr_out, &index_elem_rstr_out));
459     CeedCall(CeedElemRestrictionApply(index_elem_rstr_out, CEED_NOTRANSPOSE, index_vec_out, elem_dof_out, CEED_REQUEST_IMMEDIATE));
460     CeedCall(CeedVectorGetArrayRead(elem_dof_out, CEED_MEM_HOST, &elem_dof_a_out));
461     CeedCall(CeedVectorDestroy(&index_vec_out));
462     CeedCall(CeedElemRestrictionDestroy(&index_elem_rstr_out));
463   } else {
464     num_elem_out     = num_elem_in;
465     elem_size_out    = elem_size_in;
466     num_comp_out     = num_comp_in;
467     layout_er_out[0] = layout_er_in[0];
468     layout_er_out[1] = layout_er_in[1];
469     layout_er_out[2] = layout_er_in[2];
470     elem_dof_a_out   = elem_dof_a_in;
471   }
472   local_num_entries = elem_size_out * num_comp_out * elem_size_in * num_comp_in * num_elem_in;
473 
474   // Determine i, j locations for element matrices
475   for (CeedInt e = 0; e < num_elem_in; e++) {
476     for (CeedInt comp_in = 0; comp_in < num_comp_in; comp_in++) {
477       for (CeedInt comp_out = 0; comp_out < num_comp_out; comp_out++) {
478         for (CeedInt i = 0; i < elem_size_out; i++) {
479           for (CeedInt j = 0; j < elem_size_in; j++) {
480             const CeedInt elem_dof_index_row = i * layout_er_out[0] + comp_out * layout_er_out[1] + e * layout_er_out[2];
481             const CeedInt elem_dof_index_col = j * layout_er_in[0] + comp_in * layout_er_in[1] + e * layout_er_in[2];
482             const CeedInt row                = elem_dof_a_out[elem_dof_index_row];
483             const CeedInt col                = elem_dof_a_in[elem_dof_index_col];
484 
485             rows[offset + count] = row;
486             cols[offset + count] = col;
487             count++;
488           }
489         }
490       }
491     }
492   }
493   CeedCheck(count == local_num_entries, ceed, CEED_ERROR_MAJOR, "Error computing assembled entries");
494   CeedCall(CeedVectorRestoreArrayRead(elem_dof_in, &elem_dof_a_in));
495   CeedCall(CeedVectorDestroy(&elem_dof_in));
496   if (elem_rstr_in != elem_rstr_out) {
497     CeedCall(CeedVectorRestoreArrayRead(elem_dof_out, &elem_dof_a_out));
498     CeedCall(CeedVectorDestroy(&elem_dof_out));
499   }
500   return CEED_ERROR_SUCCESS;
501 }
502 
503 /**
504   @brief Assemble nonzero entries for non-composite `CeedOperator`.
505 
506   Users should generally use @ref CeedOperatorLinearAssemble().
507 
508   @param[in]  op     `CeedOperator` to assemble
509   @param[in]  offset Offset for number of entries
510   @param[out] values Values to assemble into matrix
511 
512   @return An error code: 0 - success, otherwise - failure
513 
514   @ref Developer
515 **/
516 static int CeedSingleOperatorAssemble(CeedOperator op, CeedInt offset, CeedVector values) {
517   Ceed ceed;
518   bool is_composite;
519 
520   CeedCall(CeedOperatorGetCeed(op, &ceed));
521   CeedCall(CeedOperatorIsComposite(op, &is_composite));
522   CeedCheck(!is_composite, ceed, CEED_ERROR_UNSUPPORTED, "Composite operator not supported");
523 
524   // Early exit for empty operator
525   {
526     CeedInt num_elem = 0;
527 
528     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
529     if (num_elem == 0) return CEED_ERROR_SUCCESS;
530   }
531 
532   if (op->LinearAssembleSingle) {
533     // Backend version
534     CeedCall(op->LinearAssembleSingle(op, offset, values));
535     return CEED_ERROR_SUCCESS;
536   } else {
537     // Operator fallback
538     CeedOperator op_fallback;
539 
540     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
541     if (op_fallback) {
542       CeedCall(CeedSingleOperatorAssemble(op_fallback, offset, values));
543       return CEED_ERROR_SUCCESS;
544     }
545   }
546 
547   // Assemble QFunction
548   CeedInt             layout_qf[3];
549   const CeedScalar   *assembled_qf_array;
550   CeedVector          assembled_qf        = NULL;
551   CeedElemRestriction assembled_elem_rstr = NULL;
552 
553   CeedCall(CeedOperatorLinearAssembleQFunctionBuildOrUpdate(op, &assembled_qf, &assembled_elem_rstr, CEED_REQUEST_IMMEDIATE));
554   CeedCall(CeedElemRestrictionGetELayout(assembled_elem_rstr, layout_qf));
555   CeedCall(CeedElemRestrictionDestroy(&assembled_elem_rstr));
556   CeedCall(CeedVectorGetArrayRead(assembled_qf, CEED_MEM_HOST, &assembled_qf_array));
557 
558   // Get assembly data
559   CeedInt                  num_elem_in, elem_size_in, num_comp_in, num_qpts_in;
560   CeedInt                  num_elem_out, elem_size_out, num_comp_out, num_qpts_out;
561   CeedSize                 local_num_entries, count = 0;
562   const CeedEvalMode     **eval_modes_in, **eval_modes_out;
563   CeedInt                  num_active_bases_in, *num_eval_modes_in, num_active_bases_out, *num_eval_modes_out;
564   CeedBasis               *active_bases_in, *active_bases_out, basis_in, basis_out;
565   const CeedScalar       **B_mats_in, **B_mats_out, *B_mat_in, *B_mat_out;
566   CeedElemRestriction      elem_rstr_in, elem_rstr_out;
567   CeedRestrictionType      elem_rstr_type_in, elem_rstr_type_out;
568   const bool              *elem_rstr_orients_in = NULL, *elem_rstr_orients_out = NULL;
569   const CeedInt8          *elem_rstr_curl_orients_in = NULL, *elem_rstr_curl_orients_out = NULL;
570   CeedOperatorAssemblyData data;
571 
572   CeedCall(CeedOperatorGetOperatorAssemblyData(op, &data));
573   CeedCall(CeedOperatorAssemblyDataGetEvalModes(data, &num_active_bases_in, &num_eval_modes_in, &eval_modes_in, NULL, &num_active_bases_out,
574                                                 &num_eval_modes_out, &eval_modes_out, NULL, NULL));
575 
576   CeedCheck(num_active_bases_in == num_active_bases_out && num_active_bases_in == 1, ceed, CEED_ERROR_UNSUPPORTED,
577             "Cannot assemble operator with multiple active bases");
578   CeedCheck(num_eval_modes_in[0] > 0 && num_eval_modes_out[0] > 0, ceed, CEED_ERROR_UNSUPPORTED, "Cannot assemble operator without inputs/outputs");
579 
580   CeedCall(CeedOperatorAssemblyDataGetBases(data, NULL, &active_bases_in, &B_mats_in, NULL, &active_bases_out, &B_mats_out));
581   CeedCall(CeedOperatorGetActiveElemRestrictions(op, &elem_rstr_in, &elem_rstr_out));
582   basis_in  = active_bases_in[0];
583   basis_out = active_bases_out[0];
584   B_mat_in  = B_mats_in[0];
585   B_mat_out = B_mats_out[0];
586 
587   CeedCall(CeedElemRestrictionGetNumElements(elem_rstr_in, &num_elem_in));
588   CeedCall(CeedElemRestrictionGetElementSize(elem_rstr_in, &elem_size_in));
589   CeedCall(CeedElemRestrictionGetNumComponents(elem_rstr_in, &num_comp_in));
590   if (basis_in == CEED_BASIS_NONE) num_qpts_in = elem_size_in;
591   else CeedCall(CeedBasisGetNumQuadraturePoints(basis_in, &num_qpts_in));
592 
593   CeedCall(CeedElemRestrictionGetType(elem_rstr_in, &elem_rstr_type_in));
594   if (elem_rstr_type_in == CEED_RESTRICTION_ORIENTED) {
595     CeedCall(CeedElemRestrictionGetOrientations(elem_rstr_in, CEED_MEM_HOST, &elem_rstr_orients_in));
596   } else if (elem_rstr_type_in == CEED_RESTRICTION_CURL_ORIENTED) {
597     CeedCall(CeedElemRestrictionGetCurlOrientations(elem_rstr_in, CEED_MEM_HOST, &elem_rstr_curl_orients_in));
598   }
599 
600   if (elem_rstr_in != elem_rstr_out) {
601     CeedCall(CeedElemRestrictionGetNumElements(elem_rstr_out, &num_elem_out));
602     CeedCheck(num_elem_in == num_elem_out, ceed, CEED_ERROR_UNSUPPORTED,
603               "Active input and output operator restrictions must have the same number of elements");
604     CeedCall(CeedElemRestrictionGetElementSize(elem_rstr_out, &elem_size_out));
605     CeedCall(CeedElemRestrictionGetNumComponents(elem_rstr_out, &num_comp_out));
606     if (basis_out == CEED_BASIS_NONE) num_qpts_out = elem_size_out;
607     else CeedCall(CeedBasisGetNumQuadraturePoints(basis_out, &num_qpts_out));
608     CeedCheck(num_qpts_in == num_qpts_out, ceed, CEED_ERROR_UNSUPPORTED,
609               "Active input and output bases must have the same number of quadrature points");
610 
611     CeedCall(CeedElemRestrictionGetType(elem_rstr_out, &elem_rstr_type_out));
612     if (elem_rstr_type_out == CEED_RESTRICTION_ORIENTED) {
613       CeedCall(CeedElemRestrictionGetOrientations(elem_rstr_out, CEED_MEM_HOST, &elem_rstr_orients_out));
614     } else if (elem_rstr_type_out == CEED_RESTRICTION_CURL_ORIENTED) {
615       CeedCall(CeedElemRestrictionGetCurlOrientations(elem_rstr_out, CEED_MEM_HOST, &elem_rstr_curl_orients_out));
616     }
617   } else {
618     num_elem_out  = num_elem_in;
619     elem_size_out = elem_size_in;
620     num_comp_out  = num_comp_in;
621     num_qpts_out  = num_qpts_in;
622 
623     elem_rstr_orients_out      = elem_rstr_orients_in;
624     elem_rstr_curl_orients_out = elem_rstr_curl_orients_in;
625   }
626   local_num_entries = elem_size_out * num_comp_out * elem_size_in * num_comp_in * num_elem_in;
627 
628   // Loop over elements and put in data structure
629   // We store B_mat_in, B_mat_out, BTD, elem_mat in row-major order
630   CeedTensorContract contract;
631   CeedScalar        *vals, *BTD_mat = NULL, *elem_mat = NULL, *elem_mat_b = NULL;
632 
633   CeedCall(CeedBasisGetTensorContract(basis_in, &contract));
634   CeedCall(CeedCalloc(elem_size_out * num_qpts_in * num_eval_modes_in[0], &BTD_mat));
635   CeedCall(CeedCalloc(elem_size_out * elem_size_in, &elem_mat));
636   if (elem_rstr_curl_orients_in || elem_rstr_curl_orients_out) CeedCall(CeedCalloc(elem_size_out * elem_size_in, &elem_mat_b));
637 
638   CeedCall(CeedVectorGetArray(values, CEED_MEM_HOST, &vals));
639   for (CeedSize e = 0; e < num_elem_in; e++) {
640     for (CeedInt comp_in = 0; comp_in < num_comp_in; comp_in++) {
641       for (CeedInt comp_out = 0; comp_out < num_comp_out; comp_out++) {
642         // Compute B^T*D
643         for (CeedSize n = 0; n < elem_size_out; n++) {
644           for (CeedSize q = 0; q < num_qpts_in; q++) {
645             for (CeedInt e_in = 0; e_in < num_eval_modes_in[0]; e_in++) {
646               const CeedSize btd_index = n * (num_qpts_in * num_eval_modes_in[0]) + q * num_eval_modes_in[0] + e_in;
647               CeedScalar     sum       = 0.0;
648 
649               for (CeedInt e_out = 0; e_out < num_eval_modes_out[0]; e_out++) {
650                 const CeedSize b_out_index     = (q * num_eval_modes_out[0] + e_out) * elem_size_out + n;
651                 const CeedSize eval_mode_index = ((e_in * num_comp_in + comp_in) * num_eval_modes_out[0] + e_out) * num_comp_out + comp_out;
652                 const CeedSize qf_index        = q * layout_qf[0] + eval_mode_index * layout_qf[1] + e * layout_qf[2];
653 
654                 sum += B_mat_out[b_out_index] * assembled_qf_array[qf_index];
655               }
656               BTD_mat[btd_index] = sum;
657             }
658           }
659         }
660 
661         // Form element matrix itself (for each block component)
662         if (contract) {
663           CeedCall(CeedTensorContractApply(contract, 1, num_qpts_in * num_eval_modes_in[0], elem_size_in, elem_size_out, BTD_mat, CEED_NOTRANSPOSE,
664                                            false, B_mat_in, elem_mat));
665         } else {
666           CeedCall(CeedMatrixMatrixMultiply(ceed, BTD_mat, B_mat_in, elem_mat, elem_size_out, elem_size_in, num_qpts_in * num_eval_modes_in[0]));
667         }
668 
669         // Transform the element matrix if required
670         if (elem_rstr_orients_out) {
671           const bool *elem_orients = &elem_rstr_orients_out[e * elem_size_out];
672 
673           for (CeedInt i = 0; i < elem_size_out; i++) {
674             const double orient = elem_orients[i] ? -1.0 : 1.0;
675 
676             for (CeedInt j = 0; j < elem_size_in; j++) {
677               elem_mat[i * elem_size_in + j] *= orient;
678             }
679           }
680         } else if (elem_rstr_curl_orients_out) {
681           const CeedInt8 *elem_curl_orients = &elem_rstr_curl_orients_out[e * 3 * elem_size_out];
682 
683           // T^T*(B^T*D*B)
684           memcpy(elem_mat_b, elem_mat, elem_size_out * elem_size_in * sizeof(CeedScalar));
685           for (CeedInt i = 0; i < elem_size_out; i++) {
686             for (CeedInt j = 0; j < elem_size_in; j++) {
687               elem_mat[i * elem_size_in + j] = elem_mat_b[i * elem_size_in + j] * elem_curl_orients[3 * i + 1] +
688                                                (i > 0 ? elem_mat_b[(i - 1) * elem_size_in + j] * elem_curl_orients[3 * i - 1] : 0.0) +
689                                                (i < elem_size_out - 1 ? elem_mat_b[(i + 1) * elem_size_in + j] * elem_curl_orients[3 * i + 3] : 0.0);
690             }
691           }
692         }
693         if (elem_rstr_orients_in) {
694           const bool *elem_orients = &elem_rstr_orients_in[e * elem_size_in];
695 
696           for (CeedInt i = 0; i < elem_size_out; i++) {
697             for (CeedInt j = 0; j < elem_size_in; j++) {
698               elem_mat[i * elem_size_in + j] *= elem_orients[j] ? -1.0 : 1.0;
699             }
700           }
701         } else if (elem_rstr_curl_orients_in) {
702           const CeedInt8 *elem_curl_orients = &elem_rstr_curl_orients_in[e * 3 * elem_size_in];
703 
704           // (B^T*D*B)*T
705           memcpy(elem_mat_b, elem_mat, elem_size_out * elem_size_in * sizeof(CeedScalar));
706           for (CeedInt i = 0; i < elem_size_out; i++) {
707             for (CeedInt j = 0; j < elem_size_in; j++) {
708               elem_mat[i * elem_size_in + j] = elem_mat_b[i * elem_size_in + j] * elem_curl_orients[3 * j + 1] +
709                                                (j > 0 ? elem_mat_b[i * elem_size_in + j - 1] * elem_curl_orients[3 * j - 1] : 0.0) +
710                                                (j < elem_size_in - 1 ? elem_mat_b[i * elem_size_in + j + 1] * elem_curl_orients[3 * j + 3] : 0.0);
711             }
712           }
713         }
714 
715         // Put element matrix in coordinate data structure
716         for (CeedInt i = 0; i < elem_size_out; i++) {
717           for (CeedInt j = 0; j < elem_size_in; j++) {
718             vals[offset + count] = elem_mat[i * elem_size_in + j];
719             count++;
720           }
721         }
722       }
723     }
724   }
725   CeedCheck(count == local_num_entries, ceed, CEED_ERROR_MAJOR, "Error computing entries");
726   CeedCall(CeedVectorRestoreArray(values, &vals));
727 
728   // Cleanup
729   CeedCall(CeedFree(&BTD_mat));
730   CeedCall(CeedFree(&elem_mat));
731   CeedCall(CeedFree(&elem_mat_b));
732   if (elem_rstr_type_in == CEED_RESTRICTION_ORIENTED) {
733     CeedCall(CeedElemRestrictionRestoreOrientations(elem_rstr_in, &elem_rstr_orients_in));
734   } else if (elem_rstr_type_in == CEED_RESTRICTION_CURL_ORIENTED) {
735     CeedCall(CeedElemRestrictionRestoreCurlOrientations(elem_rstr_in, &elem_rstr_curl_orients_in));
736   }
737   if (elem_rstr_in != elem_rstr_out) {
738     if (elem_rstr_type_out == CEED_RESTRICTION_ORIENTED) {
739       CeedCall(CeedElemRestrictionRestoreOrientations(elem_rstr_out, &elem_rstr_orients_out));
740     } else if (elem_rstr_type_out == CEED_RESTRICTION_CURL_ORIENTED) {
741       CeedCall(CeedElemRestrictionRestoreCurlOrientations(elem_rstr_out, &elem_rstr_curl_orients_out));
742     }
743   }
744   CeedCall(CeedVectorRestoreArrayRead(assembled_qf, &assembled_qf_array));
745   CeedCall(CeedVectorDestroy(&assembled_qf));
746   return CEED_ERROR_SUCCESS;
747 }
748 
749 /**
750   @brief Count number of entries for assembled `CeedOperator`
751 
752   @param[in]  op          `CeedOperator` to assemble
753   @param[out] num_entries Number of entries in assembled representation
754 
755   @return An error code: 0 - success, otherwise - failure
756 
757   @ref Utility
758 **/
759 static int CeedSingleOperatorAssemblyCountEntries(CeedOperator op, CeedSize *num_entries) {
760   bool                is_composite;
761   CeedInt             num_elem_in, elem_size_in, num_comp_in, num_elem_out, elem_size_out, num_comp_out;
762   Ceed                ceed;
763   CeedElemRestriction rstr_in, rstr_out;
764 
765   CeedCall(CeedOperatorGetCeed(op, &ceed));
766   CeedCall(CeedOperatorIsComposite(op, &is_composite));
767   CeedCheck(!is_composite, ceed, CEED_ERROR_UNSUPPORTED, "Composite operator not supported");
768 
769   CeedCall(CeedOperatorGetActiveElemRestrictions(op, &rstr_in, &rstr_out));
770   CeedCall(CeedElemRestrictionGetNumElements(rstr_in, &num_elem_in));
771   CeedCall(CeedElemRestrictionGetElementSize(rstr_in, &elem_size_in));
772   CeedCall(CeedElemRestrictionGetNumComponents(rstr_in, &num_comp_in));
773   if (rstr_in != rstr_out) {
774     CeedCall(CeedElemRestrictionGetNumElements(rstr_out, &num_elem_out));
775     CeedCheck(num_elem_in == num_elem_out, ceed, CEED_ERROR_UNSUPPORTED,
776               "Active input and output operator restrictions must have the same number of elements");
777     CeedCall(CeedElemRestrictionGetElementSize(rstr_out, &elem_size_out));
778     CeedCall(CeedElemRestrictionGetNumComponents(rstr_out, &num_comp_out));
779   } else {
780     num_elem_out  = num_elem_in;
781     elem_size_out = elem_size_in;
782     num_comp_out  = num_comp_in;
783   }
784   *num_entries = (CeedSize)elem_size_in * num_comp_in * elem_size_out * num_comp_out * num_elem_in;
785   return CEED_ERROR_SUCCESS;
786 }
787 
788 /**
789   @brief Common code for creating a multigrid coarse `CeedOperator` and level transfer `CeedOperator` for a `CeedOperator`
790 
791   @param[in]  op_fine      Fine grid `CeedOperator`
792   @param[in]  p_mult_fine  L-vector multiplicity in parallel gather/scatter, or `NULL` if not creating prolongation/restriction `CeedOperator`
793   @param[in]  rstr_coarse  Coarse grid `CeedElemRestriction`
794   @param[in]  basis_coarse Coarse grid active vector `CeedBasis`
795   @param[in]  basis_c_to_f `CeedBasis` for coarse to fine interpolation, or `NULL` if not creating prolongation/restriction operators
796   @param[out] op_coarse    Coarse grid `CeedOperator`
797   @param[out] op_prolong   Coarse to fine `CeedOperator`, or `NULL`
798   @param[out] op_restrict  Fine to coarse `CeedOperator`, or `NULL`
799 
800   @return An error code: 0 - success, otherwise - failure
801 
802   @ref Developer
803 **/
804 static int CeedSingleOperatorMultigridLevel(CeedOperator op_fine, CeedVector p_mult_fine, CeedElemRestriction rstr_coarse, CeedBasis basis_coarse,
805                                             CeedBasis basis_c_to_f, CeedOperator *op_coarse, CeedOperator *op_prolong, CeedOperator *op_restrict) {
806   bool                is_composite;
807   Ceed                ceed;
808   CeedInt             num_comp, num_input_fields, num_output_fields;
809   CeedVector          mult_vec         = NULL;
810   CeedElemRestriction rstr_p_mult_fine = NULL, rstr_fine = NULL;
811   CeedOperatorField  *input_fields, *output_fields;
812 
813   CeedCall(CeedOperatorGetCeed(op_fine, &ceed));
814 
815   // Check for composite operator
816   CeedCall(CeedOperatorIsComposite(op_fine, &is_composite));
817   CeedCheck(!is_composite, ceed, CEED_ERROR_UNSUPPORTED, "Automatic multigrid setup for composite operators not supported");
818 
819   // Coarse Grid
820   CeedCall(CeedOperatorCreate(ceed, op_fine->qf, op_fine->dqf, op_fine->dqfT, op_coarse));
821   CeedCall(CeedOperatorGetFields(op_fine, &num_input_fields, &input_fields, &num_output_fields, &output_fields));
822   // -- Clone input fields
823   for (CeedInt i = 0; i < num_input_fields; i++) {
824     const char         *field_name;
825     CeedVector          vec;
826     CeedElemRestriction rstr;
827     CeedBasis           basis;
828 
829     CeedCall(CeedOperatorFieldGetName(input_fields[i], &field_name));
830     CeedCall(CeedOperatorFieldGetVector(input_fields[i], &vec));
831     if (vec == CEED_VECTOR_ACTIVE) {
832       rstr  = rstr_coarse;
833       basis = basis_coarse;
834       CeedCall(CeedOperatorFieldGetElemRestriction(input_fields[i], &rstr_fine));
835     } else {
836       CeedCall(CeedOperatorFieldGetElemRestriction(input_fields[i], &rstr));
837       CeedCall(CeedOperatorFieldGetBasis(input_fields[i], &basis));
838     }
839     CeedCall(CeedOperatorSetField(*op_coarse, field_name, rstr, basis, vec));
840   }
841   // -- Clone output fields
842   for (CeedInt i = 0; i < num_output_fields; i++) {
843     const char         *field_name;
844     CeedVector          vec;
845     CeedElemRestriction rstr;
846     CeedBasis           basis;
847 
848     CeedCall(CeedOperatorFieldGetName(output_fields[i], &field_name));
849     CeedCall(CeedOperatorFieldGetVector(output_fields[i], &vec));
850     if (vec == CEED_VECTOR_ACTIVE) {
851       rstr  = rstr_coarse;
852       basis = basis_coarse;
853       CeedCall(CeedOperatorFieldGetElemRestriction(output_fields[i], &rstr_fine));
854     } else {
855       CeedCall(CeedOperatorFieldGetElemRestriction(output_fields[i], &rstr));
856       CeedCall(CeedOperatorFieldGetBasis(output_fields[i], &basis));
857     }
858     CeedCall(CeedOperatorSetField(*op_coarse, field_name, rstr, basis, vec));
859   }
860   // -- Clone QFunctionAssemblyData
861   CeedCall(CeedQFunctionAssemblyDataReferenceCopy(op_fine->qf_assembled, &(*op_coarse)->qf_assembled));
862 
863   // Multiplicity vector
864   if (op_restrict || op_prolong) {
865     CeedVector          mult_e_vec;
866     CeedRestrictionType rstr_type;
867 
868     CeedCall(CeedElemRestrictionGetType(rstr_fine, &rstr_type));
869     CeedCheck(rstr_type != CEED_RESTRICTION_CURL_ORIENTED, ceed, CEED_ERROR_UNSUPPORTED,
870               "Element restrictions created with CeedElemRestrictionCreateCurlOriented are not supported");
871     CeedCheck(p_mult_fine, ceed, CEED_ERROR_INCOMPATIBLE, "Prolongation or restriction operator creation requires fine grid multiplicity vector");
872     CeedCall(CeedElemRestrictionCreateUnsignedCopy(rstr_fine, &rstr_p_mult_fine));
873     CeedCall(CeedElemRestrictionCreateVector(rstr_fine, &mult_vec, &mult_e_vec));
874     CeedCall(CeedVectorSetValue(mult_e_vec, 0.0));
875     CeedCall(CeedElemRestrictionApply(rstr_p_mult_fine, CEED_NOTRANSPOSE, p_mult_fine, mult_e_vec, CEED_REQUEST_IMMEDIATE));
876     CeedCall(CeedVectorSetValue(mult_vec, 0.0));
877     CeedCall(CeedElemRestrictionApply(rstr_p_mult_fine, CEED_TRANSPOSE, mult_e_vec, mult_vec, CEED_REQUEST_IMMEDIATE));
878     CeedCall(CeedVectorDestroy(&mult_e_vec));
879     CeedCall(CeedVectorReciprocal(mult_vec));
880   }
881 
882   // Clone name
883   bool   has_name = op_fine->name;
884   size_t name_len = op_fine->name ? strlen(op_fine->name) : 0;
885   CeedCall(CeedOperatorSetName(*op_coarse, op_fine->name));
886 
887   // Check that coarse to fine basis is provided if prolong/restrict operators are requested
888   CeedCheck(basis_c_to_f || (!op_restrict && !op_prolong), ceed, CEED_ERROR_INCOMPATIBLE,
889             "Prolongation or restriction operator creation requires coarse-to-fine basis");
890 
891   // Restriction/Prolongation Operators
892   CeedCall(CeedBasisGetNumComponents(basis_coarse, &num_comp));
893 
894   // Restriction
895   if (op_restrict) {
896     CeedInt             *num_comp_r_data;
897     CeedQFunctionContext ctx_r;
898     CeedQFunction        qf_restrict;
899 
900     CeedCall(CeedQFunctionCreateInteriorByName(ceed, "Scale", &qf_restrict));
901     CeedCall(CeedCalloc(1, &num_comp_r_data));
902     num_comp_r_data[0] = num_comp;
903     CeedCall(CeedQFunctionContextCreate(ceed, &ctx_r));
904     CeedCall(CeedQFunctionContextSetData(ctx_r, CEED_MEM_HOST, CEED_OWN_POINTER, sizeof(*num_comp_r_data), num_comp_r_data));
905     CeedCall(CeedQFunctionSetContext(qf_restrict, ctx_r));
906     CeedCall(CeedQFunctionContextDestroy(&ctx_r));
907     CeedCall(CeedQFunctionAddInput(qf_restrict, "input", num_comp, CEED_EVAL_NONE));
908     CeedCall(CeedQFunctionAddInput(qf_restrict, "scale", num_comp, CEED_EVAL_NONE));
909     CeedCall(CeedQFunctionAddOutput(qf_restrict, "output", num_comp, CEED_EVAL_INTERP));
910     CeedCall(CeedQFunctionSetUserFlopsEstimate(qf_restrict, num_comp));
911 
912     CeedCall(CeedOperatorCreate(ceed, qf_restrict, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, op_restrict));
913     CeedCall(CeedOperatorSetField(*op_restrict, "input", rstr_fine, CEED_BASIS_NONE, CEED_VECTOR_ACTIVE));
914     CeedCall(CeedOperatorSetField(*op_restrict, "scale", rstr_p_mult_fine, CEED_BASIS_NONE, mult_vec));
915     CeedCall(CeedOperatorSetField(*op_restrict, "output", rstr_coarse, basis_c_to_f, CEED_VECTOR_ACTIVE));
916 
917     // Set name
918     char *restriction_name;
919 
920     CeedCall(CeedCalloc(17 + name_len, &restriction_name));
921     sprintf(restriction_name, "restriction%s%s", has_name ? " for " : "", has_name ? op_fine->name : "");
922     CeedCall(CeedOperatorSetName(*op_restrict, restriction_name));
923     CeedCall(CeedFree(&restriction_name));
924 
925     // Check
926     CeedCall(CeedOperatorCheckReady(*op_restrict));
927 
928     // Cleanup
929     CeedCall(CeedQFunctionDestroy(&qf_restrict));
930   }
931 
932   // Prolongation
933   if (op_prolong) {
934     CeedInt             *num_comp_p_data;
935     CeedQFunctionContext ctx_p;
936     CeedQFunction        qf_prolong;
937 
938     CeedCall(CeedQFunctionCreateInteriorByName(ceed, "Scale", &qf_prolong));
939     CeedCall(CeedCalloc(1, &num_comp_p_data));
940     num_comp_p_data[0] = num_comp;
941     CeedCall(CeedQFunctionContextCreate(ceed, &ctx_p));
942     CeedCall(CeedQFunctionContextSetData(ctx_p, CEED_MEM_HOST, CEED_OWN_POINTER, sizeof(*num_comp_p_data), num_comp_p_data));
943     CeedCall(CeedQFunctionSetContext(qf_prolong, ctx_p));
944     CeedCall(CeedQFunctionContextDestroy(&ctx_p));
945     CeedCall(CeedQFunctionAddInput(qf_prolong, "input", num_comp, CEED_EVAL_INTERP));
946     CeedCall(CeedQFunctionAddInput(qf_prolong, "scale", num_comp, CEED_EVAL_NONE));
947     CeedCall(CeedQFunctionAddOutput(qf_prolong, "output", num_comp, CEED_EVAL_NONE));
948     CeedCall(CeedQFunctionSetUserFlopsEstimate(qf_prolong, num_comp));
949 
950     CeedCall(CeedOperatorCreate(ceed, qf_prolong, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, op_prolong));
951     CeedCall(CeedOperatorSetField(*op_prolong, "input", rstr_coarse, basis_c_to_f, CEED_VECTOR_ACTIVE));
952     CeedCall(CeedOperatorSetField(*op_prolong, "scale", rstr_p_mult_fine, CEED_BASIS_NONE, mult_vec));
953     CeedCall(CeedOperatorSetField(*op_prolong, "output", rstr_fine, CEED_BASIS_NONE, CEED_VECTOR_ACTIVE));
954 
955     // Set name
956     char *prolongation_name;
957 
958     CeedCall(CeedCalloc(18 + name_len, &prolongation_name));
959     sprintf(prolongation_name, "prolongation%s%s", has_name ? " for " : "", has_name ? op_fine->name : "");
960     CeedCall(CeedOperatorSetName(*op_prolong, prolongation_name));
961     CeedCall(CeedFree(&prolongation_name));
962 
963     // Check
964     CeedCall(CeedOperatorCheckReady(*op_prolong));
965 
966     // Cleanup
967     CeedCall(CeedQFunctionDestroy(&qf_prolong));
968   }
969 
970   // Check
971   CeedCall(CeedOperatorCheckReady(*op_coarse));
972 
973   // Cleanup
974   CeedCall(CeedVectorDestroy(&mult_vec));
975   CeedCall(CeedElemRestrictionDestroy(&rstr_p_mult_fine));
976   CeedCall(CeedBasisDestroy(&basis_c_to_f));
977   return CEED_ERROR_SUCCESS;
978 }
979 
980 /**
981   @brief Build 1D mass matrix and Laplacian with perturbation
982 
983   @param[in]  interp_1d   Interpolation matrix in one dimension
984   @param[in]  grad_1d     Gradient matrix in one dimension
985   @param[in]  q_weight_1d Quadrature weights in one dimension
986   @param[in]  P_1d        Number of basis nodes in one dimension
987   @param[in]  Q_1d        Number of quadrature points in one dimension
988   @param[in]  dim         Dimension of basis
989   @param[out] mass        Assembled mass matrix in one dimension
990   @param[out] laplace     Assembled perturbed Laplacian in one dimension
991 
992   @return An error code: 0 - success, otherwise - failure
993 
994   @ref Developer
995 **/
996 CeedPragmaOptimizeOff
997 static int CeedBuildMassLaplace(const CeedScalar *interp_1d, const CeedScalar *grad_1d, const CeedScalar *q_weight_1d, CeedInt P_1d, CeedInt Q_1d,
998                                 CeedInt dim, CeedScalar *mass, CeedScalar *laplace) {
999   for (CeedInt i = 0; i < P_1d; i++) {
1000     for (CeedInt j = 0; j < P_1d; j++) {
1001       CeedScalar sum = 0.0;
1002       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];
1003       mass[i + j * P_1d] = sum;
1004     }
1005   }
1006   // -- Laplacian
1007   for (CeedInt i = 0; i < P_1d; i++) {
1008     for (CeedInt j = 0; j < P_1d; j++) {
1009       CeedScalar sum = 0.0;
1010 
1011       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];
1012       laplace[i + j * P_1d] = sum;
1013     }
1014   }
1015   CeedScalar perturbation = dim > 2 ? 1e-6 : 1e-4;
1016   for (CeedInt i = 0; i < P_1d; i++) laplace[i + P_1d * i] += perturbation;
1017   return CEED_ERROR_SUCCESS;
1018 }
1019 CeedPragmaOptimizeOn
1020 
1021 /// @}
1022 
1023 /// ----------------------------------------------------------------------------
1024 /// CeedOperator Backend API
1025 /// ----------------------------------------------------------------------------
1026 /// @addtogroup CeedOperatorBackend
1027 /// @{
1028 
1029 /**
1030   @brief Select correct basis matrix pointer based on @ref CeedEvalMode
1031 
1032   @param[in]  basis     `CeedBasis` from which to get the basis matrix
1033   @param[in]  eval_mode Current basis evaluation mode
1034   @param[in]  identity  Pointer to identity matrix
1035   @param[out] basis_ptr `CeedBasis` pointer to set
1036 
1037   @ref Backend
1038 **/
1039 int CeedOperatorGetBasisPointer(CeedBasis basis, CeedEvalMode eval_mode, const CeedScalar *identity, const CeedScalar **basis_ptr) {
1040   switch (eval_mode) {
1041     case CEED_EVAL_NONE:
1042       *basis_ptr = identity;
1043       break;
1044     case CEED_EVAL_INTERP:
1045       CeedCall(CeedBasisGetInterp(basis, basis_ptr));
1046       break;
1047     case CEED_EVAL_GRAD:
1048       CeedCall(CeedBasisGetGrad(basis, basis_ptr));
1049       break;
1050     case CEED_EVAL_DIV:
1051       CeedCall(CeedBasisGetDiv(basis, basis_ptr));
1052       break;
1053     case CEED_EVAL_CURL:
1054       CeedCall(CeedBasisGetCurl(basis, basis_ptr));
1055       break;
1056     case CEED_EVAL_WEIGHT:
1057       break;  // Caught by QF Assembly
1058   }
1059   assert(*basis_ptr != NULL);
1060   return CEED_ERROR_SUCCESS;
1061 }
1062 
1063 /**
1064   @brief Create point block restriction for active `CeedOperatorField`
1065 
1066   @param[in]  rstr             Original `CeedElemRestriction` for active field
1067   @param[out] point_block_rstr Address of the variable where the newly created `CeedElemRestriction` will be stored
1068 
1069   @return An error code: 0 - success, otherwise - failure
1070 
1071   @ref Backend
1072 **/
1073 int CeedOperatorCreateActivePointBlockRestriction(CeedElemRestriction rstr, CeedElemRestriction *point_block_rstr) {
1074   Ceed           ceed;
1075   CeedInt        num_elem, num_comp, shift, elem_size, comp_stride, *point_block_offsets;
1076   CeedSize       l_size;
1077   const CeedInt *offsets;
1078 
1079   CeedCall(CeedElemRestrictionGetCeed(rstr, &ceed));
1080   CeedCall(CeedElemRestrictionGetOffsets(rstr, CEED_MEM_HOST, &offsets));
1081 
1082   // Expand offsets
1083   CeedCall(CeedElemRestrictionGetNumElements(rstr, &num_elem));
1084   CeedCall(CeedElemRestrictionGetNumComponents(rstr, &num_comp));
1085   CeedCall(CeedElemRestrictionGetElementSize(rstr, &elem_size));
1086   CeedCall(CeedElemRestrictionGetCompStride(rstr, &comp_stride));
1087   CeedCall(CeedElemRestrictionGetLVectorSize(rstr, &l_size));
1088   shift = num_comp;
1089   if (comp_stride != 1) shift *= num_comp;
1090   CeedCall(CeedCalloc(num_elem * elem_size, &point_block_offsets));
1091   for (CeedInt i = 0; i < num_elem * elem_size; i++) {
1092     point_block_offsets[i] = offsets[i] * shift;
1093   }
1094 
1095   // Create new restriction
1096   CeedCall(CeedElemRestrictionCreate(ceed, num_elem, elem_size, num_comp * num_comp, 1, l_size * num_comp, CEED_MEM_HOST, CEED_OWN_POINTER,
1097                                      point_block_offsets, point_block_rstr));
1098 
1099   // Cleanup
1100   CeedCall(CeedElemRestrictionRestoreOffsets(rstr, &offsets));
1101   return CEED_ERROR_SUCCESS;
1102 }
1103 
1104 /**
1105   @brief Create object holding `CeedQFunction` assembly data for `CeedOperator`
1106 
1107   @param[in]  ceed `Ceed` object used to create the `CeedQFunctionAssemblyData`
1108   @param[out] data Address of the variable where the newly created `CeedQFunctionAssemblyData` will be stored
1109 
1110   @return An error code: 0 - success, otherwise - failure
1111 
1112   @ref Backend
1113 **/
1114 int CeedQFunctionAssemblyDataCreate(Ceed ceed, CeedQFunctionAssemblyData *data) {
1115   CeedCall(CeedCalloc(1, data));
1116   (*data)->ref_count = 1;
1117   (*data)->ceed      = ceed;
1118   CeedCall(CeedReference(ceed));
1119   return CEED_ERROR_SUCCESS;
1120 }
1121 
1122 /**
1123   @brief Increment the reference counter for a `CeedQFunctionAssemblyData`
1124 
1125   @param[in,out] data `CeedQFunctionAssemblyData` to increment the reference counter
1126 
1127   @return An error code: 0 - success, otherwise - failure
1128 
1129   @ref Backend
1130 **/
1131 int CeedQFunctionAssemblyDataReference(CeedQFunctionAssemblyData data) {
1132   data->ref_count++;
1133   return CEED_ERROR_SUCCESS;
1134 }
1135 
1136 /**
1137   @brief Set re-use of `CeedQFunctionAssemblyData`
1138 
1139   @param[in,out] data       `CeedQFunctionAssemblyData` to mark for reuse
1140   @param[in]     reuse_data Boolean flag indicating data re-use
1141 
1142   @return An error code: 0 - success, otherwise - failure
1143 
1144   @ref Backend
1145 **/
1146 int CeedQFunctionAssemblyDataSetReuse(CeedQFunctionAssemblyData data, bool reuse_data) {
1147   data->reuse_data        = reuse_data;
1148   data->needs_data_update = true;
1149   return CEED_ERROR_SUCCESS;
1150 }
1151 
1152 /**
1153   @brief Mark `CeedQFunctionAssemblyData` as stale
1154 
1155   @param[in,out] data              `CeedQFunctionAssemblyData` to mark as stale
1156   @param[in]     needs_data_update Boolean flag indicating if update is needed or completed
1157 
1158   @return An error code: 0 - success, otherwise - failure
1159 
1160   @ref Backend
1161 **/
1162 int CeedQFunctionAssemblyDataSetUpdateNeeded(CeedQFunctionAssemblyData data, bool needs_data_update) {
1163   data->needs_data_update = needs_data_update;
1164   return CEED_ERROR_SUCCESS;
1165 }
1166 
1167 /**
1168   @brief Determine if `CeedQFunctionAssemblyData` needs update
1169 
1170   @param[in]  data             `CeedQFunctionAssemblyData` to mark as stale
1171   @param[out] is_update_needed Boolean flag indicating if re-assembly is required
1172 
1173   @return An error code: 0 - success, otherwise - failure
1174 
1175   @ref Backend
1176 **/
1177 int CeedQFunctionAssemblyDataIsUpdateNeeded(CeedQFunctionAssemblyData data, bool *is_update_needed) {
1178   *is_update_needed = !data->reuse_data || data->needs_data_update;
1179   return CEED_ERROR_SUCCESS;
1180 }
1181 
1182 /**
1183   @brief Copy the pointer to a `CeedQFunctionAssemblyData`.
1184 
1185   Both pointers should be destroyed with @ref CeedQFunctionAssemblyDataDestroy().
1186 
1187   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`.
1188         This `CeedQFunctionAssemblyData` will be destroyed if ` *data_copy` is the only reference to this `CeedQFunctionAssemblyData`.
1189 
1190   @param[in]     data      `CeedQFunctionAssemblyData` to copy reference to
1191   @param[in,out] data_copy Variable to store copied reference
1192 
1193   @return An error code: 0 - success, otherwise - failure
1194 
1195   @ref Backend
1196 **/
1197 int CeedQFunctionAssemblyDataReferenceCopy(CeedQFunctionAssemblyData data, CeedQFunctionAssemblyData *data_copy) {
1198   CeedCall(CeedQFunctionAssemblyDataReference(data));
1199   CeedCall(CeedQFunctionAssemblyDataDestroy(data_copy));
1200   *data_copy = data;
1201   return CEED_ERROR_SUCCESS;
1202 }
1203 
1204 /**
1205   @brief Get setup status for internal objects for `CeedQFunctionAssemblyData`
1206 
1207   @param[in]  data     `CeedQFunctionAssemblyData` to retrieve status
1208   @param[out] is_setup Boolean flag for setup status
1209 
1210   @return An error code: 0 - success, otherwise - failure
1211 
1212   @ref Backend
1213 **/
1214 int CeedQFunctionAssemblyDataIsSetup(CeedQFunctionAssemblyData data, bool *is_setup) {
1215   *is_setup = data->is_setup;
1216   return CEED_ERROR_SUCCESS;
1217 }
1218 
1219 /**
1220   @brief Set internal objects for `CeedQFunctionAssemblyData`
1221 
1222   @param[in,out] data `CeedQFunctionAssemblyData` to set objects
1223   @param[in]     vec  `CeedVector` to store assembled `CeedQFunction` at quadrature points
1224   @param[in]     rstr `CeedElemRestriction` for `CeedVector` containing assembled `CeedQFunction`
1225 
1226   @return An error code: 0 - success, otherwise - failure
1227 
1228   @ref Backend
1229 **/
1230 int CeedQFunctionAssemblyDataSetObjects(CeedQFunctionAssemblyData data, CeedVector vec, CeedElemRestriction rstr) {
1231   CeedCall(CeedVectorReferenceCopy(vec, &data->vec));
1232   CeedCall(CeedElemRestrictionReferenceCopy(rstr, &data->rstr));
1233 
1234   data->is_setup = true;
1235   return CEED_ERROR_SUCCESS;
1236 }
1237 
1238 /**
1239   @brief Get internal objects for `CeedQFunctionAssemblyData`
1240 
1241   @param[in,out] data `CeedQFunctionAssemblyData` to set objects
1242   @param[out]    vec  `CeedVector` to store assembled `CeedQFunction` at quadrature points
1243   @param[out]    rstr `CeedElemRestriction` for `CeedVector` containing assembled `CeedQFunction`
1244 
1245   @return An error code: 0 - success, otherwise - failure
1246 
1247   @ref Backend
1248 **/
1249 int CeedQFunctionAssemblyDataGetObjects(CeedQFunctionAssemblyData data, CeedVector *vec, CeedElemRestriction *rstr) {
1250   CeedCheck(data->is_setup, data->ceed, CEED_ERROR_INCOMPLETE, "Internal objects not set; must call CeedQFunctionAssemblyDataSetObjects first.");
1251 
1252   CeedCall(CeedVectorReferenceCopy(data->vec, vec));
1253   CeedCall(CeedElemRestrictionReferenceCopy(data->rstr, rstr));
1254   return CEED_ERROR_SUCCESS;
1255 }
1256 
1257 /**
1258   @brief Destroy `CeedQFunctionAssemblyData`
1259 
1260   @param[in,out] data  `CeedQFunctionAssemblyData` to destroy
1261 
1262   @return An error code: 0 - success, otherwise - failure
1263 
1264   @ref Backend
1265 **/
1266 int CeedQFunctionAssemblyDataDestroy(CeedQFunctionAssemblyData *data) {
1267   if (!*data || --(*data)->ref_count > 0) {
1268     *data = NULL;
1269     return CEED_ERROR_SUCCESS;
1270   }
1271   CeedCall(CeedDestroy(&(*data)->ceed));
1272   CeedCall(CeedVectorDestroy(&(*data)->vec));
1273   CeedCall(CeedElemRestrictionDestroy(&(*data)->rstr));
1274 
1275   CeedCall(CeedFree(data));
1276   return CEED_ERROR_SUCCESS;
1277 }
1278 
1279 /**
1280   @brief Get `CeedOperatorAssemblyData`
1281 
1282   @param[in]  op   `CeedOperator` to assemble
1283   @param[out] data `CeedQFunctionAssemblyData`
1284 
1285   @return An error code: 0 - success, otherwise - failure
1286 
1287   @ref Backend
1288 **/
1289 int CeedOperatorGetOperatorAssemblyData(CeedOperator op, CeedOperatorAssemblyData *data) {
1290   if (!op->op_assembled) {
1291     CeedOperatorAssemblyData data;
1292 
1293     CeedCall(CeedOperatorAssemblyDataCreate(op->ceed, op, &data));
1294     op->op_assembled = data;
1295   }
1296   *data = op->op_assembled;
1297   return CEED_ERROR_SUCCESS;
1298 }
1299 
1300 /**
1301   @brief Create object holding `CeedOperator` assembly data.
1302 
1303   The `CeedOperatorAssemblyData` holds an array with references to every active `CeedBasis` used in the `CeedOperator`.
1304   An array with references to the corresponding active `CeedElemRestriction` is also stored.
1305   For each active `CeedBasis, the `CeedOperatorAssemblyData` holds an array of all input and output @ref CeedEvalMode for this `CeedBasis`.
1306   The `CeedOperatorAssemblyData` holds an array of offsets for indexing into the assembled `CeedQFunction` arrays to the row representing each @ref CeedEvalMode.
1307   The number of input columns across all active bases for the assembled `CeedQFunction` is also stored.
1308   Lastly, the `CeedOperatorAssembly` data holds assembled matrices representing the full action of the `CeedBasis` for all @ref CeedEvalMode.
1309 
1310   @param[in]  ceed `Ceed` object used to create the `CeedOperatorAssemblyData`
1311   @param[in]  op   `CeedOperator` to be assembled
1312   @param[out] data Address of the variable where the newly created `CeedOperatorAssemblyData` will be stored
1313 
1314   @return An error code: 0 - success, otherwise - failure
1315 
1316   @ref Backend
1317 **/
1318 int CeedOperatorAssemblyDataCreate(Ceed ceed, CeedOperator op, CeedOperatorAssemblyData *data) {
1319   CeedInt             num_active_bases_in = 0, num_active_bases_out = 0, offset = 0;
1320   CeedInt             num_input_fields, *num_eval_modes_in = NULL, num_output_fields, *num_eval_modes_out = NULL;
1321   CeedSize          **eval_mode_offsets_in = NULL, **eval_mode_offsets_out = NULL;
1322   CeedEvalMode      **eval_modes_in = NULL, **eval_modes_out = NULL;
1323   CeedQFunctionField *qf_fields;
1324   CeedQFunction       qf;
1325   CeedOperatorField  *op_fields;
1326   bool                is_composite;
1327 
1328   CeedCall(CeedOperatorIsComposite(op, &is_composite));
1329   CeedCheck(!is_composite, ceed, CEED_ERROR_INCOMPATIBLE, "Can only create CeedOperator assembly data for non-composite operators.");
1330 
1331   // Allocate
1332   CeedCall(CeedCalloc(1, data));
1333   (*data)->ceed = ceed;
1334   CeedCall(CeedReference(ceed));
1335 
1336   // Build OperatorAssembly data
1337   CeedCall(CeedOperatorGetQFunction(op, &qf));
1338 
1339   // Determine active input basis
1340   CeedCall(CeedQFunctionGetFields(qf, &num_input_fields, &qf_fields, NULL, NULL));
1341   CeedCall(CeedOperatorGetFields(op, NULL, &op_fields, NULL, NULL));
1342   for (CeedInt i = 0; i < num_input_fields; i++) {
1343     CeedVector vec;
1344 
1345     CeedCall(CeedOperatorFieldGetVector(op_fields[i], &vec));
1346     if (vec == CEED_VECTOR_ACTIVE) {
1347       CeedInt      index = -1, num_comp, q_comp;
1348       CeedEvalMode eval_mode;
1349       CeedBasis    basis_in = NULL;
1350 
1351       CeedCall(CeedOperatorFieldGetBasis(op_fields[i], &basis_in));
1352       CeedCall(CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode));
1353       CeedCall(CeedBasisGetNumComponents(basis_in, &num_comp));
1354       CeedCall(CeedBasisGetNumQuadratureComponents(basis_in, eval_mode, &q_comp));
1355       for (CeedInt i = 0; i < num_active_bases_in; i++) {
1356         if ((*data)->active_bases_in[i] == basis_in) index = i;
1357       }
1358       if (index == -1) {
1359         CeedElemRestriction elem_rstr_in;
1360 
1361         index = num_active_bases_in;
1362         CeedCall(CeedRealloc(num_active_bases_in + 1, &(*data)->active_bases_in));
1363         (*data)->active_bases_in[num_active_bases_in] = NULL;
1364         CeedCall(CeedBasisReferenceCopy(basis_in, &(*data)->active_bases_in[num_active_bases_in]));
1365         CeedCall(CeedRealloc(num_active_bases_in + 1, &(*data)->active_elem_rstrs_in));
1366         (*data)->active_elem_rstrs_in[num_active_bases_in] = NULL;
1367         CeedCall(CeedOperatorFieldGetElemRestriction(op_fields[i], &elem_rstr_in));
1368         CeedCall(CeedElemRestrictionReferenceCopy(elem_rstr_in, &(*data)->active_elem_rstrs_in[num_active_bases_in]));
1369         CeedCall(CeedRealloc(num_active_bases_in + 1, &num_eval_modes_in));
1370         num_eval_modes_in[index] = 0;
1371         CeedCall(CeedRealloc(num_active_bases_in + 1, &eval_modes_in));
1372         eval_modes_in[index] = NULL;
1373         CeedCall(CeedRealloc(num_active_bases_in + 1, &eval_mode_offsets_in));
1374         eval_mode_offsets_in[index] = NULL;
1375         CeedCall(CeedRealloc(num_active_bases_in + 1, &(*data)->assembled_bases_in));
1376         (*data)->assembled_bases_in[index] = NULL;
1377         num_active_bases_in++;
1378       }
1379       if (eval_mode != CEED_EVAL_WEIGHT) {
1380         // q_comp = 1 if CEED_EVAL_NONE, CEED_EVAL_WEIGHT caught by QF Assembly
1381         CeedCall(CeedRealloc(num_eval_modes_in[index] + q_comp, &eval_modes_in[index]));
1382         CeedCall(CeedRealloc(num_eval_modes_in[index] + q_comp, &eval_mode_offsets_in[index]));
1383         for (CeedInt d = 0; d < q_comp; d++) {
1384           eval_modes_in[index][num_eval_modes_in[index] + d]        = eval_mode;
1385           eval_mode_offsets_in[index][num_eval_modes_in[index] + d] = offset;
1386           offset += num_comp;
1387         }
1388         num_eval_modes_in[index] += q_comp;
1389       }
1390     }
1391   }
1392 
1393   // Determine active output basis
1394   CeedCall(CeedQFunctionGetFields(qf, NULL, NULL, &num_output_fields, &qf_fields));
1395   CeedCall(CeedOperatorGetFields(op, NULL, NULL, NULL, &op_fields));
1396   offset = 0;
1397   for (CeedInt i = 0; i < num_output_fields; i++) {
1398     CeedVector vec;
1399 
1400     CeedCall(CeedOperatorFieldGetVector(op_fields[i], &vec));
1401     if (vec == CEED_VECTOR_ACTIVE) {
1402       CeedInt      index = -1, num_comp, q_comp;
1403       CeedEvalMode eval_mode;
1404       CeedBasis    basis_out = NULL;
1405 
1406       CeedCall(CeedOperatorFieldGetBasis(op_fields[i], &basis_out));
1407       CeedCall(CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode));
1408       CeedCall(CeedBasisGetNumComponents(basis_out, &num_comp));
1409       CeedCall(CeedBasisGetNumQuadratureComponents(basis_out, eval_mode, &q_comp));
1410       for (CeedInt i = 0; i < num_active_bases_out; i++) {
1411         if ((*data)->active_bases_out[i] == basis_out) index = i;
1412       }
1413       if (index == -1) {
1414         CeedElemRestriction elem_rstr_out;
1415 
1416         index = num_active_bases_out;
1417         CeedCall(CeedRealloc(num_active_bases_out + 1, &(*data)->active_bases_out));
1418         (*data)->active_bases_out[num_active_bases_out] = NULL;
1419         CeedCall(CeedBasisReferenceCopy(basis_out, &(*data)->active_bases_out[num_active_bases_out]));
1420         CeedCall(CeedRealloc(num_active_bases_out + 1, &(*data)->active_elem_rstrs_out));
1421         (*data)->active_elem_rstrs_out[num_active_bases_out] = NULL;
1422         CeedCall(CeedOperatorFieldGetElemRestriction(op_fields[i], &elem_rstr_out));
1423         CeedCall(CeedElemRestrictionReferenceCopy(elem_rstr_out, &(*data)->active_elem_rstrs_out[num_active_bases_out]));
1424         CeedCall(CeedRealloc(num_active_bases_out + 1, &num_eval_modes_out));
1425         num_eval_modes_out[index] = 0;
1426         CeedCall(CeedRealloc(num_active_bases_out + 1, &eval_modes_out));
1427         eval_modes_out[index] = NULL;
1428         CeedCall(CeedRealloc(num_active_bases_out + 1, &eval_mode_offsets_out));
1429         eval_mode_offsets_out[index] = NULL;
1430         CeedCall(CeedRealloc(num_active_bases_out + 1, &(*data)->assembled_bases_out));
1431         (*data)->assembled_bases_out[index] = NULL;
1432         num_active_bases_out++;
1433       }
1434       if (eval_mode != CEED_EVAL_WEIGHT) {
1435         // q_comp = 1 if CEED_EVAL_NONE, CEED_EVAL_WEIGHT caught by QF Assembly
1436         CeedCall(CeedRealloc(num_eval_modes_out[index] + q_comp, &eval_modes_out[index]));
1437         CeedCall(CeedRealloc(num_eval_modes_out[index] + q_comp, &eval_mode_offsets_out[index]));
1438         for (CeedInt d = 0; d < q_comp; d++) {
1439           eval_modes_out[index][num_eval_modes_out[index] + d]        = eval_mode;
1440           eval_mode_offsets_out[index][num_eval_modes_out[index] + d] = offset;
1441           offset += num_comp;
1442         }
1443         num_eval_modes_out[index] += q_comp;
1444       }
1445     }
1446   }
1447   (*data)->num_active_bases_in   = num_active_bases_in;
1448   (*data)->num_eval_modes_in     = num_eval_modes_in;
1449   (*data)->eval_modes_in         = eval_modes_in;
1450   (*data)->eval_mode_offsets_in  = eval_mode_offsets_in;
1451   (*data)->num_active_bases_out  = num_active_bases_out;
1452   (*data)->num_eval_modes_out    = num_eval_modes_out;
1453   (*data)->eval_modes_out        = eval_modes_out;
1454   (*data)->eval_mode_offsets_out = eval_mode_offsets_out;
1455   (*data)->num_output_components = offset;
1456   return CEED_ERROR_SUCCESS;
1457 }
1458 
1459 /**
1460   @brief Get `CeedOperator` @ref CeedEvalMode for assembly.
1461 
1462   Note: See @ref CeedOperatorAssemblyDataCreate() for a full description of the data stored in this object.
1463 
1464   @param[in]  data                  `CeedOperatorAssemblyData`
1465   @param[out] num_active_bases_in   Total number of active bases for input
1466   @param[out] num_eval_modes_in     Pointer to hold array of numbers of input @ref CeedEvalMode, or `NULL`.
1467                                       `eval_modes_in[0]` holds an array of eval modes for the first active `CeedBasis`.
1468   @param[out] eval_modes_in         Pointer to hold arrays of input @ref CeedEvalMode, or `NULL`
1469   @param[out] eval_mode_offsets_in  Pointer to hold arrays of input offsets at each quadrature point
1470   @param[out] num_active_bases_out  Total number of active bases for output
1471   @param[out] num_eval_modes_out    Pointer to hold array of numbers of output @ref CeedEvalMode, or `NULL`
1472   @param[out] eval_modes_out        Pointer to hold arrays of output @ref CeedEvalMode, or `NULL`
1473   @param[out] eval_mode_offsets_out Pointer to hold arrays of output offsets at each quadrature point
1474   @param[out] num_output_components The number of columns in the assembled `CeedQFunction` matrix for each quadrature point, including contributions of all active bases
1475 
1476   @return An error code: 0 - success, otherwise - failure
1477 
1478   @ref Backend
1479 **/
1480 int CeedOperatorAssemblyDataGetEvalModes(CeedOperatorAssemblyData data, CeedInt *num_active_bases_in, CeedInt **num_eval_modes_in,
1481                                          const CeedEvalMode ***eval_modes_in, CeedSize ***eval_mode_offsets_in, CeedInt *num_active_bases_out,
1482                                          CeedInt **num_eval_modes_out, const CeedEvalMode ***eval_modes_out, CeedSize ***eval_mode_offsets_out,
1483                                          CeedSize *num_output_components) {
1484   if (num_active_bases_in) *num_active_bases_in = data->num_active_bases_in;
1485   if (num_eval_modes_in) *num_eval_modes_in = data->num_eval_modes_in;
1486   if (eval_modes_in) *eval_modes_in = (const CeedEvalMode **)data->eval_modes_in;
1487   if (eval_mode_offsets_in) *eval_mode_offsets_in = data->eval_mode_offsets_in;
1488   if (num_active_bases_out) *num_active_bases_out = data->num_active_bases_out;
1489   if (num_eval_modes_out) *num_eval_modes_out = data->num_eval_modes_out;
1490   if (eval_modes_out) *eval_modes_out = (const CeedEvalMode **)data->eval_modes_out;
1491   if (eval_mode_offsets_out) *eval_mode_offsets_out = data->eval_mode_offsets_out;
1492   if (num_output_components) *num_output_components = data->num_output_components;
1493   return CEED_ERROR_SUCCESS;
1494 }
1495 
1496 /**
1497   @brief Get `CeedOperator` `CeedBasis` data for assembly.
1498 
1499   Note: See @ref CeedOperatorAssemblyDataCreate() for a full description of the data stored in this object.
1500 
1501   @param[in]  data                 `CeedOperatorAssemblyData`
1502   @param[out] num_active_bases_in  Number of active input bases, or `NULL`
1503   @param[out] active_bases_in      Pointer to hold active input `CeedBasis`, or `NULL`
1504   @param[out] assembled_bases_in   Pointer to hold assembled active input `B` , or `NULL`
1505   @param[out] num_active_bases_out Number of active output bases, or `NULL`
1506   @param[out] active_bases_out     Pointer to hold active output `CeedBasis`, or `NULL`
1507   @param[out] assembled_bases_out  Pointer to hold assembled active output `B` , or `NULL`
1508 
1509   @return An error code: 0 - success, otherwise - failure
1510 
1511   @ref Backend
1512 **/
1513 int CeedOperatorAssemblyDataGetBases(CeedOperatorAssemblyData data, CeedInt *num_active_bases_in, CeedBasis **active_bases_in,
1514                                      const CeedScalar ***assembled_bases_in, CeedInt *num_active_bases_out, CeedBasis **active_bases_out,
1515                                      const CeedScalar ***assembled_bases_out) {
1516   // Assemble B_in, B_out if needed
1517   if (assembled_bases_in && !data->assembled_bases_in[0]) {
1518     CeedInt num_qpts;
1519 
1520     if (data->active_bases_in[0] == CEED_BASIS_NONE) CeedCall(CeedElemRestrictionGetElementSize(data->active_elem_rstrs_in[0], &num_qpts));
1521     else CeedCall(CeedBasisGetNumQuadraturePoints(data->active_bases_in[0], &num_qpts));
1522     for (CeedInt b = 0; b < data->num_active_bases_in; b++) {
1523       bool        has_eval_none = false;
1524       CeedInt     num_nodes;
1525       CeedScalar *B_in = NULL, *identity = NULL;
1526 
1527       CeedCall(CeedElemRestrictionGetElementSize(data->active_elem_rstrs_in[b], &num_nodes));
1528       CeedCall(CeedCalloc(num_qpts * num_nodes * data->num_eval_modes_in[b], &B_in));
1529 
1530       for (CeedInt i = 0; i < data->num_eval_modes_in[b]; i++) {
1531         has_eval_none = has_eval_none || (data->eval_modes_in[b][i] == CEED_EVAL_NONE);
1532       }
1533       if (has_eval_none) {
1534         CeedCall(CeedCalloc(num_qpts * num_nodes, &identity));
1535         for (CeedInt i = 0; i < (num_nodes < num_qpts ? num_nodes : num_qpts); i++) {
1536           identity[i * num_nodes + i] = 1.0;
1537         }
1538       }
1539 
1540       for (CeedInt q = 0; q < num_qpts; q++) {
1541         for (CeedInt n = 0; n < num_nodes; n++) {
1542           CeedInt      d_in              = 0, q_comp_in;
1543           CeedEvalMode eval_mode_in_prev = CEED_EVAL_NONE;
1544 
1545           for (CeedInt e_in = 0; e_in < data->num_eval_modes_in[b]; e_in++) {
1546             const CeedInt     qq = data->num_eval_modes_in[b] * q;
1547             const CeedScalar *B  = NULL;
1548 
1549             CeedCall(CeedOperatorGetBasisPointer(data->active_bases_in[b], data->eval_modes_in[b][e_in], identity, &B));
1550             CeedCall(CeedBasisGetNumQuadratureComponents(data->active_bases_in[b], data->eval_modes_in[b][e_in], &q_comp_in));
1551             if (q_comp_in > 1) {
1552               if (e_in == 0 || data->eval_modes_in[b][e_in] != eval_mode_in_prev) d_in = 0;
1553               else B = &B[(++d_in) * num_qpts * num_nodes];
1554             }
1555             eval_mode_in_prev                 = data->eval_modes_in[b][e_in];
1556             B_in[(qq + e_in) * num_nodes + n] = B[q * num_nodes + n];
1557           }
1558         }
1559       }
1560       if (identity) CeedCall(CeedFree(&identity));
1561       data->assembled_bases_in[b] = B_in;
1562     }
1563   }
1564 
1565   if (assembled_bases_out && !data->assembled_bases_out[0]) {
1566     CeedInt num_qpts;
1567 
1568     if (data->active_bases_out[0] == CEED_BASIS_NONE) CeedCall(CeedElemRestrictionGetElementSize(data->active_elem_rstrs_out[0], &num_qpts));
1569     else CeedCall(CeedBasisGetNumQuadraturePoints(data->active_bases_out[0], &num_qpts));
1570     for (CeedInt b = 0; b < data->num_active_bases_out; b++) {
1571       bool        has_eval_none = false;
1572       CeedInt     num_nodes;
1573       CeedScalar *B_out = NULL, *identity = NULL;
1574 
1575       CeedCall(CeedElemRestrictionGetElementSize(data->active_elem_rstrs_out[b], &num_nodes));
1576       CeedCall(CeedCalloc(num_qpts * num_nodes * data->num_eval_modes_out[b], &B_out));
1577 
1578       for (CeedInt i = 0; i < data->num_eval_modes_out[b]; i++) {
1579         has_eval_none = has_eval_none || (data->eval_modes_out[b][i] == CEED_EVAL_NONE);
1580       }
1581       if (has_eval_none) {
1582         CeedCall(CeedCalloc(num_qpts * num_nodes, &identity));
1583         for (CeedInt i = 0; i < (num_nodes < num_qpts ? num_nodes : num_qpts); i++) {
1584           identity[i * num_nodes + i] = 1.0;
1585         }
1586       }
1587 
1588       for (CeedInt q = 0; q < num_qpts; q++) {
1589         for (CeedInt n = 0; n < num_nodes; n++) {
1590           CeedInt      d_out              = 0, q_comp_out;
1591           CeedEvalMode eval_mode_out_prev = CEED_EVAL_NONE;
1592 
1593           for (CeedInt e_out = 0; e_out < data->num_eval_modes_out[b]; e_out++) {
1594             const CeedInt     qq = data->num_eval_modes_out[b] * q;
1595             const CeedScalar *B  = NULL;
1596 
1597             CeedCall(CeedOperatorGetBasisPointer(data->active_bases_out[b], data->eval_modes_out[b][e_out], identity, &B));
1598             CeedCall(CeedBasisGetNumQuadratureComponents(data->active_bases_out[b], data->eval_modes_out[b][e_out], &q_comp_out));
1599             if (q_comp_out > 1) {
1600               if (e_out == 0 || data->eval_modes_out[b][e_out] != eval_mode_out_prev) d_out = 0;
1601               else B = &B[(++d_out) * num_qpts * num_nodes];
1602             }
1603             eval_mode_out_prev                  = data->eval_modes_out[b][e_out];
1604             B_out[(qq + e_out) * num_nodes + n] = B[q * num_nodes + n];
1605           }
1606         }
1607       }
1608       if (identity) CeedCall(CeedFree(&identity));
1609       data->assembled_bases_out[b] = B_out;
1610     }
1611   }
1612 
1613   // Pass out assembled data
1614   if (num_active_bases_in) *num_active_bases_in = data->num_active_bases_in;
1615   if (active_bases_in) *active_bases_in = data->active_bases_in;
1616   if (assembled_bases_in) *assembled_bases_in = (const CeedScalar **)data->assembled_bases_in;
1617   if (num_active_bases_out) *num_active_bases_out = data->num_active_bases_out;
1618   if (active_bases_out) *active_bases_out = data->active_bases_out;
1619   if (assembled_bases_out) *assembled_bases_out = (const CeedScalar **)data->assembled_bases_out;
1620   return CEED_ERROR_SUCCESS;
1621 }
1622 
1623 /**
1624   @brief Get `CeedOperator` `CeedBasis` data for assembly.
1625 
1626   Note: See @ref CeedOperatorAssemblyDataCreate() for a full description of the data stored in this object.
1627 
1628   @param[in]  data                      `CeedOperatorAssemblyData`
1629   @param[out] num_active_elem_rstrs_in  Number of active input element restrictions, or `NULL`
1630   @param[out] active_elem_rstrs_in      Pointer to hold active input `CeedElemRestriction`, or `NULL`
1631   @param[out] num_active_elem_rstrs_out Number of active output element restrictions, or `NULL`
1632   @param[out] active_elem_rstrs_out     Pointer to hold active output `CeedElemRestriction`, or `NULL`
1633 
1634   @return An error code: 0 - success, otherwise - failure
1635 
1636   @ref Backend
1637 **/
1638 int CeedOperatorAssemblyDataGetElemRestrictions(CeedOperatorAssemblyData data, CeedInt *num_active_elem_rstrs_in,
1639                                                 CeedElemRestriction **active_elem_rstrs_in, CeedInt *num_active_elem_rstrs_out,
1640                                                 CeedElemRestriction **active_elem_rstrs_out) {
1641   if (num_active_elem_rstrs_in) *num_active_elem_rstrs_in = data->num_active_bases_in;
1642   if (active_elem_rstrs_in) *active_elem_rstrs_in = data->active_elem_rstrs_in;
1643   if (num_active_elem_rstrs_out) *num_active_elem_rstrs_out = data->num_active_bases_out;
1644   if (active_elem_rstrs_out) *active_elem_rstrs_out = data->active_elem_rstrs_out;
1645   return CEED_ERROR_SUCCESS;
1646 }
1647 
1648 /**
1649   @brief Destroy `CeedOperatorAssemblyData`
1650 
1651   @param[in,out] data `CeedOperatorAssemblyData` to destroy
1652 
1653   @return An error code: 0 - success, otherwise - failure
1654 
1655   @ref Backend
1656 **/
1657 int CeedOperatorAssemblyDataDestroy(CeedOperatorAssemblyData *data) {
1658   if (!*data) {
1659     *data = NULL;
1660     return CEED_ERROR_SUCCESS;
1661   }
1662   CeedCall(CeedDestroy(&(*data)->ceed));
1663   for (CeedInt b = 0; b < (*data)->num_active_bases_in; b++) {
1664     CeedCall(CeedBasisDestroy(&(*data)->active_bases_in[b]));
1665     CeedCall(CeedElemRestrictionDestroy(&(*data)->active_elem_rstrs_in[b]));
1666     CeedCall(CeedFree(&(*data)->eval_modes_in[b]));
1667     CeedCall(CeedFree(&(*data)->eval_mode_offsets_in[b]));
1668     CeedCall(CeedFree(&(*data)->assembled_bases_in[b]));
1669   }
1670   for (CeedInt b = 0; b < (*data)->num_active_bases_out; b++) {
1671     CeedCall(CeedBasisDestroy(&(*data)->active_bases_out[b]));
1672     CeedCall(CeedElemRestrictionDestroy(&(*data)->active_elem_rstrs_out[b]));
1673     CeedCall(CeedFree(&(*data)->eval_modes_out[b]));
1674     CeedCall(CeedFree(&(*data)->eval_mode_offsets_out[b]));
1675     CeedCall(CeedFree(&(*data)->assembled_bases_out[b]));
1676   }
1677   CeedCall(CeedFree(&(*data)->active_bases_in));
1678   CeedCall(CeedFree(&(*data)->active_bases_out));
1679   CeedCall(CeedFree(&(*data)->active_elem_rstrs_in));
1680   CeedCall(CeedFree(&(*data)->active_elem_rstrs_out));
1681   CeedCall(CeedFree(&(*data)->num_eval_modes_in));
1682   CeedCall(CeedFree(&(*data)->num_eval_modes_out));
1683   CeedCall(CeedFree(&(*data)->eval_modes_in));
1684   CeedCall(CeedFree(&(*data)->eval_modes_out));
1685   CeedCall(CeedFree(&(*data)->eval_mode_offsets_in));
1686   CeedCall(CeedFree(&(*data)->eval_mode_offsets_out));
1687   CeedCall(CeedFree(&(*data)->assembled_bases_in));
1688   CeedCall(CeedFree(&(*data)->assembled_bases_out));
1689 
1690   CeedCall(CeedFree(data));
1691   return CEED_ERROR_SUCCESS;
1692 }
1693 
1694 /**
1695   @brief Retrieve fallback `CeedOperator` with a reference `Ceed` for advanced `CeedOperator` functionality
1696 
1697   @param[in]  op          `CeedOperator` to retrieve fallback for
1698   @param[out] op_fallback Fallback `CeedOperator`
1699 
1700   @return An error code: 0 - success, otherwise - failure
1701 
1702   @ref Backend
1703 **/
1704 int CeedOperatorGetFallback(CeedOperator op, CeedOperator *op_fallback) {
1705   // Create if needed
1706   if (!op->op_fallback) CeedCall(CeedOperatorCreateFallback(op));
1707   if (op->op_fallback) {
1708     bool is_debug;
1709     Ceed ceed;
1710 
1711     CeedCall(CeedOperatorGetCeed(op, &ceed));
1712     CeedCall(CeedIsDebug(ceed, &is_debug));
1713     if (is_debug) {
1714       Ceed        ceed_fallback;
1715       const char *resource, *resource_fallback;
1716 
1717       CeedCall(CeedGetOperatorFallbackCeed(ceed, &ceed_fallback));
1718       CeedCall(CeedGetResource(ceed, &resource));
1719       CeedCall(CeedGetResource(ceed_fallback, &resource_fallback));
1720 
1721       CeedDebug256(ceed, CEED_DEBUG_COLOR_SUCCESS, "---------- CeedOperator Fallback ----------\n");
1722       CeedDebug(ceed, "Falling back from %s operator at address %p to %s operator at address %p\n", resource, op, resource_fallback, op->op_fallback);
1723     }
1724   }
1725   *op_fallback = op->op_fallback;
1726   return CEED_ERROR_SUCCESS;
1727 }
1728 
1729 /**
1730   @brief Get the parent `CeedOperator` for a fallback `CeedOperator`
1731 
1732   @param[in]  op     `CeedOperator` context
1733   @param[out] parent Variable to store parent `CeedOperator` context
1734 
1735   @return An error code: 0 - success, otherwise - failure
1736 
1737   @ref Backend
1738 **/
1739 int CeedOperatorGetFallbackParent(CeedOperator op, CeedOperator *parent) {
1740   *parent = op->op_fallback_parent ? op->op_fallback_parent : NULL;
1741   return CEED_ERROR_SUCCESS;
1742 }
1743 
1744 /**
1745   @brief Get the `Ceed` context of the parent `CeedOperator` for a fallback `CeedOperator`
1746 
1747   @param[in]  op     `CeedOperator` context
1748   @param[out] parent Variable to store parent `Ceed` context
1749 
1750   @return An error code: 0 - success, otherwise - failure
1751 
1752   @ref Backend
1753 **/
1754 int CeedOperatorGetFallbackParentCeed(CeedOperator op, Ceed *parent) {
1755   *parent = op->op_fallback_parent ? op->op_fallback_parent->ceed : op->ceed;
1756   return CEED_ERROR_SUCCESS;
1757 }
1758 
1759 /// @}
1760 
1761 /// ----------------------------------------------------------------------------
1762 /// CeedOperator Public API
1763 /// ----------------------------------------------------------------------------
1764 /// @addtogroup CeedOperatorUser
1765 /// @{
1766 
1767 /**
1768   @brief Assemble a linear `CeedQFunction` associated with a `CeedOperator`.
1769 
1770   This returns a `CeedVector` containing a matrix at each quadrature point providing the action of the `CeedQFunction` associated with the `CeedOperator`.
1771   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.
1772 
1773   Inputs and outputs are in the order provided by the user when adding `CeedOperator` fields.
1774   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]`.
1775 
1776   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
1777 
1778   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
1779   @param[out] assembled `CeedVector` to store assembled `CeedQFunction` at quadrature points
1780   @param[out] rstr      `CeedElemRestriction` for `CeedVector` containing assembled `CeedQFunction`
1781   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
1782 
1783   @return An error code: 0 - success, otherwise - failure
1784 
1785   @ref User
1786 **/
1787 int CeedOperatorLinearAssembleQFunction(CeedOperator op, CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
1788   CeedCall(CeedOperatorCheckReady(op));
1789 
1790   if (op->LinearAssembleQFunction) {
1791     // Backend version
1792     CeedCall(op->LinearAssembleQFunction(op, assembled, rstr, request));
1793   } else {
1794     // Operator fallback
1795     Ceed         ceed;
1796     CeedOperator op_fallback;
1797 
1798     CeedCall(CeedOperatorGetCeed(op, &ceed));
1799     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
1800     if (op_fallback) CeedCall(CeedOperatorLinearAssembleQFunction(op_fallback, assembled, rstr, request));
1801     else return CeedError(ceed, CEED_ERROR_UNSUPPORTED, "Backend does not support CeedOperatorLinearAssembleQFunction");
1802   }
1803   return CEED_ERROR_SUCCESS;
1804 }
1805 
1806 /**
1807   @brief Assemble `CeedQFunction` and store result internally.
1808 
1809   Return copied references of stored data to the caller.
1810   Caller is responsible for ownership and destruction of the copied references.
1811   See also @ref CeedOperatorLinearAssembleQFunction().
1812 
1813   Note: If the value of `assembled` or `rstr` passed to this function are non-`NULL` , then it is assumed that they hold valid pointers.
1814         These objects will be destroyed if `*assembled` or `*rstr` is the only reference to the object.
1815 
1816   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
1817   @param[out] assembled `CeedVector` to store assembled `CeedQFunction` at quadrature points
1818   @param[out] rstr      `CeedElemRestriction` for `CeedVector` containing assembled `CeedQFunction`
1819   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
1820 
1821   @return An error code: 0 - success, otherwise - failure
1822 
1823   @ref User
1824 **/
1825 int CeedOperatorLinearAssembleQFunctionBuildOrUpdate(CeedOperator op, CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
1826   int (*LinearAssembleQFunctionUpdate)(CeedOperator, CeedVector, CeedElemRestriction, CeedRequest *) = NULL;
1827   CeedOperator op_assemble                                                                           = NULL;
1828   CeedOperator op_fallback_parent                                                                    = NULL;
1829 
1830   CeedCall(CeedOperatorCheckReady(op));
1831 
1832   // Determine if fallback parent or operator has implementation
1833   CeedCall(CeedOperatorGetFallbackParent(op, &op_fallback_parent));
1834   if (op_fallback_parent && op_fallback_parent->LinearAssembleQFunctionUpdate) {
1835     // -- Backend version for op fallback parent is faster, if it exists
1836     LinearAssembleQFunctionUpdate = op_fallback_parent->LinearAssembleQFunctionUpdate;
1837     op_assemble                   = op_fallback_parent;
1838   } else if (op->LinearAssembleQFunctionUpdate) {
1839     // -- Backend version for op
1840     LinearAssembleQFunctionUpdate = op->LinearAssembleQFunctionUpdate;
1841     op_assemble                   = op;
1842   }
1843 
1844   // Assemble QFunction
1845   if (LinearAssembleQFunctionUpdate) {
1846     // Backend or fallback parent version
1847     bool                qf_assembled_is_setup;
1848     CeedVector          assembled_vec  = NULL;
1849     CeedElemRestriction assembled_rstr = NULL;
1850 
1851     CeedCall(CeedQFunctionAssemblyDataIsSetup(op->qf_assembled, &qf_assembled_is_setup));
1852     if (qf_assembled_is_setup) {
1853       bool update_needed;
1854 
1855       CeedCall(CeedQFunctionAssemblyDataGetObjects(op->qf_assembled, &assembled_vec, &assembled_rstr));
1856       CeedCall(CeedQFunctionAssemblyDataIsUpdateNeeded(op->qf_assembled, &update_needed));
1857       if (update_needed) CeedCall(LinearAssembleQFunctionUpdate(op_assemble, assembled_vec, assembled_rstr, request));
1858     } else {
1859       CeedCall(CeedOperatorLinearAssembleQFunction(op_assemble, &assembled_vec, &assembled_rstr, request));
1860       CeedCall(CeedQFunctionAssemblyDataSetObjects(op->qf_assembled, assembled_vec, assembled_rstr));
1861     }
1862     CeedCall(CeedQFunctionAssemblyDataSetUpdateNeeded(op->qf_assembled, false));
1863 
1864     // Copy reference from internally held copy
1865     CeedCall(CeedVectorReferenceCopy(assembled_vec, assembled));
1866     CeedCall(CeedElemRestrictionReferenceCopy(assembled_rstr, rstr));
1867     CeedCall(CeedVectorDestroy(&assembled_vec));
1868     CeedCall(CeedElemRestrictionDestroy(&assembled_rstr));
1869   } else {
1870     // Operator fallback
1871     Ceed         ceed;
1872     CeedOperator op_fallback;
1873 
1874     CeedCall(CeedOperatorGetCeed(op, &ceed));
1875     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
1876     if (op_fallback) CeedCall(CeedOperatorLinearAssembleQFunctionBuildOrUpdate(op_fallback, assembled, rstr, request));
1877     else return CeedError(ceed, CEED_ERROR_UNSUPPORTED, "Backend does not support CeedOperatorLinearAssembleQFunctionUpdate");
1878   }
1879   return CEED_ERROR_SUCCESS;
1880 }
1881 
1882 /**
1883   @brief Assemble the diagonal of a square linear `CeedOperator`
1884 
1885   This overwrites a `CeedVector` with the diagonal of a linear `CeedOperator`.
1886 
1887   Note: Currently only non-composite `CeedOperator` with a single field and composite `CeedOperator` with single field sub-operators are supported.
1888 
1889   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
1890 
1891   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
1892   @param[out] assembled `CeedVector` to store assembled `CeedOperator` diagonal
1893   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
1894 
1895   @return An error code: 0 - success, otherwise - failure
1896 
1897   @ref User
1898 **/
1899 int CeedOperatorLinearAssembleDiagonal(CeedOperator op, CeedVector assembled, CeedRequest *request) {
1900   bool     is_composite;
1901   CeedSize input_size = 0, output_size = 0;
1902   Ceed     ceed;
1903 
1904   CeedCall(CeedOperatorGetCeed(op, &ceed));
1905   CeedCall(CeedOperatorCheckReady(op));
1906   CeedCall(CeedOperatorIsComposite(op, &is_composite));
1907 
1908   CeedCall(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
1909   CeedCheck(input_size == output_size, ceed, CEED_ERROR_DIMENSION, "Operator must be square");
1910 
1911   // Early exit for empty operator
1912   if (!is_composite) {
1913     CeedInt num_elem = 0;
1914 
1915     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
1916     if (num_elem == 0) return CEED_ERROR_SUCCESS;
1917   }
1918 
1919   if (op->LinearAssembleDiagonal) {
1920     // Backend version
1921     CeedCall(op->LinearAssembleDiagonal(op, assembled, request));
1922     return CEED_ERROR_SUCCESS;
1923   } else if (op->LinearAssembleAddDiagonal) {
1924     // Backend version with zeroing first
1925     CeedCall(CeedVectorSetValue(assembled, 0.0));
1926     CeedCall(op->LinearAssembleAddDiagonal(op, assembled, request));
1927     return CEED_ERROR_SUCCESS;
1928   } else {
1929     // Operator fallback
1930     CeedOperator op_fallback;
1931 
1932     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
1933     if (op_fallback) {
1934       CeedCall(CeedOperatorLinearAssembleDiagonal(op_fallback, assembled, request));
1935       return CEED_ERROR_SUCCESS;
1936     }
1937   }
1938   // Default interface implementation
1939   CeedCall(CeedVectorSetValue(assembled, 0.0));
1940   CeedCall(CeedOperatorLinearAssembleAddDiagonal(op, assembled, request));
1941   return CEED_ERROR_SUCCESS;
1942 }
1943 
1944 /**
1945   @brief Assemble the diagonal of a square linear `CeedOperator`.
1946 
1947   This sums into a `CeedVector` the diagonal of a linear `CeedOperator`.
1948 
1949   Note: Currently only non-composite `CeedOperator` with a single field and composite `CeedOperator` with single field sub-operators are supported.
1950 
1951   Note: Calling this function asserts that setup is complete and sets the CeedOperator as immutable.
1952 
1953   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
1954   @param[out] assembled `CeedVector` to store assembled `CeedOperator` diagonal
1955   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
1956 
1957   @return An error code: 0 - success, otherwise - failure
1958 
1959   @ref User
1960 **/
1961 int CeedOperatorLinearAssembleAddDiagonal(CeedOperator op, CeedVector assembled, CeedRequest *request) {
1962   bool     is_composite;
1963   CeedSize input_size = 0, output_size = 0;
1964   Ceed     ceed;
1965 
1966   CeedCall(CeedOperatorGetCeed(op, &ceed));
1967   CeedCall(CeedOperatorCheckReady(op));
1968   CeedCall(CeedOperatorIsComposite(op, &is_composite));
1969 
1970   CeedCall(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
1971   CeedCheck(input_size == output_size, ceed, CEED_ERROR_DIMENSION, "Operator must be square");
1972 
1973   // Early exit for empty operator
1974   if (!is_composite) {
1975     CeedInt num_elem = 0;
1976 
1977     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
1978     if (num_elem == 0) return CEED_ERROR_SUCCESS;
1979   }
1980 
1981   if (op->LinearAssembleAddDiagonal) {
1982     // Backend version
1983     CeedCall(op->LinearAssembleAddDiagonal(op, assembled, request));
1984     return CEED_ERROR_SUCCESS;
1985   } else {
1986     // Operator fallback
1987     CeedOperator op_fallback;
1988 
1989     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
1990     if (op_fallback) {
1991       CeedCall(CeedOperatorLinearAssembleAddDiagonal(op_fallback, assembled, request));
1992       return CEED_ERROR_SUCCESS;
1993     }
1994   }
1995   // Default interface implementation
1996   if (is_composite) {
1997     CeedCall(CeedCompositeOperatorLinearAssembleAddDiagonal(op, request, false, assembled));
1998   } else {
1999     CeedCall(CeedSingleOperatorLinearAssembleAddDiagonal(op, request, false, assembled));
2000   }
2001   return CEED_ERROR_SUCCESS;
2002 }
2003 
2004 /**
2005    @brief Fully assemble the point-block diagonal pattern of a linear `CeedOperator`.
2006 
2007    Expected to be used in conjunction with @ref CeedOperatorLinearAssemblePointBlockDiagonal().
2008 
2009    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)`.
2010    Note that the `(i, j)` pairs are unique.
2011    This function returns the number of entries and their `(i, j)` locations, while @ref CeedOperatorLinearAssemblePointBlockDiagonal() provides the values in the same ordering.
2012 
2013    This will generally be slow unless your operator is low-order.
2014 
2015    Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2016 
2017    @param[in]  op          `CeedOperator` to assemble
2018    @param[out] num_entries Number of entries in coordinate nonzero pattern
2019    @param[out] rows        Row number for each entry
2020    @param[out] cols        Column number for each entry
2021 
2022    @ref User
2023 **/
2024 int CeedOperatorLinearAssemblePointBlockDiagonalSymbolic(CeedOperator op, CeedSize *num_entries, CeedInt **rows, CeedInt **cols) {
2025   Ceed          ceed;
2026   bool          is_composite;
2027   CeedInt       num_active_components, num_sub_operators;
2028   CeedOperator *sub_operators;
2029 
2030   CeedCall(CeedOperatorGetCeed(op, &ceed));
2031   CeedCall(CeedOperatorIsComposite(op, &is_composite));
2032 
2033   CeedSize input_size = 0, output_size = 0;
2034   CeedCall(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
2035   CeedCheck(input_size == output_size, ceed, CEED_ERROR_DIMENSION, "Operator must be square");
2036 
2037   if (is_composite) {
2038     CeedCall(CeedCompositeOperatorGetNumSub(op, &num_sub_operators));
2039     CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
2040   } else {
2041     sub_operators     = &op;
2042     num_sub_operators = 1;
2043   }
2044 
2045   // Verify operator can be assembled correctly
2046   {
2047     CeedOperatorAssemblyData data;
2048     CeedInt                  num_active_elem_rstrs, comp_stride;
2049     CeedElemRestriction     *active_elem_rstrs;
2050 
2051     // Get initial values to check against
2052     CeedCall(CeedOperatorGetOperatorAssemblyData(sub_operators[0], &data));
2053     CeedCall(CeedOperatorAssemblyDataGetElemRestrictions(data, &num_active_elem_rstrs, &active_elem_rstrs, NULL, NULL));
2054     CeedCall(CeedElemRestrictionGetCompStride(active_elem_rstrs[0], &comp_stride));
2055     CeedCall(CeedElemRestrictionGetNumComponents(active_elem_rstrs[0], &num_active_components));
2056 
2057     // Verify that all active element restrictions have same component stride and number of components
2058     for (CeedInt k = 0; k < num_sub_operators; k++) {
2059       CeedCall(CeedOperatorGetOperatorAssemblyData(sub_operators[k], &data));
2060       CeedCall(CeedOperatorAssemblyDataGetElemRestrictions(data, &num_active_elem_rstrs, &active_elem_rstrs, NULL, NULL));
2061       for (CeedInt i = 0; i < num_active_elem_rstrs; i++) {
2062         CeedInt comp_stride_sub, num_active_components_sub;
2063 
2064         CeedCall(CeedElemRestrictionGetCompStride(active_elem_rstrs[i], &comp_stride_sub));
2065         CeedCheck(comp_stride == comp_stride_sub, ceed, CEED_ERROR_DIMENSION,
2066                   "Active element restrictions must have the same component stride: %d vs %d", comp_stride, comp_stride_sub);
2067         CeedCall(CeedElemRestrictionGetNumComponents(active_elem_rstrs[i], &num_active_components_sub));
2068         CeedCheck(num_active_components == num_active_components_sub, ceed, CEED_ERROR_INCOMPATIBLE,
2069                   "All suboperators must have the same number of output components");
2070       }
2071     }
2072   }
2073   *num_entries = input_size * num_active_components;
2074   CeedCall(CeedCalloc(*num_entries, rows));
2075   CeedCall(CeedCalloc(*num_entries, cols));
2076 
2077   for (CeedInt o = 0; o < num_sub_operators; o++) {
2078     CeedElemRestriction active_elem_rstr, point_block_active_elem_rstr;
2079     CeedInt             comp_stride, num_elem, elem_size;
2080     const CeedInt      *offsets, *point_block_offsets;
2081 
2082     CeedCall(CeedOperatorGetActiveElemRestriction(sub_operators[o], &active_elem_rstr));
2083     CeedCall(CeedElemRestrictionGetCompStride(active_elem_rstr, &comp_stride));
2084     CeedCall(CeedElemRestrictionGetNumElements(active_elem_rstr, &num_elem));
2085     CeedCall(CeedElemRestrictionGetElementSize(active_elem_rstr, &elem_size));
2086     CeedCall(CeedElemRestrictionGetOffsets(active_elem_rstr, CEED_MEM_HOST, &offsets));
2087 
2088     CeedCall(CeedOperatorCreateActivePointBlockRestriction(active_elem_rstr, &point_block_active_elem_rstr));
2089     CeedCall(CeedElemRestrictionGetOffsets(point_block_active_elem_rstr, CEED_MEM_HOST, &point_block_offsets));
2090 
2091     for (CeedSize i = 0; i < num_elem * elem_size; i++) {
2092       for (CeedInt c_out = 0; c_out < num_active_components; c_out++) {
2093         for (CeedInt c_in = 0; c_in < num_active_components; c_in++) {
2094           (*rows)[point_block_offsets[i] + c_out * num_active_components + c_in] = offsets[i] + c_out * comp_stride;
2095           (*cols)[point_block_offsets[i] + c_out * num_active_components + c_in] = offsets[i] + c_in * comp_stride;
2096         }
2097       }
2098     }
2099 
2100     CeedCall(CeedElemRestrictionRestoreOffsets(active_elem_rstr, &offsets));
2101     CeedCall(CeedElemRestrictionRestoreOffsets(point_block_active_elem_rstr, &point_block_offsets));
2102     CeedCall(CeedElemRestrictionDestroy(&point_block_active_elem_rstr));
2103   }
2104   return CEED_ERROR_SUCCESS;
2105 }
2106 
2107 /**
2108   @brief Assemble the point block diagonal of a square linear `CeedOperator`.
2109 
2110   This overwrites a `CeedVector` with the point block diagonal of a linear `CeedOperator`.
2111 
2112   Note: Currently only non-composite `CeedOperator` with a single field and composite `CeedOperator` with single field sub-operators are supported.
2113 
2114   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2115 
2116   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
2117   @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.
2118                           The dimensions of this vector are derived from the active vector for the `CeedOperator`.
2119                           The array has shape `[nodes, component out, component in]`.
2120   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
2121 
2122   @return An error code: 0 - success, otherwise - failure
2123 
2124   @ref User
2125 **/
2126 int CeedOperatorLinearAssemblePointBlockDiagonal(CeedOperator op, CeedVector assembled, CeedRequest *request) {
2127   bool     is_composite;
2128   CeedSize input_size = 0, output_size = 0;
2129   Ceed     ceed;
2130 
2131   CeedCall(CeedOperatorGetCeed(op, &ceed));
2132   CeedCall(CeedOperatorCheckReady(op));
2133   CeedCall(CeedOperatorIsComposite(op, &is_composite));
2134 
2135   CeedCall(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
2136   CeedCheck(input_size == output_size, ceed, CEED_ERROR_DIMENSION, "Operator must be square");
2137 
2138   // Early exit for empty operator
2139   if (!is_composite) {
2140     CeedInt num_elem = 0;
2141 
2142     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
2143     if (num_elem == 0) return CEED_ERROR_SUCCESS;
2144   }
2145 
2146   if (op->LinearAssemblePointBlockDiagonal) {
2147     // Backend version
2148     CeedCall(op->LinearAssemblePointBlockDiagonal(op, assembled, request));
2149     return CEED_ERROR_SUCCESS;
2150   } else if (op->LinearAssembleAddPointBlockDiagonal) {
2151     // Backend version with zeroing first
2152     CeedCall(CeedVectorSetValue(assembled, 0.0));
2153     CeedCall(CeedOperatorLinearAssembleAddPointBlockDiagonal(op, assembled, request));
2154     return CEED_ERROR_SUCCESS;
2155   } else {
2156     // Operator fallback
2157     CeedOperator op_fallback;
2158 
2159     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
2160     if (op_fallback) {
2161       CeedCall(CeedOperatorLinearAssemblePointBlockDiagonal(op_fallback, assembled, request));
2162       return CEED_ERROR_SUCCESS;
2163     }
2164   }
2165   // Default interface implementation
2166   CeedCall(CeedVectorSetValue(assembled, 0.0));
2167   CeedCall(CeedOperatorLinearAssembleAddPointBlockDiagonal(op, assembled, request));
2168   return CEED_ERROR_SUCCESS;
2169 }
2170 
2171 /**
2172   @brief Assemble the point block diagonal of a square linear `CeedOperator`.
2173 
2174   This sums into a `CeedVector` with the point block diagonal of a linear `CeedOperator`.
2175 
2176   Note: Currently only non-composite `CeedOperator` with a single field and composite `CeedOperator` with single field sub-operators are supported.
2177 
2178   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2179 
2180   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
2181   @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.
2182                           The dimensions of this vector are derived from the active vector for the `CeedOperator`.
2183                           The array has shape `[nodes, component out, component in]`.
2184   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
2185 
2186   @return An error code: 0 - success, otherwise - failure
2187 
2188   @ref User
2189 **/
2190 int CeedOperatorLinearAssembleAddPointBlockDiagonal(CeedOperator op, CeedVector assembled, CeedRequest *request) {
2191   bool     is_composite;
2192   CeedSize input_size = 0, output_size = 0;
2193   Ceed     ceed;
2194 
2195   CeedCall(CeedOperatorGetCeed(op, &ceed));
2196   CeedCall(CeedOperatorCheckReady(op));
2197   CeedCall(CeedOperatorIsComposite(op, &is_composite));
2198 
2199   CeedCall(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
2200   CeedCheck(input_size == output_size, ceed, CEED_ERROR_DIMENSION, "Operator must be square");
2201 
2202   // Early exit for empty operator
2203   if (!is_composite) {
2204     CeedInt num_elem = 0;
2205 
2206     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
2207     if (num_elem == 0) return CEED_ERROR_SUCCESS;
2208   }
2209 
2210   if (op->LinearAssembleAddPointBlockDiagonal) {
2211     // Backend version
2212     CeedCall(op->LinearAssembleAddPointBlockDiagonal(op, assembled, request));
2213     return CEED_ERROR_SUCCESS;
2214   } else {
2215     // Operator fallback
2216     CeedOperator op_fallback;
2217 
2218     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
2219     if (op_fallback) {
2220       CeedCall(CeedOperatorLinearAssembleAddPointBlockDiagonal(op_fallback, assembled, request));
2221       return CEED_ERROR_SUCCESS;
2222     }
2223   }
2224   // Default interface implementation
2225   if (is_composite) {
2226     CeedCall(CeedCompositeOperatorLinearAssembleAddDiagonal(op, request, true, assembled));
2227   } else {
2228     CeedCall(CeedSingleOperatorLinearAssembleAddDiagonal(op, request, true, assembled));
2229   }
2230   return CEED_ERROR_SUCCESS;
2231 }
2232 
2233 /**
2234    @brief Fully assemble the nonzero pattern of a linear `CeedOperator`.
2235 
2236    Expected to be used in conjunction with @ref CeedOperatorLinearAssemble().
2237 
2238    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)`.
2239    Note that the `(i, j)` pairs are not unique and may repeat.
2240    This function returns the number of entries and their `(i, j)` locations, while @ref CeedOperatorLinearAssemble() provides the values in the same ordering.
2241 
2242    This will generally be slow unless your operator is low-order.
2243 
2244    Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2245 
2246    @param[in]  op          `CeedOperator` to assemble
2247    @param[out] num_entries Number of entries in coordinate nonzero pattern
2248    @param[out] rows        Row number for each entry
2249    @param[out] cols        Column number for each entry
2250 
2251    @ref User
2252 **/
2253 int CeedOperatorLinearAssembleSymbolic(CeedOperator op, CeedSize *num_entries, CeedInt **rows, CeedInt **cols) {
2254   bool          is_composite;
2255   CeedInt       num_suboperators, offset = 0;
2256   CeedSize      single_entries;
2257   CeedOperator *sub_operators;
2258 
2259   CeedCall(CeedOperatorCheckReady(op));
2260   CeedCall(CeedOperatorIsComposite(op, &is_composite));
2261 
2262   if (op->LinearAssembleSymbolic) {
2263     // Backend version
2264     CeedCall(op->LinearAssembleSymbolic(op, num_entries, rows, cols));
2265     return CEED_ERROR_SUCCESS;
2266   } else {
2267     // Operator fallback
2268     CeedOperator op_fallback;
2269 
2270     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
2271     if (op_fallback) {
2272       CeedCall(CeedOperatorLinearAssembleSymbolic(op_fallback, num_entries, rows, cols));
2273       return CEED_ERROR_SUCCESS;
2274     }
2275   }
2276 
2277   // Default interface implementation
2278 
2279   // Count entries and allocate rows, cols arrays
2280   *num_entries = 0;
2281   if (is_composite) {
2282     CeedCall(CeedCompositeOperatorGetNumSub(op, &num_suboperators));
2283     CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
2284     for (CeedInt k = 0; k < num_suboperators; ++k) {
2285       CeedCall(CeedSingleOperatorAssemblyCountEntries(sub_operators[k], &single_entries));
2286       *num_entries += single_entries;
2287     }
2288   } else {
2289     CeedCall(CeedSingleOperatorAssemblyCountEntries(op, &single_entries));
2290     *num_entries += single_entries;
2291   }
2292   CeedCall(CeedCalloc(*num_entries, rows));
2293   CeedCall(CeedCalloc(*num_entries, cols));
2294 
2295   // Assemble nonzero locations
2296   if (is_composite) {
2297     CeedCall(CeedCompositeOperatorGetNumSub(op, &num_suboperators));
2298     CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
2299     for (CeedInt k = 0; k < num_suboperators; ++k) {
2300       CeedCall(CeedSingleOperatorAssembleSymbolic(sub_operators[k], offset, *rows, *cols));
2301       CeedCall(CeedSingleOperatorAssemblyCountEntries(sub_operators[k], &single_entries));
2302       offset += single_entries;
2303     }
2304   } else {
2305     CeedCall(CeedSingleOperatorAssembleSymbolic(op, offset, *rows, *cols));
2306   }
2307   return CEED_ERROR_SUCCESS;
2308 }
2309 
2310 /**
2311    @brief Fully assemble the nonzero entries of a linear operator.
2312 
2313    Expected to be used in conjunction with @ref CeedOperatorLinearAssembleSymbolic().
2314 
2315    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)`.
2316    Note that the `(i, j)` pairs are not unique and may repeat.
2317    This function returns the values of the nonzero entries to be added, their `(i, j)` locations are provided by @ref CeedOperatorLinearAssembleSymbolic().
2318 
2319    This will generally be slow unless your operator is low-order.
2320 
2321    Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2322 
2323    @param[in]  op     `CeedOperator` to assemble
2324    @param[out] values Values to assemble into matrix
2325 
2326    @ref User
2327 **/
2328 int CeedOperatorLinearAssemble(CeedOperator op, CeedVector values) {
2329   bool          is_composite;
2330   CeedInt       num_suboperators, offset = 0;
2331   CeedSize      single_entries = 0;
2332   CeedOperator *sub_operators;
2333 
2334   CeedCall(CeedOperatorCheckReady(op));
2335   CeedCall(CeedOperatorIsComposite(op, &is_composite));
2336 
2337   // Early exit for empty operator
2338   if (!is_composite) {
2339     CeedInt num_elem = 0;
2340 
2341     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
2342     if (num_elem == 0) return CEED_ERROR_SUCCESS;
2343   }
2344 
2345   if (op->LinearAssemble) {
2346     // Backend version
2347     CeedCall(op->LinearAssemble(op, values));
2348     return CEED_ERROR_SUCCESS;
2349   } else {
2350     // Operator fallback
2351     CeedOperator op_fallback;
2352 
2353     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
2354     if (op_fallback) {
2355       CeedCall(CeedOperatorLinearAssemble(op_fallback, values));
2356       return CEED_ERROR_SUCCESS;
2357     }
2358   }
2359 
2360   // Default interface implementation
2361   CeedCall(CeedVectorSetValue(values, 0.0));
2362   if (is_composite) {
2363     CeedCall(CeedCompositeOperatorGetNumSub(op, &num_suboperators));
2364     CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
2365     for (CeedInt k = 0; k < num_suboperators; k++) {
2366       CeedCall(CeedSingleOperatorAssemble(sub_operators[k], offset, values));
2367       CeedCall(CeedSingleOperatorAssemblyCountEntries(sub_operators[k], &single_entries));
2368       offset += single_entries;
2369     }
2370   } else {
2371     CeedCall(CeedSingleOperatorAssemble(op, offset, values));
2372   }
2373   return CEED_ERROR_SUCCESS;
2374 }
2375 
2376 /**
2377   @brief Get the multiplicity of nodes across sub-operators in a composite `CeedOperator`.
2378 
2379   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2380 
2381   @param[in]  op               Composite `CeedOperator`
2382   @param[in]  num_skip_indices Number of sub-operators to skip
2383   @param[in]  skip_indices     Array of indices of sub-operators to skip
2384   @param[out] mult             Vector to store multiplicity (of size `l_size` )
2385 
2386   @return An error code: 0 - success, otherwise - failure
2387 
2388   @ref User
2389 **/
2390 int CeedCompositeOperatorGetMultiplicity(CeedOperator op, CeedInt num_skip_indices, CeedInt *skip_indices, CeedVector mult) {
2391   Ceed                ceed;
2392   CeedInt             num_suboperators;
2393   CeedSize            l_vec_len;
2394   CeedScalar         *mult_array;
2395   CeedVector          ones_l_vec;
2396   CeedElemRestriction elem_rstr, mult_elem_rstr;
2397   CeedOperator       *sub_operators;
2398 
2399   CeedCall(CeedOperatorCheckReady(op));
2400 
2401   CeedCall(CeedOperatorGetCeed(op, &ceed));
2402 
2403   // Zero mult vector
2404   CeedCall(CeedVectorSetValue(mult, 0.0));
2405 
2406   // Get suboperators
2407   CeedCall(CeedCompositeOperatorGetNumSub(op, &num_suboperators));
2408   CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
2409   if (num_suboperators == 0) return CEED_ERROR_SUCCESS;
2410 
2411   // Work vector
2412   CeedCall(CeedVectorGetLength(mult, &l_vec_len));
2413   CeedCall(CeedVectorCreate(ceed, l_vec_len, &ones_l_vec));
2414   CeedCall(CeedVectorSetValue(ones_l_vec, 1.0));
2415   CeedCall(CeedVectorGetArray(mult, CEED_MEM_HOST, &mult_array));
2416 
2417   // Compute multiplicity across suboperators
2418   for (CeedInt i = 0; i < num_suboperators; i++) {
2419     const CeedScalar *sub_mult_array;
2420     CeedVector        sub_mult_l_vec, ones_e_vec;
2421 
2422     // -- Check for suboperator to skip
2423     for (CeedInt j = 0; j < num_skip_indices; j++) {
2424       if (skip_indices[j] == i) continue;
2425     }
2426 
2427     // -- Sub operator multiplicity
2428     CeedCall(CeedOperatorGetActiveElemRestriction(sub_operators[i], &elem_rstr));
2429     CeedCall(CeedElemRestrictionCreateUnorientedCopy(elem_rstr, &mult_elem_rstr));
2430     CeedCall(CeedElemRestrictionCreateVector(mult_elem_rstr, &sub_mult_l_vec, &ones_e_vec));
2431     CeedCall(CeedVectorSetValue(sub_mult_l_vec, 0.0));
2432     CeedCall(CeedElemRestrictionApply(mult_elem_rstr, CEED_NOTRANSPOSE, ones_l_vec, ones_e_vec, CEED_REQUEST_IMMEDIATE));
2433     CeedCall(CeedElemRestrictionApply(mult_elem_rstr, CEED_TRANSPOSE, ones_e_vec, sub_mult_l_vec, CEED_REQUEST_IMMEDIATE));
2434     CeedCall(CeedVectorGetArrayRead(sub_mult_l_vec, CEED_MEM_HOST, &sub_mult_array));
2435     // ---- Flag every node present in the current suboperator
2436     for (CeedInt j = 0; j < l_vec_len; j++) {
2437       if (sub_mult_array[j] > 0.0) mult_array[j] += 1.0;
2438     }
2439     CeedCall(CeedVectorRestoreArrayRead(sub_mult_l_vec, &sub_mult_array));
2440     CeedCall(CeedVectorDestroy(&sub_mult_l_vec));
2441     CeedCall(CeedVectorDestroy(&ones_e_vec));
2442     CeedCall(CeedElemRestrictionDestroy(&mult_elem_rstr));
2443   }
2444   CeedCall(CeedVectorRestoreArray(mult, &mult_array));
2445   CeedCall(CeedVectorDestroy(&ones_l_vec));
2446   return CEED_ERROR_SUCCESS;
2447 }
2448 
2449 /**
2450   @brief Create a multigrid coarse `CeedOperator` and level transfer `CeedOperator` for a `CeedOperator`, creating the prolongation basis from the fine and coarse grid interpolation.
2451 
2452   Note: Calling this function asserts that setup is complete and sets all four `CeedOperator` as immutable.
2453 
2454   @param[in]  op_fine      Fine grid `CeedOperator`
2455   @param[in]  p_mult_fine  L-vector multiplicity in parallel gather/scatter, or `NULL` if not creating prolongation/restriction `CeedOperator`
2456   @param[in]  rstr_coarse  Coarse grid `CeedElemRestriction`
2457   @param[in]  basis_coarse Coarse grid active vector `CeedBasis`
2458   @param[out] op_coarse    Coarse grid `CeedOperator`
2459   @param[out] op_prolong   Coarse to fine `CeedOperator`, or `NULL`
2460   @param[out] op_restrict  Fine to coarse `CeedOperator`, or `NULL`
2461 
2462   @return An error code: 0 - success, otherwise - failure
2463 
2464   @ref User
2465 **/
2466 int CeedOperatorMultigridLevelCreate(CeedOperator op_fine, CeedVector p_mult_fine, CeedElemRestriction rstr_coarse, CeedBasis basis_coarse,
2467                                      CeedOperator *op_coarse, CeedOperator *op_prolong, CeedOperator *op_restrict) {
2468   CeedBasis basis_c_to_f = NULL;
2469 
2470   CeedCall(CeedOperatorCheckReady(op_fine));
2471 
2472   // Build prolongation matrix, if required
2473   if (op_prolong || op_restrict) {
2474     CeedBasis basis_fine;
2475 
2476     CeedCall(CeedOperatorGetActiveBasis(op_fine, &basis_fine));
2477     CeedCall(CeedBasisCreateProjection(basis_coarse, basis_fine, &basis_c_to_f));
2478   }
2479 
2480   // Core code
2481   CeedCall(CeedSingleOperatorMultigridLevel(op_fine, p_mult_fine, rstr_coarse, basis_coarse, basis_c_to_f, op_coarse, op_prolong, op_restrict));
2482   return CEED_ERROR_SUCCESS;
2483 }
2484 
2485 /**
2486   @brief Create a multigrid coarse `CeedOperator` and level transfer `CeedOperator` for a `CeedOperator` with a tensor basis for the active basis.
2487 
2488   Note: Calling this function asserts that setup is complete and sets all four `CeedOperator` as immutable.
2489 
2490   @param[in]  op_fine       Fine grid `CeedOperator`
2491   @param[in]  p_mult_fine   L-vector multiplicity in parallel gather/scatter, or `NULL` if not creating prolongation/restriction `CeedOperator`
2492   @param[in]  rstr_coarse   Coarse grid `CeedElemRestriction`
2493   @param[in]  basis_coarse  Coarse grid active vector `CeedBasis`
2494   @param[in]  interp_c_to_f Matrix for coarse to fine interpolation, or `NULL` if not creating prolongation/restriction `CeedOperator`
2495   @param[out] op_coarse     Coarse grid `CeedOperator`
2496   @param[out] op_prolong    Coarse to fine `CeedOperator`, or `NULL`
2497   @param[out] op_restrict   Fine to coarse `CeedOperator`, or `NULL`
2498 
2499   @return An error code: 0 - success, otherwise - failure
2500 
2501   @ref User
2502 **/
2503 int CeedOperatorMultigridLevelCreateTensorH1(CeedOperator op_fine, CeedVector p_mult_fine, CeedElemRestriction rstr_coarse, CeedBasis basis_coarse,
2504                                              const CeedScalar *interp_c_to_f, CeedOperator *op_coarse, CeedOperator *op_prolong,
2505                                              CeedOperator *op_restrict) {
2506   Ceed      ceed;
2507   CeedInt   Q_f, Q_c;
2508   CeedBasis basis_fine, basis_c_to_f = NULL;
2509 
2510   CeedCall(CeedOperatorCheckReady(op_fine));
2511   CeedCall(CeedOperatorGetCeed(op_fine, &ceed));
2512 
2513   // Check for compatible quadrature spaces
2514   CeedCall(CeedOperatorGetActiveBasis(op_fine, &basis_fine));
2515   CeedCall(CeedBasisGetNumQuadraturePoints(basis_fine, &Q_f));
2516   CeedCall(CeedBasisGetNumQuadraturePoints(basis_coarse, &Q_c));
2517   CeedCheck(Q_f == Q_c, ceed, CEED_ERROR_DIMENSION, "Bases must have compatible quadrature spaces");
2518 
2519   // Create coarse to fine basis, if required
2520   if (op_prolong || op_restrict) {
2521     CeedInt     dim, num_comp, num_nodes_c, P_1d_f, P_1d_c;
2522     CeedScalar *q_ref, *q_weight, *grad;
2523 
2524     // Check if interpolation matrix is provided
2525     CeedCheck(interp_c_to_f, ceed, CEED_ERROR_INCOMPATIBLE,
2526               "Prolongation or restriction operator creation requires coarse-to-fine interpolation matrix");
2527     CeedCall(CeedBasisGetDimension(basis_fine, &dim));
2528     CeedCall(CeedBasisGetNumComponents(basis_fine, &num_comp));
2529     CeedCall(CeedBasisGetNumNodes1D(basis_fine, &P_1d_f));
2530     CeedCall(CeedElemRestrictionGetElementSize(rstr_coarse, &num_nodes_c));
2531     P_1d_c = dim == 1 ? num_nodes_c : dim == 2 ? sqrt(num_nodes_c) : cbrt(num_nodes_c);
2532     CeedCall(CeedCalloc(P_1d_f, &q_ref));
2533     CeedCall(CeedCalloc(P_1d_f, &q_weight));
2534     CeedCall(CeedCalloc(P_1d_f * P_1d_c * dim, &grad));
2535     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));
2536     CeedCall(CeedFree(&q_ref));
2537     CeedCall(CeedFree(&q_weight));
2538     CeedCall(CeedFree(&grad));
2539   }
2540 
2541   // Core code
2542   CeedCall(CeedSingleOperatorMultigridLevel(op_fine, p_mult_fine, rstr_coarse, basis_coarse, basis_c_to_f, op_coarse, op_prolong, op_restrict));
2543   return CEED_ERROR_SUCCESS;
2544 }
2545 
2546 /**
2547   @brief Create a multigrid coarse `CeedOperator` and level transfer `CeedOperator` for a `CeedOperator` with a non-tensor basis for the active vector
2548 
2549   Note: Calling this function asserts that setup is complete and sets all four `CeedOperator` as immutable.
2550 
2551   @param[in]  op_fine       Fine grid `CeedOperator`
2552   @param[in]  p_mult_fine   L-vector multiplicity in parallel gather/scatter, or `NULL` if not creating prolongation/restriction `CeedOperator`
2553   @param[in]  rstr_coarse   Coarse grid `CeedElemRestriction`
2554   @param[in]  basis_coarse  Coarse grid active vector `CeedBasis`
2555   @param[in]  interp_c_to_f Matrix for coarse to fine interpolation, or `NULL` if not creating prolongation/restriction `CeedOperator`
2556   @param[out] op_coarse     Coarse grid `CeedOperator`
2557   @param[out] op_prolong    Coarse to fine `CeedOperator`, or `NULL`
2558   @param[out] op_restrict   Fine to coarse `CeedOperator`, or `NULL`
2559 
2560   @return An error code: 0 - success, otherwise - failure
2561 
2562   @ref User
2563 **/
2564 int CeedOperatorMultigridLevelCreateH1(CeedOperator op_fine, CeedVector p_mult_fine, CeedElemRestriction rstr_coarse, CeedBasis basis_coarse,
2565                                        const CeedScalar *interp_c_to_f, CeedOperator *op_coarse, CeedOperator *op_prolong,
2566                                        CeedOperator *op_restrict) {
2567   Ceed      ceed;
2568   CeedInt   Q_f, Q_c;
2569   CeedBasis basis_fine, basis_c_to_f = NULL;
2570 
2571   CeedCall(CeedOperatorCheckReady(op_fine));
2572   CeedCall(CeedOperatorGetCeed(op_fine, &ceed));
2573 
2574   // Check for compatible quadrature spaces
2575   CeedCall(CeedOperatorGetActiveBasis(op_fine, &basis_fine));
2576   CeedCall(CeedBasisGetNumQuadraturePoints(basis_fine, &Q_f));
2577   CeedCall(CeedBasisGetNumQuadraturePoints(basis_coarse, &Q_c));
2578   CeedCheck(Q_f == Q_c, ceed, CEED_ERROR_DIMENSION, "Bases must have compatible quadrature spaces");
2579 
2580   // Coarse to fine basis
2581   if (op_prolong || op_restrict) {
2582     CeedInt          dim, num_comp, num_nodes_c, num_nodes_f;
2583     CeedScalar      *q_ref, *q_weight, *grad;
2584     CeedElemTopology topo;
2585 
2586     // Check if interpolation matrix is provided
2587     CeedCheck(interp_c_to_f, ceed, CEED_ERROR_INCOMPATIBLE,
2588               "Prolongation or restriction operator creation requires coarse-to-fine interpolation matrix");
2589     CeedCall(CeedBasisGetTopology(basis_fine, &topo));
2590     CeedCall(CeedBasisGetDimension(basis_fine, &dim));
2591     CeedCall(CeedBasisGetNumComponents(basis_fine, &num_comp));
2592     CeedCall(CeedBasisGetNumNodes(basis_fine, &num_nodes_f));
2593     CeedCall(CeedElemRestrictionGetElementSize(rstr_coarse, &num_nodes_c));
2594     CeedCall(CeedCalloc(num_nodes_f * dim, &q_ref));
2595     CeedCall(CeedCalloc(num_nodes_f, &q_weight));
2596     CeedCall(CeedCalloc(num_nodes_f * num_nodes_c * dim, &grad));
2597     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));
2598     CeedCall(CeedFree(&q_ref));
2599     CeedCall(CeedFree(&q_weight));
2600     CeedCall(CeedFree(&grad));
2601   }
2602 
2603   // Core code
2604   CeedCall(CeedSingleOperatorMultigridLevel(op_fine, p_mult_fine, rstr_coarse, basis_coarse, basis_c_to_f, op_coarse, op_prolong, op_restrict));
2605   return CEED_ERROR_SUCCESS;
2606 }
2607 
2608 /**
2609   @brief Build a FDM based approximate inverse for each element for a `CeedOperator`.
2610 
2611   This returns a `CeedOperator` and `CeedVector` to apply a Fast Diagonalization Method based approximate inverse.
2612   This function obtains the simultaneous diagonalization for the 1D mass and Laplacian operators, \f$M = V^T V, K = V^T S V\f$.
2613   The assembled `CeedQFunction` is used to modify the eigenvalues from simultaneous diagonalization and obtain an approximate inverse of the form \f$V^T \hat S V\f$.
2614   The `CeedOperator` must be linear and non-composite.
2615   The associated `CeedQFunction` must therefore also be linear.
2616 
2617   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2618 
2619   @param[in]  op      `CeedOperator` to create element inverses
2620   @param[out] fdm_inv `CeedOperator` to apply the action of a FDM based inverse for each element
2621   @param[in]  request Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
2622 
2623   @return An error code: 0 - success, otherwise - failure
2624 
2625   @ref User
2626 **/
2627 int CeedOperatorCreateFDMElementInverse(CeedOperator op, CeedOperator *fdm_inv, CeedRequest *request) {
2628   Ceed                 ceed, ceed_parent;
2629   bool                 interp = false, grad = false, is_tensor_basis = true;
2630   CeedInt              num_input_fields, P_1d, Q_1d, num_nodes, num_qpts, dim, num_comp = 1, num_elem = 1;
2631   CeedSize             l_size = 1;
2632   CeedScalar          *mass, *laplace, *x, *fdm_interp, *lambda, *elem_avg;
2633   const CeedScalar    *interp_1d, *grad_1d, *q_weight_1d;
2634   CeedVector           q_data;
2635   CeedElemRestriction  rstr  = NULL, rstr_qd_i;
2636   CeedBasis            basis = NULL, fdm_basis;
2637   CeedQFunctionContext ctx_fdm;
2638   CeedQFunctionField  *qf_fields;
2639   CeedQFunction        qf, qf_fdm;
2640   CeedOperatorField   *op_fields;
2641 
2642   CeedCall(CeedOperatorCheckReady(op));
2643 
2644   if (op->CreateFDMElementInverse) {
2645     // Backend version
2646     CeedCall(op->CreateFDMElementInverse(op, fdm_inv, request));
2647     return CEED_ERROR_SUCCESS;
2648   } else {
2649     // Operator fallback
2650     CeedOperator op_fallback;
2651 
2652     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
2653     if (op_fallback) {
2654       CeedCall(CeedOperatorCreateFDMElementInverse(op_fallback, fdm_inv, request));
2655       return CEED_ERROR_SUCCESS;
2656     }
2657   }
2658 
2659   // Default interface implementation
2660   CeedCall(CeedOperatorGetCeed(op, &ceed));
2661   CeedCall(CeedOperatorGetFallbackParentCeed(op, &ceed_parent));
2662   CeedCall(CeedOperatorGetQFunction(op, &qf));
2663 
2664   // Determine active input basis
2665   CeedCall(CeedOperatorGetFields(op, &num_input_fields, &op_fields, NULL, NULL));
2666   CeedCall(CeedQFunctionGetFields(qf, NULL, &qf_fields, NULL, NULL));
2667   for (CeedInt i = 0; i < num_input_fields; i++) {
2668     CeedVector vec;
2669 
2670     CeedCall(CeedOperatorFieldGetVector(op_fields[i], &vec));
2671     if (vec == CEED_VECTOR_ACTIVE) {
2672       CeedEvalMode eval_mode;
2673 
2674       CeedCall(CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode));
2675       interp = interp || eval_mode == CEED_EVAL_INTERP;
2676       grad   = grad || eval_mode == CEED_EVAL_GRAD;
2677       CeedCall(CeedOperatorFieldGetBasis(op_fields[i], &basis));
2678       CeedCall(CeedOperatorFieldGetElemRestriction(op_fields[i], &rstr));
2679     }
2680   }
2681   CeedCheck(basis, ceed, CEED_ERROR_BACKEND, "No active field set");
2682   CeedCall(CeedBasisGetNumNodes1D(basis, &P_1d));
2683   CeedCall(CeedBasisGetNumNodes(basis, &num_nodes));
2684   CeedCall(CeedBasisGetNumQuadraturePoints1D(basis, &Q_1d));
2685   CeedCall(CeedBasisGetNumQuadraturePoints(basis, &num_qpts));
2686   CeedCall(CeedBasisGetDimension(basis, &dim));
2687   CeedCall(CeedBasisGetNumComponents(basis, &num_comp));
2688   CeedCall(CeedElemRestrictionGetNumElements(rstr, &num_elem));
2689   CeedCall(CeedElemRestrictionGetLVectorSize(rstr, &l_size));
2690 
2691   // Build and diagonalize 1D Mass and Laplacian
2692   CeedCall(CeedBasisIsTensor(basis, &is_tensor_basis));
2693   CeedCheck(is_tensor_basis, ceed, CEED_ERROR_BACKEND, "FDMElementInverse only supported for tensor bases");
2694   CeedCall(CeedCalloc(P_1d * P_1d, &mass));
2695   CeedCall(CeedCalloc(P_1d * P_1d, &laplace));
2696   CeedCall(CeedCalloc(P_1d * P_1d, &x));
2697   CeedCall(CeedCalloc(P_1d * P_1d, &fdm_interp));
2698   CeedCall(CeedCalloc(P_1d, &lambda));
2699   // -- Build matrices
2700   CeedCall(CeedBasisGetInterp1D(basis, &interp_1d));
2701   CeedCall(CeedBasisGetGrad1D(basis, &grad_1d));
2702   CeedCall(CeedBasisGetQWeights(basis, &q_weight_1d));
2703   CeedCall(CeedBuildMassLaplace(interp_1d, grad_1d, q_weight_1d, P_1d, Q_1d, dim, mass, laplace));
2704 
2705   // -- Diagonalize
2706   CeedCall(CeedSimultaneousDiagonalization(ceed, laplace, mass, x, lambda, P_1d));
2707   CeedCall(CeedFree(&mass));
2708   CeedCall(CeedFree(&laplace));
2709   for (CeedInt i = 0; i < P_1d; i++) {
2710     for (CeedInt j = 0; j < P_1d; j++) fdm_interp[i + j * P_1d] = x[j + i * P_1d];
2711   }
2712   CeedCall(CeedFree(&x));
2713 
2714   {
2715     CeedInt             layout[3], num_modes = (interp ? 1 : 0) + (grad ? dim : 0);
2716     CeedScalar          max_norm = 0;
2717     const CeedScalar   *assembled_array, *q_weight_array;
2718     CeedVector          assembled = NULL, q_weight;
2719     CeedElemRestriction rstr_qf   = NULL;
2720 
2721     // Assemble QFunction
2722     CeedCall(CeedOperatorLinearAssembleQFunctionBuildOrUpdate(op, &assembled, &rstr_qf, request));
2723     CeedCall(CeedElemRestrictionGetELayout(rstr_qf, layout));
2724     CeedCall(CeedElemRestrictionDestroy(&rstr_qf));
2725     CeedCall(CeedVectorNorm(assembled, CEED_NORM_MAX, &max_norm));
2726 
2727     // Calculate element averages
2728     CeedCall(CeedVectorCreate(ceed_parent, num_qpts, &q_weight));
2729     CeedCall(CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT, CEED_VECTOR_NONE, q_weight));
2730     CeedCall(CeedVectorGetArrayRead(assembled, CEED_MEM_HOST, &assembled_array));
2731     CeedCall(CeedVectorGetArrayRead(q_weight, CEED_MEM_HOST, &q_weight_array));
2732     CeedCall(CeedCalloc(num_elem, &elem_avg));
2733     const CeedScalar qf_value_bound = max_norm * 100 * CEED_EPSILON;
2734 
2735     for (CeedInt e = 0; e < num_elem; e++) {
2736       CeedInt count = 0;
2737 
2738       for (CeedInt q = 0; q < num_qpts; q++) {
2739         for (CeedInt i = 0; i < num_comp * num_comp * num_modes * num_modes; i++) {
2740           if (fabs(assembled_array[q * layout[0] + i * layout[1] + e * layout[2]]) > qf_value_bound) {
2741             elem_avg[e] += assembled_array[q * layout[0] + i * layout[1] + e * layout[2]] / q_weight_array[q];
2742             count++;
2743           }
2744         }
2745       }
2746       if (count) {
2747         elem_avg[e] /= count;
2748       } else {
2749         elem_avg[e] = 1.0;
2750       }
2751     }
2752     CeedCall(CeedVectorRestoreArrayRead(assembled, &assembled_array));
2753     CeedCall(CeedVectorDestroy(&assembled));
2754     CeedCall(CeedVectorRestoreArrayRead(q_weight, &q_weight_array));
2755     CeedCall(CeedVectorDestroy(&q_weight));
2756   }
2757 
2758   // Build FDM diagonal
2759   {
2760     CeedScalar *q_data_array, *fdm_diagonal;
2761 
2762     CeedCall(CeedCalloc(num_comp * num_nodes, &fdm_diagonal));
2763     const CeedScalar fdm_diagonal_bound = num_nodes * CEED_EPSILON;
2764     for (CeedInt c = 0; c < num_comp; c++) {
2765       for (CeedInt n = 0; n < num_nodes; n++) {
2766         if (interp) fdm_diagonal[c * num_nodes + n] = 1.0;
2767         if (grad) {
2768           for (CeedInt d = 0; d < dim; d++) {
2769             CeedInt i = (n / CeedIntPow(P_1d, d)) % P_1d;
2770             fdm_diagonal[c * num_nodes + n] += lambda[i];
2771           }
2772         }
2773         if (fabs(fdm_diagonal[c * num_nodes + n]) < fdm_diagonal_bound) fdm_diagonal[c * num_nodes + n] = fdm_diagonal_bound;
2774       }
2775     }
2776     CeedCall(CeedVectorCreate(ceed_parent, num_elem * num_comp * num_nodes, &q_data));
2777     CeedCall(CeedVectorSetValue(q_data, 0.0));
2778     CeedCall(CeedVectorGetArrayWrite(q_data, CEED_MEM_HOST, &q_data_array));
2779     for (CeedInt e = 0; e < num_elem; e++) {
2780       for (CeedInt c = 0; c < num_comp; c++) {
2781         for (CeedInt n = 0; n < num_nodes; n++)
2782           q_data_array[(e * num_comp + c) * num_nodes + n] = 1. / (elem_avg[e] * fdm_diagonal[c * num_nodes + n]);
2783       }
2784     }
2785     CeedCall(CeedFree(&elem_avg));
2786     CeedCall(CeedFree(&fdm_diagonal));
2787     CeedCall(CeedVectorRestoreArray(q_data, &q_data_array));
2788   }
2789 
2790   // Setup FDM operator
2791   // -- Basis
2792   {
2793     CeedScalar *grad_dummy, *q_ref_dummy, *q_weight_dummy;
2794 
2795     CeedCall(CeedCalloc(P_1d * P_1d, &grad_dummy));
2796     CeedCall(CeedCalloc(P_1d, &q_ref_dummy));
2797     CeedCall(CeedCalloc(P_1d, &q_weight_dummy));
2798     CeedCall(CeedBasisCreateTensorH1(ceed_parent, dim, num_comp, P_1d, P_1d, fdm_interp, grad_dummy, q_ref_dummy, q_weight_dummy, &fdm_basis));
2799     CeedCall(CeedFree(&fdm_interp));
2800     CeedCall(CeedFree(&grad_dummy));
2801     CeedCall(CeedFree(&q_ref_dummy));
2802     CeedCall(CeedFree(&q_weight_dummy));
2803     CeedCall(CeedFree(&lambda));
2804   }
2805 
2806   // -- Restriction
2807   {
2808     CeedInt strides[3] = {1, num_nodes, num_nodes * num_comp};
2809     CeedCall(CeedElemRestrictionCreateStrided(ceed_parent, num_elem, num_nodes, num_comp, num_elem * num_comp * num_nodes, strides, &rstr_qd_i));
2810   }
2811 
2812   // -- QFunction
2813   CeedCall(CeedQFunctionCreateInteriorByName(ceed_parent, "Scale", &qf_fdm));
2814   CeedCall(CeedQFunctionAddInput(qf_fdm, "input", num_comp, CEED_EVAL_INTERP));
2815   CeedCall(CeedQFunctionAddInput(qf_fdm, "scale", num_comp, CEED_EVAL_NONE));
2816   CeedCall(CeedQFunctionAddOutput(qf_fdm, "output", num_comp, CEED_EVAL_INTERP));
2817   CeedCall(CeedQFunctionSetUserFlopsEstimate(qf_fdm, num_comp));
2818 
2819   // -- QFunction context
2820   {
2821     CeedInt *num_comp_data;
2822 
2823     CeedCall(CeedCalloc(1, &num_comp_data));
2824     num_comp_data[0] = num_comp;
2825     CeedCall(CeedQFunctionContextCreate(ceed, &ctx_fdm));
2826     CeedCall(CeedQFunctionContextSetData(ctx_fdm, CEED_MEM_HOST, CEED_OWN_POINTER, sizeof(*num_comp_data), num_comp_data));
2827   }
2828   CeedCall(CeedQFunctionSetContext(qf_fdm, ctx_fdm));
2829   CeedCall(CeedQFunctionContextDestroy(&ctx_fdm));
2830 
2831   // -- Operator
2832   CeedCall(CeedOperatorCreate(ceed_parent, qf_fdm, NULL, NULL, fdm_inv));
2833   CeedCall(CeedOperatorSetField(*fdm_inv, "input", rstr, fdm_basis, CEED_VECTOR_ACTIVE));
2834   CeedCall(CeedOperatorSetField(*fdm_inv, "scale", rstr_qd_i, CEED_BASIS_NONE, q_data));
2835   CeedCall(CeedOperatorSetField(*fdm_inv, "output", rstr, fdm_basis, CEED_VECTOR_ACTIVE));
2836 
2837   // Cleanup
2838   CeedCall(CeedVectorDestroy(&q_data));
2839   CeedCall(CeedBasisDestroy(&fdm_basis));
2840   CeedCall(CeedElemRestrictionDestroy(&rstr_qd_i));
2841   CeedCall(CeedQFunctionDestroy(&qf_fdm));
2842   return CEED_ERROR_SUCCESS;
2843 }
2844 
2845 /// @}
2846